# doc_id = 1
# sent_id = 1
# text = We solve the word problem for free double categories without equations between generators by translating it to the word problem for 2 - categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	solve	solve	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	word	word	NOUN	NN	Number=Sing	5	compound	_	_
5	problem	problem	NOUN	NN	Number=Sing	2	dobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	free	free	ADJ	JJ	Degree=Pos	9	amod	_	_
8	double	double	ADJ	JJ	Degree=Pos	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
10	without	without	ADP	IN	_	2	prep	_	_
11	equations	equation	NOUN	NNS	Number=Plur	10	pobj	_	_
12	between	between	ADP	IN	_	11	prep	_	_
13	generators	generator	NOUN	NNS	Number=Plur	12	pobj	_	_
14	by	by	ADP	IN	_	2	prep	_	_
15	translating	translate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	pcomp	_	_
16	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	15	dobj	_	_
17	to	to	ADP	IN	_	15	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	word	word	NOUN	NN	Number=Sing	20	compound	_	_
20	problem	problem	NOUN	NN	Number=Sing	17	pobj	_	_
21	for	for	ADP	IN	_	20	prep	_	_
22	2	2	NUM	CD	NumType=Card	24	nummod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	categories	category	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This yields a quadratic algorithm deciding the equality of diagrams in a free double category.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	yields	yield	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	quadratic	quadratic	ADJ	JJ	Degree=Pos	5	amod	_	_
5	algorithm	algorithm	NOUN	NN	Number=Sing	2	dobj	_	_
6	deciding	decide	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	acl	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	equality	equality	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	diagrams	diagram	NOUN	NNS	Number=Plur	9	pobj	_	_
11	in	in	ADP	IN	_	8	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	free	free	ADJ	JJ	Degree=Pos	15	amod	_	_
14	double	double	ADJ	JJ	Degree=Pos	15	amod	_	_
15	category	category	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The translation is of interest in its own right since and can for instance be used to reason about double categories with the language of 2 - categories, sidestepping the pinwheel problem.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	translation	translation	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	interest	interest	NOUN	NN	Number=Sing	4	pobj	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	9	poss	_	_
8	own	own	ADJ	JJ	Degree=Pos	9	amod	_	_
9	right	right	NOUN	NN	Number=Sing	6	pobj	_	_
10	since	since	SCONJ	IN	_	3	prep	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
12	can	can	AUX	MD	VerbForm=Fin	16	aux	_	_
13	for	for	ADP	IN	_	16	prep	_	_
14	instance	instance	NOUN	NN	Number=Sing	13	pobj	_	_
15	be	be	AUX	VB	VerbForm=Inf	16	auxpass	_	_
16	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	conj	_	_
17	to	to	PART	TO	_	18	aux	_	_
18	reason	reason	VERB	VB	VerbForm=Inf	16	xcomp	_	_
19	about	about	ADP	IN	_	18	prep	_	_
20	double	double	ADJ	JJ	Degree=Pos	21	amod	_	_
21	categories	category	NOUN	NNS	Number=Plur	19	pobj	_	_
22	with	with	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	language	language	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	2	2	NUM	CD	NumType=Card	28	nummod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	categories	category	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
30	sidestepping	sidestep	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	18	advcl	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	pinwheel	pinwheel	NOUN	NN	Number=Sing	33	compound	_	_
33	problem	problem	NOUN	NN	Number=Sing	30	dobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = It also shows that although double categories are formally more general than 2 - categories, they are not actually more expressive, explaining the rarity of applications of this notion.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	shows	show	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	18	mark	_	_
5	although	although	SCONJ	IN	_	8	mark	_	_
6	double	double	ADJ	JJ	Degree=Pos	7	amod	_	_
7	categories	category	NOUN	NNS	Number=Plur	8	nsubj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	18	advcl	_	_
9	formally	formally	ADV	RB	_	8	advmod	_	_
10	more	more	ADV	RBR	Degree=Cmp	11	advmod	_	_
11	general	general	ADJ	JJ	Degree=Pos	8	acomp	_	_
12	than	than	ADP	IN	_	11	prep	_	_
13	2	2	NUM	CD	NumType=Card	15	nummod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
17	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	18	nsubj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
19	not	not	PART	RB	Polarity=Neg	18	neg	_	_
20	actually	actually	ADV	RB	_	18	advmod	_	_
21	more	more	ADV	RBR	Degree=Cmp	22	advmod	_	_
22	expressive	expressive	ADJ	JJ	Degree=Pos	18	acomp	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
24	explaining	explain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	18	advcl	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	rarity	rarity	NOUN	NN	Number=Sing	24	dobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	applications	application	NOUN	NNS	Number=Plur	27	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	this	this	DET	DT	Number=Sing|PronType=Dem	31	det	_	_
31	notion	notion	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 2
# sent_id = 1
# text = This paper introduces $ infty $ - and $ n $ - fold vector bundles as special functors from the $ infty $ - and $ n $ - cube categories to the category of smooth manifolds.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	introduces	introduce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	$ infty $	$ infty $	SYM	$	_	8	nmod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
7	$ n $	$ n $	SYM	$	_	4	conj	_	_
8	-	-	ADJ	JJ	Degree=Pos	11	amod	_	_
9	fold	fold	ADJ	JJ	Degree=Pos	11	amod	_	_
10	vector	vector	NOUN	NN	Number=Sing	11	compound	_	_
11	bundles	bundle	NOUN	NNS	Number=Plur	3	dobj	_	_
12	as	as	ADP	IN	_	3	prep	_	_
13	special	special	ADJ	JJ	Degree=Pos	14	amod	_	_
14	functors	functor	NOUN	NNS	Number=Plur	12	pobj	_	_
15	from	from	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
17	$ infty $	$ infty $	SYM	$	_	23	nmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
20	$ n $	$ n $	SYM	$	_	22	quantmod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	cube	cube	ADJ	JJ	Degree=Pos	17	conj	_	_
23	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	_
24	to	to	ADP	IN	_	3	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	category	category	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	smooth	smooth	ADJ	JJ	Degree=Pos	29	amod	_	_
29	manifolds	manifold	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = We study the cores and " $ n $ - pullbacks" of $ n $ - fold vector bundles and we prove that any $ n $ - fold vector bundle admits a non - canonical isomorphism to a decomposed $ n $ - fold vector bundle.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	cores	core	NOUN	NNS	Number=Plur	2	dobj	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	9	punct	_	_
7	$ n $	$ n $	SYM	$	_	9	quantmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	pullbacks	pullback	NOUN	NNS	Number=Plur	4	conj	_	SpaceAfter=No
10	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	9	punct	_	_
11	of	of	ADP	IN	_	4	prep	_	_
12	$ n $	$ n $	SYM	$	_	11	pobj	_	_
13	-	-	ADJ	JJ	Degree=Pos	11	punct	_	_
14	fold	fold	ADJ	JJ	Degree=Pos	16	amod	_	_
15	vector	vector	NOUN	NN	Number=Sing	16	compound	_	_
16	bundles	bundle	NOUN	NNS	Number=Plur	11	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
20	that	that	SCONJ	IN	_	27	mark	_	_
21	any	any	DET	DT	_	26	det	_	_
22	$ n $	$ n $	SYM	$	_	24	advmod	_	_
23	-	-	ADJ	JJ	Degree=Pos	22	punct	_	_
24	fold	fold	ADJ	JJ	Degree=Pos	26	amod	_	_
25	vector	vector	NOUN	NN	Number=Sing	26	compound	_	_
26	bundle	bundle	NOUN	NN	Number=Sing	27	nsubj	_	_
27	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	ccomp	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
29	non	non	ADJ	JJ	Degree=Pos	32	amod	_	_
30	-	-	ADJ	JJ	Degree=Pos	32	amod	_	_
31	canonical	canonical	ADJ	JJ	Degree=Pos	32	amod	_	_
32	isomorphism	isomorphism	NOUN	NN	Number=Sing	27	dobj	_	_
33	to	to	ADP	IN	_	27	prep	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	40	det	_	_
35	decomposed	decompose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	40	amod	_	_
36	$ n $	$ n $	SYM	$	_	37	nmod	_	_
37	-	-	ADJ	JJ	Degree=Pos	35	nmod	_	_
38	fold	fold	ADJ	JJ	Degree=Pos	40	amod	_	_
39	vector	vector	NOUN	NN	Number=Sing	40	compound	_	_
40	bundle	bundle	NOUN	NN	Number=Sing	33	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 3
# text = A colimit argument then shows that $ infty $ - fold vector bundles admit as well non - canonical decompositions.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	colimit	colimit	NOUN	NN	Number=Sing	3	compound	_	_
3	argument	argument	NOUN	NN	Number=Sing	5	nsubj	_	_
4	then	then	ADV	RB	PronType=Dem	5	advmod	_	_
5	shows	show	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	12	mark	_	_
7	$ infty $	$ infty $	SYM	$	_	8	advmod	_	_
8	-	-	ADJ	JJ	Degree=Pos	11	amod	_	_
9	fold	fold	ADJ	JJ	Degree=Pos	11	amod	_	_
10	vector	vector	NOUN	NN	Number=Sing	11	compound	_	_
11	bundles	bundle	NOUN	NNS	Number=Plur	12	nsubj	_	_
12	admit	admit	VERB	VBP	Tense=Pres|VerbForm=Fin	5	ccomp	_	_
13	as	as	ADV	RB	_	14	advmod	_	_
14	well	well	ADV	RB	Degree=Pos	18	intj	_	_
15	non	non	ADJ	JJ	Degree=Pos	17	amod	_	_
16	-	-	ADJ	JJ	Degree=Pos	17	punct	_	_
17	canonical	canonical	ADJ	JJ	Degree=Pos	18	amod	_	_
18	decompositions	decomposition	NOUN	NNS	Number=Plur	12	dobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = For the convenience of the reader, the case of triple vector bundles is discussed in detail.
1	For	for	ADP	IN	_	15	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	convenience	convenience	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	reader	reader	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	case	case	NOUN	NN	Number=Sing	15	nsubjpass	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	triple	triple	ADJ	JJ	Degree=Pos	13	amod	_	_
12	vector	vector	NOUN	NN	Number=Sing	13	compound	_	_
13	bundles	bundle	NOUN	NNS	Number=Plur	10	pobj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	discussed	discuss	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	detail	detail	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# doc_id = 3
# sent_id = 1
# text = We construct three classes of generalised orbifolds of Reshetikhin - Turaev theory for a modular tensor category $ C $ , using the language of defect TQFT: (i) spherical fusion categories give orbifolds for the "trivial" defect TQFT associated to $ Vect $ , (ii) $ G $ - crossed extensions of $ C $ give group orbifolds for any finite group $ G $ , and (iii) we construct orbifolds from commutative $ Delta $ - separable Frobenius algebras in $ C $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	33	ccomp	_	_
3	three	three	NUM	CD	NumType=Card	4	nummod	_	_
4	classes	class	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	generalised	generalise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
7	orbifolds	orbifold	NOUN	NNS	Number=Plur	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	Reshetikhin	Reshetikhin	PROPN	NNP	Number=Sing	11	compound	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	Turaev	Turaev	PROPN	NNP	Number=Sing	12	compound	_	_
12	theory	theory	NOUN	NN	Number=Sing	8	pobj	_	_
13	for	for	ADP	IN	_	4	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	modular	modular	ADJ	JJ	Degree=Pos	17	amod	_	_
16	tensor	tensor	NOUN	NN	Number=Sing	17	compound	_	_
17	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
18	$ C $	$ c $	SYM	$	_	17	appos	_	_
19	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
20	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	language	language	NOUN	NN	Number=Sing	20	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	defect	defect	NOUN	NN	Number=Sing	23	pobj	_	_
25	TQFT	TQFT	PROPN	NNP	Number=Sing	23	pobj	_	SpaceAfter=No
26	:	:	PUNCT	:	_	2	punct	_	_
27	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	33	punct	_	SpaceAfter=No
28	i	i	NOUN	NN	Number=Sing	32	nmod	_	SpaceAfter=No
29	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	32	punct	_	_
30	spherical	spherical	ADJ	JJ	Degree=Pos	31	amod	_	_
31	fusion	fusion	NOUN	NN	Number=Sing	32	compound	_	_
32	categories	category	NOUN	NNS	Number=Plur	33	nsubj	_	_
33	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
34	orbifolds	orbifold	NOUN	NNS	Number=Plur	33	dobj	_	_
35	for	for	ADP	IN	_	33	dative	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
37	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	40	punct	_	SpaceAfter=No
38	trivial	trivial	ADJ	JJ	Degree=Pos	40	amod	_	SpaceAfter=No
39	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	40	punct	_	_
40	defect	defect	NOUN	NN	Number=Sing	52	nmod	_	_
41	TQFT	TQFT	PROPN	NNP	Number=Sing	42	nsubj	_	_
42	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	40	acl	_	_
43	to	to	ADP	IN	_	42	prep	_	_
44	$ Vect $	$ vect $	SYM	$	_	43	pobj	_	_
45	,	,	PUNCT	,	PunctType=Comm	40	punct	_	_
46	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	40	punct	_	SpaceAfter=No
47	ii	ii	PROPN	NNP	Number=Sing	40	appos	_	SpaceAfter=No
48	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	40	punct	_	_
49	$ G $	$ g $	SYM	$	_	51	advmod	_	_
50	-	-	PUNCT	HYPH	PunctType=Dash	51	punct	_	_
51	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	52	amod	_	_
52	extensions	extension	NOUN	NNS	Number=Plur	35	pobj	_	_
53	of	of	ADP	IN	_	52	prep	_	_
54	$ C $	$ c $	SYM	$	_	53	pobj	_	_
55	give	give	VERB	VB	VerbForm=Inf	33	advcl	_	_
56	group	group	NOUN	NN	Number=Sing	57	compound	_	_
57	orbifolds	orbifold	NOUN	NNS	Number=Plur	55	dobj	_	_
58	for	for	ADP	IN	_	55	dative	_	_
59	any	any	DET	DT	_	61	det	_	_
60	finite	finite	ADJ	JJ	Degree=Pos	61	compound	_	_
61	group	group	NOUN	NN	Number=Sing	58	pobj	_	_
62	$ G $	$ g $	SYM	$	_	61	appos	_	_
63	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
64	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
65	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	66	punct	_	SpaceAfter=No
66	iii	iii	PROPN	NNP	Number=Sing	69	meta	_	SpaceAfter=No
67	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	66	punct	_	_
68	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	69	nsubj	_	_
69	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	33	conj	_	_
70	orbifolds	orbifold	NOUN	NNS	Number=Plur	69	dobj	_	_
71	from	from	ADP	IN	_	69	prep	_	_
72	commutative	commutative	ADJ	JJ	Degree=Pos	77	amod	_	_
73	$ Delta $	$ delta $	SYM	$	_	75	advmod	_	_
74	-	-	PUNCT	HYPH	PunctType=Dash	75	punct	_	_
75	separable	separable	ADJ	JJ	Degree=Pos	77	amod	_	_
76	Frobenius	Frobenius	PROPN	NNP	Number=Sing	77	compound	_	_
77	algebras	algebra	NOUN	NNS	Number=Plur	71	pobj	_	_
78	in	in	ADP	IN	_	69	prep	_	_
79	$ C $	$ c $	SYM	$	_	78	pobj	_	_
80	.	.	PUNCT	.	PunctType=Peri	33	punct	_	SpaceAfter=No

# sent_id = 2
# text = We also explain how the Turaev - Viro state sum construction fits into our framework by proving that it is isomorphic to the orbifold of case (i).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	explain	explain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	how	how	SCONJ	WRB	_	12	advmod	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
6	Turaev	Turaev	PROPN	NNP	Number=Sing	8	compound	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	Viro	Viro	PROPN	NNP	Number=Sing	11	compound	_	_
9	state	state	NOUN	NN	Number=Sing	10	compound	_	_
10	sum	sum	NOUN	NN	Number=Sing	11	compound	_	_
11	construction	construction	NOUN	NN	Number=Sing	12	nsubj	_	_
12	fits	fit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
13	into	into	ADP	IN	_	12	prep	_	_
14	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	15	poss	_	_
15	framework	framework	NOUN	NN	Number=Sing	13	pobj	_	_
16	by	by	ADP	IN	_	12	prep	_	_
17	proving	prove	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	pcomp	_	_
18	that	that	SCONJ	IN	_	20	mark	_	_
19	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	20	nsubj	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	ccomp	_	_
21	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	20	acomp	_	_
22	to	to	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	orbifold	orbifold	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	case	case	NOUN	NN	Number=Sing	25	pobj	_	_
27	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	26	punct	_	SpaceAfter=No
28	i	i	NOUN	NN	Number=Sing	26	appos	_	SpaceAfter=No
29	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	26	punct	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Moreover, we treat the cases (ii) and (iii) in the more general setting of ribbon tensor categories.
1	Moreover	moreover	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	treat	treat	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	cases	case	NOUN	NNS	Number=Plur	4	dobj	_	_
7	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	6	punct	_	SpaceAfter=No
8	ii	ii	PROPN	NNP	Number=Sing	6	appos	_	SpaceAfter=No
9	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	6	punct	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
11	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
12	iii	iii	PROPN	NNP	Number=Sing	6	conj	_	SpaceAfter=No
13	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	6	punct	_	_
14	in	in	ADP	IN	_	4	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
16	more	more	ADV	RBR	Degree=Cmp	17	advmod	_	_
17	general	general	ADJ	JJ	Degree=Pos	18	amod	_	_
18	setting	setting	NOUN	NN	Number=Sing	14	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	ribbon	ribbon	NOUN	NN	Number=Sing	22	compound	_	_
21	tensor	tensor	NOUN	NN	Number=Sing	22	compound	_	_
22	categories	category	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = For case (ii) we show how Morita equivalence leads to isomorphic orbifolds, and we discuss Tambara - Yamagami categories as particular examples.
1	For	for	ADP	IN	_	7	prep	_	_
2	case	case	NOUN	NN	Number=Sing	1	pobj	_	_
3	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	4	punct	_	SpaceAfter=No
4	ii	ii	NOUN	NN	Number=Sing	2	appos	_	SpaceAfter=No
5	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	4	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	how	how	SCONJ	WRB	_	11	advmod	_	_
9	Morita	Morita	PROPN	NNP	Number=Sing	10	compound	_	_
10	equivalence	equivalence	NOUN	NN	Number=Sing	11	nsubj	_	_
11	leads	lead	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	ccomp	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	14	amod	_	_
14	orbifolds	orbifold	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
17	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	18	nsubj	_	_
18	discuss	discuss	VERB	VBP	Tense=Pres|VerbForm=Fin	7	conj	_	_
19	Tambara	Tambara	PROPN	NNP	Number=Sing	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	Yamagami	Yamagami	PROPN	NNP	Number=Sing	22	amod	_	_
22	categories	category	NOUN	NNS	Number=Plur	18	dobj	_	_
23	as	as	ADP	IN	_	18	prep	_	_
24	particular	particular	ADJ	JJ	Degree=Pos	25	amod	_	_
25	examples	example	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# doc_id = 4
# sent_id = 1
# text = Suppose an extension map $ U: T_1 - > T_0 $ in the 2 - category $ Con $ of contexts for arithmetic universes satisfies a Chevalley criterion for being an (op)fibration in $ Con $ .
1	Suppose	suppose	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	extension	extension	NOUN	NN	Number=Sing	4	compound	_	_
4	map	map	NOUN	NN	Number=Sing	17	nsubj	_	_
5	$ U: T_1 - > T_0 $	$ u: t_1 - > t_0 $	SYM	$	_	4	appos	_	_
6	in	in	ADP	IN	_	4	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	2	2	NUM	CD	NumType=Card	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
11	$ Con $	$ con $	SYM	$	_	10	appos	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	contexts	context	NOUN	NNS	Number=Plur	12	pobj	_	_
14	for	for	ADP	IN	_	4	prep	_	_
15	arithmetic	arithmetic	ADJ	JJ	Degree=Pos	16	amod	_	_
16	universes	universe	NOUN	NNS	Number=Plur	14	pobj	_	_
17	satisfies	satisfy	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	1	ccomp	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	Chevalley	Chevalley	PROPN	NNP	Number=Sing	20	compound	_	_
20	criterion	criterion	NOUN	NN	Number=Sing	17	dobj	_	_
21	for	for	ADP	IN	_	20	prep	_	_
22	being	be	AUX	VBG	VerbForm=Ger	21	pcomp	_	_
23	an	an	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	25	punct	_	SpaceAfter=No
25	op)fibration	op)fibration	NOUN	NN	Number=Sing	22	attr	_	_
26	in	in	ADP	IN	_	25	prep	_	_
27	$ Con $	$ con $	SYM	$	_	26	pobj	_	_
28	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = If $ M $ is a model of $ T_0 $ in an elementary topos $ S $ with NNO, then the classifier $ p: S[T_1/M] - > S $ satisfies the representable definition of being an (op)fibration in the 2 - category $ ETop $ of elementary toposes (with NNO) and geometric morphisms.
1	If	if	SCONJ	IN	_	3	mark	_	_
2	$ M $	$ m $	SYM	$	_	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	advcl	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	model	model	NOUN	NN	Number=Sing	3	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	$ T_0 $	$ t_0 $	SYM	$	_	6	pobj	_	_
8	in	in	ADP	IN	_	5	prep	_	_
9	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	elementary	elementary	ADJ	JJ	Degree=Pos	11	amod	_	_
11	topos	topos	NOUN	NN	Number=Sing	8	pobj	_	_
12	$ S $	$ s $	SYM	$	_	11	appos	_	_
13	with	with	ADP	IN	_	5	prep	_	_
14	NNO	NNO	PROPN	NNP	Number=Sing	13	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
16	then	then	ADV	RB	PronType=Dem	20	advmod	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	classifier	classifier	NOUN	NN	Number=Sing	20	nsubj	_	_
19	$ p: S[T_1/M] - > S $	$ p: s[t_1/m] - > s $	SYM	$	_	20	nsubj	_	_
20	satisfies	satisfy	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	representable	representable	ADJ	JJ	Degree=Pos	23	amod	_	_
23	definition	definition	NOUN	NN	Number=Sing	20	dobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	being	be	AUX	VBG	VerbForm=Ger	24	pcomp	_	_
26	an	an	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
27	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	28	punct	_	SpaceAfter=No
28	op)fibration	op)fibration	NOUN	NN	Number=Sing	25	attr	_	_
29	in	in	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
31	2	2	NUM	CD	NumType=Card	33	nummod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	category	category	NOUN	NN	Number=Sing	34	compound	_	_
34	$ ETop $	$ etop $	SYM	$	_	29	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	elementary	elementary	ADJ	JJ	Degree=Pos	37	amod	_	_
37	toposes	topos	NOUN	NNS	Number=Plur	35	pobj	_	_
38	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	37	punct	_	SpaceAfter=No
39	with	with	ADP	IN	_	28	prep	_	_
40	NNO	NNO	PROPN	NNP	Number=Sing	39	pobj	_	SpaceAfter=No
41	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	28	punct	_	_
42	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
43	geometric	geometric	ADJ	JJ	Degree=Pos	44	amod	_	_
44	morphisms	morphism	NOUN	NNS	Number=Plur	28	conj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# doc_id = 5
# sent_id = 1
# text = In this paper we construct a symmetric monoidal closed model category of coherently commutative monoidal categories.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	symmetric	symmetric	ADJ	JJ	Degree=Pos	8	amod	_	_
8	monoidal	monoidal	NOUN	NN	Number=Sing	11	amod	_	_
9	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
10	model	model	NOUN	NN	Number=Sing	11	compound	_	_
11	category	category	NOUN	NN	Number=Sing	5	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	coherently	coherently	ADV	RB	_	14	advmod	_	_
14	commutative	commutative	ADJ	JJ	Degree=Pos	16	amod	_	_
15	monoidal	monoidal	ADJ	JJ	Degree=Pos	16	amod	_	_
16	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = The main aim of this paper is to establish a Quillen equivalence between a model category of coherently commutative monoidal categories and a natural model category of Permutative (or strict symmetric monoidal) categories, $ Perm $ , which is not a symmetric monoidal closed model category.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	aim	aim	NOUN	NN	Number=Sing	7	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	paper	paper	NOUN	NN	Number=Sing	4	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	establish	establish	VERB	VB	VerbForm=Inf	7	xcomp	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	Quillen	quillen	ADJ	JJ	Degree=Pos	12	amod	_	_
12	equivalence	equivalence	NOUN	NN	Number=Sing	9	dobj	_	_
13	between	between	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	model	model	NOUN	NN	Number=Sing	16	compound	_	_
16	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	coherently	coherently	ADV	RB	_	19	advmod	_	_
19	commutative	commutative	ADJ	JJ	Degree=Pos	21	amod	_	_
20	monoidal	monoidal	ADJ	JJ	Degree=Pos	21	amod	_	_
21	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
24	natural	natural	ADJ	JJ	Degree=Pos	25	amod	_	_
25	model	model	NOUN	NN	Number=Sing	26	compound	_	_
26	category	category	NOUN	NN	Number=Sing	16	conj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	Permutative	Permutative	PROPN	NNP	Number=Sing	27	pobj	_	_
29	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	28	punct	_	SpaceAfter=No
30	or	or	CCONJ	CC	ConjType=Cmp	28	cc	_	_
31	strict	strict	ADJ	JJ	Degree=Pos	35	amod	_	_
32	symmetric	symmetric	ADJ	JJ	Degree=Pos	33	amod	_	_
33	monoidal	monoidal	NOUN	NN	Number=Sing	35	nmod	_	SpaceAfter=No
34	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	35	punct	_	_
35	categories	category	NOUN	NNS	Number=Plur	28	conj	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
37	$ Perm $	$ perm $	SYM	$	_	35	appos	_	_
38	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
39	which	which	PRON	WDT	_	40	nsubj	_	_
40	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	35	relcl	_	_
41	not	not	PART	RB	Polarity=Neg	40	neg	_	_
42	a	a	DET	DT	Definite=Ind|PronType=Art	44	det	_	_
43	symmetric	symmetric	ADJ	JJ	Degree=Pos	44	amod	_	_
44	monoidal	monoidal	NOUN	NN	Number=Sing	47	amod	_	_
45	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	47	amod	_	_
46	model	model	NOUN	NN	Number=Sing	47	compound	_	_
47	category	category	NOUN	NN	Number=Sing	40	attr	_	SpaceAfter=No
48	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = The right adjoint of this Quillen equivalence is the classical Segal's Nerve functor.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	right	right	ADJ	JJ	Degree=Pos	3	amod	_	_
3	adjoint	adjoint	NOUN	NN	Number=Sing	8	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
6	Quillen	quillen	ADJ	JJ	Degree=Pos	7	amod	_	_
7	equivalence	equivalence	NOUN	NN	Number=Sing	4	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
10	classical	classical	ADJ	JJ	Degree=Pos	14	amod	_	_
11	Segal	Segal	PROPN	NNP	Number=Sing	14	poss	_	SpaceAfter=No
12	's	's	PART	POS	_	11	case	_	_
13	Nerve	Nerve	PROPN	NNP	Number=Sing	14	compound	_	_
14	functor	functor	NOUN	NN	Number=Sing	8	attr	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 6
# sent_id = 1
# text = We define exact sequences in the enchilada category of $ C* $ - algebras and correspondences, and prove that the reduced - crossed - product functor is not exact for the enchilada categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	exact	exact	ADJ	JJ	Degree=Pos	4	amod	_	_
4	sequences	sequence	NOUN	NNS	Number=Plur	2	dobj	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	enchilada	enchilada	NOUN	NN	Number=Sing	8	compound	_	_
8	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	$ C* $	$ c* $	SYM	$	_	12	nmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	algebras	algebra	NOUN	NNS	Number=Plur	9	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	correspondences	correspondence	NOUN	NNS	Number=Plur	12	conj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
17	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
18	that	that	SCONJ	IN	_	26	mark	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
20	reduced	reduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
22	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	product	product	NOUN	NN	Number=Sing	25	compound	_	_
25	functor	functor	NOUN	NN	Number=Sing	26	nsubj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	ccomp	_	_
27	not	not	PART	RB	Polarity=Neg	26	neg	_	_
28	exact	exact	ADJ	JJ	Degree=Pos	26	acomp	_	_
29	for	for	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	enchilada	enchilada	NOUN	NN	Number=Sing	32	compound	_	_
32	categories	category	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Our motivation was to determine whether we can have a better understanding of the Baum - Connes conjecture by using enchilada categories.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	motivation	motivation	NOUN	NN	Number=Sing	3	nsubj	_	_
3	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	0	ROOT	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	determine	determine	VERB	VB	VerbForm=Inf	3	xcomp	_	_
6	whether	whether	SCONJ	IN	_	9	mark	_	_
7	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
8	can	can	AUX	MD	VerbForm=Fin	9	aux	_	_
9	have	have	VERB	VB	VerbForm=Inf	5	ccomp	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	better	well	ADJ	JJR	Degree=Cmp	12	amod	_	_
12	understanding	understanding	NOUN	NN	Number=Sing	9	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
15	Baum	Baum	PROPN	NNP	Number=Sing	17	compound	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	Connes	Connes	PROPN	NNP	Number=Sing	18	compound	_	_
18	conjecture	conjecture	NOUN	NN	Number=Sing	13	pobj	_	_
19	by	by	ADP	IN	_	9	prep	_	_
20	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	pcomp	_	_
21	enchilada	enchilada	NOUN	NN	Number=Sing	22	compound	_	_
22	categories	category	NOUN	NNS	Number=Plur	20	dobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Along the way we prove numerous results showing that the enchilada category is rather strange.
1	Along	along	ADP	IN	_	0	ROOT	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	way	way	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	3	relcl	_	_
6	numerous	numerous	ADJ	JJ	Degree=Pos	7	amod	_	_
7	results	result	NOUN	NNS	Number=Plur	5	dobj	_	_
8	showing	show	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	acl	_	_
9	that	that	SCONJ	IN	_	13	mark	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	enchilada	enchilada	NOUN	NN	Number=Sing	12	compound	_	_
12	category	category	NOUN	NN	Number=Sing	13	nsubj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	ccomp	_	_
14	rather	rather	ADV	RB	_	15	advmod	_	_
15	strange	strange	ADJ	JJ	Degree=Pos	13	acomp	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# doc_id = 7
# sent_id = 1
# text = We construct combinatorial model category structures on the categories of (marked) categories and (marked) preadditive categories, and we characterize (marked) additive categories as fibrant objects in a Bousfield localization of preadditive categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	4	amod	_	_
4	model	model	NOUN	NN	Number=Sing	6	compound	_	_
5	category	category	NOUN	NN	Number=Sing	6	compound	_	_
6	structures	structure	NOUN	NNS	Number=Plur	2	dobj	_	_
7	on	on	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
12	marked	marked	ADJ	JJ	Degree=Pos	14	amod	_	SpaceAfter=No
13	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	14	punct	_	_
14	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	20	punct	_	SpaceAfter=No
17	marked	marked	ADJ	JJ	Degree=Pos	20	amod	_	SpaceAfter=No
18	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	20	punct	_	_
19	preadditive	preadditive	ADJ	JJ	Degree=Pos	20	amod	_	_
20	categories	category	NOUN	NNS	Number=Plur	14	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
23	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	24	nsubj	_	_
24	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
25	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	29	punct	_	SpaceAfter=No
26	marked	marked	ADJ	JJ	Degree=Pos	29	amod	_	SpaceAfter=No
27	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	29	punct	_	_
28	additive	additive	ADJ	JJ	Degree=Pos	29	amod	_	_
29	categories	category	NOUN	NNS	Number=Plur	24	dobj	_	_
30	as	as	ADP	IN	_	29	prep	_	_
31	fibrant	fibrant	ADJ	JJ	Degree=Pos	32	amod	_	_
32	objects	object	NOUN	NNS	Number=Plur	30	pobj	_	_
33	in	in	ADP	IN	_	24	prep	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
35	Bousfield	Bousfield	PROPN	NNP	Number=Sing	36	compound	_	_
36	localization	localization	NOUN	NN	Number=Sing	33	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	preadditive	preadditive	ADJ	JJ	Degree=Pos	39	amod	_	_
39	categories	category	NOUN	NNS	Number=Plur	37	pobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# sent_id = 2
# text = These model category structures are used to present the corresponding infinity - categories obtained by inverting equivalences.
1	These	these	DET	DT	Number=Plur|PronType=Dem	4	det	_	_
2	model	model	NOUN	NN	Number=Sing	4	compound	_	_
3	category	category	NOUN	NN	Number=Sing	4	compound	_	_
4	structures	structure	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	present	present	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
10	corresponding	corresponding	ADJ	JJ	Degree=Pos	13	amod	_	_
11	infinity	infinity	NOUN	NN	Number=Sing	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	categories	category	NOUN	NNS	Number=Plur	8	dobj	_	_
14	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	acl	_	_
15	by	by	ADP	IN	_	14	agent	_	_
16	inverting	inverting	NOUN	NN	Number=Sing	17	compound	_	_
17	equivalences	equivalence	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = We apply these results to explicitly calculate limits and colimits in these infinity - categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	apply	apply	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	these	these	DET	DT	Number=Plur|PronType=Dem	4	det	_	_
4	results	result	NOUN	NNS	Number=Plur	2	dobj	_	_
5	to	to	PART	TO	_	7	aux	_	_
6	explicitly	explicitly	ADV	RB	_	7	advmod	_	_
7	calculate	calculate	VERB	VB	VerbForm=Inf	2	advcl	_	_
8	limits	limit	NOUN	NNS	Number=Plur	7	dobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	colimits	colimit	NOUN	NNS	Number=Plur	8	conj	_	_
11	in	in	ADP	IN	_	7	prep	_	_
12	these	these	DET	DT	Number=Plur|PronType=Dem	15	det	_	_
13	infinity	infinity	NOUN	NN	Number=Sing	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = The motivating application is a systematic construction of the equivariant coarse algebraic $ K $ - homology with coefficients in an additive category from its non - equivariant version.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	motivating	motivating	NOUN	NN	Number=Sing	3	compound	_	_
3	application	application	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	systematic	systematic	ADJ	JJ	Degree=Pos	7	amod	_	_
7	construction	construction	NOUN	NN	Number=Sing	4	attr	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
10	equivariant	equivariant	ADJ	JJ	Degree=Pos	11	amod	_	_
11	coarse	coarse	NOUN	NN	Number=Sing	15	amod	_	_
12	algebraic	algebraic	ADJ	JJ	Degree=Pos	15	amod	_	_
13	$ K $	$ k $	SYM	$	_	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	homology	homology	NOUN	NN	Number=Sing	8	pobj	_	_
16	with	with	ADP	IN	_	7	prep	_	_
17	coefficients	coefficient	NOUN	NNS	Number=Plur	16	pobj	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	an	an	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	additive	additive	ADJ	JJ	Degree=Pos	21	amod	_	_
21	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
22	from	from	ADP	IN	_	21	prep	_	_
23	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	27	poss	_	_
24	non	non	ADJ	JJ	Degree=Pos	26	amod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	equivariant	equivariant	ADJ	JJ	Degree=Pos	27	amod	_	_
27	version	version	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 8
# sent_id = 1
# text = We generalize the notions of shifted double Poisson and shifted double Lie - Rinehart structures to monoids in a symmetric monoidal abelian category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	notions	notion	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	shifted	shift	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
7	double	double	ADJ	JJ	Degree=Pos	8	amod	_	_
8	Poisson	Poisson	PROPN	NNP	Number=Sing	5	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
10	shifted	shift	VERB	VBD	Tense=Past|VerbForm=Fin	2	conj	_	_
11	double	double	ADJ	JJ	Degree=Pos	15	amod	_	_
12	Lie	lie	NOUN	NN	Number=Sing	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	Rinehart	rinehart	ADJ	JJ	Degree=Pos	15	amod	_	_
15	structures	structure	NOUN	NNS	Number=Plur	10	dobj	_	_
16	to	to	ADP	IN	_	10	prep	_	_
17	monoids	monoid	NOUN	NNS	Number=Plur	16	pobj	_	_
18	in	in	ADP	IN	_	10	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
20	symmetric	symmetric	ADJ	JJ	Degree=Pos	23	amod	_	_
21	monoidal	monoidal	ADJ	JJ	Degree=Pos	22	amod	_	_
22	abelian	abelian	ADJ	JJ	Degree=Pos	23	compound	_	_
23	category	category	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The main result is that an $ n $ - shifted double Lie - Rinehart structure on a pair $ (A, M) $ is equivalent to a non - shifted double Lie - Rinehart structure on the pair $ (A, M[ - n]) $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	result	result	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	19	mark	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
7	$ n $	$ n $	SYM	$	_	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	shifted	shift	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
10	double	double	ADJ	JJ	Degree=Pos	14	amod	_	_
11	Lie	lie	NOUN	NN	Number=Sing	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	Rinehart	rinehart	ADJ	JJ	Degree=Pos	14	amod	_	_
14	structure	structure	NOUN	NN	Number=Sing	19	nsubj	_	_
15	on	on	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	pair	pair	NOUN	NN	Number=Sing	15	pobj	_	_
18	$ (A, M) $	$ (a, m) $	NUM	CD	NumType=Card	19	nsubj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
20	equivalent	equivalent	ADJ	JJ	Degree=Pos	19	acomp	_	_
21	to	to	ADP	IN	_	20	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
23	non	non	ADV	RB	_	25	advmod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	shifted	shift	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	30	amod	_	_
26	double	double	ADJ	JJ	Degree=Pos	30	amod	_	_
27	Lie	lie	NOUN	NN	Number=Sing	29	compound	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	Rinehart	rinehart	ADJ	JJ	Degree=Pos	30	amod	_	_
30	structure	structure	NOUN	NN	Number=Sing	21	pobj	_	_
31	on	on	ADP	IN	_	30	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
33	pair	pair	NOUN	NN	Number=Sing	31	pobj	_	_
34	$ (A, M[ - n]) $	$ (a, m[ - n]) $	SYM	$	_	19	dep	_	_
35	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 9
# sent_id = 1
# text = The goal of this article is to emphasize the role of cubical sets in enriched category theory and infinity - category theory.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	goal	goal	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	article	article	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	emphasize	emphasize	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	role	role	NOUN	NN	Number=Sing	8	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	cubical	cubical	ADJ	JJ	Degree=Pos	13	amod	_	_
13	sets	set	NOUN	NNS	Number=Plur	11	pobj	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
16	category	category	NOUN	NN	Number=Sing	17	compound	_	_
17	theory	theory	NOUN	NN	Number=Sing	14	pobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	infinity	infinity	NOUN	NN	Number=Sing	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	category	category	NOUN	NN	Number=Sing	22	compound	_	_
22	theory	theory	NOUN	NN	Number=Sing	17	conj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show in particular that categories enriched in cubical sets provide a convenient way to describe many infinity - categories appearing in the context of homological algebra.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	particular	particular	ADJ	JJ	Degree=Pos	3	amod	_	_
5	that	that	SCONJ	IN	_	11	mark	_	_
6	categories	category	NOUN	NNS	Number=Plur	11	nsubj	_	_
7	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	cubical	cubical	ADJ	JJ	Degree=Pos	10	amod	_	_
10	sets	set	NOUN	NNS	Number=Plur	8	pobj	_	_
11	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	convenient	convenient	ADJ	JJ	Degree=Pos	14	amod	_	_
14	way	way	NOUN	NN	Number=Sing	11	dobj	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	describe	describe	VERB	VB	VerbForm=Inf	14	relcl	_	_
17	many	many	ADJ	JJ	Degree=Pos	20	amod	_	_
18	infinity	infinity	NOUN	NN	Number=Sing	20	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	categories	category	NOUN	NNS	Number=Plur	16	dobj	_	_
21	appearing	appear	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	acl	_	_
22	in	in	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	context	context	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	homological	homological	ADJ	JJ	Degree=Pos	27	amod	_	_
27	algebra	algebra	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 10
# sent_id = 1
# text = Let $ PreOrd(C) $ be the category of internal preorders in an exact category $ C $ .
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ PreOrd(C) $	$ preord(c) $	SYM	$	_	3	nsubj	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	3	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	internal	internal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	preorders	preorder	NOUN	NNS	Number=Plur	6	pobj	_	_
9	in	in	ADP	IN	_	3	prep	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	exact	exact	ADJ	JJ	Degree=Pos	12	amod	_	_
12	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
13	$ C $	$ c $	SYM	$	_	12	appos	_	_
14	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that the pair $ (Eq(C), ParOrd(C)) $ is a pretorsion theory in $ PreOrd(C) $ , where $ Eq(C) $ and $ ParOrd(C) $ are the full subcategories of internal equivalence relations and of internal partial orders in $ C $ , respectively.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	pair	pair	NOUN	NN	Number=Sing	7	nsubj	_	_
6	$ (Eq(C), ParOrd(C)) $	$ (Eq(C), ParOrd(C)) $	PROPN	NNP	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	pretorsion	pretorsion	NOUN	NN	Number=Sing	10	compound	_	_
10	theory	theory	NOUN	NN	Number=Sing	7	attr	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	$ PreOrd(C) $	$ preord(c) $	SYM	$	_	11	pobj	_	_
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	where	where	SCONJ	WRB	_	18	advmod	_	_
15	$ Eq(C) $	$ eq(c) $	SYM	$	_	18	nsubj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	$ ParOrd(C) $	$ parord(c) $	SYM	$	_	15	conj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	relcl	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	full	full	ADJ	JJ	Degree=Pos	21	amod	_	_
21	subcategories	subcategorie	NOUN	NNS	Number=Plur	18	attr	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	internal	internal	ADJ	JJ	Degree=Pos	25	amod	_	_
24	equivalence	equivalence	NOUN	NN	Number=Sing	25	compound	_	_
25	relations	relation	NOUN	NNS	Number=Plur	22	pobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
27	of	of	ADP	IN	_	22	conj	_	_
28	internal	internal	ADJ	JJ	Degree=Pos	30	amod	_	_
29	partial	partial	ADJ	JJ	Degree=Pos	30	amod	_	_
30	orders	order	NOUN	NNS	Number=Plur	27	pobj	_	_
31	in	in	ADP	IN	_	30	prep	_	_
32	$ C $	$ c $	SYM	$	_	31	pobj	_	_
33	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
34	respectively	respectively	ADV	RB	_	12	advmod	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We observe that $ ParOrd(C) $ is a reflective subcategory of $ PreOrd(C) $ such that each component of the unit of the adjunction is a pullback - stable regular epimorphism.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	observe	observe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	$ ParOrd(C) $	$ parord(c) $	SYM	$	_	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	reflective	reflective	ADJ	JJ	Degree=Pos	8	amod	_	_
8	subcategory	subcategory	NOUN	NN	Number=Sing	5	attr	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	$ PreOrd(C) $	$ preord(c) $	SYM	$	_	11	nmod	_	_
11	such	such	ADJ	JJ	Degree=Pos	21	acomp	_	_
12	that	that	SCONJ	IN	_	21	mark	_	_
13	each	each	DET	DT	_	14	det	_	_
14	component	component	NOUN	NN	Number=Sing	21	nsubj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	unit	unit	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	adjunction	adjunction	NOUN	NN	Number=Sing	18	pobj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
23	pullback	pullback	ADJ	JJ	Degree=Pos	25	amod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	stable	stable	ADJ	JJ	Degree=Pos	27	amod	_	_
26	regular	regular	ADJ	JJ	Degree=Pos	27	amod	_	_
27	epimorphism	epimorphism	NOUN	NN	Number=Sing	21	attr	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = The reflector $ F: PreOrd(C) to PardOrd(C) $ turns out to have stable units in the sense of Cassidy, Hébert and Kelly, thus inducing an admissible categorical Galois structure.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	reflector	reflector	NOUN	NN	Number=Sing	4	nsubj	_	_
3	$ F: PreOrd(C) to PardOrd(C) $	$ f: preord(c) to pardord(c) $	SYM	$	_	4	nsubj	_	_
4	turns	turn	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	out	out	ADP	RP	_	4	prt	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	have	have	VERB	VB	VerbForm=Inf	4	xcomp	_	_
8	stable	stable	ADJ	JJ	Degree=Pos	9	amod	_	_
9	units	unit	NOUN	NNS	Number=Plur	7	dobj	_	_
10	in	in	ADP	IN	_	7	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	sense	sense	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	Cassidy	Cassidy	PROPN	NNP	Number=Sing	13	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	Hébert	Hébert	PROPN	NNP	Number=Sing	14	conj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	Kelly	Kelly	PROPN	NNP	Number=Sing	16	conj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
20	thus	thus	ADV	RB	_	21	advmod	_	_
21	inducing	induce	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	advcl	_	_
22	an	an	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
23	admissible	admissible	ADJ	JJ	Degree=Pos	26	amod	_	_
24	categorical	categorical	ADJ	JJ	Degree=Pos	26	amod	_	_
25	Galois	Galois	PROPN	NNP	Number=Sing	26	compound	_	_
26	structure	structure	NOUN	NN	Number=Sing	21	dobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = In particular, when $ C $ is the category $ Set $ of sets, we show that this reflection induces a monotone - light factorization system (in the sense of Carboni, Janelidze, Kelly and Paré) in $ PreOrd(Set) $ .
1	In	in	ADP	IN	_	14	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
4	when	when	SCONJ	WRB	_	6	advmod	_	_
5	$ C $	$ c $	SYM	$	_	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	advcl	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	6	attr	_	_
9	$ Set $	$ set $	SYM	$	_	8	appos	_	_
10	of	of	ADP	IN	_	8	prep	_	_
11	sets	set	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	that	that	SCONJ	IN	_	18	mark	_	_
16	this	this	DET	DT	Number=Sing|PronType=Dem	17	det	_	_
17	reflection	reflection	NOUN	NN	Number=Sing	18	nsubj	_	_
18	induces	induce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	ccomp	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
20	monotone	monotone	NOUN	NN	Number=Sing	22	amod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	light	light	ADJ	JJ	Degree=Pos	24	amod	_	_
23	factorization	factorization	NOUN	NN	Number=Sing	24	compound	_	_
24	system	system	NOUN	NN	Number=Sing	18	dobj	_	_
25	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
26	in	in	ADP	IN	_	18	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	sense	sense	NOUN	NN	Number=Sing	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	Carboni	Carboni	PROPN	NNP	Number=Sing	29	pobj	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
32	Janelidze	Janelidze	PROPN	NNP	Number=Sing	30	conj	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
34	Kelly	Kelly	PROPN	NNP	Number=Sing	32	conj	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	34	cc	_	_
36	Paré	Paré	PROPN	NNP	Number=Sing	34	conj	_	SpaceAfter=No
37	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	30	punct	_	_
38	in	in	ADP	IN	_	28	prep	_	_
39	$ PreOrd(Set) $	$ preord(set) $	SYM	$	_	38	pobj	_	_
40	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 6
# text = A topological interpretation of our results in the category of Alexandroff - discrete spaces is also given, via the well - known isomorphism between this latter category and $ PreOrd(Set) $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	topological	topological	ADJ	JJ	Degree=Pos	3	amod	_	_
3	interpretation	interpretation	NOUN	NN	Number=Sing	17	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	6	poss	_	_
6	results	result	NOUN	NNS	Number=Plur	4	pobj	_	_
7	in	in	ADP	IN	_	3	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	Alexandroff	Alexandroff	PROPN	NNP	Number=Sing	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	discrete	discrete	NOUN	NN	Number=Sing	14	compound	_	_
14	spaces	space	NOUN	NNS	Number=Plur	10	pobj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	auxpass	_	_
16	also	also	ADV	RB	_	17	advmod	_	_
17	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	via	via	ADP	IN	_	17	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
21	well	well	ADV	RB	Degree=Pos	23	advmod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
24	isomorphism	isomorphism	NOUN	NN	Number=Sing	19	pobj	_	_
25	between	between	ADP	IN	_	24	prep	_	_
26	this	this	DET	DT	Number=Sing|PronType=Dem	28	det	_	_
27	latter	latter	ADJ	JJ	Degree=Pos	28	amod	_	_
28	category	category	NOUN	NN	Number=Sing	25	pobj	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	$ PreOrd(Set) $	$ preord(set) $	SYM	$	_	28	conj	_	_
31	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# doc_id = 11
# sent_id = 1
# text = In this article the notion of virtual double category (also known as fc - multicategory) is extended as follows.
1	In	in	ADP	IN	_	19	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	article	article	NOUN	NN	Number=Sing	1	pobj	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	notion	notion	NOUN	NN	Number=Sing	19	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	virtual	virtual	ADJ	JJ	Degree=Pos	9	amod	_	_
8	double	double	ADJ	JJ	Degree=Pos	9	amod	_	_
9	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
10	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	9	punct	_	SpaceAfter=No
11	also	also	ADV	RB	_	12	advmod	_	_
12	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	acl	_	_
13	as	as	ADP	IN	_	12	prep	_	_
14	fc	fc	ADV	RB	_	16	advmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	multicategory	multicategory	ADJ	JJ	Degree=Pos	13	pobj	_	SpaceAfter=No
17	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	9	punct	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	auxpass	_	_
19	extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
20	as	as	SCONJ	IN	_	21	mark	_	_
21	follows	follow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	advcl	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 2
# text = While cells in a virtual double category classically have a horizontal multi - source and single horizontal target, the notion of augmented virtual double category introduced here extends the latter notion by including cells with empty horizontal target as well.
1	While	while	SCONJ	IN	_	9	mark	_	_
2	cells	cell	NOUN	NNS	Number=Plur	9	nsubj	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	virtual	virtual	ADJ	JJ	Degree=Pos	7	amod	_	_
6	double	double	ADJ	JJ	Degree=Pos	7	amod	_	_
7	category	category	NOUN	NN	Number=Sing	3	pobj	_	_
8	classically	classically	ADV	RB	_	9	advmod	_	_
9	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	29	advcl	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
11	horizontal	horizontal	ADJ	JJ	Degree=Pos	14	amod	_	_
12	multi	multi	NOUN	NN	Number=Sing	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	source	source	NOUN	NN	Number=Sing	9	dobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	single	single	ADJ	JJ	Degree=Pos	18	amod	_	_
17	horizontal	horizontal	ADJ	JJ	Degree=Pos	18	amod	_	_
18	target	target	NOUN	NN	Number=Sing	14	conj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	notion	notion	NOUN	NN	Number=Sing	29	nsubj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	augmented	augment	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
24	virtual	virtual	ADJ	JJ	Degree=Pos	26	amod	_	_
25	double	double	ADJ	JJ	Degree=Pos	26	amod	_	_
26	category	category	NOUN	NN	Number=Sing	22	pobj	_	_
27	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	acl	_	_
28	here	here	ADV	RB	PronType=Dem	27	advmod	_	_
29	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	latter	latter	ADJ	JJ	Degree=Pos	32	amod	_	_
32	notion	notion	NOUN	NN	Number=Sing	29	dobj	_	_
33	by	by	ADP	IN	_	29	prep	_	_
34	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	33	pcomp	_	_
35	cells	cell	NOUN	NNS	Number=Plur	34	pobj	_	_
36	with	with	ADP	IN	_	35	prep	_	_
37	empty	empty	ADJ	JJ	Degree=Pos	39	amod	_	_
38	horizontal	horizontal	ADJ	JJ	Degree=Pos	39	amod	_	_
39	target	target	NOUN	NN	Number=Sing	36	pobj	_	_
40	as	as	ADV	RB	_	41	advmod	_	_
41	well	well	ADV	RB	Degree=Pos	34	advmod	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	29	punct	_	SpaceAfter=No

# sent_id = 3
# text = Any augmented virtual double category comes with a built - in notion of "locally small object" and we describe advantages of using augmented virtual double categories as a setting for formal category rather than 2 - categories, which are classically equipped with a notion of "admissible object" by means of a yoneda structure in the sense of Street and Walters.
1	Any	any	DET	DT	_	5	det	_	_
2	augmented	augmented	ADJ	JJ	Degree=Pos	5	amod	_	_
3	virtual	virtual	ADJ	JJ	Degree=Pos	5	amod	_	_
4	double	double	ADJ	JJ	Degree=Pos	5	amod	_	_
5	category	category	NOUN	NN	Number=Sing	6	nsubj	_	_
6	comes	come	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	with	with	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
9	built	build	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
11	in	in	ADP	RP	_	9	prt	_	_
12	notion	notion	NOUN	NN	Number=Sing	7	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	17	punct	_	SpaceAfter=No
15	locally	locally	ADV	RB	_	16	advmod	_	_
16	small	small	ADJ	JJ	Degree=Pos	17	amod	_	_
17	object	object	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
18	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	17	punct	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
20	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	21	nsubj	_	_
21	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	6	conj	_	_
22	advantages	advantage	NOUN	NNS	Number=Plur	21	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	23	pcomp	_	_
25	augmented	augment	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	amod	_	_
26	virtual	virtual	ADJ	JJ	Degree=Pos	28	amod	_	_
27	double	double	ADJ	JJ	Degree=Pos	28	amod	_	_
28	categories	category	NOUN	NNS	Number=Plur	24	dobj	_	_
29	as	as	ADP	IN	_	24	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
31	setting	setting	NOUN	NN	Number=Sing	29	pobj	_	_
32	for	for	ADP	IN	_	31	prep	_	_
33	formal	formal	ADJ	JJ	Degree=Pos	34	amod	_	_
34	category	category	NOUN	NN	Number=Sing	32	pobj	_	_
35	rather	rather	ADV	RB	_	36	advmod	_	_
36	than	than	ADP	IN	_	34	cc	_	_
37	2	2	NUM	CD	NumType=Card	39	nummod	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	categories	category	NOUN	NNS	Number=Plur	34	conj	_	SpaceAfter=No
40	,	,	PUNCT	,	PunctType=Comm	39	punct	_	_
41	which	which	PRON	WDT	_	44	nsubjpass	_	_
42	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	44	auxpass	_	_
43	classically	classically	ADV	RB	_	44	advmod	_	_
44	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	39	relcl	_	_
45	with	with	ADP	IN	_	44	prep	_	_
46	a	a	DET	DT	Definite=Ind|PronType=Art	47	det	_	_
47	notion	notion	NOUN	NN	Number=Sing	45	pobj	_	_
48	of	of	ADP	IN	_	47	prep	_	_
49	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	51	punct	_	SpaceAfter=No
50	admissible	admissible	ADJ	JJ	Degree=Pos	51	amod	_	_
51	object	object	NOUN	NN	Number=Sing	48	pobj	_	SpaceAfter=No
52	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	51	punct	_	_
53	by	by	ADP	IN	_	47	prep	_	_
54	means	mean	NOUN	NNS	Number=Plur	53	pobj	_	_
55	of	of	ADP	IN	_	54	prep	_	_
56	a	a	DET	DT	Definite=Ind|PronType=Art	58	det	_	_
57	yoneda	yoneda	NOUN	NN	Number=Sing	58	compound	_	_
58	structure	structure	NOUN	NN	Number=Sing	55	pobj	_	_
59	in	in	ADP	IN	_	44	prep	_	_
60	the	the	DET	DT	Definite=Def|PronType=Art	61	det	_	_
61	sense	sense	NOUN	NN	Number=Sing	59	pobj	_	_
62	of	of	ADP	IN	_	61	prep	_	_
63	Street	Street	PROPN	NNP	Number=Sing	62	pobj	_	_
64	and	and	CCONJ	CC	ConjType=Cmp	63	cc	_	_
65	Walters	Walters	PROPN	NNP	Number=Sing	63	conj	_	SpaceAfter=No
66	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# sent_id = 4
# text = An object is locally small precisely if it admits a horizontal unit, and we show that the notions of augmented virtual double category and virtual double category coincide in the presence of all horizontal units.
1	An	an	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	object	object	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	locally	locally	ADV	RB	_	5	advmod	_	_
5	small	small	ADJ	JJ	Degree=Pos	3	acomp	_	_
6	precisely	precisely	ADV	RB	_	9	advmod	_	_
7	if	if	SCONJ	IN	_	9	mark	_	_
8	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	9	nsubj	_	_
9	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	advcl	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	horizontal	horizontal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	unit	unit	NOUN	NN	Number=Sing	9	dobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
15	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	16	nsubj	_	_
16	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	3	conj	_	_
17	that	that	SCONJ	IN	_	29	mark	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	notions	notion	NOUN	NNS	Number=Plur	29	nsubj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	augmented	augment	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
22	virtual	virtual	ADJ	JJ	Degree=Pos	24	amod	_	_
23	double	double	ADJ	JJ	Degree=Pos	24	amod	_	_
24	category	category	NOUN	NN	Number=Sing	20	pobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	virtual	virtual	ADJ	JJ	Degree=Pos	29	amod	_	_
27	double	double	ADJ	JJ	Degree=Pos	28	amod	_	_
28	category	category	NOUN	NN	Number=Sing	29	compound	_	_
29	coincide	coincide	NOUN	NN	Number=Sing	16	ccomp	_	_
30	in	in	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	presence	presence	NOUN	NN	Number=Sing	30	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	all	all	DET	DT	_	36	det	_	_
35	horizontal	horizontal	ADJ	JJ	Degree=Pos	36	amod	_	_
36	units	unit	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 5
# text = Without assuming the existence of horizontal units we show that most of the basic theory for virtual double categories, such as that of restriction and composition of horizontal morphisms, extends to augmented virtual double categories.
1	Without	without	ADP	IN	_	0	ROOT	_	_
2	assuming	assume	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	1	pcomp	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	existence	existence	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	horizontal	horizontal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	units	unit	NOUN	NNS	Number=Plur	5	pobj	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
10	that	that	SCONJ	IN	_	32	mark	_	_
11	most	most	ADJ	JJS	Degree=Sup	32	nsubj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	basic	basic	ADJ	JJ	Degree=Pos	15	amod	_	_
15	theory	theory	NOUN	NN	Number=Sing	12	pobj	_	_
16	for	for	ADP	IN	_	15	prep	_	_
17	virtual	virtual	ADJ	JJ	Degree=Pos	19	amod	_	_
18	double	double	ADJ	JJ	Degree=Pos	19	amod	_	_
19	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	such	such	ADJ	JJ	Degree=Pos	22	amod	_	_
22	as	as	ADP	IN	_	19	prep	_	_
23	that	that	PRON	DT	Number=Sing|PronType=Dem	22	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	restriction	restriction	NOUN	NN	Number=Sing	24	pobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	composition	composition	NOUN	NN	Number=Sing	25	conj	_	_
28	of	of	ADP	IN	_	25	prep	_	_
29	horizontal	horizontal	ADJ	JJ	Degree=Pos	30	amod	_	_
30	morphisms	morphism	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
32	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	ccomp	_	_
33	to	to	ADP	IN	_	32	prep	_	_
34	augmented	augment	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	37	amod	_	_
35	virtual	virtual	ADJ	JJ	Degree=Pos	37	amod	_	_
36	double	double	ADJ	JJ	Degree=Pos	37	amod	_	_
37	categories	category	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 6
# text = We introduce and study in augmented virtual double categories the notion of "pointwise" composition of horizontal morphisms, which formalises the classical composition of profunctors given by the coend formula.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	study	study	NOUN	NN	Number=Sing	2	conj	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	augmented	augmented	ADJ	JJ	Degree=Pos	9	amod	_	_
7	virtual	virtual	ADJ	JJ	Degree=Pos	9	amod	_	_
8	double	double	ADJ	JJ	Degree=Pos	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	16	punct	_	SpaceAfter=No
14	pointwise	pointwise	NOUN	NN	Number=Sing	16	nmod	_	SpaceAfter=No
15	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	16	punct	_	_
16	composition	composition	NOUN	NN	Number=Sing	12	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	horizontal	horizontal	ADJ	JJ	Degree=Pos	19	amod	_	_
19	morphisms	morphism	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	which	which	PRON	WDT	_	22	nsubj	_	_
22	formalises	formalise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	relcl	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	classical	classical	ADJ	JJ	Degree=Pos	25	amod	_	_
25	composition	composition	NOUN	NN	Number=Sing	22	dobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	profunctors	profunctor	NOUN	NNS	Number=Plur	26	pobj	_	_
28	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	acl	_	_
29	by	by	ADP	IN	_	28	agent	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	coend	coend	NOUN	NN	Number=Sing	32	compound	_	_
32	formula	formula	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 12
# sent_id = 1
# text = We define the homology of a simplicial set with coefficients in a Segal's Gamma - set ( $ s $ - module).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	homology	homology	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	simplicial	simplicial	NOUN	NN	Number=Sing	5	pobj	_	_
8	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	acl	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	coefficients	coefficient	NOUN	NNS	Number=Plur	9	pobj	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	Segal	Segal	PROPN	NNP	Number=Sing	17	poss	_	SpaceAfter=No
14	's	's	PART	POS	_	13	case	_	_
15	Gamma	Gamma	PROPN	NNP	Number=Sing	17	compound	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	pobj	_	_
18	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	21	punct	_	_
19	$ s $	$ s $	SYM	$	_	21	nummod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	module	module	NOUN	NN	Number=Sing	17	appos	_	SpaceAfter=No
22	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	17	punct	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show the relevance of this new homology with values in $ s $ - modules by proving that taking as coefficients the $ s $ - modules at the archimedean place over the structure sheaf on $ Spec(Z) $ , one obtains on the singular homology with real coefficients of a topological space $ X $ , a norm equivalent to the Gromov norm.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	relevance	relevance	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	this	this	DET	DT	Number=Sing|PronType=Dem	8	det	_	_
7	new	new	ADJ	JJ	Degree=Pos	8	amod	_	_
8	homology	homology	NOUN	NN	Number=Sing	5	pobj	_	_
9	with	with	ADP	IN	_	4	prep	_	_
10	values	value	NOUN	NNS	Number=Plur	9	pobj	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	$ s $	$ s $	SYM	$	_	14	nummod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	modules	module	NOUN	NNS	Number=Plur	11	pobj	_	_
15	by	by	ADP	IN	_	2	prep	_	_
16	proving	prove	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	pcomp	_	_
17	that	that	SCONJ	IN	_	16	dobj	_	_
18	taking	take	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	nmod	_	_
19	as	as	ADP	IN	_	18	prep	_	_
20	coefficients	coefficient	NOUN	NNS	Number=Plur	19	pobj	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
22	$ s $	$ s $	SYM	$	_	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	modules	module	NOUN	NNS	Number=Plur	18	dobj	_	_
25	at	at	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	archimedean	archimedean	ADJ	JJ	Degree=Pos	28	compound	_	_
28	place	place	NOUN	NN	Number=Sing	25	pobj	_	_
29	over	over	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	structure	structure	NOUN	NN	Number=Sing	32	compound	_	_
32	sheaf	sheaf	NOUN	NN	Number=Sing	29	pobj	_	_
33	on	on	ADP	IN	_	32	prep	_	_
34	$ Spec(Z) $	$ spec(z) $	SYM	$	_	33	pobj	_	_
35	,	,	PUNCT	,	PunctType=Comm	34	punct	_	_
36	one	one	NUM	CD	NumType=Card	37	nummod	_	_
37	obtains	obtain	NOUN	NNS	Number=Plur	16	ccomp	_	_
38	on	on	ADP	IN	_	37	prep	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
40	singular	singular	ADJ	JJ	Degree=Pos	41	amod	_	_
41	homology	homology	NOUN	NN	Number=Sing	38	pobj	_	_
42	with	with	ADP	IN	_	37	prep	_	_
43	real	real	ADJ	JJ	Degree=Pos	44	amod	_	_
44	coefficients	coefficient	NOUN	NNS	Number=Plur	42	pobj	_	_
45	of	of	ADP	IN	_	44	prep	_	_
46	a	a	DET	DT	Definite=Ind|PronType=Art	48	det	_	_
47	topological	topological	ADJ	JJ	Degree=Pos	48	amod	_	_
48	space	space	NOUN	NN	Number=Sing	45	pobj	_	_
49	$ X $	$ x $	SYM	$	_	48	appos	_	_
50	,	,	PUNCT	,	PunctType=Comm	48	punct	_	_
51	a	a	DET	DT	Definite=Ind|PronType=Art	52	det	_	_
52	norm	norm	NOUN	NN	Number=Sing	2	dobj	_	_
53	equivalent	equivalent	ADJ	JJ	Degree=Pos	52	amod	_	_
54	to	to	ADP	IN	_	53	prep	_	_
55	the	the	DET	DT	Definite=Def|PronType=Art	57	det	_	_
56	Gromov	Gromov	PROPN	NNP	Number=Sing	57	compound	_	_
57	norm	norm	NOUN	NN	Number=Sing	54	pobj	_	SpaceAfter=No
58	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Moreover, we prove that the two norms agree when $ X $ is an oriented compact Riemann surface.
1	Moreover	moreover	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	9	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	two	two	NUM	CD	NumType=Card	8	nummod	_	_
8	norms	norm	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	agree	agree	VERB	VBP	Tense=Pres|VerbForm=Fin	4	ccomp	_	_
10	when	when	SCONJ	WRB	_	12	advmod	_	_
11	$ X $	$ x $	SYM	$	_	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	advcl	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
14	oriented	orient	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
15	compact	compact	ADJ	JJ	Degree=Pos	17	amod	_	_
16	Riemann	Riemann	PROPN	NNP	Number=Sing	17	compound	_	_
17	surface	surface	NOUN	NN	Number=Sing	12	attr	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 13
# sent_id = 1
# text = We derive three equivalent necessary conditions for a small category to have homological dimension one, generalizing a result of Novikov.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	derive	derive	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	three	three	NUM	CD	NumType=Card	6	nummod	_	_
4	equivalent	equivalent	ADJ	JJ	Degree=Pos	6	amod	_	_
5	necessary	necessary	ADJ	JJ	Degree=Pos	6	amod	_	_
6	conditions	condition	NOUN	NNS	Number=Plur	2	dobj	_	_
7	for	for	SCONJ	IN	_	12	mark	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	small	small	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	12	nsubj	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	have	have	VERB	VB	VerbForm=Inf	2	advcl	_	_
13	homological	homological	ADJ	JJ	Degree=Pos	14	amod	_	_
14	dimension	dimension	NOUN	NN	Number=Sing	15	compound	_	_
15	one	one	NUM	CD	NumType=Card	12	dobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
17	generalizing	generalize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	advcl	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	result	result	NOUN	NN	Number=Sing	17	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	Novikov	Novikov	PROPN	NNP	Number=Sing	20	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = As a consequence, any small cancellative category of homological dimension one is embeddable in a groupoid.
1	As	as	ADP	IN	_	13	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	consequence	consequence	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
5	any	any	DET	DT	_	8	det	_	_
6	small	small	ADJ	JJ	Degree=Pos	8	amod	_	_
7	cancellative	cancellative	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	13	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	homological	homological	ADJ	JJ	Degree=Pos	11	amod	_	_
11	dimension	dimension	NOUN	NN	Number=Sing	12	compound	_	_
12	one	one	NOUN	NN	Number=Sing	9	pobj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	embeddable	embeddable	ADJ	JJ	Degree=Pos	13	acomp	_	_
15	in	in	ADP	IN	_	13	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	groupoid	groupoid	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# doc_id = 14
# sent_id = 1
# text = In this article we give necessary and sufficient conditions for a binary product to exist in a partial morphism category.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	article	article	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	necessary	necessary	ADJ	JJ	Degree=Pos	9	amod	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	sufficient	sufficient	ADJ	JJ	Degree=Pos	6	conj	_	_
9	conditions	condition	NOUN	NNS	Number=Plur	5	dobj	_	_
10	for	for	SCONJ	IN	_	15	mark	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	binary	binary	ADJ	JJ	Degree=Pos	13	amod	_	_
13	product	product	NOUN	NN	Number=Sing	15	nsubj	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	exist	exist	VERB	VB	VerbForm=Inf	5	advcl	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
18	partial	partial	ADJ	JJ	Degree=Pos	20	amod	_	_
19	morphism	morphism	NOUN	NN	Number=Sing	20	compound	_	_
20	category	category	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = We also give necessary and sufficient conditions for the existence of a productive terminal in such categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	necessary	necessary	ADJ	JJ	Degree=Pos	7	amod	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	sufficient	sufficient	ADJ	JJ	Degree=Pos	4	conj	_	_
7	conditions	condition	NOUN	NNS	Number=Plur	3	dobj	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	existence	existence	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	productive	productive	ADJ	JJ	Degree=Pos	14	amod	_	_
14	terminal	terminal	NOUN	NN	Number=Sing	11	pobj	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	such	such	ADJ	JJ	Degree=Pos	17	amod	_	_
17	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 15
# sent_id = 1
# text = Persistence has proved to be a valuable tool to analyze real world data robustly.
1	Persistence	persistence	NOUN	NN	Number=Sing	3	nsubj	_	_
2	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	aux	_	_
3	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	be	be	AUX	VB	VerbForm=Inf	3	xcomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	valuable	valuable	ADJ	JJ	Degree=Pos	8	amod	_	_
8	tool	tool	NOUN	NN	Number=Sing	5	attr	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	analyze	analyze	VERB	VB	VerbForm=Inf	8	acl	_	_
11	real	real	ADJ	JJ	Degree=Pos	13	amod	_	_
12	world	world	NOUN	NN	Number=Sing	13	compound	_	_
13	data	datum	NOUN	NNS	Number=Plur	10	dobj	_	_
14	robustly	robustly	ADV	RB	_	10	advmod	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = Several approaches to persistence have been attempted over time, some topological in flavor, based on the vector space - valued homology functor, others combinatorial, based on arbitrary set - valued functors.
1	Several	several	ADJ	JJ	Degree=Pos	2	amod	_	_
2	approaches	approach	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	persistence	persistence	NOUN	NN	Number=Sing	3	pobj	_	_
5	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	aux	_	_
6	been	be	AUX	VBN	Tense=Past|VerbForm=Part	7	auxpass	_	_
7	attempted	attempt	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	over	over	ADP	IN	_	7	prep	_	_
9	time	time	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
11	some	some	PRON	DT	_	13	nsubj	_	_
12	topological	topological	ADJ	JJ	Degree=Pos	11	amod	_	_
13	in	in	ADP	IN	_	7	prep	_	_
14	flavor	flavor	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
16	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	prep	_	_
17	on	on	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
19	vector	vector	NOUN	NN	Number=Sing	24	nmod	_	_
20	space	space	NOUN	NN	Number=Sing	22	npadvmod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
23	homology	homology	NOUN	NN	Number=Sing	24	compound	_	_
24	functor	functor	PROPN	NNP	Number=Sing	17	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
26	others	other	NOUN	NNS	Number=Plur	27	nsubj	_	_
27	combinatorial	combinatorial	VERB	VBP	Tense=Pres|VerbForm=Fin	7	conj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
29	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	prep	_	_
30	on	on	ADP	IN	_	29	prep	_	_
31	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	35	amod	_	_
32	set	set	NOUN	NN	Number=Sing	34	npadvmod	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	35	amod	_	_
35	functors	functor	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = To unify the study of topological and combinatorial persistence in a common categorical framework, we give axioms for a generalized rank function on objects in a target category so that functors to that category induce persistence functions.
1	To	to	PART	TO	_	2	aux	_	_
2	unify	unify	VERB	VB	VerbForm=Inf	17	advcl	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	study	study	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	topological	topological	ADJ	JJ	Degree=Pos	9	amod	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	6	conj	_	_
9	persistence	persistence	NOUN	NN	Number=Sing	5	pobj	_	_
10	in	in	ADP	IN	_	4	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
12	common	common	ADJ	JJ	Degree=Pos	14	amod	_	_
13	categorical	categorical	ADJ	JJ	Degree=Pos	14	amod	_	_
14	framework	framework	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
16	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	17	nsubj	_	_
17	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
18	axioms	axiom	NOUN	NNS	Number=Plur	17	dobj	_	_
19	for	for	ADP	IN	_	17	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
21	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	amod	_	_
22	rank	rank	NOUN	NN	Number=Sing	23	compound	_	_
23	function	function	NOUN	NN	Number=Sing	19	pobj	_	_
24	on	on	ADP	IN	_	23	prep	_	_
25	objects	object	NOUN	NNS	Number=Plur	24	pobj	_	_
26	in	in	ADP	IN	_	17	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	target	target	NOUN	NN	Number=Sing	29	compound	_	_
29	category	category	NOUN	NN	Number=Sing	26	pobj	_	_
30	so	so	SCONJ	IN	_	36	mark	_	_
31	that	that	SCONJ	IN	_	36	mark	_	_
32	functors	functor	NOUN	NNS	Number=Plur	36	nsubj	_	_
33	to	to	ADP	IN	_	32	prep	_	_
34	that	that	DET	DT	Number=Sing|PronType=Dem	35	det	_	_
35	category	category	NOUN	NN	Number=Sing	33	pobj	_	_
36	induce	induce	VERB	VB	VerbForm=Inf	17	advcl	_	_
37	persistence	persistence	NOUN	NN	Number=Sing	38	compound	_	_
38	functions	function	NOUN	NNS	Number=Plur	36	dobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 4
# text = We port the interleaving and bottleneck distances to this novel framework and generalize classical equalities and inequalities.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	port	port	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
4	interleaving	interleaving	ADJ	JJ	Degree=Pos	7	amod	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	bottleneck	bottleneck	NOUN	NN	Number=Sing	4	conj	_	_
7	distances	distance	NOUN	NNS	Number=Plur	2	dobj	_	_
8	to	to	ADP	IN	_	7	prep	_	_
9	this	this	DET	DT	Number=Sing|PronType=Dem	11	det	_	_
10	novel	novel	ADJ	JJ	Degree=Pos	11	amod	_	_
11	framework	framework	NOUN	NN	Number=Sing	8	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
13	generalize	generalize	VERB	VB	VerbForm=Inf	2	conj	_	_
14	classical	classical	ADJ	JJ	Degree=Pos	15	amod	_	_
15	equalities	equality	NOUN	NNS	Number=Plur	13	dobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	inequalities	inequality	NOUN	NNS	Number=Plur	15	conj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = Unlike sets and vector spaces, in many categories the rank of an object does not identify it up to isomorphism: to preserve information about the structure of persistence modules, we define colorable ranks, persistence diagrams and prove the equality between multicolored bottleneck distance and interleaving distance in semisimple Abelian categories.
1	Unlike	unlike	ADP	IN	_	17	prep	_	_
2	sets	set	NOUN	NNS	Number=Plur	1	pobj	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	vector	vector	NOUN	NN	Number=Sing	5	compound	_	_
5	spaces	space	NOUN	NNS	Number=Plur	2	conj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
7	in	in	ADP	IN	_	17	prep	_	_
8	many	many	ADJ	JJ	Degree=Pos	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	rank	rank	NOUN	NN	Number=Sing	17	nsubj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	object	object	NOUN	NN	Number=Sing	12	pobj	_	_
15	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	aux	_	_
16	not	not	PART	RB	Polarity=Neg	17	neg	_	_
17	identify	identify	VERB	VB	VerbForm=Inf	34	advcl	_	_
18	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	17	dobj	_	_
19	up	up	ADP	RP	_	17	prt	_	_
20	to	to	ADP	IN	_	19	prep	_	_
21	isomorphism	isomorphism	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
22	:	:	PUNCT	:	_	17	punct	_	_
23	to	to	PART	TO	_	24	aux	_	_
24	preserve	preserve	VERB	VB	VerbForm=Inf	17	advcl	_	_
25	information	information	NOUN	NN	Number=Sing	24	dobj	_	_
26	about	about	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	structure	structure	NOUN	NN	Number=Sing	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	persistence	persistence	NOUN	NN	Number=Sing	31	compound	_	_
31	modules	module	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	34	punct	_	_
33	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	34	nsubj	_	_
34	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
35	colorable	colorable	ADJ	JJ	Degree=Pos	36	amod	_	_
36	ranks	rank	NOUN	NNS	Number=Plur	34	dobj	_	SpaceAfter=No
37	,	,	PUNCT	,	PunctType=Comm	34	punct	_	_
38	persistence	persistence	NOUN	NN	Number=Sing	39	compound	_	_
39	diagrams	diagram	NOUN	NNS	Number=Plur	34	conj	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	34	cc	_	_
41	prove	prove	VERB	VB	VerbForm=Inf	34	conj	_	_
42	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
43	equality	equality	NOUN	NN	Number=Sing	41	dobj	_	_
44	between	between	ADP	IN	_	43	prep	_	_
45	multicolored	multicolore	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	47	amod	_	_
46	bottleneck	bottleneck	NOUN	NN	Number=Sing	47	compound	_	_
47	distance	distance	NOUN	NN	Number=Sing	44	pobj	_	_
48	and	and	CCONJ	CC	ConjType=Cmp	47	cc	_	_
49	interleaving	interleave	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	50	amod	_	_
50	distance	distance	NOUN	NN	Number=Sing	47	conj	_	_
51	in	in	ADP	IN	_	47	prep	_	_
52	semisimple	semisimple	ADJ	JJ	Degree=Pos	54	amod	_	_
53	Abelian	abelian	ADJ	JJ	Degree=Pos	54	amod	_	_
54	categories	category	NOUN	NNS	Number=Plur	51	pobj	_	SpaceAfter=No
55	.	.	PUNCT	.	PunctType=Peri	34	punct	_	SpaceAfter=No

# sent_id = 6
# text = To illustrate our framework in practice, we give examples of multicolored persistent homology on filtered topological spaces with a group action and labeled point cloud data.
1	To	to	PART	TO	_	2	aux	_	_
2	illustrate	illustrate	VERB	VB	VerbForm=Inf	9	advcl	_	_
3	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	4	poss	_	_
4	framework	framework	NOUN	NN	Number=Sing	2	dobj	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	practice	practice	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	examples	example	NOUN	NNS	Number=Plur	9	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	multicolored	multicolore	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
13	persistent	persistent	ADJ	JJ	Degree=Pos	14	amod	_	_
14	homology	homology	NOUN	NN	Number=Sing	11	pobj	_	_
15	on	on	ADP	IN	_	9	prep	_	_
16	filtered	filter	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
17	topological	topological	ADJ	JJ	Degree=Pos	18	amod	_	_
18	spaces	space	NOUN	NNS	Number=Plur	15	pobj	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	group	group	NOUN	NN	Number=Sing	22	compound	_	_
22	action	action	NOUN	NN	Number=Sing	19	pobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	labeled	label	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	amod	_	_
25	point	point	NOUN	NN	Number=Sing	26	compound	_	_
26	cloud	cloud	NOUN	NN	Number=Sing	27	compound	_	_
27	data	datum	NOUN	NNS	Number=Plur	22	conj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 16
# sent_id = 1
# text = We prove that, given any reflective subfibration $ L $ on an $ infty $ - topos $ E $ , there exists a reflective subfibration $ L' $ on $ E $ whose local maps are the $ L $ - separated maps, that is, the maps whose diagonals are $ L $ - local.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	18	mark	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
5	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	prep	_	_
6	any	any	DET	DT	_	8	det	_	_
7	reflective	reflective	ADJ	JJ	Degree=Pos	8	amod	_	_
8	subfibration	subfibration	NOUN	NN	Number=Sing	5	pobj	_	_
9	$ L $	$ l $	SYM	$	_	8	appos	_	_
10	on	on	ADP	IN	_	8	prep	_	_
11	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
12	$ infty $	$ infty $	SYM	$	_	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	topos	topos	NOUN	NN	Number=Sing	15	compound	_	_
15	$ E $	$ e $	SYM	$	_	10	pobj	_	_
16	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
17	there	there	PRON	EX	_	18	expl	_	_
18	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	reflective	reflective	ADJ	JJ	Degree=Pos	21	amod	_	_
21	subfibration	subfibration	NOUN	NN	Number=Sing	18	dobj	_	_
22	$ L' $	$ l' $	SYM	$	_	21	appos	_	_
23	on	on	ADP	IN	_	28	prep	_	_
24	$ E $	$ e $	SYM	$	_	23	pobj	_	_
25	whose	whose	DET	WP$	Poss=Yes	27	poss	_	_
26	local	local	ADJ	JJ	Degree=Pos	27	amod	_	_
27	maps	map	NOUN	NNS	Number=Plur	28	nsubj	_	_
28	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	21	relcl	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
30	$ L $	$ l $	SYM	$	_	32	advmod	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	separated	separate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	amod	_	_
33	maps	map	NOUN	NNS	Number=Plur	28	attr	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
35	that	that	ADV	RB	_	36	advmod	_	_
36	is	is	ADV	RB	_	39	advmod	_	SpaceAfter=No
37	,	,	PUNCT	,	PunctType=Comm	39	punct	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
39	maps	map	NOUN	NNS	Number=Plur	21	appos	_	_
40	whose	whose	DET	WP$	Poss=Yes	41	poss	_	_
41	diagonals	diagonal	NOUN	NNS	Number=Plur	42	nsubj	_	_
42	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	39	relcl	_	_
43	$ L $	$ l $	SYM	$	_	45	advmod	_	_
44	-	-	PUNCT	HYPH	PunctType=Dash	45	punct	_	_
45	local	local	ADJ	JJ	Degree=Pos	42	acomp	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 17
# sent_id = 1
# text = We use the homotopy invariance of equivariant principal bundles to prove that the equivariant $ A $ - category of Clapp and Puppe is invariant under Morita equivalence.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	homotopy	homotopy	NOUN	NN	Number=Sing	5	compound	_	_
5	invariance	invariance	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	equivariant	equivariant	ADJ	JJ	Degree=Pos	9	amod	_	_
8	principal	principal	ADJ	JJ	Degree=Pos	9	amod	_	_
9	bundles	bundle	NOUN	NNS	Number=Plur	6	pobj	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	prove	prove	VERB	VB	VerbForm=Inf	2	xcomp	_	_
12	that	that	SCONJ	IN	_	22	mark	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
14	equivariant	equivariant	ADJ	JJ	Degree=Pos	17	amod	_	_
15	$ A $	$ a $	SYM	$	_	17	nummod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	category	category	NOUN	NN	Number=Sing	22	nsubj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	Clapp	Clapp	PROPN	NNP	Number=Sing	18	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	Puppe	Puppe	PROPN	NNP	Number=Sing	19	conj	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	ccomp	_	_
23	invariant	invariant	ADJ	JJ	Degree=Pos	22	acomp	_	_
24	under	under	ADP	IN	_	22	prep	_	_
25	Morita	Morita	PROPN	NNP	Number=Sing	26	compound	_	_
26	equivalence	equivalence	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = As a corollary, we obtain that both the equivariant Lusternik - Schnirelmann category of a group action and the invariant topological complexity are invariant under Morita equivalence.
1	As	as	ADP	IN	_	6	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	corollary	corollary	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	24	mark	_	_
8	both	both	CCONJ	CC	ConjType=Cmp	14	preconj	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
10	equivariant	equivariant	ADJ	JJ	Degree=Pos	14	amod	_	_
11	Lusternik	Lusternik	PROPN	NNP	Number=Sing	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	Schnirelmann	Schnirelmann	PROPN	NNP	Number=Sing	14	compound	_	_
14	category	category	NOUN	NN	Number=Sing	24	nsubj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	group	group	NOUN	NN	Number=Sing	18	compound	_	_
18	action	action	NOUN	NN	Number=Sing	15	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
21	invariant	invariant	ADJ	JJ	Degree=Pos	23	amod	_	_
22	topological	topological	ADJ	JJ	Degree=Pos	23	amod	_	_
23	complexity	complexity	NOUN	NN	Number=Sing	14	conj	_	_
24	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
25	invariant	invariant	ADJ	JJ	Degree=Pos	24	acomp	_	_
26	under	under	ADP	IN	_	24	prep	_	_
27	Morita	Morita	PROPN	NNP	Number=Sing	28	compound	_	_
28	equivalence	equivalence	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = This allows a definition of topological complexity for orbifolds.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	definition	definition	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	topological	topological	ADJ	JJ	Degree=Pos	7	amod	_	_
7	complexity	complexity	NOUN	NN	Number=Sing	5	pobj	_	_
8	for	for	ADP	IN	_	4	prep	_	_
9	orbifolds	orbifold	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 18
# sent_id = 1
# text = The term ``Boolean category'' should be used for describing an object that is to categories what a Boolean algebra is to posets.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	term	term	NOUN	NN	Number=Sing	6	nmod	_	_
3	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	6	punct	_	SpaceAfter=No
4	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	6	punct	_	SpaceAfter=No
5	Boolean	boolean	ADJ	JJ	Degree=Pos	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	10	nsubjpass	_	SpaceAfter=No
7	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	6	punct	_	_
8	should	should	AUX	MD	VerbForm=Fin	10	aux	_	_
9	be	be	AUX	VB	VerbForm=Inf	10	auxpass	_	_
10	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	describing	describe	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	pcomp	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	object	object	NOUN	NN	Number=Sing	12	dobj	_	_
15	that	that	PRON	WDT	PronType=Rel	16	nsubj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	_
19	what	what	PRON	WP	_	23	attr	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	Boolean	boolean	ADJ	JJ	Degree=Pos	22	amod	_	_
22	algebra	algebra	NOUN	NN	Number=Sing	23	nsubj	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	ccomp	_	_
24	to	to	ADP	IN	_	23	prep	_	_
25	posets	poset	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = More specifically, a Boolean category should provide the abstract algebraic structure underlying the proofs in Boolean Logic, in the same sense as a Cartesian closed category captures the proofs in intuitionistic logic and a $ * $ - autonomous category captures the proofs in linear logic.
1	More	more	ADV	RBR	Degree=Cmp	2	advmod	_	_
2	specifically	specifically	ADV	RB	_	8	advmod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	Boolean	boolean	ADJ	JJ	Degree=Pos	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	8	nsubj	_	_
7	should	should	AUX	MD	VerbForm=Fin	8	aux	_	_
8	provide	provide	VERB	VB	VerbForm=Inf	0	ROOT	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
10	abstract	abstract	ADJ	JJ	Degree=Pos	12	amod	_	_
11	algebraic	algebraic	ADJ	JJ	Degree=Pos	12	amod	_	_
12	structure	structure	NOUN	NN	Number=Sing	8	dobj	_	_
13	underlying	underlie	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	acl	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	proofs	proof	NOUN	NNS	Number=Plur	13	dobj	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	Boolean	Boolean	PROPN	NNP	Number=Sing	18	compound	_	_
18	Logic	Logic	PROPN	NNP	Number=Sing	16	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
20	in	in	ADP	IN	_	29	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	same	same	ADJ	JJ	Degree=Pos	23	amod	_	_
23	sense	sense	NOUN	NN	Number=Sing	20	pobj	_	_
24	as	as	SCONJ	IN	_	29	mark	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
26	Cartesian	Cartesian	PROPN	NNP	Number=Sing	28	amod	_	_
27	closed	closed	ADJ	JJ	Degree=Pos	28	amod	_	_
28	category	category	NOUN	NN	Number=Sing	29	nsubj	_	_
29	captures	capture	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	conj	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	proofs	proof	NOUN	NNS	Number=Plur	29	dobj	_	_
32	in	in	ADP	IN	_	29	prep	_	_
33	intuitionistic	intuitionistic	ADJ	JJ	Degree=Pos	34	amod	_	_
34	logic	logic	NOUN	NN	Number=Sing	32	pobj	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
36	a	a	DET	DT	Definite=Ind|PronType=Art	40	det	_	_
37	$ * $	$ * $	SYM	$	_	39	advmod	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	autonomous	autonomous	ADJ	JJ	Degree=Pos	40	amod	_	_
40	category	category	NOUN	NN	Number=Sing	41	nsubj	_	_
41	captures	capture	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	conj	_	_
42	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
43	proofs	proof	NOUN	NNS	Number=Plur	41	dobj	_	_
44	in	in	ADP	IN	_	41	prep	_	_
45	linear	linear	ADJ	JJ	Degree=Pos	46	amod	_	_
46	logic	logic	NOUN	NN	Number=Sing	44	pobj	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 3
# text = However, recent work has shown that there is no canonical axiomatisation of a Boolean category.
1	However	however	ADV	RB	_	6	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
3	recent	recent	ADJ	JJ	Degree=Pos	4	amod	_	_
4	work	work	NOUN	NN	Number=Sing	6	nsubj	_	_
5	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	aux	_	_
6	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	that	that	SCONJ	IN	_	9	mark	_	_
8	there	there	PRON	EX	_	9	expl	_	_
9	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
10	no	no	DET	DT	_	12	det	_	_
11	canonical	canonical	ADJ	JJ	Degree=Pos	12	amod	_	_
12	axiomatisation	axiomatisation	NOUN	NN	Number=Sing	9	attr	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	Boolean	boolean	ADJ	JJ	Degree=Pos	16	amod	_	_
16	category	category	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = In this work, we will see a series (with increasing strength) of possible such axiomatisations, all based on the notion of $ * $ - autonomous category.
1	In	in	ADP	IN	_	7	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	work	work	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
6	will	will	AUX	MD	VerbForm=Fin	7	aux	_	_
7	see	see	VERB	VB	VerbForm=Inf	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	series	series	NOUN	NN	Number=Sing	7	dobj	_	_
10	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	9	punct	_	SpaceAfter=No
11	with	with	ADP	IN	_	9	prep	_	_
12	increasing	increase	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	amod	_	_
13	strength	strength	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
14	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	13	punct	_	_
15	of	of	ADP	IN	_	13	prep	_	_
16	possible	possible	ADJ	JJ	Degree=Pos	18	amod	_	_
17	such	such	ADJ	JJ	Degree=Pos	18	amod	_	_
18	axiomatisations	axiomatisation	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
20	all	all	PRON	DT	_	9	appos	_	_
21	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	acl	_	_
22	on	on	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	notion	notion	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	$ * $	$ * $	SYM	$	_	28	advmod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	autonomous	autonomous	ADJ	JJ	Degree=Pos	29	amod	_	_
29	category	category	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 5
# text = We will particularly focus on the medial map, which has its origin in an inference rule in $ KS $ , a cut - free deductive system for Boolean logic in the calculus of structures.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
2	will	will	AUX	MD	VerbForm=Fin	4	aux	_	_
3	particularly	particularly	ADV	RB	_	4	advmod	_	_
4	focus	focus	VERB	VB	VerbForm=Inf	0	ROOT	_	_
5	on	on	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	medial	medial	ADJ	JJ	Degree=Pos	8	amod	_	_
8	map	map	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
10	which	which	PRON	WDT	_	11	nsubj	_	_
11	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	relcl	_	_
12	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	13	poss	_	_
13	origin	origin	NOUN	NN	Number=Sing	11	dobj	_	_
14	in	in	ADP	IN	_	11	prep	_	_
15	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	inference	inference	NOUN	NN	Number=Sing	17	compound	_	_
17	rule	rule	NOUN	NN	Number=Sing	14	pobj	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	$ KS $	$ ks $	SYM	$	_	18	pobj	_	_
20	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
22	cut	cut	NOUN	NN	Number=Sing	24	npadvmod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	free	free	ADJ	JJ	Degree=Pos	26	amod	_	_
25	deductive	deductive	ADJ	JJ	Degree=Pos	26	amod	_	_
26	system	system	NOUN	NN	Number=Sing	8	appos	_	_
27	for	for	ADP	IN	_	26	prep	_	_
28	Boolean	boolean	ADJ	JJ	Degree=Pos	29	amod	_	_
29	logic	logic	NOUN	NN	Number=Sing	27	pobj	_	_
30	in	in	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	calculus	calculus	NOUN	NN	Number=Sing	30	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	structures	structure	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 6
# text = Finally, we will present a category of proof nets as a particularly well - behaved example of a Boolean category.
1	Finally	finally	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
4	will	will	AUX	MD	VerbForm=Fin	5	aux	_	_
5	present	present	VERB	VB	VerbForm=Inf	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	category	category	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	proof	proof	NOUN	NN	Number=Sing	10	compound	_	_
10	nets	net	NOUN	NNS	Number=Plur	8	pobj	_	_
11	as	as	ADP	IN	_	5	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
13	particularly	particularly	ADV	RB	_	16	advmod	_	_
14	well	well	ADV	RB	Degree=Pos	16	advmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	behaved	behave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	example	example	NOUN	NN	Number=Sing	11	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	Boolean	boolean	ADJ	JJ	Degree=Pos	21	amod	_	_
21	category	category	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 19
# sent_id = 1
# text = We raise the question of saying what it means for a functor between abelian categories to preserve homology.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	raise	raise	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	question	question	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	saying	say	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	what	what	PRON	WP	_	9	dobj	_	_
8	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	9	nsubj	_	_
9	means	mean	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
10	for	for	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	functor	functor	NOUN	NN	Number=Sing	10	pobj	_	_
13	between	between	ADP	IN	_	12	prep	_	_
14	abelian	abelian	ADJ	JJ	Degree=Pos	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	_
16	to	to	PART	TO	_	17	aux	_	_
17	preserve	preserve	VERB	VB	VerbForm=Inf	9	advcl	_	_
18	homology	homology	NOUN	NN	Number=Sing	17	dobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We give a kind of answer and explore the reasons it is unsatisfactory in general (although fine for left or right exact functors).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	kind	kind	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	answer	answer	NOUN	NN	Number=Sing	5	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
8	explore	explore	VERB	VB	VerbForm=Inf	2	conj	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	reasons	reason	NOUN	NNS	Number=Plur	8	dobj	_	_
11	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	relcl	_	_
13	unsatisfactory	unsatisfactory	ADJ	JJ	Degree=Pos	12	acomp	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	general	general	ADJ	JJ	Degree=Pos	14	amod	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	8	punct	_	SpaceAfter=No
17	although	although	SCONJ	IN	_	18	mark	_	_
18	fine	fine	ADJ	JJ	Degree=Pos	8	advcl	_	_
19	for	for	ADP	IN	_	18	prep	_	_
20	left	left	ADJ	JJ	Degree=Pos	24	amod	_	_
21	or	or	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	right	right	ADJ	JJ	Degree=Pos	20	conj	_	_
23	exact	exact	ADJ	JJ	Degree=Pos	24	amod	_	_
24	functors	functor	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
25	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	18	punct	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 20
# sent_id = 1
# text = A category $ C $ is additive if and only if, for every object $ B $ of $ C $ , the category $ Pt(C, B) $ of pointed objects in the comma category $ (C, B) $ is canonically equivalent to $ C $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	4	nsubj	_	_
3	$ C $	$ c $	SYM	$	_	2	appos	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	additive	additive	ADJ	JJ	Degree=Pos	4	acomp	_	_
6	if	if	SCONJ	IN	_	29	mark	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
8	only	only	ADV	RB	_	9	advmod	_	_
9	if	if	SCONJ	IN	_	29	mark	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
11	for	for	ADP	IN	_	29	prep	_	_
12	every	every	DET	DT	_	13	det	_	_
13	object	object	NOUN	NN	Number=Sing	11	pobj	_	_
14	$ B $	$ b $	SYM	$	_	11	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	$ C $	$ c $	SYM	$	_	15	pobj	_	_
17	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	category	category	NOUN	NN	Number=Sing	29	nsubj	_	_
20	$ Pt(C, B) $	$ pt(c, b) $	SYM	$	_	19	appos	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	pointed	pointed	ADJ	JJ	Degree=Pos	23	amod	_	_
23	objects	object	NOUN	NNS	Number=Plur	21	pobj	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	comma	comma	ADJ	JJ	Degree=Pos	27	amod	_	_
27	category	category	NOUN	NN	Number=Sing	24	pobj	_	_
28	$ (C, B) $	$ (c, b) $	X	FW	Foreign=Yes	27	appos	_	_
29	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	advcl	_	_
30	canonically	canonically	ADV	RB	_	31	advmod	_	_
31	equivalent	equivalent	ADJ	JJ	Degree=Pos	29	acomp	_	_
32	to	to	ADP	IN	_	31	prep	_	_
33	$ C $	$ c $	SYM	$	_	32	pobj	_	_
34	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = We reformulate the proof of this known result in order to obtain a stronger one that uses not all objects of $ B $ of $ C $ , but only a conveniently defined generating class $ S $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	reformulate	reformulate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	proof	proof	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	this	this	DET	DT	Number=Sing|PronType=Dem	8	det	_	_
7	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
8	result	result	NOUN	NN	Number=Sing	5	pobj	_	_
9	in	in	ADP	IN	_	2	prep	_	_
10	order	order	NOUN	NN	Number=Sing	9	pobj	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	obtain	obtain	VERB	VB	VerbForm=Inf	10	acl	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	stronger	strong	ADJ	JJR	Degree=Cmp	15	amod	_	_
15	one	one	NOUN	NN	Number=Sing	12	dobj	_	_
16	that	that	PRON	WDT	PronType=Rel	17	nsubj	_	_
17	uses	use	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	relcl	_	_
18	not	not	PART	RB	Polarity=Neg	20	neg	_	_
19	all	all	DET	DT	_	20	det	_	_
20	objects	object	NOUN	NNS	Number=Plur	17	dobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	$ B $	$ b $	SYM	$	_	21	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	$ C $	$ c $	SYM	$	_	23	pobj	_	_
25	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
26	but	but	CCONJ	CC	ConjType=Cmp	2	cc	_	_
27	only	only	ADV	RB	_	32	advmod	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
29	conveniently	conveniently	ADV	RB	_	30	advmod	_	_
30	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	amod	_	_
31	generating	generating	NOUN	NN	Number=Sing	32	compound	_	_
32	class	class	NOUN	NN	Number=Sing	33	compound	_	_
33	$ S $	$ s $	SYM	$	_	2	conj	_	_
34	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = If $ C $ is a variety of universal algebras, then one can take $ S $ to be the class consisting of any single free algebra on a non - empty set.
1	If	if	SCONJ	IN	_	3	mark	_	_
2	$ C $	$ c $	SYM	$	_	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	advcl	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	variety	variety	NOUN	NN	Number=Sing	3	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	universal	universal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	algebras	algebra	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
10	then	then	ADV	RB	PronType=Dem	13	advmod	_	_
11	one	one	PRON	PRP	PronType=Prs	13	nsubj	_	_
12	can	can	AUX	MD	VerbForm=Fin	13	aux	_	_
13	take	take	VERB	VB	VerbForm=Inf	0	ROOT	_	_
14	$ S $	$ s $	SYM	$	_	13	dep	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	be	be	AUX	VB	VerbForm=Inf	13	xcomp	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	class	class	NOUN	NN	Number=Sing	16	attr	_	_
19	consisting	consist	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	18	acl	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	any	any	DET	DT	_	24	det	_	_
22	single	single	ADJ	JJ	Degree=Pos	24	amod	_	_
23	free	free	ADJ	JJ	Degree=Pos	24	amod	_	_
24	algebra	algebra	NOUN	NNS	Number=Plur	20	pobj	_	_
25	on	on	ADP	IN	_	24	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
27	non	non	ADJ	JJ	Degree=Pos	29	amod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	empty	empty	ADJ	JJ	Degree=Pos	30	amod	_	_
30	set	set	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# doc_id = 21
# sent_id = 1
# text = Lawvere has urged a project of characterizing petit toposes which have the character of generalized spaces and gros toposes which have the character of categories of spaces.
1	Lawvere	Lawvere	PROPN	NNP	Number=Sing	3	nsubj	_	_
2	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	aux	_	_
3	urged	urge	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	project	project	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	characterizing	characterize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	pcomp	_	_
8	petit	petit	NOUN	NN	Number=Sing	9	compound	_	_
9	toposes	topos	NOUN	NNS	Number=Plur	7	dobj	_	_
10	which	which	PRON	WDT	_	11	nsubj	_	_
11	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	relcl	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	character	character	NOUN	NN	Number=Sing	11	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
16	spaces	space	NOUN	NNS	Number=Plur	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	gros	gro	NOUN	NNS	Number=Plur	19	compound	_	_
19	toposes	topos	NOUN	NNS	Number=Plur	13	conj	_	_
20	which	which	PRON	WDT	_	21	nsubj	_	_
21	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	relcl	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	character	character	NOUN	NN	Number=Sing	21	dobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	categories	category	NOUN	NNS	Number=Plur	24	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	spaces	space	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = Etendues and locally decidable toposes are seemingly petit and have a natural common generalization in sites with all idempotents identities.
1	Etendues	etendue	NOUN	NNS	Number=Plur	6	nsubj	_	_
2	and	and	CCONJ	CC	ConjType=Cmp	1	cc	_	_
3	locally	locally	ADV	RB	_	4	advmod	_	_
4	decidable	decidable	ADJ	JJ	Degree=Pos	5	amod	_	_
5	toposes	topos	NOUN	NNS	Number=Plur	1	conj	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	seemingly	seemingly	ADV	RB	_	6	advmod	_	_
8	petit	petit	ADJ	JJ	Degree=Pos	6	acomp	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
10	have	have	VERB	VB	VerbForm=Inf	6	conj	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
12	natural	natural	ADJ	JJ	Degree=Pos	14	amod	_	_
13	common	common	ADJ	JJ	Degree=Pos	14	amod	_	_
14	generalization	generalization	NOUN	NN	Number=Sing	10	dobj	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	sites	site	NOUN	NNS	Number=Plur	15	pobj	_	_
17	with	with	ADP	IN	_	16	prep	_	_
18	all	all	DET	DT	_	20	det	_	_
19	idempotents	idempotent	NOUN	NNS	Number=Plur	20	compound	_	_
20	identities	identity	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = This note shows every Grothendieck topos has such a site.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	note	note	NOUN	NN	Number=Sing	3	nsubj	_	_
3	shows	show	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	every	every	DET	DT	_	6	det	_	_
5	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	6	compound	_	_
6	topos	topos	PROPN	NNP	Number=Sing	7	nsubj	_	_
7	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
8	such	such	DET	PDT	_	10	predet	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	site	site	NOUN	NN	Number=Sing	7	dobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = More, it defines slanted products which take any site to an equivalent one way site, a site where all endomorphisms are identities.
1	More	More	ADJ	JJR	Degree=Cmp	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	4	nsubj	_	_
4	defines	define	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	slanted	slanted	ADJ	JJ	Degree=Pos	6	amod	_	_
6	products	product	NOUN	NNS	Number=Plur	4	dobj	_	_
7	which	which	PRON	WDT	_	8	nsubj	_	_
8	take	take	VERB	VBP	Tense=Pres|VerbForm=Fin	6	relcl	_	_
9	any	any	DET	DT	_	10	det	_	_
10	site	site	NOUN	NN	Number=Sing	8	dobj	_	_
11	to	to	ADP	IN	_	8	prep	_	_
12	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
13	equivalent	equivalent	ADJ	JJ	Degree=Pos	16	amod	_	_
14	one	one	NUM	CD	NumType=Card	15	nummod	_	_
15	way	way	NOUN	NN	Number=Sing	16	compound	_	_
16	site	site	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	site	site	NOUN	NN	Number=Sing	16	appos	_	_
20	where	where	SCONJ	WRB	_	23	advmod	_	_
21	all	all	DET	DT	_	22	det	_	_
22	endomorphisms	endomorphism	NOUN	NNS	Number=Plur	23	nsubj	_	_
23	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	19	relcl	_	_
24	identities	identity	NOUN	NNS	Number=Plur	23	attr	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = On the other hand subcanonical one - way sites are very special.
1	On	on	ADP	IN	_	10	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	other	other	ADJ	JJ	Degree=Pos	4	amod	_	_
4	hand	hand	NOUN	NN	Number=Sing	1	pobj	_	_
5	subcanonical	subcanonical	ADJ	JJ	Degree=Pos	9	amod	_	_
6	one	one	NUM	CD	NumType=Card	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	way	way	NOUN	NN	Number=Sing	9	compound	_	_
9	sites	site	NOUN	NNS	Number=Plur	10	nsubj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	very	very	ADV	RB	_	12	advmod	_	_
12	special	special	ADJ	JJ	Degree=Pos	10	acomp	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 6
# text = A site criterion for petit toposes will probably require subcanonical sites.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	site	site	NOUN	NN	Number=Sing	3	compound	_	_
3	criterion	criterion	NOUN	NN	Number=Sing	9	nsubj	_	_
4	for	for	ADP	IN	_	3	prep	_	_
5	petit	petit	NOUN	NN	Number=Sing	6	compound	_	_
6	toposes	topos	NOUN	NNS	Number=Plur	4	pobj	_	_
7	will	will	AUX	MD	VerbForm=Fin	9	aux	_	_
8	probably	probably	ADV	RB	_	9	advmod	_	_
9	require	require	VERB	VB	VerbForm=Inf	0	ROOT	_	_
10	subcanonical	subcanonical	ADJ	JJ	Degree=Pos	11	amod	_	_
11	sites	site	NOUN	NNS	Number=Plur	9	dobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 22
# sent_id = 1
# text = In this paper we explain the relationship between Frobenius objects in monoidal categories and adjunctions in 2 - categories.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	explain	explain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	relationship	relationship	NOUN	NN	Number=Sing	5	dobj	_	_
8	between	between	ADP	IN	_	7	prep	_	_
9	Frobenius	Frobenius	PROPN	NNP	Number=Sing	10	compound	_	_
10	objects	object	NOUN	NNS	Number=Plur	8	pobj	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	monoidal	monoidal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	adjunctions	adjunction	NOUN	NNS	Number=Plur	13	conj	_	_
16	in	in	ADP	IN	_	10	prep	_	_
17	2	2	NUM	CD	NumType=Card	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = Specifically, we show that every Frobenius object in a monoidal category $ M $ arises from an ambijunction (simultaneous left and right adjoints) in some 2 - category $ mathcal{D} $ into which $ M $ fully and faithfully embeds.
1	Specifically	specifically	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	14	mark	_	_
6	every	every	DET	DT	_	8	det	_	_
7	Frobenius	Frobenius	PROPN	NNP	Number=Sing	8	compound	_	_
8	object	object	NOUN	NN	Number=Sing	14	nsubj	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	monoidal	monoidal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
13	$ M $	$ m $	SYM	$	_	8	appos	_	_
14	arises	arise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
15	from	from	ADP	IN	_	14	prep	_	_
16	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	ambijunction	ambijunction	NOUN	NN	Number=Sing	15	pobj	_	_
18	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	23	punct	_	SpaceAfter=No
19	simultaneous	simultaneous	ADJ	JJ	Degree=Pos	23	amod	_	_
20	left	left	ADJ	JJ	Degree=Pos	23	amod	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	right	right	ADJ	JJ	Degree=Pos	20	conj	_	_
23	adjoints	adjoint	NOUN	NNS	Number=Plur	17	appos	_	SpaceAfter=No
24	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	23	punct	_	_
25	in	in	ADP	IN	_	17	prep	_	_
26	some	some	DET	DT	_	30	det	_	_
27	2	2	NUM	CD	NumType=Card	29	nummod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	category	category	NOUN	NN	Number=Sing	30	nmod	_	_
30	$ mathcal{D} $	$ mathcal{d} $	SYM	$	_	25	pobj	_	_
31	into	into	ADP	IN	_	37	prep	_	_
32	which	which	PRON	WDT	_	31	pobj	_	_
33	$ M $	$ m $	SYM	$	_	37	dep	_	_
34	fully	fully	ADV	RB	_	37	advmod	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	34	cc	_	_
36	faithfully	faithfully	ADV	RB	_	34	conj	_	_
37	embeds	embed	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	relcl	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = Since a 2D topological quantum field theory is equivalent to a commutative Frobenius algebra, this result also shows that every 2D TQFT is obtained from an ambijunction in some 2 - category.
1	Since	since	SCONJ	IN	_	8	mark	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
3	2D	2D	PROPN	NNP	Number=Sing	7	compound	_	_
4	topological	topological	ADJ	JJ	Degree=Pos	7	amod	_	_
5	quantum	quantum	NOUN	NN	Number=Sing	6	compound	_	_
6	field	field	NOUN	NN	Number=Sing	7	compound	_	_
7	theory	theory	NOUN	NN	Number=Sing	8	nsubj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	advcl	_	_
9	equivalent	equivalent	ADJ	JJ	Degree=Pos	8	acomp	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
12	commutative	commutative	ADJ	JJ	Degree=Pos	14	amod	_	_
13	Frobenius	Frobenius	PROPN	NNP	Number=Sing	14	compound	_	_
14	algebra	algebra	PROPN	NNP	Number=Sing	10	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
16	this	this	DET	DT	Number=Sing|PronType=Dem	17	det	_	_
17	result	result	NOUN	NN	Number=Sing	19	nsubj	_	_
18	also	also	ADV	RB	_	19	advmod	_	_
19	shows	show	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	that	that	SCONJ	IN	_	25	mark	_	_
21	every	every	DET	DT	_	23	det	_	_
22	2D	2D	PROPN	NNP	Number=Sing	23	compound	_	_
23	TQFT	TQFT	PROPN	NNP	Number=Sing	25	nsubjpass	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	auxpass	_	_
25	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	ccomp	_	_
26	from	from	ADP	IN	_	25	prep	_	_
27	an	an	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	ambijunction	ambijunction	NOUN	NN	Number=Sing	26	pobj	_	_
29	in	in	ADP	IN	_	28	prep	_	_
30	some	some	DET	DT	_	33	det	_	_
31	2	2	NUM	CD	NumType=Card	33	nummod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	category	category	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 4
# text = Our theorem is proved by extending the theory of adjoint monads to the context of an arbitrary 2 - category and utilizing the free completion under Eilenberg - Moore objects.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	theorem	theorem	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	by	by	ADP	IN	_	4	agent	_	_
6	extending	extend	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	theory	theory	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	adjoint	adjoint	NOUN	NN	Number=Sing	11	compound	_	_
11	monads	monad	NOUN	NNS	Number=Plur	9	pobj	_	_
12	to	to	ADP	IN	_	6	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	context	context	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	an	an	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
17	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	20	amod	_	_
18	2	2	NUM	CD	NumType=Card	20	nummod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
22	utilizing	utilize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	conj	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	free	free	ADJ	JJ	Degree=Pos	25	amod	_	_
25	completion	completion	NOUN	NN	Number=Sing	22	dobj	_	_
26	under	under	ADP	IN	_	22	prep	_	_
27	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	29	compound	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	Moore	Moore	PROPN	NNP	Number=Sing	30	compound	_	_
30	objects	object	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = We then categorify this theorem by replacing the monoidal category $ M $ with a semistrict monoidal 2 - category $ M $ , and replacing the 2 - category $ mathcal{D} $ into which it embeds by a semistrict 3 - category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	categorify	categorify	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	theorem	theorem	ADJ	JJ	Degree=Pos	3	dobj	_	_
6	by	by	ADP	IN	_	3	prep	_	_
7	replacing	replace	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	pcomp	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	monoidal	monoidal	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	7	dobj	_	_
11	$ M $	$ m $	SYM	$	_	7	dep	_	_
12	with	with	ADP	IN	_	7	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	semistrict	semistrict	ADJ	JJ	Degree=Pos	15	amod	_	_
15	monoidal	monoidal	ADJ	JJ	Degree=Pos	12	pobj	_	_
16	2	2	NUM	CD	NumType=Card	18	nummod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	category	category	NOUN	NN	Number=Sing	19	compound	_	_
19	$ M $	$ m $	SYM	$	_	7	dep	_	_
20	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
22	replacing	replace	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	conj	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
24	2	2	NUM	CD	NumType=Card	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	category	category	NOUN	NN	Number=Sing	27	nmod	_	_
27	$ mathcal{D} $	$ mathcal{d} $	SYM	$	_	22	dobj	_	_
28	into	into	ADP	IN	_	31	prep	_	_
29	which	which	PRON	WDT	_	28	pobj	_	_
30	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	31	nsubj	_	_
31	embeds	embed	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	relcl	_	_
32	by	by	ADP	IN	_	31	prep	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
34	semistrict	semistrict	ADJ	JJ	Degree=Pos	37	amod	_	_
35	3	3	NUM	CD	NumType=Card	37	nummod	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	category	category	NOUN	NN	Number=Sing	32	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = To state this more powerful result, we must first define the notion of a `Frobenius pseudomonoid', which categorifies that of a Frobenius object.
1	To	to	PART	TO	_	2	aux	_	_
2	state	state	VERB	VB	VerbForm=Inf	11	advcl	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
4	more	more	ADV	RBR	Degree=Cmp	5	advmod	_	_
5	powerful	powerful	ADJ	JJ	Degree=Pos	6	amod	_	_
6	result	result	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	11	nsubj	_	_
9	must	must	AUX	MD	VerbForm=Fin	11	aux	_	_
10	first	first	ADV	RB	_	11	advmod	_	_
11	define	define	VERB	VB	VerbForm=Inf	0	ROOT	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	notion	notion	NOUN	NN	Number=Sing	11	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
16	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	18	punct	_	SpaceAfter=No
17	Frobenius	Frobenius	PROPN	NNP	Number=Sing	18	compound	_	_
18	pseudomonoid	pseudomonoid	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
19	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	18	punct	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
21	which	which	PRON	WDT	_	22	nsubj	_	_
22	categorifies	categorifie	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	relcl	_	_
23	that	that	PRON	DT	Number=Sing|PronType=Dem	22	dobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
26	Frobenius	Frobenius	PROPN	NNP	Number=Sing	27	compound	_	_
27	object	object	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 7
# text = We then define the notion of a `pseudo ambijunction', categorifying that of an ambijunction.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	notion	notion	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	10	punct	_	SpaceAfter=No
9	pseudo	pseudo	NOUN	NN	Number=Sing	10	compound	_	_
10	ambijunction	ambijunction	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
11	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	3	punct	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
13	categorifying	categorifye	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	advcl	_	_
14	that	that	PRON	DT	Number=Sing|PronType=Dem	13	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	ambijunction	ambijunction	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 8
# text = In each case, the idea is that all the usual axioms now hold only up to coherent isomorphism.
1	In	in	ADP	IN	_	7	prep	_	_
2	each	each	DET	DT	_	3	det	_	_
3	case	case	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	idea	idea	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	that	that	SCONJ	IN	_	14	mark	_	_
9	all	all	DET	PDT	_	12	predet	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	usual	usual	ADJ	JJ	Degree=Pos	12	amod	_	_
12	axioms	axiom	NOUN	NNS	Number=Plur	14	nsubj	_	_
13	now	now	ADV	RB	_	14	advmod	_	_
14	hold	hold	VERB	VBP	Tense=Pres|VerbForm=Fin	7	ccomp	_	_
15	only	only	ADV	RB	_	16	advmod	_	_
16	up	up	ADP	IN	_	14	prep	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	coherent	coherent	ADJ	JJ	Degree=Pos	19	amod	_	_
19	isomorphism	isomorphism	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 9
# text = Finally, we show that every Frobenius pseudomonoid in a semistrict monoidal 2 - category arises from a pseudo ambijunction in some semistrict 3 - category.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	16	mark	_	_
6	every	every	DET	DT	_	8	det	_	_
7	Frobenius	Frobenius	PROPN	NNP	Number=Sing	8	compound	_	_
8	pseudomonoid	pseudomonoid	NOUN	NN	Number=Sing	16	nsubj	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
11	semistrict	semistrict	ADJ	JJ	Degree=Pos	15	amod	_	_
12	monoidal	monoidal	ADJ	JJ	Degree=Pos	15	amod	_	_
13	2	2	NUM	CD	NumType=Card	15	nummod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
16	arises	arise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
17	from	from	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	pseudo	pseudo	NOUN	NN	Number=Sing	20	compound	_	_
20	ambijunction	ambijunction	NOUN	NN	Number=Sing	17	pobj	_	_
21	in	in	ADP	IN	_	20	prep	_	_
22	some	some	DET	DT	_	26	det	_	_
23	semistrict	semistrict	ADJ	JJ	Degree=Pos	26	amod	_	_
24	3	3	NUM	CD	NumType=Card	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	category	category	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 23
# sent_id = 1
# text = A flow is homotopy continuous if it is indefinitely divisible up to $ S $ - homotopy.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	flow	flow	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	homotopy	homotopy	VERB	VB	VerbForm=Inf	0	ROOT	_	_
5	continuous	continuous	ADJ	JJ	Degree=Pos	4	oprd	_	_
6	if	if	SCONJ	IN	_	8	mark	_	_
7	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	8	nsubj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	advcl	_	_
9	indefinitely	indefinitely	ADV	RB	_	10	advmod	_	_
10	divisible	divisible	ADJ	JJ	Degree=Pos	8	acomp	_	_
11	up	up	ADP	IN	_	15	advmod	_	_
12	to	to	PART	TO	_	11	prep	_	_
13	$ S $	$ s $	SYM	$	_	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	homotopy	homotopy	NOUN	NN	Number=Sing	4	advmod	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = The full subcategory of cofibrant homotopy continuous flows has nice features.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	full	full	ADJ	JJ	Degree=Pos	3	amod	_	_
3	subcategory	subcategory	NOUN	NN	Number=Sing	9	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	cofibrant	cofibrant	NOUN	NN	Number=Sing	6	compound	_	_
6	homotopy	homotopy	PROPN	NNP	Number=Sing	8	nmod	_	_
7	continuous	continuous	ADJ	JJ	Degree=Pos	8	amod	_	_
8	flows	flow	NOUN	NNS	Number=Plur	4	pobj	_	_
9	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	nice	nice	ADJ	JJ	Degree=Pos	11	amod	_	_
11	features	feature	NOUN	NNS	Number=Plur	9	dobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 3
# text = Not only it is big enough to contain all dihomotopy types, but also a morphism between them is a weak dihomotopy equivalence if and only if it is invertible up to dihomotopy.
1	Not	not	PART	RB	Polarity=Neg	4	preconj	_	_
2	only	only	ADV	RB	_	1	advmod	_	_
3	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	big	big	ADJ	JJ	Degree=Pos	4	acomp	_	_
6	enough	enough	ADV	RB	_	5	advmod	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	contain	contain	VERB	VB	VerbForm=Inf	5	xcomp	_	_
9	all	all	DET	DT	_	11	det	_	_
10	dihomotopy	dihomotopy	NOUN	NN	Number=Sing	11	amod	_	_
11	types	type	NOUN	NNS	Number=Plur	8	dobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
13	but	but	CCONJ	CC	ConjType=Cmp	4	cc	_	_
14	also	also	ADV	RB	_	13	advmod	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	morphism	morphism	NOUN	NN	Number=Sing	19	nsubj	_	_
17	between	between	ADP	IN	_	16	prep	_	_
18	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	17	pobj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	conj	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
21	weak	weak	ADJ	JJ	Degree=Pos	23	amod	_	_
22	dihomotopy	dihomotopy	NOUN	NN	Number=Sing	23	compound	_	_
23	equivalence	equivalence	NOUN	NN	Number=Sing	19	attr	_	_
24	if	if	SCONJ	IN	_	29	mark	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
26	only	only	ADV	RB	_	29	advmod	_	_
27	if	if	SCONJ	IN	_	29	mark	_	_
28	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	29	nsubj	_	_
29	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	advcl	_	_
30	invertible	invertible	ADJ	JJ	Degree=Pos	29	acomp	_	_
31	up	up	ADP	RP	_	29	prep	_	_
32	to	to	ADP	IN	_	31	prep	_	_
33	dihomotopy	dihomotopy	VERB	VB	VerbForm=Inf	32	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 4
# text = Thus, the category of cofibrant homotopy continuous flows provides an implementation of Whitehead's theorem for the full dihomotopy relation, and not only for $ S $ - homotopy as in previous works of the author.
1	Thus	thus	ADV	RB	_	10	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	category	category	NOUN	NN	Number=Sing	10	nsubj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	cofibrant	cofibrant	NOUN	NN	Number=Sing	7	compound	_	_
7	homotopy	homotopy	PROPN	NNP	Number=Sing	5	pobj	_	_
8	continuous	continuous	ADJ	JJ	Degree=Pos	9	amod	_	_
9	flows	flow	NOUN	NNS	Number=Plur	4	appos	_	_
10	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	implementation	implementation	NOUN	NN	Number=Sing	10	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	Whitehead	Whitehead	PROPN	NNP	Number=Sing	16	poss	_	SpaceAfter=No
15	's	's	PART	POS	_	14	case	_	_
16	theorem	theorem	ADJ	JJ	Degree=Pos	13	pobj	_	_
17	for	for	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
19	full	full	ADJ	JJ	Degree=Pos	21	amod	_	_
20	dihomotopy	dihomotopy	NOUN	NN	Number=Sing	21	compound	_	_
21	relation	relation	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
24	not	not	PART	RB	Polarity=Neg	26	preconj	_	_
25	only	only	ADV	RB	_	24	advmod	_	_
26	for	for	ADP	IN	_	10	conj	_	_
27	$ S $	$ s $	SYM	$	_	29	compound	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	homotopy	homotopy	NOUN	NN	Number=Sing	26	pobj	_	_
30	as	as	ADP	IN	_	29	prep	_	_
31	in	in	ADP	IN	_	30	prep	_	_
32	previous	previous	ADJ	JJ	Degree=Pos	33	amod	_	_
33	works	work	NOUN	NNS	Number=Plur	31	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	author	author	NOUN	NN	Number=Sing	34	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 5
# text = This fact is not the consequence of the existence of a model structure on the category of flows because it is known that there does not exist any model structure on it whose weak equivalences are exactly the weak dihomotopy equivalences.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	fact	fact	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	not	not	PART	RB	Polarity=Neg	3	neg	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	consequence	consequence	NOUN	NN	Number=Sing	3	attr	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	existence	existence	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	model	model	NOUN	NN	Number=Sing	13	compound	_	_
13	structure	structure	NOUN	NN	Number=Sing	10	pobj	_	_
14	on	on	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	category	category	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	flows	flow	NOUN	NNS	Number=Plur	17	pobj	_	_
19	because	because	SCONJ	IN	_	22	mark	_	_
20	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	22	nsubjpass	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	auxpass	_	_
22	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	36	advcl	_	_
23	that	that	SCONJ	IN	_	27	mark	_	_
24	there	there	PRON	EX	_	27	expl	_	_
25	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	aux	_	_
26	not	not	PART	RB	Polarity=Neg	27	neg	_	_
27	exist	exist	VERB	VB	VerbForm=Inf	22	ccomp	_	_
28	any	any	DET	DT	_	30	det	_	_
29	model	model	NOUN	NN	Number=Sing	30	compound	_	_
30	structure	structure	NOUN	NN	Number=Sing	27	dobj	_	_
31	on	on	ADP	IN	_	30	prep	_	_
32	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	31	pobj	_	_
33	whose	whose	DET	WP$	Poss=Yes	35	poss	_	_
34	weak	weak	ADJ	JJ	Degree=Pos	35	amod	_	_
35	equivalences	equivalence	NOUN	NNS	Number=Plur	36	nsubj	_	_
36	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
37	exactly	exactly	ADV	RB	_	41	advmod	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
39	weak	weak	ADJ	JJ	Degree=Pos	41	amod	_	_
40	dihomotopy	dihomotopy	NOUN	NN	Number=Sing	41	compound	_	_
41	equivalences	equivalence	NOUN	NNS	Number=Plur	36	attr	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = This fact is an application of a general result for the localization of a model category with respect to a weak factorization system.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	fact	fact	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	application	application	NOUN	NN	Number=Sing	3	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	general	general	ADJ	JJ	Degree=Pos	9	amod	_	_
9	result	result	NOUN	NN	Number=Sing	6	pobj	_	_
10	for	for	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	localization	localization	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	model	model	NOUN	NN	Number=Sing	16	compound	_	_
16	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
17	with	with	ADP	IN	_	12	prep	_	_
18	respect	respect	NOUN	NN	Number=Sing	17	pobj	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
21	weak	weak	ADJ	JJ	Degree=Pos	23	amod	_	_
22	factorization	factorization	NOUN	NN	Number=Sing	23	compound	_	_
23	system	system	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 24
# sent_id = 1
# text = We give here some examples of non pointed protomodular categories $ mathbb C $ satisfying a property similar to the property of representation of actions which holds for the pointed protomodular category $ Gp $ of groups: any slice category of $ Gp $ , any category of groupoids with a fixed set of objects, any essentially affine category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	here	here	ADV	RB	PronType=Dem	2	advmod	_	_
4	some	some	DET	DT	_	5	det	_	_
5	examples	example	NOUN	NNS	Number=Plur	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	non	non	PROPN	NNP	Number=Sing	8	compound	_	_
8	pointed	point	VERB	VBD	Tense=Past|VerbForm=Fin	10	amod	_	_
9	protomodular	protomodular	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
11	$ mathbb C $	$ mathbb c $	SYM	$	_	2	dobj	_	_
12	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	property	property	NOUN	NN	Number=Sing	12	dobj	_	_
15	similar	similar	ADJ	JJ	Degree=Pos	14	amod	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	property	property	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	representation	representation	NOUN	NN	Number=Sing	19	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	actions	action	NOUN	NNS	Number=Plur	21	pobj	_	_
23	which	which	PRON	WDT	_	24	nsubj	_	_
24	holds	hold	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	relcl	_	_
25	for	for	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
27	pointed	pointed	ADJ	JJ	Degree=Pos	29	amod	_	_
28	protomodular	protomodular	ADJ	JJ	Degree=Pos	29	amod	_	_
29	category	category	NOUN	NN	Number=Sing	25	pobj	_	_
30	$ Gp $	$ gp $	SYM	$	_	29	appos	_	_
31	of	of	ADP	IN	_	29	prep	_	_
32	groups	group	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
33	:	:	PUNCT	:	_	2	punct	_	_
34	any	any	DET	DT	_	36	det	_	_
35	slice	slice	NOUN	NN	Number=Sing	36	compound	_	_
36	category	category	NOUN	NN	Number=Sing	5	appos	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	$ Gp $	$ gp $	SYM	$	_	37	pobj	_	_
39	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
40	any	any	DET	DT	_	41	det	_	_
41	category	category	NOUN	NN	Number=Sing	36	appos	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	groupoids	groupoid	NOUN	NNS	Number=Plur	42	pobj	_	_
44	with	with	ADP	IN	_	41	prep	_	_
45	a	a	DET	DT	Definite=Ind|PronType=Art	47	det	_	_
46	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	47	amod	_	_
47	set	set	NOUN	NN	Number=Sing	44	pobj	_	_
48	of	of	ADP	IN	_	47	prep	_	_
49	objects	object	NOUN	NNS	Number=Plur	48	pobj	_	SpaceAfter=No
50	,	,	PUNCT	,	PunctType=Comm	47	punct	_	_
51	any	any	DET	DT	_	54	det	_	_
52	essentially	essentially	ADV	RB	_	53	advmod	_	_
53	affine	affine	ADJ	JJ	Degree=Pos	54	amod	_	_
54	category	category	NOUN	NN	Number=Sing	36	appos	_	SpaceAfter=No
55	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This property gives rise to an internal construction of the center of any object $ X $ , and consequently to a specific characterization of the abelian objects in $ mathbb C $ .
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	property	property	NOUN	NN	Number=Sing	3	nsubj	_	_
3	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	rise	rise	VERB	VB	VerbForm=Inf	3	dobj	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	internal	internal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	construction	construction	NOUN	NN	Number=Sing	5	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	center	center	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	any	any	DET	DT	_	14	det	_	_
14	object	object	NOUN	NN	Number=Sing	12	pobj	_	_
15	$ X $	$ x $	SYM	$	_	3	dobj	_	_
16	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
18	consequently	consequently	ADV	RB	_	19	advmod	_	_
19	to	to	ADP	IN	_	3	conj	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	specific	specific	ADJ	JJ	Degree=Pos	22	amod	_	_
22	characterization	characterization	NOUN	NN	Number=Sing	19	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	abelian	abelian	ADJ	JJ	Degree=Pos	26	amod	_	_
26	objects	object	NOUN	NNS	Number=Plur	23	pobj	_	_
27	in	in	ADP	IN	_	22	prep	_	_
28	$ mathbb C $	$ mathbb c $	SYM	$	_	27	pobj	_	_
29	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 25
# sent_id = 1
# text = The paper generalizes the notion of a congruence on a category and pursues some of its applications.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	notion	notion	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	congruence	congruence	NOUN	NN	Number=Sing	6	pobj	_	_
9	on	on	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
13	pursues	pursue	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
14	some	some	PRON	DT	_	13	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	17	poss	_	_
17	applications	application	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = In particular, generalized congruences are used to provide a concrete construction of coequalizers in $ {cal C}at $ .
1	In	in	ADP	IN	_	7	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
4	generalized	generalized	ADJ	JJ	Degree=Pos	5	amod	_	_
5	congruences	congruence	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	provide	provide	VERB	VB	VerbForm=Inf	7	xcomp	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	concrete	concrete	ADJ	JJ	Degree=Pos	12	amod	_	_
12	construction	construction	NOUN	NN	Number=Sing	9	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	coequalizers	coequalizer	NOUN	NNS	Number=Plur	13	pobj	_	_
15	in	in	ADP	IN	_	12	prep	_	_
16	$ {cal C}at $	$ {cal c}at $	SYM	$	_	15	pobj	_	_
17	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = Extremal, regular and various other classes of epimorphic functors are characterized and inter - related.
1	Extremal	Extremal	PROPN	NNP	Number=Sing	11	nsubj	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	1	punct	_	_
3	regular	regular	ADJ	JJ	Degree=Pos	7	amod	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	various	various	ADJ	JJ	Degree=Pos	3	conj	_	_
6	other	other	ADJ	JJ	Degree=Pos	7	amod	_	_
7	classes	class	NOUN	NNS	Number=Plur	1	appos	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	epimorphic	epimorphic	ADJ	JJ	Degree=Pos	10	amod	_	_
10	functors	functor	NOUN	NNS	Number=Plur	8	pobj	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acomp	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	inter	inter	ADV	RB	_	16	advmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	conj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# doc_id = 26
# sent_id = 1
# text = We prove that certain categories arising from atoms in a Grothendieck topos are themselves Grothendieck toposes.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	13	mark	_	_
4	certain	certain	ADJ	JJ	Degree=Pos	5	amod	_	_
5	categories	category	NOUN	NNS	Number=Plur	13	nsubj	_	_
6	arising	arise	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	acl	_	_
7	from	from	ADP	IN	_	6	prep	_	_
8	atoms	atom	NOUN	NNS	Number=Plur	7	pobj	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	12	compound	_	_
12	topos	topo	NOUN	NNS	Number=Plur	9	pobj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
14	themselves	themselves	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs|Reflex=Yes	13	attr	_	_
15	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	16	compound	_	_
16	toposes	topos	NOUN	NNS	Number=Plur	13	attr	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We also investigate enrichments of these categories over the base topos; there are in fact often two distinct enrichments.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	14	ccomp	_	_
4	enrichments	enrichment	NOUN	NNS	Number=Plur	3	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	these	these	DET	DT	Number=Plur|PronType=Dem	7	det	_	_
7	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
8	over	over	ADP	IN	_	4	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	base	base	NOUN	NN	Number=Sing	11	compound	_	_
11	topos	topos	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
12	;	;	PUNCT	:	_	14	punct	_	_
13	there	there	PRON	EX	_	14	expl	_	_
14	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	fact	fact	NOUN	NN	Number=Sing	15	pobj	_	_
17	often	often	ADV	RB	_	14	advmod	_	_
18	two	two	NUM	CD	NumType=Card	20	nummod	_	_
19	distinct	distinct	ADJ	JJ	Degree=Pos	20	amod	_	_
20	enrichments	enrichment	NOUN	NNS	Number=Plur	14	attr	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# doc_id = 27
# sent_id = 1
# text = A category may bear many monoidal structures, but (to within a unique isomorphism) only one structure of `category with finite products'.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	4	nsubj	_	_
3	may	may	AUX	MD	VerbForm=Fin	4	aux	_	_
4	bear	bear	VERB	VB	VerbForm=Inf	0	ROOT	_	_
5	many	many	ADJ	JJ	Degree=Pos	7	amod	_	_
6	monoidal	monoidal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	structures	structure	NOUN	NNS	Number=Plur	4	dobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
9	but	but	CCONJ	CC	ConjType=Cmp	4	cc	_	_
10	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	11	punct	_	SpaceAfter=No
11	to	to	PART	TO	_	4	conj	_	_
12	within	within	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	unique	unique	ADJ	JJ	Degree=Pos	15	amod	_	_
15	isomorphism	isomorphism	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	11	punct	_	_
17	only	only	ADV	RB	_	18	advmod	_	_
18	one	one	NUM	CD	NumType=Card	19	nummod	_	_
19	structure	structure	NOUN	NN	Number=Sing	11	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	20	punct	_	SpaceAfter=No
22	category	category	NOUN	NN	Number=Sing	20	pobj	_	_
23	with	with	ADP	IN	_	22	prep	_	_
24	finite	finite	ADJ	JJ	Degree=Pos	25	compound	_	_
25	products	product	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	11	punct	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = To capture such distinctions, we consider on a 2 - category those 2 - monads for which algebra structure is essentially unique if it exists, giving a precise mathematical definition of `essentially unique' and investigating its consequences.
1	To	to	PART	TO	_	2	aux	_	_
2	capture	capture	VERB	VB	VerbForm=Inf	7	advcl	_	_
3	such	such	ADJ	JJ	Degree=Pos	4	amod	_	_
4	distinctions	distinction	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	on	on	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
10	2	2	NUM	CD	NumType=Card	12	nummod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
13	those	those	DET	DT	Number=Plur|PronType=Dem	16	det	_	_
14	2	2	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	monads	monad	NOUN	NNS	Number=Plur	7	dobj	_	_
17	for	for	ADP	IN	_	21	prep	_	_
18	which	which	PRON	WDT	_	17	pobj	_	_
19	algebra	algebra	NOUN	NN	Number=Sing	20	compound	_	_
20	structure	structure	NOUN	NN	Number=Sing	21	nsubj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	relcl	_	_
22	essentially	essentially	ADV	RB	_	23	advmod	_	_
23	unique	unique	ADJ	JJ	Degree=Pos	21	acomp	_	_
24	if	if	SCONJ	IN	_	26	mark	_	_
25	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	26	nsubj	_	_
26	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	21	advcl	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
28	giving	give	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	advcl	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
30	precise	precise	ADJ	JJ	Degree=Pos	32	amod	_	_
31	mathematical	mathematical	ADJ	JJ	Degree=Pos	32	amod	_	_
32	definition	definition	NOUN	NN	Number=Sing	28	dobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	33	punct	_	SpaceAfter=No
35	essentially	essentially	ADV	RB	_	36	advmod	_	_
36	unique	unique	ADJ	JJ	Degree=Pos	33	amod	_	SpaceAfter=No
37	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	33	punct	_	_
38	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
39	investigating	investigate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	28	conj	_	_
40	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	41	poss	_	_
41	consequences	consequence	NOUN	NNS	Number=Plur	39	dobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = We call such 2 - monads property - like.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	such	such	ADJ	JJ	Degree=Pos	9	amod	_	_
4	2	2	NUM	CD	NumType=Card	6	nummod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	monads	monad	NOUN	NNS	Number=Plur	9	compound	_	_
7	property	property	NOUN	NN	Number=Sing	9	npadvmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	like	like	ADJ	JJ	Degree=Pos	2	oprd	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We further consider the more restricted class of fully property - like 2 - monads, consisting of those property - like 2 - monads for which all 2 - cells between (even lax) algebra morphisms are algebra 2 - cells.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	further	far	ADV	RB	_	3	advmod	_	_
3	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	more	more	ADV	RBR	Degree=Cmp	6	advmod	_	_
6	restricted	restricted	ADJ	JJ	Degree=Pos	7	amod	_	_
7	class	class	NOUN	NN	Number=Sing	3	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	fully	fully	ADV	RB	_	12	advmod	_	_
10	property	property	NOUN	NN	Number=Sing	12	npadvmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	like	like	ADJ	JJ	Degree=Pos	15	amod	_	_
13	2	2	NUM	CD	NumType=Card	15	nummod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	monads	monad	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
17	consisting	consist	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	39	csubj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	those	those	DET	DT	Number=Plur|PronType=Dem	20	det	_	_
20	property	property	NOUN	NN	Number=Sing	25	nmod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
22	like	like	ADJ	JJ	Degree=Pos	20	prep	_	_
23	2	2	NUM	CD	NumType=Card	25	nummod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	monads	monad	NOUN	NNS	Number=Plur	38	nmod	_	_
26	for	for	ADP	IN	_	25	prep	_	_
27	which	which	PRON	WDT	_	26	pobj	_	_
28	all	all	DET	DT	_	31	det	_	_
29	2	2	NUM	CD	NumType=Card	31	nummod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	cells	cell	NOUN	NNS	Number=Plur	38	nmod	_	_
32	between	between	ADP	IN	_	31	prep	_	_
33	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	35	punct	_	SpaceAfter=No
34	even	even	ADV	RB	_	35	advmod	_	_
35	lax	lax	ADJ	JJ	Degree=Pos	32	pobj	_	SpaceAfter=No
36	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	31	punct	_	_
37	algebra	algebra	PROPN	NNP	Number=Sing	38	compound	_	_
38	morphisms	morphism	NOUN	NNS	Number=Plur	18	pobj	_	_
39	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
40	algebra	algebra	NOUN	NN	Number=Sing	43	nmod	_	_
41	2	2	NUM	CD	NumType=Card	43	nummod	_	_
42	-	-	PUNCT	HYPH	PunctType=Dash	43	punct	_	_
43	cells	cell	NOUN	NNS	Number=Plur	39	attr	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = The consideration of lax morphisms leads us to a new characterization of those monads, studied by Kock and Zoberlein, for which `structure is adjoint to unit', and which we now call lax - idempotent 2 - monads: both these and their colax - idempotent duals are fully property - like.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	consideration	consideration	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	lax	lax	ADJ	JJ	Degree=Pos	5	amod	_	_
5	morphisms	morphism	NOUN	NNS	Number=Plur	3	pobj	_	_
6	leads	lead	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	52	ccomp	_	_
7	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	6	dobj	_	_
8	to	to	ADP	IN	_	6	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	new	new	ADJ	JJ	Degree=Pos	11	amod	_	_
11	characterization	characterization	NOUN	NN	Number=Sing	8	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	those	those	DET	DT	Number=Plur|PronType=Dem	14	det	_	_
14	monads	monad	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
16	studied	study	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acl	_	_
17	by	by	ADP	IN	_	16	agent	_	_
18	Kock	Kock	PROPN	NNP	Number=Sing	17	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	Zoberlein	Zoberlein	PROPN	NNP	Number=Sing	18	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
22	for	for	ADP	IN	_	26	prep	_	_
23	which	which	PRON	WDT	_	22	pobj	_	_
24	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	SpaceAfter=No
25	structure	structure	NOUN	NN	Number=Sing	26	nsubj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	relcl	_	_
27	adjoint	adjoint	NOUN	NN	Number=Sing	26	acomp	_	_
28	to	to	ADP	IN	_	27	prep	_	_
29	unit	unit	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
30	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	6	punct	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
33	which	which	PRON	WDT	_	36	dobj	_	_
34	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	36	nsubj	_	_
35	now	now	ADV	RB	_	36	advmod	_	_
36	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	6	conj	_	_
37	lax	lax	ADJ	JJ	Degree=Pos	39	npadvmod	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	idempotent	idempotent	ADJ	JJ	Degree=Pos	42	amod	_	_
40	2	2	NUM	CD	NumType=Card	42	nummod	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	monads	monad	NOUN	NNS	Number=Plur	36	dobj	_	SpaceAfter=No
43	:	:	PUNCT	:	_	52	punct	_	_
44	both	both	CCONJ	CC	ConjType=Cmp	45	preconj	_	_
45	these	these	PRON	DT	Number=Plur|PronType=Dem	52	nsubj	_	_
46	and	and	CCONJ	CC	ConjType=Cmp	45	cc	_	_
47	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	51	poss	_	_
48	colax	colax	ADJ	JJ	Degree=Pos	50	amod	_	_
49	-	-	PUNCT	HYPH	PunctType=Dash	50	punct	_	_
50	idempotent	idempotent	ADJ	JJ	Degree=Pos	51	amod	_	_
51	duals	dual	NOUN	NNS	Number=Plur	45	conj	_	_
52	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
53	fully	fully	ADV	RB	_	52	advmod	_	_
54	property	property	NOUN	NN	Number=Sing	56	npadvmod	_	_
55	-	-	PUNCT	HYPH	PunctType=Dash	56	punct	_	_
56	like	like	ADJ	JJ	Degree=Pos	52	acomp	_	SpaceAfter=No
57	.	.	PUNCT	.	PunctType=Peri	52	punct	_	SpaceAfter=No

# sent_id = 6
# text = We end by showing that (at least for finitary 2 - monads) the classes of property - likes, fully property - likes, and lax - idempotents are each coreflective among all 2 - monads.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	end	end	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	by	by	ADP	IN	_	2	prep	_	_
4	showing	show	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	pcomp	_	_
5	that	that	PRON	DT	Number=Sing|PronType=Dem	4	dobj	_	_
6	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	9	punct	_	SpaceAfter=No
7	at	at	ADP	IN	_	8	advmod	_	_
8	least	least	ADJ	JJS	Degree=Sup	9	advmod	_	_
9	for	for	ADP	IN	_	4	prep	_	_
10	finitary	finitary	ADJ	JJ	Degree=Pos	13	amod	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	monads	monad	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
14	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	4	punct	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	classes	class	NOUN	NNS	Number=Plur	31	nsubj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	property	property	NOUN	NN	Number=Sing	20	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	likes	like	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	fully	fully	ADV	RB	_	25	advmod	_	_
23	property	property	NOUN	NN	Number=Sing	25	compound	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	likes	like	NOUN	NNS	Number=Plur	20	conj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
28	lax	lax	NOUN	NN	Number=Sing	30	compound	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	idempotents	idempotent	NOUN	NNS	Number=Plur	31	nsubj	_	_
31	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	conj	_	_
32	each	each	PRON	DT	_	31	dep	_	_
33	coreflective	coreflective	ADJ	JJ	Degree=Pos	31	acomp	_	_
34	among	among	ADP	IN	_	33	prep	_	_
35	all	all	DET	DT	_	38	det	_	_
36	2	2	NUM	CD	NumType=Card	38	nummod	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	38	punct	_	_
38	monads	monad	NOUN	NNS	Number=Plur	34	pobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	31	punct	_	SpaceAfter=No

# doc_id = 28
# sent_id = 1
# text = Given a bicategory, 2, with stable local coequalizers, we construct a bicategory of monads $ Y - mnd $ by using lax functors from the generic 0 - cell, 1 - cell and 2 - cell, respectively, into Y.
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	bicategory	bicategory	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	2	2	NUM	CD	NumType=Card	3	appos	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
7	with	with	ADP	IN	_	3	prep	_	_
8	stable	stable	ADJ	JJ	Degree=Pos	10	amod	_	_
9	local	local	ADJ	JJ	Degree=Pos	10	amod	_	_
10	coequalizers	coequalizer	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	bicategory	bicategory	NOUN	NN	Number=Sing	13	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	monads	monad	NOUN	NNS	Number=Plur	16	pobj	_	_
18	$ Y - mnd $	$ y - mnd $	SYM	$	_	13	dep	_	_
19	by	by	ADP	IN	_	13	prep	_	_
20	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	pcomp	_	_
21	lax	lax	ADJ	JJ	Degree=Pos	22	amod	_	_
22	functors	functor	NOUN	NNS	Number=Plur	20	dobj	_	_
23	from	from	ADP	IN	_	20	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
25	generic	generic	ADJ	JJ	Degree=Pos	28	amod	_	_
26	0	0	NUM	CD	NumType=Card	28	nummod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	cell	cell	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
30	1	1	NUM	CD	NumType=Card	32	nummod	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	cell	cell	NOUN	NN	Number=Sing	28	conj	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
34	2	2	NUM	CD	NumType=Card	36	nummod	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	36	punct	_	_
36	cell	cell	NOUN	NN	Number=Sing	32	conj	_	SpaceAfter=No
37	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
38	respectively	respectively	ADV	RB	_	28	advmod	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
40	into	into	ADP	IN	_	20	prep	_	_
41	Y.	Y.	PROPN	NNP	Number=Sing	40	pobj	_	SpaceAfter=No

# sent_id = 2
# text = Any lax functor into $ Y $ factors through $ Y - mnd $ and the 1 - cells turn out to be the familiar bimodules.
1	Any	any	DET	DT	_	3	det	_	_
2	lax	lax	ADJ	JJ	Degree=Pos	3	amod	_	_
3	functor	functor	NOUN	NN	Number=Sing	14	nsubj	_	_
4	into	into	ADP	IN	_	3	prep	_	_
5	$ Y $	$ y $	SYM	$	_	6	nmod	_	_
6	factors	factor	NOUN	NNS	Number=Plur	4	pobj	_	_
7	through	through	ADP	IN	_	3	prep	_	_
8	$ Y - mnd $	$ y - mnd $	SYM	$	_	7	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
11	1	1	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	cells	cell	NOUN	NNS	Number=Plur	8	conj	_	_
14	turn	turn	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	out	out	ADP	RP	_	14	prt	_	_
16	to	to	PART	TO	_	17	aux	_	_
17	be	be	AUX	VB	VerbForm=Inf	14	xcomp	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	familiar	familiar	ADJ	JJ	Degree=Pos	20	amod	_	_
20	bimodules	bimodule	NOUN	NNS	Number=Plur	17	attr	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 3
# text = The locally ordered bicategory $ rel $ and its bicategory of monads both fail to be Cauchy - complete, but have a well - known Cauchy - completion in common.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	locally	locally	ADV	RB	_	3	advmod	_	_
3	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	amod	_	_
4	bicategory	bicategory	NOUN	NN	Number=Sing	12	nsubj	_	_
5	$ rel $	$ rel $	SYM	$	_	4	appos	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
7	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	8	poss	_	_
8	bicategory	bicategory	NOUN	NN	Number=Sing	4	conj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	monads	monad	NOUN	NNS	Number=Plur	9	pobj	_	_
11	both	both	PRON	DT	_	12	preconj	_	_
12	fail	fail	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	be	be	AUX	VB	VerbForm=Inf	12	xcomp	_	_
15	Cauchy	cauchy	NOUN	NN	Number=Sing	17	npadvmod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	complete	complete	ADJ	JJ	Degree=Pos	14	acomp	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
19	but	but	CCONJ	CC	ConjType=Cmp	12	cc	_	_
20	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	conj	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
22	well	well	ADV	RB	Degree=Pos	24	advmod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	amod	_	_
25	Cauchy	cauchy	NOUN	NN	Number=Sing	27	compound	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	completion	completion	NOUN	NN	Number=Sing	20	dobj	_	_
28	in	in	ADP	IN	_	20	prep	_	_
29	common	common	ADJ	JJ	Degree=Pos	28	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 4
# text = This prompts us to formulate a concept of Cauchy - completeness for bicategories that are not locally ordered and suggests a weakening of the notion of monad.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	prompts	prompt	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	2	dobj	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	formulate	formulate	VERB	VB	VerbForm=Inf	2	advcl	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	concept	concept	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	Cauchy	Cauchy	PROPN	NNP	Number=Sing	11	compound	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	completeness	completeness	NOUN	NN	Number=Sing	8	pobj	_	_
12	for	for	ADP	IN	_	5	prep	_	_
13	bicategories	bicategorie	NOUN	NNS	Number=Plur	12	pobj	_	_
14	that	that	PRON	WDT	PronType=Rel	18	nsubjpass	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	18	auxpass	_	_
16	not	not	PART	RB	Polarity=Neg	18	neg	_	_
17	locally	locally	ADV	RB	_	18	advmod	_	_
18	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	relcl	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	suggests	suggest	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	conj	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	weakening	weakening	NOUN	NN	Number=Sing	20	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	notion	notion	NOUN	NN	Number=Sing	23	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	monad	monad	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = For this purpose, we develop a calculus of general modules between unstructured endo - 1 - cells.
1	For	for	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	purpose	purpose	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	calculus	calculus	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	general	general	ADJ	JJ	Degree=Pos	11	amod	_	_
11	modules	module	NOUN	NNS	Number=Plur	9	pobj	_	_
12	between	between	ADP	IN	_	11	prep	_	_
13	unstructured	unstructured	ADJ	JJ	Degree=Pos	18	amod	_	_
14	endo	endo	X	FW	Foreign=Yes	18	nmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	1	1	NUM	CD	NumType=Card	18	nummod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	cells	cell	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 6
# text = These behave well with respect to composition, but in general fail to have identities.
1	These	these	PRON	DT	Number=Plur|PronType=Dem	2	nsubj	_	_
2	behave	behave	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	well	well	ADV	RB	Degree=Pos	2	advmod	_	_
4	with	with	ADP	IN	_	2	prep	_	_
5	respect	respect	NOUN	NN	Number=Sing	4	pobj	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	composition	composition	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
9	but	but	CCONJ	CC	ConjType=Cmp	2	cc	_	_
10	in	in	ADP	IN	_	12	prep	_	_
11	general	general	ADJ	JJ	Degree=Pos	10	amod	_	_
12	fail	fail	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	have	have	VERB	VB	VerbForm=Inf	12	xcomp	_	_
15	identities	identity	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 7
# text = To overcome this problem, we do not need to impose the full structure of a monad on endo - 1 - cells.
1	To	to	PART	TO	_	2	aux	_	_
2	overcome	overcome	VERB	VB	VerbForm=Inf	9	advcl	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	problem	problem	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
7	do	do	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	aux	_	_
8	not	not	PART	RB	Polarity=Neg	9	neg	_	_
9	need	need	VERB	VB	VerbForm=Inf	0	ROOT	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	impose	impose	VERB	VB	VerbForm=Inf	9	xcomp	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	full	full	ADJ	JJ	Degree=Pos	14	amod	_	_
14	structure	structure	NOUN	NN	Number=Sing	11	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	monad	monad	NOUN	NNS	Number=Plur	15	pobj	_	_
18	on	on	ADP	IN	_	17	prep	_	_
19	endo	endo	PROPN	NNP	Number=Sing	23	nmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
21	1	1	NUM	CD	NumType=Card	23	nummod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	cells	cell	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 8
# text = We show that associative coequalizing multiplications suffice and call the resulting structures interpolads.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	associative	associative	ADJ	JJ	Degree=Pos	7	nsubj	_	_
5	coequalizing	coequalize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	acl	_	_
6	multiplications	multiplication	NOUN	NNS	Number=Plur	5	dobj	_	_
7	suffice	suffice	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	call	call	VERB	VB	VerbForm=Inf	7	conj	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	amod	_	_
12	structures	structure	NOUN	NNS	Number=Plur	9	dobj	_	_
13	interpolads	interpolad	NOUN	NNS	Number=Plur	9	oprd	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 9
# text = Together with structure - preserving i - modules these form a bicategory $ Y - int $ that is indeed Cauchy - complete, in our sense, and contains the bicategory of monads as a not necessarily full sub - bicategory.
1	Together	together	ADV	RB	_	2	advmod	_	_
2	with	with	ADP	IN	_	0	ROOT	_	_
3	structure	structure	NOUN	NN	Number=Sing	5	npadvmod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	amod	_	_
6	i	i	PROPN	NNP	Case=Nom|Number=Sing|Person=1|PronType=Prs	8	nsubj	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	modules	module	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	pobj	_	_
9	these	these	PRON	DT	Number=Plur|PronType=Dem	10	nsubj	_	_
10	form	form	VERB	VBP	Tense=Pres|VerbForm=Fin	8	dative	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	bicategory	bicategory	NOUN	NN	Number=Sing	8	npadvmod	_	_
13	$ Y - int $	$ y - int $	SYM	$	_	12	appos	_	_
14	that	that	PRON	WDT	PronType=Rel	15	nsubj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	relcl	_	_
16	indeed	indeed	ADV	RB	_	15	advmod	_	_
17	Cauchy	cauchy	NOUN	NN	Number=Sing	19	npadvmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	complete	complete	ADJ	JJ	Degree=Pos	15	acomp	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
21	in	in	ADP	IN	_	8	prep	_	_
22	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	23	poss	_	_
23	sense	sense	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
26	contains	contain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	bicategory	bicategory	NOUN	NN	Number=Sing	26	dobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	monads	monad	NOUN	NNS	Number=Plur	29	pobj	_	_
31	as	as	ADP	IN	_	26	prep	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
33	not	not	PART	RB	Polarity=Neg	34	neg	_	_
34	necessarily	necessarily	ADV	RB	_	35	advmod	_	_
35	full	full	ADJ	JJ	Degree=Pos	38	amod	_	_
36	sub	sub	NOUN	NN	Number=Sing	38	compound	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	38	punct	_	_
38	bicategory	bicategory	NOUN	NN	Number=Sing	31	pobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 10
# text = Interpolads over rel are idempotent relations, over the suspension of set they correspond to interpolative semi - groups, and over spn they lead to a notion of ``category without identities'' also known as ``taxonomy''.
1	Interpolads	interpolad	NOUN	NNS	Number=Plur	4	nsubj	_	_
2	over	over	ADP	IN	_	1	prep	_	_
3	rel	rel	NOUN	NN	Number=Sing	2	pobj	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	idempotent	idempotent	ADJ	JJ	Degree=Pos	6	amod	_	_
6	relations	relation	NOUN	NNS	Number=Plur	4	attr	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	over	over	ADP	IN	_	14	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	suspension	suspension	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	set	set	NOUN	NN	Number=Sing	11	pobj	_	_
13	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	14	nsubj	_	_
14	correspond	correspond	VERB	VBP	Tense=Pres|VerbForm=Fin	4	conj	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	interpolative	interpolative	VERB	VB	VerbForm=Inf	14	xcomp	_	_
17	semi	semi	ADJ	JJ	Degree=Pos	16	advmod	_	_
18	-	-	NOUN	NNS	Number=Plur	16	punct	_	_
19	groups	group	NOUN	NNS	Number=Plur	16	dobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
22	over	over	ADP	IN	_	25	prep	_	_
23	spn	spn	NOUN	NN	Number=Sing	22	pobj	_	_
24	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	25	nsubj	_	_
25	lead	lead	VERB	VBP	Tense=Pres|VerbForm=Fin	14	conj	_	_
26	to	to	ADP	IN	_	25	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	notion	notion	NOUN	NN	Number=Sing	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	29	punct	_	SpaceAfter=No
31	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	29	punct	_	SpaceAfter=No
32	category	category	NOUN	NN	Number=Sing	29	pobj	_	_
33	without	without	ADP	IN	_	32	prep	_	_
34	identities	identity	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
35	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	32	punct	_	_
36	also	also	ADV	RB	_	37	advmod	_	_
37	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	acl	_	_
38	as	as	ADP	IN	_	37	prep	_	_
39	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	38	punct	_	SpaceAfter=No
40	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	38	punct	_	SpaceAfter=No
41	taxonomy	taxonomy	NOUN	NN	Number=Sing	38	pobj	_	SpaceAfter=No
42	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	25	punct	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 11
# text = If $ Y $ locally has equalizers, then modules in general, and the bicategories $ Y - mnd $ and $ Y - int $ in particular, inherit the property of being closed with respect to 1 - cell composition.
1	If	if	SCONJ	IN	_	4	mark	_	_
2	$ Y $	$ y $	SYM	$	_	4	nsubj	_	_
3	locally	locally	ADV	RB	_	4	advmod	_	_
4	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	advcl	_	_
5	equalizers	equalizer	NOUN	NNS	Number=Plur	4	dobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
7	then	then	ADV	RB	PronType=Dem	8	advmod	_	_
8	modules	module	NOUN	NNS	Number=Plur	0	ROOT	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	general	general	ADJ	JJ	Degree=Pos	9	amod	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	bicategories	bicategorie	NOUN	NNS	Number=Plur	21	nsubj	_	_
15	$ Y - mnd $	$ y - mnd $	SYM	$	_	14	appos	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	$ Y - int $	$ y - int $	SYM	$	_	15	conj	_	_
18	in	in	ADP	IN	_	15	prep	_	_
19	particular	particular	ADJ	JJ	Degree=Pos	18	amod	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
21	inherit	inherit	VERB	VB	VerbForm=Inf	8	conj	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	property	property	NOUN	NN	Number=Sing	21	dobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	being	be	AUX	VBG	VerbForm=Ger	26	auxpass	_	_
26	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	pcomp	_	_
27	with	with	ADP	IN	_	26	prep	_	_
28	respect	respect	NOUN	NN	Number=Sing	27	pobj	_	_
29	to	to	ADP	IN	_	28	prep	_	_
30	1	1	NUM	CD	NumType=Card	32	nummod	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	cell	cell	NOUN	NN	Number=Sing	33	compound	_	_
33	composition	composition	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# doc_id = 29
# sent_id = 1
# text = For $ m >= n > 0 $ , a map $ f $ between pointed spaces is said to be a weak $ [n, m] $ - equivalence if $ f $ induces isomorphisms of the homotopy groups $ pi_k for n <= k <= m~ $ .
1	For	for	ADP	IN	_	11	prep	_	_
2	$ m >= n > 0 $	$ m >= n > 0 $	SYM	$	_	1	pobj	_	_
3	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	map	map	NOUN	NN	Number=Sing	11	nsubjpass	_	_
6	$ f $	$ f $	SYM	$	_	5	dep	_	_
7	between	between	ADP	IN	_	5	prep	_	_
8	pointed	pointed	ADJ	JJ	Degree=Pos	9	amod	_	_
9	spaces	space	NOUN	NNS	Number=Plur	7	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	said	say	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
12	to	to	PART	TO	_	13	aux	_	_
13	be	be	AUX	VB	VerbForm=Inf	11	xcomp	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
15	weak	weak	ADJ	JJ	Degree=Pos	18	amod	_	_
16	$ [n, m] $	$ [n, m] $	SYM	$	_	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	equivalence	equivalence	NOUN	NN	Number=Sing	13	attr	_	_
19	if	if	SCONJ	IN	_	21	mark	_	_
20	$ f $	$ f $	SYM	$	_	21	nsubj	_	_
21	induces	induce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	advcl	_	_
22	isomorphisms	isomorphism	NOUN	NNS	Number=Plur	21	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	homotopy	homotopy	NOUN	NN	Number=Sing	26	compound	_	_
26	groups	group	NOUN	NNS	Number=Plur	23	pobj	_	_
27	$ pi_k for n <= k <= m~ $	$ pi_k for n <= k <= m~ $	SYM	$	_	13	npadvmod	_	_
28	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 2
# text = Associated with this notion we give two different closed model category structures to the category of pointed spaces.
1	Associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	advcl	_	_
2	with	with	ADP	IN	_	1	prep	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	pobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	two	two	NUM	CD	NumType=Card	12	nummod	_	_
8	different	different	ADJ	JJ	Degree=Pos	12	amod	_	_
9	closed	closed	ADJ	JJ	Degree=Pos	12	amod	_	_
10	model	model	NOUN	NN	Number=Sing	12	compound	_	_
11	category	category	NOUN	NN	Number=Sing	12	compound	_	_
12	structures	structure	NOUN	NNS	Number=Plur	6	dobj	_	_
13	to	to	ADP	IN	_	6	dative	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	pointed	pointed	ADJ	JJ	Degree=Pos	18	amod	_	_
18	spaces	space	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = Both structures have the same class of weak equivalences but different classes of fibrations and therefore of cofibrations.
1	Both	both	DET	DT	_	2	det	_	_
2	structures	structure	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	same	same	ADJ	JJ	Degree=Pos	6	amod	_	_
6	class	class	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	weak	weak	ADJ	JJ	Degree=Pos	9	amod	_	_
9	equivalences	equivalence	NOUN	NNS	Number=Plur	7	pobj	_	_
10	but	but	CCONJ	CC	ConjType=Cmp	6	cc	_	_
11	different	different	ADJ	JJ	Degree=Pos	12	amod	_	_
12	classes	class	NOUN	NNS	Number=Plur	6	conj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	fibrations	fibration	NOUN	NNS	Number=Plur	13	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
16	therefore	therefore	ADV	RB	_	17	advmod	_	_
17	of	of	ADP	IN	_	6	prep	_	_
18	cofibrations	cofibration	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = Using one of these structures, one obtains that the localized category is equivalent to the category of $ n $ - reduced CW - complexes with dimension less than or equal to $ m+1 $ and $ m $ - homotopy classes of cellular pointed maps.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	csubj	_	_
2	one	one	NUM	CD	NumType=Card	1	dobj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	these	these	DET	DT	Number=Plur|PronType=Dem	5	det	_	_
5	structures	structure	NOUN	NNS	Number=Plur	3	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	1	punct	_	_
7	one	one	NUM	CD	NumType=Card	8	nummod	_	_
8	obtains	obtain	NOUN	NNS	Number=Plur	0	ROOT	_	_
9	that	that	PRON	WDT	PronType=Rel	13	mark	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	localized	localize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
12	category	category	NOUN	NN	Number=Sing	13	nsubj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	ccomp	_	_
14	equivalent	equivalent	ADJ	JJ	Degree=Pos	13	acomp	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	$ n $	$ n $	SYM	$	_	21	advmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	reduced	reduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
22	CW	CW	PROPN	NNP	Number=Sing	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	complexes	complex	NOUN	NNS	Number=Plur	18	pobj	_	_
25	with	with	ADP	IN	_	17	prep	_	_
26	dimension	dimension	NOUN	NN	Number=Sing	25	pobj	_	_
27	less	less	ADJ	JJR	Degree=Cmp	13	advmod	_	_
28	than	than	ADP	IN	_	27	prep	_	_
29	or	or	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	equal	equal	ADJ	JJ	Degree=Pos	28	conj	_	_
31	to	to	ADP	IN	_	30	prep	_	_
32	$ m+1 $	$ m+1 $	SYM	$	_	31	pobj	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
34	$ m $	$ m $	SYM	$	_	36	quantmod	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	36	punct	_	_
36	homotopy	homotopy	NOUN	NN	Number=Sing	37	compound	_	_
37	classes	class	NOUN	NNS	Number=Plur	31	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	cellular	cellular	ADJ	JJ	Degree=Pos	41	amod	_	_
40	pointed	point	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	41	amod	_	_
41	maps	map	NOUN	NNS	Number=Plur	38	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 5
# text = Using the other structure we see that the localized category is also equivalent to the homotopy category of $ (n - 1) $ - connected $ (m+1) $ - coconnected CW - complexes.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	advcl	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	other	other	ADJ	JJ	Degree=Pos	4	amod	_	_
4	structure	structure	NOUN	NN	Number=Sing	1	dobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	see	see	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	11	mark	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	localized	localize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	11	nsubj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
12	also	also	ADV	RB	_	11	advmod	_	_
13	equivalent	equivalent	ADJ	JJ	Degree=Pos	11	acomp	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	homotopy	homotopy	NOUN	NN	Number=Sing	17	compound	_	_
17	category	category	NOUN	NN	Number=Sing	14	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	$ (n - 1) $	$ (n - 1) $	SYM	$	_	21	advmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	amod	_	_
22	$ (m+1) $	$ (m+1) $	SYM	$	_	24	advmod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	coconnected	coconnecte	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	amod	_	_
25	CW	cw	NOUN	NN	Number=Sing	27	compound	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	complexes	complex	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 30
# sent_id = 1
# text = In this paper, we construct a neat description of the passage from crossed squares of commutative algebras to 2 - crossed modules analogous to that given by Conduche in the group case.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	neat	neat	ADJ	JJ	Degree=Pos	9	amod	_	_
9	description	description	NOUN	NN	Number=Sing	6	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	passage	passage	NOUN	NN	Number=Sing	10	pobj	_	_
13	from	from	ADP	IN	_	9	prep	_	_
14	crossed	crossed	ADJ	JJ	Degree=Pos	15	amod	_	_
15	squares	square	NOUN	NNS	Number=Plur	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	commutative	commutative	ADJ	JJ	Degree=Pos	18	amod	_	_
18	algebras	algebra	NOUN	NNS	Number=Plur	16	pobj	_	_
19	to	to	ADP	IN	_	9	prep	_	_
20	2	2	NUM	CD	NumType=Card	22	npadvmod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	amod	_	_
23	modules	module	NOUN	NNS	Number=Plur	19	pobj	_	_
24	analogous	analogous	ADJ	JJ	Degree=Pos	23	amod	_	_
25	to	to	ADP	IN	_	24	prep	_	_
26	that	that	PRON	DT	Number=Sing|PronType=Dem	25	pobj	_	_
27	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	prep	_	_
28	by	by	ADP	IN	_	27	agent	_	_
29	Conduche	Conduche	PROPN	NNP	Number=Sing	28	pobj	_	_
30	in	in	ADP	IN	_	27	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	group	group	NOUN	NN	Number=Sing	33	compound	_	_
33	case	case	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = We also give an analogue, for commutative algebra, of $ T $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	analogue	analogue	NOUN	NN	Number=Sing	3	dobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
7	for	for	ADP	IN	_	3	prep	_	_
8	commutative	commutative	ADJ	JJ	Degree=Pos	9	amod	_	_
9	algebra	algebra	PROPN	NNP	Number=Sing	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	of	of	ADP	IN	_	9	prep	_	_
12	$ T $	$ t $	SYM	$	_	11	pobj	_	_
13	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Porter's simplicial groups to $ n $ - cubes of groups which implies an inverse functor to Conduche's one.
1	Porter	Porter	PROPN	NNP	Number=Sing	4	poss	_	SpaceAfter=No
2	's	's	PART	POS	_	1	case	_	_
3	simplicial	simplicial	ADJ	JJ	Degree=Pos	4	amod	_	_
4	groups	group	NOUN	NNS	Number=Plur	0	ROOT	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	$ n $	$ n $	SYM	$	_	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	cubes	cube	NOUN	NNS	Number=Plur	5	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	groups	group	NOUN	NNS	Number=Plur	9	pobj	_	_
11	which	which	PRON	WDT	_	12	nsubj	_	_
12	implies	imply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	relcl	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	inverse	inverse	ADJ	JJ	Degree=Pos	15	amod	_	_
15	functor	functor	NOUN	NN	Number=Sing	12	dobj	_	_
16	to	to	ADP	IN	_	12	prep	_	_
17	Conduche	Conduche	PROPN	NNP	Number=Sing	19	poss	_	SpaceAfter=No
18	's	's	PART	POS	_	17	case	_	_
19	one	one	NUM	CD	NumType=Card	16	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 31
# sent_id = 1
# text = We give a precise characterization for when the models of the tensor product of sketches are structurally isomorphic to the models of either sketch in the models of the other.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	precise	precise	ADJ	JJ	Degree=Pos	5	amod	_	_
5	characterization	characterization	NOUN	NN	Number=Sing	2	dobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	when	when	SCONJ	WRB	_	16	advmod	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	models	model	NOUN	NNS	Number=Plur	16	nsubj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	tensor	tensor	NOUN	NN	Number=Sing	13	compound	_	_
13	product	product	NOUN	NN	Number=Sing	10	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	sketches	sketch	NOUN	NNS	Number=Plur	14	pobj	_	_
16	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	pcomp	_	_
17	structurally	structurally	ADV	RB	_	18	advmod	_	_
18	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	16	acomp	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	models	model	NOUN	NNS	Number=Plur	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	either	either	PRON	DT	_	24	preconj	_	_
24	sketch	sketch	NOUN	NN	Number=Sing	22	pobj	_	_
25	in	in	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	models	model	NOUN	NNS	Number=Plur	25	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	other	other	ADJ	JJ	Degree=Pos	28	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = For each base category $ K $ call the just mentioned property (sketch) $ K $ - multilinearity.
1	For	for	ADP	IN	_	6	prep	_	_
2	each	each	DET	DT	_	4	det	_	_
3	base	base	NOUN	NN	Number=Sing	4	compound	_	_
4	category	category	NOUN	NN	Number=Sing	1	pobj	_	_
5	$ K $	$ k $	SYM	$	_	1	dep	_	_
6	call	call	VERB	VB	VerbForm=Inf	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	just	just	ADV	RB	_	9	advmod	_	_
9	mentioned	mention	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	property	property	NOUN	NN	Number=Sing	6	dobj	_	_
11	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
12	sketch	sketch	NOUN	NN	Number=Sing	10	appos	_	SpaceAfter=No
13	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	10	punct	_	_
14	$ K $	$ k $	SYM	$	_	16	compound	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	multilinearity	multilinearity	NOUN	NN	Number=Sing	10	appos	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = Say that two sketches are $ K $ - compatible with respect to base category $ K $ just in case in each $ K $ - model, the limits for each limit specification in each sketch commute with the colimits for each colimit specification in the other sketch and all limits and colimits are pointwise.
1	Say	say	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	that	that	SCONJ	IN	_	5	mark	_	_
3	two	two	NUM	CD	NumType=Card	4	nummod	_	_
4	sketches	sketch	NOUN	NNS	Number=Plur	5	nsubj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	1	ccomp	_	_
6	$ K $	$ k $	SYM	$	_	8	advmod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	compatible	compatible	ADJ	JJ	Degree=Pos	5	acomp	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	respect	respect	NOUN	NN	Number=Sing	9	pobj	_	_
11	to	to	ADP	IN	_	10	prep	_	_
12	base	base	NOUN	NN	Number=Sing	13	compound	_	_
13	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
14	$ K $	$ k $	SYM	$	_	15	nmod	_	_
15	just	just	ADV	RB	_	5	advmod	_	_
16	in	in	ADP	IN	_	5	prep	_	_
17	case	case	NOUN	NN	Number=Sing	16	pobj	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	each	each	DET	DT	_	22	det	_	_
20	$ K $	$ k $	SYM	$	_	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	model	model	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	limits	limit	NOUN	NNS	Number=Plur	50	nsubj	_	_
26	for	for	ADP	IN	_	25	prep	_	_
27	each	each	DET	DT	_	29	det	_	_
28	limit	limit	NOUN	NN	Number=Sing	29	compound	_	_
29	specification	specification	NOUN	NN	Number=Sing	26	pobj	_	_
30	in	in	ADP	IN	_	29	prep	_	_
31	each	each	DET	DT	_	33	det	_	_
32	sketch	sketch	NOUN	NN	Number=Sing	33	compound	_	_
33	commute	commute	NOUN	NN	Number=Sing	30	pobj	_	_
34	with	with	ADP	IN	_	33	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	colimits	colimit	NOUN	NNS	Number=Plur	34	pobj	_	_
37	for	for	ADP	IN	_	29	prep	_	_
38	each	each	DET	DT	_	40	det	_	_
39	colimit	colimit	NOUN	NN	Number=Sing	40	compound	_	_
40	specification	specification	NOUN	NN	Number=Sing	37	pobj	_	_
41	in	in	ADP	IN	_	40	prep	_	_
42	the	the	DET	DT	Definite=Def|PronType=Art	44	det	_	_
43	other	other	ADJ	JJ	Degree=Pos	44	amod	_	_
44	sketch	sketch	NOUN	NN	Number=Sing	41	pobj	_	_
45	and	and	CCONJ	CC	ConjType=Cmp	44	cc	_	_
46	all	all	DET	DT	_	47	det	_	_
47	limits	limit	NOUN	NNS	Number=Plur	25	conj	_	_
48	and	and	CCONJ	CC	ConjType=Cmp	47	cc	_	_
49	colimits	colimit	NOUN	NNS	Number=Plur	47	conj	_	_
50	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	conj	_	_
51	pointwise	pointwise	ADJ	JJ	Degree=Pos	50	attr	_	SpaceAfter=No
52	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 4
# text = Two sketches are $ K $ - multilinear if and only if the two sketches are $ K $ - compatible.
1	Two	two	NUM	CD	NumType=Card	2	nummod	_	_
2	sketches	sketch	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	$ K $	$ k $	SYM	$	_	6	det	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	multilinear	multilinear	NOUN	NN	Number=Sing	3	acomp	_	_
7	if	if	SCONJ	IN	_	14	mark	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
9	only	only	ADV	RB	_	14	advmod	_	_
10	if	if	SCONJ	IN	_	14	mark	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	two	two	NUM	CD	NumType=Card	13	nummod	_	_
13	sketches	sketch	NOUN	NNS	Number=Plur	14	nsubj	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	advcl	_	_
15	$ K $	$ k $	SYM	$	_	17	advmod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	compatible	compatible	ADJ	JJ	Degree=Pos	14	acomp	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = This property then extends to strong Colimits of sketches.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	property	property	NOUN	NN	Number=Sing	4	nsubj	_	_
3	then	then	ADV	RB	PronType=Dem	4	advmod	_	_
4	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	strong	strong	ADJ	JJ	Degree=Pos	7	amod	_	_
7	Colimits	colimit	NOUN	NNS	Number=Plur	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	sketches	sketch	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 6
# text = We shall use the technically useful property of limited completeness and completeness of every category of models of sketches.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	shall	shall	AUX	MD	VerbType=Mod	3	aux	_	_
3	use	use	VERB	VB	VerbForm=Inf	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	technically	technically	ADV	RB	_	6	advmod	_	_
6	useful	useful	ADJ	JJ	Degree=Pos	7	amod	_	_
7	property	property	NOUN	NN	Number=Sing	3	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	limited	limited	ADJ	JJ	Degree=Pos	10	amod	_	_
10	completeness	completeness	NOUN	NN	Number=Sing	8	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	completeness	completeness	NOUN	NN	Number=Sing	10	conj	_	_
13	of	of	ADP	IN	_	10	prep	_	_
14	every	every	DET	DT	_	15	det	_	_
15	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	models	model	NOUN	NNS	Number=Plur	16	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	sketches	sketch	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = That is, categories of sketch models have all limits commuting with the sketched colimits and and all colimits commuting with the sketched limits.
1	That	that	ADV	RB	_	2	advmod	_	_
2	is	is	ADV	RB	_	8	advmod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
4	categories	category	NOUN	NNS	Number=Plur	8	nsubj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	sketch	sketch	NOUN	NN	Number=Sing	7	compound	_	_
7	models	model	NOUN	NNS	Number=Plur	5	pobj	_	_
8	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	all	all	DET	DT	_	10	det	_	_
10	limits	limit	NOUN	NNS	Number=Plur	8	dobj	_	_
11	commuting	commute	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	acl	_	_
12	with	with	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	sketched	sketch	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
15	colimits	colimit	NOUN	NNS	Number=Plur	12	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
18	all	all	DET	DT	_	19	det	_	_
19	colimits	colimit	NOUN	NNS	Number=Plur	8	conj	_	_
20	commuting	commute	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	acl	_	_
21	with	with	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	sketched	sketch	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
24	limits	limit	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 8
# text = Often used implicitly, the precise statement of this property and its proof appears here.
1	Often	often	ADV	RB	_	2	advmod	_	_
2	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	advcl	_	_
3	implicitly	implicitly	ADV	RB	_	2	advmod	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	precise	precise	ADJ	JJ	Degree=Pos	7	amod	_	_
7	statement	statement	NOUN	NN	Number=Sing	14	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	this	this	DET	DT	Number=Sing|PronType=Dem	10	det	_	_
10	property	property	NOUN	NN	Number=Sing	8	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
12	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	13	poss	_	_
13	proof	proof	NOUN	NN	Number=Sing	14	nsubj	_	_
14	appears	appear	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	here	here	ADV	RB	PronType=Dem	14	advmod	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# doc_id = 32
# sent_id = 1
# text = Each full reflective subcategory $ X $ of a finitely - complete category $ C $ gives rise to a factorization system $ (E, M) $ on $ C $ , where $ E $ consists of the morphisms of $ C $ inverted by the reflexion $ I : C - - > X $ .
1	Each	each	DET	DT	_	4	det	_	_
2	full	full	ADJ	JJ	Degree=Pos	4	amod	_	_
3	reflective	reflective	ADJ	JJ	Degree=Pos	4	amod	_	_
4	subcategory	subcategory	NOUN	NN	Number=Sing	13	nsubj	_	_
5	$ X $	$ x $	SYM	$	_	4	appos	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	finitely	finitely	ADV	RB	_	10	advmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	complete	complete	ADJ	JJ	Degree=Pos	11	amod	_	_
11	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
12	$ C $	$ c $	SYM	$	_	13	nsubj	_	_
13	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	rise	rise	NOUN	NN	Number=Sing	13	dobj	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	factorization	factorization	NOUN	NN	Number=Sing	18	compound	_	_
18	system	system	NOUN	NN	Number=Sing	15	pobj	_	_
19	$ (E, M) $	$ (e, m) $	SYM	$	_	18	appos	_	_
20	on	on	ADP	IN	_	14	prep	_	_
21	$ C $	$ c $	SYM	$	_	20	pobj	_	_
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	where	where	SCONJ	WRB	_	25	advmod	_	_
24	$ E $	$ e $	SYM	$	_	25	nsubj	_	_
25	consists	consist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	21	relcl	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	morphisms	morphism	NOUN	NNS	Number=Plur	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	$ C $	$ c $	SYM	$	_	29	pobj	_	_
31	inverted	invert	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	advcl	_	_
32	by	by	ADP	IN	_	31	agent	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
34	reflexion	reflexion	NOUN	NN	Number=Sing	32	pobj	_	_
35	$ I : C - - > X $	$ i : c - - > x $	SYM	$	_	13	dep	_	_
36	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 2
# text = Under a simplifying assumption which is satisfied in many practical examples, a morphism $ f : A - - > B $ lies in $ M $ precisely when it is the pullback along the unit $ etaB : B - - > IB $ of its reflexion $ If : IA - - > IB $ ; whereupon $ f $ is said to be a trivial covering of $ B $ .
1	Under	under	ADP	IN	_	16	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	simplifying	simplifying	NOUN	NN	Number=Sing	4	amod	_	_
4	assumption	assumption	NOUN	NN	Number=Sing	1	pobj	_	_
5	which	which	PRON	WDT	_	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	relcl	_	_
7	satisfied	satisfied	ADJ	JJ	Degree=Pos	6	acomp	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	many	many	ADJ	JJ	Degree=Pos	11	amod	_	_
10	practical	practical	ADJ	JJ	Degree=Pos	11	amod	_	_
11	examples	example	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	morphism	morphism	NOUN	NN	Number=Sing	16	nsubj	_	_
15	$ f : A - - > B $	$ f : a - - > b $	SYM	$	_	16	nsubj	_	_
16	lies	lie	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	37	ccomp	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	$ M $	$ m $	SYM	$	_	17	pobj	_	_
19	precisely	precisely	ADV	RB	_	20	advmod	_	_
20	when	when	SCONJ	WRB	_	22	advmod	_	_
21	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	22	nsubj	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	advcl	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	pullback	pullback	NOUN	NN	Number=Sing	22	attr	_	_
25	along	along	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	unit	unit	NOUN	NN	Number=Sing	25	pobj	_	_
28	$ etaB : B - - > IB $	$ etab : b - - > ib $	SYM	$	_	27	appos	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	31	poss	_	_
31	reflexion	reflexion	NOUN	NN	Number=Sing	29	pobj	_	_
32	$ If : IA - - > IB $	$ if : ia - - > ib $	SYM	$	_	22	dep	_	_
33	;	;	PUNCT	:	_	37	punct	_	_
34	whereupon	whereupon	NOUN	NN	Number=Sing	37	nsubjpass	_	_
35	$ f $	$ f $	SYM	$	_	34	advmod	_	_
36	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	37	auxpass	_	_
37	said	say	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
38	to	to	PART	TO	_	39	aux	_	_
39	be	be	AUX	VB	VerbForm=Inf	37	xcomp	_	_
40	a	a	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
41	trivial	trivial	ADJ	JJ	Degree=Pos	42	amod	_	_
42	covering	covering	NOUN	NN	Number=Sing	39	attr	_	_
43	of	of	ADP	IN	_	42	prep	_	_
44	$ B $	$ b $	SYM	$	_	43	pobj	_	_
45	.	.	PUNCT	.	PunctType=Peri	37	punct	_	SpaceAfter=No

# sent_id = 3
# text = Finally, the morphism $ f : A - - > B $ is said to be a covering of $ B $ if, for some effective descent morphism $ p : E - - > B $ , the pullback $ p^*f $ of $ f $ along $ p $ is a trivial covering of $ E $ .
1	Finally	finally	ADV	RB	_	7	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	morphism	morphism	NOUN	NN	Number=Sing	7	nsubjpass	_	_
5	$ f : A - - > B $	$ f : a - - > b $	SYM	$	_	4	appos	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	said	say	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	be	be	AUX	VB	VerbForm=Inf	7	xcomp	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	covering	covering	NOUN	NN	Number=Sing	9	attr	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	$ B $	$ b $	SYM	$	_	12	pobj	_	_
14	if	if	SCONJ	IN	_	11	prep	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
16	for	for	ADP	IN	_	30	prep	_	_
17	some	some	DET	DT	_	20	det	_	_
18	effective	effective	ADJ	JJ	Degree=Pos	20	amod	_	_
19	descent	descent	NOUN	NN	Number=Sing	20	compound	_	_
20	morphism	morphism	NOUN	NN	Number=Sing	16	pobj	_	_
21	$ p : E - - > B $	$ p : e - - > b $	SYM	$	_	16	pobj	_	_
22	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	pullback	pullback	NOUN	NN	Number=Sing	30	nsubj	_	_
25	$ p^*f $	$ p^*f $	SYM	$	_	24	appos	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	$ f $	$ f $	SYM	$	_	26	pobj	_	_
28	along	along	ADP	IN	_	29	advmod	_	_
29	$ p $	$ p $	SYM	$	_	24	appos	_	_
30	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	ccomp	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
32	trivial	trivial	ADJ	JJ	Degree=Pos	33	amod	_	_
33	covering	covering	NOUN	NN	Number=Sing	30	attr	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	$ E $	$ e $	SYM	$	_	34	pobj	_	_
36	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = This is the absolute notion of covering; there is also a more general relative one, where some class $ Theta $ of morphisms of $ C $ is given, and the class $ Cov(B) $ of coverings of $ B $ is a subclass—or rather a subcategory—of the category $ C downarrow B subset C/B $ whose objects are those $ f : A - - > B $ with $ f $ in $ Theta $ .
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	ccomp	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	absolute	absolute	ADJ	JJ	Degree=Pos	5	amod	_	_
5	notion	notion	NOUN	NN	Number=Sing	2	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	covering	covering	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
8	;	;	PUNCT	:	_	10	punct	_	_
9	there	there	PRON	EX	_	10	expl	_	_
10	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	also	also	ADV	RB	_	10	advmod	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
13	more	more	ADV	RBR	Degree=Cmp	14	advmod	_	_
14	general	general	ADJ	JJ	Degree=Pos	16	amod	_	_
15	relative	relative	ADJ	JJ	Degree=Pos	16	amod	_	_
16	one	one	NUM	CD	NumType=Card	10	attr	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	where	where	SCONJ	WRB	_	27	advmod	_	_
19	some	some	DET	DT	_	20	det	_	_
20	class	class	NOUN	NN	Number=Sing	27	nsubjpass	_	_
21	$ Theta $	$ theta $	SYM	$	_	20	appos	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	morphisms	morphism	NOUN	NNS	Number=Plur	22	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	$ C $	$ c $	SYM	$	_	24	pobj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	auxpass	_	_
27	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	relcl	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	class	class	NOUN	NN	Number=Sing	37	nsubj	_	_
32	$ Cov(B) $	$ cov(b) $	SYM	$	_	31	appos	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	coverings	covering	NOUN	NNS	Number=Plur	33	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	$ B $	$ b $	SYM	$	_	35	pobj	_	_
37	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	conj	_	_
38	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
39	subclass	subclass	NOUN	NN	Number=Sing	37	attr	_	SpaceAfter=No
40	—	—	PUNCT	:	_	39	punct	_	SpaceAfter=No
41	or	or	CCONJ	CC	ConjType=Cmp	39	cc	_	_
42	rather	rather	ADV	RB	_	44	advmod	_	_
43	a	a	DET	DT	Definite=Ind|PronType=Art	44	det	_	_
44	subcategory	subcategory	NOUN	NN	Number=Sing	39	conj	_	SpaceAfter=No
45	—	—	PUNCT	:	_	44	punct	_	SpaceAfter=No
46	of	of	ADP	IN	_	44	prep	_	_
47	the	the	DET	DT	Definite=Def|PronType=Art	48	det	_	_
48	category	category	NOUN	NN	Number=Sing	46	pobj	_	_
49	$ C downarrow B subset C/B $	$ c downarrow b subset c/b $	SYM	$	_	44	appos	_	_
50	whose	whose	DET	WP$	Poss=Yes	51	poss	_	_
51	objects	object	NOUN	NNS	Number=Plur	52	nsubj	_	_
52	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	49	relcl	_	_
53	those	those	PRON	DT	Number=Plur|PronType=Dem	52	attr	_	_
54	$ f : A - - > B $	$ f : a - - > b $	SYM	$	_	53	npadvmod	_	_
55	with	with	ADP	IN	_	54	prep	_	_
56	$ f $	$ f $	SYM	$	_	55	pobj	_	_
57	in	in	ADP	IN	_	55	prep	_	_
58	$ Theta $	$ theta $	SYM	$	_	57	pobj	_	_
59	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 5
# text = Many questions in mathematics can be reduced to asking whether $ Cov(B) $ is reflective in $ C downarrow B $ ; and we give a number of disparate conditions, each sufficient for this to be so.
1	Many	many	ADJ	JJ	Degree=Pos	2	amod	_	_
2	questions	question	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	mathematics	mathematic	NOUN	NNS	Number=Plur	3	pobj	_	_
5	can	can	AUX	MD	VerbForm=Fin	7	aux	_	_
6	be	be	AUX	VB	VerbForm=Inf	7	auxpass	_	_
7	reduced	reduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	to	to	ADP	IN	_	7	prep	_	_
9	asking	ask	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	pcomp	_	_
10	whether	whether	SCONJ	IN	_	12	mark	_	_
11	$ Cov(B) $	$ cov(b) $	SYM	$	_	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	ccomp	_	_
13	reflective	reflective	ADJ	JJ	Degree=Pos	12	acomp	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	$ C downarrow B $	$ c downarrow b $	SYM	$	_	14	pobj	_	_
16	;	;	PUNCT	:	_	7	punct	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	7	conj	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	number	number	NOUN	NN	Number=Sing	19	dobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	disparate	disparate	ADJ	JJ	Degree=Pos	24	amod	_	_
24	conditions	condition	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
26	each	each	DET	DT	_	27	det	_	_
27	sufficient	sufficient	ADJ	JJ	Degree=Pos	19	conj	_	_
28	for	for	SCONJ	IN	_	31	mark	_	_
29	this	this	PRON	DT	Number=Sing|PronType=Dem	31	nsubj	_	_
30	to	to	PART	TO	_	31	aux	_	_
31	be	be	AUX	VB	VerbForm=Inf	27	advcl	_	_
32	so	so	ADV	RB	_	31	advmod	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 6
# text = In this way we recapture old results and establish new ones on the reflexion of local homeomorphisms into coverings, on the Galois theory of commutative rings, and on generalized central extensions of universal algebras.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	way	way	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	recapture	recapture	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	old	old	ADJ	JJ	Degree=Pos	7	amod	_	_
7	results	result	NOUN	NNS	Number=Plur	5	dobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
9	establish	establish	VERB	VB	VerbForm=Inf	5	conj	_	_
10	new	new	ADJ	JJ	Degree=Pos	11	amod	_	_
11	ones	one	NOUN	NNS	Number=Plur	9	dobj	_	_
12	on	on	ADP	IN	_	9	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	reflexion	reflexion	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	local	local	ADJ	JJ	Degree=Pos	17	amod	_	_
17	homeomorphisms	homeomorphism	NOUN	NNS	Number=Plur	15	pobj	_	_
18	into	into	ADP	IN	_	9	prep	_	_
19	coverings	covering	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
21	on	on	ADP	IN	_	9	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	Galois	Galois	PROPN	NNP	Number=Sing	24	compound	_	_
24	theory	theory	NOUN	NN	Number=Sing	21	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	commutative	commutative	ADJ	JJ	Degree=Pos	27	amod	_	_
27	rings	ring	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
30	on	on	ADP	IN	_	5	prep	_	_
31	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	amod	_	_
32	central	central	ADJ	JJ	Degree=Pos	33	amod	_	_
33	extensions	extension	NOUN	NNS	Number=Plur	30	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	universal	universal	ADJ	JJ	Degree=Pos	36	amod	_	_
36	algebras	algebra	NOUN	NNS	Number=Plur	34	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 33
# sent_id = 1
# text = We define a localization $ L $ of a category $ E $ to be quintessential if the left adjoint to the inclusion functor is also right adjoint to it, and persistent if $ L $ is closed under subobjects in $ E $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	localization	localization	NOUN	NN	Number=Sing	2	dobj	_	_
5	$ L $	$ l $	SYM	$	_	4	appos	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
9	$ E $	$ e $	SYM	$	_	2	dep	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	be	be	AUX	VB	VerbForm=Inf	2	advcl	_	_
12	quintessential	quintessential	ADJ	JJ	Degree=Pos	11	acomp	_	_
13	if	if	SCONJ	IN	_	21	mark	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	left	left	ADJ	JJ	Degree=Pos	16	amod	_	_
16	adjoint	adjoint	NOUN	NN	Number=Sing	21	nsubj	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	inclusion	inclusion	NOUN	NN	Number=Sing	20	compound	_	_
20	functor	functor	NOUN	NN	Number=Sing	17	pobj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	advcl	_	_
22	also	also	ADV	RB	_	21	advmod	_	_
23	right	right	ADJ	JJ	Degree=Pos	24	amod	_	_
24	adjoint	adjoint	NOUN	NN	Number=Sing	21	attr	_	_
25	to	to	ADP	IN	_	24	prep	_	_
26	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	25	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
29	persistent	persistent	ADJ	JJ	Degree=Pos	21	conj	_	_
30	if	if	SCONJ	IN	_	33	mark	_	_
31	$ L $	$ l $	SYM	$	_	33	nsubjpass	_	_
32	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	33	auxpass	_	_
33	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	ccomp	_	_
34	under	under	ADP	IN	_	33	prep	_	_
35	subobjects	subobject	NOUN	NNS	Number=Plur	34	pobj	_	_
36	in	in	ADP	IN	_	35	prep	_	_
37	$ E $	$ e $	SYM	$	_	36	pobj	_	_
38	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that quintessential localizations of an arbitrary Cauchy - complete category correspond to idempotent natural endomorphisms of its identity functor, and that they are necessarily persistent.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	13	mark	_	_
4	quintessential	quintessential	ADJ	JJ	Degree=Pos	5	amod	_	_
5	localizations	localization	NOUN	NNS	Number=Plur	13	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
8	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	12	amod	_	_
9	Cauchy	Cauchy	PROPN	NNP	Number=Sing	11	npadvmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	complete	complete	ADJ	JJ	Degree=Pos	12	amod	_	_
12	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
13	correspond	correspond	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	idempotent	idempotent	ADJ	JJ	Degree=Pos	17	amod	_	_
16	natural	natural	ADJ	JJ	Degree=Pos	17	amod	_	_
17	endomorphisms	endomorphism	NOUN	NNS	Number=Plur	14	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	21	poss	_	_
20	identity	identity	NOUN	NN	Number=Sing	21	compound	_	_
21	functor	functor	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
24	that	that	SCONJ	IN	_	26	mark	_	_
25	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	26	nsubj	_	_
26	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	conj	_	_
27	necessarily	necessarily	ADV	RB	_	26	advmod	_	_
28	persistent	persistent	ADJ	JJ	Degree=Pos	26	acomp	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Our investigation of persistent localizations is largely restricted to the case when $ E $ is a topos: we show that persistence is equivalence to the closure of $ L $ under finite coproducts and quotients, and that it implies that $ L $ is coreflective as well as reflective, at least provided $ E $ admits a geometric morphism to a Boolean topos.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	investigation	investigation	NOUN	NN	Number=Sing	8	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	persistent	persistent	ADJ	JJ	Degree=Pos	5	amod	_	_
5	localizations	localization	NOUN	NNS	Number=Plur	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
7	largely	largely	ADV	RB	_	8	advmod	_	_
8	restricted	restrict	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	ccomp	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	case	case	NOUN	NN	Number=Sing	9	pobj	_	_
12	when	when	SCONJ	WRB	_	14	advmod	_	_
13	$ E $	$ e $	SYM	$	_	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	advcl	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	topos	topos	NOUN	NN	Number=Sing	14	attr	_	SpaceAfter=No
17	:	:	PUNCT	:	_	19	punct	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	that	that	SCONJ	IN	_	22	mark	_	_
21	persistence	persistence	NOUN	NN	Number=Sing	22	nsubj	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	ccomp	_	_
23	equivalence	equivalence	NOUN	NN	Number=Sing	22	attr	_	_
24	to	to	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	closure	closure	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	$ L $	$ l $	SYM	$	_	27	pobj	_	_
29	under	under	ADP	IN	_	26	prep	_	_
30	finite	finite	ADJ	JJ	Degree=Pos	31	compound	_	_
31	coproducts	coproduct	NOUN	NNS	Number=Plur	29	pobj	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	quotients	quotient	NOUN	NNS	Number=Plur	31	conj	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
36	that	that	SCONJ	IN	_	38	mark	_	_
37	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	38	nsubj	_	_
38	implies	imply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	conj	_	_
39	that	that	SCONJ	IN	_	41	mark	_	_
40	$ L $	$ l $	SYM	$	_	41	nsubj	_	_
41	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	38	ccomp	_	_
42	coreflective	coreflective	ADJ	JJ	Degree=Pos	41	acomp	_	_
43	as	as	ADV	RB	_	45	advmod	_	_
44	well	well	ADV	RB	Degree=Pos	45	advmod	_	_
45	as	as	ADP	IN	_	42	cc	_	_
46	reflective	reflective	ADJ	JJ	Degree=Pos	42	conj	_	SpaceAfter=No
47	,	,	PUNCT	,	PunctType=Comm	41	punct	_	_
48	at	at	ADP	IN	_	49	advmod	_	_
49	least	least	ADJ	JJS	Degree=Sup	50	advmod	_	_
50	provided	provide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	52	nsubj	_	_
51	$ E $	$ e $	SYM	$	_	52	nsubj	_	_
52	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	38	conj	_	_
53	a	a	DET	DT	Definite=Ind|PronType=Art	55	det	_	_
54	geometric	geometric	ADJ	JJ	Degree=Pos	55	amod	_	_
55	morphism	morphism	NOUN	NN	Number=Sing	52	dobj	_	_
56	to	to	ADP	IN	_	52	prep	_	_
57	a	a	DET	DT	Definite=Ind|PronType=Art	59	det	_	_
58	Boolean	boolean	ADJ	JJ	Degree=Pos	59	amod	_	_
59	topos	topos	NOUN	NN	Number=Sing	56	pobj	_	SpaceAfter=No
60	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 4
# text = However, we provide examples to show that the reflector and coreflector need not coincide.
1	However	however	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	examples	example	NOUN	NNS	Number=Plur	4	dobj	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	show	show	VERB	VB	VerbForm=Inf	4	advcl	_	_
8	that	that	SCONJ	IN	_	15	mark	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	reflector	reflector	NOUN	NN	Number=Sing	15	nsubj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	coreflector	coreflector	NOUN	NN	Number=Sing	10	conj	_	_
13	need	need	AUX	VBP	Tense=Pres|VerbForm=Fin	15	aux	_	_
14	not	not	PART	RB	Polarity=Neg	15	neg	_	_
15	coincide	coincide	VERB	VB	VerbForm=Inf	7	ccomp	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 34
# sent_id = 1
# text = We analyze the Bianchi Identity as an instance of a basic fact of combinatorial groupoid theory, related to the Homotopy Addition Lemma.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	analyze	analyze	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	Bianchi	Bianchi	PROPN	NNP	Number=Sing	5	compound	_	_
5	Identity	Identity	PROPN	NNP	Number=Sing	2	dobj	_	_
6	as	as	ADP	IN	_	2	prep	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	instance	instance	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	basic	basic	ADJ	JJ	Degree=Pos	12	amod	_	_
12	fact	fact	NOUN	NN	Number=Sing	9	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	16	amod	_	_
15	groupoid	groupoid	NOUN	NN	Number=Sing	16	compound	_	_
16	theory	theory	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
18	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	advcl	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
21	Homotopy	Homotopy	PROPN	NNP	Number=Sing	22	compound	_	_
22	Addition	Addition	PROPN	NNP	Number=Sing	23	compound	_	_
23	Lemma	Lemma	PROPN	NNP	Number=Sing	19	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Here it becomes formulated in terms of 2 - forms with values in the gauge group bundle of a groupoid, and leads in particular to the (Chern - Weil) construction of characteristic classes.
1	Here	here	ADV	RB	PronType=Dem	3	advmod	_	_
2	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubj	_	_
3	becomes	become	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	formulated	formulate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	acomp	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	terms	term	NOUN	NNS	Number=Plur	5	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	2	2	NUM	CD	NumType=Card	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	forms	form	NOUN	NNS	Number=Plur	7	pobj	_	_
11	with	with	ADP	IN	_	10	prep	_	_
12	values	value	NOUN	NNS	Number=Plur	11	pobj	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
15	gauge	gauge	NOUN	NN	Number=Sing	16	compound	_	_
16	group	group	NOUN	NN	Number=Sing	17	compound	_	_
17	bundle	bundle	NOUN	NN	Number=Sing	13	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	groupoid	groupoid	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
23	leads	lead	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
24	in	in	ADV	RB	_	23	advmod	_	_
25	particular	particular	ADJ	JJ	Degree=Pos	24	amod	_	_
26	to	to	ADP	IN	_	23	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
28	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	33	punct	_	SpaceAfter=No
29	Chern	Chern	PROPN	NNP	Number=Sing	31	nmod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	Weil	Weil	PROPN	NNP	Number=Sing	33	nmod	_	SpaceAfter=No
32	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	33	punct	_	_
33	construction	construction	NOUN	NN	Number=Sing	26	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	characteristic	characteristic	ADJ	JJ	Degree=Pos	36	amod	_	_
36	classes	class	NOUN	NNS	Number=Plur	34	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = The method is that of synthetic differential geometry, using ``the first neighbourhood of the diagonal'' of a manifold as its basic combinatorial structure.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	method	method	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	PRON	DT	Number=Sing|PronType=Dem	3	attr	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	synthetic	synthetic	ADJ	JJ	Degree=Pos	8	amod	_	_
7	differential	differential	ADJ	JJ	Degree=Pos	8	amod	_	_
8	geometry	geometry	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
10	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	advcl	_	_
11	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	10	punct	_	SpaceAfter=No
12	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	10	punct	_	SpaceAfter=No
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	first	first	ADJ	JJ	Degree=Pos	15	amod	_	_
15	neighbourhood	neighbourhood	NOUN	NN	Number=Sing	10	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	diagonal	diagonal	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
19	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	15	punct	_	_
20	of	of	ADP	IN	_	15	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	manifold	manifold	NOUN	NN	Number=Sing	20	pobj	_	_
23	as	as	ADP	IN	_	22	prep	_	_
24	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	27	poss	_	_
25	basic	basic	ADJ	JJ	Degree=Pos	27	amod	_	_
26	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	27	amod	_	_
27	structure	structure	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = We introduce as a tool a new and simple description of wedge (exterior) products of differential forms in this context.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	as	as	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	tool	tool	NOUN	NN	Number=Sing	3	pobj	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
7	new	new	ADJ	JJ	Degree=Pos	10	amod	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	simple	simple	ADJ	JJ	Degree=Pos	7	conj	_	_
10	description	description	NOUN	NN	Number=Sing	2	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	wedge	wedge	NOUN	NN	Number=Sing	16	nmod	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	16	punct	_	SpaceAfter=No
14	exterior	exterior	ADJ	JJ	Degree=Pos	16	amod	_	SpaceAfter=No
15	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	16	punct	_	_
16	products	product	NOUN	NNS	Number=Plur	11	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	differential	differential	ADJ	JJ	Degree=Pos	19	amod	_	_
19	forms	form	NOUN	NNS	Number=Plur	17	pobj	_	_
20	in	in	ADP	IN	_	10	prep	_	_
21	this	this	DET	DT	Number=Sing|PronType=Dem	22	det	_	_
22	context	context	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 35
# sent_id = 1
# text = Results on the finiteness of induced crossed modules are proved both algebraically and topologically.
1	Results	result	NOUN	NNS	Number=Plur	10	nsubjpass	_	_
2	on	on	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	finiteness	finiteness	NOUN	NN	Number=Sing	2	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
7	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
8	modules	module	NOUN	NNS	Number=Plur	5	pobj	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	both	both	PRON	DT	_	12	advmod	_	_
12	algebraically	algebraically	ADV	RB	_	10	advmod	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	topologically	topologically	ADV	RB	_	12	conj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = Using the Van Kampen type theorem for the fundamental crossed module, applications are given to the 2 - types of mapping cones of classifying spaces of groups.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	csubj	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
3	Van	Van	PROPN	NNP	Number=Sing	4	compound	_	_
4	Kampen	Kampen	PROPN	NNP	Number=Sing	5	compound	_	_
5	type	type	NOUN	NN	Number=Sing	1	dobj	_	_
6	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	15	advcl	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
9	fundamental	fundamental	ADJ	JJ	Degree=Pos	11	amod	_	_
10	crossed	crossed	ADJ	JJ	Degree=Pos	11	amod	_	_
11	module	module	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
13	applications	application	NOUN	NNS	Number=Plur	15	nsubjpass	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
16	to	to	ADP	IN	_	15	dative	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
18	2	2	NUM	CD	NumType=Card	20	nummod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	types	type	NOUN	NNS	Number=Plur	16	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	mapping	mapping	NOUN	NN	Number=Sing	23	compound	_	_
23	cones	cone	NOUN	NNS	Number=Plur	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	classifying	classify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	24	pcomp	_	_
26	spaces	space	NOUN	NNS	Number=Plur	25	dobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	groups	group	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 3
# text = Calculations of the cohomology classes of some finite crossed modules are given, using crossed complex methods.
1	Calculations	calculation	NOUN	NNS	Number=Plur	12	nsubjpass	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	cohomology	cohomology	NOUN	NN	Number=Sing	5	compound	_	_
5	classes	class	NOUN	NNS	Number=Plur	2	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	some	some	DET	DT	_	10	det	_	_
8	finite	finite	NOUN	NN	Number=Sing	10	amod	_	_
9	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	modules	module	NOUN	NNS	Number=Plur	6	pobj	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	advcl	_	_
15	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
16	complex	complex	ADJ	JJ	Degree=Pos	17	amod	_	_
17	methods	method	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# doc_id = 36
# sent_id = 1
# text = The classical infinite loopspace machines in fact induce an equivalence of categories between a localization of the category of symmetric monoidal categories and the stable homotopy category of - 1 - connective spectra.
1	The	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
2	classical	classical	ADJ	JJ	Degree=Pos	5	amod	_	_
3	infinite	infinite	NOUN	NN	Number=Sing	5	compound	_	_
4	loopspace	loopspace	NOUN	NN	Number=Sing	5	compound	_	_
5	machines	machine	NOUN	NNS	Number=Plur	8	nsubj	_	_
6	in	in	ADP	IN	_	8	prep	_	_
7	fact	fact	NOUN	NN	Number=Sing	6	pobj	_	_
8	induce	induce	VERB	VB	VerbForm=Inf	0	ROOT	_	_
9	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	equivalence	equivalence	NOUN	NN	Number=Sing	8	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
13	between	between	ADP	IN	_	10	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	localization	localization	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	category	category	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	symmetric	symmetric	ADJ	JJ	Degree=Pos	22	amod	_	_
21	monoidal	monoidal	ADJ	JJ	Degree=Pos	22	amod	_	_
22	categories	category	NOUN	NNS	Number=Plur	19	pobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
25	stable	stable	ADJ	JJ	Degree=Pos	27	amod	_	_
26	homotopy	homotopy	NOUN	NN	Number=Sing	27	compound	_	_
27	category	category	NOUN	NN	Number=Sing	15	conj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
30	1	1	NUM	CD	NumType=Card	32	nummod	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	connective	connective	ADJ	JJ	Degree=Pos	33	amod	_	_
33	spectra	spectra	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 37
# sent_id = 1
# text = Strong promonoidal functors are defined.
1	Strong	strong	ADJ	JJ	Degree=Pos	3	amod	_	_
2	promonoidal	promonoidal	NOUN	NN	Number=Sing	3	amod	_	_
3	functors	functor	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
6	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = Left Kan extension (also called "existential quantification") along a strong promonoidal functor is shown to be a strong monoidal functor.
1	Left	Left	PROPN	NNP	Number=Sing	2	compound	_	_
2	Kan	Kan	PROPN	NNP	Number=Sing	3	compound	_	_
3	extension	extension	NOUN	NN	Number=Sing	18	nsubjpass	_	_
4	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	3	punct	_	SpaceAfter=No
5	also	also	ADV	RB	_	6	advmod	_	_
6	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	acl	_	_
7	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	9	punct	_	SpaceAfter=No
8	existential	existential	ADJ	JJ	Degree=Pos	9	amod	_	_
9	quantification	quantification	NOUN	NN	Number=Sing	6	oprd	_	SpaceAfter=No
10	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	9	punct	_	SpaceAfter=No
11	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	3	punct	_	_
12	along	along	ADP	IN	_	3	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
14	strong	strong	ADJ	JJ	Degree=Pos	16	amod	_	_
15	promonoidal	promonoidal	NOUN	NN	Number=Sing	16	compound	_	_
16	functor	functor	NOUN	NN	Number=Sing	12	pobj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	auxpass	_	_
18	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
19	to	to	PART	TO	_	20	aux	_	_
20	be	be	AUX	VB	VerbForm=Inf	18	xcomp	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
22	strong	strong	ADJ	JJ	Degree=Pos	24	amod	_	_
23	monoidal	monoidal	ADJ	JJ	Degree=Pos	24	amod	_	_
24	functor	functor	NOUN	NN	Number=Sing	20	attr	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# sent_id = 3
# text = A construction for the free monoidal category on a promonoidal category is provided.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	construction	construction	NOUN	NN	Number=Sing	13	nsubjpass	_	_
3	for	for	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	free	free	ADJ	JJ	Degree=Pos	7	amod	_	_
6	monoidal	monoidal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	category	category	NOUN	NN	Number=Sing	3	pobj	_	_
8	on	on	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	promonoidal	promonoidal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	provided	provide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 4
# text = A Fourier - like transform of presheaves is defined and shown to take convolution product to cartesian product.
1	A	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
2	Fourier	Fourier	PROPN	NNP	Number=Sing	4	npadvmod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	like	like	ADJ	JJ	Degree=Pos	5	amod	_	_
5	transform	transform	NOUN	NN	Number=Sing	9	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	presheaves	presheave	NOUN	NNS	Number=Plur	6	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	conj	_	_
12	to	to	PART	TO	_	13	aux	_	_
13	take	take	VERB	VB	VerbForm=Inf	11	xcomp	_	_
14	convolution	convolution	NOUN	NN	Number=Sing	15	compound	_	_
15	product	product	NOUN	NN	Number=Sing	13	dobj	_	_
16	to	to	ADP	IN	_	13	prep	_	_
17	cartesian	cartesian	ADJ	JJ	Degree=Pos	18	amod	_	_
18	product	product	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 38
# sent_id = 1
# text = In this paper we study the lattice of quantic conuclei for orthomudular lattices.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	lattice	lattice	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	quantic	quantic	ADJ	JJ	Degree=Pos	10	amod	_	_
10	conuclei	conuclei	NOUN	NN	Number=Sing	8	pobj	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	orthomudular	orthomudular	ADJ	JJ	Degree=Pos	13	amod	_	_
13	lattices	lattice	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that under certain condition we can get a complete characterization of all quantic conuclei.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	9	mark	_	_
4	under	under	ADP	IN	_	9	prep	_	_
5	certain	certain	ADJ	JJ	Degree=Pos	6	amod	_	_
6	condition	condition	NOUN	NN	Number=Sing	4	pobj	_	_
7	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
8	can	can	AUX	MD	VerbForm=Fin	9	aux	_	_
9	get	get	VERB	VB	VerbForm=Inf	2	ccomp	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	complete	complete	ADJ	JJ	Degree=Pos	12	amod	_	_
12	characterization	characterization	NOUN	NN	Number=Sing	9	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	all	all	DET	DT	_	16	det	_	_
15	quantic	quantic	ADJ	JJ	Degree=Pos	16	amod	_	_
16	conuclei	conuclei	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The thing to note is we use a non commutative, non associative disjunction operation which can be thought of as non commutative, non associative linear logic.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	thing	thing	NOUN	NN	Number=Sing	5	nsubj	_	_
3	to	to	PART	TO	_	4	aux	_	_
4	note	note	VERB	VB	VerbForm=Inf	2	relcl	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	5	ccomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
9	non	non	PROPN	NNP	Number=Sing	10	nmod	_	_
10	commutative	commutative	ADJ	JJ	Degree=Pos	15	amod	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
12	non	non	PROPN	NNP	Number=Sing	15	compound	_	_
13	associative	associative	ADJ	JJ	Degree=Pos	14	amod	_	_
14	disjunction	disjunction	NOUN	NN	Number=Sing	15	compound	_	_
15	operation	operation	NOUN	NN	Number=Sing	7	dobj	_	_
16	which	which	PRON	WDT	_	19	nsubjpass	_	_
17	can	can	AUX	MD	VerbForm=Fin	19	aux	_	_
18	be	be	AUX	VB	VerbForm=Inf	19	auxpass	_	_
19	thought	think	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	relcl	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	as	as	ADP	IN	_	19	prep	_	_
22	non	non	PROPN	NNP	Number=Sing	23	compound	_	_
23	commutative	commutative	PROPN	NNP	Number=Sing	21	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
25	non	non	PROPN	NNP	Number=Sing	28	nmod	_	_
26	associative	associative	ADJ	JJ	Degree=Pos	28	amod	_	_
27	linear	linear	PROPN	NNP	Number=Sing	28	compound	_	_
28	logic	logic	NOUN	NN	Number=Sing	19	oprd	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 39
# sent_id = 1
# text = We discuss two versions of a conjecture attributed to M Barr.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	discuss	discuss	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	two	two	NUM	CD	NumType=Card	4	nummod	_	_
4	versions	version	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	conjecture	conjecture	NOUN	NN	Number=Sing	5	pobj	_	_
8	attributed	attribute	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	acl	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	M	M	PROPN	NNP	Number=Sing	11	compound	_	_
11	Barr	Barr	PROPN	NNP	Number=Sing	9	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The Harrison cohomology of a commutative algebra is known to coincide with the Andre/Quillen cohomology over a field of characteristic zero but not in prime characteristics.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	Harrison	Harrison	PROPN	NNP	Number=Sing	3	compound	_	_
3	cohomology	cohomology	NOUN	NN	Number=Sing	9	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	commutative	commutative	ADJ	JJ	Degree=Pos	7	amod	_	_
7	algebra	algebra	PROPN	NNP	Number=Sing	4	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	coincide	coincide	VERB	VB	VerbForm=Inf	9	xcomp	_	_
12	with	with	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
14	Andre	Andre	PROPN	NNP	Number=Sing	16	nmod	_	SpaceAfter=No
15	/	/	SYM	SYM	_	16	punct	_	SpaceAfter=No
16	Quillen	Quillen	PROPN	NNP	Number=Sing	17	compound	_	_
17	cohomology	cohomology	NOUN	NN	Number=Sing	12	pobj	_	_
18	over	over	ADP	IN	_	11	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	field	field	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	characteristic	characteristic	ADJ	JJ	Degree=Pos	23	amod	_	_
23	zero	zero	NUM	CD	NumType=Card	21	pobj	_	_
24	but	but	CCONJ	CC	ConjType=Cmp	18	cc	_	_
25	not	not	PART	RB	Polarity=Neg	26	neg	_	_
26	in	in	ADP	IN	_	18	conj	_	_
27	prime	prime	ADJ	JJ	Degree=Pos	28	amod	_	_
28	characteristics	characteristic	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 3
# text = The conjecture is that a modified version of Harrison cohomology, taking into account torsion, always agrees with Andre/Quillen cohomology.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	conjecture	conjecture	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	18	mark	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	modified	modified	ADJ	JJ	Degree=Pos	7	amod	_	_
7	version	version	NOUN	NN	Number=Sing	18	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	Harrison	Harrison	PROPN	NNP	Number=Sing	10	compound	_	_
10	cohomology	cohomology	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
12	taking	take	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	acl	_	_
13	into	into	ADP	IN	_	12	prep	_	_
14	account	account	NOUN	NN	Number=Sing	15	compound	_	_
15	torsion	torsion	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
17	always	always	ADV	RB	_	18	advmod	_	_
18	agrees	agree	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	Andre	Andre	PROPN	NNP	Number=Sing	22	nmod	_	SpaceAfter=No
21	/	/	SYM	SYM	_	22	punct	_	SpaceAfter=No
22	Quillen	Quillen	PROPN	NNP	Number=Sing	23	compound	_	_
23	cohomology	cohomology	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = We give a counterexample.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	counterexample	counterexample	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
5	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 40
# sent_id = 1
# text = The purpose is to give a simple proof that a category is equivalent to a small category if and only if both it and its presheaf category are locally small.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	purpose	purpose	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	give	give	VERB	VB	VerbForm=Inf	3	xcomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	simple	simple	ADJ	JJ	Degree=Pos	8	amod	_	_
8	proof	proof	NOUN	NN	Number=Sing	5	dobj	_	_
9	that	that	SCONJ	IN	_	12	mark	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	category	category	NOUN	NN	Number=Sing	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	acl	_	_
13	equivalent	equivalent	ADJ	JJ	Degree=Pos	12	acomp	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	small	small	ADJ	JJ	Degree=Pos	17	amod	_	_
17	category	category	NOUN	NN	Number=Sing	14	pobj	_	_
18	if	if	SCONJ	IN	_	28	mark	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	only	only	ADV	RB	_	28	advmod	_	_
21	if	if	SCONJ	IN	_	28	mark	_	_
22	both	both	CCONJ	CC	ConjType=Cmp	23	preconj	_	_
23	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	28	nsubj	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	27	poss	_	_
26	presheaf	presheaf	ADJ	JJ	Degree=Pos	27	compound	_	_
27	category	category	NOUN	NN	Number=Sing	23	conj	_	_
28	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	advcl	_	_
29	locally	locally	ADV	RB	_	30	advmod	_	_
30	small	small	ADJ	JJ	Degree=Pos	28	acomp	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 41
# sent_id = 1
# text = We introduce MD - sketches, which are a particular kind of Finite Sum sketches.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	MD	MD	PROPN	NNP	Number=Sing	5	compound	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	sketches	sketch	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	which	which	PRON	WDT	_	8	nsubj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	relcl	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	particular	particular	ADJ	JJ	Degree=Pos	11	amod	_	_
11	kind	kind	NOUN	NN	Number=Sing	8	attr	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	Finite	Finite	PROPN	NNP	Number=Sing	14	compound	_	_
14	Sum	Sum	PROPN	NNP	Number=Sing	15	compound	_	_
15	sketches	sketch	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Two interesting results about MD - sketches are proved.
1	Two	two	NUM	CD	NumType=Card	3	nummod	_	_
2	interesting	interesting	ADJ	JJ	Degree=Pos	3	amod	_	_
3	results	result	NOUN	NNS	Number=Plur	9	nsubjpass	_	_
4	about	about	ADP	IN	_	3	prep	_	_
5	MD	MD	PROPN	NNP	Number=Sing	7	compound	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	sketches	sketch	NOUN	NNS	Number=Plur	4	pobj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 3
# text = First, we show that, given two MD - sketches, it is algorithmically decidable whether their model categories are equivalent.
1	First	first	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	14	mark	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
7	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	prep	_	_
8	two	two	NUM	CD	NumType=Card	11	nummod	_	_
9	MD	MD	PROPN	NNP	Number=Sing	11	compound	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	sketches	sketch	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
13	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
15	algorithmically	algorithmically	ADV	RB	_	16	advmod	_	_
16	decidable	decidable	ADJ	JJ	Degree=Pos	14	acomp	_	_
17	whether	whether	SCONJ	IN	_	21	mark	_	_
18	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	20	poss	_	_
19	model	model	NOUN	NN	Number=Sing	20	compound	_	_
20	categories	category	NOUN	NNS	Number=Plur	21	nsubj	_	_
21	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	ccomp	_	_
22	equivalent	equivalent	ADJ	JJ	Degree=Pos	21	acomp	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = Next we show that data - specifications, as used in database - design and software engineering, can be translated to MD - sketches.
1	Next	next	ADV	RB	_	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	21	mark	_	_
5	data	datum	NOUN	NNS	Number=Plur	7	compound	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	specifications	specification	NOUN	NNS	Number=Plur	21	nsubjpass	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	as	as	SCONJ	IN	_	10	mark	_	_
10	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	advcl	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	database	database	NOUN	NN	Number=Sing	14	nmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	design	design	NOUN	NN	Number=Sing	17	nmod	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	software	software	NOUN	NN	Number=Sing	14	conj	_	_
17	engineering	engineering	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
19	can	can	AUX	MD	VerbForm=Fin	21	aux	_	_
20	be	be	AUX	VB	VerbForm=Inf	21	auxpass	_	_
21	translated	translate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	ccomp	_	_
22	to	to	ADP	IN	_	21	prep	_	_
23	MD	MD	PROPN	NNP	Number=Sing	25	compound	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	sketches	sketch	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = As a corollary, we obtain that equivalence of data - specifications is decidable.
1	As	as	ADP	IN	_	6	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	corollary	corollary	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	DET	DT	Number=Sing|PronType=Dem	8	det	_	_
8	equivalence	equivalence	NOUN	NN	Number=Sing	13	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	data	datum	NOUN	NNS	Number=Plur	12	compound	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	specifications	specification	NOUN	NNS	Number=Plur	9	pobj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
14	decidable	decidable	ADJ	JJ	Degree=Pos	13	acomp	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 42
# sent_id = 1
# text = The Medial rule was first devised as a deduction rule in the Calculus of Structures.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	Medial	medial	ADJ	JJ	Degree=Pos	3	compound	_	_
3	rule	rule	NOUN	NN	Number=Sing	6	nsubjpass	_	_
4	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	6	auxpass	_	_
5	first	first	ADV	RB	_	6	advmod	_	_
6	devised	devise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	as	as	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	deduction	deduction	NOUN	NN	Number=Sing	10	compound	_	_
10	rule	rule	NOUN	NN	Number=Sing	7	pobj	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	Calculus	Calculus	PROPN	NNP	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	Structures	Structures	PROPN	NNP	Number=Sing	14	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper we explore it from the point of view of category theory, as additional structure on a $ * $ - autonomous category.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	explore	explore	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	5	dobj	_	_
7	from	from	ADP	IN	_	5	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	point	point	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	view	view	NOUN	NN	Number=Sing	10	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	category	category	NOUN	NN	Number=Sing	14	compound	_	_
14	theory	theory	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
16	as	as	ADP	IN	_	5	prep	_	_
17	additional	additional	ADJ	JJ	Degree=Pos	18	amod	_	_
18	structure	structure	NOUN	NN	Number=Sing	16	pobj	_	_
19	on	on	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
21	$ * $	$ * $	SYM	$	_	23	advmod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	autonomous	autonomous	ADJ	JJ	Degree=Pos	24	amod	_	_
24	category	category	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = This gives us some insights on the denotational semantics of classical propositional logic, and allows us to construct new models for it, based on suitable generalizations of the theory of coherence spaces.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	2	dative	_	_
4	some	some	DET	DT	_	5	det	_	_
5	insights	insight	NOUN	NNS	Number=Plur	2	dobj	_	_
6	on	on	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	denotational	denotational	ADJ	JJ	Degree=Pos	9	amod	_	_
9	semantics	semantic	NOUN	NNS	Number=Plur	6	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	classical	classical	ADJ	JJ	Degree=Pos	13	amod	_	_
12	propositional	propositional	ADJ	JJ	Degree=Pos	13	amod	_	_
13	logic	logic	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
16	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
17	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
18	to	to	PART	TO	_	19	aux	_	_
19	construct	construct	VERB	VB	VerbForm=Inf	16	ccomp	_	_
20	new	new	ADJ	JJ	Degree=Pos	21	amod	_	_
21	models	model	NOUN	NNS	Number=Plur	19	dobj	_	_
22	for	for	ADP	IN	_	21	prep	_	_
23	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	22	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
25	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	prep	_	_
26	on	on	ADP	IN	_	25	prep	_	_
27	suitable	suitable	ADJ	JJ	Degree=Pos	28	amod	_	_
28	generalizations	generalization	NOUN	NNS	Number=Plur	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	theory	theory	NOUN	NN	Number=Sing	29	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	coherence	coherence	NOUN	NN	Number=Sing	34	compound	_	_
34	spaces	space	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 43
# sent_id = 1
# text = Tilings of rectangles with rectangles, and tileorders (the associated double order structures) are useful as ``templates'' for composition in double categories.
1	Tilings	tiling	NOUN	NNS	Number=Plur	16	nsubj	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	rectangles	rectangle	NOUN	NNS	Number=Plur	2	pobj	_	_
4	with	with	ADP	IN	_	3	prep	_	_
5	rectangles	rectangle	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	1	punct	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	1	cc	_	_
8	tileorders	tileorder	NOUN	NNS	Number=Plur	1	conj	_	_
9	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	8	punct	_	SpaceAfter=No
10	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
11	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
12	double	double	ADJ	JJ	Degree=Pos	13	amod	_	_
13	order	order	NOUN	NN	Number=Sing	14	compound	_	_
14	structures	structure	NOUN	NNS	Number=Plur	8	appos	_	SpaceAfter=No
15	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	8	punct	_	_
16	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
17	useful	useful	ADJ	JJ	Degree=Pos	16	acomp	_	_
18	as	as	ADP	IN	_	17	prep	_	_
19	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	21	punct	_	SpaceAfter=No
20	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	21	punct	_	SpaceAfter=No
21	templates	template	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
22	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	21	punct	_	_
23	for	for	ADP	IN	_	21	prep	_	_
24	composition	composition	NOUN	NN	Number=Sing	23	pobj	_	_
25	in	in	ADP	IN	_	24	prep	_	_
26	double	double	ADJ	JJ	Degree=Pos	27	amod	_	_
27	categories	category	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this context, it is particularly relevant to ask which tilings may be joined together, two rectangles at a time, to form one large rectangle.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	context	context	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	particularly	particularly	ADV	RB	_	8	advmod	_	_
8	relevant	relevant	ADJ	JJ	Degree=Pos	6	acomp	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	ask	ask	VERB	VB	VerbForm=Inf	6	xcomp	_	_
11	which	which	DET	WDT	_	12	det	_	_
12	tilings	tiling	NOUN	NNS	Number=Plur	15	nsubjpass	_	_
13	may	may	AUX	MD	VerbForm=Fin	15	aux	_	_
14	be	be	AUX	VB	VerbForm=Inf	15	auxpass	_	_
15	joined	join	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	ccomp	_	_
16	together	together	ADV	RB	_	15	advmod	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
18	two	two	NUM	CD	NumType=Card	19	nummod	_	_
19	rectangles	rectangle	NOUN	NNS	Number=Plur	6	attr	_	_
20	at	at	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	time	time	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
24	to	to	PART	TO	_	25	aux	_	_
25	form	form	VERB	VB	VerbForm=Inf	6	advcl	_	_
26	one	one	NUM	CD	NumType=Card	28	nummod	_	_
27	large	large	ADJ	JJ	Degree=Pos	28	amod	_	_
28	rectangle	rectangle	NOUN	NN	Number=Sing	25	dobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = We characterize such tilings via forbidden suborders, in a manner analogous to Kuratowski's characterization of planar graphs.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	such	such	ADJ	JJ	Degree=Pos	4	amod	_	_
4	tilings	tiling	NOUN	NNS	Number=Plur	2	dobj	_	_
5	via	via	ADP	IN	_	4	prep	_	_
6	forbidden	forbidden	ADJ	JJ	Degree=Pos	7	amod	_	_
7	suborders	suborder	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
9	in	in	ADP	IN	_	2	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	manner	manner	NOUN	NN	Number=Sing	9	pobj	_	_
12	analogous	analogous	ADJ	JJ	Degree=Pos	11	amod	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	Kuratowski	Kuratowski	PROPN	NNP	Number=Sing	16	poss	_	SpaceAfter=No
15	's	's	PART	POS	_	14	case	_	_
16	characterization	characterization	NOUN	NN	Number=Sing	13	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	planar	planar	ADJ	JJ	Degree=Pos	19	amod	_	_
19	graphs	graph	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 44
# sent_id = 1
# text = We formulate three slightly different notions of oriented singular chain complexes and show that all three are naturally homotopic to ordinary singular chain complexes.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	formulate	formulate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	three	three	NUM	CD	NumType=Card	6	nummod	_	_
4	slightly	slightly	ADV	RB	_	5	advmod	_	_
5	different	different	ADJ	JJ	Degree=Pos	6	amod	_	_
6	notions	notion	NOUN	NNS	Number=Plur	2	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	oriented	orient	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
9	singular	singular	ADJ	JJ	Degree=Pos	11	amod	_	_
10	chain	chain	NOUN	NN	Number=Sing	11	compound	_	_
11	complexes	complex	NOUN	NNS	Number=Plur	7	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
13	show	show	VERB	VB	VerbForm=Inf	2	conj	_	_
14	that	that	SCONJ	IN	_	17	mark	_	_
15	all	all	DET	DT	_	16	det	_	_
16	three	three	NUM	CD	NumType=Card	17	nsubj	_	_
17	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
18	naturally	naturally	ADV	RB	_	17	advmod	_	_
19	homotopic	homotopic	ADJ	JJ	Degree=Pos	17	acomp	_	_
20	to	to	ADP	IN	_	17	prep	_	_
21	ordinary	ordinary	ADJ	JJ	Degree=Pos	24	amod	_	_
22	singular	singular	ADJ	JJ	Degree=Pos	24	amod	_	_
23	chain	chain	NOUN	NN	Number=Sing	24	compound	_	_
24	complexes	complex	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 45
# sent_id = 1
# text = In 1975, Brown constructed a functor $ cal P $ which carries the tower of fundamental groups of the end of a (nice) space to the Brown - Grossman fundamental group.
1	In	in	ADP	IN	_	5	prep	_	_
2	1975	1975	NUM	CD	NumType=Card	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	Brown	Brown	PROPN	NNP	Number=Sing	5	nsubj	_	_
5	constructed	construct	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	functor	functor	NOUN	NN	Number=Sing	8	compound	_	_
8	$ cal P $	$ cal p $	SYM	$	_	5	dobj	_	_
9	which	which	PRON	WDT	_	10	nsubj	_	_
10	carries	carry	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	advcl	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	tower	tower	NOUN	NN	Number=Sing	10	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	fundamental	fundamental	ADJ	JJ	Degree=Pos	15	amod	_	_
15	groups	group	NOUN	NNS	Number=Plur	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	end	end	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
21	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
22	nice	nice	ADJ	JJ	Degree=Pos	24	amod	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	24	punct	_	_
24	space	space	NOUN	NN	Number=Sing	19	pobj	_	_
25	to	to	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
27	Brown	Brown	PROPN	NNP	Number=Sing	29	nmod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	Grossman	Grossman	PROPN	NNP	Number=Sing	31	nmod	_	_
30	fundamental	fundamental	ADJ	JJ	Degree=Pos	31	amod	_	_
31	group	group	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this work, we study this functor and its extensions and analogues defined for pro - sets, pro - pointed sets, pro - groups and pro - abelian groups.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	work	work	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	this	this	DET	DT	Number=Sing|PronType=Dem	8	det	_	_
8	functor	functor	NOUN	NN	Number=Sing	6	dobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	11	poss	_	_
11	extensions	extension	NOUN	NNS	Number=Plur	8	conj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	analogues	analogue	NOUN	NNS	Number=Plur	11	conj	_	_
14	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
15	for	for	ADP	IN	_	14	prep	_	_
16	pro	pro	ADJ	JJ	Degree=Pos	18	amod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	sets	set	NOUN	NNS	Number=Plur	23	nmod	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
20	pro	pro	ADJ	JJ	Degree=Pos	22	advmod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	pointed	point	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	amod	_	_
23	sets	set	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
25	pro	pro	ADJ	JJ	Degree=Pos	27	amod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	groups	group	NOUN	NNS	Number=Plur	23	conj	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
29	pro	pro	ADJ	JJ	Degree=Pos	31	amod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	abelian	abelian	ADJ	JJ	Degree=Pos	32	amod	_	_
32	groups	group	NOUN	NNS	Number=Plur	27	conj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = The new versions of the $ cal P $ functor are provided with more algebraic structure.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	new	new	ADJ	JJ	Degree=Pos	3	amod	_	_
3	versions	version	NOUN	NNS	Number=Plur	9	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	$ cal P $	$ cal p $	SYM	$	_	7	nmod	_	_
7	functor	functor	NOUN	NN	Number=Sing	4	pobj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	provided	provide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	more	more	ADJ	JJR	Degree=Cmp	12	advmod	_	_
12	algebraic	algebraic	ADJ	JJ	Degree=Pos	13	amod	_	_
13	structure	structure	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 4
# text = Examples given in the paper prove that in general the $ cal P $ functors are not faithful, however, one of our main results establishes that the restrictions of the corresponding $ cal P $ functors to the full subcategories of towers are faithful.
1	Examples	example	NOUN	NNS	Number=Plur	6	nsubj	_	_
2	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	1	acl	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	paper	paper	NOUN	NN	Number=Sing	3	pobj	_	_
6	prove	prove	VERB	VB	VerbForm=Inf	0	ROOT	_	_
7	that	that	SCONJ	IN	_	13	mark	_	_
8	in	in	ADP	IN	_	13	prep	_	_
9	general	general	ADJ	JJ	Degree=Pos	8	amod	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	$ cal P $	$ cal p $	SYM	$	_	12	nummod	_	_
12	functors	functor	NOUN	NNS	Number=Plur	13	nsubj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
14	not	not	PART	RB	Polarity=Neg	13	neg	_	_
15	faithful	faithful	ADJ	JJ	Degree=Pos	13	acomp	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
17	however	however	ADV	RB	_	13	advmod	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
19	one	one	NUM	CD	NumType=Card	24	nsubj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	23	poss	_	_
22	main	main	ADJ	JJ	Degree=Pos	23	amod	_	_
23	results	result	NOUN	NNS	Number=Plur	20	pobj	_	_
24	establishes	establish	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
25	that	that	SCONJ	IN	_	39	mark	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	restrictions	restriction	NOUN	NNS	Number=Plur	39	nsubj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
30	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	32	amod	_	_
31	$ cal P $	$ cal p $	SYM	$	_	32	nmod	_	_
32	functors	functor	NOUN	NNS	Number=Plur	28	pobj	_	_
33	to	to	ADP	IN	_	27	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
35	full	full	ADJ	JJ	Degree=Pos	36	amod	_	_
36	subcategories	subcategorie	NOUN	NNS	Number=Plur	33	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	towers	tower	NOUN	NNS	Number=Plur	37	pobj	_	_
39	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	24	ccomp	_	_
40	faithful	faithful	ADJ	JJ	Degree=Pos	39	acomp	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = We also prove that the restrictions of the $ cal P $ functors to the corresponding full subcategories of finitely generated towers are also full.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	20	mark	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	restrictions	restriction	NOUN	NNS	Number=Plur	20	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	$ cal P $	$ cal p $	SYM	$	_	10	nmod	_	_
10	functors	functor	NOUN	NNS	Number=Plur	7	pobj	_	_
11	to	to	ADP	IN	_	6	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
13	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	amod	_	_
14	full	full	ADJ	JJ	Degree=Pos	15	amod	_	_
15	subcategories	subcategorie	NOUN	NNS	Number=Plur	11	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	finitely	finitely	ADV	RB	_	18	advmod	_	_
18	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
19	towers	tower	NOUN	NNS	Number=Plur	16	pobj	_	_
20	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
21	also	also	ADV	RB	_	20	advmod	_	_
22	full	full	ADJ	JJ	Degree=Pos	20	acomp	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = Consequently, in these cases, the towers of objects in the categories of sets, pointed sets, groups and abelian groups, can be replaced by adequate algebraic models ( $ M $ - sets, $ M $ - pointed sets, near - modules and modules.)
1	Consequently	consequently	ADV	RB	_	27	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
3	in	in	ADP	IN	_	27	prep	_	_
4	these	these	DET	DT	Number=Plur|PronType=Dem	5	det	_	_
5	cases	case	NOUN	NNS	Number=Plur	3	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	towers	tower	NOUN	NNS	Number=Plur	27	nsubjpass	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	objects	object	NOUN	NNS	Number=Plur	9	pobj	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	sets	set	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	pointed	pointed	ADJ	JJ	Degree=Pos	18	amod	_	_
18	sets	set	NOUN	NNS	Number=Plur	15	conj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	groups	group	NOUN	NNS	Number=Plur	18	conj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	abelian	abelian	ADJ	JJ	Degree=Pos	23	compound	_	_
23	groups	group	NOUN	NNS	Number=Plur	20	conj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
25	can	can	AUX	MD	VerbForm=Fin	27	aux	_	_
26	be	be	AUX	VB	VerbForm=Inf	27	auxpass	_	_
27	replaced	replace	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
28	by	by	ADP	IN	_	27	agent	_	_
29	adequate	adequate	ADJ	JJ	Degree=Pos	31	amod	_	_
30	algebraic	algebraic	ADJ	JJ	Degree=Pos	31	amod	_	_
31	models	model	NOUN	NNS	Number=Plur	28	pobj	_	_
32	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	31	punct	_	_
33	$ M $	$ m $	SYM	$	_	35	nmod	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	sets	set	NOUN	NNS	Number=Plur	31	appos	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
37	$ M $	$ m $	SYM	$	_	39	advmod	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	pointed	point	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	40	amod	_	_
40	sets	set	NOUN	NNS	Number=Plur	35	conj	_	SpaceAfter=No
41	,	,	PUNCT	,	PunctType=Comm	40	punct	_	_
42	near	near	ADJ	JJ	Degree=Pos	44	amod	_	_
43	-	-	PUNCT	HYPH	PunctType=Dash	44	punct	_	_
44	modules	module	NOUN	NNS	Number=Plur	40	conj	_	_
45	and	and	CCONJ	CC	ConjType=Cmp	44	cc	_	_
46	modules	module	NOUN	NNS	Number=Plur	44	conj	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	27	punct	_	SpaceAfter=No
48	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	27	punct	_	SpaceAfter=No

# sent_id = 7
# text = The article also contains the construction of left adjoints for the $ cal P $ functors.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	article	article	NOUN	NN	Number=Sing	4	nsubj	_	_
3	also	also	ADV	RB	_	4	advmod	_	_
4	contains	contain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	construction	construction	NOUN	NN	Number=Sing	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	left	left	ADJ	JJ	Degree=Pos	9	amod	_	_
9	adjoints	adjoint	NOUN	NNS	Number=Plur	7	pobj	_	_
10	for	for	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	$ cal P $	$ cal p $	SYM	$	_	13	nmod	_	_
13	functors	functor	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 46
# sent_id = 1
# text = Free regular and exact completions of categories with various ranks of weak limits are presented as subcategories of presheaf categories.
1	Free	free	ADJ	JJ	Degree=Pos	5	amod	_	_
2	regular	regular	ADJ	JJ	Degree=Pos	5	amod	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	exact	exact	ADJ	JJ	Degree=Pos	2	conj	_	_
5	completions	completion	NOUN	NNS	Number=Plur	15	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
8	with	with	ADP	IN	_	5	prep	_	_
9	various	various	ADJ	JJ	Degree=Pos	10	amod	_	_
10	ranks	rank	NOUN	NNS	Number=Plur	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	weak	weak	ADJ	JJ	Degree=Pos	13	amod	_	_
13	limits	limit	NOUN	NNS	Number=Plur	11	pobj	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
16	as	as	ADP	IN	_	15	prep	_	_
17	subcategories	subcategorie	NOUN	NNS	Number=Plur	16	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	presheaf	presheaf	ADJ	JJ	Degree=Pos	20	amod	_	_
20	categories	category	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 2
# text = Their universal properties can then be derived with standard techniques as used in duality theory.
1	Their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	3	poss	_	_
2	universal	universal	ADJ	JJ	Degree=Pos	3	amod	_	_
3	properties	property	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
4	can	can	AUX	MD	VerbForm=Fin	7	aux	_	_
5	then	then	ADV	RB	PronType=Dem	7	advmod	_	_
6	be	be	AUX	VB	VerbForm=Inf	7	auxpass	_	_
7	derived	derive	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	with	with	ADP	IN	_	7	prep	_	_
9	standard	standard	ADJ	JJ	Degree=Pos	10	amod	_	_
10	techniques	technique	NOUN	NNS	Number=Plur	8	pobj	_	_
11	as	as	SCONJ	IN	_	12	mark	_	_
12	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	advcl	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	duality	duality	NOUN	NN	Number=Sing	15	compound	_	_
15	theory	theory	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 47
# sent_id = 1
# text = For an adjoint string $ V - | W - | X - | Y : B - - > C $ , with $ Y $ fully faithful, it is frequently, but not always, the case that the composite $ VY $ underlies an idempotent monad.
1	For	for	ADP	IN	_	13	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	adjoint	adjoint	NOUN	NN	Number=Sing	4	compound	_	_
4	string	string	NOUN	NN	Number=Sing	1	pobj	_	_
5	$ V - | W - | X - | Y : B - - > C $	$ v - | w - | x - | y : b - - > c $	SYM	$	_	1	dep	_	_
6	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
7	with	with	ADP	IN	_	13	prep	_	_
8	$ Y $	$ y $	SYM	$	_	10	neg	_	_
9	fully	fully	ADV	RB	_	10	advmod	_	_
10	faithful	faithful	ADJ	JJ	Degree=Pos	7	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
12	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	13	nsubj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	frequently	frequently	ADV	RB	_	13	advmod	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
16	but	but	CCONJ	CC	ConjType=Cmp	13	cc	_	_
17	not	not	PART	RB	Polarity=Neg	18	neg	_	_
18	always	always	ADV	RB	_	13	conj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	case	case	NOUN	NN	Number=Sing	13	attr	_	_
22	that	that	SCONJ	IN	_	26	mark	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	composite	composite	ADJ	JJ	Degree=Pos	25	amod	_	_
25	$ VY $	$ vy $	SYM	$	_	26	nsubj	_	_
26	underlies	underlie	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	21	acl	_	_
27	an	an	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	idempotent	idempotent	ADJ	JJ	Degree=Pos	29	amod	_	_
29	monad	monad	NOUN	NNS	Number=Plur	26	dobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 2
# text = When it does, we call the string distributive.
1	When	when	SCONJ	WRB	_	3	advmod	_	_
2	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubj	_	_
3	does	do	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	advcl	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	string	string	NOUN	NN	Number=Sing	9	compound	_	_
9	distributive	distributive	NOUN	NN	Number=Sing	6	oprd	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also study shorter and longer `distributive' adjoint strings and how to generate them.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	shorter	short	ADJ	JJR	Degree=Cmp	11	amod	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	longer	long	ADV	RBR	Degree=Cmp	8	advmod	_	_
7	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	8	punct	_	SpaceAfter=No
8	distributive	distributive	ADJ	JJ	Degree=Pos	11	amod	_	SpaceAfter=No
9	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	11	punct	_	_
10	adjoint	adjoint	NOUN	NN	Number=Sing	11	compound	_	_
11	strings	string	NOUN	NNS	Number=Plur	3	dobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	how	how	SCONJ	WRB	_	15	advmod	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	generate	generate	VERB	VB	VerbForm=Inf	11	conj	_	_
16	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	15	dobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = These provide a new construction of the simplicial 2 - category, $ Delta $ .
1	These	these	PRON	DT	Number=Plur|PronType=Dem	2	nsubj	_	_
2	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	new	new	ADJ	JJ	Degree=Pos	5	amod	_	_
5	construction	construction	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
8	simplicial	simplicial	ADJ	JJ	Degree=Pos	11	amod	_	_
9	2	2	NUM	CD	NumType=Card	11	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	category	category	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	$ Delta $	$ delta $	SYM	$	_	2	dep	_	_
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 48
# sent_id = 1
# text = We prove how any (elementary) topos may be reconstructed from the data of two complemented subtoposes together with a pair of left exact ``glueing functors''.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	how	how	SCONJ	WRB	_	11	advmod	_	_
4	any	any	DET	DT	_	8	det	_	_
5	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	8	punct	_	SpaceAfter=No
6	elementary	elementary	ADJ	JJ	Degree=Pos	8	amod	_	SpaceAfter=No
7	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	8	punct	_	_
8	topos	topo	NOUN	NNS	Number=Plur	11	nsubjpass	_	_
9	may	may	AUX	MD	VerbForm=Fin	11	aux	_	_
10	be	be	AUX	VB	VerbForm=Inf	11	auxpass	_	_
11	reconstructed	reconstruct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
12	from	from	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	data	datum	NOUN	NNS	Number=Plur	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	two	two	NUM	CD	NumType=Card	18	nummod	_	_
17	complemented	complement	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
18	subtoposes	subtopose	NOUN	NNS	Number=Plur	15	pobj	_	_
19	together	together	ADV	RB	_	20	advmod	_	_
20	with	with	ADP	IN	_	11	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	pair	pair	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	left	left	ADJ	JJ	Degree=Pos	25	amod	_	_
25	exact	exact	ADJ	JJ	Degree=Pos	23	pobj	_	_
26	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	11	punct	_	SpaceAfter=No
27	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	11	punct	_	SpaceAfter=No
28	glueing	glue	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	advcl	_	_
29	functors	functor	NOUN	NNS	Number=Plur	28	dobj	_	SpaceAfter=No
30	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	28	punct	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This generalizes the classical glueing theorem for toposes, which deals with the special case of an open subtopos and its closed complement.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	classical	classical	ADJ	JJ	Degree=Pos	5	amod	_	_
5	glueing	glueing	NOUN	NN	Number=Sing	2	dobj	_	_
6	theorem	theorem	ADJ	JJ	Degree=Pos	5	acl	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	toposes	topos	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
10	which	which	PRON	WDT	_	11	nsubj	_	_
11	deals	deal	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	relcl	_	_
12	with	with	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	special	special	ADJ	JJ	Degree=Pos	15	amod	_	_
15	case	case	NOUN	NN	Number=Sing	12	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	an	an	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	open	open	ADJ	JJ	Degree=Pos	19	amod	_	_
19	subtopos	subtopos	NOUN	NN	Number=Sing	16	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	23	poss	_	_
22	closed	closed	ADJ	JJ	Degree=Pos	23	amod	_	_
23	complement	complement	NOUN	NN	Number=Sing	19	conj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Our glueing analysis applies in a particularly simple form to a locally closed subtopos and its complement, and one of the important properties (prolongation by zero for abelian groups) can be succinctly described in terms of it.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	3	poss	_	_
2	glueing	glue	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	amod	_	_
3	analysis	analysis	NOUN	NN	Number=Sing	4	nsubj	_	_
4	applies	apply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	particularly	particularly	ADV	RB	_	8	advmod	_	_
8	simple	simple	ADJ	JJ	Degree=Pos	9	amod	_	_
9	form	form	NOUN	NN	Number=Sing	5	pobj	_	_
10	to	to	ADP	IN	_	4	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
12	locally	locally	ADV	RB	_	13	advmod	_	_
13	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
14	subtopos	subtopos	NOUN	NN	Number=Sing	10	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	17	poss	_	_
17	complement	complement	NOUN	NN	Number=Sing	14	conj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
20	one	one	NUM	CD	NumType=Card	36	nsubjpass	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	important	important	ADJ	JJ	Degree=Pos	24	amod	_	_
24	properties	property	NOUN	NNS	Number=Plur	21	pobj	_	_
25	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
26	prolongation	prolongation	NOUN	NN	Number=Sing	24	appos	_	_
27	by	by	ADP	IN	_	26	prep	_	_
28	zero	zero	NUM	CD	NumType=Card	27	pobj	_	_
29	for	for	ADP	IN	_	26	prep	_	_
30	abelian	abelian	ADJ	JJ	Degree=Pos	31	compound	_	_
31	groups	group	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
32	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	24	punct	_	_
33	can	can	AUX	MD	VerbForm=Fin	36	aux	_	_
34	be	be	AUX	VB	VerbForm=Inf	36	auxpass	_	_
35	succinctly	succinctly	ADV	RB	_	36	advmod	_	_
36	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	conj	_	_
37	in	in	ADP	IN	_	36	prep	_	_
38	terms	term	NOUN	NNS	Number=Plur	37	pobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	39	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	36	punct	_	SpaceAfter=No

# doc_id = 49
# sent_id = 1
# text = Locally finitely presentable categories are known to be precisely the categories of models of essentially algebraic theories, that is, categories of partial algebras whose domains of definition are determined by equations in total operations.
1	Locally	locally	ADV	RB	_	2	advmod	_	_
2	finitely	finitely	ADV	RB	_	4	amod	_	_
3	presentable	presentable	ADJ	JJ	Degree=Pos	4	amod	_	_
4	categories	category	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	be	be	AUX	VB	VerbForm=Inf	6	xcomp	_	_
9	precisely	precisely	ADV	RB	_	11	advmod	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	categories	category	NOUN	NNS	Number=Plur	8	attr	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	models	model	NOUN	NNS	Number=Plur	12	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	essentially	essentially	ADV	RB	_	16	advmod	_	_
16	algebraic	algebraic	ADJ	JJ	Degree=Pos	17	amod	_	_
17	theories	theory	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
19	that	that	ADV	RB	_	20	advmod	_	_
20	is	is	ADV	RB	_	22	advmod	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
22	categories	category	NOUN	NNS	Number=Plur	8	attr	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	partial	partial	ADJ	JJ	Degree=Pos	25	amod	_	_
25	algebras	algebra	NOUN	NNS	Number=Plur	23	pobj	_	_
26	whose	whose	DET	WP$	Poss=Yes	27	poss	_	_
27	domains	domain	NOUN	NNS	Number=Plur	31	nsubjpass	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	definition	definition	NOUN	NN	Number=Sing	28	pobj	_	_
30	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	31	auxpass	_	_
31	determined	determine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	relcl	_	_
32	by	by	ADP	IN	_	31	agent	_	_
33	equations	equation	NOUN	NNS	Number=Plur	32	pobj	_	_
34	in	in	ADP	IN	_	33	prep	_	_
35	total	total	ADJ	JJ	Degree=Pos	36	amod	_	_
36	operations	operation	NOUN	NNS	Number=Plur	34	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = Here we show an analogous description of locally finitely multipresentable categories.
1	Here	here	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	analogous	analogous	ADJ	JJ	Degree=Pos	6	amod	_	_
6	description	description	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	locally	locally	ADV	RB	_	11	advmod	_	_
9	finitely	finitely	ADV	RB	_	11	amod	_	_
10	multipresentable	multipresentable	ADJ	JJ	Degree=Pos	11	amod	_	_
11	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also prove that locally finitely multipresentable categories are precisely categories of models of sketches with finite limit and countable coproduct specifications, and we present an example of a locally finitely multipresentable category not sketchable by a sketch with finite limit and finite colimit specifications.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	9	mark	_	_
5	locally	locally	ADV	RB	_	8	advmod	_	_
6	finitely	finitely	ADJ	JJ	Degree=Pos	8	amod	_	_
7	multipresentable	multipresentable	ADJ	JJ	Degree=Pos	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
10	precisely	precisely	ADV	RB	_	11	advmod	_	_
11	categories	category	NOUN	NNS	Number=Plur	9	attr	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	models	model	NOUN	NNS	Number=Plur	12	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	sketches	sketch	NOUN	NNS	Number=Plur	14	pobj	_	_
16	with	with	ADP	IN	_	11	prep	_	_
17	finite	finite	ADJ	JJ	Degree=Pos	18	compound	_	_
18	limit	limit	NOUN	NN	Number=Sing	16	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	countable	countable	ADJ	JJ	Degree=Pos	22	amod	_	_
21	coproduct	coproduct	NOUN	NN	Number=Sing	22	compound	_	_
22	specifications	specification	NOUN	NNS	Number=Plur	18	conj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
25	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	26	nsubj	_	_
26	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	9	conj	_	_
27	an	an	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	example	example	NOUN	NN	Number=Sing	26	dobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
31	locally	locally	ADV	RB	_	32	advmod	_	_
32	finitely	finitely	ADV	RB	_	34	amod	_	_
33	multipresentable	multipresentable	ADJ	JJ	Degree=Pos	34	amod	_	_
34	category	category	NOUN	NN	Number=Sing	29	pobj	_	_
35	not	not	PART	RB	Polarity=Neg	36	neg	_	_
36	sketchable	sketchable	ADJ	JJ	Degree=Pos	34	acl	_	_
37	by	by	ADP	IN	_	36	agent	_	_
38	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
39	sketch	sketch	NOUN	NN	Number=Sing	37	pobj	_	_
40	with	with	ADP	IN	_	39	prep	_	_
41	finite	finite	ADJ	JJ	Degree=Pos	42	compound	_	_
42	limit	limit	NOUN	NN	Number=Sing	40	pobj	_	_
43	and	and	CCONJ	CC	ConjType=Cmp	42	cc	_	_
44	finite	finite	ADJ	JJ	Degree=Pos	45	amod	_	_
45	colimit	colimit	NOUN	NN	Number=Sing	46	compound	_	_
46	specifications	specification	NOUN	NNS	Number=Plur	42	conj	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	26	punct	_	SpaceAfter=No

# doc_id = 50
# sent_id = 1
# text = Some sufficient conditions for finiteness of a generalized non - abelian tensor product of groups are established extending Ellis' result for compatible actions.
1	Some	some	DET	DT	_	3	det	_	_
2	sufficient	sufficient	ADJ	JJ	Degree=Pos	3	amod	_	_
3	conditions	condition	NOUN	NNS	Number=Plur	17	nsubjpass	_	_
4	for	for	ADP	IN	_	3	prep	_	_
5	finiteness	finiteness	NOUN	NN	Number=Sing	4	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
8	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
9	non	non	PROPN	NNP	Number=Sing	11	amod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	abelian	abelian	ADJ	JJ	Degree=Pos	13	amod	_	_
12	tensor	tensor	NOUN	NN	Number=Sing	13	compound	_	_
13	product	product	NOUN	NN	Number=Sing	6	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	groups	group	NOUN	NNS	Number=Plur	14	pobj	_	_
16	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	17	auxpass	_	_
17	established	establish	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
18	extending	extend	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	advcl	_	_
19	Ellis	Ellis	PROPN	NNP	Number=Sing	21	poss	_	SpaceAfter=No
20	'	'	PART	POS	_	19	case	_	_
21	result	result	NOUN	NN	Number=Sing	18	dobj	_	_
22	for	for	ADP	IN	_	21	prep	_	_
23	compatible	compatible	ADJ	JJ	Degree=Pos	24	amod	_	_
24	actions	action	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# doc_id = 51
# sent_id = 1
# text = We take another look at the Chu construction and show how to simplify it by looking at it as a module category in a trivial Chu category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	take	take	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	another	another	DET	DT	_	4	det	_	_
4	look	look	NOUN	NN	Number=Sing	2	dobj	_	_
5	at	at	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	Chu	Chu	PROPN	NNP	Number=Sing	8	compound	_	_
8	construction	construction	NOUN	NN	Number=Sing	5	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
10	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
11	how	how	SCONJ	WRB	_	13	advmod	_	_
12	to	to	PART	TO	_	13	aux	_	_
13	simplify	simplify	VERB	VB	VerbForm=Inf	10	xcomp	_	_
14	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	13	dobj	_	_
15	by	by	ADP	IN	_	13	prep	_	_
16	looking	look	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	pcomp	_	_
17	at	at	ADP	IN	_	16	prep	_	_
18	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	17	pobj	_	_
19	as	as	ADP	IN	_	16	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	module	module	NOUN	NN	Number=Sing	22	compound	_	_
22	category	category	NOUN	NN	Number=Sing	19	pobj	_	_
23	in	in	ADP	IN	_	22	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
25	trivial	trivial	ADJ	JJ	Degree=Pos	27	amod	_	_
26	Chu	Chu	PROPN	NNP	Number=Sing	27	compound	_	_
27	category	category	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This simplifies the construction substantially, especially in the case of a non - symmetric biclosed monoidal category.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	simplifies	simplify	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	construction	construction	NOUN	NN	Number=Sing	2	dobj	_	_
5	substantially	substantially	ADV	RB	_	2	advmod	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
7	especially	especially	ADV	RB	_	8	advmod	_	_
8	in	in	ADP	IN	_	2	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	case	case	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
13	non	non	ADJ	JJ	Degree=Pos	15	amod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	symmetric	symmetric	ADJ	JJ	Degree=Pos	18	amod	_	_
16	biclosed	biclosed	ADJ	JJ	Degree=Pos	18	amod	_	_
17	monoidal	monoidal	ADJ	JJ	Degree=Pos	18	amod	_	_
18	category	category	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also show that if the original category is accessible, then for any of a large class of ``polynomial - like'' functors, the category of coalgebras has cofree objects.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	32	mark	_	_
5	if	if	SCONJ	IN	_	9	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	original	original	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	9	nsubj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	32	advcl	_	_
10	accessible	accessible	ADJ	JJ	Degree=Pos	9	acomp	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
12	then	then	ADV	RB	PronType=Dem	13	advmod	_	_
13	for	for	ADP	IN	_	32	prep	_	_
14	any	any	PRON	DT	_	13	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	large	large	ADJ	JJ	Degree=Pos	18	amod	_	_
18	class	class	NOUN	NN	Number=Sing	15	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	19	punct	_	SpaceAfter=No
21	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	SpaceAfter=No
22	polynomial	polynomial	ADJ	JJ	Degree=Pos	24	amod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	like	like	ADJ	JJ	Degree=Pos	26	amod	_	SpaceAfter=No
25	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	26	punct	_	_
26	functors	functor	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	category	category	NOUN	NN	Number=Sing	32	nsubj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	coalgebras	coalgebras	PROPN	NNP	Number=Sing	30	pobj	_	_
32	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
33	cofree	cofree	ADJ	JJ	Degree=Pos	34	amod	_	_
34	objects	object	NOUN	NNS	Number=Plur	32	dobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 52
# sent_id = 1
# text = We obtain some explicit calculations of crossed $ Q $ - modules induced from a crossed module over a normal subgroup $ P $ of $ Q $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	some	some	DET	DT	_	5	det	_	_
4	explicit	explicit	ADJ	JJ	Degree=Pos	5	amod	_	_
5	calculations	calculation	NOUN	NNS	Number=Plur	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
8	$ Q $	$ q $	SYM	$	_	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	modules	module	NOUN	NNS	Number=Plur	6	pobj	_	_
11	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acl	_	_
12	from	from	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	crossed	crossed	ADJ	JJ	Degree=Pos	15	amod	_	_
15	module	module	NOUN	NN	Number=Sing	12	pobj	_	_
16	over	over	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	normal	normal	ADJ	JJ	Degree=Pos	19	amod	_	_
19	subgroup	subgroup	NOUN	NN	Number=Sing	16	pobj	_	_
20	$ P $	$ p $	SYM	$	_	19	appos	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	$ Q $	$ q $	SYM	$	_	21	pobj	_	_
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = By virtue of theorems of Brown and Higgins, this enables the computation of the homotopy 2 - types and second homotopy modules of certain homotopy pushouts of maps of classifying spaces of discrete groups.
1	By	by	ADP	IN	_	11	prep	_	_
2	virtue	virtue	NOUN	NN	Number=Sing	1	pobj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	theorems	theorem	NOUN	NNS	Number=Plur	3	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	Brown	Brown	PROPN	NNP	Number=Sing	5	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	Higgins	Higgins	PROPN	NNP	Number=Sing	6	conj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
10	this	this	PRON	DT	Number=Sing|PronType=Dem	11	nsubj	_	_
11	enables	enable	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	computation	computation	NOUN	NN	Number=Sing	11	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	homotopy	homotopy	NOUN	NN	Number=Sing	14	pobj	_	_
17	2	2	NUM	CD	NumType=Card	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	types	type	NOUN	NNS	Number=Plur	16	appos	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	second	second	ADJ	JJ	Degree=Pos	23	amod	_	_
22	homotopy	homotopy	NOUN	NN	Number=Sing	23	compound	_	_
23	modules	module	NOUN	NNS	Number=Plur	19	conj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	certain	certain	ADJ	JJ	Degree=Pos	27	amod	_	_
26	homotopy	homotopy	NOUN	NN	Number=Sing	27	compound	_	_
27	pushouts	pushout	NOUN	NNS	Number=Plur	24	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	maps	map	NOUN	NNS	Number=Plur	28	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	classifying	classify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	30	pcomp	_	_
32	spaces	space	NOUN	NNS	Number=Plur	31	dobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	discrete	discrete	ADJ	JJ	Degree=Pos	35	amod	_	_
35	groups	group	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# doc_id = 53
# sent_id = 1
# text = This note applies techniques we have developed to study coherence in monoidal categories with two tensors, corresponding to the tensor - par fragment of linear logic, to several new situations, including Hyland and de Paiva's Full Intuitionistic Linear Logic (FILL), and Lambek's Bilinear Logic (BILL).
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	note	note	NOUN	NN	Number=Sing	3	nsubj	_	_
3	applies	apply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	techniques	technique	NOUN	NNS	Number=Plur	3	dobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
6	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	aux	_	_
7	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	relcl	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	study	study	VERB	VB	VerbForm=Inf	7	xcomp	_	_
10	coherence	coherence	NOUN	NN	Number=Sing	9	dobj	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	monoidal	monoidal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
14	with	with	ADP	IN	_	9	prep	_	_
15	two	two	NUM	CD	NumType=Card	16	nummod	_	_
16	tensors	tensor	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
18	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	advcl	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
21	tensor	tensor	NOUN	NN	Number=Sing	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	par	par	NOUN	NN	Number=Sing	24	compound	_	_
24	fragment	fragment	NOUN	NN	Number=Sing	19	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	linear	linear	ADJ	JJ	Degree=Pos	27	amod	_	_
27	logic	logic	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
29	to	to	ADP	IN	_	18	prep	_	_
30	several	several	ADJ	JJ	Degree=Pos	32	amod	_	_
31	new	new	ADJ	JJ	Degree=Pos	32	amod	_	_
32	situations	situation	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
34	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	32	prep	_	_
35	Hyland	Hyland	PROPN	NNP	Number=Sing	34	pobj	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
37	de	de	PROPN	NNP	Number=Sing	38	compound	_	_
38	Paiva	Paiva	PROPN	NNP	Number=Sing	43	poss	_	SpaceAfter=No
39	's	's	PART	POS	_	38	case	_	_
40	Full	Full	PROPN	NNP	Number=Sing	43	amod	_	_
41	Intuitionistic	Intuitionistic	PROPN	NNP	Number=Sing	43	compound	_	_
42	Linear	Linear	PROPN	NNP	Number=Sing	43	compound	_	_
43	Logic	Logic	PROPN	NNP	Number=Sing	35	conj	_	_
44	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	43	punct	_	SpaceAfter=No
45	FILL	FILL	PROPN	NNP	Number=Sing	43	appos	_	SpaceAfter=No
46	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	43	punct	_	SpaceAfter=No
47	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
48	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
49	Lambek	Lambek	PROPN	NNP	Number=Sing	52	poss	_	SpaceAfter=No
50	's	's	PART	POS	_	49	case	_	_
51	Bilinear	Bilinear	PROPN	NNP	Number=Sing	52	compound	_	_
52	Logic	Logic	PROPN	NNP	Number=Sing	3	conj	_	_
53	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	52	punct	_	SpaceAfter=No
54	BILL	BILL	PROPN	NNP	Number=Sing	52	appos	_	SpaceAfter=No
55	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	52	punct	_	SpaceAfter=No
56	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = Note that the latter is a noncommutative logic; we also consider the noncommutative version of FILL.
1	Note	note	VERB	VB	VerbForm=Inf	12	ccomp	_	_
2	that	that	SCONJ	IN	_	5	mark	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	latter	latter	NOUN	NN	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	1	ccomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	noncommutative	noncommutative	ADJ	JJ	Degree=Pos	8	amod	_	_
8	logic	logic	NOUN	NN	Number=Sing	5	attr	_	SpaceAfter=No
9	;	;	PUNCT	:	_	12	punct	_	_
10	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	12	nsubj	_	_
11	also	also	ADV	RB	_	12	advmod	_	_
12	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	noncommutative	noncommutative	ADJ	JJ	Degree=Pos	15	amod	_	_
15	version	version	NOUN	NN	Number=Sing	12	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	FILL	FILL	PROPN	NNP	Number=Sing	16	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 3
# text = The essential difference between FILL and BILL lies in requiring that a certain tensorial strength be an isomorphism.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	essential	essential	ADJ	JJ	Degree=Pos	3	amod	_	_
3	difference	difference	NOUN	NN	Number=Sing	8	nsubj	_	_
4	between	between	ADP	IN	_	3	prep	_	_
5	FILL	FILL	PROPN	NNP	Number=Sing	4	pobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	BILL	BILL	PROPN	NNP	Number=Sing	5	conj	_	_
8	lies	lie	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	requiring	require	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	pcomp	_	_
11	that	that	SCONJ	IN	_	16	mark	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	certain	certain	ADJ	JJ	Degree=Pos	15	amod	_	_
14	tensorial	tensorial	ADJ	JJ	Degree=Pos	15	amod	_	_
15	strength	strength	NOUN	NN	Number=Sing	16	nsubj	_	_
16	be	be	AUX	VB	VerbForm=Inf	10	ccomp	_	_
17	an	an	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	isomorphism	isomorphism	NOUN	NN	Number=Sing	16	attr	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 4
# text = In any FILL category, it is possible to isolate a full subcategory of objects (the ``nucleus'') for which this transformation is an isomorphism.
1	In	in	ADP	IN	_	7	prep	_	_
2	any	any	DET	DT	_	4	det	_	_
3	FILL	FILL	PROPN	NNP	Number=Sing	4	compound	_	_
4	category	category	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	possible	possible	ADJ	JJ	Degree=Pos	7	acomp	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	isolate	isolate	VERB	VB	VerbForm=Inf	7	xcomp	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	full	full	ADJ	JJ	Degree=Pos	13	amod	_	_
13	subcategory	subcategory	NOUN	NN	Number=Sing	10	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	objects	object	NOUN	NNS	Number=Plur	14	pobj	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	20	punct	_	SpaceAfter=No
17	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
18	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	20	punct	_	SpaceAfter=No
19	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	20	punct	_	SpaceAfter=No
20	nucleus	nucleus	NOUN	NN	Number=Sing	13	appos	_	SpaceAfter=No
21	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	20	punct	_	SpaceAfter=No
22	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	20	punct	_	_
23	for	for	ADP	IN	_	27	prep	_	_
24	which	which	PRON	WDT	_	23	pobj	_	_
25	this	this	DET	DT	Number=Sing|PronType=Dem	26	det	_	_
26	transformation	transformation	NOUN	NN	Number=Sing	27	nsubj	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	relcl	_	_
28	an	an	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
29	isomorphism	isomorphism	NOUN	NN	Number=Sing	27	attr	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 5
# text = In addition, we define and study the appropriate categorical structure underlying the MIX rule.
1	In	in	ADP	IN	_	5	prep	_	_
2	addition	addition	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	study	study	VERB	VB	VerbForm=Inf	5	conj	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
9	appropriate	appropriate	ADJ	JJ	Degree=Pos	11	amod	_	_
10	categorical	categorical	ADJ	JJ	Degree=Pos	11	amod	_	_
11	structure	structure	NOUN	NN	Number=Sing	7	dobj	_	_
12	underlying	underlie	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	acl	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	MIX	MIX	PROPN	NNP	Number=Sing	15	compound	_	_
15	rule	rule	NOUN	NN	Number=Sing	12	dobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 6
# text = For all these structures, we do not restrict consideration to the ``pure'' logic as we allow non - logical axioms.
1	For	for	ADP	IN	_	9	prep	_	_
2	all	all	DET	PDT	_	4	predet	_	_
3	these	these	DET	DT	Number=Plur|PronType=Dem	4	det	_	_
4	structures	structure	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
7	do	do	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	aux	_	_
8	not	not	PART	RB	Polarity=Neg	9	neg	_	_
9	restrict	restrict	VERB	VB	VerbForm=Inf	0	ROOT	_	_
10	consideration	consideration	NOUN	NN	Number=Sing	9	dobj	_	_
11	to	to	ADP	IN	_	9	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
13	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	17	punct	_	SpaceAfter=No
14	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	17	punct	_	SpaceAfter=No
15	pure	pure	ADJ	JJ	Degree=Pos	17	amod	_	SpaceAfter=No
16	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	17	punct	_	_
17	logic	logic	NOUN	NN	Number=Sing	11	pobj	_	_
18	as	as	SCONJ	IN	_	20	mark	_	_
19	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	20	nsubj	_	_
20	allow	allow	VERB	VBP	Tense=Pres|VerbForm=Fin	9	advcl	_	_
21	non	non	ADJ	JJ	Degree=Pos	23	amod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	logical	logical	ADJ	JJ	Degree=Pos	24	amod	_	_
24	axioms	axiom	NOUN	NNS	Number=Plur	20	dobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 7
# text = We define the appropriate notion of proof nets for these logics, and use them to describe coherence results for the corresponding categorical structures.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	appropriate	appropriate	ADJ	JJ	Degree=Pos	5	amod	_	_
5	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	proof	proof	NOUN	NN	Number=Sing	8	compound	_	_
8	nets	net	NOUN	NNS	Number=Plur	6	pobj	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	these	these	DET	DT	Number=Plur|PronType=Dem	11	det	_	_
11	logics	logic	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
14	use	use	VERB	VB	VerbForm=Inf	2	conj	_	_
15	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	14	dobj	_	_
16	to	to	PART	TO	_	17	aux	_	_
17	describe	describe	VERB	VB	VerbForm=Inf	14	xcomp	_	_
18	coherence	coherence	NOUN	NN	Number=Sing	19	compound	_	_
19	results	result	NOUN	NNS	Number=Plur	17	dobj	_	_
20	for	for	ADP	IN	_	17	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
22	corresponding	corresponding	ADJ	JJ	Degree=Pos	24	amod	_	_
23	categorical	categorical	ADJ	JJ	Degree=Pos	24	amod	_	_
24	structures	structure	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 54
# sent_id = 1
# text = We establish a general coherence theorem for lax operad actions on an $ n $ - category which implies that an $ n $ - category with such an action is lax equivalent to one with a strict action.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	establish	establish	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	general	general	ADJ	JJ	Degree=Pos	5	amod	_	_
5	coherence	coherence	NOUN	NN	Number=Sing	6	compound	_	_
6	theorem	theorem	ADJ	JJ	Degree=Pos	2	dobj	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	lax	lax	ADJ	JJ	Degree=Pos	10	amod	_	_
9	operad	operad	ADJ	JJ	Degree=Pos	10	amod	_	_
10	actions	action	NOUN	NNS	Number=Plur	7	pobj	_	_
11	on	on	ADP	IN	_	10	prep	_	_
12	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	$ n $	$ n $	SYM	$	_	15	nummod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
16	which	which	PRON	WDT	_	17	nsubj	_	_
17	implies	imply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	relcl	_	_
18	that	that	SCONJ	IN	_	27	mark	_	_
19	an	an	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
20	$ n $	$ n $	SYM	$	_	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	category	category	NOUN	NN	Number=Sing	27	nsubj	_	_
23	with	with	ADP	IN	_	22	prep	_	_
24	such	such	DET	PDT	_	26	predet	_	_
25	an	an	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
26	action	action	NOUN	NN	Number=Sing	23	pobj	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	ccomp	_	_
28	lax	lax	ADJ	JJ	Degree=Pos	27	acomp	_	_
29	equivalent	equivalent	ADJ	JJ	Degree=Pos	28	advmod	_	_
30	to	to	ADP	IN	_	29	prep	_	_
31	one	one	NUM	CD	NumType=Card	30	pobj	_	_
32	with	with	ADP	IN	_	31	prep	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
34	strict	strict	ADJ	JJ	Degree=Pos	35	amod	_	_
35	action	action	NOUN	NN	Number=Sing	32	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This includes familiar coherence results (for example, for symmetric monoidal categories) and many new ones.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	includes	include	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	familiar	familiar	ADJ	JJ	Degree=Pos	5	amod	_	_
4	coherence	coherence	NOUN	NN	Number=Sing	5	compound	_	_
5	results	result	NOUN	NNS	Number=Plur	2	dobj	_	_
6	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	5	punct	_	SpaceAfter=No
7	for	for	ADP	IN	_	5	prep	_	_
8	example	example	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
10	for	for	ADP	IN	_	5	prep	_	_
11	symmetric	symmetric	ADJ	JJ	Degree=Pos	13	amod	_	_
12	monoidal	monoidal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
14	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	10	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
16	many	many	ADJ	JJ	Degree=Pos	18	amod	_	_
17	new	new	ADJ	JJ	Degree=Pos	18	amod	_	_
18	ones	one	NOUN	NNS	Number=Plur	5	conj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = In particular, any braided monoidal $ n $ - category is lax equivalent to a strict braided monoidal $ n $ - category.
1	In	in	ADP	IN	_	10	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
4	any	any	DET	DT	_	6	det	_	_
5	braided	braid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	amod	_	_
6	monoidal	monoidal	NOUN	NN	Number=Sing	9	amod	_	_
7	$ n $	$ n $	SYM	$	_	9	nummod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	category	category	NOUN	NN	Number=Sing	10	nsubj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	lax	lax	ADJ	JJ	Degree=Pos	10	acomp	_	_
12	equivalent	equivalent	ADJ	JJ	Degree=Pos	11	advmod	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
15	strict	strict	ADJ	JJ	Degree=Pos	17	amod	_	_
16	braided	braid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	monoidal	monoidal	NOUN	NN	Number=Sing	20	amod	_	_
18	$ n $	$ n $	SYM	$	_	20	nummod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	category	category	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 4
# text = We also obtain coherence theorems for $ A_{infty} $ and $ E_{infty} $ rings and for lax modules over such rings.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	coherence	coherence	NOUN	NN	Number=Sing	5	compound	_	_
5	theorems	theorem	NOUN	NNS	Number=Plur	3	dobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	$ A_{infty} $	$ a_{infty} $	SYM	$	_	6	pobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	$ E_{infty} $	$ e_{infty} $	SYM	$	_	10	nmod	_	_
10	rings	ring	NOUN	NNS	Number=Plur	7	conj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
12	for	for	ADP	IN	_	3	prep	_	_
13	lax	lax	ADJ	JJ	Degree=Pos	14	amod	_	_
14	modules	module	NOUN	NNS	Number=Plur	12	pobj	_	_
15	over	over	ADP	IN	_	14	prep	_	_
16	such	such	ADJ	JJ	Degree=Pos	17	amod	_	_
17	rings	ring	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = Using these results we give an extension of Morita equivalence to $ A_{infty} $ rings and some applications to infinite loop spaces and algebraic $ K $ - theory.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	advcl	_	_
2	these	these	DET	DT	Number=Plur|PronType=Dem	3	det	_	_
3	results	result	NOUN	NNS	Number=Plur	1	dobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	extension	extension	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	Morita	Morita	PROPN	NNP	Number=Sing	10	compound	_	_
10	equivalence	equivalence	NOUN	NN	Number=Sing	8	pobj	_	_
11	to	to	ADP	IN	_	7	prep	_	_
12	$ A_{infty} $	$ a_{infty} $	SYM	$	_	13	nmod	_	_
13	rings	ring	NOUN	NNS	Number=Plur	11	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	some	some	DET	DT	_	16	det	_	_
16	applications	application	NOUN	NNS	Number=Plur	13	conj	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	infinite	infinite	VERB	VB	VerbForm=Inf	20	amod	_	_
19	loop	loop	NOUN	NN	Number=Sing	20	compound	_	_
20	spaces	space	NOUN	NNS	Number=Plur	17	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	algebraic	algebraic	ADJ	JJ	Degree=Pos	25	amod	_	_
23	$ K $	$ k $	SYM	$	_	25	compound	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	theory	theory	NOUN	NN	Number=Sing	20	conj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 55
# sent_id = 1
# text = In a 1981 book, Putnam claimed that in a pure relational language without equality, for any model of a relation that was neither empty nor full, there was another model that satisfies the same first order sentences.
1	In	in	ADP	IN	_	7	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	1981	1981	NUM	CD	NumType=Card	4	nummod	_	_
4	book	book	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	Putnam	Putnam	PROPN	NNP	Number=Sing	7	nsubj	_	_
7	claimed	claim	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
8	that	that	SCONJ	IN	_	31	mark	_	_
9	in	in	ADP	IN	_	31	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	pure	pure	ADJ	JJ	Degree=Pos	13	amod	_	_
12	relational	relational	ADJ	JJ	Degree=Pos	13	amod	_	_
13	language	language	NOUN	NN	Number=Sing	9	pobj	_	_
14	without	without	ADP	IN	_	13	prep	_	_
15	equality	equality	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
17	for	for	ADP	IN	_	31	prep	_	_
18	any	any	DET	DT	_	19	det	_	_
19	model	model	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	relation	relation	NOUN	NN	Number=Sing	20	pobj	_	_
23	that	that	PRON	WDT	PronType=Rel	24	nsubj	_	_
24	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	22	relcl	_	_
25	neither	neither	CCONJ	CC	ConjType=Cmp	26	preconj	_	_
26	empty	empty	ADJ	JJ	Degree=Pos	24	acomp	_	_
27	nor	nor	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	full	full	ADJ	JJ	Degree=Pos	26	conj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
30	there	there	PRON	EX	_	31	expl	_	_
31	was	be	VERB	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	7	ccomp	_	_
32	another	another	DET	DT	_	33	det	_	_
33	model	model	NOUN	NN	Number=Sing	31	attr	_	_
34	that	that	PRON	WDT	PronType=Rel	35	nsubj	_	_
35	satisfies	satisfy	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	33	relcl	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
37	same	same	ADJ	JJ	Degree=Pos	40	amod	_	_
38	first	first	ADJ	JJ	Degree=Pos	40	amod	_	_
39	order	order	NOUN	NN	Number=Sing	40	compound	_	_
40	sentences	sentence	NOUN	NNS	Number=Plur	35	dobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 2
# text = Ed Keenan observed that this was false for finite models since equality is a definable predicate in such cases.
1	Ed	Ed	PROPN	NNP	Number=Sing	2	compound	_	_
2	Keenan	Keenan	PROPN	NNP	Number=Sing	3	nsubj	_	_
3	observed	observe	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	6	mark	_	_
5	this	this	PRON	DT	Number=Sing|PronType=Dem	6	nsubj	_	_
6	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	3	ccomp	_	_
7	false	false	ADJ	JJ	Degree=Pos	6	acomp	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	finite	finite	ADJ	JJ	Degree=Pos	10	compound	_	_
10	models	model	NOUN	NNS	Number=Plur	8	pobj	_	_
11	since	since	SCONJ	IN	_	13	mark	_	_
12	equality	equality	NOUN	NN	Number=Sing	13	nsubj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	advcl	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	definable	definable	ADJ	JJ	Degree=Pos	16	amod	_	_
16	predicate	predicate	NOUN	NN	Number=Sing	13	attr	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	such	such	ADJ	JJ	Degree=Pos	19	amod	_	_
19	cases	case	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = This note shows that Putnam's claim is true for infinite models, although it requires a more sophisticated proof than the one outlined by Putnam.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	note	note	NOUN	NN	Number=Sing	3	nsubj	_	_
3	shows	show	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	8	mark	_	_
5	Putnam	Putnam	PROPN	NNP	Number=Sing	7	poss	_	SpaceAfter=No
6	's	's	PART	POS	_	5	case	_	_
7	claim	claim	NOUN	NN	Number=Sing	8	nsubj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
9	true	true	ADJ	JJ	Degree=Pos	8	acomp	_	_
10	for	for	ADP	IN	_	8	prep	_	_
11	infinite	infinite	ADJ	JJ	Degree=Pos	12	amod	_	_
12	models	model	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
14	although	although	SCONJ	IN	_	16	mark	_	_
15	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	16	nsubj	_	_
16	requires	require	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	advcl	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
18	more	more	ADV	RBR	Degree=Cmp	19	advmod	_	_
19	sophisticated	sophisticated	ADJ	JJ	Degree=Pos	20	amod	_	_
20	proof	proof	NOUN	NN	Number=Sing	16	dobj	_	_
21	than	than	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	one	one	NOUN	NN	Number=Sing	21	pobj	_	_
24	outlined	outline	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	acl	_	_
25	by	by	ADP	IN	_	24	agent	_	_
26	Putnam	Putnam	PROPN	NNP	Number=Sing	25	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 56
# sent_id = 1
# text = We pursue the definition of a $ KZ $ - doctrine in terms of a fully faithful adjoint string $ Dd - | m - | dD $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	pursue	pursue	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	definition	definition	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	$ KZ $	$ kz $	SYM	$	_	9	nmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	doctrine	doctrine	NOUN	NN	Number=Sing	5	pobj	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	terms	term	NOUN	NNS	Number=Plur	10	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
14	fully	fully	ADV	RB	_	15	advmod	_	_
15	faithful	faithful	ADJ	JJ	Degree=Pos	17	amod	_	_
16	adjoint	adjoint	NOUN	NN	Number=Sing	17	compound	_	_
17	string	string	NOUN	NN	Number=Sing	12	pobj	_	_
18	$ Dd - | m - | dD $	$ dd - | m - | dd $	X	ADD	_	2	npadvmod	_	_
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We give the definition in any Gray - category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	definition	definition	NOUN	NN	Number=Sing	2	dobj	_	_
5	in	in	ADP	IN	_	2	prep	_	_
6	any	any	DET	DT	_	9	det	_	_
7	Gray	Gray	PROPN	NNP	Number=Sing	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	category	category	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The concept of algebra is given as an adjunction with invertible counit.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	concept	concept	NOUN	NN	Number=Sing	6	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	algebra	algebra	PROPN	NNP	Number=Sing	3	pobj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	as	as	ADP	IN	_	6	prep	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	adjunction	adjunction	NOUN	NN	Number=Sing	7	pobj	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	invertible	invertible	ADJ	JJ	Degree=Pos	12	amod	_	_
12	counit	counit	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show that these doctrines are instances of more general pseudomonads.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	6	mark	_	_
4	these	these	DET	DT	Number=Plur|PronType=Dem	5	det	_	_
5	doctrines	doctrine	NOUN	NNS	Number=Plur	6	nsubj	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
7	instances	instance	NOUN	NNS	Number=Plur	6	attr	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	more	more	ADJ	JJR	Degree=Cmp	11	amod	_	_
10	general	general	ADJ	JJ	Degree=Pos	11	amod	_	_
11	pseudomonads	pseudomonad	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = The algebras for a pseudomonad are defined in more familiar terms and shown to be the same as the ones defined as adjunctions when we start with a $ KZ $ - doctrine.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	algebras	algebra	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
3	for	for	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	pseudomonad	pseudomonad	NOUN	NNS	Number=Plur	3	pobj	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	more	more	ADV	RBR	Degree=Cmp	10	advmod	_	_
10	familiar	familiar	ADJ	JJ	Degree=Pos	11	amod	_	_
11	terms	term	NOUN	NNS	Number=Plur	8	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
13	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	conj	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	be	be	AUX	VB	VerbForm=Inf	13	xcomp	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	same	same	ADJ	JJ	Degree=Pos	15	attr	_	_
18	as	as	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	ones	one	NOUN	NNS	Number=Plur	18	pobj	_	_
21	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	acl	_	_
22	as	as	ADP	IN	_	21	prep	_	_
23	adjunctions	adjunction	NOUN	NNS	Number=Plur	22	pobj	_	_
24	when	when	SCONJ	WRB	_	26	advmod	_	_
25	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	26	nsubj	_	_
26	start	start	VERB	VBP	Tense=Pres|VerbForm=Fin	21	advcl	_	_
27	with	with	ADP	IN	_	26	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
29	$ KZ $	$ kz $	SYM	$	_	31	compound	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	doctrine	doctrine	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 57
# sent_id = 1
# text = Let $ E $ be a simplicial commutative algebra such that $ E_n $ is generated by degenerate elements.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ E $	$ e $	SYM	$	_	3	nsubj	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	simplicial	simplicial	ADJ	JJ	Degree=Pos	7	amod	_	_
6	commutative	commutative	ADJ	JJ	Degree=Pos	7	amod	_	_
7	algebra	algebra	PROPN	NNP	Number=Sing	3	attr	_	_
8	such	such	ADJ	JJ	Degree=Pos	9	amod	_	_
9	that	that	SCONJ	IN	_	12	dobj	_	_
10	$ E_n $	$ e_n $	SYM	$	_	12	nsubjpass	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	relcl	_	_
13	by	by	ADP	IN	_	12	agent	_	_
14	degenerate	degenerate	ADJ	JJ	Degree=Pos	15	amod	_	_
15	elements	element	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = It is shown that in this case the $ n $ th term of the Moore complex of $ E $ is generated by images of certain pairings from lower dimensions.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	SCONJ	IN	_	19	mark	_	_
5	in	in	ADP	IN	_	11	prep	_	_
6	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
7	case	case	NOUN	NN	Number=Sing	5	pobj	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
9	$ n $	$ n $	SYM	$	_	10	nmod	_	_
10	th	th	PRON	DT	_	11	compound	_	_
11	term	term	NOUN	NN	Number=Sing	19	nsubjpass	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	Moore	Moore	PROPN	NNP	Number=Sing	15	compound	_	_
15	complex	complex	NOUN	NN	Number=Sing	12	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	$ E $	$ e $	SYM	$	_	16	pobj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	auxpass	_	_
19	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	ccomp	_	_
20	by	by	ADP	IN	_	19	agent	_	_
21	images	image	NOUN	NNS	Number=Plur	20	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	certain	certain	ADJ	JJ	Degree=Pos	24	amod	_	_
24	pairings	pairing	NOUN	NNS	Number=Plur	22	pobj	_	_
25	from	from	ADP	IN	_	24	prep	_	_
26	lower	low	ADJ	JJR	Degree=Cmp	27	amod	_	_
27	dimensions	dimension	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = This is then used to give a description of the boundaries in dimension $ n - 1 $ for $ n = 2 $ , 3, and 4.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	4	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
3	then	then	ADV	RB	PronType=Dem	4	advmod	_	_
4	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	give	give	VERB	VB	VerbForm=Inf	4	xcomp	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	description	description	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	boundaries	boundary	NOUN	NNS	Number=Plur	9	pobj	_	_
12	in	in	ADP	IN	_	6	prep	_	_
13	dimension	dimension	NOUN	NN	Number=Sing	12	pobj	_	_
14	$ n - 1 $	$ n - 1 $	SYM	$	_	13	appos	_	_
15	for	for	ADP	IN	_	6	prep	_	_
16	$ n = 2 $	$ n = 2 $	SYM	$	_	15	pobj	_	_
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	3	3	NUM	CD	NumType=Card	16	conj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
21	4	4	X	LS	NumType=Ord	4	conj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 58
# sent_id = 1
# text = The notion of separable (alternatively unramified, or decidable}) objects and their place in a categorical theory of space have been described by Lawvere, drawing on notions of separable from algebra and unramified from geometry.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	notion	notion	NOUN	NN	Number=Sing	13	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	separable	separable	NOUN	NN	Number=Sing	3	pobj	_	_
5	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	4	punct	_	SpaceAfter=No
6	alternatively	alternatively	ADV	RB	_	7	advmod	_	_
7	unramified	unramifie	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	or	or	CCONJ	CC	ConjType=Cmp	7	cc	_	_
10	decidable	decidable	ADJ	JJ	Degree=Pos	13	amod	_	SpaceAfter=No
11	}	}	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	13	punct	_	SpaceAfter=No
12	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	13	punct	_	_
13	objects	object	NOUN	NNS	Number=Plur	25	nsubjpass	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	16	poss	_	_
16	place	place	NOUN	NN	Number=Sing	13	conj	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	categorical	categorical	ADJ	JJ	Degree=Pos	20	amod	_	_
20	theory	theory	NOUN	NN	Number=Sing	17	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	space	space	NOUN	NN	Number=Sing	21	pobj	_	_
23	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	25	aux	_	_
24	been	be	AUX	VBN	Tense=Past|VerbForm=Part	25	auxpass	_	_
25	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
26	by	by	ADP	IN	_	25	agent	_	_
27	Lawvere	Lawvere	PROPN	NNP	Number=Sing	26	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
29	drawing	draw	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	25	advcl	_	_
30	on	on	ADP	IN	_	29	prep	_	_
31	notions	notion	NOUN	NNS	Number=Plur	30	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	separable	separable	NOUN	NN	Number=Sing	32	pobj	_	_
34	from	from	ADP	IN	_	29	prep	_	_
35	algebra	algebra	PROPN	NNP	Number=Sing	34	pobj	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
37	unramified	unramifie	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	conj	_	_
38	from	from	ADP	IN	_	37	prep	_	_
39	geometry	geometry	NOUN	NN	Number=Sing	38	pobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	25	punct	_	SpaceAfter=No

# sent_id = 2
# text = In his work, Schanuel constructed the generic separable object in an extensive category with products as an object of the free category with finite sums on the dual of the category of finite sets and injections.
1	In	in	ADP	IN	_	6	prep	_	_
2	his	his	PRON	PRP$	Gender=Masc|Number=Sing|Person=3|Poss=Yes|PronType=Prs	3	poss	_	_
3	work	work	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	Schanuel	Schanuel	PROPN	NNP	Number=Sing	6	nsubj	_	_
6	constructed	construct	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	generic	generic	ADJ	JJ	Degree=Pos	9	amod	_	_
9	separable	separable	ADJ	JJ	Degree=Pos	10	amod	_	_
10	object	object	NOUN	NN	Number=Sing	6	dobj	_	_
11	in	in	ADP	IN	_	6	prep	_	_
12	an	an	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	extensive	extensive	ADJ	JJ	Degree=Pos	14	amod	_	_
14	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
15	with	with	ADP	IN	_	14	prep	_	_
16	products	product	NOUN	NNS	Number=Plur	15	pobj	_	_
17	as	as	ADP	IN	_	16	prep	_	_
18	an	an	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	object	object	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	free	free	ADJ	JJ	Degree=Pos	23	amod	_	_
23	category	category	NOUN	NN	Number=Sing	20	pobj	_	_
24	with	with	ADP	IN	_	23	prep	_	_
25	finite	finite	ADJ	JJ	Degree=Pos	26	compound	_	_
26	sums	sum	NOUN	NNS	Number=Plur	24	pobj	_	_
27	on	on	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	dual	dual	ADJ	JJ	Degree=Pos	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	category	category	NOUN	NN	Number=Sing	30	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	finite	finite	ADJ	JJ	Degree=Pos	35	compound	_	_
35	sets	set	NOUN	NNS	Number=Plur	33	pobj	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
37	injections	injection	NOUN	NNS	Number=Plur	35	conj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = We present here a generalization of the work of Schaunel, replacing the category of finite sets and injections by a category $ cat A $ with a suitable factorization system.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	here	here	ADV	RB	PronType=Dem	2	advmod	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	generalization	generalization	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	work	work	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Schaunel	Schaunel	PROPN	NNP	Number=Sing	9	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
12	replacing	replace	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	category	category	NOUN	NN	Number=Sing	12	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	finite	finite	ADJ	JJ	Degree=Pos	17	compound	_	_
17	sets	set	NOUN	NNS	Number=Plur	15	pobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	injections	injection	NOUN	NNS	Number=Plur	17	conj	_	_
20	by	by	ADP	IN	_	12	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	category	category	NOUN	NN	Number=Sing	23	compound	_	_
23	$ cat A $	$ cat a $	SYM	$	_	20	pobj	_	_
24	with	with	ADP	IN	_	12	prep	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
26	suitable	suitable	ADJ	JJ	Degree=Pos	28	amod	_	_
27	factorization	factorization	NOUN	NN	Number=Sing	28	compound	_	_
28	system	system	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We describe the analogous construction, and identify and prove a universal property of the constructed category for both extensive categories and extensive categories with products (in the case $ cat A $ admits sums).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	analogous	analogous	ADJ	JJ	Degree=Pos	5	amod	_	_
5	construction	construction	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
8	identify	identify	VERB	VB	VerbForm=Inf	2	conj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	prove	prove	VERB	VB	VerbForm=Inf	8	conj	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	universal	universal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	property	property	NOUN	NN	Number=Sing	10	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	category	category	NOUN	NN	Number=Sing	14	pobj	_	_
18	for	for	ADP	IN	_	17	prep	_	_
19	both	both	CCONJ	CC	ConjType=Cmp	21	det	_	_
20	extensive	extensive	ADJ	JJ	Degree=Pos	21	amod	_	_
21	categories	category	NOUN	NNS	Number=Plur	18	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	extensive	extensive	ADJ	JJ	Degree=Pos	24	amod	_	_
24	categories	category	NOUN	NNS	Number=Plur	21	conj	_	_
25	with	with	ADP	IN	_	10	prep	_	_
26	products	product	NOUN	NNS	Number=Plur	25	pobj	_	_
27	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	10	punct	_	SpaceAfter=No
28	in	in	ADP	IN	_	32	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	case	case	NOUN	NN	Number=Sing	28	pobj	_	_
31	$ cat A $	$ cat a $	SYM	$	_	32	nsubj	_	_
32	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	conj	_	_
33	sums	sum	NOUN	NNS	Number=Plur	32	dobj	_	SpaceAfter=No
34	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	32	punct	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = In constructing the machinery for proving the required universal property, we recall briefly the boolean algebra structure of the summands of an object in an extensive category.
1	In	in	ADP	IN	_	13	prep	_	_
2	constructing	construct	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	1	pcomp	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	machinery	machinery	NOUN	NN	Number=Sing	2	dobj	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	proving	prove	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	required	require	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
9	universal	universal	ADJ	JJ	Degree=Pos	10	amod	_	_
10	property	property	NOUN	NN	Number=Sing	6	dobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	recall	recall	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	briefly	briefly	ADV	RB	_	13	advmod	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
16	boolean	boolean	PROPN	NNP	Number=Sing	18	compound	_	_
17	algebra	algebra	PROPN	NNP	Number=Sing	18	compound	_	_
18	structure	structure	NOUN	NN	Number=Sing	13	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	summands	summand	NOUN	NNS	Number=Plur	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	an	an	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	object	object	NOUN	NN	Number=Sing	22	pobj	_	_
25	in	in	ADP	IN	_	24	prep	_	_
26	an	an	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
27	extensive	extensive	ADJ	JJ	Degree=Pos	28	amod	_	_
28	category	category	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 6
# text = We further present a notion of direct image for certain maps in an extensive category, to allow construction of left adjoints to the inverse image maps obtained from pullbacks.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	further	far	ADV	RB	_	3	advmod	_	_
3	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	notion	notion	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	direct	direct	ADJ	JJ	Degree=Pos	8	amod	_	_
8	image	image	NOUN	NN	Number=Sing	6	pobj	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	certain	certain	ADJ	JJ	Degree=Pos	11	amod	_	_
11	maps	map	NOUN	NNS	Number=Plur	9	pobj	_	_
12	in	in	ADP	IN	_	3	prep	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	extensive	extensive	ADJ	JJ	Degree=Pos	15	amod	_	_
15	category	category	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
17	to	to	PART	TO	_	18	aux	_	_
18	allow	allow	VERB	VB	VerbForm=Inf	3	advcl	_	_
19	construction	construction	NOUN	NN	Number=Sing	18	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	left	left	ADJ	JJ	Degree=Pos	22	amod	_	_
22	adjoints	adjoint	NOUN	NNS	Number=Plur	20	pobj	_	_
23	to	to	ADP	IN	_	18	dative	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
25	inverse	inverse	ADJ	JJ	Degree=Pos	27	amod	_	_
26	image	image	NOUN	NN	Number=Sing	27	compound	_	_
27	maps	map	NOUN	NNS	Number=Plur	23	pobj	_	_
28	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	acl	_	_
29	from	from	ADP	IN	_	28	prep	_	_
30	pullbacks	pullback	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = Please note the electronically available References at http://www.tac.mta.ca/tac/volumes/1998/n10/reference.html
1	Please	please	INTJ	UH	_	2	intj	_	_
2	note	note	VERB	VB	VerbForm=Inf	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
4	electronically	electronically	ADV	RB	_	5	advmod	_	_
5	available	available	ADJ	JJ	Degree=Pos	6	amod	_	_
6	References	reference	NOUN	NNS	Number=Plur	2	dobj	_	_
7	at	at	ADP	IN	_	2	prep	_	_
8	http://www.tac.mta.ca/tac/volumes/1998/n10/reference.html	http://www.tac.mta.ca/tac/volumes/1998/n10/reference.html	PROPN	NNP	Number=Sing	7	pobj	_	SpaceAfter=No

# doc_id = 59
# sent_id = 1
# text = In terms of synthetic differential geometry, we give a variational characterization of the connection (parallelism) associated to a pseudo - Riemannian metric on a manifold.
1	In	in	ADP	IN	_	9	prep	_	_
2	terms	term	NOUN	NNS	Number=Plur	1	pobj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	synthetic	synthetic	ADJ	JJ	Degree=Pos	6	amod	_	_
5	differential	differential	ADJ	JJ	Degree=Pos	6	amod	_	_
6	geometry	geometry	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	variational	variational	ADJ	JJ	Degree=Pos	12	amod	_	_
12	characterization	characterization	NOUN	NN	Number=Sing	9	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	connection	connection	NOUN	NN	Number=Sing	13	pobj	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	15	punct	_	SpaceAfter=No
17	parallelism	parallelism	NOUN	NN	Number=Sing	15	appos	_	SpaceAfter=No
18	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	15	punct	_	_
19	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
20	to	to	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	pseudo	pseudo	NOUN	NN	Number=Sing	20	pobj	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	Riemannian	riemannian	ADJ	JJ	Degree=Pos	25	amod	_	_
25	metric	metric	NOUN	NN	Number=Sing	20	pobj	_	_
26	on	on	ADP	IN	_	19	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	manifold	manifold	ADJ	JJ	Degree=Pos	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 60
# sent_id = 1
# text = Using free simplicial groups, it is shown how to construct a free or totally free 2 - crossed module on suitable construction data.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	advcl	_	_
2	free	free	ADJ	JJ	Degree=Pos	4	amod	_	_
3	simplicial	simplicial	ADJ	JJ	Degree=Pos	4	amod	_	_
4	groups	group	NOUN	NNS	Number=Plur	1	dobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
6	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	8	nsubjpass	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	how	how	SCONJ	WRB	_	11	advmod	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	construct	construct	VERB	VB	VerbForm=Inf	8	xcomp	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
13	free	free	ADJ	JJ	Degree=Pos	20	amod	_	_
14	or	or	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	totally	totally	ADV	RB	_	16	advmod	_	_
16	free	free	ADJ	JJ	Degree=Pos	13	conj	_	_
17	2	2	NUM	CD	NumType=Card	19	advmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	amod	_	_
20	module	module	NOUN	NN	Number=Sing	11	dobj	_	_
21	on	on	ADP	IN	_	20	prep	_	_
22	suitable	suitable	ADJ	JJ	Degree=Pos	24	amod	_	_
23	construction	construction	NOUN	NN	Number=Sing	24	compound	_	_
24	data	datum	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = 2 - crossed complexes are introduced and similar freeness results for these are discussed.
1	2	2	X	LS	NumType=Ord	3	npadvmod	_	_
2	-	-	PUNCT	HYPH	PunctType=Dash	3	punct	_	_
3	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	amod	_	_
4	complexes	complex	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	similar	similar	ADJ	JJ	Degree=Pos	10	amod	_	_
9	freeness	freeness	ADJ	JJ	Degree=Pos	10	amod	_	_
10	results	result	NOUN	NNS	Number=Plur	14	nsubjpass	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	these	these	PRON	DT	Number=Plur|PronType=Dem	11	pobj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	discussed	discuss	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	conj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# doc_id = 61
# sent_id = 1
# text = Generalising a result of Brown and Loday, we give for $ n=3 $ and 4, a decomposition of the group, $ d_nNG_n, of boundaries of a simplicial group G as a product of commutator subgroups.
1	Generalising	generalise	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	advcl	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	result	result	NOUN	NN	Number=Sing	1	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	Brown	Brown	PROPN	NNP	Number=Sing	4	pobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	Loday	Loday	PROPN	NNP	Number=Sing	5	conj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
9	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
10	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	$ n=3 $	$ n=3 $	SYM	$	_	11	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	4	4	NUM	CD	NumType=Card	12	conj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	decomposition	decomposition	NOUN	NN	Number=Sing	10	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	group	group	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	$	$	SYM	$	_	23	nmod	_	_
23	d_nNG_n	d_nng_n	ADJ	JJ	Degree=Pos	20	appos	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
25	of	of	ADP	IN	_	20	prep	_	_
26	boundaries	boundary	NOUN	NNS	Number=Plur	25	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
29	simplicial	simplicial	ADJ	JJ	Degree=Pos	30	amod	_	_
30	group	group	NOUN	NN	Number=Sing	27	pobj	_	_
31	G	G	PROPN	NNP	Number=Sing	30	appos	_	_
32	as	as	ADP	IN	_	17	prep	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
34	product	product	NOUN	NN	Number=Sing	32	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	commutator	commutator	NOUN	NN	Number=Sing	37	compound	_	_
37	subgroups	subgroup	NOUN	NNS	Number=Plur	35	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = Partial results are given for higher dimensions.
1	Partial	partial	ADJ	JJ	Degree=Pos	2	amod	_	_
2	results	result	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	higher	high	ADJ	JJR	Degree=Cmp	7	amod	_	_
7	dimensions	dimension	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = Applications to 2 - crossed modules and quadratic modules are discussed.
1	Applications	application	NOUN	NNS	Number=Plur	11	nsubjpass	_	_
2	to	to	ADP	IN	_	1	prep	_	_
3	2	2	NUM	CD	NumType=Card	5	advmod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	amod	_	_
6	modules	module	NOUN	NNS	Number=Plur	2	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	quadratic	quadratic	ADJ	JJ	Degree=Pos	9	amod	_	_
9	modules	module	NOUN	NNS	Number=Plur	6	conj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	discussed	discuss	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# doc_id = 62
# sent_id = 1
# text = This paper shows that, given a factorization system, $ E/M $ on a closed symmetric monoidal category, the full subcategory of separated extensional objects of the Chu category is also star - autonomous under weaker conditions than had been given previously.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	shows	show	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	30	mark	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
6	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	30	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	factorization	factorization	NOUN	NN	Number=Sing	9	compound	_	_
9	system	system	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	$ E/M $	$ e/m $	SYM	$	_	6	dep	_	_
12	on	on	ADP	IN	_	6	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
14	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
15	symmetric	symmetric	ADJ	JJ	Degree=Pos	17	amod	_	_
16	monoidal	monoidal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	category	category	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	full	full	ADJ	JJ	Degree=Pos	21	amod	_	_
21	subcategory	subcategory	NOUN	NN	Number=Sing	30	nsubj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	separated	separated	ADJ	JJ	Degree=Pos	25	amod	_	_
24	extensional	extensional	ADJ	JJ	Degree=Pos	25	amod	_	_
25	objects	object	NOUN	NNS	Number=Plur	22	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	Chu	Chu	PROPN	NNP	Number=Sing	29	compound	_	_
29	category	category	NOUN	NN	Number=Sing	26	pobj	_	_
30	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
31	also	also	ADV	RB	_	30	advmod	_	_
32	star	star	NOUN	NN	Number=Sing	34	npadvmod	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	autonomous	autonomous	ADJ	JJ	Degree=Pos	30	acomp	_	_
35	under	under	ADP	IN	_	34	prep	_	_
36	weaker	weak	ADJ	JJR	Degree=Cmp	37	amod	_	_
37	conditions	condition	NOUN	NNS	Number=Plur	35	pobj	_	_
38	than	than	SCONJ	IN	_	41	mark	_	_
39	had	have	AUX	VBD	Tense=Past|VerbForm=Fin	41	aux	_	_
40	been	be	AUX	VBN	Tense=Past|VerbForm=Part	41	auxpass	_	_
41	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	30	advcl	_	_
42	previously	previously	ADV	RB	_	41	advmod	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = In the process we find conditions under which the intersection of a full reflective subcategory and its coreflective dual in a Chu category is star - autonomous.
1	In	in	ADP	IN	_	5	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	process	process	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	find	find	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	conditions	condition	NOUN	NNS	Number=Plur	5	dobj	_	_
7	under	under	ADP	IN	_	24	prep	_	_
8	which	which	PRON	WDT	_	7	pobj	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	intersection	intersection	NOUN	NN	Number=Sing	24	nsubj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	full	full	ADJ	JJ	Degree=Pos	15	amod	_	_
14	reflective	reflective	ADJ	JJ	Degree=Pos	15	amod	_	_
15	subcategory	subcategory	NOUN	NN	Number=Sing	11	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	19	poss	_	_
18	coreflective	coreflective	ADJ	JJ	Degree=Pos	19	amod	_	_
19	dual	dual	ADJ	JJ	Degree=Pos	15	conj	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	Chu	Chu	PROPN	NNP	Number=Sing	23	compound	_	_
23	category	category	NOUN	NN	Number=Sing	20	pobj	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	relcl	_	_
25	star	star	NOUN	NN	Number=Sing	27	compound	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	autonomous	autonomous	PROPN	NNP	Number=Sing	24	acomp	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 63
# sent_id = 1
# text = We introduce a notion of equipment which generalizes the earlier notion of pro - arrow equipment and includes such familiar constructs as $ relK $ , $ spnK $ , $ parK $ , and $ proK $ for a suitable category $ K $ , along with related constructs such as the $ V $ - $ pro $ arising from a suitable monoidal category $ V $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	equipment	equipment	NOUN	NN	Number=Sing	5	pobj	_	_
7	which	which	PRON	WDT	_	8	nsubj	_	_
8	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	relcl	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	earlier	early	ADJ	JJR	Degree=Cmp	11	amod	_	_
11	notion	notion	NOUN	NN	Number=Sing	8	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	pro	pro	ADJ	JJ	Degree=Pos	15	amod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	arrow	arrow	NOUN	NN	Number=Sing	16	compound	_	_
16	equipment	equipment	NOUN	NN	Number=Sing	12	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
18	includes	include	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	conj	_	_
19	such	such	ADJ	JJ	Degree=Pos	21	amod	_	_
20	familiar	familiar	ADJ	JJ	Degree=Pos	21	amod	_	_
21	constructs	construct	NOUN	NNS	Number=Plur	18	dobj	_	_
22	as	as	ADP	IN	_	21	prep	_	_
23	$ relK $	$ relk $	SYM	$	_	22	pobj	_	_
24	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
25	$ spnK $	$ spnk $	SYM	$	_	23	conj	_	_
26	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
27	$ parK $	$ park $	SYM	$	_	25	conj	_	_
28	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
30	$ proK $	$ prok $	SYM	$	_	22	pobj	_	_
31	for	for	ADP	IN	_	18	prep	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
33	suitable	suitable	ADJ	JJ	Degree=Pos	34	amod	_	_
34	category	category	NOUN	NN	Number=Sing	31	pobj	_	_
35	$ K $	$ k $	SYM	$	_	34	appos	_	_
36	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
37	along	along	ADP	IN	_	18	prep	_	_
38	with	with	ADP	IN	_	37	prep	_	_
39	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	40	amod	_	_
40	constructs	construct	NOUN	NNS	Number=Plur	38	pobj	_	_
41	such	such	ADJ	JJ	Degree=Pos	42	amod	_	_
42	as	as	ADP	IN	_	40	prep	_	_
43	the	the	DET	DT	Definite=Def|PronType=Art	46	det	_	_
44	$ V $	$ v $	SYM	$	_	46	nmod	_	_
45	-	-	PUNCT	HYPH	PunctType=Dash	46	punct	_	_
46	$ pro $	$ pro $	SYM	$	_	42	pobj	_	_
47	arising	arise	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	46	acl	_	_
48	from	from	ADP	IN	_	47	prep	_	_
49	a	a	DET	DT	Definite=Ind|PronType=Art	52	det	_	_
50	suitable	suitable	ADJ	JJ	Degree=Pos	52	amod	_	_
51	monoidal	monoidal	ADJ	JJ	Degree=Pos	52	amod	_	_
52	category	category	NOUN	NN	Number=Sing	48	pobj	_	_
53	$ V $	$ v $	SYM	$	_	52	nummod	_	_
54	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We further exhibit the equipments as the objects of a 2 - category, in such a way that arbitrary functors $ F:eL - - - > K $ induce equipment arrows $ rel F:releL - - - >relK $ , $ spn F:spneL - - - > spnK $ , and so on, and similarly for arbitrary monoidal functors $ V - - - > W $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	further	far	ADV	RB	_	3	advmod	_	_
3	exhibit	exhibit	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	equipments	equipment	NOUN	NNS	Number=Plur	3	dobj	_	_
6	as	as	ADP	IN	_	3	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	objects	object	NOUN	NNS	Number=Plur	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	category	category	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
15	in	in	ADP	IN	_	3	prep	_	_
16	such	such	DET	PDT	_	18	predet	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	way	way	NOUN	NN	Number=Sing	15	pobj	_	_
19	that	that	PRON	WDT	PronType=Rel	23	advmod	_	_
20	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	21	amod	_	_
21	functors	functor	NOUN	NNS	Number=Plur	23	nsubj	_	_
22	$ F:eL - - - > K $	$ f:el - - - > k $	SYM	$	_	21	appos	_	_
23	induce	induce	VERB	VB	VerbForm=Inf	18	relcl	_	_
24	equipment	equipment	NOUN	NN	Number=Sing	25	compound	_	_
25	arrows	arrow	NOUN	NNS	Number=Plur	23	dobj	_	_
26	$ rel F:releL - - - >relK $	$ rel f:relel - - - >relk $	SYM	$	_	18	appos	_	_
27	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
28	$ spn F:spneL - - - > spnK $	$ spn f:spnel - - - > spnk $	SYM	$	_	18	appos	_	_
29	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
31	so	so	ADV	RB	_	32	advmod	_	_
32	on	on	ADV	RB	_	15	conj	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
34	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
35	similarly	similarly	ADV	RB	_	36	advmod	_	_
36	for	for	ADP	IN	_	32	conj	_	_
37	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	39	amod	_	_
38	monoidal	monoidal	ADJ	JJ	Degree=Pos	39	amod	_	_
39	functors	functor	NOUN	NNS	Number=Plur	36	pobj	_	_
40	$ V - - - > W $	$ v - - - > w $	SYM	$	_	3	dep	_	_
41	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = The article I with the title above dealt with those equipments $ M $ having each $ M(A, B) $ only an ordered set, and contained a detailed analysis of the case $ M =relK $ ; in the present article we allow the $ M(A, B) $ to be general categories, and illustrate our results by a detailed study of the case $ M=spnK $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	article	article	NOUN	NN	Number=Sing	36	nsubj	_	_
3	I	I	PRON	PRP	Case=Nom|Number=Sing|Person=1|PronType=Prs	2	appos	_	_
4	with	with	ADP	IN	_	2	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	title	title	NOUN	NN	Number=Sing	4	pobj	_	_
7	above	above	ADV	RB	_	6	advmod	_	_
8	dealt	deal	VERB	VBD	Tense=Past|VerbForm=Fin	2	acl	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	those	those	DET	DT	Number=Plur|PronType=Dem	11	det	_	_
11	equipments	equipment	NOUN	NNS	Number=Plur	9	pobj	_	_
12	$ M $	$ m $	SYM	$	_	2	appos	_	_
13	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	acl	_	_
14	each	each	DET	DT	_	19	det	_	_
15	$ M(A, B) $	$ m(a, b) $	SYM	$	_	19	predet	_	_
16	only	only	ADV	RB	_	19	advmod	_	_
17	an	an	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
19	set	set	NOUN	NN	Number=Sing	13	dobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
22	contained	contain	VERB	VBD	Tense=Past|VerbForm=Fin	2	conj	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	detailed	detailed	ADJ	JJ	Degree=Pos	25	amod	_	_
25	analysis	analysis	NOUN	NN	Number=Sing	22	dobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	case	case	NOUN	NN	Number=Sing	26	pobj	_	_
29	$ M =relK $	$ m =relk $	SYM	$	_	22	dep	_	_
30	;	;	PUNCT	:	_	36	punct	_	_
31	in	in	ADP	IN	_	36	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
33	present	present	ADJ	JJ	Degree=Pos	34	amod	_	_
34	article	article	NOUN	NN	Number=Sing	31	pobj	_	_
35	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	36	nsubj	_	_
36	allow	allow	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	$ M(A, B) $	$ m(a, b) $	SYM	$	_	40	nsubj	_	_
39	to	to	PART	TO	_	40	aux	_	_
40	be	be	AUX	VB	VerbForm=Inf	36	ccomp	_	_
41	general	general	ADJ	JJ	Degree=Pos	42	amod	_	_
42	categories	category	NOUN	NNS	Number=Plur	40	attr	_	SpaceAfter=No
43	,	,	PUNCT	,	PunctType=Comm	40	punct	_	_
44	and	and	CCONJ	CC	ConjType=Cmp	40	cc	_	_
45	illustrate	illustrate	VERB	VB	VerbForm=Inf	40	conj	_	_
46	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	47	poss	_	_
47	results	result	NOUN	NNS	Number=Plur	45	dobj	_	_
48	by	by	ADP	IN	_	45	prep	_	_
49	a	a	DET	DT	Definite=Ind|PronType=Art	51	det	_	_
50	detailed	detailed	ADJ	JJ	Degree=Pos	51	amod	_	_
51	study	study	NOUN	NN	Number=Sing	48	pobj	_	_
52	of	of	ADP	IN	_	51	prep	_	_
53	the	the	DET	DT	Definite=Def|PronType=Art	54	det	_	_
54	case	case	NOUN	NN	Number=Sing	52	pobj	_	_
55	$ M=spnK $	$ m=spnk $	SYM	$	_	45	dobj	_	_
56	.	.	PUNCT	.	PunctType=Peri	36	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show in particular that $ spn $ is a locally - fully - faithful 2 - functor to the 2 - category of equipments, and determine its image on arrows.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	particular	particular	ADJ	JJ	Degree=Pos	3	amod	_	_
5	that	that	SCONJ	IN	_	7	mark	_	_
6	$ spn $	$ spn $	SYM	$	_	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
9	locally	locally	ADV	RB	_	13	advmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
11	fully	fully	ADV	RB	_	13	advmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	faithful	faithful	ADJ	JJ	Degree=Pos	16	amod	_	_
14	2	2	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	functor	functor	NOUN	NN	Number=Sing	7	attr	_	_
17	to	to	ADP	IN	_	7	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
19	2	2	NUM	CD	NumType=Card	21	nummod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	category	category	NOUN	NN	Number=Sing	17	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	equipments	equipment	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
26	determine	determine	VERB	VB	VerbForm=Inf	7	conj	_	_
27	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	28	poss	_	_
28	image	image	NOUN	NN	Number=Sing	26	dobj	_	_
29	on	on	ADP	IN	_	28	prep	_	_
30	arrows	arrow	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = After analyzing the nature of adjunctions in the 2 - category of equipments, we are able to give a simple characterization of those $ spn G $ which arise from a geometric morphism $ G $ .
1	After	after	ADP	IN	_	16	prep	_	_
2	analyzing	analyze	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	1	pcomp	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	nature	nature	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	adjunctions	adjunction	NOUN	NNS	Number=Plur	5	pobj	_	_
7	in	in	ADP	IN	_	2	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
9	2	2	NUM	CD	NumType=Card	11	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	equipments	equipment	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
15	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	16	nsubj	_	_
16	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
17	able	able	ADJ	JJ	Degree=Pos	16	acomp	_	_
18	to	to	PART	TO	_	19	aux	_	_
19	give	give	VERB	VB	VerbForm=Inf	17	xcomp	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	simple	simple	ADJ	JJ	Degree=Pos	22	amod	_	_
22	characterization	characterization	NOUN	NN	Number=Sing	19	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	those	those	DET	DT	Number=Plur|PronType=Dem	25	det	_	_
25	$ spn G $	$ spn g $	SYM	$	_	23	pobj	_	_
26	which	which	PRON	WDT	_	27	nsubj	_	_
27	arise	arise	VERB	VBP	Tense=Pres|VerbForm=Fin	25	relcl	_	_
28	from	from	ADP	IN	_	27	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	geometric	geometric	ADJ	JJ	Degree=Pos	31	amod	_	_
31	morphism	morphism	NOUN	NN	Number=Sing	28	pobj	_	_
32	$ G $	$ g $	SYM	$	_	27	dobj	_	_
33	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# doc_id = 64
# sent_id = 1
# text = The theory of enriched accessible categories over a suitable base category $ V $ is developed.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	theory	theory	NOUN	NN	Number=Sing	14	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	amod	_	_
5	accessible	accessible	ADJ	JJ	Degree=Pos	6	amod	_	_
6	categories	category	NOUN	NNS	Number=Plur	3	pobj	_	_
7	over	over	ADP	IN	_	2	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	suitable	suitable	ADJ	JJ	Degree=Pos	11	amod	_	_
10	base	base	NOUN	NN	Number=Sing	11	compound	_	_
11	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
12	$ V $	$ v $	SYM	$	_	2	appos	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 2
# text = It is proved that these enriched accessible categories coincide with the categories of flat functors, but also with the categories of models of enriched sketches.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	SCONJ	IN	_	9	mark	_	_
5	these	these	DET	DT	Number=Plur|PronType=Dem	8	det	_	_
6	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
7	accessible	accessible	ADJ	JJ	Degree=Pos	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	coincide	coincide	VERB	VBP	Tense=Pres|VerbForm=Fin	3	ccomp	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	flat	flat	ADJ	JJ	Degree=Pos	15	amod	_	_
15	functors	functor	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
17	but	but	CCONJ	CC	ConjType=Cmp	9	cc	_	_
18	also	also	ADV	RB	_	17	advmod	_	_
19	with	with	ADP	IN	_	9	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	categories	category	NOUN	NNS	Number=Plur	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	models	model	NOUN	NNS	Number=Plur	22	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	enriched	enriched	ADJ	JJ	Degree=Pos	26	amod	_	_
26	sketches	sketch	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = A particular attention is devoted to enriched locally presentable categories and enriched functors.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	3	amod	_	_
3	attention	attention	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	devoted	devote	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
8	locally	locally	ADV	RB	_	10	advmod	_	_
9	presentable	presentable	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	enriched	enriched	ADJ	JJ	Degree=Pos	13	amod	_	_
13	functors	functor	NOUN	NNS	Number=Plur	10	conj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 65
# sent_id = 1
# text = We show that the homotopy category of simplicial diagrams $ I - SS $ indexed by a small category $ I $ is equivalent to a homotopy category of $ SSdownarrow NI $ simplicial sets over the nerve $ NI $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	17	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	homotopy	homotopy	NOUN	NN	Number=Sing	6	compound	_	_
6	category	category	NOUN	NN	Number=Sing	17	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	simplicial	simplicial	ADJ	JJ	Degree=Pos	9	amod	_	_
9	diagrams	diagram	NOUN	NNS	Number=Plur	7	pobj	_	_
10	$ I - SS $	$ i - ss $	SYM	$	_	6	appos	_	_
11	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
12	by	by	ADP	IN	_	11	agent	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	small	small	ADJ	JJ	Degree=Pos	15	amod	_	_
15	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
16	$ I $	$ i $	SYM	$	_	15	appos	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
18	equivalent	equivalent	ADJ	JJ	Degree=Pos	17	acomp	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	homotopy	homotopy	NOUN	NN	Number=Sing	22	compound	_	_
22	category	category	NOUN	NN	Number=Sing	19	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	$ SSdownarrow NI $	$ ssdownarrow ni $	SYM	$	_	26	nmod	_	_
25	simplicial	simplicial	ADJ	JJ	Degree=Pos	26	amod	_	_
26	sets	set	NOUN	NNS	Number=Plur	23	pobj	_	_
27	over	over	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	nerve	nerve	NOUN	NN	Number=Sing	27	pobj	_	_
30	$ NI $	$ ni $	SYM	$	_	17	dep	_	_
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Then their equivalences, by means of the nerve functor N : Cat - - > SS $ from the category $ Cat $ of small categories, with respective homotopy categories associated to $ Cat $ are established.
1	Then	then	ADV	RB	PronType=Dem	26	advmod	_	_
2	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	3	poss	_	_
3	equivalences	equivalence	NOUN	NNS	Number=Plur	26	nsubjpass	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
5	by	by	ADP	IN	_	3	prep	_	_
6	means	mean	NOUN	NNS	Number=Plur	5	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	nerve	nerve	NOUN	NN	Number=Sing	10	compound	_	_
10	functor	functor	NOUN	NN	Number=Sing	7	pobj	_	_
11	N	N	PROPN	NNP	Number=Sing	3	appos	_	_
12	:	:	PUNCT	:	_	26	punct	_	_
13	Cat	Cat	PROPN	NNP	Number=Sing	21	nmod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
16	&	&	CCONJ	CC	ConjType=Cmp	13	cc	_	SpaceAfter=No
17	gt	gt	PROPN	NNP	Number=Sing	13	conj	_	SpaceAfter=No
18	;	;	PUNCT	:	_	13	punct	_	_
19	SS	SS	PROPN	NNP	Number=Sing	13	conj	_	_
20	$ from the category $	$ from the category $	SYM	$	_	21	nmod	_	_
21	Cat	Cat	PROPN	NNP	Number=Sing	26	nsubjpass	_	_
22	$ of small categories, with respective homotopy categories associated to $	$ of small categories, with respective homotopy categories associated to $	SYM	$	_	23	nmod	_	_
23	Cat	Cat	PROPN	NNP	Number=Sing	21	appos	_	_
24	$	$	PRON	WP	_	21	appos	_	_
25	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	26	auxpass	_	_
26	established	establish	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	26	punct	_	SpaceAfter=No

# sent_id = 3
# text = Consequently, an equivariant simplicial version of the Whitehead Theorem is derived.
1	Consequently	consequently	ADV	RB	_	12	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
4	equivariant	equivariant	ADJ	JJ	Degree=Pos	6	amod	_	_
5	simplicial	simplicial	ADJ	JJ	Degree=Pos	6	amod	_	_
6	version	version	NOUN	NN	Number=Sing	12	nsubjpass	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	Whitehead	Whitehead	PROPN	NNP	Number=Sing	10	compound	_	_
10	Theorem	Theorem	PROPN	NNP	Number=Sing	7	pobj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	derived	derive	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# doc_id = 66
# sent_id = 1
# text = Using descent theory we give various forms of short five - lemma in protomodular categories, known in the case of exact protomodular categories.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	advcl	_	_
2	descent	descent	NOUN	NN	Number=Sing	3	compound	_	_
3	theory	theory	NOUN	NN	Number=Sing	1	dobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	various	various	ADJ	JJ	Degree=Pos	7	amod	_	_
7	forms	form	NOUN	NNS	Number=Plur	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	short	short	ADJ	JJ	Degree=Pos	12	amod	_	_
10	five	five	NUM	CD	NumType=Card	12	nummod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	lemma	lemma	NOUN	NN	Number=Sing	8	pobj	_	_
13	in	in	ADP	IN	_	5	prep	_	_
14	protomodular	protomodular	ADJ	JJ	Degree=Pos	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	case	case	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	exact	exact	ADJ	JJ	Degree=Pos	24	amod	_	_
23	protomodular	protomodular	ADJ	JJ	Degree=Pos	24	amod	_	_
24	categories	category	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = We also describe the situation where the notion of a semidirect product can be defined categorically.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	situation	situation	NOUN	NN	Number=Sing	3	dobj	_	_
6	where	where	SCONJ	WRB	_	15	advmod	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	notion	notion	NOUN	NN	Number=Sing	15	nsubjpass	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	semidirect	semidirect	NOUN	NN	Number=Sing	12	compound	_	_
12	product	product	NOUN	NN	Number=Sing	9	pobj	_	_
13	can	can	AUX	MD	VerbForm=Fin	15	aux	_	_
14	be	be	AUX	VB	VerbForm=Inf	15	auxpass	_	_
15	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	relcl	_	_
16	categorically	categorically	ADV	RB	_	15	advmod	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 67
# sent_id = 1
# text = In the literature there are several kinds of concrete and abstract cell complexes representing composition in $ n $ - categories, $ omega $ - categories or $ infty $ - categories, and the slightly more general partial $ omega $ - categories.
1	In	in	ADP	IN	_	5	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	literature	literature	NOUN	NN	Number=Sing	1	pobj	_	_
4	there	there	PRON	EX	_	5	expl	_	_
5	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	several	several	ADJ	JJ	Degree=Pos	7	amod	_	_
7	kinds	kind	NOUN	NNS	Number=Plur	5	attr	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	concrete	concrete	ADJ	JJ	Degree=Pos	13	amod	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	abstract	abstract	ADJ	JJ	Degree=Pos	9	conj	_	_
12	cell	cell	NOUN	NN	Number=Sing	13	compound	_	_
13	complexes	complex	NOUN	NNS	Number=Plur	8	pobj	_	_
14	representing	represent	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	acl	_	_
15	composition	composition	NOUN	NN	Number=Sing	14	dobj	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	$ n $	$ n $	SYM	$	_	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	$ omega $	$ omega $	SYM	$	_	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	categories	category	NOUN	NNS	Number=Plur	19	conj	_	_
24	or	or	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	$ infty $	$ infty $	SYM	$	_	27	nmod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	categories	category	NOUN	NNS	Number=Plur	23	conj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
31	slightly	slightly	ADV	RB	_	32	advmod	_	_
32	more	more	ADV	RBR	Degree=Cmp	33	advmod	_	_
33	general	general	ADJ	JJ	Degree=Pos	37	amod	_	_
34	partial	partial	ADJ	JJ	Degree=Pos	37	amod	_	_
35	$ omega $	$ omega $	SYM	$	_	37	compound	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	categories	category	NOUN	NNS	Number=Plur	5	conj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = Some examples are parity complexes, pasting schemes and directed complexes.
1	Some	some	DET	DT	_	2	det	_	_
2	examples	example	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	parity	parity	NOUN	NN	Number=Sing	5	compound	_	_
5	complexes	complex	NOUN	NNS	Number=Plur	3	attr	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	pasting	paste	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	advcl	_	_
8	schemes	scheme	NOUN	NNS	Number=Plur	7	dobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
11	complexes	complex	NOUN	NNS	Number=Plur	8	conj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this paper we give an axiomatic treatment: that is to say, we study the class of ` $ omeg $ - complexes' which consists of all complexes representing partial $ omega $ - categories.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	16	ccomp	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	axiomatic	axiomatic	ADJ	JJ	Degree=Pos	8	amod	_	_
8	treatment	treatment	NOUN	NN	Number=Sing	5	dobj	_	SpaceAfter=No
9	:	:	PUNCT	:	_	16	punct	_	_
10	that	that	PRON	DT	Number=Sing|PronType=Dem	11	nsubj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	parataxis	_	_
12	to	to	PART	TO	_	13	aux	_	_
13	say	say	VERB	VB	VerbForm=Inf	11	xcomp	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
15	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	16	nsubj	_	_
16	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	class	class	NOUN	NN	Number=Sing	16	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	19	punct	_	_
21	$ omeg $	$ omeg $	SYM	$	_	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	complexes	complex	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
24	'	'	PART	POS	_	23	punct	_	_
25	which	which	PRON	WDT	_	26	nsubj	_	_
26	consists	consist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	relcl	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	all	all	DET	DT	_	29	det	_	_
29	complexes	complex	NOUN	NNS	Number=Plur	27	pobj	_	_
30	representing	represent	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	29	acl	_	_
31	partial	partial	ADJ	JJ	Degree=Pos	34	amod	_	_
32	$ omega $	$ omega $	SYM	$	_	34	compound	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	categories	category	NOUN	NNS	Number=Plur	30	dobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show that $ omega $ - complexes can be given geometric structures and that in most important examples they become well - behaved CW complexes; we characterise $ omega $ - complexes by conditions on their cells; we show that a product of $ omega $ - complexes is again an $ omega $ - complex; and we describe some products in detail.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	9	mark	_	_
4	$ omega $	$ omega $	SYM	$	_	6	compound	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	complexes	complex	NOUN	NNS	Number=Plur	9	nsubjpass	_	_
7	can	can	AUX	MD	VerbForm=Fin	9	aux	_	_
8	be	be	AUX	VB	VerbForm=Inf	9	auxpass	_	_
9	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
10	geometric	geometric	ADJ	JJ	Degree=Pos	11	amod	_	_
11	structures	structure	NOUN	NNS	Number=Plur	9	dobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
13	that	that	SCONJ	IN	_	19	mark	_	_
14	in	in	ADP	IN	_	19	prep	_	_
15	most	most	ADV	RBS	Degree=Sup	16	advmod	_	_
16	important	important	ADJ	JJ	Degree=Pos	17	amod	_	_
17	examples	example	NOUN	NNS	Number=Plur	14	pobj	_	_
18	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	19	nsubj	_	_
19	become	become	VERB	VBP	Tense=Pres|VerbForm=Fin	9	conj	_	_
20	well	well	ADV	RB	Degree=Pos	22	advmod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	behaved	behave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
23	CW	CW	PROPN	NNP	Number=Sing	24	compound	_	_
24	complexes	complex	NOUN	NNS	Number=Plur	19	attr	_	SpaceAfter=No
25	;	;	PUNCT	:	_	27	punct	_	_
26	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	27	nsubj	_	_
27	characterise	characterise	VERB	VBP	Tense=Pres|VerbForm=Fin	38	ccomp	_	_
28	$ omega $	$ omega $	SYM	$	_	30	compound	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	complexes	complex	NOUN	NNS	Number=Plur	27	dobj	_	_
31	by	by	ADP	IN	_	30	prep	_	_
32	conditions	condition	NOUN	NNS	Number=Plur	31	pobj	_	_
33	on	on	ADP	IN	_	32	prep	_	_
34	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	35	poss	_	_
35	cells	cell	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
36	;	;	PUNCT	:	_	38	punct	_	_
37	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	38	nsubj	_	_
38	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
39	that	that	SCONJ	IN	_	46	mark	_	_
40	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
41	product	product	NOUN	NN	Number=Sing	46	nsubj	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	$ omega $	$ omega $	SYM	$	_	45	compound	_	_
44	-	-	PUNCT	HYPH	PunctType=Dash	45	punct	_	_
45	complexes	complex	NOUN	NNS	Number=Plur	42	pobj	_	_
46	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	38	ccomp	_	_
47	again	again	ADV	RB	_	46	advmod	_	_
48	an	an	DET	DT	Definite=Ind|PronType=Art	51	det	_	_
49	$ omega $	$ omega $	SYM	$	_	51	nmod	_	_
50	-	-	PUNCT	HYPH	PunctType=Dash	51	punct	_	_
51	complex	complex	ADJ	JJ	Degree=Pos	46	attr	_	SpaceAfter=No
52	;	;	PUNCT	:	_	2	punct	_	_
53	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
54	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	55	nsubj	_	_
55	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
56	some	some	DET	DT	_	57	det	_	_
57	products	product	NOUN	NNS	Number=Plur	55	dobj	_	_
58	in	in	ADP	IN	_	55	prep	_	_
59	detail	detail	NOUN	NN	Number=Sing	58	pobj	_	SpaceAfter=No
60	.	.	PUNCT	.	PunctType=Peri	55	punct	_	SpaceAfter=No

# doc_id = 68
# sent_id = 1
# text = If $ cal M $ is both an abelian category and a symmetric monoidal closed category, then it is natural to ask whether projective objects in $ cal M $ are flat, and whether the tensor product of two projective objects is projective.
1	If	if	SCONJ	IN	_	3	mark	_	_
2	$ cal M $	$ cal m $	SYM	$	_	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	advcl	_	_
4	both	both	PRON	DT	_	7	preconj	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	abelian	abelian	ADJ	JJ	Degree=Pos	7	compound	_	_
7	category	category	NOUN	NN	Number=Sing	3	attr	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
10	symmetric	symmetric	ADJ	JJ	Degree=Pos	11	amod	_	_
11	monoidal	monoidal	NOUN	NN	Number=Sing	13	amod	_	_
12	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	7	conj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
15	then	then	ADV	RB	PronType=Dem	17	advmod	_	_
16	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	17	nsubj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
18	natural	natural	ADJ	JJ	Degree=Pos	17	acomp	_	_
19	to	to	PART	TO	_	20	aux	_	_
20	ask	ask	VERB	VB	VerbForm=Inf	17	xcomp	_	_
21	whether	whether	SCONJ	IN	_	26	mark	_	_
22	projective	projective	ADJ	JJ	Degree=Pos	23	amod	_	_
23	objects	object	NOUN	NNS	Number=Plur	26	nsubj	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	$ cal M $	$ cal m $	SYM	$	_	24	pobj	_	_
26	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	20	ccomp	_	_
27	flat	flat	ADJ	JJ	Degree=Pos	26	acomp	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
30	whether	whether	SCONJ	IN	_	38	mark	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	tensor	tensor	NOUN	NN	Number=Sing	33	compound	_	_
33	product	product	NOUN	NN	Number=Sing	38	nsubj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	two	two	NUM	CD	NumType=Card	37	nummod	_	_
36	projective	projective	ADJ	JJ	Degree=Pos	37	amod	_	_
37	objects	object	NOUN	NNS	Number=Plur	34	pobj	_	_
38	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	conj	_	_
39	projective	projective	ADJ	JJ	Degree=Pos	38	acomp	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 2
# text = In the most familiar such categories, the answer to these questions is obviously yes.
1	In	in	ADP	IN	_	13	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
3	most	most	ADV	RBS	Degree=Sup	4	advmod	_	_
4	familiar	familiar	ADJ	JJ	Degree=Pos	6	amod	_	_
5	such	such	ADJ	JJ	Degree=Pos	6	amod	_	_
6	categories	category	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	answer	answer	NOUN	NN	Number=Sing	13	nsubj	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	these	these	DET	DT	Number=Plur|PronType=Dem	12	det	_	_
12	questions	question	NOUN	NNS	Number=Plur	10	pobj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	obviously	obviously	ADV	RB	_	13	advmod	_	_
15	yes	yes	INTJ	UH	_	13	intj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 3
# text = However, the category $ cal M_G $ of Mackey functors for a compact Lie group $ G $ is a category of this type in which projective objects need not be so well - behaved.
1	However	however	ADV	RB	_	15	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	category	category	NOUN	NN	Number=Sing	15	nsubj	_	_
5	$ cal M_G $	$ cal m_g $	SYM	$	_	4	appos	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Mackey	Mackey	PROPN	NNP	Number=Sing	8	compound	_	_
8	functors	functor	NOUN	NNS	Number=Plur	6	pobj	_	_
9	for	for	ADP	IN	_	5	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	compact	compact	ADJ	JJ	Degree=Pos	12	amod	_	_
12	Lie	lie	NOUN	NN	Number=Sing	13	compound	_	_
13	group	group	NOUN	NN	Number=Sing	9	pobj	_	_
14	$ G $	$ g $	SYM	$	_	4	appos	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	category	category	NOUN	NN	Number=Sing	15	attr	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	this	this	DET	DT	Number=Sing|PronType=Dem	20	det	_	_
20	type	type	NOUN	NN	Number=Sing	18	pobj	_	_
21	in	in	ADP	IN	_	27	prep	_	_
22	which	which	PRON	WDT	_	21	pobj	_	_
23	projective	projective	ADJ	JJ	Degree=Pos	24	amod	_	_
24	objects	object	NOUN	NNS	Number=Plur	27	nsubj	_	_
25	need	need	AUX	VBP	Tense=Pres|VerbForm=Fin	27	aux	_	_
26	not	not	PART	RB	Polarity=Neg	27	neg	_	_
27	be	be	AUX	VB	VerbForm=Inf	17	relcl	_	_
28	so	so	ADV	RB	_	31	advmod	_	_
29	well	well	ADV	RB	Degree=Pos	31	advmod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	behaved	behave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	acomp	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 4
# text = This category is of interest since good equivariant cohomology theories are Mackey functor valued.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	interest	interest	NOUN	NN	Number=Sing	4	pobj	_	_
6	since	since	SCONJ	IN	_	11	mark	_	_
7	good	good	ADJ	JJ	Degree=Pos	9	amod	_	_
8	equivariant	equivariant	ADJ	JJ	Degree=Pos	9	amod	_	_
9	cohomology	cohomology	NOUN	NN	Number=Sing	10	compound	_	_
10	theories	theory	NOUN	NNS	Number=Plur	11	nsubj	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	advcl	_	_
12	Mackey	Mackey	PROPN	NNP	Number=Sing	13	compound	_	_
13	functor	functor	NOUN	NN	Number=Sing	11	attr	_	_
14	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	acl	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = The tensor product on $ cal M_G $ is important in this context because of the role it plays in the not yet fully understood universal coefficient and K"{u}nneth formulae.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	tensor	tensor	NOUN	NN	Number=Sing	3	compound	_	_
3	product	product	NOUN	NN	Number=Sing	6	nsubj	_	_
4	on	on	ADP	IN	_	3	prep	_	_
5	$ cal M_G $	$ cal m_g $	SYM	$	_	4	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	important	important	ADJ	JJ	Degree=Pos	6	acomp	_	_
8	in	in	ADP	IN	_	6	prep	_	_
9	this	this	DET	DT	Number=Sing|PronType=Dem	10	det	_	_
10	context	context	NOUN	NN	Number=Sing	8	pobj	_	_
11	because	because	SCONJ	IN	_	6	prep	_	_
12	of	of	ADP	IN	_	11	pcomp	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	role	role	NOUN	NN	Number=Sing	11	pobj	_	_
15	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	16	nsubj	_	_
16	plays	play	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
19	not	not	PART	RB	Polarity=Neg	20	neg	_	_
20	yet	yet	ADV	RB	_	21	advmod	_	_
21	fully	fully	ADV	RB	_	22	advmod	_	_
22	understood	understand	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
23	universal	universal	ADJ	JJ	Degree=Pos	24	amod	_	_
24	coefficient	coefficient	NOUN	NN	Number=Sing	17	pobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	K"{u}nneth	K"{u}nneth	PROPN	NNP	Number=Sing	27	compound	_	_
27	formulae	formulae	PROPN	NNP	Number=Sing	24	conj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 6
# text = This role makes the relationship between projective objects and the tensor product especially critical.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	role	role	NOUN	NN	Number=Sing	3	nsubj	_	_
3	makes	make	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	relationship	relationship	NOUN	NN	Number=Sing	14	nsubj	_	_
6	between	between	ADP	IN	_	5	prep	_	_
7	projective	projective	ADJ	JJ	Degree=Pos	8	amod	_	_
8	objects	object	NOUN	NNS	Number=Plur	6	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	tensor	tensor	NOUN	NN	Number=Sing	12	compound	_	_
12	product	product	NOUN	NN	Number=Sing	8	conj	_	_
13	especially	especially	ADV	RB	_	14	advmod	_	_
14	critical	critical	ADJ	JJ	Degree=Pos	3	ccomp	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = Unfortunately, if $ G $ is, for example, $ O(n) $ , then projectives need not be flat in $ cal M_G $ and the tensor product of projective objects need not be projective.
1	Unfortunately	unfortunately	ADV	RB	_	16	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
3	if	if	SCONJ	IN	_	5	mark	_	_
4	$ G $	$ g $	SYM	$	_	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	advcl	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
7	for	for	ADP	IN	_	10	prep	_	_
8	example	example	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
10	$ O(n) $	$ o(n) $	SYM	$	_	5	attr	_	_
11	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
12	then	then	ADV	RB	PronType=Dem	16	advmod	_	_
13	projectives	projective	NOUN	NNS	Number=Plur	16	nsubj	_	_
14	need	need	AUX	MD	VerbType=Mod	16	aux	_	_
15	not	not	PART	RB	Polarity=Neg	16	neg	_	_
16	be	be	AUX	VB	VerbForm=Inf	0	ROOT	_	_
17	flat	flat	ADJ	JJ	Degree=Pos	16	acomp	_	_
18	in	in	ADP	IN	_	16	prep	_	_
19	$ cal M_G $	$ cal m_g $	SYM	$	_	18	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	tensor	tensor	NOUN	NN	Number=Sing	23	compound	_	_
23	product	product	NOUN	NN	Number=Sing	29	nsubj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	projective	projective	ADJ	JJ	Degree=Pos	26	amod	_	_
26	objects	object	NOUN	NNS	Number=Plur	24	pobj	_	_
27	need	need	AUX	VBP	Tense=Pres|VerbForm=Fin	29	aux	_	_
28	not	not	PART	RB	Polarity=Neg	29	neg	_	_
29	be	be	AUX	VB	VerbForm=Inf	16	conj	_	_
30	projective	projective	ADJ	JJ	Degree=Pos	29	acomp	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	29	punct	_	SpaceAfter=No

# sent_id = 8
# text = This misbe haviorcomplicates the search for full strength equivariant universal coefficient and K"{u}nneth formulae.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	misbe	misbe	NOUN	NN	Number=Sing	3	nsubj	_	_
3	haviorcomplicates	haviorcomplicate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	search	search	NOUN	NN	Number=Sing	3	dobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	full	full	ADJ	JJ	Degree=Pos	11	amod	_	_
8	strength	strength	NOUN	NN	Number=Sing	9	nmod	_	_
9	equivariant	equivariant	ADJ	JJ	Degree=Pos	11	amod	_	_
10	universal	universal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	coefficient	coefficient	NOUN	NN	Number=Sing	6	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	K"{u}nneth	K"{u}nneth	PROPN	NNP	Number=Sing	14	compound	_	_
14	formulae	formulae	PROPN	NNP	Number=Sing	11	conj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 9
# text = The primary purpose of this article is to investigate these questions about the interaction of the tensor product with projective objects in symmetric monoidal abelian categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	primary	primary	ADJ	JJ	Degree=Pos	3	amod	_	_
3	purpose	purpose	NOUN	NN	Number=Sing	7	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	article	article	NOUN	NN	Number=Sing	4	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	investigate	investigate	VERB	VB	VerbForm=Inf	7	xcomp	_	_
10	these	these	DET	DT	Number=Plur|PronType=Dem	11	det	_	_
11	questions	question	NOUN	NNS	Number=Plur	9	dobj	_	_
12	about	about	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	interaction	interaction	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	tensor	tensor	NOUN	NN	Number=Sing	18	compound	_	_
18	product	product	NOUN	NN	Number=Sing	15	pobj	_	_
19	with	with	ADP	IN	_	14	prep	_	_
20	projective	projective	ADJ	JJ	Degree=Pos	21	amod	_	_
21	objects	object	NOUN	NNS	Number=Plur	19	pobj	_	_
22	in	in	ADP	IN	_	21	prep	_	_
23	symmetric	symmetric	ADJ	JJ	Degree=Pos	26	amod	_	_
24	monoidal	monoidal	ADJ	JJ	Degree=Pos	26	amod	_	_
25	abelian	abelian	ADJ	JJ	Degree=Pos	26	compound	_	_
26	categories	category	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 10
# text = Our focus is on functor categories whose monoidal structures arise in a fashion described by Day.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	focus	focus	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	on	on	ADP	IN	_	3	prep	_	_
5	functor	functor	NOUN	NN	Number=Sing	6	compound	_	_
6	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	_
7	whose	whose	DET	WP$	Poss=Yes	9	poss	_	_
8	monoidal	monoidal	ADJ	JJ	Degree=Pos	9	amod	_	_
9	structures	structure	NOUN	NNS	Number=Plur	10	nsubj	_	_
10	arise	arise	VERB	VBP	Tense=Pres|VerbForm=Fin	6	relcl	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	fashion	fashion	NOUN	NN	Number=Sing	11	pobj	_	_
14	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	acl	_	_
15	by	by	ADP	IN	_	14	agent	_	_
16	Day	Day	PROPN	NNP	Number=Sing	15	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 11
# text = Conditions are given under which such a structure interacts appropriately with projective objects.
1	Conditions	condition	NOUN	NNS	Number=Plur	3	nsubjpass	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	under	under	ADP	IN	_	9	prep	_	_
5	which	which	PRON	WDT	_	4	pobj	_	_
6	such	such	DET	PDT	_	8	predet	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	structure	structure	NOUN	NN	Number=Sing	9	nsubj	_	_
9	interacts	interact	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	advcl	_	_
10	appropriately	appropriately	ADV	RB	_	9	advmod	_	_
11	with	with	ADP	IN	_	9	prep	_	_
12	projective	projective	ADJ	JJ	Degree=Pos	13	amod	_	_
13	objects	object	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 12
# text = Further, examples are given to show that, when these conditions aren't met, this interaction can be quite bad.
1	Further	far	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	examples	example	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	show	show	VERB	VB	VerbForm=Inf	5	advcl	_	_
8	that	that	SCONJ	IN	_	20	mark	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
10	when	when	SCONJ	WRB	_	15	advmod	_	_
11	these	these	DET	DT	Number=Plur|PronType=Dem	12	det	_	_
12	conditions	condition	NOUN	NNS	Number=Plur	15	nsubjpass	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	auxpass	_	SpaceAfter=No
14	n't	not	PART	RB	Polarity=Neg	15	neg	_	_
15	met	meet	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	advcl	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
17	this	this	DET	DT	Number=Sing|PronType=Dem	18	det	_	_
18	interaction	interaction	NOUN	NN	Number=Sing	20	nsubj	_	_
19	can	can	AUX	MD	VerbForm=Fin	20	aux	_	_
20	be	be	AUX	VB	VerbForm=Inf	7	ccomp	_	_
21	quite	quite	ADV	RB	_	22	advmod	_	_
22	bad	bad	ADJ	JJ	Degree=Pos	20	acomp	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 13
# text = These examples were not fabricated to illustrate the abstract possibility of misbehavior.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	examples	example	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
3	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	5	auxpass	_	_
4	not	not	PART	RB	Polarity=Neg	5	neg	_	_
5	fabricated	fabricate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	illustrate	illustrate	VERB	VB	VerbForm=Inf	5	xcomp	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	abstract	abstract	ADJ	JJ	Degree=Pos	10	amod	_	_
10	possibility	possibility	NOUN	NN	Number=Sing	7	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	misbehavior	misbehavior	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 14
# text = Rather, they are drawn from the literature.
1	Rather	rather	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	5	nsubjpass	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	drawn	draw	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	from	from	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	literature	literature	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 15
# text = In particular, $ cal M_G $ is badly behaved not only for the groups $ O(n) $ , but also for the groups $ SO(n) $ , $ U(n) $ , $ SU(n) $ , $ Sp(n) $ , and $ Spin(n) $ .
1	In	in	ADP	IN	_	7	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
4	$ cal M_G $	$ cal m_g $	SYM	$	_	7	nsubjpass	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
6	badly	badly	ADV	RB	_	7	advmod	_	_
7	behaved	behave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	not	not	PART	RB	Polarity=Neg	10	preconj	_	_
9	only	only	ADV	RB	_	8	advmod	_	_
10	for	for	ADP	IN	_	7	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	groups	group	NOUN	NNS	Number=Plur	10	pobj	_	_
13	$ O(n) $	$ o(n) $	SYM	$	_	12	appos	_	_
14	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
15	but	but	CCONJ	CC	ConjType=Cmp	10	cc	_	_
16	also	also	ADV	RB	_	15	advmod	_	_
17	for	for	ADP	IN	_	10	conj	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	groups	group	NOUN	NNS	Number=Plur	17	pobj	_	_
20	$ SO(n) $	$ so(n) $	SYM	$	_	7	dep	_	_
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	$ U(n) $	$ u(n) $	SYM	$	_	20	conj	_	_
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	$ SU(n) $	$ su(n) $	SYM	$	_	4	acl	_	_
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	$ Sp(n) $	$ sp(n) $	SYM	$	_	24	conj	_	_
27	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
29	$ Spin(n) $	$ spin(n) $	SYM	$	_	26	conj	_	_
30	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 16
# text = Similar misbehavior occurs in two categories of global Mackey functors which are widely used in the study of classifying spaces of finite groups.
1	Similar	similar	ADJ	JJ	Degree=Pos	2	amod	_	_
2	misbehavior	misbehavior	NOUN	NN	Number=Sing	3	nsubj	_	_
3	occurs	occur	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	in	in	ADP	IN	_	3	prep	_	_
5	two	two	NUM	CD	NumType=Card	6	nummod	_	_
6	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	global	global	ADJ	JJ	Degree=Pos	10	amod	_	_
9	Mackey	Mackey	PROPN	NNP	Number=Sing	10	compound	_	_
10	functors	functor	NOUN	NNS	Number=Plur	7	pobj	_	_
11	which	which	PRON	WDT	_	14	nsubjpass	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
13	widely	widely	ADV	RB	_	14	advmod	_	_
14	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	relcl	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	study	study	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	classifying	classify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	amod	_	_
20	spaces	space	NOUN	NNS	Number=Plur	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	finite	finite	ADJ	JJ	Degree=Pos	23	amod	_	_
23	groups	group	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 17
# text = Given the extent of the homological misbehavior in Mackey functor categories described here, it is reasonable to expect that similar problems occur in other functor categories carrying symmetric monoidal closed structures provided by Day's machinery.
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	extent	extent	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	homological	homological	ADJ	JJ	Degree=Pos	7	amod	_	_
7	misbehavior	misbehavior	NOUN	NN	Number=Sing	4	pobj	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	Mackey	Mackey	PROPN	NNP	Number=Sing	11	compound	_	_
10	functor	functor	NOUN	NN	Number=Sing	11	compound	_	_
11	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	_
12	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	acl	_	_
13	here	here	ADV	RB	PronType=Dem	12	advmod	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
15	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	16	nsubj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
17	reasonable	reasonable	ADJ	JJ	Degree=Pos	16	acomp	_	_
18	to	to	PART	TO	_	19	aux	_	_
19	expect	expect	VERB	VB	VerbForm=Inf	16	xcomp	_	_
20	that	that	SCONJ	IN	_	23	mark	_	_
21	similar	similar	ADJ	JJ	Degree=Pos	22	amod	_	_
22	problems	problem	NOUN	NNS	Number=Plur	23	nsubj	_	_
23	occur	occur	VERB	VBP	Tense=Pres|VerbForm=Fin	19	ccomp	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	other	other	ADJ	JJ	Degree=Pos	27	amod	_	_
26	functor	functor	NOUN	NN	Number=Sing	27	compound	_	_
27	categories	category	NOUN	NNS	Number=Plur	24	pobj	_	_
28	carrying	carry	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	27	acl	_	_
29	symmetric	symmetric	ADJ	JJ	Degree=Pos	30	amod	_	_
30	monoidal	monoidal	NOUN	NN	Number=Sing	28	dobj	_	_
31	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	amod	_	_
32	structures	structure	NOUN	NNS	Number=Plur	28	dobj	_	_
33	provided	provide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	acl	_	_
34	by	by	ADP	IN	_	33	agent	_	_
35	Day	Day	PROPN	NNP	Number=Sing	37	poss	_	SpaceAfter=No
36	's	's	PART	POS	_	35	case	_	_
37	machinery	machinery	NOUN	NN	Number=Sing	34	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# doc_id = 69
# sent_id = 1
# text = We give an abstract characterization of categories which are localizations of Maltsev varieties.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	abstract	abstract	ADJ	JJ	Degree=Pos	5	amod	_	_
5	characterization	characterization	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
8	which	which	PRON	WDT	_	9	nsubj	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	relcl	_	_
10	localizations	localization	NOUN	NNS	Number=Plur	9	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	Maltsev	Maltsev	PROPN	NNP	Number=Sing	13	compound	_	_
13	varieties	variety	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = These results can be applied to characterize localizations of naturally Maltsev varieties.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	results	result	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
3	can	can	AUX	MD	VerbForm=Fin	5	aux	_	_
4	be	be	AUX	VB	VerbForm=Inf	5	auxpass	_	_
5	applied	apply	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	characterize	characterize	VERB	VB	VerbForm=Inf	5	advcl	_	_
8	localizations	localization	NOUN	NNS	Number=Plur	7	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	naturally	naturally	ADV	RB	_	11	advmod	_	_
11	Maltsev	Maltsev	PROPN	NNP	Number=Sing	12	amod	_	_
12	varieties	variety	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 70
# sent_id = 1
# text = Using the Chu - construction, we define a group algebra for topological Hausdorff groups.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	advcl	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
3	Chu	Chu	PROPN	NNP	Number=Sing	5	compound	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	construction	construction	NOUN	NN	Number=Sing	1	dobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
7	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	8	nsubj	_	_
8	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	group	group	NOUN	NN	Number=Sing	11	compound	_	_
11	algebra	algebra	NOUN	NN	Number=Sing	8	dobj	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	topological	topological	ADJ	JJ	Degree=Pos	15	amod	_	_
14	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	15	compound	_	_
15	groups	group	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = Furthermore, for isometric, weakly continuous representations of a subgroup $ H $ of a Hausdorff group $ G $ induced representations are constructed.
1	Furthermore	furthermore	ADV	RB	_	21	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
3	for	for	ADP	IN	_	21	prep	_	_
4	isometric	isometric	ADJ	JJ	Degree=Pos	8	amod	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
6	weakly	weakly	ADJ	JJ	Degree=Pos	8	amod	_	_
7	continuous	continuous	ADJ	JJ	Degree=Pos	8	amod	_	_
8	representations	representation	NOUN	NNS	Number=Plur	21	nsubjpass	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	subgroup	subgroup	NOUN	NN	Number=Sing	9	pobj	_	_
12	$ H $	$ h $	SYM	$	_	11	appos	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	16	compound	_	_
16	group	group	NOUN	NN	Number=Sing	13	pobj	_	_
17	$ G $	$ g $	SYM	$	_	19	nmod	_	_
18	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
19	representations	representation	NOUN	NNS	Number=Plur	9	pobj	_	_
20	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	21	auxpass	_	_
21	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# doc_id = 71
# sent_id = 1
# text = Exponentiable spaces are characterized in terms of convergence.
1	Exponentiable	exponentiable	ADJ	JJ	Degree=Pos	2	amod	_	_
2	spaces	space	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	terms	term	NOUN	NNS	Number=Plur	5	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	convergence	convergence	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = More precisely, we prove that a relation $ R:{cal U}X rightharpoonup X $ between ultrafilters and elements of a set $ X $ is the convergence relation for a quasi - locally - compact (that is, exponentiable) topology on $ X $ if and only if the following conditions are satisfied: (i) $ id subseteq Rcirceta $ , (ii) $ Rcirc {cal U}R = Rcircmu $ where $ eta : X to {cal U}X $ and $ mu : {cal U}({cal U}X) to {cal U}X $ are the unit and the multiplication of the ultrafilter monad, and $ {cal U} : bi{Rel} to bi{Rel} $ extends the ultrafilter functor $ {cal U} : bi{Set} to bi{Set} $ to the category of sets and relations. $ ({cal U}, eta, mu) $ fails to be a monad on $ bi{Rel} $ only because $ eta $ is not a strict natural transformation.
1	More	more	ADV	RBR	Degree=Cmp	2	advmod	_	_
2	precisely	precisely	ADV	RB	_	5	advmod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	18	mark	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	relation	relation	NOUN	NN	Number=Sing	18	nsubj	_	_
9	$ R:{cal U}X rightharpoonup X $	$ r:{cal u}x rightharpoonup x $	SYM	$	_	8	appos	_	_
10	between	between	ADP	IN	_	8	prep	_	_
11	ultrafilters	ultrafilter	NOUN	NNS	Number=Plur	10	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	elements	element	NOUN	NNS	Number=Plur	11	conj	_	_
14	of	of	ADP	IN	_	11	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	set	set	NOUN	NN	Number=Sing	17	amod	_	_
17	$ X $	$ x $	SYM	$	_	14	pobj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	convergence	convergence	NOUN	NN	Number=Sing	21	compound	_	_
21	relation	relation	NOUN	NN	Number=Sing	18	attr	_	_
22	for	for	ADP	IN	_	21	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
24	quasi	quasi	ADJ	JJ	Degree=Pos	35	nmod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
26	locally	locally	ADV	RB	_	28	advmod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	compact	compact	ADJ	JJ	Degree=Pos	24	amod	_	_
29	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	31	punct	_	SpaceAfter=No
30	that	that	ADV	RB	_	31	advmod	_	_
31	is	is	ADV	RB	_	24	parataxis	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
33	exponentiable	exponentiable	ADJ	JJ	Degree=Pos	35	amod	_	SpaceAfter=No
34	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	35	punct	_	_
35	topology	topology	NOUN	NN	Number=Sing	22	pobj	_	_
36	on	on	ADP	IN	_	35	prep	_	_
37	$ X $	$ x $	SYM	$	_	36	pobj	_	_
38	if	if	SCONJ	IN	_	46	prep	_	_
39	and	and	CCONJ	CC	ConjType=Cmp	38	cc	_	_
40	only	only	ADV	RB	_	45	advmod	_	_
41	if	if	SCONJ	IN	_	45	mark	_	_
42	the	the	DET	DT	Definite=Def|PronType=Art	44	det	_	_
43	following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	44	amod	_	_
44	conditions	condition	NOUN	NNS	Number=Plur	45	nsubj	_	_
45	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	18	advcl	_	_
46	satisfied	satisfied	ADJ	JJ	Degree=Pos	45	acomp	_	SpaceAfter=No
47	:	:	PUNCT	:	_	46	punct	_	_
48	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	49	punct	_	SpaceAfter=No
49	i	i	NOUN	NN	Case=Nom|Number=Sing|Person=1|PronType=Prs	61	nsubj	_	SpaceAfter=No
50	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	49	punct	_	_
51	$ id subseteq Rcirceta $	$ id subseteq rcirceta $	SYM	$	_	49	appos	_	_
52	,	,	PUNCT	,	PunctType=Comm	49	punct	_	_
53	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	49	punct	_	SpaceAfter=No
54	ii	ii	PROPN	NNP	Number=Sing	49	appos	_	SpaceAfter=No
55	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	49	punct	_	_
56	$ Rcirc {cal U}R = Rcircmu $	$ rcirc {cal u}r = rcircmu $	SYM	$	_	49	appos	_	_
57	where	where	SCONJ	WRB	_	58	advmod	_	_
58	$ eta : X to {cal U}X $	$ eta : x to {cal u}x $	SYM	$	_	49	relcl	_	_
59	and	and	CCONJ	CC	ConjType=Cmp	58	cc	_	_
60	$ mu : {cal U}({cal U}X) to {cal U}X $	$ mu : {cal u}({cal u}x) to {cal u}x $	SYM	$	_	58	conj	_	_
61	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	46	ccomp	_	_
62	the	the	DET	DT	Definite=Def|PronType=Art	63	det	_	_
63	unit	unit	NOUN	NN	Number=Sing	61	attr	_	_
64	and	and	CCONJ	CC	ConjType=Cmp	63	cc	_	_
65	the	the	DET	DT	Definite=Def|PronType=Art	66	det	_	_
66	multiplication	multiplication	NOUN	NN	Number=Sing	63	conj	_	_
67	of	of	ADP	IN	_	66	prep	_	_
68	the	the	DET	DT	Definite=Def|PronType=Art	70	det	_	_
69	ultrafilter	ultrafilter	ADJ	JJ	Degree=Pos	70	compound	_	_
70	monad	monad	NOUN	NNS	Number=Plur	67	pobj	_	SpaceAfter=No
71	,	,	PUNCT	,	PunctType=Comm	66	punct	_	_
72	and	and	CCONJ	CC	ConjType=Cmp	66	cc	_	_
73	$ {cal U} : bi{Rel} to bi{Rel} $	$ {cal u} : bi{rel} to bi{rel} $	SYM	$	_	74	nsubj	_	_
74	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	61	conj	_	_
75	the	the	DET	DT	Definite=Def|PronType=Art	77	det	_	_
76	ultrafilter	ultrafilter	NOUN	NN	Number=Sing	77	compound	_	_
77	functor	functor	NOUN	NN	Number=Sing	74	dobj	_	_
78	$ {cal U} : bi{Set} to bi{Set} $	$ {cal u} : bi{set} to bi{set} $	SYM	$	_	74	dep	_	_
79	to	to	ADP	IN	_	74	prep	_	_
80	the	the	DET	DT	Definite=Def|PronType=Art	81	det	_	_
81	category	category	NOUN	NN	Number=Sing	79	pobj	_	_
82	of	of	ADP	IN	_	81	prep	_	_
83	sets	set	NOUN	NNS	Number=Plur	82	pobj	_	_
84	and	and	CCONJ	CC	ConjType=Cmp	83	cc	_	_
85	relations	relation	NOUN	NNS	Number=Plur	83	conj	_	SpaceAfter=No
86	.	.	PUNCT	.	PunctType=Peri	5	punct	_	_
87	$ ({cal U}, eta, mu) $	$ ({cal U}, eta, mu) $	PROPN	NNP	Number=Sing	88	nsubj	_	_
88	fails	fail	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
89	to	to	PART	TO	_	90	aux	_	_
90	be	be	AUX	VB	VerbForm=Inf	88	xcomp	_	_
91	a	a	DET	DT	Definite=Ind|PronType=Art	92	det	_	_
92	monad	monad	NOUN	NNS	Number=Plur	90	attr	_	_
93	on	on	ADP	IN	_	92	prep	_	_
94	$ bi{Rel} $	$ bi{rel} $	SYM	$	_	93	pobj	_	_
95	only	only	ADV	RB	_	94	advmod	_	_
96	because	because	SCONJ	IN	_	98	mark	_	_
97	$ eta $	$ eta $	SYM	$	_	98	nsubj	_	_
98	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	88	advcl	_	_
99	not	not	PART	RB	Polarity=Neg	98	neg	_	_
100	a	a	DET	DT	Definite=Ind|PronType=Art	103	det	_	_
101	strict	strict	ADJ	JJ	Degree=Pos	103	amod	_	_
102	natural	natural	ADJ	JJ	Degree=Pos	103	amod	_	_
103	transformation	transformation	NOUN	NN	Number=Sing	98	attr	_	SpaceAfter=No
104	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = So, exponentiable spaces are the lax (with respect to the unit law) algebras for a lax monad on $ bi{Rel} $ .
1	So	so	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	exponentiable	exponentiable	ADJ	JJ	Degree=Pos	4	amod	_	_
4	spaces	space	NOUN	NNS	Number=Plur	5	nsubj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	lax	lax	ADJ	JJ	Degree=Pos	5	attr	_	_
8	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	7	punct	_	SpaceAfter=No
9	with	with	ADP	IN	_	7	prep	_	_
10	respect	respect	NOUN	NN	Number=Sing	9	pobj	_	_
11	to	to	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	unit	unit	NOUN	NN	Number=Sing	14	compound	_	_
14	law	law	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
15	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	7	punct	_	_
16	algebras	algebra	NOUN	NNS	Number=Plur	7	appos	_	_
17	for	for	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	lax	lax	ADJ	JJ	Degree=Pos	20	amod	_	_
20	monad	monad	NOUN	NNS	Number=Plur	17	pobj	_	_
21	on	on	ADP	IN	_	20	prep	_	_
22	$ bi{Rel} $	$ bi{rel} $	SYM	$	_	21	pobj	_	_
23	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = Strict algebras are exponentiable and $ T_1 $ spaces.
1	Strict	strict	ADJ	JJ	Degree=Pos	2	amod	_	_
2	algebras	algebra	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	exponentiable	exponentiable	ADJ	JJ	Degree=Pos	3	acomp	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	$ T_1 $	$ t_1 $	SYM	$	_	7	nmod	_	_
7	spaces	space	NOUN	NNS	Number=Plur	4	conj	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 72
# sent_id = 1
# text = We define distributive laws between pseudomonads in a Gray - category $ A $ , as the classical two triangles and the two pentagons but commuting only up to isomorphism.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	distributive	distributive	ADJ	JJ	Degree=Pos	4	amod	_	_
4	laws	law	NOUN	NNS	Number=Plur	2	dobj	_	_
5	between	between	ADP	IN	_	4	prep	_	_
6	pseudomonads	pseudomonad	NOUN	NNS	Number=Plur	5	pobj	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
9	Gray	Gray	PROPN	NNP	Number=Sing	11	compound	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	category	category	NOUN	NN	Number=Sing	12	compound	_	_
12	$ A $	$ a $	SYM	$	_	7	pobj	_	_
13	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
14	as	as	ADP	IN	_	2	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
16	classical	classical	ADJ	JJ	Degree=Pos	18	amod	_	_
17	two	two	NUM	CD	NumType=Card	18	nummod	_	_
18	triangles	triangle	NOUN	NNS	Number=Plur	14	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	two	two	NUM	CD	NumType=Card	22	nummod	_	_
22	pentagons	pentagon	NOUN	NNS	Number=Plur	18	conj	_	_
23	but	but	CCONJ	CC	ConjType=Cmp	2	cc	_	_
24	commuting	commute	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	conj	_	_
25	only	only	ADV	RB	_	26	advmod	_	_
26	up	up	ADP	IN	_	24	prep	_	_
27	to	to	ADP	IN	_	26	prep	_	_
28	isomorphism	isomorphism	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = These isomorphisms must satisfy nine coherence conditions.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	isomorphisms	isomorphism	NOUN	NNS	Number=Plur	4	nsubj	_	_
3	must	must	AUX	MD	VerbForm=Fin	4	aux	_	_
4	satisfy	satisfy	VERB	VB	VerbForm=Inf	0	ROOT	_	_
5	nine	nine	NUM	CD	NumType=Card	7	nummod	_	_
6	coherence	coherence	NOUN	NN	Number=Sing	7	compound	_	_
7	conditions	condition	NOUN	NNS	Number=Plur	4	dobj	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also define the gray - category $ PSM(A) $ of pseudomonads in $ A $ , and define a lifting to be a pseudomonad in $ PSM(A) $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
5	gray	gray	ADJ	JJ	Degree=Pos	7	amod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	category	category	NOUN	NN	Number=Sing	8	nmod	_	_
8	$ PSM(A) $	$ psm(a) $	SYM	$	_	3	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	pseudomonads	pseudomonad	NOUN	NNS	Number=Plur	9	pobj	_	_
11	in	in	ADP	IN	_	8	prep	_	_
12	$ A $	$ a $	SYM	$	_	11	pobj	_	_
13	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
15	define	define	VERB	VB	VerbForm=Inf	3	conj	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	lifting	lifting	NOUN	NN	Number=Sing	15	dobj	_	_
18	to	to	PART	TO	_	19	aux	_	_
19	be	be	AUX	VB	VerbForm=Inf	15	advcl	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	pseudomonad	pseudomonad	NOUN	NNS	Number=Plur	19	attr	_	_
22	in	in	ADP	IN	_	21	prep	_	_
23	$ PSM(A) $	$ psm(a) $	SYM	$	_	22	pobj	_	_
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = We define what is a pseudomonad with compatible structure with respect to two given pseudomonads.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	what	what	PRON	WP	_	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	pseudomonad	pseudomonad	NOUN	NNS	Number=Plur	4	attr	_	_
7	with	with	ADP	IN	_	6	prep	_	_
8	compatible	compatible	ADJ	JJ	Degree=Pos	9	amod	_	_
9	structure	structure	NOUN	NN	Number=Sing	7	pobj	_	_
10	with	with	ADP	IN	_	4	prep	_	_
11	respect	respect	NOUN	NN	Number=Sing	10	pobj	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	two	two	NUM	CD	NumType=Card	15	nummod	_	_
14	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
15	pseudomonads	pseudomonad	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = We show how to obtain a pseudomonad with compatible structure from a distributive law, how to get a lifting from a pseudomonad with compatible structure, and how to obtain a distributive law from a lifting.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	how	how	SCONJ	WRB	_	5	advmod	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	obtain	obtain	VERB	VB	VerbForm=Inf	2	xcomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	pseudomonad	pseudomonad	NOUN	NNS	Number=Plur	5	dobj	_	_
8	with	with	ADP	IN	_	5	prep	_	_
9	compatible	compatible	ADJ	JJ	Degree=Pos	10	amod	_	_
10	structure	structure	NOUN	NN	Number=Sing	8	pobj	_	_
11	from	from	ADP	IN	_	5	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	distributive	distributive	ADJ	JJ	Degree=Pos	14	amod	_	_
14	law	law	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
16	how	how	SCONJ	WRB	_	18	advmod	_	_
17	to	to	PART	TO	_	18	aux	_	_
18	get	get	VERB	VB	VerbForm=Inf	5	conj	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	lifting	lifting	NOUN	NN	Number=Sing	18	dobj	_	_
21	from	from	ADP	IN	_	18	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
23	pseudomonad	pseudomonad	NOUN	NNS	Number=Plur	21	pobj	_	_
24	with	with	ADP	IN	_	23	prep	_	_
25	compatible	compatible	ADJ	JJ	Degree=Pos	26	amod	_	_
26	structure	structure	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
29	how	how	SCONJ	WRB	_	31	advmod	_	_
30	to	to	PART	TO	_	31	aux	_	_
31	obtain	obtain	VERB	VB	VerbForm=Inf	18	conj	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
33	distributive	distributive	ADJ	JJ	Degree=Pos	34	amod	_	_
34	law	law	NOUN	NN	Number=Sing	31	dobj	_	_
35	from	from	ADP	IN	_	31	prep	_	_
36	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
37	lifting	lifting	NOUN	NN	Number=Sing	35	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = We show that one triangle suffices to define a distributive law in case that one of the pseudomonads is a (co - )KZ - doctrine and the other a KZ - doctrine.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	6	mark	_	_
4	one	one	NUM	CD	NumType=Card	5	nummod	_	_
5	triangle	triangle	NOUN	NN	Number=Sing	6	nsubj	_	_
6	suffices	suffice	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	define	define	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	distributive	distributive	ADJ	JJ	Degree=Pos	11	amod	_	_
11	law	law	NOUN	NN	Number=Sing	8	dobj	_	_
12	in	in	ADP	IN	_	8	prep	_	_
13	case	case	NOUN	NN	Number=Sing	12	pobj	_	_
14	that	that	SCONJ	IN	_	19	mark	_	_
15	one	one	NUM	CD	NumType=Card	19	nsubj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	pseudomonads	pseudomonad	NOUN	NNS	Number=Plur	16	pobj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	acl	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
21	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	27	punct	_	SpaceAfter=No
22	co	co	NOUN	NN	Number=Sing	27	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
24	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	27	punct	_	SpaceAfter=No
25	KZ	KZ	PROPN	NNP	Number=Sing	27	compound	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	doctrine	doctrine	PROPN	NNP	Number=Sing	19	attr	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	other	other	ADJ	JJ	Degree=Pos	27	conj	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
32	KZ	KZ	PROPN	NNP	Number=Sing	34	compound	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	doctrine	doctrine	NOUN	NN	Number=Sing	27	appos	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 73
# sent_id = 1
# text = The main result is that two possible structures which may be imposed on an edge symmetric double category, namely a connection pair and a thin structure, are equivalent.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	result	result	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	29	mark	_	_
6	two	two	NUM	CD	NumType=Card	8	nummod	_	_
7	possible	possible	ADJ	JJ	Degree=Pos	8	amod	_	_
8	structures	structure	NOUN	NNS	Number=Plur	29	nsubj	_	_
9	which	which	PRON	WDT	_	12	nsubjpass	_	_
10	may	may	AUX	MD	VerbForm=Fin	12	aux	_	_
11	be	be	AUX	VB	VerbForm=Inf	12	auxpass	_	_
12	imposed	impose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	relcl	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
15	edge	edge	NOUN	NN	Number=Sing	18	nmod	_	_
16	symmetric	symmetric	ADJ	JJ	Degree=Pos	18	amod	_	_
17	double	double	ADJ	JJ	Degree=Pos	18	amod	_	_
18	category	category	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	namely	namely	ADV	RB	_	23	advmod	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	connection	connection	NOUN	NN	Number=Sing	23	compound	_	_
23	pair	pair	NOUN	NN	Number=Sing	18	appos	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
26	thin	thin	ADJ	JJ	Degree=Pos	27	amod	_	_
27	structure	structure	NOUN	NN	Number=Sing	23	conj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
29	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
30	equivalent	equivalent	ADJ	JJ	Degree=Pos	29	acomp	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = A full proof is also given of the theorem of Spencer, that the category of small 2 - categories is equivalent to the category of edge symmetric double categories with thin structure.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	full	full	ADJ	JJ	Degree=Pos	3	amod	_	_
3	proof	proof	NOUN	NN	Number=Sing	6	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
5	also	also	ADV	RB	_	6	advmod	_	_
6	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	theorem	theorem	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	Spencer	Spencer	PROPN	NNP	Number=Sing	10	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
13	that	that	SCONJ	IN	_	21	mark	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	category	category	NOUN	NN	Number=Sing	21	nsubj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	small	small	ADJ	JJ	Degree=Pos	20	amod	_	_
18	2	2	NUM	CD	NumType=Card	20	nummod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
22	equivalent	equivalent	ADJ	JJ	Degree=Pos	21	acomp	_	_
23	to	to	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	category	category	NOUN	NN	Number=Sing	23	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	edge	edge	NOUN	NN	Number=Sing	26	pobj	_	_
28	symmetric	symmetric	ADJ	JJ	Degree=Pos	30	amod	_	_
29	double	double	ADJ	JJ	Degree=Pos	30	amod	_	_
30	categories	category	NOUN	NNS	Number=Plur	25	appos	_	_
31	with	with	ADP	IN	_	30	prep	_	_
32	thin	thin	ADJ	JJ	Degree=Pos	33	amod	_	_
33	structure	structure	NOUN	NN	Number=Sing	31	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 74
# sent_id = 1
# text = All the useful categories in the study of the mixed abelian groups (for example, Warf and Walk) ignore the torsion.
1	All	all	DET	PDT	_	4	predet	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	useful	useful	ADJ	JJ	Degree=Pos	4	amod	_	_
4	categories	category	NOUN	NNS	Number=Plur	21	nsubj	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	study	study	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
10	mixed	mixed	ADJ	JJ	Degree=Pos	11	amod	_	_
11	abelian	abelian	ADJ	JJ	Degree=Pos	12	compound	_	_
12	groups	group	NOUN	NNS	Number=Plur	8	pobj	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
14	for	for	ADP	IN	_	4	prep	_	_
15	example	example	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
17	Warf	Warf	PROPN	NNP	Number=Sing	4	appos	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	Walk	Walk	PROPN	NNP	Number=Sing	17	conj	_	SpaceAfter=No
20	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	4	punct	_	_
21	ignore	ignore	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	torsion	torsion	NOUN	NN	Number=Sing	21	dobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# sent_id = 2
# text = We introduce a new category denoted $ {cal A} $ which ignores the torsion - freeness and could characterize some classes of nonsplitting mixed groups with the aid of {bf Walk.}
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	new	new	ADJ	JJ	Degree=Pos	5	amod	_	_
5	category	category	NOUN	NN	Number=Sing	2	dobj	_	_
6	denoted	denote	VERB	VBD	Tense=Past|VerbForm=Fin	5	acl	_	_
7	$ {cal A} $	$ {cal a} $	SYM	$	_	6	dobj	_	_
8	which	which	PRON	WDT	_	9	nsubj	_	_
9	ignores	ignore	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	relcl	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
11	torsion	torsion	NOUN	NN	Number=Sing	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	freeness	freeness	NOUN	NN	Number=Sing	9	dobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
15	could	could	AUX	MD	VerbForm=Fin	16	aux	_	_
16	characterize	characterize	VERB	VB	VerbForm=Inf	9	conj	_	_
17	some	some	DET	DT	_	18	det	_	_
18	classes	class	NOUN	NNS	Number=Plur	16	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	nonsplitting	nonsplitte	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	amod	_	_
21	mixed	mixed	ADJ	JJ	Degree=Pos	22	amod	_	_
22	groups	group	NOUN	NNS	Number=Plur	19	pobj	_	_
23	with	with	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	aid	aid	NOUN	NN	Number=Sing	23	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	{	{	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	26	punct	_	SpaceAfter=No
28	bf	bf	NOUN	NN	Number=Sing	29	compound	_	_
29	Walk	Walk	PROPN	NNP	Number=Sing	26	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No
31	}	}	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	6	punct	_	SpaceAfter=No

# doc_id = 75
# sent_id = 1
# text = A new description of the exact completion $ cal C_{ex/reg} $ of a regular category $ cal C $ is given, using a certain topos $ Shv(cal C) $ of sheaves on $ cal C $ ; the exact completion is then constructed as the closure of $ cal C $ in $ Shv(cal C) $ under finite limits and coequalizers of equivalence relations.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	new	new	ADJ	JJ	Degree=Pos	3	amod	_	_
3	description	description	NOUN	NN	Number=Sing	32	dep	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	exact	exact	ADJ	JJ	Degree=Pos	7	amod	_	_
7	completion	completion	NOUN	NN	Number=Sing	4	pobj	_	_
8	$ cal C_{ex/reg} $	$ cal c_{ex/reg} $	SYM	$	_	15	nsubjpass	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	regular	regular	ADJ	JJ	Degree=Pos	12	amod	_	_
12	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
13	$ cal C $	$ cal c $	SYM	$	_	8	appos	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	relcl	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
17	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	acl	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	certain	certain	ADJ	JJ	Degree=Pos	20	amod	_	_
20	topos	topos	NOUN	NN	Number=Sing	17	dobj	_	_
21	$ Shv(cal C) $	$ shv(cal c) $	SYM	$	_	20	appos	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	sheaves	sheaf	NOUN	NNS	Number=Plur	22	pobj	_	_
24	on	on	ADP	IN	_	23	prep	_	_
25	$ cal C $	$ cal c $	SYM	$	_	24	pobj	_	_
26	;	;	PUNCT	:	_	32	punct	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	exact	exact	ADJ	JJ	Degree=Pos	29	amod	_	_
29	completion	completion	NOUN	NN	Number=Sing	32	nsubjpass	_	_
30	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	32	auxpass	_	_
31	then	then	ADV	RB	PronType=Dem	32	advmod	_	_
32	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
33	as	as	ADP	IN	_	32	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	closure	closure	NOUN	NN	Number=Sing	33	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	$ cal C $	$ cal c $	SYM	$	_	36	pobj	_	_
38	in	in	ADP	IN	_	35	prep	_	_
39	$ Shv(cal C) $	$ shv(cal c) $	SYM	$	_	38	pobj	_	_
40	under	under	ADP	IN	_	32	prep	_	_
41	finite	finite	ADJ	JJ	Degree=Pos	42	compound	_	_
42	limits	limit	NOUN	NNS	Number=Plur	40	pobj	_	_
43	and	and	CCONJ	CC	ConjType=Cmp	42	cc	_	_
44	coequalizers	coequalizer	NOUN	NNS	Number=Plur	42	conj	_	_
45	of	of	ADP	IN	_	42	prep	_	_
46	equivalence	equivalence	NOUN	NN	Number=Sing	47	compound	_	_
47	relations	relation	NOUN	NNS	Number=Plur	45	pobj	_	SpaceAfter=No
48	.	.	PUNCT	.	PunctType=Peri	32	punct	_	SpaceAfter=No

# sent_id = 2
# text = An infinitary generalization is proved, and the classical description of the exact completion is derived.
1	An	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	infinitary	infinitary	ADJ	JJ	Degree=Pos	3	amod	_	_
3	generalization	generalization	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	classical	classical	ADJ	JJ	Degree=Pos	10	amod	_	_
10	description	description	NOUN	NN	Number=Sing	16	nsubjpass	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	exact	exact	ADJ	JJ	Degree=Pos	14	amod	_	_
14	completion	completion	NOUN	NN	Number=Sing	11	pobj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	auxpass	_	_
16	derived	derive	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	conj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# doc_id = 76
# sent_id = 1
# text = The class of functors known as discrete Conduché fibrations forms a common generalization of discrete fibrations and discrete opfibrations, and shares many of the formal properties of these two classes.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	class	class	NOUN	NN	Number=Sing	9	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	functors	functor	NOUN	NNS	Number=Plur	3	pobj	_	_
5	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	acl	_	_
6	as	as	ADP	IN	_	5	prep	_	_
7	discrete	discrete	ADJ	JJ	Degree=Pos	8	compound	_	_
8	Conduché	Conduché	PROPN	NNP	Number=Sing	6	pobj	_	_
9	fibrations	fibration	NOUN	NNS	Number=Plur	10	nsubj	_	_
10	forms	form	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	common	common	ADJ	JJ	Degree=Pos	13	amod	_	_
13	generalization	generalization	NOUN	NN	Number=Sing	10	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	discrete	discrete	ADJ	JJ	Degree=Pos	16	amod	_	_
16	fibrations	fibration	NOUN	NNS	Number=Plur	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	discrete	discrete	ADJ	JJ	Degree=Pos	19	amod	_	_
19	opfibrations	opfibration	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
22	shares	share	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	conj	_	_
23	many	many	ADJ	JJ	Degree=Pos	22	dobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	formal	formal	ADJ	JJ	Degree=Pos	27	amod	_	_
27	properties	property	NOUN	NNS	Number=Plur	24	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	these	these	DET	DT	Number=Plur|PronType=Dem	31	det	_	_
30	two	two	NUM	CD	NumType=Card	31	nummod	_	_
31	classes	class	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = F. Lamarche conjectured that, for any small category $ cal B $ , the category $ {bf DCF}/{cal B} $ of discrete Conduché fibrations over $ cal B $ should be a topos.
1	F.	F.	PROPN	NNP	Number=Sing	2	compound	_	_
2	Lamarche	Lamarche	PROPN	NNP	Number=Sing	3	nsubj	_	_
3	conjectured	conjecture	VERB	VBD	Tense=Past|VerbForm=Fin	22	ccomp	_	_
4	that	that	PRON	DT	Number=Sing|PronType=Dem	3	dobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
6	for	for	ADP	IN	_	18	prep	_	_
7	any	any	DET	DT	_	9	det	_	_
8	small	small	ADJ	JJ	Degree=Pos	9	amod	_	_
9	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
10	$ cal B $	$ cal b $	SYM	$	_	9	nummod	_	_
11	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	category	category	NOUN	NN	Number=Sing	18	nsubj	_	_
14	$ {bf DCF}/{cal B} $	$ {bf dcf}/{cal b} $	SYM	$	_	13	appos	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	discrete	discrete	ADJ	JJ	Degree=Pos	17	amod	_	_
17	Conduché	Conduché	PROPN	NNP	Number=Sing	15	pobj	_	_
18	fibrations	fibration	NOUN	NNS	Number=Plur	22	nsubj	_	_
19	over	over	ADP	IN	_	18	prep	_	_
20	$ cal B $	$ cal b $	SYM	$	_	22	nsubj	_	_
21	should	should	AUX	MD	VerbForm=Fin	22	aux	_	_
22	be	be	AUX	VB	VerbForm=Inf	0	ROOT	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	topos	topos	NOUN	NN	Number=Sing	22	attr	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this note we show that, although for suitable categories $ cal B $ the discrete Conduch&eacute fibrations over $ cal B $ may be presented as the `sheaves' for a family of coverings on a category $ {cal B}_{tw} $ constructed from $ cal B $ , they are in general very far from forming a topos.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	note	note	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	21	mark	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
8	although	although	SCONJ	IN	_	16	mark	_	_
9	for	for	ADP	IN	_	16	prep	_	_
10	suitable	suitable	ADJ	JJ	Degree=Pos	11	amod	_	_
11	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	_
12	$ cal B $	$ cal b $	SYM	$	_	15	predet	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	discrete	discrete	ADJ	JJ	Degree=Pos	15	amod	_	_
15	Conduch&eacute	Conduch&eacute	PROPN	NNP	Number=Sing	16	nsubj	_	_
16	fibrations	fibration	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	21	nsubjpass	_	_
17	over	over	ADP	IN	_	16	prep	_	_
18	$ cal B $	$ cal b $	SYM	$	_	21	nsubjpass	_	_
19	may	may	AUX	MD	VerbForm=Fin	21	aux	_	_
20	be	be	AUX	VB	VerbForm=Inf	21	auxpass	_	_
21	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	ccomp	_	_
22	as	as	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	25	punct	_	SpaceAfter=No
25	sheaves	sheaf	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
26	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	25	punct	_	_
27	for	for	ADP	IN	_	25	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
29	family	family	NOUN	NN	Number=Sing	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	coverings	covering	NOUN	NNS	Number=Plur	30	pobj	_	_
32	on	on	ADP	IN	_	21	prep	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
34	category	category	NOUN	NN	Number=Sing	32	pobj	_	_
35	$ {cal B}_{tw} $	$ {cal b}_{tw} $	NOUN	NN	Number=Sing	34	appos	_	_
36	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	34	acl	_	_
37	from	from	ADP	IN	_	36	prep	_	_
38	$ cal B $	$ cal b $	SYM	$	_	37	pobj	_	_
39	,	,	PUNCT	,	PunctType=Comm	41	punct	_	_
40	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	41	nsubj	_	_
41	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
42	in	in	ADP	IN	_	41	prep	_	_
43	general	general	ADJ	JJ	Degree=Pos	42	amod	_	_
44	very	very	ADV	RB	_	45	advmod	_	_
45	far	far	ADV	RB	_	41	advmod	_	_
46	from	from	ADP	IN	_	45	prep	_	_
47	forming	form	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	46	pcomp	_	_
48	a	a	DET	DT	Definite=Ind|PronType=Art	49	det	_	_
49	topos	topos	NOUN	NN	Number=Sing	47	dobj	_	SpaceAfter=No
50	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 77
# sent_id = 1
# text = In this paper I extend Gray's tensor product of 2 - categories to a new tensor product of Gray - categories.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	I	I	PRON	PRP	Case=Nom|Number=Sing|Person=1|PronType=Prs	5	nsubj	_	_
5	extend	extend	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	Gray	Gray	PROPN	NNP	Number=Sing	9	poss	_	SpaceAfter=No
7	's	's	PART	POS	_	6	case	_	_
8	tensor	tensor	NOUN	NN	Number=Sing	9	compound	_	_
9	product	product	NOUN	NN	Number=Sing	5	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
14	to	to	ADP	IN	_	5	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
16	new	new	ADJ	JJ	Degree=Pos	18	amod	_	_
17	tensor	tensor	NOUN	NN	Number=Sing	18	compound	_	_
18	product	product	NOUN	NN	Number=Sing	14	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	Gray	Gray	PROPN	NNP	Number=Sing	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	categories	category	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = I give a description in terms of generators and relations, one of the relations being an ``interchange'' relation, and a description similar to Gray's description of his tensor product of 2 - categories.
1	I	I	PRON	PRP	Case=Nom|Number=Sing|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	description	description	NOUN	NN	Number=Sing	2	dobj	_	_
5	in	in	ADP	IN	_	2	prep	_	_
6	terms	term	NOUN	NNS	Number=Plur	5	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	generators	generator	NOUN	NNS	Number=Plur	7	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	relations	relation	NOUN	NNS	Number=Plur	8	conj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
12	one	one	NUM	CD	NumType=Card	16	nsubj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	relations	relation	NOUN	NNS	Number=Plur	13	pobj	_	_
16	being	be	AUX	VBG	VerbForm=Ger	2	advcl	_	_
17	an	an	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
18	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	22	punct	_	SpaceAfter=No
19	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	22	punct	_	SpaceAfter=No
20	interchange	interchange	ADJ	JJ	Degree=Pos	22	amod	_	SpaceAfter=No
21	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	22	punct	_	_
22	relation	relation	NOUN	NN	Number=Sing	16	attr	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
26	description	description	NOUN	NN	Number=Sing	22	conj	_	_
27	similar	similar	ADJ	JJ	Degree=Pos	26	amod	_	_
28	to	to	ADP	IN	_	27	prep	_	_
29	Gray	Gray	PROPN	NNP	Number=Sing	31	poss	_	SpaceAfter=No
30	's	's	PART	POS	_	29	case	_	_
31	description	description	NOUN	NN	Number=Sing	28	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	his	his	PRON	PRP$	Gender=Masc|Number=Sing|Person=3|Poss=Yes|PronType=Prs	35	poss	_	_
34	tensor	tensor	NOUN	NN	Number=Sing	35	compound	_	_
35	product	product	NOUN	NN	Number=Sing	32	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	2	2	NUM	CD	NumType=Card	39	nummod	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	categories	category	NOUN	NNS	Number=Plur	36	pobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = I show that this tensor product of Gray - categories satisfies a universal property with respect to quasi - functors of two variables, which are defined in terms of lax - natural transformations between Gray - categories.
1	I	I	PRON	PRP	Case=Nom|Number=Sing|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	11	mark	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
5	tensor	tensor	NOUN	NN	Number=Sing	6	compound	_	_
6	product	product	NOUN	NN	Number=Sing	11	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	Gray	Gray	PROPN	NNP	Number=Sing	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
11	satisfies	satisfy	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	universal	universal	ADJ	JJ	Degree=Pos	14	amod	_	_
14	property	property	NOUN	NN	Number=Sing	11	dobj	_	_
15	with	with	ADP	IN	_	14	prep	_	_
16	respect	respect	NOUN	NN	Number=Sing	15	pobj	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	quasi	quasi	NOUN	NNS	Number=Plur	17	pobj	_	_
19	-	-	NOUN	NNS	Number=Plur	17	pobj	_	_
20	functors	functor	NOUN	NNS	Number=Plur	17	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	two	two	NUM	CD	NumType=Card	23	nummod	_	_
23	variables	variable	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
25	which	which	PRON	WDT	_	27	nsubjpass	_	_
26	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	27	auxpass	_	_
27	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	relcl	_	_
28	in	in	ADP	IN	_	27	prep	_	_
29	terms	term	NOUN	NNS	Number=Plur	28	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	lax	lax	ADJ	JJ	Degree=Pos	33	amod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	natural	natural	ADJ	JJ	Degree=Pos	34	amod	_	_
34	transformations	transformation	NOUN	NNS	Number=Plur	30	pobj	_	_
35	between	between	ADP	IN	_	34	prep	_	_
36	Gray	Gray	PROPN	NNP	Number=Sing	38	compound	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	38	punct	_	_
38	categories	category	NOUN	NNS	Number=Plur	35	pobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = The main result is that this tensor product is part of a monoidal structure on $ Gray - Cat $ , the proof requiring interchange in an essential way.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	result	result	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	9	mark	_	_
6	this	this	DET	DT	Number=Sing|PronType=Dem	8	det	_	_
7	tensor	tensor	NOUN	NN	Number=Sing	8	compound	_	_
8	product	product	NOUN	NN	Number=Sing	9	nsubj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
10	part	part	NOUN	NN	Number=Sing	9	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	monoidal	monoidal	ADJ	JJ	Degree=Pos	14	amod	_	_
14	structure	structure	NOUN	NN	Number=Sing	11	pobj	_	_
15	on	on	ADP	IN	_	14	prep	_	_
16	$ Gray - Cat $	$ gray - cat $	SYM	$	_	15	pobj	_	_
17	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	proof	proof	NOUN	NN	Number=Sing	9	attr	_	_
20	requiring	require	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	acl	_	_
21	interchange	interchange	NOUN	NN	Number=Sing	20	dobj	_	_
22	in	in	ADP	IN	_	20	prep	_	_
23	an	an	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	essential	essential	ADJ	JJ	Degree=Pos	25	amod	_	_
25	way	way	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = However, this does not give a monoidal (bi)closed structure, precisely because of interchange.
1	However	however	ADV	RB	_	6	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
3	this	this	PRON	DT	Number=Sing|PronType=Dem	6	nsubj	_	_
4	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	aux	_	_
5	not	not	PART	RB	Polarity=Neg	6	neg	_	_
6	give	give	VERB	VB	VerbForm=Inf	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	monoidal	monoidal	NOUN	NN	Number=Sing	6	dobj	_	_
9	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	11	punct	_	SpaceAfter=No
10	bi)closed	bi)closed	ADJ	JJ	Degree=Pos	11	amod	_	_
11	structure	structure	NOUN	NN	Number=Sing	8	appos	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
13	precisely	precisely	ADV	RB	_	14	advmod	_	_
14	because	because	SCONJ	IN	_	6	prep	_	_
15	of	of	ADP	IN	_	14	pcomp	_	_
16	interchange	interchange	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 6
# text = And although I define composition of lax - natural transformations, this composite need not be a lax - natural transformation again, making $ Gray - Cat $ only a partial $ Gray - Catotimes - CATegory $ .
1	And	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
2	although	although	SCONJ	IN	_	4	mark	_	_
3	I	I	PRON	PRP	Case=Nom|Number=Sing|Person=1|PronType=Prs	4	nsubj	_	_
4	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	16	advcl	_	_
5	composition	composition	NOUN	NN	Number=Sing	4	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	lax	lax	ADJ	JJ	Degree=Pos	9	amod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	natural	natural	ADJ	JJ	Degree=Pos	10	amod	_	_
10	transformations	transformation	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
12	this	this	DET	DT	Number=Sing|PronType=Dem	14	det	_	_
13	composite	composite	ADJ	JJ	Degree=Pos	14	amod	_	_
14	need	need	AUX	NN	Number=Sing	16	aux	_	_
15	not	not	PART	RB	Polarity=Neg	16	neg	_	_
16	be	be	AUX	VB	VerbForm=Inf	0	ROOT	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
18	lax	lax	ADJ	JJ	Degree=Pos	20	amod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	natural	natural	ADJ	JJ	Degree=Pos	21	amod	_	_
21	transformation	transformation	NOUN	NN	Number=Sing	16	attr	_	_
22	again	again	ADV	RB	_	16	advmod	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
24	making	make	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	advcl	_	_
25	$ Gray - Cat $	$ gray - cat $	SYM	$	_	24	ccomp	_	_
26	only	only	ADV	RB	_	29	advmod	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	partial	partial	ADJ	JJ	Degree=Pos	29	amod	_	_
29	$ Gray - Catotimes - CATegory $	$ gray - catotimes - category $	SYM	$	_	24	ccomp	_	_
30	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# doc_id = 78
# sent_id = 1
# text = In this paper certain proof - theoretic techniques of [BCST] are applied to non - symmetric linearly distributive categories, corresponding to non - commutative negation - free multiplicative linear logic (mLL).
1	In	in	ADP	IN	_	14	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	certain	certain	ADJ	JJ	Degree=Pos	8	amod	_	_
5	proof	proof	NOUN	NN	Number=Sing	7	npadvmod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	theoretic	theoretic	ADJ	JJ	Degree=Pos	8	amod	_	_
8	techniques	technique	NOUN	NNS	Number=Plur	14	nsubjpass	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	[	[	X	XX	_	9	pobj	_	SpaceAfter=No
11	BCST	bcst	X	XX	_	9	pobj	_	SpaceAfter=No
12	]	]	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	8	punct	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	applied	apply	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	non	non	ADJ	JJ	Degree=Pos	21	amod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
18	symmetric	symmetric	ADJ	JJ	Degree=Pos	21	amod	_	_
19	linearly	linearly	ADV	RB	_	20	advmod	_	_
20	distributive	distributive	ADJ	JJ	Degree=Pos	21	amod	_	_
21	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
23	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	advcl	_	_
24	to	to	ADP	IN	_	23	prep	_	_
25	non	non	ADJ	JJ	Degree=Pos	27	amod	_	_
26	-	-	ADJ	JJ	Degree=Pos	27	punct	_	_
27	commutative	commutative	ADJ	JJ	Degree=Pos	33	amod	_	_
28	negation	negation	NOUN	NN	Number=Sing	30	npadvmod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	free	free	ADJ	JJ	Degree=Pos	33	amod	_	_
31	multiplicative	multiplicative	ADJ	JJ	Degree=Pos	33	amod	_	_
32	linear	linear	ADJ	JJ	Degree=Pos	33	amod	_	_
33	logic	logic	NOUN	NN	Number=Sing	24	pobj	_	_
34	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	33	punct	_	SpaceAfter=No
35	mLL	mLL	PROPN	NNP	Number=Sing	33	npadvmod	_	SpaceAfter=No
36	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	23	punct	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 2
# text = First, the correctness criterion for the two - sided proof nets developed in BCST is adjusted to work in the non - commutative setting.
1	First	first	ADV	RB	_	17	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	correctness	correctness	NOUN	NN	Number=Sing	5	compound	_	_
5	criterion	criterion	NOUN	NN	Number=Sing	17	nsubjpass	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
8	two	two	NUM	CD	NumType=Card	10	advmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	sided	sided	ADJ	JJ	Degree=Pos	12	amod	_	_
11	proof	proof	NOUN	NN	Number=Sing	12	compound	_	_
12	nets	net	NOUN	NNS	Number=Plur	6	pobj	_	_
13	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	BCST	BCST	PROPN	NNP	Number=Sing	14	pobj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	auxpass	_	_
17	adjusted	adjust	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	work	work	NOUN	NN	Number=Sing	18	pobj	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
22	non	non	ADJ	JJ	Degree=Pos	24	amod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	commutative	commutative	ADJ	JJ	Degree=Pos	25	amod	_	_
25	setting	setting	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 3
# text = Second, these proof nets are used to represent morphisms in a (non - symmetric) linearly distributive category; a notion of proof - net equivalence is developed which permits a considerable sharpening of the previous coherence results concerning these categories, including a decision procedure for the equality of maps when there is a certain restriction on the units.
1	Second	second	ADV	RB	_	7	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
3	these	these	DET	DT	Number=Plur|PronType=Dem	5	det	_	_
4	proof	proof	NOUN	NN	Number=Sing	5	compound	_	_
5	nets	net	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	30	ccomp	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	represent	represent	VERB	VB	VerbForm=Inf	7	xcomp	_	_
10	morphisms	morphism	NOUN	NNS	Number=Plur	9	dobj	_	_
11	in	in	ADP	IN	_	9	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	16	punct	_	SpaceAfter=No
14	non	non	ADJ	JJ	Degree=Pos	16	amod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	symmetric	symmetric	ADJ	JJ	Degree=Pos	20	amod	_	SpaceAfter=No
17	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	16	punct	_	_
18	linearly	linearly	ADV	RB	_	19	advmod	_	_
19	distributive	distributive	ADJ	JJ	Degree=Pos	20	amod	_	_
20	category	category	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
21	;	;	PUNCT	:	_	30	punct	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
23	notion	notion	NOUN	NN	Number=Sing	30	nsubjpass	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	proof	proof	NOUN	NN	Number=Sing	24	pobj	_	_
26	-	-	PUNCT	:	_	30	punct	_	_
27	net	net	ADJ	JJ	Degree=Pos	28	amod	_	_
28	equivalence	equivalence	NOUN	NN	Number=Sing	30	nsubjpass	_	_
29	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	auxpass	_	_
30	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
31	which	which	PRON	WDT	_	32	nsubj	_	_
32	permits	permit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	ccomp	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
34	considerable	considerable	ADJ	JJ	Degree=Pos	35	amod	_	_
35	sharpening	sharpening	NOUN	NN	Number=Sing	32	dobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
38	previous	previous	ADJ	JJ	Degree=Pos	40	amod	_	_
39	coherence	coherence	NOUN	NN	Number=Sing	40	compound	_	_
40	results	result	NOUN	NNS	Number=Plur	36	pobj	_	_
41	concerning	concern	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	40	acl	_	_
42	these	these	DET	DT	Number=Plur|PronType=Dem	43	det	_	_
43	categories	category	NOUN	NNS	Number=Plur	41	dobj	_	SpaceAfter=No
44	,	,	PUNCT	,	PunctType=Comm	43	punct	_	_
45	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	43	prep	_	_
46	a	a	DET	DT	Definite=Ind|PronType=Art	48	det	_	_
47	decision	decision	NOUN	NN	Number=Sing	48	compound	_	_
48	procedure	procedure	NOUN	NN	Number=Sing	45	pobj	_	_
49	for	for	ADP	IN	_	48	prep	_	_
50	the	the	DET	DT	Definite=Def|PronType=Art	51	det	_	_
51	equality	equality	NOUN	NN	Number=Sing	49	pobj	_	_
52	of	of	ADP	IN	_	51	prep	_	_
53	maps	map	NOUN	NNS	Number=Plur	52	pobj	_	_
54	when	when	SCONJ	WRB	_	56	advmod	_	_
55	there	there	PRON	EX	_	56	expl	_	_
56	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	32	advcl	_	_
57	a	a	DET	DT	Definite=Ind|PronType=Art	59	det	_	_
58	certain	certain	ADJ	JJ	Degree=Pos	59	amod	_	_
59	restriction	restriction	NOUN	NN	Number=Sing	56	attr	_	_
60	on	on	ADP	IN	_	59	prep	_	_
61	the	the	DET	DT	Definite=Def|PronType=Art	62	det	_	_
62	units	unit	NOUN	NNS	Number=Plur	60	pobj	_	SpaceAfter=No
63	.	.	PUNCT	.	PunctType=Peri	30	punct	_	SpaceAfter=No

# sent_id = 4
# text = In particular a decision procedure is obtained for the equivalence of proofs in non - commutative negation - free multiplicative linear logic without non - logical axioms.
1	In	in	ADP	IN	_	7	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	decision	decision	NOUN	NN	Number=Sing	5	compound	_	_
5	procedure	procedure	NOUN	NN	Number=Sing	7	nsubjpass	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	equivalence	equivalence	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	proofs	proof	NOUN	NNS	Number=Plur	11	pobj	_	_
13	in	in	ADP	IN	_	10	prep	_	_
14	non	non	ADJ	JJ	Degree=Pos	16	amod	_	_
15	-	-	ADJ	JJ	Degree=Pos	16	punct	_	_
16	commutative	commutative	ADJ	JJ	Degree=Pos	22	amod	_	_
17	negation	negation	NOUN	NN	Number=Sing	19	npadvmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	free	free	ADJ	JJ	Degree=Pos	22	amod	_	_
20	multiplicative	multiplicative	ADJ	JJ	Degree=Pos	22	amod	_	_
21	linear	linear	ADJ	JJ	Degree=Pos	22	amod	_	_
22	logic	logic	NOUN	NN	Number=Sing	13	pobj	_	_
23	without	without	ADP	IN	_	10	prep	_	_
24	non	non	ADJ	JJ	Degree=Pos	26	amod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	logical	logical	ADJ	JJ	Degree=Pos	27	amod	_	_
27	axioms	axiom	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 79
# sent_id = 1
# text = We characterize when the coequalizer and the exact completion of a category $ cal C $ with finite sums and weak finite limits coincide.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	when	when	SCONJ	WRB	_	5	advmod	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	coequalizer	coequalizer	NOUN	NN	Number=Sing	2	advcl	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	exact	exact	ADJ	JJ	Degree=Pos	9	amod	_	_
9	completion	completion	NOUN	NN	Number=Sing	5	conj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
13	$ cal C $	$ cal c $	SYM	$	_	12	appos	_	_
14	with	with	ADP	IN	_	12	prep	_	_
15	finite	finite	ADJ	JJ	Degree=Pos	16	compound	_	_
16	sums	sum	NOUN	NNS	Number=Plur	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	weak	weak	ADJ	JJ	Degree=Pos	21	amod	_	_
19	finite	finite	ADJ	JJ	Degree=Pos	20	compound	_	_
20	limits	limit	NOUN	NNS	Number=Plur	21	compound	_	_
21	coincide	coincide	NOUN	NN	Number=Sing	16	conj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 80
# sent_id = 1
# text = A von Neumann regular extension of a semiprime ring naturally defines a epimorphic extension in the category of rings.
1	A	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
2	von	von	PROPN	NNP	Number=Sing	3	nmod	_	_
3	Neumann	Neumann	PROPN	NNP	Number=Sing	5	nmod	_	_
4	regular	regular	ADJ	JJ	Degree=Pos	5	amod	_	_
5	extension	extension	NOUN	NN	Number=Sing	11	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	semiprime	semiprime	NOUN	NN	Number=Sing	9	compound	_	_
9	ring	ring	NOUN	NN	Number=Sing	6	pobj	_	_
10	naturally	naturally	ADV	RB	_	11	advmod	_	_
11	defines	define	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	epimorphic	epimorphic	ADJ	JJ	Degree=Pos	14	amod	_	_
14	extension	extension	NOUN	NN	Number=Sing	11	dobj	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	rings	ring	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 2
# text = These are studied, and four natural examples are considered, two in commutative ring theory, and two in rings of continuous functions.
1	These	these	PRON	DT	Number=Plur|PronType=Dem	3	nsubjpass	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	studied	study	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
6	four	four	NUM	CD	NumType=Card	8	nummod	_	_
7	natural	natural	ADJ	JJ	Degree=Pos	8	amod	_	_
8	examples	example	NOUN	NNS	Number=Plur	10	nsubjpass	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	conj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	two	two	NUM	CD	NumType=Card	8	appos	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	commutative	commutative	ADJ	JJ	Degree=Pos	16	amod	_	_
15	ring	ring	NOUN	NN	Number=Sing	16	compound	_	_
16	theory	theory	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
19	two	two	NUM	CD	NumType=Card	12	conj	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	rings	ring	NOUN	NNS	Number=Plur	20	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	continuous	continuous	ADJ	JJ	Degree=Pos	24	amod	_	_
24	functions	function	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# doc_id = 81
# sent_id = 1
# text = We define the notion of enriched Lawvere theory, for enrichment over a monoidal biclosed category $ V $ that is locally finitely presentable as a closed category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	enriched	enriched	ADJ	JJ	Degree=Pos	8	amod	_	_
7	Lawvere	Lawvere	PROPN	NNP	Number=Sing	8	compound	_	_
8	theory	theory	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
10	for	for	ADP	IN	_	2	prep	_	_
11	enrichment	enrichment	NOUN	NN	Number=Sing	10	pobj	_	_
12	over	over	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
14	monoidal	monoidal	ADJ	JJ	Degree=Pos	15	amod	_	_
15	biclosed	biclose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
16	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
17	$ V $	$ v $	SYM	$	_	16	appos	_	_
18	that	that	PRON	WDT	PronType=Rel	19	nsubj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
20	locally	locally	ADV	RB	_	22	advmod	_	_
21	finitely	finitely	ADV	RB	_	22	advmod	_	_
22	presentable	presentable	ADJ	JJ	Degree=Pos	19	acomp	_	_
23	as	as	ADP	IN	_	22	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
25	closed	closed	ADJ	JJ	Degree=Pos	26	amod	_	_
26	category	category	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We prove that the category of enriched Lawvere theories is equivalent to the category of finitary monads on $ V $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	10	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	10	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	enriched	enriched	ADJ	JJ	Degree=Pos	9	amod	_	_
8	Lawvere	Lawvere	PROPN	NNP	Number=Sing	9	compound	_	_
9	theories	theory	NOUN	NNS	Number=Plur	6	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
11	equivalent	equivalent	ADJ	JJ	Degree=Pos	10	acomp	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	finitary	finitary	ADJ	JJ	Degree=Pos	17	amod	_	_
17	monads	monad	NOUN	NNS	Number=Plur	15	pobj	_	_
18	on	on	ADP	IN	_	17	prep	_	_
19	$ V $	$ v $	SYM	$	_	18	pobj	_	_
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Moreover, the $ V $ - category of models of a Lawvere $ V $ - theory is equivalent to the $ V $ - category of algebras for the corresponding $ V $ - monad.
1	Moreover	moreover	ADV	RB	_	15	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
4	$ V $	$ v $	SYM	$	_	6	nmod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	category	category	NOUN	NN	Number=Sing	15	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	models	model	NOUN	NNS	Number=Plur	7	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
11	Lawvere	Lawvere	PROPN	NNP	Number=Sing	14	nmod	_	_
12	$ V $	$ v $	SYM	$	_	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	theory	theory	NOUN	NN	Number=Sing	9	pobj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	equivalent	equivalent	ADJ	JJ	Degree=Pos	15	acomp	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
19	$ V $	$ v $	SYM	$	_	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	category	category	NOUN	NN	Number=Sing	17	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	algebras	algebra	NOUN	NNS	Number=Plur	22	pobj	_	_
24	for	for	ADP	IN	_	21	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
26	corresponding	corresponding	ADJ	JJ	Degree=Pos	29	amod	_	_
27	$ V $	$ v $	SYM	$	_	29	compound	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	monad	monad	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 4
# text = This all extends routinely to local presentability with respect to any regular cardinal.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	3	nsubj	_	_
2	all	all	PRON	DT	_	1	appos	_	_
3	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	routinely	routinely	ADV	RB	_	3	advmod	_	_
5	to	to	ADP	IN	_	3	prep	_	_
6	local	local	ADJ	JJ	Degree=Pos	7	amod	_	_
7	presentability	presentability	NOUN	NN	Number=Sing	5	pobj	_	_
8	with	with	ADP	IN	_	7	prep	_	_
9	respect	respect	NOUN	NN	Number=Sing	8	pobj	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	any	any	DET	DT	_	13	det	_	_
12	regular	regular	ADJ	JJ	Degree=Pos	13	amod	_	_
13	cardinal	cardinal	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = We finally consider the special case where $ V $ is $ Cat $ , and explain how the correspondence extends to pseudo maps of algebras.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	finally	finally	ADV	RB	_	3	advmod	_	_
3	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	special	special	ADJ	JJ	Degree=Pos	6	amod	_	_
6	case	case	NOUN	NN	Number=Sing	3	dobj	_	_
7	where	where	SCONJ	WRB	_	9	advmod	_	_
8	$ V $	$ v $	SYM	$	_	9	nsubj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	relcl	_	_
10	$ Cat $	$ cat $	SYM	$	_	9	attr	_	_
11	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
13	explain	explain	VERB	VB	VerbForm=Inf	9	conj	_	_
14	how	how	SCONJ	WRB	_	17	advmod	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	correspondence	correspondence	NOUN	NN	Number=Sing	17	nsubj	_	_
17	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
18	to	to	PART	TO	_	19	aux	_	_
19	pseudo	pseudo	NOUN	NN	Number=Sing	17	xcomp	_	_
20	maps	map	NOUN	NNS	Number=Plur	19	dobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	algebras	algebra	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 82
# sent_id = 1
# text = We characterize the numerical functions which arise as the cardinalities of contravariant functors on finite sets, as those which have a series expansion in terms of Stirling functions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	numerical	numerical	PROPN	NNP	Number=Sing	5	compound	_	_
5	functions	function	NOUN	NNS	Number=Plur	2	dobj	_	_
6	which	which	PRON	WDT	_	7	nsubj	_	_
7	arise	arise	VERB	VBP	Tense=Pres|VerbForm=Fin	5	relcl	_	_
8	as	as	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	cardinalities	cardinality	NOUN	NNS	Number=Plur	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	contravariant	contravariant	ADJ	JJ	Degree=Pos	13	amod	_	_
13	functors	functor	NOUN	NNS	Number=Plur	11	pobj	_	_
14	on	on	ADP	IN	_	13	prep	_	_
15	finite	finite	ADJ	JJ	Degree=Pos	16	compound	_	_
16	sets	set	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
18	as	as	ADP	IN	_	7	prep	_	_
19	those	those	PRON	DT	Number=Plur|PronType=Dem	18	pobj	_	_
20	which	which	PRON	WDT	_	21	nsubj	_	_
21	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	19	relcl	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
23	series	series	NOUN	NN	Number=Sing	24	compound	_	_
24	expansion	expansion	NOUN	NN	Number=Sing	21	dobj	_	_
25	in	in	ADP	IN	_	24	prep	_	_
26	terms	term	NOUN	NNS	Number=Plur	25	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	Stirling	Stirling	PROPN	NNP	Number=Sing	29	compound	_	_
29	functions	function	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We give a procedure for calculating the coefficients in such series and a concrete test for determining whether a function is of this type.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	procedure	procedure	NOUN	NN	Number=Sing	2	dobj	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	calculating	calculate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	coefficients	coefficient	NOUN	NNS	Number=Plur	6	dobj	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	such	such	ADJ	JJ	Degree=Pos	11	amod	_	_
11	series	series	NOUN	NN	Number=Sing	9	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	concrete	concrete	ADJ	JJ	Degree=Pos	15	amod	_	_
15	test	test	NOUN	NN	Number=Sing	11	conj	_	_
16	for	for	ADP	IN	_	15	prep	_	_
17	determining	determine	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	pcomp	_	_
18	whether	whether	SCONJ	IN	_	21	mark	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	function	function	NOUN	NN	Number=Sing	21	nsubj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	ccomp	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	this	this	DET	DT	Number=Sing|PronType=Dem	24	det	_	_
24	type	type	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = A number of examples are considered.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	number	number	NOUN	NN	Number=Sing	6	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	examples	example	NOUN	NNS	Number=Plur	3	pobj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
7	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 83
# sent_id = 1
# text = Uniqueness for higher type term constructors in lambda calculi (for example surjective pairing for product types, or uniqueness of iterators on the natural numbers) is easily expressed using universally quantified conditional equations.
1	Uniqueness	uniqueness	VERB	VB	VerbForm=Inf	30	nsubjpass	_	_
2	for	for	ADP	IN	_	1	prep	_	_
3	higher	high	ADJ	JJR	Degree=Cmp	5	amod	_	_
4	type	type	NOUN	NN	Number=Sing	5	compound	_	_
5	term	term	NOUN	NN	Number=Sing	6	compound	_	_
6	constructors	constructor	NOUN	NNS	Number=Plur	2	pobj	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	lambda	lambda	PROPN	NNP	Number=Sing	9	compound	_	_
9	calculi	calculi	PROPN	NNP	Number=Sing	7	pobj	_	_
10	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	1	punct	_	SpaceAfter=No
11	for	for	ADP	IN	_	1	prep	_	_
12	example	example	NOUN	NN	Number=Sing	11	pobj	_	_
13	surjective	surjective	ADJ	JJ	Degree=Pos	1	punct	_	_
14	pairing	pair	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	1	advcl	_	_
15	for	for	ADP	IN	_	14	prep	_	_
16	product	product	NOUN	NN	Number=Sing	17	compound	_	_
17	types	type	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
19	or	or	CCONJ	CC	ConjType=Cmp	14	cc	_	_
20	uniqueness	uniqueness	NOUN	NN	Number=Sing	14	conj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	iterators	iterator	NOUN	NNS	Number=Plur	21	pobj	_	_
23	on	on	ADP	IN	_	20	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	natural	natural	ADJ	JJ	Degree=Pos	26	amod	_	_
26	numbers	number	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
27	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	1	punct	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	auxpass	_	_
29	easily	easily	ADV	RB	_	30	advmod	_	_
30	expressed	express	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
31	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	30	xcomp	_	_
32	universally	universally	ADV	RB	_	33	advmod	_	_
33	quantified	quantify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	35	amod	_	_
34	conditional	conditional	ADJ	JJ	Degree=Pos	35	amod	_	_
35	equations	equation	NOUN	NNS	Number=Plur	31	dobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	30	punct	_	SpaceAfter=No

# sent_id = 2
# text = We use a technique of Lambek involving Maltsev operators to equationally express uniqueness of iteration (more generally, higher - order primitive recursion) in a simply typed lambda calculus, essentially Godel's $ T $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	technique	technique	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	Lambek	Lambek	PROPN	NNP	Number=Sing	5	pobj	_	_
7	involving	involve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	acl	_	_
8	Maltsev	Maltsev	PROPN	NNP	Number=Sing	9	compound	_	_
9	operators	operator	NOUN	NNS	Number=Plur	7	dobj	_	_
10	to	to	PART	TO	_	12	aux	_	_
11	equationally	equationally	ADV	RB	_	12	advmod	_	_
12	express	express	VERB	VB	VerbForm=Inf	2	xcomp	_	_
13	uniqueness	uniqueness	NOUN	NN	Number=Sing	12	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	iteration	iteration	NOUN	NN	Number=Sing	14	pobj	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	22	punct	_	SpaceAfter=No
17	more	more	ADV	RBR	Degree=Cmp	18	advmod	_	_
18	generally	generally	ADV	RB	_	22	advmod	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
20	higher	high	ADJ	JJR	Degree=Cmp	22	amod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	order	order	NOUN	NN	Number=Sing	24	nmod	_	_
23	primitive	primitive	ADJ	JJ	Degree=Pos	24	amod	_	_
24	recursion	recursion	NOUN	NN	Number=Sing	15	appos	_	SpaceAfter=No
25	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	12	punct	_	_
26	in	in	ADP	IN	_	12	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
28	simply	simply	ADV	RB	_	29	advmod	_	_
29	typed	type	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	amod	_	_
30	lambda	lambda	PROPN	NNP	Number=Sing	31	compound	_	_
31	calculus	calculus	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
33	essentially	essentially	ADV	RB	_	36	advmod	_	_
34	Godel	Godel	PROPN	NNP	Number=Sing	36	poss	_	SpaceAfter=No
35	's	's	PART	POS	_	34	case	_	_
36	$ T $	$ t $	SYM	$	_	31	appos	_	_
37	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We prove the following facts about typed lambda calculus with uniqueness for primitive recursors: (i) It is undecidable, (ii) Church - Rosser fails, although ground Church - Rosser holds, (iii) strong normalization (termination) is still valid.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	amod	_	_
5	facts	fact	NOUN	NNS	Number=Plur	2	dobj	_	_
6	about	about	ADP	IN	_	5	prep	_	_
7	typed	type	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	amod	_	_
8	lambda	lambda	PROPN	NNP	Number=Sing	9	compound	_	_
9	calculus	calculus	NOUN	NN	Number=Sing	6	pobj	_	_
10	with	with	ADP	IN	_	5	prep	_	_
11	uniqueness	uniqueness	NOUN	NN	Number=Sing	10	pobj	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	primitive	primitive	ADJ	JJ	Degree=Pos	14	amod	_	_
14	recursors	recursor	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	:	:	PUNCT	:	_	5	punct	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	17	punct	_	SpaceAfter=No
17	i	i	NOUN	NN	Number=Sing	20	dep	_	SpaceAfter=No
18	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	17	punct	_	_
19	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	20	nsubj	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	46	ccomp	_	_
21	undecidable	undecidable	ADJ	JJ	Degree=Pos	20	acomp	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
23	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	28	punct	_	SpaceAfter=No
24	ii	ii	PROPN	NNP	Number=Sing	28	nmod	_	SpaceAfter=No
25	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	28	punct	_	_
26	Church	Church	PROPN	NNP	Number=Sing	28	compound	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	Rosser	Rosser	PROPN	NNP	Number=Sing	29	nsubj	_	_
29	fails	fail	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	46	parataxis	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
31	although	although	SCONJ	IN	_	36	mark	_	_
32	ground	ground	NOUN	NN	Number=Sing	35	compound	_	_
33	Church	Church	PROPN	NNP	Number=Sing	35	compound	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	Rosser	Rosser	PROPN	NNP	Number=Sing	36	nsubj	_	_
36	holds	hold	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	46	advcl	_	SpaceAfter=No
37	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
38	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	42	punct	_	SpaceAfter=No
39	iii	iii	NOUN	NN	Number=Sing	42	nmod	_	SpaceAfter=No
40	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	42	punct	_	_
41	strong	strong	ADJ	JJ	Degree=Pos	42	amod	_	_
42	normalization	normalization	NOUN	NN	Number=Sing	46	nsubj	_	_
43	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	42	punct	_	SpaceAfter=No
44	termination	termination	NOUN	NN	Number=Sing	42	appos	_	SpaceAfter=No
45	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	42	punct	_	_
46	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
47	still	still	ADV	RB	_	46	advmod	_	_
48	valid	valid	ADJ	JJ	Degree=Pos	46	acomp	_	SpaceAfter=No
49	.	.	PUNCT	.	PunctType=Peri	46	punct	_	SpaceAfter=No

# sent_id = 4
# text = This entails the undecidability of the coherence problem for cartesian closed categories with strong natural numbers objects, as well as providing a natural example of the following computational paradigm: a non - CR, ground CR, undecidable, terminating rewriting system.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	entails	entail	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	undecidability	undecidability	NOUN	NN	Number=Sing	11	nsubj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	coherence	coherence	NOUN	NN	Number=Sing	8	compound	_	_
8	problem	problem	NOUN	NN	Number=Sing	5	pobj	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	cartesian	cartesian	ADJ	JJ	Degree=Pos	9	pobj	_	_
11	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
12	categories	category	NOUN	NNS	Number=Plur	2	dobj	_	_
13	with	with	ADP	IN	_	12	prep	_	_
14	strong	strong	ADJ	JJ	Degree=Pos	17	amod	_	_
15	natural	natural	ADJ	JJ	Degree=Pos	16	amod	_	_
16	numbers	number	NOUN	NNS	Number=Plur	17	compound	_	_
17	objects	object	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
19	as	as	ADV	RB	_	21	advmod	_	_
20	well	well	ADV	RB	Degree=Pos	21	advmod	_	_
21	as	as	ADP	IN	_	2	cc	_	_
22	providing	provide	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	natural	natural	ADJ	JJ	Degree=Pos	25	amod	_	_
25	example	example	NOUN	NN	Number=Sing	22	dobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
28	following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	30	amod	_	_
29	computational	computational	ADJ	JJ	Degree=Pos	30	amod	_	_
30	paradigm	paradigm	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
31	:	:	PUNCT	:	_	30	punct	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
33	non	non	ADJ	JJ	Degree=Pos	35	amod	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	CR	cr	ADJ	JJ	Degree=Pos	38	amod	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
37	ground	ground	NOUN	NN	Number=Sing	38	compound	_	_
38	CR	CR	PROPN	NNP	Number=Sing	30	appos	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	38	punct	_	_
40	undecidable	undecidable	ADJ	JJ	Degree=Pos	38	amod	_	SpaceAfter=No
41	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
42	terminating	terminate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	advcl	_	_
43	rewriting	rewrite	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	44	amod	_	_
44	system	system	NOUN	NN	Number=Sing	42	dobj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 84
# sent_id = 1
# text = We demonstrate how the identity $ Notimes N cong N $ in a monoidal category allows us to construct a functor from the full subcategory generated by $ N $ and $ otimes $ to the endomorphism monoid of the object $ N $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	demonstrate	demonstrate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	how	how	SCONJ	WRB	_	5	advmod	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	identity	identity	NOUN	NN	Number=Sing	6	nsubj	_	_
6	$ Notimes N cong N $	$ notimes n cong n $	SYM	$	_	2	ccomp	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	monoidal	monoidal	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
11	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
12	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	construct	construct	VERB	VB	VerbForm=Inf	11	ccomp	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	functor	functor	NOUN	NN	Number=Sing	14	dobj	_	_
17	from	from	ADP	IN	_	14	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	full	full	ADJ	JJ	Degree=Pos	20	amod	_	_
20	subcategory	subcategory	NOUN	NN	Number=Sing	17	pobj	_	_
21	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	acl	_	_
22	by	by	ADP	IN	_	21	agent	_	_
23	$ N $	$ n $	SYM	$	_	22	pobj	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
25	$ otimes $	$ otimes $	SYM	$	_	14	advmod	_	_
26	to	to	ADP	IN	_	14	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	endomorphism	endomorphism	NOUN	NN	Number=Sing	29	compound	_	_
29	monoid	monoid	NOUN	NN	Number=Sing	26	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	object	object	NOUN	NN	Number=Sing	30	pobj	_	_
33	$ N $	$ n $	SYM	$	_	14	dep	_	_
34	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This provides a categorical foundation for one - object analogues of the symmetric monoidal categories used by J. - Y. Girard in his Geometry of Interaction series of papers, and explicitly described in terms of inverse semigroup theory in [6, 11].
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	categorical	categorical	ADJ	JJ	Degree=Pos	5	amod	_	_
5	foundation	foundation	NOUN	NN	Number=Sing	2	dobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	one	one	NUM	CD	NumType=Card	9	nummod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	object	object	NOUN	NN	Number=Sing	10	compound	_	_
10	analogues	analogue	NOUN	NNS	Number=Plur	6	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
13	symmetric	symmetric	ADJ	JJ	Degree=Pos	15	amod	_	_
14	monoidal	monoidal	ADJ	JJ	Degree=Pos	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
16	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
17	by	by	ADP	IN	_	16	agent	_	_
18	J.	J.	PROPN	NNP	Number=Sing	21	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
20	Y.	Y.	PROPN	NNP	Number=Sing	21	compound	_	_
21	Girard	Girard	PROPN	NNP	Number=Sing	17	pobj	_	_
22	in	in	ADP	IN	_	16	prep	_	_
23	his	his	PRON	PRP$	Gender=Masc|Number=Sing|Person=3|Poss=Yes|PronType=Prs	27	poss	_	_
24	Geometry	Geometry	PROPN	NNP	Number=Sing	27	nmod	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	Interaction	Interaction	PROPN	NNP	Number=Sing	25	pobj	_	_
27	series	series	NOUN	NN	Number=Sing	22	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	papers	paper	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
32	explicitly	explicitly	ADV	RB	_	33	advmod	_	_
33	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	conj	_	_
34	in	in	ADP	IN	_	33	prep	_	_
35	terms	term	NOUN	NNS	Number=Plur	34	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	inverse	inverse	ADJ	JJ	Degree=Pos	38	amod	_	_
38	semigroup	semigroup	NOUN	NN	Number=Sing	39	compound	_	_
39	theory	theory	NOUN	NN	Number=Sing	36	pobj	_	_
40	in	in	ADP	IN	_	33	prep	_	_
41	[	[	PROPN	NNP	Number=Sing	40	pobj	_	SpaceAfter=No
42	6	6	NUM	CD	NumType=Card	41	nummod	_	SpaceAfter=No
43	,	,	PUNCT	,	PunctType=Comm	42	punct	_	_
44	11	11	NUM	CD	NumType=Card	42	appos	_	SpaceAfter=No
45	]	]	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	40	pobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = This functor also allows the construction of one - object analogues of other categorical structures.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	functor	functor	NOUN	NN	Number=Sing	4	nsubj	_	_
3	also	also	ADV	RB	_	4	advmod	_	_
4	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	construction	construction	NOUN	NN	Number=Sing	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	one	one	NUM	CD	NumType=Card	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	object	object	NOUN	NN	Number=Sing	11	compound	_	_
11	analogues	analogue	NOUN	NNS	Number=Plur	7	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	other	other	ADJ	JJ	Degree=Pos	15	amod	_	_
14	categorical	categorical	ADJ	JJ	Degree=Pos	15	amod	_	_
15	structures	structure	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = We give the example of one - object analogues of the categorical trace, and compact closedness.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	example	example	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	one	one	NUM	CD	NumType=Card	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	object	object	NOUN	NN	Number=Sing	9	compound	_	_
9	analogues	analogue	NOUN	NNS	Number=Plur	5	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	categorical	categorical	ADJ	JJ	Degree=Pos	13	amod	_	_
13	trace	trace	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
16	compact	compact	ADJ	JJ	Degree=Pos	17	amod	_	_
17	closedness	closedness	NOUN	NN	Number=Sing	13	conj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = Finally, we demonstrate how the categorical theory of self - similarity can be related to the algebraic theory (as presented in [11]), and Girard's dynamical algebra, by considering one - object analogues of projections and inclusions.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	demonstrate	demonstrate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	how	how	SCONJ	WRB	_	15	advmod	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	categorical	categorical	ADJ	JJ	Degree=Pos	8	amod	_	_
8	theory	theory	NOUN	NN	Number=Sing	15	nsubjpass	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	self	self	NOUN	NN	Number=Sing	12	compound	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	similarity	similarity	NOUN	NN	Number=Sing	9	pobj	_	_
13	can	can	AUX	MD	VerbForm=Fin	15	aux	_	_
14	be	be	AUX	VB	VerbForm=Inf	15	auxpass	_	_
15	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	ccomp	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	algebraic	algebraic	ADJ	JJ	Degree=Pos	19	amod	_	_
19	theory	theory	NOUN	NN	Number=Sing	16	pobj	_	_
20	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	19	punct	_	SpaceAfter=No
21	as	as	SCONJ	IN	_	22	mark	_	_
22	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	acl	_	_
23	in	in	ADP	IN	_	22	prep	_	_
24	[	[	X	XX	_	23	pobj	_	SpaceAfter=No
25	11	11	NUM	CD	NumType=Card	23	pobj	_	SpaceAfter=No
26	]	]	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	23	pobj	_	SpaceAfter=No
27	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	19	punct	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
30	Girard	Girard	PROPN	NNP	Number=Sing	33	poss	_	SpaceAfter=No
31	's	's	PART	POS	_	30	case	_	_
32	dynamical	dynamical	ADJ	JJ	Degree=Pos	33	amod	_	_
33	algebra	algebra	NOUN	NN	Number=Sing	4	conj	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
35	by	by	ADP	IN	_	33	prep	_	_
36	considering	consider	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	35	pcomp	_	_
37	one	one	NUM	CD	NumType=Card	39	nummod	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	object	object	NOUN	NN	Number=Sing	40	compound	_	_
40	analogues	analogue	NOUN	NNS	Number=Plur	36	dobj	_	_
41	of	of	ADP	IN	_	40	prep	_	_
42	projections	projection	NOUN	NNS	Number=Plur	41	pobj	_	_
43	and	and	CCONJ	CC	ConjType=Cmp	42	cc	_	_
44	inclusions	inclusion	NOUN	NNS	Number=Plur	42	conj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 85
# sent_id = 1
# text = This represents a new and more comprehensive approach to the $ * $ - autonomous categories constructed in the monograph by Barr.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	represents	represent	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
4	new	new	ADJ	JJ	Degree=Pos	8	amod	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	more	more	ADV	RBR	Degree=Cmp	7	advmod	_	_
7	comprehensive	comprehensive	ADJ	JJ	Degree=Pos	4	conj	_	_
8	approach	approach	NOUN	NN	Number=Sing	2	dobj	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
11	$ * $	$ * $	SYM	$	_	13	advmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	autonomous	autonomous	ADJ	JJ	Degree=Pos	14	amod	_	_
14	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	_
15	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	acl	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	monograph	monograph	NOUN	NN	Number=Sing	16	pobj	_	_
19	by	by	ADP	IN	_	15	agent	_	_
20	Barr	Barr	PROPN	NNP	Number=Sing	19	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The main tool in the new approach is the Chu construction.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	tool	tool	NOUN	NN	Number=Sing	8	nsubj	_	_
4	in	in	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	new	new	ADJ	JJ	Degree=Pos	7	amod	_	_
7	approach	approach	NOUN	NN	Number=Sing	4	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	Chu	Chu	PROPN	NNP	Number=Sing	11	compound	_	_
11	construction	construction	NOUN	NN	Number=Sing	8	attr	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 3
# text = The main conclusion is that the category of separated extensional Chu objects for certain kinds of equational categories is equivalent to two usually distinct subcategories of the categories of uniform algebras of those categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	conclusion	conclusion	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	19	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	category	category	NOUN	NN	Number=Sing	19	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	separated	separated	ADJ	JJ	Degree=Pos	12	amod	_	_
10	extensional	extensional	ADJ	JJ	Degree=Pos	12	amod	_	_
11	Chu	Chu	PROPN	NNP	Number=Sing	12	compound	_	_
12	objects	object	NOUN	NNS	Number=Plur	8	pobj	_	_
13	for	for	ADP	IN	_	12	prep	_	_
14	certain	certain	ADJ	JJ	Degree=Pos	15	amod	_	_
15	kinds	kind	NOUN	NNS	Number=Plur	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	equational	equational	ADJ	JJ	Degree=Pos	18	amod	_	_
18	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
20	equivalent	equivalent	ADJ	JJ	Degree=Pos	19	acomp	_	_
21	to	to	ADP	IN	_	20	prep	_	_
22	two	two	NUM	CD	NumType=Card	25	nummod	_	_
23	usually	usually	ADV	RB	_	24	advmod	_	_
24	distinct	distinct	ADJ	JJ	Degree=Pos	25	amod	_	_
25	subcategories	subcategorie	NOUN	NNS	Number=Plur	21	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	categories	category	NOUN	NNS	Number=Plur	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	uniform	uniform	ADJ	JJ	Degree=Pos	31	amod	_	_
31	algebras	algebra	NOUN	NNS	Number=Plur	29	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	those	those	DET	DT	Number=Plur|PronType=Dem	34	det	_	_
34	categories	category	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 86
# sent_id = 1
# text = The contravariant powerset, and its generalisations $ Sigma^X $ to the lattices of open subsets of a locally compact topological space and of recursively enumerable subsets of numbers, satisfy the Euclidean principle that $ phimeet F(phi)=phimeet F(top) $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	contravariant	contravariant	ADJ	JJ	Degree=Pos	3	amod	_	_
3	powerset	powerset	NOUN	NN	Number=Sing	29	nsubj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
6	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	7	poss	_	_
7	generalisations	generalisation	NOUN	NNS	Number=Plur	3	conj	_	_
8	$ Sigma^X $	$ sigma^x $	SYM	$	_	7	appos	_	_
9	to	to	ADP	IN	_	7	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	lattices	lattice	NOUN	NNS	Number=Plur	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	open	open	ADJ	JJ	Degree=Pos	14	amod	_	_
14	subsets	subset	NOUN	NNS	Number=Plur	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
17	locally	locally	ADV	RB	_	18	advmod	_	_
18	compact	compact	ADJ	JJ	Degree=Pos	20	amod	_	_
19	topological	topological	ADJ	JJ	Degree=Pos	20	amod	_	_
20	space	space	NOUN	NN	Number=Sing	15	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
22	of	of	ADP	IN	_	15	conj	_	_
23	recursively	recursively	ADV	RB	_	24	advmod	_	_
24	enumerable	enumerable	ADJ	JJ	Degree=Pos	25	amod	_	_
25	subsets	subset	NOUN	NNS	Number=Plur	22	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	numbers	number	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
29	satisfy	satisfy	VERB	VB	VerbForm=Inf	0	ROOT	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	Euclidean	Euclidean	PROPN	NNP	Number=Sing	32	amod	_	_
32	principle	principle	NOUN	NN	Number=Sing	29	dobj	_	_
33	that	that	SCONJ	IN	_	34	nsubj	_	_
34	$ phimeet F(phi)=phimeet F(top) $	$ phimeet f(phi)=phimeet f(top) $	SYM	$	_	32	relcl	_	_
35	.	.	PUNCT	.	PunctType=Peri	29	punct	_	SpaceAfter=No

# sent_id = 2
# text = Conversely, when the adjunction $ Sigma^{( - )}dashvSigma^{( - )} $ is monadic, this equation implies that $ Sigma $ classifies some class of monos, and the Frobenius law $ exists x.(phi(x)meetpsi)=(exists x.phi(x))meetpsi) $ for the existential quantifier.
1	Conversely	conversely	ADV	RB	_	12	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
3	when	when	SCONJ	WRB	_	7	advmod	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	adjunction	adjunction	NOUN	NN	Number=Sing	7	nsubj	_	_
6	$ Sigma^{( - )}dashvSigma^{( - )} $	$ sigma^{( - )}dashvsigma^{( - )} $	SYM	$	_	5	appos	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	advcl	_	_
8	monadic	monadic	ADJ	JJ	Degree=Pos	7	acomp	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
10	this	this	DET	DT	Number=Sing|PronType=Dem	11	det	_	_
11	equation	equation	NOUN	NN	Number=Sing	12	nsubj	_	_
12	implies	imply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	that	that	SCONJ	IN	_	15	mark	_	_
14	$ Sigma $	$ sigma $	SYM	$	_	15	nsubj	_	_
15	classifies	classify	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	ccomp	_	_
16	some	some	DET	DT	_	17	det	_	_
17	class	class	NOUN	NN	Number=Sing	15	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	monos	mono	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	Frobenius	Frobenius	PROPN	NNP	Number=Sing	24	compound	_	_
24	law	law	NOUN	NN	Number=Sing	12	conj	_	_
25	$ exists x.(phi(x)meetpsi)=(exists x.phi(x))meetpsi) $	$ exists x.(phi(x)meetpsi)=(exists x.phi(x))meetpsi) $	NOUN	NN	Number=Sing	24	appos	_	_
26	for	for	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	existential	existential	ADJ	JJ	Degree=Pos	29	amod	_	_
29	quantifier	quantifier	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 3
# text = In topology, the lattice duals of these equations also hold, and are related to the Phoa principle in synthetic domain theory.
1	In	in	ADP	IN	_	11	prep	_	_
2	topology	topology	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	lattice	lattice	NOUN	NN	Number=Sing	6	compound	_	_
6	duals	dual	NOUN	NNS	Number=Plur	11	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	these	these	DET	DT	Number=Plur|PronType=Dem	9	det	_	_
9	equations	equation	NOUN	NNS	Number=Plur	7	pobj	_	_
10	also	also	ADV	RB	_	11	advmod	_	_
11	hold	hold	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	conj	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	Phoa	Phoa	PROPN	NNP	Number=Sing	19	compound	_	_
19	principle	principle	NOUN	NN	Number=Sing	16	pobj	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	synthetic	synthetic	ADJ	JJ	Degree=Pos	22	amod	_	_
22	domain	domain	NOUN	NN	Number=Sing	23	compound	_	_
23	theory	theory	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 4
# text = The natural definitions of discrete and Hausdorff spaces correspond to equality and inequality, whilst the quantifiers considered as adjoints characterise open (or, as we call them, overt) and compact spaces.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	natural	natural	ADJ	JJ	Degree=Pos	3	amod	_	_
3	definitions	definition	NOUN	NNS	Number=Plur	9	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	discrete	discrete	ADJ	JJ	Degree=Pos	4	pobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
7	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	8	compound	_	_
8	spaces	space	NOUN	NNS	Number=Plur	3	conj	_	_
9	correspond	correspond	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	equality	equality	NOUN	NN	Number=Sing	10	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	inequality	inequality	NOUN	NN	Number=Sing	11	conj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
15	whilst	whilst	SCONJ	IN	_	18	mark	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	quantifiers	quantifier	NOUN	NNS	Number=Plur	18	nsubj	_	_
18	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	advcl	_	_
19	as	as	SCONJ	IN	_	21	mark	_	_
20	adjoints	adjoint	NOUN	NNS	Number=Plur	21	nsubj	_	_
21	characterise	characterise	VERB	VBP	Tense=Pres|VerbForm=Fin	18	advcl	_	_
22	open	open	ADJ	JJ	Degree=Pos	21	acomp	_	_
23	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	21	punct	_	SpaceAfter=No
24	or	or	CCONJ	CC	ConjType=Cmp	18	cc	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
26	as	as	SCONJ	IN	_	28	mark	_	_
27	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	28	nsubj	_	_
28	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	9	advcl	_	_
29	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	28	dobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
31	overt	overt	NOUN	NN	Number=Sing	28	dep	_	SpaceAfter=No
32	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	28	punct	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
34	compact	compact	ADJ	JJ	Degree=Pos	35	amod	_	_
35	spaces	space	NOUN	NNS	Number=Plur	28	conj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 5
# text = Our treatment of overt discrete spaces and open maps is precisely dual to that of compact Hausdorff spaces and proper maps.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	treatment	treatment	NOUN	NN	Number=Sing	10	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	overt	overt	ADJ	JJ	Degree=Pos	6	amod	_	_
5	discrete	discrete	ADJ	JJ	Degree=Pos	6	amod	_	_
6	spaces	space	NOUN	NNS	Number=Plur	3	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	open	open	ADJ	JJ	Degree=Pos	9	amod	_	_
9	maps	map	NOUN	NNS	Number=Plur	6	conj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	precisely	precisely	ADV	RB	_	12	advmod	_	_
12	dual	dual	ADJ	JJ	Degree=Pos	10	acomp	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	that	that	PRON	DT	Number=Sing|PronType=Dem	13	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	compact	compact	ADJ	JJ	Degree=Pos	18	amod	_	_
17	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	18	compound	_	_
18	spaces	space	NOUN	NNS	Number=Plur	15	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	proper	proper	ADJ	JJ	Degree=Pos	21	amod	_	_
21	maps	map	NOUN	NNS	Number=Plur	18	conj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 6
# text = The category of overt discrete spaces forms a pretopos and the paper concludes with a converse of Paré's theorem (that the contravariant powerset functor is monadic) that characterises elementary toposes by means of the monadic and Euclidean properties together with all quantifiers, making no reference to subsets.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	7	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	overt	overt	PROPN	NNP	Number=Sing	6	compound	_	_
5	discrete	discrete	ADJ	JJ	Degree=Pos	6	compound	_	_
6	spaces	space	NOUN	NNS	Number=Plur	3	pobj	_	_
7	forms	form	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	pretopos	pretopos	NOUN	NN	Number=Sing	7	dobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	paper	paper	NOUN	NN	Number=Sing	13	nsubj	_	_
13	concludes	conclude	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	conj	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	converse	converse	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	Paré	Paré	PROPN	NNP	Number=Sing	20	poss	_	SpaceAfter=No
19	's	's	PART	POS	_	18	case	_	_
20	theorem	theorem	ADJ	JJ	Degree=Pos	17	pobj	_	_
21	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	27	punct	_	SpaceAfter=No
22	that	that	SCONJ	IN	_	27	mark	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
24	contravariant	contravariant	ADJ	JJ	Degree=Pos	26	amod	_	_
25	powerset	powerset	NOUN	NN	Number=Sing	26	compound	_	_
26	functor	functor	NOUN	NN	Number=Sing	27	nsubj	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
28	monadic	monadic	ADJ	JJ	Degree=Pos	27	acomp	_	SpaceAfter=No
29	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	27	punct	_	_
30	that	that	PRON	WDT	PronType=Rel	31	nsubj	_	_
31	characterises	characterise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
32	elementary	elementary	ADJ	JJ	Degree=Pos	33	amod	_	_
33	toposes	topos	NOUN	NNS	Number=Plur	31	dobj	_	_
34	by	by	ADP	IN	_	31	prep	_	_
35	means	mean	NOUN	NNS	Number=Plur	34	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
38	monadic	monadic	ADJ	JJ	Degree=Pos	41	amod	_	_
39	and	and	CCONJ	CC	ConjType=Cmp	38	cc	_	_
40	Euclidean	euclidean	ADJ	JJ	Degree=Pos	38	conj	_	_
41	properties	property	NOUN	NNS	Number=Plur	36	pobj	_	_
42	together	together	ADV	RB	_	43	advmod	_	_
43	with	with	ADP	IN	_	31	prep	_	_
44	all	all	DET	DT	_	45	det	_	_
45	quantifiers	quantifier	NOUN	NNS	Number=Plur	43	pobj	_	SpaceAfter=No
46	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
47	making	make	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	31	advcl	_	_
48	no	no	DET	DT	_	49	det	_	_
49	reference	reference	NOUN	NN	Number=Sing	47	dobj	_	_
50	to	to	ADP	IN	_	49	prep	_	_
51	subsets	subset	NOUN	NNS	Number=Plur	50	pobj	_	SpaceAfter=No
52	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# doc_id = 87
# sent_id = 1
# text = In this paper we use Quillen's model structure given by Dwyer - Kan for the category of simplicial groupoids (with discrete object of objects) to describe in this category, in the simplicial language, the fundamental homotopy theoretical constructions of path and cylinder objects.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	Quillen	Quillen	PROPN	NNP	Number=Sing	9	poss	_	SpaceAfter=No
7	's	's	PART	POS	_	6	case	_	_
8	model	model	NOUN	NN	Number=Sing	9	compound	_	_
9	structure	structure	NOUN	NN	Number=Sing	5	dobj	_	_
10	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	acl	_	_
11	by	by	ADP	IN	_	10	agent	_	_
12	Dwyer	Dwyer	PROPN	NNP	Number=Sing	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	Kan	Kan	PROPN	NNP	Number=Sing	11	pobj	_	_
15	for	for	ADP	IN	_	10	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	simplicial	simplicial	ADJ	JJ	Degree=Pos	20	amod	_	_
20	groupoids	groupoid	NOUN	NNS	Number=Plur	18	pobj	_	_
21	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	9	punct	_	SpaceAfter=No
22	with	with	ADP	IN	_	5	prep	_	_
23	discrete	discrete	ADJ	JJ	Degree=Pos	24	amod	_	_
24	object	object	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	objects	object	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
27	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	5	punct	_	_
28	to	to	PART	TO	_	29	aux	_	_
29	describe	describe	VERB	VB	VerbForm=Inf	5	xcomp	_	_
30	in	in	ADP	IN	_	29	prep	_	_
31	this	this	DET	DT	Number=Sing|PronType=Dem	32	det	_	_
32	category	category	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
34	in	in	ADP	IN	_	29	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
36	simplicial	simplicial	ADJ	JJ	Degree=Pos	37	amod	_	_
37	language	language	NOUN	NN	Number=Sing	34	pobj	_	SpaceAfter=No
38	,	,	PUNCT	,	PunctType=Comm	43	punct	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
40	fundamental	fundamental	ADJ	JJ	Degree=Pos	43	amod	_	_
41	homotopy	homotopy	NOUN	NN	Number=Sing	43	nmod	_	_
42	theoretical	theoretical	ADJ	JJ	Degree=Pos	43	amod	_	_
43	constructions	construction	NOUN	NNS	Number=Plur	5	dobj	_	_
44	of	of	ADP	IN	_	43	prep	_	_
45	path	path	NOUN	NN	Number=Sing	48	nmod	_	_
46	and	and	CCONJ	CC	ConjType=Cmp	45	cc	_	_
47	cylinder	cylinder	NOUN	NN	Number=Sing	48	compound	_	_
48	objects	object	NOUN	NNS	Number=Plur	44	pobj	_	SpaceAfter=No
49	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = We then characterize the associated left and right homotopy relations in terms of simplicial identities and give a simplicial description of the homotopy category of simplicial groupoids.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
5	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
6	left	left	ADJ	JJ	Degree=Pos	5	nmod	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	right	right	ADJ	JJ	Degree=Pos	6	conj	_	_
9	homotopy	homotopy	NOUN	NN	Number=Sing	10	compound	_	_
10	relations	relation	NOUN	NNS	Number=Plur	3	dobj	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	terms	term	NOUN	NNS	Number=Plur	11	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	simplicial	simplicial	ADJ	JJ	Degree=Pos	15	amod	_	_
15	identities	identity	NOUN	NNS	Number=Plur	13	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
17	give	give	VERB	VB	VerbForm=Inf	3	conj	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	simplicial	simplicial	ADJ	JJ	Degree=Pos	20	amod	_	_
20	description	description	NOUN	NN	Number=Sing	17	dobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	homotopy	homotopy	NOUN	NN	Number=Sing	24	compound	_	_
24	category	category	NOUN	NN	Number=Sing	21	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	simplicial	simplicial	ADJ	JJ	Degree=Pos	27	amod	_	_
27	groupoids	groupoid	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Finally, we show loop and suspension functors in the pointed case.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	loop	loop	NOUN	NN	Number=Sing	8	nmod	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	suspension	suspension	NOUN	NN	Number=Sing	5	conj	_	_
8	functors	functor	NOUN	NNS	Number=Plur	4	dobj	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	pointed	pointed	ADJ	JJ	Degree=Pos	12	amod	_	_
12	case	case	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 88
# sent_id = 1
# text = The purpose of this paper is to indicate some bicategorical properties of ring theory.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	purpose	purpose	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	paper	paper	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	indicate	indicate	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	some	some	DET	DT	_	11	det	_	_
10	bicategorical	bicategorical	ADJ	JJ	Degree=Pos	11	amod	_	_
11	properties	property	NOUN	NNS	Number=Plur	8	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	ring	ring	NOUN	NN	Number=Sing	14	compound	_	_
14	theory	theory	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this interaction, static modules are analyzed.
1	In	in	ADP	IN	_	8	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	interaction	interaction	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
5	static	static	ADJ	JJ	Degree=Pos	6	compound	_	_
6	modules	module	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	analyzed	analyze	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 89
# sent_id = 1
# text = This paper defines a solution manifold and a stable submanifold for a system of differential equations.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	defines	define	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	solution	solution	NOUN	NN	Number=Sing	3	dobj	_	_
6	manifold	manifold	ADJ	JJ	Degree=Pos	5	amod	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	stable	stable	ADJ	JJ	Degree=Pos	10	amod	_	_
10	submanifold	submanifold	NOUN	NN	Number=Sing	5	conj	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	system	system	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	differential	differential	ADJ	JJ	Degree=Pos	16	amod	_	_
16	equations	equation	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = Although we eventually work in the smooth topos, the first two sections do not mention topos theory and should be of interest to non - topos theorists.
1	Although	although	SCONJ	IN	_	4	mark	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
3	eventually	eventually	ADV	RB	_	4	advmod	_	_
4	work	work	VERB	VBP	Tense=Pres|VerbForm=Fin	16	advcl	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	smooth	smooth	ADJ	JJ	Degree=Pos	8	amod	_	_
8	topos	topos	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
11	first	first	ADJ	JJ	Degree=Pos	13	amod	_	_
12	two	two	NUM	CD	NumType=Card	13	nummod	_	_
13	sections	section	NOUN	NNS	Number=Plur	16	nsubj	_	_
14	do	do	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	16	aux	_	_
15	not	not	PART	RB	Polarity=Neg	16	neg	_	_
16	mention	mention	VERB	VB	VerbForm=Inf	0	ROOT	_	_
17	topos	topos	NOUN	NN	Number=Sing	18	compound	_	_
18	theory	theory	NOUN	NN	Number=Sing	16	dobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
20	should	should	AUX	MD	VerbForm=Fin	21	aux	_	_
21	be	be	AUX	VB	VerbForm=Inf	16	conj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	interest	interest	NOUN	NN	Number=Sing	22	pobj	_	_
24	to	to	ADP	IN	_	23	prep	_	_
25	non	non	ADJ	JJ	Degree=Pos	27	compound	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	topos	topos	ADJ	JJ	Degree=Pos	28	compound	_	_
28	theorists	theorist	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 3
# text = The paper characterizes solutions in terms of barriers to growth and defines solutions in what are called filter rings (characterized as $ C^{infty} $ - reduced rings in a paper of Moerdijk and Reyes).
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	characterizes	characterize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	solutions	solution	NOUN	NNS	Number=Plur	3	dobj	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	terms	term	NOUN	NNS	Number=Plur	5	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	barriers	barrier	NOUN	NNS	Number=Plur	7	pobj	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	growth	growth	NOUN	NN	Number=Sing	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	defines	define	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	conj	_	_
13	solutions	solution	NOUN	NNS	Number=Plur	12	dobj	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	what	what	PRON	WP	_	17	nsubjpass	_	_
16	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	17	auxpass	_	_
17	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	pcomp	_	_
18	filter	filter	NOUN	NN	Number=Sing	19	compound	_	_
19	rings	ring	NOUN	NNS	Number=Plur	17	oprd	_	_
20	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	21	punct	_	SpaceAfter=No
21	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	ccomp	_	_
22	as	as	ADP	IN	_	21	prep	_	_
23	$ C^{infty} $	$ c^{infty} $	SYM	$	_	25	advmod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	reduced	reduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
26	rings	ring	NOUN	NNS	Number=Plur	22	pobj	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
29	paper	paper	NOUN	NN	Number=Sing	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	Moerdijk	Moerdijk	PROPN	NNP	Number=Sing	30	pobj	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	Reyes	Reyes	PROPN	NNP	Number=Sing	31	conj	_	SpaceAfter=No
34	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	21	punct	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = We examine standardization, stabilization, perturbation, change of variables, non - standard solutions, strange attractors and cycles at infinity.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	examine	examine	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	standardization	standardization	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	stabilization	stabilization	NOUN	NN	Number=Sing	3	conj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	perturbation	perturbation	NOUN	NN	Number=Sing	5	conj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	change	change	NOUN	NN	Number=Sing	7	conj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	variables	variable	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	non	non	ADJ	JJ	Degree=Pos	15	amod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	standard	standard	ADJ	JJ	Degree=Pos	16	amod	_	_
16	solutions	solution	NOUN	NNS	Number=Plur	11	conj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
18	strange	strange	ADJ	JJ	Degree=Pos	19	amod	_	_
19	attractors	attractor	NOUN	NNS	Number=Plur	9	conj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	cycles	cycle	NOUN	NNS	Number=Plur	19	conj	_	_
22	at	at	ADP	IN	_	9	prep	_	_
23	infinity	infinity	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 90
# sent_id = 1
# text = In analogy with the varietal case, we give an abstract characterization of those categories occurring as regular epireflective subcategories of presheaf categories such that the inclusion functor preserves small sums.
1	In	in	ADP	IN	_	9	prep	_	_
2	analogy	analogy	NOUN	NN	Number=Sing	1	pobj	_	_
3	with	with	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	varietal	varietal	ADJ	JJ	Degree=Pos	6	amod	_	_
6	case	case	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	abstract	abstract	ADJ	JJ	Degree=Pos	12	amod	_	_
12	characterization	characterization	NOUN	NN	Number=Sing	9	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	those	those	DET	DT	Number=Plur|PronType=Dem	15	det	_	_
15	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	_
16	occurring	occur	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	acl	_	_
17	as	as	ADP	IN	_	16	prep	_	_
18	regular	regular	ADJ	JJ	Degree=Pos	20	amod	_	_
19	epireflective	epireflective	ADJ	JJ	Degree=Pos	20	amod	_	_
20	subcategories	subcategorie	NOUN	NNS	Number=Plur	17	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	presheaf	presheaf	ADJ	JJ	Degree=Pos	23	amod	_	_
23	categories	category	NOUN	NNS	Number=Plur	21	pobj	_	_
24	such	such	ADJ	JJ	Degree=Pos	29	amod	_	_
25	that	that	SCONJ	IN	_	29	mark	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	inclusion	inclusion	NOUN	NN	Number=Sing	28	compound	_	_
28	functor	functor	NOUN	NN	Number=Sing	29	nsubj	_	_
29	preserves	preserve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	advcl	_	_
30	small	small	ADJ	JJ	Degree=Pos	31	amod	_	_
31	sums	sum	NOUN	NNS	Number=Plur	29	dobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 91
# sent_id = 1
# text = We investigate preserving of projectivity and injectivity by the object - wise tensor product of $ RBbb{C} $ - modules, where $ Bbb{C} $ is a small category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	projectivity	projectivity	NOUN	NN	Number=Sing	4	pobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	injectivity	injectivity	NOUN	NN	Number=Sing	5	conj	_	_
8	by	by	ADP	IN	_	3	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
10	object	object	NOUN	NN	Number=Sing	12	npadvmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	wise	wise	ADJ	JJ	Degree=Pos	14	amod	_	_
13	tensor	tensor	NOUN	NN	Number=Sing	14	compound	_	_
14	product	product	NOUN	NN	Number=Sing	8	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	$ RBbb{C} $	$ rbbb{c} $	SYM	$	_	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	modules	module	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	where	where	SCONJ	WRB	_	22	advmod	_	_
21	$ Bbb{C} $	$ bbb{c} $	SYM	$	_	22	nsubj	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	relcl	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	small	small	ADJ	JJ	Degree=Pos	25	amod	_	_
25	category	category	NOUN	NN	Number=Sing	22	attr	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In particular, let $ {cal O}(G, X) $ be the category of canonical orbits of a discrete group $ G $ , over a $ G $ - set $ X $ .
1	In	in	ADP	IN	_	4	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
4	let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
5	$ {cal O}(G, X) $	$ {cal o}(g, x) $	SYM	$	_	6	nsubj	_	_
6	be	be	AUX	VB	VerbForm=Inf	4	ccomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	6	attr	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	canonical	canonical	ADJ	JJ	Degree=Pos	11	amod	_	_
11	orbits	orbit	NOUN	NNS	Number=Plur	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	discrete	discrete	ADJ	JJ	Degree=Pos	15	amod	_	_
15	group	group	NOUN	NN	Number=Sing	12	pobj	_	_
16	$ G $	$ g $	SYM	$	_	15	appos	_	_
17	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
18	over	over	ADP	IN	_	6	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
20	$ G $	$ g $	SYM	$	_	22	dep	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	amod	_	_
23	$ X $	$ x $	SYM	$	_	18	pobj	_	_
24	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that projectivity of $ R{cal O}(G, X) $ - modules is preserved by this tensor product.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	10	mark	_	_
4	projectivity	projectivity	NOUN	NN	Number=Sing	10	nsubjpass	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	$ R{cal O}(G, X) $	$ r{cal o}(g, x) $	SYM	$	_	8	compound	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	modules	module	NOUN	NNS	Number=Plur	10	nsubjpass	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	preserved	preserve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
11	by	by	ADP	IN	_	10	agent	_	_
12	this	this	DET	DT	Number=Sing|PronType=Dem	14	det	_	_
13	tensor	tensor	NOUN	NN	Number=Sing	14	compound	_	_
14	product	product	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = Moreover, if $ G $ is a finite group, $ X $ a finite $ G $ - set and $ R $ is an integral domain then such a tensor product of two injective $ R{cal O}(G, X) $ - modules is again injective.
1	Moreover	moreover	ADV	RB	_	18	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
3	if	if	SCONJ	IN	_	5	mark	_	_
4	$ G $	$ g $	SYM	$	_	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	advcl	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	finite	finite	ADJ	JJ	Degree=Pos	8	amod	_	_
8	group	group	NOUN	NN	Number=Sing	5	attr	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
10	$ X $	$ x $	SYM	$	_	17	nmod	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	finite	finite	NOUN	NN	Number=Sing	10	nsubj	_	_
13	$ G $	$ g $	SYM	$	_	15	advmod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	conj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	$ R $	$ r $	SYM	$	_	18	nsubj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	33	ccomp	_	_
19	an	an	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	integral	integral	ADJ	JJ	Degree=Pos	21	amod	_	_
21	domain	domain	NOUN	NN	Number=Sing	18	attr	_	_
22	then	then	ADV	RB	PronType=Dem	18	advmod	_	_
23	such	such	DET	PDT	_	26	predet	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
25	tensor	tensor	NOUN	NN	Number=Sing	26	compound	_	_
26	product	product	NOUN	NN	Number=Sing	33	nsubj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	two	two	NUM	CD	NumType=Card	32	nummod	_	_
29	injective	injective	ADJ	JJ	Degree=Pos	32	amod	_	_
30	$ R{cal O}(G, X) $	$ r{cal o}(g, x) $	SYM	$	_	32	compound	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	modules	module	NOUN	NNS	Number=Plur	27	pobj	_	_
33	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
34	again	again	ADV	RB	_	35	advmod	_	_
35	injective	injective	ADJ	JJ	Degree=Pos	33	acomp	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	33	punct	_	SpaceAfter=No

# doc_id = 92
# sent_id = 1
# text = We show that every algebraically - central extension in a Maltsev variety - that is, every surjective homomorphism $ f : A longrightarrow B $ whose kernel - congruence is contained in the centre of $ A $ , as defined using the theory of commutators - is also a central extension in the sense of categorical Galois theory; this was previously known only for varieties of $ Omega $ - groups, while its converse is easily seen to hold for any congruence - modular variety.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	41	ccomp	_	_
3	that	that	SCONJ	IN	_	26	mark	_	_
4	every	every	DET	DT	_	8	det	_	_
5	algebraically	algebraically	ADV	RB	_	7	advmod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	central	central	ADJ	JJ	Degree=Pos	8	amod	_	_
8	extension	extension	NOUN	NN	Number=Sing	26	nsubjpass	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	Maltsev	Maltsev	PROPN	NNP	Number=Sing	12	compound	_	_
12	variety	variety	NOUN	NN	Number=Sing	9	pobj	_	_
13	-	-	PUNCT	:	_	8	punct	_	_
14	that	that	ADV	RB	_	15	nsubj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	advmod	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
17	every	every	DET	DT	_	19	det	_	_
18	surjective	surjective	ADJ	JJ	Degree=Pos	19	amod	_	_
19	homomorphism	homomorphism	NOUN	NN	Number=Sing	8	appos	_	_
20	$ f : A longrightarrow B $	$ f : a longrightarrow b $	SYM	$	_	19	nmod	_	_
21	whose	whose	DET	WP$	Poss=Yes	24	poss	_	_
22	kernel	kernel	NOUN	NN	Number=Sing	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	congruence	congruence	NOUN	NN	Number=Sing	26	nsubjpass	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	auxpass	_	_
26	contained	contain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	centre	centre	NOUN	NN	Number=Sing	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	$ A $	$ a $	SYM	$	_	30	pobj	_	_
32	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
33	as	as	SCONJ	IN	_	34	mark	_	_
34	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	advcl	_	_
35	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	34	xcomp	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	theory	theory	NOUN	NN	Number=Sing	35	dobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	commutators	commutator	NOUN	NNS	Number=Plur	38	pobj	_	_
40	-	-	PUNCT	,	PunctType=Comm	41	punct	_	_
41	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	57	ccomp	_	_
42	also	also	ADV	RB	_	41	advmod	_	_
43	a	a	DET	DT	Definite=Ind|PronType=Art	45	det	_	_
44	central	central	ADJ	JJ	Degree=Pos	45	amod	_	_
45	extension	extension	NOUN	NN	Number=Sing	41	attr	_	_
46	in	in	ADP	IN	_	45	prep	_	_
47	the	the	DET	DT	Definite=Def|PronType=Art	48	det	_	_
48	sense	sense	NOUN	NN	Number=Sing	46	pobj	_	_
49	of	of	ADP	IN	_	48	prep	_	_
50	categorical	categorical	ADJ	JJ	Degree=Pos	52	amod	_	_
51	Galois	Galois	PROPN	NNP	Number=Sing	52	compound	_	_
52	theory	theory	NOUN	NN	Number=Sing	49	pobj	_	SpaceAfter=No
53	;	;	PUNCT	:	_	57	punct	_	_
54	this	this	PRON	DT	Number=Sing|PronType=Dem	57	nsubjpass	_	_
55	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	57	auxpass	_	_
56	previously	previously	ADV	RB	_	57	advmod	_	_
57	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
58	only	only	ADV	RB	_	59	advmod	_	_
59	for	for	ADP	IN	_	57	prep	_	_
60	varieties	variety	NOUN	NNS	Number=Plur	59	pobj	_	_
61	of	of	ADP	IN	_	60	prep	_	_
62	$ Omega $	$ omega $	SYM	$	_	64	compound	_	_
63	-	-	PUNCT	HYPH	PunctType=Dash	64	punct	_	_
64	groups	group	NOUN	NNS	Number=Plur	61	pobj	_	SpaceAfter=No
65	,	,	PUNCT	,	PunctType=Comm	57	punct	_	_
66	while	while	SCONJ	IN	_	71	mark	_	_
67	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	68	poss	_	_
68	converse	converse	NOUN	NN	Number=Sing	71	nsubjpass	_	_
69	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	71	auxpass	_	_
70	easily	easily	ADV	RB	_	71	advmod	_	_
71	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	57	advcl	_	_
72	to	to	PART	TO	_	73	aux	_	_
73	hold	hold	VERB	VB	VerbForm=Inf	71	xcomp	_	_
74	for	for	ADP	IN	_	73	prep	_	_
75	any	any	DET	DT	_	79	det	_	_
76	congruence	congruence	NOUN	NN	Number=Sing	78	compound	_	_
77	-	-	PUNCT	HYPH	PunctType=Dash	78	punct	_	_
78	modular	modular	ADJ	JJ	Degree=Pos	79	amod	_	_
79	variety	variety	NOUN	NN	Number=Sing	74	pobj	_	SpaceAfter=No
80	.	.	PUNCT	.	PunctType=Peri	57	punct	_	SpaceAfter=No

# doc_id = 93
# sent_id = 1
# text = The notion of normal subobject having an intrinsic meaning in any protomodular category, we introduce the notion of normal functor, namely left exact conservative functor which reflects normal subobjects.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	notion	notion	NOUN	NN	Number=Sing	16	advcl	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	normal	normal	ADJ	JJ	Degree=Pos	5	amod	_	_
5	subobject	subobject	NOUN	NN	Number=Sing	3	pobj	_	_
6	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	acl	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	intrinsic	intrinsic	ADJ	JJ	Degree=Pos	9	amod	_	_
9	meaning	meaning	NOUN	NN	Number=Sing	6	dobj	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	any	any	DET	DT	_	13	det	_	_
12	protomodular	protomodular	ADJ	JJ	Degree=Pos	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
15	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	16	nsubj	_	_
16	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	notion	notion	NOUN	NN	Number=Sing	16	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	normal	normal	ADJ	JJ	Degree=Pos	21	amod	_	_
21	functor	functor	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	namely	namely	ADV	RB	_	24	advmod	_	_
24	left	leave	VERB	VBD	Tense=Past|VerbForm=Fin	18	acl	_	_
25	exact	exact	ADJ	JJ	Degree=Pos	27	amod	_	_
26	conservative	conservative	ADJ	JJ	Degree=Pos	27	amod	_	_
27	functor	functor	NOUN	NN	Number=Sing	24	dobj	_	_
28	which	which	PRON	WDT	_	29	nsubj	_	_
29	reflects	reflect	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	relcl	_	_
30	normal	normal	ADJ	JJ	Degree=Pos	31	amod	_	_
31	subobjects	subobject	NOUN	NNS	Number=Plur	29	dobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 2
# text = The point is that for the category $ {bf Gp} $ of groups the change of base functors, with respect to the fibration of pointed objects, are not only conservative (this is the definition of a protomodular category), but also normal.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	point	point	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	26	mark	_	_
5	for	for	ADP	IN	_	26	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
8	$ {bf Gp} $	$ {bf gp} $	SYM	$	_	7	appos	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	groups	group	NOUN	NNS	Number=Plur	9	pobj	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	change	change	NOUN	NN	Number=Sing	26	nsubj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	base	base	NOUN	NN	Number=Sing	15	compound	_	_
15	functors	functor	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
17	with	with	ADP	IN	_	12	prep	_	_
18	respect	respect	NOUN	NN	Number=Sing	17	pobj	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	fibration	fibration	NOUN	NN	Number=Sing	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	pointed	pointed	ADJ	JJ	Degree=Pos	24	amod	_	_
24	objects	object	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
26	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	32	ccomp	_	_
27	not	not	PART	RB	Polarity=Neg	26	neg	_	_
28	only	only	ADV	RB	_	26	advmod	_	_
29	conservative	conservative	ADJ	JJ	Degree=Pos	26	acomp	_	_
30	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	32	punct	_	SpaceAfter=No
31	this	this	PRON	DT	Number=Sing|PronType=Dem	32	nsubj	_	_
32	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
34	definition	definition	NOUN	NN	Number=Sing	32	attr	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	a	a	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
37	protomodular	protomodular	ADJ	JJ	Degree=Pos	38	amod	_	_
38	category	category	NOUN	NN	Number=Sing	35	pobj	_	SpaceAfter=No
39	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	32	punct	_	SpaceAfter=No
40	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
41	but	but	CCONJ	CC	ConjType=Cmp	32	cc	_	_
42	also	also	ADV	RB	_	41	advmod	_	_
43	normal	normal	ADJ	JJ	Degree=Pos	32	conj	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = This leads to the notion of strongly protomodular category.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	leads	lead	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	notion	notion	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	strongly	strongly	ADV	RB	_	8	advmod	_	_
8	protomodular	protomodular	ADJ	JJ	Degree=Pos	9	amod	_	_
9	category	category	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = Some of their properties are given, the main one being that this notion is inherited by the slice categories.
1	Some	some	PRON	DT	_	6	nsubjpass	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	4	poss	_	_
4	properties	property	NOUN	NNS	Number=Plur	2	pobj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	main	main	ADJ	JJ	Degree=Pos	10	amod	_	_
10	one	one	NOUN	NN	Number=Sing	6	dobj	_	_
11	being	be	AUX	VBG	VerbForm=Ger	10	acl	_	_
12	that	that	SCONJ	IN	_	16	mark	_	_
13	this	this	DET	DT	Number=Sing|PronType=Dem	14	det	_	_
14	notion	notion	NOUN	NN	Number=Sing	16	nsubjpass	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	auxpass	_	_
16	inherited	inherit	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	relcl	_	_
17	by	by	ADP	IN	_	16	agent	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	slice	slice	NOUN	NN	Number=Sing	20	compound	_	_
20	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 94
# sent_id = 1
# text = For a set $ {cal M} $ of graphs the category $ {bf Cat}_{cal M} $ of all $ {cal M} $ - complete categories and all strictly $ {cal M} $ - continuous functors is known to be monadic over $ {bf Cat} $ .
1	For	for	ADP	IN	_	24	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	set	set	NOUN	NN	Number=Sing	4	amod	_	_
4	$ {cal M} $	$ {cal m} $	SYM	$	_	22	nmod	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	graphs	graph	NOUN	NNS	Number=Plur	5	pobj	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	6	dobj	_	_
9	$ {bf Cat}_{cal M} $	$ {bf cat}_{cal m} $	SYM	$	_	8	appos	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	all	all	DET	DT	_	15	det	_	_
12	$ {cal M} $	$ {cal m} $	SYM	$	_	14	advmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	complete	complete	ADJ	JJ	Degree=Pos	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
17	all	all	PRON	DT	_	21	advmod	_	_
18	strictly	strictly	ADV	RB	_	21	advmod	_	_
19	$ {cal M} $	$ {cal m} $	X	LS	NumType=Ord	21	advmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	continuous	continuous	ADJ	JJ	Degree=Pos	22	amod	_	_
22	functors	functor	NOUN	NNS	Number=Plur	24	nsubjpass	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	auxpass	_	_
24	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
25	to	to	PART	TO	_	26	aux	_	_
26	be	be	AUX	VB	VerbForm=Inf	24	xcomp	_	_
27	monadic	monadic	ADJ	JJ	Degree=Pos	26	acomp	_	_
28	over	over	ADP	IN	_	27	prep	_	_
29	$ {bf Cat} $	$ {bf cat} $	SYM	$	_	28	pobj	_	_
30	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# sent_id = 2
# text = The question of monadicity of $ {bf Cat}_{cal M} $ over the category of graphs is known to have an affirmative answer when $ {cal M} $ specifies either (i) all finite limits, or (ii) all finite products, or (iii) equalizers and terminal objects, or (iv) just terminal objects.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	question	question	NOUN	NN	Number=Sing	13	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	monadicity	monadicity	NOUN	NN	Number=Sing	3	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	$ {bf Cat}_{cal M} $	$ {bf cat}_{cal m} $	SYM	$	_	5	pobj	_	_
7	over	over	ADP	IN	_	2	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	graphs	graph	NOUN	NNS	Number=Plur	10	pobj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	have	have	VERB	VB	VerbForm=Inf	13	xcomp	_	_
16	an	an	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	affirmative	affirmative	ADJ	JJ	Degree=Pos	18	amod	_	_
18	answer	answer	NOUN	NN	Number=Sing	15	dobj	_	_
19	when	when	SCONJ	WRB	_	21	advmod	_	_
20	$ {cal M} $	$ {cal m} $	SYM	$	_	21	nsubj	_	_
21	specifies	specifie	NOUN	NNS	Number=Plur	15	advcl	_	_
22	either	either	CCONJ	CC	ConjType=Cmp	21	preconj	_	_
23	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
24	i	i	NOUN	NN	Number=Sing	21	appos	_	SpaceAfter=No
25	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	24	punct	_	_
26	all	all	DET	DT	_	28	det	_	_
27	finite	finite	PROPN	NNP	Number=Sing	28	compound	_	_
28	limits	limit	NOUN	NNS	Number=Plur	21	conj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
30	or	or	CCONJ	CC	ConjType=Cmp	28	cc	_	_
31	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	32	punct	_	SpaceAfter=No
32	ii	ii	PROPN	NNP	Number=Sing	28	conj	_	SpaceAfter=No
33	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	32	punct	_	_
34	all	all	DET	DT	_	36	det	_	_
35	finite	finite	ADJ	JJ	Degree=Pos	36	compound	_	_
36	products	product	NOUN	NNS	Number=Plur	28	conj	_	SpaceAfter=No
37	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
38	or	or	CCONJ	CC	ConjType=Cmp	36	cc	_	_
39	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	42	punct	_	SpaceAfter=No
40	iii	iii	NOUN	NN	Number=Sing	42	nmod	_	SpaceAfter=No
41	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	42	punct	_	_
42	equalizers	equalizer	NOUN	NNS	Number=Plur	36	conj	_	_
43	and	and	CCONJ	CC	ConjType=Cmp	42	cc	_	_
44	terminal	terminal	ADJ	JJ	Degree=Pos	45	amod	_	_
45	objects	object	NOUN	NNS	Number=Plur	42	conj	_	SpaceAfter=No
46	,	,	PUNCT	,	PunctType=Comm	45	punct	_	_
47	or	or	CCONJ	CC	ConjType=Cmp	45	cc	_	_
48	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	49	punct	_	SpaceAfter=No
49	iv	iv	PROPN	NNP	Number=Sing	28	appos	_	SpaceAfter=No
50	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	49	punct	_	_
51	just	just	ADV	RB	_	53	advmod	_	_
52	terminal	terminal	ADJ	JJ	Degree=Pos	53	amod	_	_
53	objects	object	NOUN	NNS	Number=Plur	28	appos	_	SpaceAfter=No
54	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 3
# text = We prove that, conversely, these four cases are (essentially) the only cases of monadicity of $ Cat_M $ over the category of graphs, provided that $ {cal M} $ is a set of finite graphs containing the empty graph.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	10	mark	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
5	conversely	conversely	ADV	RB	_	10	advmod	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
7	these	these	DET	DT	Number=Plur|PronType=Dem	9	det	_	_
8	four	four	NUM	CD	NumType=Card	9	nummod	_	_
9	cases	case	NOUN	NNS	Number=Plur	10	nsubj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
11	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	10	punct	_	SpaceAfter=No
12	essentially	essentially	ADV	RB	_	10	advmod	_	SpaceAfter=No
13	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	10	punct	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	only	only	ADJ	JJ	Degree=Pos	16	amod	_	_
16	cases	case	NOUN	NNS	Number=Plur	10	attr	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	monadicity	monadicity	NOUN	NN	Number=Sing	17	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	$ Cat_M $	$ cat_m $	SYM	$	_	19	pobj	_	_
21	over	over	ADP	IN	_	16	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	category	category	NOUN	NN	Number=Sing	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	graphs	graph	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
27	provided	provide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	prep	_	_
28	that	that	SCONJ	IN	_	30	mark	_	_
29	$ {cal M} $	$ {cal m} $	SYM	$	_	30	nsubj	_	_
30	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	pcomp	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
32	set	set	NOUN	NN	Number=Sing	30	attr	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	finite	finite	ADJ	JJ	Degree=Pos	35	amod	_	_
35	graphs	graph	NOUN	NNS	Number=Plur	33	pobj	_	_
36	containing	contain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	35	acl	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
38	empty	empty	ADJ	JJ	Degree=Pos	39	amod	_	_
39	graph	graph	NOUN	NN	Number=Sing	36	dobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 95
# sent_id = 1
# text = There is a 2 - category $ {cal J}{bf - Colim} $ of small categories equipped with a choice of colimit for each diagram whose domain $ J $ lies in a given small class $ {cal J} $ of small categories, functors strictly preserving such colimits, and natural transformations.
1	There	there	PRON	EX	_	2	expl	_	_
2	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
4	2	2	NUM	CD	NumType=Card	6	nummod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	category	category	NOUN	NN	Number=Sing	7	nmod	_	_
7	$ {cal J}{bf - Colim} $	$ {cal j}{bf - colim} $	NOUN	NN	Number=Sing	2	attr	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	small	small	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	_
11	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acl	_	_
12	with	with	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	choice	choice	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	colimit	colimit	NOUN	NN	Number=Sing	15	pobj	_	_
17	for	for	ADP	IN	_	16	prep	_	_
18	each	each	DET	DT	_	19	det	_	_
19	diagram	diagram	NOUN	NN	Number=Sing	17	pobj	_	_
20	whose	whose	DET	WP$	Poss=Yes	21	poss	_	_
21	domain	domain	NOUN	NN	Number=Sing	23	nsubj	_	_
22	$ J $	$ j $	SYM	$	_	21	prep	_	_
23	lies	lie	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	relcl	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
26	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	amod	_	_
27	small	small	ADJ	JJ	Degree=Pos	28	amod	_	_
28	class	class	NOUN	NN	Number=Sing	24	pobj	_	_
29	$ {cal J} $	$ {cal J} $	PROPN	NNP	Number=Sing	28	appos	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	small	small	ADJ	JJ	Degree=Pos	32	amod	_	_
32	categories	category	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
34	functors	functor	NOUN	NNS	Number=Plur	36	nsubj	_	_
35	strictly	strictly	ADV	RB	_	36	advmod	_	_
36	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
37	such	such	ADJ	JJ	Degree=Pos	38	amod	_	_
38	colimits	colimit	NOUN	NNS	Number=Plur	36	dobj	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	38	punct	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	38	cc	_	_
41	natural	natural	ADJ	JJ	Degree=Pos	42	amod	_	_
42	transformations	transformation	NOUN	NNS	Number=Plur	38	conj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The evident forgetful 2 - functor from $ {cal J}{bf - Colim} $ to the 2 - category $ {bf Cat} $ of small categories is known to be monadic.
1	The	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
2	evident	evident	ADJ	JJ	Degree=Pos	6	amod	_	_
3	forgetful	forgetful	ADJ	JJ	Degree=Pos	6	amod	_	_
4	2	2	NUM	CD	NumType=Card	6	nummod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	functor	functor	NOUN	NN	Number=Sing	19	nsubjpass	_	_
7	from	from	ADP	IN	_	6	prep	_	_
8	$ {cal J}{bf - Colim} $	$ {cal j}{bf - colim} $	SYM	$	_	7	pobj	_	_
9	to	to	ADP	IN	_	7	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	category	category	NOUN	NN	Number=Sing	14	nmod	_	_
14	$ {bf Cat} $	$ {bf cat} $	NOUN	NN	Number=Sing	9	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	small	small	ADJ	JJ	Degree=Pos	17	amod	_	_
17	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	auxpass	_	_
19	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
20	to	to	PART	TO	_	21	aux	_	_
21	be	be	AUX	VB	VerbForm=Inf	19	xcomp	_	_
22	monadic	monadic	ADJ	JJ	Degree=Pos	21	acomp	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 3
# text = We extend this result by considering not just conical colimits, but general weighted colimits; not just ordinary categories but enriched ones; and not just small classes of colimits but large ones; in this last case we are forced to move from the 2 - category $ {cal V}{bf - Cat} $ of small $ {cal V} $ - categories to $ {cal V} $ - categories with object - set in some larger universe.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	extend	extend	VERB	VBP	Tense=Pres|VerbForm=Fin	42	ccomp	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	result	result	NOUN	NN	Number=Sing	2	dobj	_	_
5	by	by	ADP	IN	_	2	prep	_	_
6	considering	consider	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	not	not	PART	RB	Polarity=Neg	10	neg	_	_
8	just	just	ADV	RB	_	7	advmod	_	_
9	conical	conical	ADJ	JJ	Degree=Pos	10	amod	_	_
10	colimits	colimit	NOUN	NNS	Number=Plur	6	dobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
12	but	but	CCONJ	CC	ConjType=Cmp	2	cc	_	_
13	general	general	ADJ	JJ	Degree=Pos	14	nsubj	_	_
14	weighted	weight	VERB	VBD	Tense=Past|VerbForm=Fin	2	conj	_	_
15	colimits	colimit	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
16	;	;	PUNCT	:	_	14	punct	_	_
17	not	not	PART	RB	Polarity=Neg	20	neg	_	_
18	just	just	ADV	RB	_	20	advmod	_	_
19	ordinary	ordinary	ADJ	JJ	Degree=Pos	20	amod	_	_
20	categories	category	NOUN	NNS	Number=Plur	14	dep	_	_
21	but	but	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	enriched	enriched	ADJ	JJ	Degree=Pos	23	amod	_	_
23	ones	one	NOUN	NNS	Number=Plur	20	conj	_	SpaceAfter=No
24	;	;	PUNCT	:	_	20	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
26	not	not	PART	RB	Polarity=Neg	29	neg	_	_
27	just	just	ADV	RB	_	29	advmod	_	_
28	small	small	ADJ	JJ	Degree=Pos	29	amod	_	_
29	classes	class	NOUN	NNS	Number=Plur	20	conj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	colimits	colimit	NOUN	NNS	Number=Plur	30	pobj	_	_
32	but	but	CCONJ	CC	ConjType=Cmp	29	cc	_	_
33	large	large	ADJ	JJ	Degree=Pos	34	amod	_	_
34	ones	one	NOUN	NNS	Number=Plur	29	conj	_	SpaceAfter=No
35	;	;	PUNCT	:	_	42	punct	_	_
36	in	in	ADP	IN	_	42	prep	_	_
37	this	this	DET	DT	Number=Sing|PronType=Dem	39	det	_	_
38	last	last	ADJ	JJ	Degree=Pos	39	amod	_	_
39	case	case	NOUN	NN	Number=Sing	36	pobj	_	_
40	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	42	nsubjpass	_	_
41	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	42	auxpass	_	_
42	forced	force	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
43	to	to	PART	TO	_	44	aux	_	_
44	move	move	VERB	VB	VerbForm=Inf	42	xcomp	_	_
45	from	from	ADP	IN	_	44	prep	_	_
46	the	the	DET	DT	Definite=Def|PronType=Art	50	det	_	_
47	2	2	NUM	CD	NumType=Card	49	nummod	_	_
48	-	-	PUNCT	HYPH	PunctType=Dash	49	punct	_	_
49	category	category	NOUN	NN	Number=Sing	50	nmod	_	_
50	$ {cal V}{bf - Cat} $	$ {cal v}{bf - cat} $	NOUN	NN	Number=Sing	45	pobj	_	_
51	of	of	ADP	IN	_	50	prep	_	_
52	small	small	ADJ	JJ	Degree=Pos	55	amod	_	_
53	$ {cal V} $	$ {cal v} $	SYM	$	_	55	compound	_	_
54	-	-	PUNCT	HYPH	PunctType=Dash	55	punct	_	_
55	categories	category	NOUN	NNS	Number=Plur	51	pobj	_	_
56	to	to	ADP	IN	_	44	prep	_	_
57	$ {cal V} $	$ {cal v} $	SYM	$	_	59	nmod	_	_
58	-	-	PUNCT	HYPH	PunctType=Dash	59	punct	_	_
59	categories	category	NOUN	NNS	Number=Plur	56	pobj	_	_
60	with	with	ADP	IN	_	44	prep	_	_
61	object	object	NOUN	NN	Number=Sing	63	npadvmod	_	_
62	-	-	PUNCT	HYPH	PunctType=Dash	63	punct	_	_
63	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	60	pobj	_	_
64	in	in	ADP	IN	_	63	prep	_	_
65	some	some	DET	DT	_	67	det	_	_
66	larger	large	ADJ	JJR	Degree=Cmp	67	amod	_	_
67	universe	universe	NOUN	NN	Number=Sing	64	pobj	_	SpaceAfter=No
68	.	.	PUNCT	.	PunctType=Peri	42	punct	_	SpaceAfter=No

# sent_id = 4
# text = In each case, the functors preserving the colimits in the usual ``up - to - isomorphism'' sense are recovered as the $ {em pseudomorphisms} $ between algebras for the 2 - monad in question.
1	In	in	ADP	IN	_	23	prep	_	_
2	each	each	DET	DT	_	3	det	_	_
3	case	case	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	functors	functor	NOUN	NNS	Number=Plur	23	nsubjpass	_	_
7	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	acl	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	colimits	colimit	NOUN	NNS	Number=Plur	7	dobj	_	_
10	in	in	ADP	IN	_	7	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
12	usual	usual	ADJ	JJ	Degree=Pos	21	amod	_	_
13	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	21	punct	_	SpaceAfter=No
14	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	21	punct	_	SpaceAfter=No
15	up	up	ADV	RB	_	21	nmod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
17	to	to	ADP	IN	_	15	prep	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
19	isomorphism	isomorphism	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
20	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	21	punct	_	_
21	sense	sense	NOUN	NN	Number=Sing	10	pobj	_	_
22	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	23	auxpass	_	_
23	recovered	recover	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
24	as	as	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	$ {em pseudomorphisms} $	$ {em pseudomorphisms} $	SYM	$	_	24	pobj	_	_
27	between	between	ADP	IN	_	26	prep	_	_
28	algebras	algebra	NOUN	NNS	Number=Plur	27	pobj	_	_
29	for	for	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
31	2	2	NUM	CD	NumType=Card	33	nummod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	monad	monad	NOUN	NNS	Number=Plur	29	pobj	_	_
34	in	in	ADP	IN	_	33	prep	_	_
35	question	question	NOUN	NN	Number=Sing	34	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# doc_id = 96
# sent_id = 1
# text = A balanced coalgebroid is a $ {cal V}^{op} $ - category with extra structure ensuring that its category of representations is a balanced monoidal category.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	balanced	balanced	ADJ	JJ	Degree=Pos	3	amod	_	_
3	coalgebroid	coalgebroid	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
6	$ {cal V}^{op} $	$ {cal v}^{op} $	ADV	RB	_	8	compound	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	category	category	NOUN	NN	Number=Sing	4	attr	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	extra	extra	ADJ	JJ	Degree=Pos	11	amod	_	_
11	structure	structure	NOUN	NN	Number=Sing	9	pobj	_	_
12	ensuring	ensure	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	acl	_	_
13	that	that	SCONJ	IN	_	18	mark	_	_
14	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	15	poss	_	_
15	category	category	NOUN	NN	Number=Sing	18	nsubj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	representations	representation	NOUN	NNS	Number=Plur	16	pobj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	ccomp	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
20	balanced	balanced	ADJ	JJ	Degree=Pos	22	amod	_	_
21	monoidal	monoidal	ADJ	JJ	Degree=Pos	22	amod	_	_
22	category	category	NOUN	NN	Number=Sing	18	attr	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show, in a sense to be made precise, that a balanced structure on a coalgebroid may be reconstructed from the corresponding structure on its category of representations.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
4	in	in	ADP	IN	_	2	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	sense	sense	NOUN	NN	Number=Sing	4	pobj	_	_
7	to	to	PART	TO	_	9	aux	_	_
8	be	be	AUX	VB	VerbForm=Inf	9	auxpass	_	_
9	made	make	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
10	precise	precise	ADJ	JJ	Degree=Pos	9	oprd	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
12	that	that	SCONJ	IN	_	21	mark	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	balanced	balanced	ADJ	JJ	Degree=Pos	15	amod	_	_
15	structure	structure	NOUN	NN	Number=Sing	21	nsubjpass	_	_
16	on	on	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	coalgebroid	coalgebroid	NOUN	NN	Number=Sing	16	pobj	_	_
19	may	may	AUX	MD	VerbForm=Fin	21	aux	_	_
20	be	be	AUX	VB	VerbForm=Inf	21	auxpass	_	_
21	reconstructed	reconstruct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
22	from	from	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	corresponding	corresponding	ADJ	JJ	Degree=Pos	25	amod	_	_
25	structure	structure	NOUN	NN	Number=Sing	22	pobj	_	_
26	on	on	ADP	IN	_	25	prep	_	_
27	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	28	poss	_	_
28	category	category	NOUN	NN	Number=Sing	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	representations	representation	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = This includes the reconstruction of dual quasi - bialgebras, quasi - triangular dual quasi - bialgebras, and balanced quasi - triangular dual quasi - bialgebras; the latter of which is a quantum group when equipped with a compatible antipode.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	includes	include	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	33	ccomp	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	reconstruction	reconstruction	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	dual	dual	ADJ	JJ	Degree=Pos	7	amod	_	_
7	quasi	quasi	NOUN	NNS	Number=Plur	5	pobj	_	_
8	-	-	NOUN	NNS	Number=Plur	5	pobj	_	_
9	bialgebras	bialgebra	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	quasi	quasi	ADJ	JJ	Degree=Pos	15	amod	_	_
12	-	-	ADJ	JJ	Degree=Pos	15	amod	_	_
13	triangular	triangular	ADJ	JJ	Degree=Pos	15	amod	_	_
14	dual	dual	ADJ	JJ	Degree=Pos	15	amod	_	_
15	quasi	quasi	NOUN	NNS	Number=Plur	9	conj	_	_
16	-	-	NOUN	NNS	Number=Plur	9	conj	_	_
17	bialgebras	bialgebra	NOUN	NNS	Number=Plur	9	conj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
20	balanced	balanced	ADJ	JJ	Degree=Pos	25	amod	_	_
21	quasi	quasi	ADJ	JJ	Degree=Pos	25	compound	_	_
22	-	-	ADJ	JJ	Degree=Pos	25	amod	_	_
23	triangular	triangular	ADJ	JJ	Degree=Pos	25	amod	_	_
24	dual	dual	ADJ	JJ	Degree=Pos	25	amod	_	_
25	quasi	quasi	NOUN	NNS	Number=Plur	17	conj	_	_
26	-	-	NOUN	NNS	Number=Plur	9	conj	_	_
27	bialgebras	bialgebra	NOUN	NNS	Number=Plur	9	conj	_	SpaceAfter=No
28	;	;	PUNCT	:	_	33	punct	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	latter	latter	ADJ	JJ	Degree=Pos	33	nsubj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	which	which	PRON	WDT	_	31	pobj	_	_
33	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
35	quantum	quantum	NOUN	NN	Number=Sing	36	compound	_	_
36	group	group	NOUN	NN	Number=Sing	33	attr	_	_
37	when	when	SCONJ	WRB	_	38	advmod	_	_
38	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	advcl	_	_
39	with	with	ADP	IN	_	38	prep	_	_
40	a	a	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
41	compatible	compatible	ADJ	JJ	Degree=Pos	42	amod	_	_
42	antipode	antipode	NOUN	NN	Number=Sing	39	pobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	33	punct	_	SpaceAfter=No

# sent_id = 4
# text = As an application we construct a balanced coalgebroid whose category of representations is equivalent to the symmetric monoidal category of chain complexes.
1	As	as	ADP	IN	_	5	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	balanced	balanced	ADJ	JJ	Degree=Pos	8	amod	_	_
8	coalgebroid	coalgebroid	NOUN	NN	Number=Sing	5	dobj	_	_
9	whose	whose	DET	WP$	Poss=Yes	10	poss	_	_
10	category	category	NOUN	NN	Number=Sing	13	nsubj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	representations	representation	NOUN	NNS	Number=Plur	11	pobj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	relcl	_	_
14	equivalent	equivalent	ADJ	JJ	Degree=Pos	13	acomp	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
17	symmetric	symmetric	ADJ	JJ	Degree=Pos	19	amod	_	_
18	monoidal	monoidal	ADJ	JJ	Degree=Pos	19	amod	_	_
19	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	chain	chain	NOUN	NN	Number=Sing	22	compound	_	_
22	complexes	complex	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = The appendix provides the definitions of a braided monoidal bicategory and sylleptic monoidal bicategory.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	appendix	appendix	NOUN	NN	Number=Sing	3	nsubj	_	_
3	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	definitions	definition	NOUN	NNS	Number=Plur	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	braided	braid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
9	monoidal	monoidal	ADJ	JJ	Degree=Pos	10	amod	_	_
10	bicategory	bicategory	NOUN	NN	Number=Sing	6	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	sylleptic	sylleptic	ADJ	JJ	Degree=Pos	14	amod	_	_
13	monoidal	monoidal	ADJ	JJ	Degree=Pos	14	amod	_	_
14	bicategory	bicategory	NOUN	NN	Number=Sing	10	conj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 97
# sent_id = 1
# text = This paper is a first step in the study of symmetric cat - groups as the 2 - dimensional analogue of abelian groups.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	first	first	ADJ	JJ	Degree=Pos	6	amod	_	_
6	step	step	NOUN	NN	Number=Sing	3	attr	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	study	study	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	symmetric	symmetric	ADJ	JJ	Degree=Pos	14	amod	_	_
12	cat	cat	NOUN	NN	Number=Sing	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	groups	group	NOUN	NNS	Number=Plur	10	pobj	_	_
15	as	as	ADP	IN	_	6	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
17	2	2	NUM	CD	NumType=Card	19	advmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	dimensional	dimensional	ADJ	JJ	Degree=Pos	20	amod	_	_
20	analogue	analogue	NOUN	NN	Number=Sing	15	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	abelian	abelian	ADJ	JJ	Degree=Pos	23	compound	_	_
23	groups	group	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that a morphism of symmetric cat - groups can be factorized as an essentially surjective functor followed by a full and faithful one, as well as a full and essentially surjective functor followed by a faithful one.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	13	mark	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	morphism	morphism	NOUN	NN	Number=Sing	13	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	symmetric	symmetric	ADJ	JJ	Degree=Pos	10	amod	_	_
8	cat	cat	NOUN	NN	Number=Sing	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	groups	group	NOUN	NNS	Number=Plur	6	pobj	_	_
11	can	can	AUX	MD	VerbForm=Fin	13	aux	_	_
12	be	be	AUX	VB	VerbForm=Inf	13	auxpass	_	_
13	factorized	factorize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
14	as	as	ADP	IN	_	13	prep	_	_
15	an	an	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
16	essentially	essentially	ADV	RB	_	17	advmod	_	_
17	surjective	surjective	ADJ	JJ	Degree=Pos	18	amod	_	_
18	functor	functor	NOUN	NN	Number=Sing	14	pobj	_	_
19	followed	follow	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	acl	_	_
20	by	by	ADP	IN	_	19	agent	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
22	full	full	ADJ	JJ	Degree=Pos	25	amod	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	faithful	faithful	ADJ	JJ	Degree=Pos	22	conj	_	_
25	one	one	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
27	as	as	ADV	RB	_	29	advmod	_	_
28	well	well	ADV	RB	Degree=Pos	29	advmod	_	_
29	as	as	ADP	IN	_	25	cc	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
31	full	full	ADJ	JJ	Degree=Pos	35	amod	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	essentially	essentially	ADV	RB	_	34	advmod	_	_
34	surjective	surjective	ADJ	JJ	Degree=Pos	31	conj	_	_
35	functor	functor	NOUN	NN	Number=Sing	13	dobj	_	_
36	followed	follow	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	35	acl	_	_
37	by	by	ADP	IN	_	36	agent	_	_
38	a	a	DET	DT	Definite=Ind|PronType=Art	40	det	_	_
39	faithful	faithful	ADJ	JJ	Degree=Pos	40	amod	_	_
40	one	one	NUM	CD	NumType=Card	37	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Both these factorizations give rise to a factorization system, in a suitable 2 - categorical sense, in the 2 - category of symmetric cat - groups.
1	Both	both	PRON	DT	_	3	predet	_	_
2	these	these	DET	DT	Number=Plur|PronType=Dem	3	det	_	_
3	factorizations	factorization	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	rise	rise	NOUN	NN	Number=Sing	4	dobj	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	factorization	factorization	NOUN	NN	Number=Sing	9	compound	_	_
9	system	system	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
11	in	in	ADP	IN	_	4	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
13	suitable	suitable	ADJ	JJ	Degree=Pos	17	amod	_	_
14	2	2	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	categorical	categorical	ADJ	JJ	Degree=Pos	17	amod	_	_
17	sense	sense	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
19	in	in	ADP	IN	_	4	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
21	2	2	NUM	CD	NumType=Card	23	nummod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	category	category	NOUN	NN	Number=Sing	19	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	symmetric	symmetric	ADJ	JJ	Degree=Pos	28	amod	_	_
26	cat	cat	NOUN	NN	Number=Sing	28	compound	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	groups	group	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = An application to exact sequences is given.
1	An	an	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	application	application	NOUN	NN	Number=Sing	7	nsubjpass	_	_
3	to	to	PART	TO	_	4	aux	_	_
4	exact	exact	VERB	VB	VerbForm=Inf	2	acl	_	_
5	sequences	sequence	NOUN	NNS	Number=Plur	4	dobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 98
# sent_id = 1
# text = The term ``saturated, '' referring to a class of morphisms in a category, is used in the literature for two nonequivalent concepts.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	term	term	NOUN	NN	Number=Sing	5	nsubj	_	_
3	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	5	punct	_	SpaceAfter=No
4	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	5	punct	_	SpaceAfter=No
5	saturated	saturate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	csubjpass	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	5	punct	_	_
8	referring	refer	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	advcl	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	class	class	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	morphisms	morphism	NOUN	NNS	Number=Plur	12	pobj	_	_
14	in	in	ADP	IN	_	8	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	category	category	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	auxpass	_	_
19	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	literature	literature	NOUN	NN	Number=Sing	20	pobj	_	_
23	for	for	ADP	IN	_	19	prep	_	_
24	two	two	NUM	CD	NumType=Card	26	nummod	_	_
25	nonequivalent	nonequivalent	ADJ	JJ	Degree=Pos	26	amod	_	_
26	concepts	concept	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 2
# text = We make precise the relationship between these two concepts and show that the class of equivalences associated with any monad is saturated in both senses.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	make	make	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	precise	precise	ADJ	JJ	Degree=Pos	2	ccomp	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	relationship	relationship	NOUN	NN	Number=Sing	2	dobj	_	_
6	between	between	ADP	IN	_	5	prep	_	_
7	these	these	DET	DT	Number=Plur|PronType=Dem	9	det	_	_
8	two	two	NUM	CD	NumType=Card	9	nummod	_	_
9	concepts	concept	NOUN	NNS	Number=Plur	6	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
11	show	show	VERB	VB	VerbForm=Inf	2	conj	_	_
12	that	that	SCONJ	IN	_	22	mark	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	class	class	NOUN	NN	Number=Sing	22	nsubjpass	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	equivalences	equivalence	NOUN	NNS	Number=Plur	15	pobj	_	_
17	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	acl	_	_
18	with	with	ADP	IN	_	17	prep	_	_
19	any	any	DET	DT	_	20	det	_	_
20	monad	monad	NOUN	NNS	Number=Plur	18	pobj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	auxpass	_	_
22	saturated	saturate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	ccomp	_	_
23	in	in	ADP	IN	_	22	prep	_	_
24	both	both	DET	DT	_	25	det	_	_
25	senses	sense	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 99
# sent_id = 1
# text = The purpose of this paper is to give a new proof of the Joyal - Tierney theorem (unpublished), which asserts that a morphism $ f:Rrightarrow S $ of commutative rings is an effective descent morphism for modules if and only if $ f $ is pure as a morphism of $ R $ - modules.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	purpose	purpose	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	paper	paper	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	give	give	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	new	new	ADJ	JJ	Degree=Pos	11	amod	_	_
11	proof	proof	NOUN	NN	Number=Sing	8	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
14	Joyal	Joyal	PROPN	NNP	Number=Sing	16	compound	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	Tierney	Tierney	PROPN	NNP	Number=Sing	17	compound	_	_
17	theorem	theorem	NOUN	NN	Number=Sing	12	pobj	_	_
18	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	19	punct	_	SpaceAfter=No
19	unpublished	unpublished	ADJ	JJ	Degree=Pos	17	amod	_	SpaceAfter=No
20	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	17	punct	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
22	which	which	PRON	WDT	_	23	nsubj	_	_
23	asserts	assert	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
24	that	that	SCONJ	IN	_	31	mark	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
26	morphism	morphism	NOUN	NN	Number=Sing	31	nsubj	_	_
27	$ f:Rrightarrow S $	$ f:rrightarrow s $	SYM	$	_	26	appos	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	commutative	commutative	ADJ	JJ	Degree=Pos	30	amod	_	_
30	rings	ring	NOUN	NNS	Number=Plur	28	pobj	_	_
31	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	ccomp	_	_
32	an	an	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
33	effective	effective	ADJ	JJ	Degree=Pos	35	amod	_	_
34	descent	descent	NOUN	NN	Number=Sing	35	compound	_	_
35	morphism	morphism	NOUN	NN	Number=Sing	31	attr	_	_
36	for	for	ADP	IN	_	35	prep	_	_
37	modules	module	NOUN	NNS	Number=Plur	36	pobj	_	_
38	if	if	SCONJ	IN	_	43	mark	_	_
39	and	and	CCONJ	CC	ConjType=Cmp	43	cc	_	_
40	only	only	ADV	RB	_	41	advmod	_	_
41	if	if	SCONJ	IN	_	43	mark	_	_
42	$ f $	$ f $	SYM	$	_	43	nsubj	_	_
43	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	31	advcl	_	_
44	pure	pure	ADJ	JJ	Degree=Pos	43	acomp	_	_
45	as	as	ADP	IN	_	44	prep	_	_
46	a	a	DET	DT	Definite=Ind|PronType=Art	47	det	_	_
47	morphism	morphism	NOUN	NN	Number=Sing	45	pobj	_	_
48	of	of	ADP	IN	_	47	prep	_	_
49	$ R $	$ r $	SYM	$	_	51	compound	_	_
50	-	-	PUNCT	HYPH	PunctType=Dash	51	punct	_	_
51	modules	module	NOUN	NNS	Number=Plur	48	pobj	_	SpaceAfter=No
52	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 100
# sent_id = 1
# text = It is well - known that, given a Dedekind category $ {cal R} $ the category of (typed) matrices with coefficients from $ {cal R} $ is a Dedekind category with arbitrary relational sums.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	well	well	ADV	RB	Degree=Pos	5	advmod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acomp	_	_
6	that	that	SCONJ	IN	_	24	mark	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
8	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	nmod	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	Dedekind	Dedekind	PROPN	NNP	Number=Sing	11	compound	_	_
11	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
12	$ {cal R} $	$ {cal r} $	SYM	$	_	24	nsubj	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	category	category	NOUN	NN	Number=Sing	12	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	15	punct	_	SpaceAfter=No
17	typed	type	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	SpaceAfter=No
18	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	17	punct	_	_
19	matrices	matrix	NOUN	NNS	Number=Plur	15	pobj	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	coefficients	coefficient	NOUN	NNS	Number=Plur	20	pobj	_	_
22	from	from	ADP	IN	_	21	prep	_	_
23	$ {cal R} $	$ {cal r} $	SYM	$	_	22	pobj	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
26	Dedekind	Dedekind	PROPN	NNP	Number=Sing	27	compound	_	_
27	category	category	NOUN	NN	Number=Sing	24	attr	_	_
28	with	with	ADP	IN	_	27	prep	_	_
29	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	31	amod	_	_
30	relational	relational	ADJ	JJ	Degree=Pos	31	amod	_	_
31	sums	sum	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper we show that under slightly stronger assumptions the converse is also true.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	13	mark	_	_
7	under	under	ADP	IN	_	13	prep	_	_
8	slightly	slightly	ADV	RB	_	9	advmod	_	_
9	stronger	strong	ADJ	JJR	Degree=Cmp	10	amod	_	_
10	assumptions	assumption	NOUN	NNS	Number=Plur	7	pobj	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	converse	converse	NOUN	NN	Number=Sing	13	nsubj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
14	also	also	ADV	RB	_	13	advmod	_	_
15	true	true	ADJ	JJ	Degree=Pos	13	acomp	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = Every atomic Dedekind category $ {cal R} $ with relational sums and subobjects is equivalent to a category of matrices over a suitable basis.
1	Every	every	DET	DT	_	4	det	_	_
2	atomic	atomic	ADJ	JJ	Degree=Pos	3	amod	_	_
3	Dedekind	dedekind	NOUN	NN	Number=Sing	4	compound	_	_
4	category	category	NOUN	NN	Number=Sing	11	nsubj	_	_
5	$ {cal R} $	$ {cal r} $	SYM	$	_	4	appos	_	_
6	with	with	ADP	IN	_	4	prep	_	_
7	relational	relational	ADJ	JJ	Degree=Pos	8	amod	_	_
8	sums	sum	NOUN	NNS	Number=Plur	6	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	subobjects	subobject	NOUN	NNS	Number=Plur	8	conj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	equivalent	equivalent	ADJ	JJ	Degree=Pos	11	acomp	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	matrices	matrix	NOUN	NNS	Number=Plur	16	pobj	_	_
18	over	over	ADP	IN	_	15	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	suitable	suitable	ADJ	JJ	Degree=Pos	21	amod	_	_
21	basis	basis	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 4
# text = This basis is the full proper subcategory induced by the integral objects of $ {cal R} $ .
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	basis	basis	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	full	full	ADJ	JJ	Degree=Pos	7	amod	_	_
6	proper	proper	ADJ	JJ	Degree=Pos	7	amod	_	_
7	subcategory	subcategory	NOUN	NN	Number=Sing	3	attr	_	_
8	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	acl	_	_
9	by	by	ADP	IN	_	8	agent	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	integral	integral	ADJ	JJ	Degree=Pos	12	amod	_	_
12	objects	object	NOUN	NNS	Number=Plur	9	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	$ {cal R} $	$ {cal r} $	SYM	$	_	13	pobj	_	_
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = Furthermore, we use our concept of a basis to extend a known result from the theory of heterogeneous relation algebras.
1	Furthermore	furthermore	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	6	poss	_	_
6	concept	concept	NOUN	NN	Number=Sing	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	basis	basis	NOUN	NN	Number=Sing	7	pobj	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	extend	extend	VERB	VB	VerbForm=Inf	9	acl	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
14	result	result	NOUN	NN	Number=Sing	11	dobj	_	_
15	from	from	ADP	IN	_	11	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	theory	theory	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	heterogeneous	heterogeneous	ADJ	JJ	Degree=Pos	21	amod	_	_
20	relation	relation	NOUN	NN	Number=Sing	21	compound	_	_
21	algebras	algebra	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 101
# sent_id = 1
# text = We show, for a monoidal closed category $ V = (V_0, otimes, I) $ , that the category $ V $ - Cat of small $ V $ - categories is locally $ lambda $ - presentable if $ V_0 $ is so, and that it is locally $ lambda $ - bounded if the closed category $ V $ is so, meaning that $ V_0 $ is locally $ lambda $ - bounded and that a side condition involving the monoidal structure is satisfied.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
4	for	for	ADP	IN	_	2	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	monoidal	monoidal	ADJ	JJ	Degree=Pos	7	nsubj	_	_
7	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
9	$ V = (V_0, otimes, I) $	$ v = (v_0, otimes, i) $	SYM	$	_	2	dep	_	_
10	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
11	that	that	SCONJ	IN	_	22	mark	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
13	category	category	NOUN	NN	Number=Sing	16	nmod	_	_
14	$ V $	$ v $	SYM	$	_	16	nmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	Cat	cat	NOUN	NN	Number=Sing	22	nsubj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	small	small	ADJ	JJ	Degree=Pos	21	amod	_	_
19	$ V $	$ v $	SYM	$	_	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
23	locally	locally	ADV	RB	_	22	advmod	_	_
24	$ lambda $	$ lambda $	SYM	$	_	26	advmod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	presentable	presentable	ADJ	JJ	Degree=Pos	22	acomp	_	_
27	if	if	SCONJ	IN	_	29	mark	_	_
28	$ V_0 $	$ v_0 $	SYM	$	_	29	nsubj	_	_
29	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	advcl	_	_
30	so	so	ADV	RB	_	29	acomp	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
33	that	that	SCONJ	IN	_	35	mark	_	_
34	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	35	nsubj	_	_
35	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	conj	_	_
36	locally	locally	ADV	RB	_	35	advmod	_	_
37	$ lambda $	$ lambda $	SYM	$	_	39	advmod	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	bounded	bound	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	35	acomp	_	_
40	if	if	SCONJ	IN	_	45	mark	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
42	closed	closed	ADJ	JJ	Degree=Pos	43	amod	_	_
43	category	category	NOUN	NN	Number=Sing	45	nsubj	_	_
44	$ V $	$ v $	SYM	$	_	43	appos	_	_
45	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	35	advcl	_	_
46	so	so	ADV	RB	_	45	acomp	_	SpaceAfter=No
47	,	,	PUNCT	,	PunctType=Comm	45	punct	_	_
48	meaning	mean	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	45	advcl	_	_
49	that	that	SCONJ	IN	_	51	mark	_	_
50	$ V_0 $	$ v_0 $	SYM	$	_	51	nsubj	_	_
51	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	48	ccomp	_	_
52	locally	locally	ADV	RB	_	55	advmod	_	_
53	$ lambda $	$ lambda $	SYM	$	_	55	advmod	_	_
54	-	-	PUNCT	HYPH	PunctType=Dash	55	punct	_	_
55	bounded	bound	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	51	acomp	_	_
56	and	and	CCONJ	CC	ConjType=Cmp	51	cc	_	_
57	that	that	SCONJ	IN	_	65	mark	_	_
58	a	a	DET	DT	Definite=Ind|PronType=Art	60	det	_	_
59	side	side	NOUN	NN	Number=Sing	60	compound	_	_
60	condition	condition	NOUN	NN	Number=Sing	65	nsubj	_	_
61	involving	involve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	60	acl	_	_
62	the	the	DET	DT	Definite=Def|PronType=Art	64	det	_	_
63	monoidal	monoidal	ADJ	JJ	Degree=Pos	64	amod	_	_
64	structure	structure	NOUN	NN	Number=Sing	61	dobj	_	_
65	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	51	conj	_	_
66	satisfied	satisfied	ADJ	JJ	Degree=Pos	65	acomp	_	SpaceAfter=No
67	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 102
# sent_id = 1
# text = We present some new findings concerning branched covers in topos theory.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	some	some	DET	DT	_	5	det	_	_
4	new	new	ADJ	JJ	Degree=Pos	5	amod	_	_
5	findings	finding	NOUN	NNS	Number=Plur	2	dobj	_	_
6	concerning	concern	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	acl	_	_
7	branched	branched	NOUN	NN	Number=Sing	8	compound	_	_
8	covers	cover	NOUN	NNS	Number=Plur	6	dobj	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	topos	topos	NOUN	NN	Number=Sing	11	compound	_	_
11	theory	theory	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Our discussion involves a particular subtopos of a given topos that can be described as the smallest subtopos closed under small coproducts in the including topos.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	discussion	discussion	NOUN	NN	Number=Sing	3	nsubj	_	_
3	involves	involve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	particular	particular	ADJ	JJ	Degree=Pos	6	amod	_	_
6	subtopos	subtopos	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	topos	topo	NOUN	NNS	Number=Plur	7	pobj	_	_
11	that	that	PRON	WDT	PronType=Rel	14	nsubjpass	_	_
12	can	can	AUX	MD	VerbForm=Fin	14	aux	_	_
13	be	be	AUX	VB	VerbForm=Inf	14	auxpass	_	_
14	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	relcl	_	_
15	as	as	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	smallest	small	ADJ	JJS	Degree=Sup	18	amod	_	_
18	subtopos	subtopo	NOUN	NNS	Number=Plur	15	pobj	_	_
19	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	18	acl	_	_
20	under	under	ADP	IN	_	19	prep	_	_
21	small	small	ADJ	JJ	Degree=Pos	22	amod	_	_
22	coproducts	coproduct	NOUN	NNS	Number=Plur	20	pobj	_	_
23	in	in	ADP	IN	_	22	prep	_	_
24	the	the	PRON	DT	Definite=Def|PronType=Art	23	pobj	_	_
25	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	prep	_	_
26	topos	topos	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Our main result is a description of the covers of this subtopos as a category of fractions of branched covers, in the sense of Fox, of the including topos.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	3	poss	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	result	result	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	description	description	NOUN	NN	Number=Sing	4	attr	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	covers	cover	NOUN	NNS	Number=Plur	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	this	this	DET	DT	Number=Sing|PronType=Dem	12	det	_	_
12	subtopos	subtopos	NOUN	NN	Number=Sing	10	pobj	_	_
13	as	as	ADP	IN	_	6	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	fractions	fraction	NOUN	NNS	Number=Plur	16	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	branched	branched	NOUN	NN	Number=Sing	20	compound	_	_
20	covers	cover	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
22	in	in	ADP	IN	_	6	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	sense	sense	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	Fox	Fox	PROPN	NNP	Number=Sing	25	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
28	of	of	ADP	IN	_	26	prep	_	_
29	the	the	PRON	DT	Definite=Def|PronType=Art	28	pobj	_	_
30	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	29	prep	_	_
31	topos	topos	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = We also have some new results concerning the general theory of KZ - doctrines, such as the closure under composition of discrete fibrations for a KZ - doctrine, in the sense of Bunge and Funk.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	some	some	DET	DT	_	6	det	_	_
5	new	new	ADJ	JJ	Degree=Pos	6	amod	_	_
6	results	result	NOUN	NNS	Number=Plur	3	dobj	_	_
7	concerning	concern	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	acl	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	general	general	ADJ	JJ	Degree=Pos	10	amod	_	_
10	theory	theory	NOUN	NN	Number=Sing	7	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	KZ	KZ	PROPN	NNP	Number=Sing	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	doctrines	doctrine	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	such	such	ADJ	JJ	Degree=Pos	17	amod	_	_
17	as	as	ADP	IN	_	14	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	closure	closure	NOUN	NN	Number=Sing	17	pobj	_	_
20	under	under	ADP	IN	_	19	prep	_	_
21	composition	composition	NOUN	NN	Number=Sing	20	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	discrete	discrete	ADJ	JJ	Degree=Pos	24	amod	_	_
24	fibrations	fibration	NOUN	NNS	Number=Plur	22	pobj	_	_
25	for	for	ADP	IN	_	24	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
27	KZ	KZ	PROPN	NNP	Number=Sing	29	compound	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	doctrine	doctrine	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
31	in	in	ADP	IN	_	3	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
33	sense	sense	NOUN	NN	Number=Sing	31	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	Bunge	Bunge	PROPN	NNP	Number=Sing	34	pobj	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
37	Funk	Funk	PROPN	NNP	Number=Sing	35	conj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 103
# sent_id = 1
# text = A category with finite products and finite coproducts is said to be distributive if the canonical map $ A times B + A times C to A times (B + C) $ is invertible for all objects $ A $ , $ B $ , and $ C $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	10	nsubjpass	_	_
3	with	with	ADP	IN	_	2	prep	_	_
4	finite	finite	ADJ	JJ	Degree=Pos	5	amod	_	_
5	products	product	NOUN	NNS	Number=Plur	3	pobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	finite	finite	ADJ	JJ	Degree=Pos	8	amod	_	_
8	coproducts	coproduct	NOUN	NNS	Number=Plur	5	conj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	said	say	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	be	be	AUX	VB	VerbForm=Inf	10	xcomp	_	_
13	distributive	distributive	ADJ	JJ	Degree=Pos	12	acomp	_	_
14	if	if	SCONJ	IN	_	19	mark	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	canonical	canonical	NOUN	NN	Number=Sing	17	amod	_	_
17	map	map	NOUN	NN	Number=Sing	19	nsubj	_	_
18	$ A times B + A times C to A times (B + C) $	$ a times b + a times c to a times (b + c) $	SYM	$	_	19	nsubj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	advcl	_	_
20	invertible	invertible	ADJ	JJ	Degree=Pos	19	acomp	_	_
21	for	for	ADP	IN	_	20	prep	_	_
22	all	all	DET	DT	_	23	det	_	_
23	objects	object	NOUN	NNS	Number=Plur	21	pobj	_	_
24	$ A $	$ a $	SYM	$	_	23	nummod	_	_
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	$ B $	$ b $	SYM	$	_	24	conj	_	_
27	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
29	$ C $	$ c $	SYM	$	_	19	dep	_	_
30	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = Given a distributive category $ cal D $ , we describe a universal functor $ cal D to cal D_{ex} $ preserving finite products and finite coproducts, for which $ cal D_{ex} $ is extensive; that is, for all objects $ A $ and $ B $ the functor $ cal D_{ex}/A times cal D_{ex}/B to cal D_{ex}/(A + B) $ is an equivalence of categories.
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	distributive	distributive	ADJ	JJ	Degree=Pos	4	amod	_	_
4	category	category	NOUN	NN	Number=Sing	1	pobj	_	_
5	$ cal D $	$ cal d $	SYM	$	_	4	nummod	_	_
6	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
7	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	8	nsubj	_	_
8	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	38	ccomp	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	universal	universal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	functor	functor	NOUN	NN	Number=Sing	8	dobj	_	_
12	$ cal D to cal D_{ex} $	$ cal d to cal d_{ex} $	SYM	$	_	13	advmod	_	_
13	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	advcl	_	_
14	finite	finite	ADJ	JJ	Degree=Pos	15	compound	_	_
15	products	product	NOUN	NNS	Number=Plur	13	dobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	finite	finite	ADJ	JJ	Degree=Pos	18	amod	_	_
18	coproducts	coproduct	NOUN	NNS	Number=Plur	15	conj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
20	for	for	ADP	IN	_	22	prep	_	_
21	which	which	PRON	WDT	_	20	pobj	_	_
22	$ cal D_{ex} $	$ cal d_{ex} $	SYM	$	_	23	nsubj	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	conj	_	_
24	extensive	extensive	ADJ	JJ	Degree=Pos	23	acomp	_	SpaceAfter=No
25	;	;	PUNCT	:	_	38	punct	_	_
26	that	that	PRON	DT	Number=Sing|PronType=Dem	27	nsubj	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	38	advmod	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
29	for	for	ADP	IN	_	27	prep	_	_
30	all	all	DET	DT	_	31	det	_	_
31	objects	object	NOUN	NNS	Number=Plur	29	pobj	_	_
32	$ A $	$ a $	SYM	$	_	31	nmod	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
34	$ B $	$ b $	SYM	$	_	32	conj	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	functor	functor	NOUN	NN	Number=Sing	38	nsubj	_	_
37	$ cal D_{ex}/A times cal D_{ex}/B to cal D_{ex}/(A + B) $	$ cal d_{ex}/a times cal d_{ex}/b to cal d_{ex}/(a + b) $	SYM	$	_	38	nsubj	_	_
38	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
39	an	an	DET	DT	Definite=Ind|PronType=Art	40	det	_	_
40	equivalence	equivalence	NOUN	NN	Number=Sing	38	attr	_	_
41	of	of	ADP	IN	_	40	prep	_	_
42	categories	category	NOUN	NNS	Number=Plur	41	pobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	38	punct	_	SpaceAfter=No

# sent_id = 3
# text = As an application, we show that a distributive category $ cal D $ has a full distributive embedding into the product of an extensive category with products and a distributive preorder.
1	As	as	ADP	IN	_	6	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	12	mark	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	distributive	distributive	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	12	nsubj	_	_
11	$ cal D $	$ cal d $	SYM	$	_	10	appos	_	_
12	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
14	full	full	ADJ	JJ	Degree=Pos	15	amod	_	_
15	distributive	distributive	ADJ	JJ	Degree=Pos	16	amod	_	_
16	embedding	embed	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	dobj	_	_
17	into	into	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	product	product	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	extensive	extensive	ADJ	JJ	Degree=Pos	23	amod	_	_
23	category	category	NOUN	NN	Number=Sing	20	pobj	_	_
24	with	with	ADP	IN	_	23	prep	_	_
25	products	product	NOUN	NNS	Number=Plur	24	pobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	distributive	distributive	ADJ	JJ	Degree=Pos	29	amod	_	_
29	preorder	preorder	NOUN	NN	Number=Sing	25	conj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 104
# sent_id = 1
# text = In analogy with the relation between closure operators in presheaf toposes and Grothendieck topologies, we identify the structure in a category with finite limits that corresponds to universal closure operators in its regular and exact completions.
1	In	in	ADP	IN	_	17	prep	_	_
2	analogy	analogy	NOUN	NN	Number=Sing	1	pobj	_	_
3	with	with	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	relation	relation	NOUN	NN	Number=Sing	3	pobj	_	_
6	between	between	ADP	IN	_	5	prep	_	_
7	closure	closure	NOUN	NN	Number=Sing	8	compound	_	_
8	operators	operator	NOUN	NNS	Number=Plur	6	pobj	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	presheaf	presheaf	ADJ	JJ	Degree=Pos	11	compound	_	_
11	toposes	topos	NOUN	NNS	Number=Plur	9	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	14	compound	_	_
14	topologies	topology	NOUN	NNS	Number=Plur	11	conj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
16	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	17	nsubj	_	_
17	identify	identify	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	structure	structure	NOUN	NN	Number=Sing	17	dobj	_	_
20	in	in	ADP	IN	_	17	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	category	category	NOUN	NN	Number=Sing	20	pobj	_	_
23	with	with	ADP	IN	_	22	prep	_	_
24	finite	finite	ADJ	JJ	Degree=Pos	25	compound	_	_
25	limits	limit	NOUN	NNS	Number=Plur	23	pobj	_	_
26	that	that	PRON	WDT	PronType=Rel	27	nsubj	_	_
27	corresponds	correspond	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	relcl	_	_
28	to	to	ADP	IN	_	27	prep	_	_
29	universal	universal	ADJ	JJ	Degree=Pos	31	amod	_	_
30	closure	closure	NOUN	NN	Number=Sing	31	compound	_	_
31	operators	operator	NOUN	NNS	Number=Plur	28	pobj	_	_
32	in	in	ADP	IN	_	31	prep	_	_
33	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	37	poss	_	_
34	regular	regular	ADJ	JJ	Degree=Pos	37	amod	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	34	cc	_	_
36	exact	exact	ADJ	JJ	Degree=Pos	34	conj	_	_
37	completions	completion	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 2
# text = The study of separated objects in exact completions will then allow us to give conceptual proofs of local cartesian closure of different categories of pseudo equivalence relations.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	study	study	NOUN	NN	Number=Sing	11	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	separated	separate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	amod	_	_
5	objects	object	NOUN	NNS	Number=Plur	3	pobj	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	exact	exact	ADJ	JJ	Degree=Pos	8	amod	_	_
8	completions	completion	NOUN	NNS	Number=Plur	6	pobj	_	_
9	will	will	AUX	MD	VerbForm=Fin	11	aux	_	_
10	then	then	ADV	RB	PronType=Dem	11	advmod	_	_
11	allow	allow	VERB	VB	VerbForm=Inf	0	ROOT	_	_
12	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	give	give	VERB	VB	VerbForm=Inf	11	ccomp	_	_
15	conceptual	conceptual	ADJ	JJ	Degree=Pos	16	amod	_	_
16	proofs	proof	NOUN	NNS	Number=Plur	14	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	local	local	ADJ	JJ	Degree=Pos	20	amod	_	_
19	cartesian	cartesian	ADJ	JJ	Degree=Pos	20	compound	_	_
20	closure	closure	NOUN	NN	Number=Sing	17	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	different	different	ADJ	JJ	Degree=Pos	23	amod	_	_
23	categories	category	NOUN	NNS	Number=Plur	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	pseudo	pseudo	NOUN	NN	Number=Sing	26	compound	_	_
26	equivalence	equivalence	NOUN	NN	Number=Sing	27	compound	_	_
27	relations	relation	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 3
# text = Finally, we characterize when certain categories of sheaves are toposes.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	when	when	SCONJ	WRB	_	10	advmod	_	_
6	certain	certain	ADJ	JJ	Degree=Pos	7	amod	_	_
7	categories	category	NOUN	NNS	Number=Plur	10	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	sheaves	sheaf	NOUN	NNS	Number=Plur	8	pobj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	advcl	_	_
11	toposes	topos	NOUN	NNS	Number=Plur	10	attr	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 105
# sent_id = 1
# text = We show that lax epimorphisms in the category Cat are precisely the functors $ P : {cal E} to {cal B} $ for which the functor $ P^{*}: [{cal B}, Set] to [{cal E}, Set] $ of composition with $ P $ is fully faithful.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	10	mark	_	_
4	lax	lax	ADJ	JJ	Degree=Pos	5	amod	_	_
5	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	10	nsubj	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
9	Cat	Cat	PROPN	NNP	Number=Sing	8	appos	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
11	precisely	precisely	ADV	RB	_	10	advmod	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	functors	functor	NOUN	NNS	Number=Plur	10	attr	_	_
14	$ P : {cal E} to {cal B} $	$ p : {cal e} to {cal b} $	SYM	$	_	13	appos	_	_
15	for	for	ADP	IN	_	24	prep	_	_
16	which	which	PRON	WDT	_	15	pobj	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	functor	functor	NOUN	NN	Number=Sing	24	nsubj	_	_
19	$ P^{*}: [{cal B}, Set] to [{cal E}, Set] $	$ p^{*}: [{cal b}, set] to [{cal e}, set] $	SYM	$	_	24	nsubj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	composition	composition	NOUN	NN	Number=Sing	20	pobj	_	_
22	with	with	ADP	IN	_	21	prep	_	_
23	$ P $	$ p $	SYM	$	_	22	pobj	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
25	fully	fully	ADV	RB	_	26	advmod	_	_
26	faithful	faithful	ADJ	JJ	Degree=Pos	24	acomp	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We present two other characterizations.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	two	two	NUM	CD	NumType=Card	5	nummod	_	_
4	other	other	ADJ	JJ	Degree=Pos	5	amod	_	_
5	characterizations	characterization	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
6	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Firstly, lax epimorphisms are precisely the ``absolutely dense'' functors, that is, functors $ P $ such that every object $ B $ of $ {cal B} $ is an absolute colimit of all arrows $ P(E)to B $ for $ E $ in $ {cal E} $ .
1	Firstly	firstly	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	lax	lax	ADJ	JJ	Degree=Pos	4	amod	_	_
4	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	5	nsubj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	precisely	precisely	ADV	RB	_	5	advmod	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
8	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	13	punct	_	SpaceAfter=No
9	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	13	punct	_	SpaceAfter=No
10	absolutely	absolutely	ADV	RB	_	11	advmod	_	_
11	dense	dense	ADJ	JJ	Degree=Pos	13	amod	_	SpaceAfter=No
12	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	13	punct	_	_
13	functors	functor	NOUN	NNS	Number=Plur	5	attr	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	that	that	ADV	RB	_	16	advmod	_	_
16	is	is	ADV	RB	_	13	relcl	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
18	functors	functor	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	appos	_	_
19	$ P $	$ p $	SYM	$	_	13	appos	_	_
20	such	such	ADJ	JJ	Degree=Pos	13	appos	_	_
21	that	that	SCONJ	IN	_	27	mark	_	_
22	every	every	DET	DT	_	23	det	_	_
23	object	object	NOUN	NN	Number=Sing	27	nsubj	_	_
24	$ B $	$ b $	SYM	$	_	23	appos	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	$ {cal B} $	$ {cal b} $	SYM	$	_	25	pobj	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	relcl	_	_
28	an	an	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
29	absolute	absolute	ADJ	JJ	Degree=Pos	30	amod	_	_
30	colimit	colimit	NOUN	NN	Number=Sing	27	attr	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	all	all	DET	DT	_	33	det	_	_
33	arrows	arrow	NOUN	NNS	Number=Plur	31	pobj	_	_
34	$ P(E)to B $	$ p(e)to b $	SYM	$	_	33	appos	_	_
35	for	for	ADP	IN	_	30	prep	_	_
36	$ E $	$ e $	SYM	$	_	35	pobj	_	_
37	in	in	ADP	IN	_	36	prep	_	_
38	$ {cal E} $	$ {cal e} $	SYM	$	_	37	pobj	_	_
39	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = Secondly, lax epimorphisms are precisely the functors $ P $ such that for every morphism $ f $ of $ {cal B} $ the category of all factorizations through objects of $ P[{cal E}] $ is connected.
1	Secondly	secondly	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	lax	lax	ADJ	JJ	Degree=Pos	4	amod	_	_
4	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	5	nsubj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	28	ccomp	_	_
6	precisely	precisely	ADV	RB	_	5	advmod	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	functors	functor	NOUN	NNS	Number=Plur	5	attr	_	_
9	$ P $	$ p $	SYM	$	_	8	appos	_	_
10	such	such	ADJ	JJ	Degree=Pos	11	amod	_	_
11	that	that	SCONJ	IN	_	4	appos	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	every	every	DET	DT	_	14	det	_	_
14	morphism	morphism	NOUN	NN	Number=Sing	12	pobj	_	_
15	$ f $	$ f $	SYM	$	_	14	prep	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	$ {cal B} $	$ {cal b} $	SYM	$	_	5	dep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	category	category	NOUN	NN	Number=Sing	17	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	all	all	DET	DT	_	22	det	_	_
22	factorizations	factorization	NOUN	NNS	Number=Plur	20	pobj	_	_
23	through	through	ADP	IN	_	19	prep	_	_
24	objects	object	NOUN	NNS	Number=Plur	23	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	$ P[{cal E}] $	$ p[{cal e}] $	SYM	$	_	28	nsubjpass	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	28	auxpass	_	_
28	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	28	punct	_	SpaceAfter=No

# sent_id = 5
# text = A relationship between pseudoepimorphisms and lax epimorphisms is discussed.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	relationship	relationship	NOUN	NN	Number=Sing	9	nsubjpass	_	_
3	between	between	ADP	IN	_	2	prep	_	_
4	pseudoepimorphisms	pseudoepimorphism	NOUN	NNS	Number=Plur	3	pobj	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	lax	lax	ADJ	JJ	Degree=Pos	7	amod	_	_
7	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	4	conj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	discussed	discuss	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 106
# sent_id = 1
# text = The context of enriched sheaf theory introduced in the author's thesis provides a convenient viewpoint for models of the stable homotopy category as well as categories of finite loop spaces.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	context	context	NOUN	NN	Number=Sing	13	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	amod	_	_
5	sheaf	sheaf	NOUN	NN	Number=Sing	6	compound	_	_
6	theory	theory	NOUN	NN	Number=Sing	3	pobj	_	_
7	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	author	author	NOUN	NN	Number=Sing	12	poss	_	SpaceAfter=No
11	's	's	PART	POS	_	10	case	_	_
12	thesis	thesis	NOUN	NN	Number=Sing	8	pobj	_	_
13	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	convenient	convenient	ADJ	JJ	Degree=Pos	16	amod	_	_
16	viewpoint	viewpoint	NOUN	NN	Number=Sing	13	dobj	_	_
17	for	for	ADP	IN	_	16	prep	_	_
18	models	model	NOUN	NNS	Number=Plur	17	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
21	stable	stable	ADJ	JJ	Degree=Pos	23	amod	_	_
22	homotopy	homotopy	NOUN	NN	Number=Sing	23	compound	_	_
23	category	category	NOUN	NN	Number=Sing	19	pobj	_	_
24	as	as	ADV	RB	_	26	advmod	_	_
25	well	well	ADV	RB	Degree=Pos	26	advmod	_	_
26	as	as	ADP	IN	_	18	cc	_	_
27	categories	category	NOUN	NNS	Number=Plur	18	conj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	finite	finite	PROPN	NNP	Number=Sing	31	compound	_	_
30	loop	loop	NOUN	NN	Number=Sing	31	compound	_	_
31	spaces	space	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 2
# text = Also, the languages of algebraic geometry and algebraic topology have been interacting quite heavily in recent years, primarily due to the work of Voevodsky and that of Hopkins.
1	Also	also	ADV	RB	_	13	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	languages	language	NOUN	NNS	Number=Plur	13	nsubj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	algebraic	algebraic	ADJ	JJ	Degree=Pos	7	amod	_	_
7	geometry	geometry	NOUN	NN	Number=Sing	5	pobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
9	algebraic	algebraic	ADJ	JJ	Degree=Pos	10	amod	_	_
10	topology	topology	NOUN	NN	Number=Sing	4	conj	_	_
11	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	aux	_	_
12	been	be	AUX	VBN	Tense=Past|VerbForm=Part	13	aux	_	_
13	interacting	interact	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	0	ROOT	_	_
14	quite	quite	ADV	RB	_	15	advmod	_	_
15	heavily	heavily	ADV	RB	_	13	advmod	_	_
16	in	in	ADP	IN	_	13	prep	_	_
17	recent	recent	ADJ	JJ	Degree=Pos	18	amod	_	_
18	years	year	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
20	primarily	primarily	ADV	RB	_	21	advmod	_	_
21	due	due	ADP	IN	_	13	prep	_	_
22	to	to	ADP	IN	_	21	pcomp	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	work	work	NOUN	NN	Number=Sing	21	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	Voevodsky	Voevodsky	PROPN	NNP	Number=Sing	25	pobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
28	that	that	PRON	DT	Number=Sing|PronType=Dem	24	conj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	Hopkins	Hopkins	PROPN	NNPS	Number=Plur	29	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 3
# text = Thus, the language of Grothendieck topologies is becoming a necessary tool for the algebraic topologist.
1	Thus	thus	ADV	RB	_	9	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	language	language	NOUN	NN	Number=Sing	9	nsubj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	7	compound	_	_
7	topologies	topology	NOUN	NNS	Number=Plur	5	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	aux	_	_
9	becoming	become	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	0	ROOT	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	necessary	necessary	ADJ	JJ	Degree=Pos	12	amod	_	_
12	tool	tool	NOUN	NN	Number=Sing	9	attr	_	_
13	for	for	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	algebraic	algebraic	ADJ	JJ	Degree=Pos	16	amod	_	_
16	topologist	topologist	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 4
# text = The current article is intended to give a somewhat relaxed introduction to this language of sheaves in a topological context, using familiar examples such as n - fold loop spaces and pointed $ G $ - spaces.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	current	current	ADJ	JJ	Degree=Pos	3	amod	_	_
3	article	article	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	intended	intend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	give	give	VERB	VB	VerbForm=Inf	5	xcomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	somewhat	somewhat	ADV	RB	_	10	advmod	_	_
10	relaxed	relaxed	ADJ	JJ	Degree=Pos	11	amod	_	_
11	introduction	introduction	NOUN	NN	Number=Sing	7	dobj	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	this	this	DET	DT	Number=Sing|PronType=Dem	14	det	_	_
14	language	language	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	sheaves	sheaf	NOUN	NNS	Number=Plur	15	pobj	_	_
17	in	in	ADP	IN	_	7	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	topological	topological	ADJ	JJ	Degree=Pos	20	amod	_	_
20	context	context	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
22	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	advcl	_	_
23	familiar	familiar	ADJ	JJ	Degree=Pos	24	amod	_	_
24	examples	example	NOUN	NNS	Number=Plur	22	dobj	_	_
25	such	such	ADJ	JJ	Degree=Pos	26	amod	_	_
26	as	as	ADP	IN	_	24	prep	_	_
27	n	n	ADV	RB	_	31	amod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
29	fold	fold	VERB	VB	VerbForm=Inf	31	amod	_	_
30	loop	loop	NOUN	NN	Number=Sing	31	compound	_	_
31	spaces	space	NOUN	NNS	Number=Plur	26	pobj	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
33	pointed	point	VERB	VBD	Tense=Past|VerbForm=Fin	5	conj	_	_
34	$ G $	$ g $	SYM	$	_	36	compound	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	36	punct	_	_
36	spaces	space	NOUN	NNS	Number=Plur	33	dobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = This language also includes the diagram categories of spectra as well as spectra in the sense of Lewis, which will be discussed in some detail.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	language	language	NOUN	NN	Number=Sing	4	nsubj	_	_
3	also	also	ADV	RB	_	4	advmod	_	_
4	includes	include	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	diagram	diagram	NOUN	NN	Number=Sing	7	compound	_	_
7	categories	category	NOUN	NNS	Number=Plur	4	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	spectra	spectra	PROPN	NNP	Number=Sing	8	pobj	_	_
10	as	as	ADV	RB	_	12	advmod	_	_
11	well	well	ADV	RB	Degree=Pos	12	advmod	_	_
12	as	as	ADP	IN	_	9	cc	_	_
13	spectra	spectra	PROPN	NNP	Number=Sing	9	conj	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	sense	sense	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	Lewis	Lewis	PROPN	NNP	Number=Sing	17	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	which	which	PRON	WDT	_	23	nsubjpass	_	_
21	will	will	AUX	MD	VerbForm=Fin	23	aux	_	_
22	be	be	AUX	VB	VerbForm=Inf	23	auxpass	_	_
23	discussed	discuss	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	relcl	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	some	some	DET	DT	_	26	det	_	_
26	detail	detail	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 107
# sent_id = 1
# text = A cartesian closed topological hull of the construct $ CLS $ of closure spaces and continuous maps is constructed.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	cartesian	cartesian	NOUN	NN	Number=Sing	3	nsubj	_	_
3	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	17	nsubjpass	_	_
4	topological	topological	ADJ	JJ	Degree=Pos	5	amod	_	_
5	hull	hull	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	construct	construct	NOUN	NN	Number=Sing	6	pobj	_	_
9	$ CLS $	$ cls $	SYM	$	_	3	dep	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	closure	closure	NOUN	NN	Number=Sing	12	compound	_	_
12	spaces	space	NOUN	NNS	Number=Plur	10	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	continuous	continuous	ADJ	JJ	Degree=Pos	15	amod	_	_
15	maps	map	NOUN	NNS	Number=Plur	12	conj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	auxpass	_	_
17	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 2
# text = The construction is performed in two steps.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	construction	construction	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	performed	perform	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	two	two	NUM	CD	NumType=Card	7	nummod	_	_
7	steps	step	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = First a cartesian closed extension $ L $ of $ CLS $ is obtained.
1	First	first	ADV	RB	_	4	advmod	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	cartesian	cartesian	NOUN	NN	Number=Sing	4	nsubj	_	_
4	closed	closed	ADJ	JJ	Degree=Pos	10	nsubjpass	_	_
5	extension	extension	NOUN	NN	Number=Sing	4	dobj	_	_
6	$ L $	$ l $	SYM	$	_	4	npadvmod	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	$ CLS $	$ cls $	SYM	$	_	7	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 4
# text = We apply a method worked out by Adamek and Reiterman for constructing extensions of constructs that in some sense ``resemble'' the construct of uniform spaces.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	apply	apply	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	method	method	NOUN	NN	Number=Sing	2	dobj	_	_
5	worked	work	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	acl	_	_
6	out	out	ADP	RP	_	5	prt	_	_
7	by	by	ADP	IN	_	5	agent	_	_
8	Adamek	Adamek	PROPN	NNP	Number=Sing	7	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	Reiterman	Reiterman	PROPN	NNP	Number=Sing	8	conj	_	_
11	for	for	ADP	IN	_	5	prep	_	_
12	constructing	construct	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	pcomp	_	_
13	extensions	extension	NOUN	NNS	Number=Plur	12	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	constructs	construct	NOUN	NNS	Number=Plur	14	pobj	_	_
16	that	that	SCONJ	IN	_	22	mark	_	_
17	in	in	ADP	IN	_	22	prep	_	_
18	some	some	DET	DT	_	19	det	_	_
19	sense	sense	NOUN	NN	Number=Sing	17	pobj	_	_
20	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	22	punct	_	SpaceAfter=No
21	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	22	punct	_	SpaceAfter=No
22	resemble	resemble	VERB	VB	VerbForm=Inf	15	relcl	_	SpaceAfter=No
23	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	22	punct	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	construct	construct	NOUN	NN	Number=Sing	22	dobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	uniform	uniform	ADJ	JJ	Degree=Pos	28	amod	_	_
28	spaces	space	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = Secondly, within this extension $ L $ the cartesian closed topological hull $ L* $ of $ CLS $ is characterized as a full subconstruct.
1	Secondly	secondly	ADV	RB	_	9	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
3	within	within	ADP	IN	_	9	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	extension	extension	NOUN	NN	Number=Sing	3	pobj	_	_
6	$ L $	$ l $	SYM	$	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	cartesian	cartesian	NOUN	NN	Number=Sing	9	nsubj	_	_
9	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
10	topological	topological	ADJ	JJ	Degree=Pos	11	amod	_	_
11	hull	hull	NOUN	NN	Number=Sing	9	dobj	_	_
12	$ L* $	$ l* $	SYM	$	_	16	nsubjpass	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	$ CLS $	$ cls $	SYM	$	_	13	pobj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	auxpass	_	_
16	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	conj	_	_
17	as	as	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	full	full	ADJ	JJ	Degree=Pos	20	amod	_	_
20	subconstruct	subconstruct	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 6
# text = In order to find the internal characterization of the objects of $ L* $ we produce a concrete functor to the category of power closed collections based on $ CLS $ as introduced by Adamek, Reiterman and Strecker.
1	In	in	ADP	IN	_	14	prep	_	_
2	order	order	NOUN	NN	Number=Sing	1	pobj	_	_
3	to	to	PART	TO	_	4	aux	_	_
4	find	find	VERB	VB	VerbForm=Inf	2	acl	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	internal	internal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	characterization	characterization	NOUN	NN	Number=Sing	4	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	objects	object	NOUN	NNS	Number=Plur	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	$ L* $	$ l* $	SYM	$	_	11	pobj	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	produce	produce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	concrete	concrete	ADJ	JJ	Degree=Pos	17	amod	_	_
17	functor	functor	NOUN	NN	Number=Sing	14	dobj	_	_
18	to	to	ADP	IN	_	14	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	power	power	NOUN	NN	Number=Sing	21	pobj	_	_
23	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	24	amod	_	_
24	collections	collection	NOUN	NNS	Number=Plur	14	dobj	_	_
25	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	acl	_	_
26	on	on	ADP	IN	_	25	prep	_	_
27	$ CLS $	$ cls $	SYM	$	_	26	pobj	_	_
28	as	as	SCONJ	IN	_	29	mark	_	_
29	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	advcl	_	_
30	by	by	ADP	IN	_	29	agent	_	_
31	Adamek	Adamek	PROPN	NNP	Number=Sing	30	pobj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
33	Reiterman	Reiterman	PROPN	NNP	Number=Sing	31	conj	_	_
34	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
35	Strecker	Strecker	PROPN	NNP	Number=Sing	33	conj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# doc_id = 108
# sent_id = 1
# text = We prove the universal property of the infinitary exact completion of a category with weak small limits.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	universal	universal	ADJ	JJ	Degree=Pos	5	amod	_	_
5	property	property	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	infinitary	infinitary	ADJ	JJ	Degree=Pos	10	amod	_	_
9	exact	exact	ADJ	JJ	Degree=Pos	10	amod	_	_
10	completion	completion	NOUN	NN	Number=Sing	6	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	weak	weak	ADJ	JJ	Degree=Pos	17	amod	_	_
16	small	small	ADJ	JJ	Degree=Pos	17	amod	_	_
17	limits	limit	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = As an application, we slightly weaken the conditions characterizing essential localizations of varieties (in particular, of module categories) and of presheaf categories.
1	As	as	ADP	IN	_	7	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
6	slightly	slightly	ADV	RB	_	7	advmod	_	_
7	weaken	weaken	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	conditions	condition	NOUN	NNS	Number=Plur	7	dobj	_	_
10	characterizing	characterize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	acl	_	_
11	essential	essential	ADJ	JJ	Degree=Pos	12	amod	_	_
12	localizations	localization	NOUN	NNS	Number=Plur	10	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	varieties	variety	NOUN	NNS	Number=Plur	13	pobj	_	_
15	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
16	in	in	ADP	IN	_	14	prep	_	_
17	particular	particular	ADJ	JJ	Degree=Pos	16	amod	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
19	of	of	ADP	IN	_	10	prep	_	_
20	module	module	NOUN	NN	Number=Sing	21	compound	_	_
21	categories	category	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
22	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	21	punct	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
24	of	of	ADP	IN	_	19	conj	_	_
25	presheaf	presheaf	ADJ	JJ	Degree=Pos	26	amod	_	_
26	categories	category	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 109
# sent_id = 1
# text = A categorical proof of the statement given by the title is provided, in generalization of a result for topological spaces proved recently by Clementino, Hofmann and Tholen.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	categorical	categorical	ADJ	JJ	Degree=Pos	3	amod	_	_
3	proof	proof	NOUN	NN	Number=Sing	0	ROOT	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	statement	statement	NOUN	NN	Number=Sing	4	pobj	_	_
7	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
8	by	by	ADP	IN	_	7	agent	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	title	title	NOUN	NN	Number=Sing	8	pobj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	provided	provide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
14	in	in	ADP	IN	_	3	prep	_	_
15	generalization	generalization	NOUN	NN	Number=Sing	14	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	result	result	NOUN	NN	Number=Sing	16	pobj	_	_
19	for	for	ADP	IN	_	18	prep	_	_
20	topological	topological	ADJ	JJ	Degree=Pos	21	amod	_	_
21	spaces	space	NOUN	NNS	Number=Plur	19	pobj	_	_
22	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	acl	_	_
23	recently	recently	ADV	RB	_	22	advmod	_	_
24	by	by	ADP	IN	_	22	agent	_	_
25	Clementino	Clementino	PROPN	NNP	Number=Sing	24	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
27	Hofmann	Hofmann	PROPN	NNP	Number=Sing	25	conj	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
29	Tholen	Tholen	PROPN	NNP	Number=Sing	27	conj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 110
# sent_id = 1
# text = In the context of Maltsev categories, a left exact root for the congruence distributive property is given and investigated, namely the property that there is no non trivial internal group inside the fibres of the fibration of pointed objects.
1	In	in	ADP	IN	_	18	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	context	context	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	Maltsev	maltsev	ADJ	JJ	Degree=Pos	6	amod	_	_
6	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	left	left	ADJ	JJ	Degree=Pos	11	amod	_	_
10	exact	exact	ADJ	JJ	Degree=Pos	11	amod	_	_
11	root	root	NOUN	NN	Number=Sing	18	nsubjpass	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
14	congruence	congruence	NOUN	NN	Number=Sing	15	npadvmod	_	_
15	distributive	distributive	ADJ	JJ	Degree=Pos	16	amod	_	_
16	property	property	NOUN	NN	Number=Sing	12	pobj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	auxpass	_	_
18	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	investigated	investigate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	namely	namely	ADV	RB	_	24	advmod	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	property	property	NOUN	NN	Number=Sing	20	dobj	_	_
25	that	that	PRON	WDT	PronType=Rel	27	mark	_	_
26	there	there	PRON	EX	_	27	expl	_	_
27	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	acl	_	_
28	no	no	DET	DT	_	32	det	_	_
29	non	non	ADJ	JJ	Degree=Pos	30	amod	_	_
30	trivial	trivial	ADJ	JJ	Degree=Pos	32	amod	_	_
31	internal	internal	ADJ	JJ	Degree=Pos	32	amod	_	_
32	group	group	NOUN	NN	Number=Sing	27	attr	_	_
33	inside	inside	ADP	IN	_	32	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	fibres	fibre	NOUN	NNS	Number=Plur	33	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	fibration	fibration	NOUN	NN	Number=Sing	36	pobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	pointed	pointed	ADJ	JJ	Degree=Pos	41	amod	_	_
41	objects	object	NOUN	NNS	Number=Plur	39	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# sent_id = 2
# text = Indeed, when moreover the basic category $ mathbb{C} $ is Barr exact, the two previous properties are shown to be equivalent.
1	Indeed	indeed	ADV	RB	_	9	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
3	when	when	SCONJ	WRB	_	4	advmod	_	_
4	moreover	moreover	ADV	RB	_	9	advmod	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	basic	basic	ADJ	JJ	Degree=Pos	7	amod	_	_
7	category	category	NOUN	NN	Number=Sing	9	nsubj	_	_
8	$ mathbb{C} $	$ mathbb{c} $	SYM	$	_	7	appos	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	ccomp	_	_
10	Barr	Barr	PROPN	NNP	Number=Sing	11	compound	_	_
11	exact	exact	ADJ	JJ	Degree=Pos	9	attr	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
14	two	two	NUM	CD	NumType=Card	16	nummod	_	_
15	previous	previous	ADJ	JJ	Degree=Pos	16	amod	_	_
16	properties	property	NOUN	NNS	Number=Plur	18	nsubjpass	_	_
17	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	18	auxpass	_	_
18	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
19	to	to	PART	TO	_	20	aux	_	_
20	be	be	AUX	VB	VerbForm=Inf	18	xcomp	_	_
21	equivalent	equivalent	ADJ	JJ	Degree=Pos	20	acomp	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# doc_id = 111
# sent_id = 1
# text = For a broad collection of categories $ cal K $ , including all presheaf categories, the following statement is proved to be consistent: every left exact (that is, finite - limits preserving) functor from $ cal K $ to $ Set $ is small, that is, a small colimit of representables.
1	For	for	ADP	IN	_	18	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	broad	broad	ADJ	JJ	Degree=Pos	4	amod	_	_
4	collection	collection	NOUN	NN	Number=Sing	1	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
7	$ cal K $	$ cal k $	SYM	$	_	4	appos	_	_
8	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
9	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	prep	_	_
10	all	all	DET	DT	_	12	det	_	_
11	presheaf	presheaf	ADJ	JJ	Degree=Pos	12	amod	_	_
12	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	amod	_	_
16	statement	statement	NOUN	NN	Number=Sing	18	nsubjpass	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	auxpass	_	_
18	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	40	ccomp	_	_
19	to	to	PART	TO	_	20	aux	_	_
20	be	be	AUX	VB	VerbForm=Inf	18	xcomp	_	_
21	consistent	consistent	ADJ	JJ	Degree=Pos	20	acomp	_	SpaceAfter=No
22	:	:	PUNCT	:	_	18	punct	_	_
23	every	every	DET	DT	_	25	det	_	_
24	left	left	ADJ	JJ	Degree=Pos	25	amod	_	_
25	exact	exact	ADJ	JJ	Degree=Pos	22	nmod	_	_
26	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	25	punct	_	SpaceAfter=No
27	that	that	ADV	RB	_	28	advmod	_	_
28	is	is	ADV	RB	_	35	advmod	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
30	finite	finite	NOUN	NN	Number=Sing	32	compound	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	limits	limit	NOUN	NNS	Number=Plur	33	nsubj	_	_
33	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	35	amod	_	SpaceAfter=No
34	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	35	punct	_	_
35	functor	functor	NOUN	NN	Number=Sing	40	nsubj	_	_
36	from	from	ADP	IN	_	35	prep	_	_
37	$ cal K $	$ cal k $	SYM	$	_	36	pobj	_	_
38	to	to	PART	TO	_	36	prep	_	_
39	$ Set $	$ set $	SYM	$	_	38	pobj	_	_
40	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
41	small	small	ADJ	JJ	Degree=Pos	40	acomp	_	SpaceAfter=No
42	,	,	PUNCT	,	PunctType=Comm	40	punct	_	_
43	that	that	ADV	RB	_	44	advmod	_	_
44	is	is	ADV	RB	_	48	advmod	_	SpaceAfter=No
45	,	,	PUNCT	,	PunctType=Comm	48	punct	_	_
46	a	a	DET	DT	Definite=Ind|PronType=Art	48	det	_	_
47	small	small	ADJ	JJ	Degree=Pos	48	amod	_	_
48	colimit	colimit	NOUN	NN	Number=Sing	40	attr	_	_
49	of	of	ADP	IN	_	48	prep	_	_
50	representables	representable	NOUN	NNS	Number=Plur	49	pobj	_	SpaceAfter=No
51	.	.	PUNCT	.	PunctType=Peri	40	punct	_	SpaceAfter=No

# sent_id = 2
# text = In contrast, for the (presheaf) category $ {cal K}=Alg(1, 1) $ of unary algebras we construct a functor from $ Alg(1, 1) $ to $ Set $ which preserves finite products and is not small.
1	In	in	ADP	IN	_	15	prep	_	_
2	contrast	contrast	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
4	for	for	ADP	IN	_	15	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
6	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	9	punct	_	SpaceAfter=No
7	presheaf	presheaf	ADJ	JJ	Degree=Pos	9	amod	_	SpaceAfter=No
8	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	9	punct	_	_
9	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
10	$ {cal K}=Alg(1, 1) $	$ {cal k}=alg(1, 1) $	SYM	$	_	9	appos	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	unary	unary	ADJ	JJ	Degree=Pos	13	amod	_	_
13	algebras	algebra	NOUN	NNS	Number=Plur	11	pobj	_	_
14	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	15	nsubj	_	_
15	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	functor	functor	NOUN	NN	Number=Sing	15	dobj	_	_
18	from	from	ADP	IN	_	15	prep	_	_
19	$ Alg(1, 1) $	$ alg(1, 1) $	SYM	$	_	18	pobj	_	_
20	to	to	ADP	IN	_	18	prep	_	_
21	$ Set $	$ set $	SYM	$	_	20	pobj	_	_
22	which	which	PRON	WDT	_	23	nsubj	_	_
23	preserves	preserve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	advcl	_	_
24	finite	finite	ADJ	JJ	Degree=Pos	25	compound	_	_
25	products	product	NOUN	NNS	Number=Plur	23	dobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	conj	_	_
28	not	not	PART	RB	Polarity=Neg	27	neg	_	_
29	small	small	ADJ	JJ	Degree=Pos	27	acomp	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also describe all left exact set - valued functors as directed unions of ``reduced representables'', generalizing reduced products.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	all	all	PRON	DT	_	3	dobj	_	_
5	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	ccomp	_	_
6	exact	exact	ADJ	JJ	Degree=Pos	10	amod	_	_
7	set	set	NOUN	NN	Number=Sing	9	npadvmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	functors	functor	NOUN	NNS	Number=Plur	5	dobj	_	_
11	as	as	ADP	IN	_	5	prep	_	_
12	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
13	unions	union	NOUN	NNS	Number=Plur	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	18	punct	_	SpaceAfter=No
16	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	18	punct	_	SpaceAfter=No
17	reduced	reduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
18	representables	representable	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
19	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	18	punct	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
21	generalizing	generalize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	advcl	_	_
22	reduced	reduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	amod	_	_
23	products	product	NOUN	NNS	Number=Plur	21	dobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 112
# sent_id = 1
# text = We develop a new approach to Commutator theory based on the theory of internal categorical structures, especially of so called pseudogroupoids.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	new	new	ADJ	JJ	Degree=Pos	5	amod	_	_
5	approach	approach	NOUN	NN	Number=Sing	2	dobj	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	Commutator	Commutator	PROPN	NNP	Number=Sing	8	compound	_	_
8	theory	theory	NOUN	NN	Number=Sing	6	pobj	_	_
9	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	acl	_	_
10	on	on	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	theory	theory	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	internal	internal	ADJ	JJ	Degree=Pos	16	amod	_	_
15	categorical	categorical	ADJ	JJ	Degree=Pos	16	amod	_	_
16	structures	structure	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
18	especially	especially	ADV	RB	_	19	advmod	_	_
19	of	of	ADP	IN	_	5	prep	_	_
20	so	so	ADV	RB	_	21	advmod	_	_
21	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	amod	_	_
22	pseudogroupoids	pseudogroupoid	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = It is motivated by our previous work on internal categories and groupoids in congruence modular varieties.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	by	by	ADP	IN	_	3	agent	_	_
5	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	7	poss	_	_
6	previous	previous	ADJ	JJ	Degree=Pos	7	amod	_	_
7	work	work	NOUN	NN	Number=Sing	4	pobj	_	_
8	on	on	ADP	IN	_	7	prep	_	_
9	internal	internal	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	groupoids	groupoid	NOUN	NNS	Number=Plur	10	conj	_	_
13	in	in	ADP	IN	_	10	prep	_	_
14	congruence	congruence	NOUN	NN	Number=Sing	16	nmod	_	_
15	modular	modular	ADJ	JJ	Degree=Pos	16	amod	_	_
16	varieties	variety	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 113
# sent_id = 1
# text = We explore the combinatorial properties of the branching areas of execution paths in higher dimensional automata.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	explore	explore	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	5	amod	_	_
5	properties	property	NOUN	NNS	Number=Plur	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	branching	branching	NOUN	NN	Number=Sing	9	compound	_	_
9	areas	area	NOUN	NNS	Number=Plur	6	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	execution	execution	NOUN	NN	Number=Sing	12	compound	_	_
12	paths	path	NOUN	NNS	Number=Plur	10	pobj	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	higher	high	ADJ	JJR	Degree=Cmp	16	amod	_	_
15	dimensional	dimensional	ADJ	JJ	Degree=Pos	16	amod	_	_
16	automata	automata	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Mathematically, this means that we investigate the combinatorics of the negative corner (or branching) homology of a globular $ omega $ - category and the combinatorics of a new homology theory called the reduced branching homology.
1	Mathematically	mathematically	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	this	this	PRON	DT	Number=Sing|PronType=Dem	4	nsubj	_	_
4	means	mean	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	7	mark	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	4	ccomp	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	combinatorics	combinatoric	NOUN	NNS	Number=Plur	7	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	negative	negative	ADJ	JJ	Degree=Pos	13	amod	_	_
13	corner	corner	NOUN	NN	Number=Sing	10	pobj	_	_
14	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	13	punct	_	SpaceAfter=No
15	or	or	CCONJ	CC	ConjType=Cmp	13	cc	_	_
16	branching	branching	NOUN	NN	Number=Sing	18	nmod	_	SpaceAfter=No
17	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	18	punct	_	_
18	homology	homology	NOUN	NN	Number=Sing	13	conj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
21	globular	globular	ADJ	JJ	Degree=Pos	24	amod	_	_
22	$ omega $	$ omega $	SYM	$	_	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	category	category	NOUN	NN	Number=Sing	19	pobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	combinatorics	combinatoric	NOUN	NNS	Number=Plur	18	conj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
30	new	new	ADJ	JJ	Degree=Pos	32	amod	_	_
31	homology	homology	NOUN	NN	Number=Sing	32	compound	_	_
32	theory	theory	NOUN	NN	Number=Sing	28	pobj	_	_
33	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	9	acl	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
35	reduced	reduced	ADJ	JJ	Degree=Pos	37	amod	_	_
36	branching	branching	NOUN	NN	Number=Sing	37	compound	_	_
37	homology	homology	NOUN	NN	Number=Sing	33	oprd	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = The latter is the homology of the quotient of the branching complex by the sub - complex generated by its thin elements.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	latter	latter	ADJ	JJ	Degree=Pos	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	homology	homology	NOUN	NN	Number=Sing	3	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	quotient	quotient	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	branching	branch	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	amod	_	_
12	complex	complex	NOUN	NN	Number=Sing	9	pobj	_	_
13	by	by	ADP	IN	_	8	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
15	sub	sub	NOUN	NN	Number=Sing	17	compound	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	complex	complex	ADJ	JJ	Degree=Pos	13	pobj	_	_
18	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
19	by	by	ADP	IN	_	18	agent	_	_
20	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	22	poss	_	_
21	thin	thin	ADJ	JJ	Degree=Pos	22	amod	_	_
22	elements	element	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = Conjecturally it coincides with the non reduced theory for higher dimensional automata, that is $ omega $ - categories freely generated by precubical sets.
1	Conjecturally	conjecturally	ADV	RB	_	3	advmod	_	_
2	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubj	_	_
3	coincides	coincide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	with	with	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
6	non	non	PROPN	NNP	Number=Sing	7	advmod	_	_
7	reduced	reduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
8	theory	theory	NOUN	NN	Number=Sing	4	pobj	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	higher	high	ADJ	JJR	Degree=Cmp	12	amod	_	_
11	dimensional	dimensional	ADJ	JJ	Degree=Pos	12	amod	_	_
12	automata	automata	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
14	that	that	PRON	WDT	PronType=Rel	15	nsubj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	advcl	_	_
16	$ omega $	$ omega $	SYM	$	_	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	categories	category	NOUN	NNS	Number=Plur	15	attr	_	_
19	freely	freely	ADV	RB	_	20	advmod	_	_
20	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	acl	_	_
21	by	by	ADP	IN	_	20	agent	_	_
22	precubical	precubical	ADJ	JJ	Degree=Pos	23	amod	_	_
23	sets	set	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = As application, we calculate the branching homology of some $ omega $ - categories and we give some invariance results for the reduced branching homology.
1	As	as	ADP	IN	_	5	prep	_	_
2	application	application	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	calculate	calculate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	branching	branching	NOUN	NN	Number=Sing	8	compound	_	_
8	homology	homology	NOUN	NN	Number=Sing	5	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	some	some	DET	DT	_	13	det	_	_
11	$ omega $	$ omega $	SYM	$	_	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
15	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	16	nsubj	_	_
16	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	5	conj	_	_
17	some	some	DET	DT	_	19	det	_	_
18	invariance	invariance	NOUN	NN	Number=Sing	19	compound	_	_
19	results	result	NOUN	NNS	Number=Plur	16	dobj	_	_
20	for	for	ADP	IN	_	16	dative	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
22	reduced	reduced	ADJ	JJ	Degree=Pos	24	amod	_	_
23	branching	branching	NOUN	NN	Number=Sing	24	compound	_	_
24	homology	homology	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 6
# text = We only treat the branching side.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	only	only	ADV	RB	_	3	advmod	_	_
3	treat	treat	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	branching	branching	NOUN	NN	Number=Sing	6	compound	_	_
6	side	side	NOUN	NN	Number=Sing	3	dobj	_	SpaceAfter=No
7	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = The merging side, that is the case of merging areas of execution paths is similar and can be easily deduced from the branching side.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	merging	merging	NOUN	NN	Number=Sing	3	compound	_	_
3	side	side	NOUN	NN	Number=Sing	15	nsubj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	that	that	PRON	DT	Number=Sing|PronType=Dem	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	relcl	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	case	case	NOUN	NN	Number=Sing	6	attr	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	merging	merge	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	compound	_	_
11	areas	area	NOUN	NNS	Number=Plur	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	execution	execution	NOUN	NN	Number=Sing	14	compound	_	_
14	paths	path	NOUN	NNS	Number=Plur	12	pobj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	similar	similar	ADJ	JJ	Degree=Pos	15	acomp	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
18	can	can	AUX	MD	VerbForm=Fin	21	aux	_	_
19	be	be	AUX	VB	VerbForm=Inf	21	auxpass	_	_
20	easily	easily	ADV	RB	_	21	advmod	_	_
21	deduced	deduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	conj	_	_
22	from	from	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	branching	branching	NOUN	NN	Number=Sing	25	compound	_	_
25	side	side	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# doc_id = 114
# sent_id = 1
# text = We give an abstract characterization of the categories of models of sketches all of whose distinguished cones are based on connected (respectively non empty) categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	abstract	abstract	ADJ	JJ	Degree=Pos	5	amod	_	_
5	characterization	characterization	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	models	model	NOUN	NNS	Number=Plur	9	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	sketches	sketch	NOUN	NNS	Number=Plur	11	pobj	_	_
13	all	all	PRON	DT	_	19	nsubjpass	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	whose	whose	DET	WP$	Poss=Yes	17	poss	_	_
16	distinguished	distinguished	ADJ	JJ	Degree=Pos	17	amod	_	_
17	cones	cone	NOUN	NNS	Number=Plur	14	pobj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	19	auxpass	_	_
19	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	advcl	_	_
20	on	on	ADP	IN	_	19	prep	_	_
21	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	amod	_	_
22	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	27	punct	_	SpaceAfter=No
23	respectively	respectively	ADV	RB	_	24	advmod	_	_
24	non	non	ADJ	JJ	Degree=Pos	25	nmod	_	_
25	empty	empty	ADJ	JJ	Degree=Pos	27	amod	_	SpaceAfter=No
26	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	27	punct	_	_
27	categories	category	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 115
# sent_id = 1
# text = The 2 - category $ VAR $ of finitary varieties is not varietal over $ CAT $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
2	2	2	NUM	CD	NumType=Card	4	nummod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	category	category	NOUN	NN	Number=Sing	9	nsubj	_	_
5	$ VAR $	$ var $	SYM	$	_	4	nummod	_	_
6	of	of	ADP	IN	_	4	prep	_	_
7	finitary	finitary	ADJ	JJ	Degree=Pos	8	amod	_	_
8	varieties	variety	NOUN	NNS	Number=Plur	6	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	not	not	PART	RB	Polarity=Neg	9	neg	_	_
11	varietal	varietal	ADJ	JJ	Degree=Pos	9	acomp	_	_
12	over	over	ADP	IN	_	11	prep	_	_
13	$ CAT $	$ cat $	SYM	$	_	9	dep	_	_
14	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 2
# text = We introduce the concept of an algebraically exact category and prove that the 2 - category $ ALG $ of all algebraically exact categories is an equational hull of $ VAR $ with respect to all operations with rank.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	concept	concept	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	algebraically	algebraically	ADV	RB	_	8	advmod	_	_
8	exact	exact	ADJ	JJ	Degree=Pos	9	amod	_	_
9	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
11	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
12	that	that	SCONJ	IN	_	23	mark	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
14	2	2	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	category	category	NOUN	NN	Number=Sing	17	compound	_	_
17	$ ALG $	$ alg $	SYM	$	_	23	nsubj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	all	all	DET	DT	_	22	det	_	_
20	algebraically	algebraically	ADV	RB	_	21	advmod	_	_
21	exact	exact	ADJ	JJ	Degree=Pos	22	amod	_	_
22	categories	category	NOUN	NNS	Number=Plur	18	pobj	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	ccomp	_	_
24	an	an	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
25	equational	equational	ADJ	JJ	Degree=Pos	26	amod	_	_
26	hull	hull	NOUN	NN	Number=Sing	23	attr	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	$ VAR $	$ var $	SYM	$	_	27	pobj	_	_
29	with	with	ADP	IN	_	26	prep	_	_
30	respect	respect	NOUN	NN	Number=Sing	29	pobj	_	_
31	to	to	ADP	IN	_	30	prep	_	_
32	all	all	DET	DT	_	33	det	_	_
33	operations	operation	NOUN	NNS	Number=Plur	31	pobj	_	_
34	with	with	ADP	IN	_	30	prep	_	_
35	rank	rank	NOUN	NN	Number=Sing	34	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Every algebraically exact category $ cal K $ is complete, exact, and has filtered colimits which (i) commute with finite limits and (ii) distribute over products; besides (iii) regular epimorphisms in $ cal K $ are product - stable.
1	Every	every	DET	DT	_	4	det	_	_
2	algebraically	algebraically	ADV	RB	_	3	advmod	_	_
3	exact	exact	ADJ	JJ	Degree=Pos	4	amod	_	_
4	category	category	NOUN	NN	Number=Sing	6	nsubj	_	_
5	$ cal K $	$ cal k $	SYM	$	_	4	appos	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	39	ccomp	_	_
7	complete	complete	ADJ	JJ	Degree=Pos	6	acomp	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	exact	exact	ADJ	JJ	Degree=Pos	7	conj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
12	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	aux	_	_
13	filtered	filter	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	conj	_	_
14	colimits	colimit	NOUN	NNS	Number=Plur	13	dobj	_	_
15	which	which	PRON	WDT	_	19	nsubj	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	19	punct	_	SpaceAfter=No
17	i	i	NOUN	NN	Number=Sing	19	nmod	_	SpaceAfter=No
18	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	19	punct	_	_
19	commute	commute	NOUN	NN	Number=Sing	14	relcl	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	finite	finite	ADJ	JJ	Degree=Pos	22	compound	_	_
22	limits	limit	NOUN	NNS	Number=Plur	20	pobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	25	punct	_	SpaceAfter=No
25	ii	ii	PROPN	NNP	Number=Sing	22	conj	_	SpaceAfter=No
26	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	22	punct	_	_
27	distribute	distribute	VERB	VB	VerbForm=Inf	13	conj	_	_
28	over	over	ADP	IN	_	27	prep	_	_
29	products	product	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
30	;	;	PUNCT	:	_	39	punct	_	_
31	besides	besides	SCONJ	IN	_	39	prep	_	_
32	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	33	punct	_	SpaceAfter=No
33	iii	iii	NOUN	NN	Number=Sing	31	intj	_	SpaceAfter=No
34	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	36	punct	_	_
35	regular	regular	ADJ	JJ	Degree=Pos	36	amod	_	_
36	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	31	pobj	_	_
37	in	in	ADP	IN	_	36	prep	_	_
38	$ cal K $	$ cal k $	SYM	$	_	37	pobj	_	_
39	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
40	product	product	NOUN	NN	Number=Sing	42	npadvmod	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	stable	stable	ADJ	JJ	Degree=Pos	39	acomp	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	39	punct	_	SpaceAfter=No

# sent_id = 4
# text = It is not known whether the three conditions characterize algebraic exactness.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	4	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
3	not	not	PART	RB	Polarity=Neg	4	neg	_	_
4	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	whether	whether	SCONJ	IN	_	9	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	three	three	NUM	CD	NumType=Card	8	nummod	_	_
8	conditions	condition	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	4	ccomp	_	_
10	algebraic	algebraic	ADJ	JJ	Degree=Pos	11	amod	_	_
11	exactness	exactness	NOUN	NN	Number=Sing	9	dobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = An equational hull of $ VAR $ with respect to all operations is also discussed.
1	An	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	equational	equational	ADJ	JJ	Degree=Pos	3	amod	_	_
3	hull	hull	NOUN	NN	Number=Sing	13	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	$ VAR $	$ var $	SYM	$	_	4	pobj	_	_
6	with	with	ADP	IN	_	3	prep	_	_
7	respect	respect	NOUN	NN	Number=Sing	6	pobj	_	_
8	to	to	ADP	IN	_	7	prep	_	_
9	all	all	DET	DT	_	10	det	_	_
10	operations	operation	NOUN	NNS	Number=Plur	8	pobj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
12	also	also	ADV	RB	_	13	advmod	_	_
13	discussed	discuss	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# doc_id = 116
# sent_id = 1
# text = Let $ cal C $ be a full subcategory of the category of topological abelian groups and $ SPcal C $ denote the full subcategory of subobjects of products of objects of $ cal C $ .
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ cal C $	$ cal c $	SYM	$	_	3	nsubj	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	full	full	ADJ	JJ	Degree=Pos	6	amod	_	_
6	subcategory	subcategory	NOUN	NN	Number=Sing	3	attr	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	topological	topological	ADJ	JJ	Degree=Pos	13	amod	_	_
12	abelian	abelian	ADJ	JJ	Degree=Pos	13	compound	_	_
13	groups	group	NOUN	NNS	Number=Plur	10	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
15	$ SPcal C $	$ spcal c $	SYM	$	_	3	dep	_	_
16	denote	denote	VERB	VBD	Tense=Past|VerbForm=Fin	1	ccomp	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	full	full	ADJ	JJ	Degree=Pos	19	amod	_	_
19	subcategory	subcategory	NOUN	NN	Number=Sing	16	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	subobjects	subobject	NOUN	NNS	Number=Plur	20	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	products	product	NOUN	NNS	Number=Plur	22	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	objects	object	NOUN	NNS	Number=Plur	24	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	$ cal C $	$ cal c $	SYM	$	_	26	pobj	_	_
28	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = We say that $ SPcal C $ has Mackey coreflections if there is a functor that assigns to each object $ A $ of $ SPcal C $ an object $ tau A $ that has the same group of characters as $ A $ and is the finest topology with that property.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	say	say	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	$ SPcal C $	$ spcal c $	SYM	$	_	5	nsubj	_	_
5	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	Mackey	Mackey	PROPN	NNP	Number=Sing	7	compound	_	_
7	coreflections	coreflection	NOUN	NNS	Number=Plur	5	dobj	_	_
8	if	if	SCONJ	IN	_	10	mark	_	_
9	there	there	PRON	EX	_	10	expl	_	_
10	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	advcl	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	functor	functor	NOUN	NN	Number=Sing	10	attr	_	_
13	that	that	PRON	WDT	PronType=Rel	14	nsubj	_	_
14	assigns	assign	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	relcl	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	each	each	DET	DT	_	17	det	_	_
17	object	object	NOUN	NN	Number=Sing	15	pobj	_	_
18	$ A $	$ a $	SYM	$	_	14	prep	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	$ SPcal C $	$ spcal c $	SYM	$	_	14	punct	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	object	object	NOUN	NN	Number=Sing	14	dobj	_	_
23	$ tau A $	$ tau a $	SYM	$	_	22	appos	_	_
24	that	that	PRON	WDT	PronType=Rel	25	nsubj	_	_
25	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	relcl	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	same	same	ADJ	JJ	Degree=Pos	28	amod	_	_
28	group	group	NOUN	NN	Number=Sing	25	dobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	characters	character	NOUN	NNS	Number=Plur	29	pobj	_	_
31	as	as	ADP	IN	_	25	prep	_	_
32	$ A $	$ a $	SYM	$	_	31	pobj	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
34	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	conj	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
36	finest	fine	ADJ	JJS	Degree=Sup	37	amod	_	_
37	topology	topology	NOUN	NN	Number=Sing	34	attr	_	_
38	with	with	ADP	IN	_	37	prep	_	_
39	that	that	DET	DT	Number=Sing|PronType=Dem	40	det	_	_
40	property	property	NOUN	NN	Number=Sing	38	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that the existence of Mackey coreflections in $ SPcal C $ is equivalent to the injectivity of the circle with respect to topological subgroups of groups in $ cal C $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	11	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	existence	existence	NOUN	NN	Number=Sing	11	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Mackey	Mackey	PROPN	NNP	Number=Sing	8	compound	_	_
8	coreflections	coreflection	NOUN	NNS	Number=Plur	6	pobj	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	$ SPcal C $	$ spcal c $	SYM	$	_	9	pobj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
12	equivalent	equivalent	ADJ	JJ	Degree=Pos	11	acomp	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	injectivity	injectivity	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	circle	circle	NOUN	NN	Number=Sing	16	pobj	_	_
19	with	with	ADP	IN	_	11	prep	_	_
20	respect	respect	NOUN	NN	Number=Sing	19	pobj	_	_
21	to	to	ADP	IN	_	20	prep	_	_
22	topological	topological	ADJ	JJ	Degree=Pos	23	amod	_	_
23	subgroups	subgroup	NOUN	NNS	Number=Plur	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	groups	group	NOUN	NNS	Number=Plur	24	pobj	_	_
26	in	in	ADP	IN	_	25	prep	_	_
27	$ cal C $	$ cal c $	SYM	$	_	26	pobj	_	_
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 117
# sent_id = 1
# text = The category of finite cardinals (or, equivalently, of finite sets) is the symmetric analogue of the category of finite ordinals, and the ground category of a relevant category of presheaves, the augmented symmetric simplicial sets.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	15	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	finite	finite	ADJ	JJ	Degree=Pos	5	amod	_	_
5	cardinals	cardinal	NOUN	NNS	Number=Plur	3	pobj	_	_
6	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	5	punct	_	SpaceAfter=No
7	or	or	CCONJ	CC	ConjType=Cmp	2	cc	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
9	equivalently	equivalently	ADV	RB	_	2	advmod	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
11	of	of	ADP	IN	_	2	prep	_	_
12	finite	finite	PROPN	NNP	Number=Sing	13	compound	_	_
13	sets	set	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
14	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	2	punct	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	symmetric	symmetric	ADJ	JJ	Degree=Pos	18	amod	_	_
18	analogue	analogue	NOUN	NN	Number=Sing	15	attr	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	category	category	NOUN	NN	Number=Sing	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	finite	finite	ADJ	JJ	Degree=Pos	24	compound	_	_
24	ordinals	ordinal	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	ground	ground	NOUN	NN	Number=Sing	29	compound	_	_
29	category	category	NOUN	NN	Number=Sing	15	conj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
32	relevant	relevant	ADJ	JJ	Degree=Pos	33	amod	_	_
33	category	category	NOUN	NN	Number=Sing	30	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	presheaves	presheave	NOUN	NNS	Number=Plur	34	pobj	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
38	augmented	augment	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	41	amod	_	_
39	symmetric	symmetric	ADJ	JJ	Degree=Pos	41	amod	_	_
40	simplicial	simplicial	ADJ	JJ	Degree=Pos	41	amod	_	_
41	sets	set	NOUN	NNS	Number=Plur	29	appos	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 2
# text = We prove here that this ground category has characterisations similar to the classical ones for the category of finite ordinals, by the existence of a universal symmetric monoid, or by generators and relations.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	here	here	ADV	RB	PronType=Dem	2	advmod	_	_
4	that	that	SCONJ	IN	_	8	mark	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
6	ground	ground	NOUN	NN	Number=Sing	7	compound	_	_
7	category	category	NOUN	NN	Number=Sing	8	nsubj	_	_
8	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
9	characterisations	characterisation	NOUN	NNS	Number=Plur	8	dobj	_	_
10	similar	similar	ADJ	JJ	Degree=Pos	9	amod	_	_
11	to	to	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	classical	classical	ADJ	JJ	Degree=Pos	14	amod	_	_
14	ones	one	NOUN	NNS	Number=Plur	11	pobj	_	_
15	for	for	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	finite	finite	ADJ	JJ	Degree=Pos	20	compound	_	_
20	ordinals	ordinal	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
22	by	by	ADP	IN	_	8	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	existence	existence	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
27	universal	universal	ADJ	JJ	Degree=Pos	29	amod	_	_
28	symmetric	symmetric	ADJ	JJ	Degree=Pos	29	amod	_	_
29	monoid	monoid	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
31	or	or	CCONJ	CC	ConjType=Cmp	22	cc	_	_
32	by	by	ADP	IN	_	22	conj	_	_
33	generators	generator	NOUN	NNS	Number=Plur	32	pobj	_	_
34	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
35	relations	relation	NOUN	NNS	Number=Plur	33	conj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The latter provides a definition of symmetric simplicial sets by faces, degeneracies and transpositions, under suitable relations.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	latter	latter	ADJ	JJ	Degree=Pos	3	nsubj	_	_
3	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	definition	definition	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	symmetric	symmetric	ADJ	JJ	Degree=Pos	9	amod	_	_
8	simplicial	simplicial	ADJ	JJ	Degree=Pos	9	amod	_	_
9	sets	set	NOUN	NNS	Number=Plur	6	pobj	_	_
10	by	by	ADP	IN	_	9	prep	_	_
11	faces	face	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	degeneracies	degeneracy	NOUN	NNS	Number=Plur	11	conj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	transpositions	transposition	NOUN	NNS	Number=Plur	13	conj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
17	under	under	ADP	IN	_	3	prep	_	_
18	suitable	suitable	ADJ	JJ	Degree=Pos	19	amod	_	_
19	relations	relation	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 118
# sent_id = 1
# text = Joyal has introduced the category $ cal D $ of the so - called finite disks, and used it to define the concept of $ theta $ - category, a notion of weak $ omega $ - category.
1	Joyal	Joyal	PROPN	NNP	Number=Sing	3	nsubj	_	_
2	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	aux	_	_
3	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	3	dobj	_	_
6	$ cal D $	$ cal d $	SYM	$	_	5	appos	_	_
7	of	of	ADP	IN	_	5	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
9	so	so	ADV	RB	_	11	advmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
12	finite	finite	NOUN	NN	Number=Sing	13	compound	_	_
13	disks	disk	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
16	used	use	VERB	VBD	Tense=Past|VerbForm=Fin	3	conj	_	_
17	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	16	dobj	_	_
18	to	to	PART	TO	_	19	aux	_	_
19	define	define	VERB	VB	VerbForm=Inf	16	xcomp	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	concept	concept	NOUN	NN	Number=Sing	19	dobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	$ theta $	$ theta $	SYM	$	_	25	compound	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	category	category	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	notion	notion	NOUN	NN	Number=Sing	16	dobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	weak	weak	ADJ	JJ	Degree=Pos	33	amod	_	_
31	$ omega $	$ omega $	SYM	$	_	33	compound	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	category	category	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = We introduce the notion of an $ omega $ - graph being composable (meaning roughly that 'it has a unique composite'), and call an $ omega $ - category simple if it is freely generated by a composable $ omega $ - graph.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
7	$ omega $	$ omega $	SYM	$	_	9	nmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	graph	graph	NOUN	NN	Number=Sing	10	compound	_	_
10	being	be	AUX	VBG	VerbForm=Ger	5	pobj	_	_
11	composable	composable	ADJ	JJ	Degree=Pos	10	acomp	_	_
12	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	13	punct	_	SpaceAfter=No
13	meaning	mean	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	acl	_	_
14	roughly	roughly	ADV	RB	_	18	advmod	_	_
15	that	that	SCONJ	IN	_	18	mark	_	_
16	'	'	PUNCT	``	PunctSide=Ini|PunctType=Quot	18	punct	_	SpaceAfter=No
17	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	18	nsubj	_	_
18	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	unique	unique	ADJ	JJ	Degree=Pos	21	amod	_	_
21	composite	composite	NOUN	NN	Number=Sing	18	dobj	_	SpaceAfter=No
22	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	13	punct	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	13	punct	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
26	call	call	VERB	VB	VerbForm=Inf	13	conj	_	_
27	an	an	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
28	$ omega $	$ omega $	SYM	$	_	30	nmod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	category	category	NOUN	NN	Number=Sing	31	compound	_	_
31	simple	simple	ADJ	JJ	Degree=Pos	26	oprd	_	_
32	if	if	SCONJ	IN	_	36	mark	_	_
33	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	36	nsubjpass	_	_
34	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	36	auxpass	_	_
35	freely	freely	ADV	RB	_	36	advmod	_	_
36	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	advcl	_	_
37	by	by	ADP	IN	_	36	agent	_	_
38	a	a	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
39	composable	composable	ADJ	JJ	Degree=Pos	42	amod	_	_
40	$ omega $	$ omega $	SYM	$	_	42	compound	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	graph	graph	NOUN	NN	Number=Sing	37	pobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The category $ cal S $ of simple $ omega $ - categories is a full subcategory of the category, with strict $ omega $ - functors as morphisms, of all $ omega $ - categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	9	nsubj	_	_
3	$ cal S $	$ cal s $	SYM	$	_	2	appos	_	_
4	of	of	ADP	IN	_	2	prep	_	_
5	simple	simple	ADJ	JJ	Degree=Pos	8	amod	_	_
6	$ omega $	$ omega $	SYM	$	_	8	compound	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	full	full	ADJ	JJ	Degree=Pos	12	amod	_	_
12	subcategory	subcategory	NOUN	NN	Number=Sing	9	attr	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	category	category	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
17	with	with	ADP	IN	_	9	prep	_	_
18	strict	strict	ADJ	JJ	Degree=Pos	21	amod	_	_
19	$ omega $	$ omega $	SYM	$	_	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	functors	functor	NOUN	NNS	Number=Plur	17	pobj	_	_
22	as	as	ADP	IN	_	21	prep	_	_
23	morphisms	morphism	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
25	of	of	ADP	IN	_	21	prep	_	_
26	all	all	DET	DT	_	29	det	_	_
27	$ omega $	$ omega $	SYM	$	_	29	compound	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	categories	category	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 4
# text = The category $ cal S $ is a key ingredient in another concept of weak $ omega $ - category, called protocategory.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	4	nsubj	_	_
3	$ cal S $	$ cal s $	SYM	$	_	2	appos	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	key	key	ADJ	JJ	Degree=Pos	7	amod	_	_
7	ingredient	ingredient	NOUN	NN	Number=Sing	4	attr	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	another	another	DET	DT	_	10	det	_	_
10	concept	concept	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	weak	weak	ADJ	JJ	Degree=Pos	15	amod	_	_
13	$ omega $	$ omega $	SYM	$	_	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	category	category	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
17	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	dep	_	_
18	protocategory	protocategory	NOUN	NN	Number=Sing	17	oprd	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = We prove that $ cal D $ and $ cal S $ are contravariantly equivalent, by a duality induced by a suitable schizophrenic object living in both categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	$ cal D $	$ cal d $	SYM	$	_	7	nsubj	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	$ cal S $	$ cal s $	SYM	$	_	4	conj	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	contravariantly	contravariantly	ADV	RB	_	9	advmod	_	_
9	equivalent	equivalent	ADJ	JJ	Degree=Pos	7	acomp	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
11	by	by	ADP	IN	_	7	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	duality	duality	NOUN	NN	Number=Sing	11	pobj	_	_
14	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	acl	_	_
15	by	by	ADP	IN	_	14	agent	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
17	suitable	suitable	ADJ	JJ	Degree=Pos	19	amod	_	_
18	schizophrenic	schizophrenic	ADJ	JJ	Degree=Pos	19	amod	_	_
19	object	object	NOUN	NN	Number=Sing	15	pobj	_	_
20	living	live	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	acl	_	_
21	in	in	ADP	IN	_	20	prep	_	_
22	both	both	DET	DT	_	23	det	_	_
23	categories	category	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = In one paper, this result is one of the tools used to show that the concept of $ theta $ - category and that of protocategory are equivalent in a suitable sense.
1	In	in	ADP	IN	_	7	prep	_	_
2	one	one	NUM	CD	NumType=Card	3	nummod	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	result	result	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	one	one	NUM	CD	NumType=Card	7	attr	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	tools	tool	NOUN	NNS	Number=Plur	9	pobj	_	_
12	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acl	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	show	show	VERB	VB	VerbForm=Inf	12	xcomp	_	_
15	that	that	SCONJ	IN	_	26	mark	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	concept	concept	NOUN	NN	Number=Sing	26	nsubj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	$ theta $	$ theta $	SYM	$	_	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
23	that	that	PRON	DT	Number=Sing|PronType=Dem	26	nsubj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	protocategory	protocategory	NOUN	NN	Number=Sing	24	pobj	_	_
26	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	ccomp	_	_
27	equivalent	equivalent	ADJ	JJ	Degree=Pos	26	acomp	_	_
28	in	in	ADP	IN	_	27	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	suitable	suitable	ADJ	JJ	Degree=Pos	31	amod	_	_
31	sense	sense	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 7
# text = We also prove that composable $ omega $ - graphs coincide with the $ omega $ - graphs of the form $ T^* $ considered by Batanin, which were characterized by Street and called `globular cardinals'.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	9	mark	_	_
5	composable	composable	ADJ	JJ	Degree=Pos	9	amod	_	_
6	$ omega $	$ omega $	SYM	$	_	8	compound	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	graphs	graph	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	coincide	coincide	NOUN	NN	Number=Sing	3	ccomp	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
12	$ omega $	$ omega $	SYM	$	_	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	graphs	graph	NOUN	NNS	Number=Plur	10	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	form	form	NOUN	NN	Number=Sing	15	pobj	_	_
18	$ T^* $	$ t^* $	SYM	$	_	9	punct	_	_
19	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	acl	_	_
20	by	by	ADP	IN	_	19	agent	_	_
21	Batanin	Batanin	PROPN	NNP	Number=Sing	20	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	which	which	PRON	WDT	_	25	nsubjpass	_	_
24	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	25	auxpass	_	_
25	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	relcl	_	_
26	by	by	ADP	IN	_	25	agent	_	_
27	Street	Street	PROPN	NNP	Number=Sing	26	pobj	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
29	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	25	conj	_	_
30	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	32	punct	_	SpaceAfter=No
31	globular	globular	ADJ	JJ	Degree=Pos	32	amod	_	_
32	cardinals	cardinal	NOUN	NNS	Number=Plur	29	oprd	_	SpaceAfter=No
33	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	3	punct	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 8
# text = Batanin's construction, using globular cardinals, of the free $ omega $ - category on a globular set plays an important role in our paper.
1	Batanin	Batanin	PROPN	NNP	Number=Sing	3	poss	_	SpaceAfter=No
2	's	's	PART	POS	_	1	case	_	_
3	construction	construction	NOUN	NN	Number=Sing	5	nsubj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	csubj	_	_
6	globular	globular	ADJ	JJ	Degree=Pos	7	amod	_	_
7	cardinals	cardinal	NOUN	NNS	Number=Plur	5	dobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
9	of	of	ADP	IN	_	5	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
11	free	free	ADJ	JJ	Degree=Pos	14	amod	_	_
12	$ omega $	$ omega $	SYM	$	_	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
15	on	on	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	globular	globular	ADJ	JJ	Degree=Pos	18	amod	_	_
18	set	set	NOUN	NN	Number=Sing	15	pobj	_	_
19	plays	play	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	an	an	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	important	important	ADJ	JJ	Degree=Pos	22	amod	_	_
22	role	role	NOUN	NN	Number=Sing	19	dobj	_	_
23	in	in	ADP	IN	_	22	prep	_	_
24	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	25	poss	_	_
25	paper	paper	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 9
# text = We give a self - contained presentation of Batanin's construction that suits our purposes.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
4	self	self	NOUN	NN	Number=Sing	6	npadvmod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	contained	contain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
7	presentation	presentation	NOUN	NN	Number=Sing	2	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	Batanin	Batanin	PROPN	NNP	Number=Sing	11	poss	_	SpaceAfter=No
10	's	's	PART	POS	_	9	case	_	_
11	construction	construction	NOUN	NN	Number=Sing	8	pobj	_	_
12	that	that	PRON	WDT	PronType=Rel	13	nsubj	_	_
13	suits	suit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	relcl	_	_
14	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	15	poss	_	_
15	purposes	purpose	NOUN	NNS	Number=Plur	13	dobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 119
# sent_id = 1
# text = There are well - known characterizations of the hereditary quotient maps in the category of topological spaces, (that is, of quotient maps stable under pullback along embeddings), as well as of universal quotient maps (that is, of quotient maps stable under pullback).
1	There	there	PRON	EX	_	2	expl	_	_
2	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	well	well	ADV	RB	Degree=Pos	5	advmod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	amod	_	_
6	characterizations	characterization	NOUN	NNS	Number=Plur	2	attr	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
9	hereditary	hereditary	ADJ	JJ	Degree=Pos	11	amod	_	_
10	quotient	quotient	NOUN	NN	Number=Sing	11	compound	_	_
11	maps	map	NOUN	NNS	Number=Plur	7	pobj	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	topological	topological	ADJ	JJ	Degree=Pos	17	amod	_	_
17	spaces	space	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
19	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	6	punct	_	SpaceAfter=No
20	that	that	ADV	RB	_	21	advmod	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	advmod	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	of	of	ADP	IN	_	6	prep	_	_
24	quotient	quotient	NOUN	NN	Number=Sing	25	compound	_	_
25	maps	map	NOUN	NNS	Number=Plur	23	pobj	_	_
26	stable	stable	ADJ	JJ	Degree=Pos	25	amod	_	_
27	under	under	ADP	IN	_	26	prep	_	_
28	pullback	pullback	NOUN	NN	Number=Sing	27	pobj	_	_
29	along	along	ADP	IN	_	26	prep	_	_
30	embeddings	embedding	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
31	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	25	punct	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
33	as	as	ADV	RB	_	35	advmod	_	_
34	well	well	ADV	RB	Degree=Pos	35	advmod	_	_
35	as	as	ADP	IN	_	2	cc	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	universal	universal	ADJ	JJ	Degree=Pos	39	amod	_	_
38	quotient	quotient	NOUN	NN	Number=Sing	39	compound	_	_
39	maps	map	NOUN	NNS	Number=Plur	36	pobj	_	_
40	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	39	punct	_	SpaceAfter=No
41	that	that	ADV	RB	_	42	advmod	_	_
42	is	is	ADV	RB	_	39	parataxis	_	SpaceAfter=No
43	,	,	PUNCT	,	PunctType=Comm	39	punct	_	_
44	of	of	ADP	IN	_	39	prep	_	_
45	quotient	quotient	NOUN	NN	Number=Sing	46	compound	_	_
46	maps	map	NOUN	NNS	Number=Plur	44	pobj	_	_
47	stable	stable	ADJ	JJ	Degree=Pos	46	amod	_	_
48	under	under	ADP	IN	_	47	prep	_	_
49	pullback	pullback	NOUN	NN	Number=Sing	48	pobj	_	SpaceAfter=No
50	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	39	punct	_	SpaceAfter=No
51	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = These are precisely the so - called pseudo - open maps, as shown by Arhangelskii, and the bi - quotient maps of Michael, as shown by Day and Kelly, respectively.
1	These	these	PRON	DT	Number=Plur|PronType=Dem	2	nsubj	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	precisely	precisely	ADV	RB	_	11	advmod	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
5	so	so	ADV	RB	_	7	advmod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
8	pseudo	pseudo	NOUN	NN	Number=Sing	10	npadvmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	open	open	ADJ	JJ	Degree=Pos	11	amod	_	_
11	maps	map	NOUN	NNS	Number=Plur	2	attr	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
13	as	as	SCONJ	IN	_	14	mark	_	_
14	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	advcl	_	_
15	by	by	ADP	IN	_	14	agent	_	_
16	Arhangelskii	Arhangelskii	PROPN	NNP	Number=Sing	15	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
20	bi	bi	PROPN	NNP	Number=Sing	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	quotient	quotient	ADJ	JJ	Degree=Pos	23	compound	_	_
23	maps	map	NOUN	NNS	Number=Plur	2	conj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	Michael	Michael	PROPN	NNP	Number=Sing	24	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
27	as	as	SCONJ	IN	_	28	mark	_	_
28	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	advcl	_	_
29	by	by	ADP	IN	_	28	agent	_	_
30	Day	Day	PROPN	NNP	Number=Sing	29	pobj	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
32	Kelly	Kelly	PROPN	NNP	Number=Sing	30	conj	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
34	respectively	respectively	ADV	RB	_	23	advmod	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this paper hereditary and stable quotient maps are characterized in the broader context given by a category equipped with a closure operator.
1	In	in	ADP	IN	_	10	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	hereditary	hereditary	ADJ	JJ	Degree=Pos	8	amod	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	stable	stable	ADJ	JJ	Degree=Pos	4	conj	_	_
7	quotient	quotient	NOUN	NN	Number=Sing	8	compound	_	_
8	maps	map	NOUN	NNS	Number=Plur	10	nsubjpass	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	broader	broad	ADJ	JJR	Degree=Cmp	14	amod	_	_
14	context	context	NOUN	NN	Number=Sing	11	pobj	_	_
15	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	acl	_	_
16	by	by	ADP	IN	_	15	agent	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	category	category	NOUN	NN	Number=Sing	16	pobj	_	_
19	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	acl	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	closure	closure	NOUN	NN	Number=Sing	23	compound	_	_
23	operator	operator	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 4
# text = To this end, we derive explicit formulae and conditions for the closure in the codomain of such a quotient map in terms of the closure in its domain.
1	To	to	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	end	end	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	derive	derive	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	explicit	explicit	ADJ	JJ	Degree=Pos	8	amod	_	_
8	formulae	formulae	NOUN	NN	Number=Sing	6	dobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	conditions	condition	NOUN	NNS	Number=Plur	8	conj	_	_
11	for	for	ADP	IN	_	6	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	closure	closure	NOUN	NN	Number=Sing	11	pobj	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	codomain	codomain	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	such	such	DET	PDT	_	21	predet	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	quotient	quotient	NOUN	NN	Number=Sing	21	compound	_	_
21	map	map	NOUN	NN	Number=Sing	17	pobj	_	_
22	in	in	ADP	IN	_	21	prep	_	_
23	terms	term	NOUN	NNS	Number=Plur	22	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	closure	closure	NOUN	NN	Number=Sing	24	pobj	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	29	poss	_	_
29	domain	domain	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 120
# sent_id = 1
# text = Filtered colimits, that is, colimits over schemes $ cal D $ such that $ cal D $ - colimits in $ Set $ commute with finite limits, have a natural generalization to sifted colimits: these are colimits over schemes $ cal D $ such that $ cal D $ - colimits in $ Set $ commute with finite products.
1	Filtered	filter	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	amod	_	_
2	colimits	colimit	NOUN	NNS	Number=Plur	23	nsubj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
4	that	that	ADV	RB	_	5	advmod	_	_
5	is	is	ADV	RB	_	7	advmod	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	colimits	colimit	NOUN	NNS	Number=Plur	2	appos	_	_
8	over	over	ADP	IN	_	7	prep	_	_
9	schemes	scheme	NOUN	NNS	Number=Plur	8	pobj	_	_
10	$ cal D $	$ cal d $	SYM	$	_	11	amod	_	_
11	such	such	ADJ	JJ	Degree=Pos	9	appos	_	_
12	that	that	SCONJ	IN	_	15	det	_	_
13	$ cal D $	$ cal d $	SYM	$	_	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	colimits	colimit	NOUN	NNS	Number=Plur	2	appos	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	$ Set $	$ set $	SYM	$	_	18	nummod	_	_
18	commute	commute	NOUN	NN	Number=Sing	16	pobj	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	finite	finite	ADJ	JJ	Degree=Pos	21	compound	_	_
21	limits	limit	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
23	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	32	ccomp	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
25	natural	natural	ADJ	JJ	Degree=Pos	26	amod	_	_
26	generalization	generalization	NOUN	NN	Number=Sing	23	dobj	_	_
27	to	to	ADP	IN	_	26	prep	_	_
28	sifted	sifted	ADJ	JJ	Degree=Pos	29	amod	_	_
29	colimits	colimit	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	:	:	PUNCT	:	_	32	punct	_	_
31	these	these	PRON	DT	Number=Plur|PronType=Dem	32	nsubj	_	_
32	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
33	colimits	colimit	NOUN	NNS	Number=Plur	32	attr	_	_
34	over	over	ADP	IN	_	33	prep	_	_
35	schemes	scheme	NOUN	NNS	Number=Plur	34	pobj	_	_
36	$ cal D $	$ cal d $	SYM	$	_	37	amod	_	_
37	such	such	ADJ	JJ	Degree=Pos	35	appos	_	_
38	that	that	SCONJ	IN	_	41	det	_	_
39	$ cal D $	$ cal d $	SYM	$	_	41	compound	_	_
40	-	-	PUNCT	HYPH	PunctType=Dash	41	punct	_	_
41	colimits	colimit	NOUN	NNS	Number=Plur	32	dep	_	_
42	in	in	ADP	IN	_	41	prep	_	_
43	$ Set $	$ set $	SYM	$	_	44	nummod	_	_
44	commute	commute	NOUN	NN	Number=Sing	42	pobj	_	_
45	with	with	ADP	IN	_	44	prep	_	_
46	finite	finite	ADJ	JJ	Degree=Pos	47	amod	_	_
47	products	product	NOUN	NNS	Number=Plur	45	pobj	_	SpaceAfter=No
48	.	.	PUNCT	.	PunctType=Peri	32	punct	_	SpaceAfter=No

# sent_id = 2
# text = An important example: reflexive coequalizers are sifted colimits.
1	An	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	important	important	ADJ	JJ	Degree=Pos	3	amod	_	_
3	example	example	NOUN	NN	Number=Sing	0	ROOT	_	SpaceAfter=No
4	:	:	PUNCT	:	_	8	punct	_	_
5	reflexive	reflexive	ADJ	JJ	Degree=Pos	6	amod	_	_
6	coequalizers	coequalizer	NOUN	NNS	Number=Plur	7	nsubj	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	sifted	sift	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	amod	_	_
9	colimits	colimit	NOUN	NNS	Number=Plur	3	appos	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Generalized varieties are defined as free completions of small categories under sifted - colimits (analogously to finitely accessible categories which are free filtered - colimit completions of small categories).
1	Generalized	generalized	ADJ	JJ	Degree=Pos	2	amod	_	_
2	varieties	variety	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	as	as	ADP	IN	_	4	prep	_	_
6	free	free	ADJ	JJ	Degree=Pos	7	amod	_	_
7	completions	completion	NOUN	NNS	Number=Plur	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	small	small	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	_
11	under	under	ADP	IN	_	7	prep	_	_
12	sifted	sift	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	colimits	colimit	NOUN	NNS	Number=Plur	11	pobj	_	_
15	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
16	analogously	analogously	ADV	RB	_	14	advmod	_	_
17	to	to	PART	TO	_	14	prep	_	_
18	finitely	finitely	ADV	RB	_	19	advmod	_	_
19	accessible	accessible	ADJ	JJ	Degree=Pos	20	amod	_	_
20	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	_
21	which	which	PRON	WDT	_	22	nsubj	_	_
22	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	20	relcl	_	_
23	free	free	ADJ	JJ	Degree=Pos	27	amod	_	_
24	filtered	filter	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	colimit	colimit	NOUN	NN	Number=Sing	27	compound	_	_
27	completions	completion	NOUN	NNS	Number=Plur	22	attr	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	small	small	ADJ	JJ	Degree=Pos	30	amod	_	_
30	categories	category	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
31	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	20	punct	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = Among complete categories, generalized varieties are precisely the varieties.
1	Among	among	ADP	IN	_	7	prep	_	_
2	complete	complete	ADJ	JJ	Degree=Pos	3	amod	_	_
3	categories	category	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
5	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	amod	_	_
6	varieties	variety	NOUN	NNS	Number=Plur	7	nsubj	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	precisely	precisely	ADV	RB	_	7	advmod	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	varieties	variety	NOUN	NNS	Number=Plur	7	attr	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 5
# text = Further examples: category of fields, category of linearly ordered sets, category of nonempty sets.
1	Further	further	ADJ	JJ	Degree=Pos	2	amod	_	_
2	examples	example	NOUN	NNS	Number=Plur	0	ROOT	_	SpaceAfter=No
3	:	:	PUNCT	:	_	2	punct	_	_
4	category	category	NOUN	NN	Number=Sing	2	appos	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	fields	field	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
8	category	category	NOUN	NN	Number=Sing	4	appos	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	linearly	linearly	ADV	RB	_	11	advmod	_	_
11	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
12	sets	set	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
14	category	category	NOUN	NN	Number=Sing	4	appos	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	nonempty	nonempty	ADJ	JJ	Degree=Pos	17	amod	_	_
17	sets	set	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 121
# sent_id = 1
# text = In this paper, we consider those morphisms $ p : Pto B $ of posets for which the induced geometric morphism of presheaf toposes is exponentiable in the category of Grothendieck toposes.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	those	those	DET	DT	Number=Plur|PronType=Dem	8	det	_	_
8	morphisms	morphism	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	$ p : Pto B $	$ p : pto b $	SYM	$	_	28	nsubj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	posets	poset	NOUN	NNS	Number=Plur	10	pobj	_	_
12	for	for	ADP	IN	_	21	prep	_	_
13	which	which	PRON	WDT	_	12	pobj	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
15	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
16	geometric	geometric	ADJ	JJ	Degree=Pos	17	amod	_	_
17	morphism	morphism	NOUN	NN	Number=Sing	21	nsubj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	presheaf	presheaf	ADJ	JJ	Degree=Pos	20	compound	_	_
20	toposes	topos	NOUN	NNS	Number=Plur	18	pobj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	relcl	_	_
22	exponentiable	exponentiable	ADJ	JJ	Degree=Pos	21	acomp	_	_
23	in	in	ADP	IN	_	21	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	category	category	NOUN	NN	Number=Sing	23	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	26	pobj	_	_
28	toposes	topos	NOUN	NNS	Number=Plur	6	ccomp	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = In particular, we show that a necessary condition is that the induced map $ p^{downarrow} : P^{downarrow}to B^{downarrow} $ is exponentiable in the category of topological spaces, where $ P^{downarrow} $ is the space whose points are elements of $ P $ and open sets are downward closed subsets of $ P $ .
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	10	mark	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	necessary	necessary	ADJ	JJ	Degree=Pos	9	amod	_	_
9	condition	condition	NOUN	NN	Number=Sing	10	nsubj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
11	that	that	SCONJ	IN	_	16	mark	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
14	map	map	NOUN	NN	Number=Sing	16	nsubj	_	_
15	$ p^{downarrow} : P^{downarrow}to B^{downarrow} $	$ p^{downarrow} : p^{downarrow}to b^{downarrow} $	SYM	$	_	16	nsubj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	ccomp	_	_
17	exponentiable	exponentiable	ADJ	JJ	Degree=Pos	16	acomp	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	topological	topological	ADJ	JJ	Degree=Pos	23	amod	_	_
23	spaces	space	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
25	where	where	SCONJ	WRB	_	27	advmod	_	_
26	$ P^{downarrow} $	$ p^{downarrow} $	SYM	$	_	27	nsubj	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	relcl	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	space	space	NOUN	NN	Number=Sing	27	attr	_	_
30	whose	whose	DET	WP$	Poss=Yes	31	poss	_	_
31	points	point	NOUN	NNS	Number=Plur	32	nsubj	_	_
32	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	29	relcl	_	_
33	elements	element	NOUN	NNS	Number=Plur	32	attr	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	$ P $	$ p $	SYM	$	_	34	pobj	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
37	open	open	ADJ	JJ	Degree=Pos	38	amod	_	_
38	sets	set	NOUN	NNS	Number=Plur	39	nsubj	_	_
39	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	16	conj	_	_
40	downward	downward	ADV	RB	_	42	amod	_	_
41	closed	closed	ADJ	JJ	Degree=Pos	42	amod	_	_
42	subsets	subset	NOUN	NNS	Number=Plur	39	attr	_	_
43	of	of	ADP	IN	_	42	prep	_	_
44	$ P $	$ p $	SYM	$	_	43	pobj	_	_
45	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = Along the way, we show that $ p^{downarrow} : P^{downarrow}to B^{downarrow} $ is exponentiable if and only if $ p : Pto B $ is exponentiable in the category of posets and satisfies an additional compactness condition.
1	Along	along	ADP	IN	_	6	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	way	way	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	9	mark	_	_
8	$ p^{downarrow} : P^{downarrow}to B^{downarrow} $	$ p^{downarrow} : p^{downarrow}to b^{downarrow} $	SYM	$	_	9	nsubj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
10	exponentiable	exponentiable	ADJ	JJ	Degree=Pos	9	acomp	_	_
11	if	if	SCONJ	IN	_	16	mark	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
13	only	only	ADV	RB	_	16	advmod	_	_
14	if	if	SCONJ	IN	_	16	mark	_	_
15	$ p : Pto B $	$ p : pto b $	SYM	$	_	16	nsubj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	advcl	_	_
17	exponentiable	exponentiable	ADJ	JJ	Degree=Pos	16	acomp	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	posets	poset	NOUN	NNS	Number=Plur	21	pobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
24	satisfies	satisfie	NOUN	NNS	Number=Plur	20	conj	_	_
25	an	an	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
26	additional	additional	ADJ	JJ	Degree=Pos	28	amod	_	_
27	compactness	compactness	ADJ	JJ	Degree=Pos	28	amod	_	_
28	condition	condition	NOUN	NN	Number=Sing	24	dobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = The criteria for exponentiability of morphisms of posets is related to (but weaker than) the factorization - lifting property for exponentiability of morphisms in the category of small categories (considered independently by Giraud and Conduché).
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	criteria	criterion	NOUN	NNS	Number=Plur	10	nsubjpass	_	_
3	for	for	ADP	IN	_	2	prep	_	_
4	exponentiability	exponentiability	NOUN	NN	Number=Sing	3	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	morphisms	morphism	NOUN	NNS	Number=Plur	5	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	posets	poset	NOUN	NNS	Number=Plur	7	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	to	to	ADP	IN	_	10	prep	_	_
12	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	11	punct	_	SpaceAfter=No
13	but	but	CCONJ	CC	ConjType=Cmp	11	cc	_	_
14	weaker	weak	ADJ	JJR	Degree=Cmp	21	amod	_	_
15	than	than	ADP	IN	_	14	prep	_	SpaceAfter=No
16	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	15	punct	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
18	factorization	factorization	NOUN	NN	Number=Sing	20	npadvmod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	lifting	lift	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	21	amod	_	_
21	property	property	NOUN	NN	Number=Sing	11	pobj	_	_
22	for	for	ADP	IN	_	21	prep	_	_
23	exponentiability	exponentiability	NOUN	NN	Number=Sing	22	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	morphisms	morphism	NOUN	NNS	Number=Plur	24	pobj	_	_
26	in	in	ADP	IN	_	21	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	category	category	NOUN	NN	Number=Sing	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	small	small	ADJ	JJ	Degree=Pos	31	amod	_	_
31	categories	category	NOUN	NNS	Number=Plur	29	pobj	_	_
32	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	31	punct	_	SpaceAfter=No
33	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	acl	_	_
34	independently	independently	ADV	RB	_	33	advmod	_	_
35	by	by	ADP	IN	_	33	agent	_	_
36	Giraud	Giraud	PROPN	NNP	Number=Sing	35	pobj	_	_
37	and	and	CCONJ	CC	ConjType=Cmp	36	cc	_	_
38	Conduché	Conduché	PROPN	NNP	Number=Sing	36	conj	_	SpaceAfter=No
39	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	21	punct	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# doc_id = 122
# sent_id = 1
# text = We characterize $ n $ - permutable locally finitely presentable categories $ Lex[{mathcal C}^{op}, Set] $ by a condition on the dual of the essentially algebraic theory $ mathcal C^{op} $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	$ n $	$ n $	SYM	$	_	5	advmod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	permutable	permutable	ADJ	JJ	Degree=Pos	9	amod	_	_
6	locally	locally	ADV	RB	_	7	advmod	_	_
7	finitely	finitely	ADV	RB	_	9	amod	_	_
8	presentable	presentable	ADJ	JJ	Degree=Pos	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	2	dobj	_	_
10	$ Lex[{mathcal C}^{op}, Set] $	$ lex[{mathcal c}^{op}, set] $	SYM	$	_	11	dep	_	_
11	by	by	ADP	IN	_	2	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	condition	condition	NOUN	NN	Number=Sing	11	pobj	_	_
14	on	on	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	dual	dual	ADJ	JJ	Degree=Pos	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
19	essentially	essentially	ADV	RB	_	20	advmod	_	_
20	algebraic	algebraic	ADJ	JJ	Degree=Pos	21	amod	_	_
21	theory	theory	NOUN	NN	Number=Sing	17	pobj	_	_
22	$ mathcal C^{op} $	$ mathcal c^{op} $	SYM	$	_	21	appos	_	_
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We apply these results to exact Maltsev categories as well as to $ n $ - permutable quasivarieties and varieties.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	apply	apply	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	these	these	DET	DT	Number=Plur|PronType=Dem	4	det	_	_
4	results	result	NOUN	NNS	Number=Plur	2	dobj	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	exact	exact	VERB	VB	VerbForm=Inf	2	advcl	_	_
7	Maltsev	Maltsev	PROPN	NNP	Number=Sing	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	6	dobj	_	_
9	as	as	ADV	RB	_	11	advmod	_	_
10	well	well	ADV	RB	Degree=Pos	11	advmod	_	_
11	as	as	ADP	IN	_	6	cc	_	_
12	to	to	ADP	IN	_	6	prep	_	_
13	$ n $	$ n $	SYM	$	_	15	advmod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	permutable	permutable	ADJ	JJ	Degree=Pos	16	amod	_	_
16	quasivarieties	quasivarietie	NOUN	NNS	Number=Plur	12	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	varieties	variety	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 123
# sent_id = 1
# text = To a bicategory $ B $ (in the sense of Bénabou) we assign a simplicial set $ Ner(B) $ , the (geometric) nerve of $ B $ , which completely encodes the structure of $ B $ as a bicategory.
1	To	to	ADP	IN	_	13	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	bicategory	bicategory	NOUN	NN	Number=Sing	1	pobj	_	_
4	$ B $	$ b $	SYM	$	_	3	prep	_	_
5	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	13	punct	_	SpaceAfter=No
6	in	in	ADP	IN	_	13	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	sense	sense	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Bénabou	Bénabou	PROPN	NNP	Number=Sing	9	pobj	_	SpaceAfter=No
11	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	13	punct	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	assign	assign	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	simplicial	simplicial	NOUN	NN	Number=Sing	13	dobj	_	_
16	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
17	$ Ner(B) $	$ ner(b) $	SYM	$	_	13	dep	_	_
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
20	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	23	punct	_	SpaceAfter=No
21	geometric	geometric	ADJ	JJ	Degree=Pos	23	amod	_	SpaceAfter=No
22	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	23	punct	_	_
23	nerve	nerve	NOUN	NN	Number=Sing	17	conj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	$ B $	$ b $	SYM	$	_	24	pobj	_	_
26	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
27	which	which	PRON	WDT	_	29	nsubj	_	_
28	completely	completely	ADV	RB	_	29	advmod	_	_
29	encodes	encode	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	relcl	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	structure	structure	NOUN	NN	Number=Sing	29	dobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	$ B $	$ b $	SYM	$	_	32	pobj	_	_
34	as	as	ADP	IN	_	29	prep	_	_
35	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
36	bicategory	bicategory	NOUN	NN	Number=Sing	34	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 2
# text = As a simplicial set $ Ner(B) $ is a subcomplex of its 2 - Coskeleton and itself isomorphic to its 3 - Coskeleton, what we call a 2 - dimensional Postnikov complex.
1	As	as	SCONJ	IN	_	6	mark	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	simplicial	simplicial	NOUN	NN	Number=Sing	6	nsubj	_	_
4	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	acl	_	_
5	$ Ner(B) $	$ ner(b) $	SYM	$	_	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	subcomplex	subcomplex	NOUN	NN	Number=Sing	6	attr	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	13	poss	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	Coskeleton	Coskeleton	PROPN	NNP	Number=Sing	9	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	itself	itself	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs|Reflex=Yes	13	conj	_	_
16	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	6	acomp	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	21	poss	_	_
19	3	3	NUM	CD	NumType=Card	21	nummod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	Coskeleton	Coskeleton	PROPN	NNP	Number=Sing	17	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	what	what	PRON	WP	_	25	dobj	_	_
24	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	25	nsubj	_	_
25	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	6	ccomp	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
27	2	2	NUM	CD	NumType=Card	29	npadvmod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	dimensional	dimensional	ADJ	JJ	Degree=Pos	31	amod	_	_
30	Postnikov	postnikov	ADJ	JJ	Degree=Pos	31	compound	_	_
31	complex	complex	NOUN	NN	Number=Sing	25	oprd	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = We then give, somewhat more delicately, a complete characterization of those simplicial sets which are the nerves of bicategories as certain 2 - dimensional Postnikov complexes which satisfy certain restricted `exact horn - lifting' conditions whose satisfaction is controlled by (and here defines) subsets of (abstractly) invertible 2 and 1 - simplices.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	somewhat	somewhat	ADV	RB	_	6	advmod	_	_
6	more	more	ADV	RBR	Degree=Cmp	7	advmod	_	_
7	delicately	delicately	ADV	RB	_	3	advmod	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	complete	complete	ADJ	JJ	Degree=Pos	11	amod	_	_
11	characterization	characterization	NOUN	NN	Number=Sing	3	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	those	those	DET	DT	Number=Plur|PronType=Dem	15	det	_	_
14	simplicial	simplicial	ADJ	JJ	Degree=Pos	15	amod	_	_
15	sets	set	NOUN	NNS	Number=Plur	12	pobj	_	_
16	which	which	PRON	WDT	_	17	nsubj	_	_
17	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	relcl	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	nerves	nerve	NOUN	NNS	Number=Plur	17	attr	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	bicategories	bicategorie	NOUN	NNS	Number=Plur	20	pobj	_	_
22	as	as	ADP	IN	_	17	prep	_	_
23	certain	certain	ADJ	JJ	Degree=Pos	28	amod	_	_
24	2	2	NUM	CD	NumType=Card	26	advmod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	dimensional	dimensional	ADJ	JJ	Degree=Pos	28	amod	_	_
27	Postnikov	Postnikov	PROPN	NNP	Number=Sing	28	compound	_	_
28	complexes	complex	NOUN	NNS	Number=Plur	22	pobj	_	_
29	which	which	PRON	WDT	_	30	nsubj	_	_
30	satisfy	satisfy	VERB	VBP	Tense=Pres|VerbForm=Fin	28	relcl	_	_
31	certain	certain	ADJ	JJ	Degree=Pos	37	amod	_	_
32	restricted	restrict	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	37	amod	_	_
33	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	37	punct	_	SpaceAfter=No
34	exact	exact	ADJ	JJ	Degree=Pos	37	amod	_	_
35	horn	horn	NOUN	NN	Number=Sing	37	compound	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	lifting	lift	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	39	poss	_	SpaceAfter=No
38	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	37	case	_	_
39	conditions	condition	NOUN	NNS	Number=Plur	30	dobj	_	_
40	whose	whose	DET	WP$	Poss=Yes	41	poss	_	_
41	satisfaction	satisfaction	NOUN	NN	Number=Sing	43	nsubjpass	_	_
42	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	43	auxpass	_	_
43	controlled	control	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	39	relcl	_	_
44	by	by	ADP	IN	_	43	agent	_	_
45	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	44	punct	_	SpaceAfter=No
46	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
47	here	here	ADV	RB	PronType=Dem	48	advmod	_	_
48	defines	define	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	28	conj	_	SpaceAfter=No
49	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	48	punct	_	_
50	subsets	subset	NOUN	NNS	Number=Plur	48	nsubj	_	_
51	of	of	ADP	IN	_	50	prep	_	_
52	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	51	punct	_	SpaceAfter=No
53	abstractly	abstractly	ADV	RB	_	51	pcomp	_	SpaceAfter=No
54	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	51	punct	_	_
55	invertible	invertible	ADJ	JJ	Degree=Pos	60	amod	_	_
56	2	2	NUM	CD	NumType=Card	60	nummod	_	_
57	and	and	CCONJ	CC	ConjType=Cmp	56	cc	_	_
58	1	1	NUM	CD	NumType=Card	56	conj	_	_
59	-	-	PUNCT	HYPH	PunctType=Dash	60	punct	_	_
60	simplices	simplice	NOUN	NNS	Number=Plur	51	pobj	_	SpaceAfter=No
61	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = Those complexes which have, at minimum, their degenerate 2 - simplices always invertible and have an invertible 2 - simplex $ chi_2^1(x_{12}, x_{01}) $ present for each `composable pair' $ (x_{12}, _ , x_{01}) in mhorn_2^1 $ are exactly the nerves of bicategories.
1	Those	those	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	complexes	complex	NOUN	NNS	Number=Plur	15	nsubj	_	_
3	which	which	PRON	WDT	_	4	nsubj	_	_
4	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	aux	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
6	at	at	ADP	IN	_	15	prep	_	_
7	minimum	minimum	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
9	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	13	poss	_	_
10	degenerate	degenerate	ADJ	JJ	Degree=Pos	13	amod	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	simplices	simplice	NOUN	NNS	Number=Plur	15	nsubj	_	_
14	always	always	ADV	RB	_	15	advmod	_	_
15	invertible	invertible	ADJ	JJ	Degree=Pos	0	ROOT	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	conj	_	_
18	an	an	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
19	invertible	invertible	ADJ	JJ	Degree=Pos	24	amod	_	_
20	2	2	NUM	CD	NumType=Card	22	nummod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	simplex	simplex	NOUN	NN	Number=Sing	24	nmod	_	_
23	$ chi_2^1(x_{12}, x_{01}) $	$ chi_2^1(x_{12}, x_{01}) $	PROPN	NNP	Number=Sing	24	nmod	_	_
24	present	present	ADJ	JJ	Degree=Pos	17	dobj	_	_
25	for	for	ADP	IN	_	24	prep	_	_
26	each	each	DET	DT	_	29	det	_	_
27	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	29	punct	_	SpaceAfter=No
28	composable	composable	ADJ	JJ	Degree=Pos	29	amod	_	_
29	pair	pair	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
30	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	29	punct	_	_
31	$ (x_{12}, _ , x_{01}) in mhorn_2^1 $	$ (x_{12}, _ , x_{01}) in mhorn_2^1 $	SYM	$	_	29	appos	_	_
32	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	conj	_	_
33	exactly	exactly	ADV	RB	_	35	advmod	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	nerves	nerve	NOUN	NNS	Number=Plur	32	attr	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	bicategories	bicategorie	NOUN	NNS	Number=Plur	36	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 5
# text = At the other extreme, where all 2 and 1 - simplices are invertible, are those Kan complexes in which the Kan conditions are satisfied exactly in all dimensions $ >2 $ .
1	At	at	ADP	IN	_	16	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	other	other	ADJ	JJ	Degree=Pos	4	amod	_	_
4	extreme	extreme	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
6	where	where	SCONJ	WRB	_	13	advmod	_	_
7	all	all	DET	DT	_	12	det	_	_
8	2	2	NUM	CD	NumType=Card	12	nummod	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	1	1	NUM	CD	NumType=Card	8	conj	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	simplices	simplice	NOUN	NNS	Number=Plur	13	nsubj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	relcl	_	_
14	invertible	invertible	ADJ	JJ	Degree=Pos	13	acomp	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
16	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
17	those	those	DET	DT	Number=Plur|PronType=Dem	19	det	_	_
18	Kan	Kan	PROPN	NNP	Number=Sing	19	compound	_	_
19	complexes	complex	NOUN	NNS	Number=Plur	16	attr	_	_
20	in	in	ADP	IN	_	25	prep	_	_
21	which	which	PRON	WDT	_	20	pobj	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	Kan	Kan	PROPN	NNP	Number=Sing	24	compound	_	_
24	conditions	condition	NOUN	NNS	Number=Plur	25	nsubj	_	_
25	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	19	relcl	_	_
26	satisfied	satisfied	ADJ	JJ	Degree=Pos	25	acomp	_	_
27	exactly	exactly	ADV	RB	_	28	advmod	_	_
28	in	in	ADP	IN	_	26	prep	_	_
29	all	all	DET	DT	_	30	det	_	_
30	dimensions	dimension	NOUN	NNS	Number=Plur	28	pobj	_	_
31	$ >2 $	$ >2 $	SYM	$	_	30	appos	_	_
32	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 6
# text = These are exactly the nerves of bigroupoids - all 2 - cells are isomorphisms and all 1 - cells are equivalences.
1	These	these	PRON	DT	Number=Plur|PronType=Dem	2	nsubj	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	exactly	exactly	ADV	RB	_	5	advmod	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	nerves	nerve	NOUN	NNS	Number=Plur	2	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	bigroupoids	bigroupoid	NOUN	NNS	Number=Plur	6	pobj	_	_
8	-	-	PUNCT	,	PunctType=Comm	5	punct	_	_
9	all	all	DET	DT	_	12	det	_	_
10	2	2	NUM	CD	NumType=Card	12	nummod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	cells	cell	NOUN	NNS	Number=Plur	13	nsubj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	relcl	_	_
14	isomorphisms	isomorphism	NOUN	NNS	Number=Plur	13	attr	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	all	all	DET	DT	_	19	det	_	_
17	1	1	NUM	CD	NumType=Card	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	cells	cell	NOUN	NNS	Number=Plur	20	nsubj	_	_
20	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	relcl	_	_
21	equivalences	equivalence	NOUN	NNS	Number=Plur	20	attr	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 124
# sent_id = 1
# text = The alternation hierarchy problem asks whether every $ mu $ - term $ phi $ , that is, a term built up also using a least fixed point constructor as well as a greatest fixed point constructor, is equivalent to a $ mu $ - term where the number of nested fixed points of a different type is bounded by a constant independent of $ phi $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	alternation	alternation	NOUN	NN	Number=Sing	3	compound	_	_
3	hierarchy	hierarchy	NOUN	NN	Number=Sing	4	compound	_	_
4	problem	problem	NOUN	NN	Number=Sing	5	nsubj	_	_
5	asks	ask	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	whether	whether	SCONJ	IN	_	36	mark	_	_
7	every	every	DET	DT	_	10	det	_	_
8	$ mu $	$ mu $	SYM	$	_	10	amod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	term	term	NOUN	NN	Number=Sing	36	nsubj	_	_
11	$ phi $	$ phi $	SYM	$	_	10	appos	_	_
12	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
13	that	that	ADV	RB	_	14	advmod	_	_
14	is	is	ADV	RB	_	36	advmod	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	term	term	NOUN	NN	Number=Sing	36	nsubj	_	_
18	built	build	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
19	up	up	ADP	RP	_	18	prt	_	_
20	also	also	ADV	RB	_	21	advmod	_	_
21	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	18	advcl	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
23	least	least	ADJ	JJS	Degree=Sup	24	advmod	_	_
24	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	amod	_	_
25	point	point	NOUN	NN	Number=Sing	26	compound	_	_
26	constructor	constructor	NOUN	NN	Number=Sing	21	dobj	_	_
27	as	as	ADV	RB	_	29	advmod	_	_
28	well	well	ADV	RB	Degree=Pos	29	advmod	_	_
29	as	as	ADP	IN	_	26	cc	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
31	greatest	great	ADJ	JJS	Degree=Sup	34	amod	_	_
32	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	amod	_	_
33	point	point	NOUN	NN	Number=Sing	34	compound	_	_
34	constructor	constructor	NOUN	NN	Number=Sing	26	conj	_	SpaceAfter=No
35	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
36	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
37	equivalent	equivalent	ADJ	JJ	Degree=Pos	36	acomp	_	_
38	to	to	ADP	IN	_	37	prep	_	_
39	a	a	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
40	$ mu $	$ mu $	SYM	$	_	42	amod	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	term	term	NOUN	NN	Number=Sing	38	pobj	_	_
43	where	where	SCONJ	WRB	_	55	advmod	_	_
44	the	the	DET	DT	Definite=Def|PronType=Art	45	det	_	_
45	number	number	NOUN	NN	Number=Sing	55	nsubjpass	_	_
46	of	of	ADP	IN	_	45	prep	_	_
47	nested	nested	ADJ	JJ	Degree=Pos	49	amod	_	_
48	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	49	amod	_	_
49	points	point	NOUN	NNS	Number=Plur	46	pobj	_	_
50	of	of	ADP	IN	_	49	prep	_	_
51	a	a	DET	DT	Definite=Ind|PronType=Art	53	det	_	_
52	different	different	ADJ	JJ	Degree=Pos	53	amod	_	_
53	type	type	NOUN	NN	Number=Sing	50	pobj	_	_
54	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	55	auxpass	_	_
55	bounded	bound	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	42	relcl	_	_
56	by	by	ADP	IN	_	55	agent	_	_
57	a	a	DET	DT	Definite=Ind|PronType=Art	59	det	_	_
58	constant	constant	ADJ	JJ	Degree=Pos	59	amod	_	_
59	independent	independent	NOUN	NN	Number=Sing	56	pobj	_	_
60	of	of	ADP	IN	_	59	prep	_	_
61	$ phi $	$ phi $	SYM	$	_	60	pobj	_	_
62	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper we give a proof that the alternation hierarchy for the theory of $ mu $ - lattices is strict, meaning that such a constant does not exist if $ mu $ - terms are built up from the basic lattice operations and are interpreted as expected.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	proof	proof	NOUN	NN	Number=Sing	5	dobj	_	_
8	that	that	SCONJ	IN	_	19	mark	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	alternation	alternation	NOUN	NN	Number=Sing	11	compound	_	_
11	hierarchy	hierarchy	NOUN	NN	Number=Sing	19	nsubj	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	theory	theory	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	$ mu $	$ mu $	SYM	$	_	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	lattices	lattice	NOUN	NNS	Number=Plur	15	pobj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	acl	_	_
20	strict	strict	ADJ	JJ	Degree=Pos	19	acomp	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
22	meaning	mean	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	advcl	_	_
23	that	that	SCONJ	IN	_	29	mark	_	_
24	such	such	DET	PDT	_	26	predet	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
26	constant	constant	ADJ	JJ	Degree=Pos	29	nsubj	_	_
27	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	aux	_	_
28	not	not	PART	RB	Polarity=Neg	29	neg	_	_
29	exist	exist	VERB	VB	VerbForm=Inf	22	ccomp	_	_
30	if	if	SCONJ	IN	_	35	mark	_	_
31	$ mu $	$ mu $	SYM	$	_	33	nmod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	terms	term	NOUN	NNS	Number=Plur	35	nsubjpass	_	_
34	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	35	auxpass	_	_
35	built	build	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	advcl	_	_
36	up	up	ADP	RP	_	35	prt	_	_
37	from	from	ADP	IN	_	35	prep	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
39	basic	basic	ADJ	JJ	Degree=Pos	41	amod	_	_
40	lattice	lattice	NOUN	NN	Number=Sing	41	compound	_	_
41	operations	operation	NOUN	NNS	Number=Plur	37	pobj	_	_
42	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
43	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	44	auxpass	_	_
44	interpreted	interpret	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	35	conj	_	_
45	as	as	SCONJ	IN	_	46	mark	_	_
46	expected	expect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	44	advcl	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = The proof relies on the explicit characterization of free $ mu $ - lattices by means of games and strategies.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	proof	proof	NOUN	NN	Number=Sing	3	nsubj	_	_
3	relies	rely	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	on	on	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	explicit	explicit	ADJ	JJ	Degree=Pos	7	amod	_	_
7	characterization	characterization	NOUN	NN	Number=Sing	4	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	free	free	ADJ	JJ	Degree=Pos	12	amod	_	_
10	$ mu $	$ mu $	SYM	$	_	12	nmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	lattices	lattice	NOUN	NNS	Number=Plur	8	pobj	_	_
13	by	by	ADP	IN	_	3	prep	_	_
14	means	mean	NOUN	NNS	Number=Plur	13	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	games	game	NOUN	NNS	Number=Plur	15	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	strategies	strategy	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 125
# sent_id = 1
# text = We analyse the classical property of centrality of equivalence relations in terms of normal monomorphisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	analyse	analyse	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	classical	classical	ADJ	JJ	Degree=Pos	5	amod	_	_
5	property	property	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	centrality	centrality	NOUN	NN	Number=Sing	6	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	equivalence	equivalence	NOUN	NN	Number=Sing	10	compound	_	_
10	relations	relation	NOUN	NNS	Number=Plur	8	pobj	_	_
11	in	in	ADP	IN	_	5	prep	_	_
12	terms	term	NOUN	NNS	Number=Plur	11	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	normal	normal	ADJ	JJ	Degree=Pos	15	amod	_	_
15	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = For this purpose, the internal structure of connector is introduced, allowing to clarify classical results in Maltsev categories and to prove new ones in protomodular categories.
1	For	for	ADP	IN	_	11	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	purpose	purpose	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	internal	internal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	structure	structure	NOUN	NN	Number=Sing	11	nsubjpass	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	connector	connector	NOUN	NN	Number=Sing	8	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	allowing	allow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	advcl	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	clarify	clarify	VERB	VB	VerbForm=Inf	13	xcomp	_	_
16	classical	classical	ADJ	JJ	Degree=Pos	17	amod	_	_
17	results	result	NOUN	NNS	Number=Plur	15	dobj	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	Maltsev	Maltsev	PROPN	NNP	Number=Sing	20	amod	_	_
20	categories	category	NOUN	NNS	Number=Plur	18	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
22	to	to	PART	TO	_	23	aux	_	_
23	prove	prove	VERB	VB	VerbForm=Inf	15	conj	_	_
24	new	new	ADJ	JJ	Degree=Pos	25	amod	_	_
25	ones	one	NOUN	NNS	Number=Plur	23	dobj	_	_
26	in	in	ADP	IN	_	25	prep	_	_
27	protomodular	protomodular	ADJ	JJ	Degree=Pos	28	amod	_	_
28	categories	category	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 3
# text = This approach allows to work in the general context of finitely complete categories, without requiring the usual Barr exactness assumption.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	approach	approach	NOUN	NN	Number=Sing	3	nsubj	_	_
3	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	work	work	VERB	VB	VerbForm=Inf	3	xcomp	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	general	general	ADJ	JJ	Degree=Pos	9	amod	_	_
9	context	context	NOUN	NN	Number=Sing	6	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	finitely	finitely	ADV	RB	_	12	advmod	_	_
12	complete	complete	ADJ	JJ	Degree=Pos	13	amod	_	_
13	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
15	without	without	ADP	IN	_	5	prep	_	_
16	requiring	require	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	pcomp	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
18	usual	usual	ADJ	JJ	Degree=Pos	21	amod	_	_
19	Barr	Barr	PROPN	NNP	Number=Sing	20	compound	_	_
20	exactness	exactness	NOUN	NN	Number=Sing	21	compound	_	_
21	assumption	assumption	NOUN	NN	Number=Sing	16	dobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 126
# sent_id = 1
# text = In connection with the so - called Hurwitz action of homeomorphisms in ramified covers we define a groupoid, which we call a ramification groupoid of the 2 - sphere, constructed as a certain path groupoid of the universal ramified cover of the 2 - sphere with finitely many marked - points.
1	In	in	ADP	IN	_	16	prep	_	_
2	connection	connection	NOUN	NN	Number=Sing	1	pobj	_	_
3	with	with	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
5	so	so	ADV	RB	_	7	advmod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	amod	_	_
8	Hurwitz	Hurwitz	PROPN	NNP	Number=Sing	9	compound	_	_
9	action	action	NOUN	NN	Number=Sing	3	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	homeomorphisms	homeomorphism	NOUN	NNS	Number=Plur	10	pobj	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	ramified	ramify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
14	covers	cover	NOUN	NNS	Number=Plur	12	pobj	_	_
15	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	16	nsubj	_	_
16	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	groupoid	groupoid	NOUN	NN	Number=Sing	16	dobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	which	which	PRON	WDT	_	22	dobj	_	_
21	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	22	nsubj	_	_
22	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	18	relcl	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	ramification	ramification	NOUN	NN	Number=Sing	25	compound	_	_
25	groupoid	groupoid	NOUN	NN	Number=Sing	22	oprd	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
28	2	2	NUM	CD	NumType=Card	30	nummod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	sphere	sphere	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
32	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	acl	_	_
33	as	as	ADP	IN	_	32	prep	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
35	certain	certain	ADJ	JJ	Degree=Pos	37	amod	_	_
36	path	path	NOUN	NN	Number=Sing	37	compound	_	_
37	groupoid	groupoid	NOUN	NN	Number=Sing	33	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	42	det	_	_
40	universal	universal	ADJ	JJ	Degree=Pos	42	amod	_	_
41	ramified	ramify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	42	amod	_	_
42	cover	cover	NOUN	NN	Number=Sing	38	pobj	_	_
43	of	of	ADP	IN	_	42	prep	_	_
44	the	the	DET	DT	Definite=Def|PronType=Art	47	det	_	_
45	2	2	NUM	CD	NumType=Card	47	nummod	_	_
46	-	-	PUNCT	HYPH	PunctType=Dash	47	punct	_	_
47	sphere	sphere	NOUN	NN	Number=Sing	43	pobj	_	_
48	with	with	ADP	IN	_	47	prep	_	_
49	finitely	finitely	ADV	RB	_	50	advmod	_	_
50	many	many	ADJ	JJ	Degree=Pos	53	amod	_	_
51	marked	mark	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	53	amod	_	_
52	-	-	PUNCT	HYPH	PunctType=Dash	53	punct	_	_
53	points	point	NOUN	NNS	Number=Plur	48	pobj	_	SpaceAfter=No
54	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 2
# text = Our approach to ramified covers is based on cosheaf spaces, which are closely related to Fox's complete spreads.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	approach	approach	NOUN	NN	Number=Sing	7	nsubjpass	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	ramified	ramify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	amod	_	_
5	covers	cover	NOUN	NNS	Number=Plur	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	on	on	ADP	IN	_	7	prep	_	_
9	cosheaf	cosheaf	ADJ	JJ	Degree=Pos	10	amod	_	_
10	spaces	space	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	which	which	PRON	WDT	_	15	nsubjpass	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
14	closely	closely	ADV	RB	_	15	advmod	_	_
15	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	relcl	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	Fox	Fox	PROPN	NNP	Number=Sing	20	poss	_	SpaceAfter=No
18	's	's	PART	POS	_	17	case	_	_
19	complete	complete	ADJ	JJ	Degree=Pos	20	amod	_	_
20	spreads	spread	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = A feature of a ramification groupoid is that it carries a certain order structure.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	feature	feature	NOUN	NN	Number=Sing	7	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	ramification	ramification	NOUN	NN	Number=Sing	6	compound	_	_
6	groupoid	groupoid	NOUN	NN	Number=Sing	3	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	that	that	SCONJ	IN	_	10	mark	_	_
9	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	10	nsubj	_	_
10	carries	carry	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	ccomp	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
12	certain	certain	ADJ	JJ	Degree=Pos	14	amod	_	_
13	order	order	NOUN	NN	Number=Sing	14	compound	_	_
14	structure	structure	NOUN	NN	Number=Sing	10	dobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = The Artin group of braids of $ n $ strands has an order - invariant action in the ramification groupoid of the sphere with $ n+1 $ marked - points.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	Artin	Artin	PROPN	NNP	Number=Sing	3	compound	_	_
3	group	group	NOUN	NN	Number=Sing	9	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	braids	braid	NOUN	NNS	Number=Plur	4	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	$ n $	$ n $	SYM	$	_	8	nmod	_	_
8	strands	strand	NOUN	NNS	Number=Plur	6	pobj	_	_
9	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
11	order	order	NOUN	NN	Number=Sing	13	npadvmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	invariant	invariant	ADJ	JJ	Degree=Pos	14	amod	_	_
14	action	action	NOUN	NN	Number=Sing	9	dobj	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	ramification	ramification	NOUN	NN	Number=Sing	18	compound	_	_
18	groupoid	groupoid	NOUN	NN	Number=Sing	15	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	sphere	sphere	NOUN	NN	Number=Sing	19	pobj	_	_
22	with	with	ADP	IN	_	14	prep	_	_
23	$ n+1 $	$ n+1 $	SYM	$	_	26	nmod	_	_
24	marked	mark	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	points	point	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 5
# text = Left - invariant linear orderings of the braid group such as the Dehornoy ordering may be retrieved.
1	Left	left	ADJ	JJ	Degree=Pos	3	amod	_	_
2	-	-	PUNCT	HYPH	PunctType=Dash	3	punct	_	_
3	invariant	invariant	ADJ	JJ	Degree=Pos	5	amod	_	_
4	linear	linear	ADJ	JJ	Degree=Pos	5	compound	_	_
5	orderings	ordering	NOUN	NNS	Number=Plur	17	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	braid	braid	PROPN	NNP	Number=Sing	9	compound	_	_
9	group	group	NOUN	NN	Number=Sing	6	pobj	_	_
10	such	such	ADJ	JJ	Degree=Pos	11	amod	_	_
11	as	as	ADP	IN	_	9	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	Dehornoy	Dehornoy	PROPN	NNP	Number=Sing	14	compound	_	_
14	ordering	ordering	NOUN	NN	Number=Sing	11	pobj	_	_
15	may	may	AUX	MD	VerbForm=Fin	17	aux	_	_
16	be	be	AUX	VB	VerbForm=Inf	17	auxpass	_	_
17	retrieved	retrieve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 6
# text = Our work extends naturally to the braid group on countably many generators.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	work	work	NOUN	NN	Number=Sing	3	nsubj	_	_
3	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	naturally	naturally	ADV	RB	_	3	advmod	_	_
5	to	to	ADP	IN	_	3	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	braid	braid	PROPN	NNP	Number=Sing	8	compound	_	_
8	group	group	NOUN	NN	Number=Sing	5	pobj	_	_
9	on	on	ADP	IN	_	3	prep	_	_
10	countably	countably	ADV	RB	_	11	advmod	_	_
11	many	many	ADJ	JJ	Degree=Pos	12	amod	_	_
12	generators	generator	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = In particular, we show that the underlying set of a free group on countably many generators (minus the identity element) can be linearly ordered in such a way that the classical Artin representation of a braid as an automorphism of the free group is an order - preserving action.
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	27	mark	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	underlying	underlie	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	amod	_	_
9	set	set	NOUN	NN	Number=Sing	27	nsubjpass	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	free	free	ADJ	JJ	Degree=Pos	13	amod	_	_
13	group	group	NOUN	NN	Number=Sing	10	pobj	_	_
14	on	on	ADP	IN	_	9	prep	_	_
15	countably	countably	ADV	RB	_	16	advmod	_	_
16	many	many	ADJ	JJ	Degree=Pos	17	amod	_	_
17	generators	generator	NOUN	NNS	Number=Plur	14	pobj	_	_
18	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	17	punct	_	SpaceAfter=No
19	minus	minus	CCONJ	CC	ConjType=Cmp	17	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	identity	identity	NOUN	NN	Number=Sing	22	compound	_	_
22	element	element	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	17	punct	_	_
24	can	can	AUX	MD	VerbForm=Fin	27	aux	_	_
25	be	be	AUX	VB	VerbForm=Inf	27	auxpass	_	_
26	linearly	linearly	ADV	RB	_	27	advmod	_	_
27	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	ccomp	_	_
28	in	in	ADP	IN	_	27	prep	_	_
29	such	such	DET	PDT	_	31	predet	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
31	way	way	NOUN	NN	Number=Sing	28	pobj	_	_
32	that	that	PRON	WDT	PronType=Rel	47	mark	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
34	classical	classical	ADJ	JJ	Degree=Pos	36	amod	_	_
35	Artin	Artin	PROPN	NNP	Number=Sing	36	compound	_	_
36	representation	representation	NOUN	NN	Number=Sing	47	nsubj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
39	braid	braid	NOUN	NN	Number=Sing	37	pobj	_	_
40	as	as	ADP	IN	_	39	prep	_	_
41	an	an	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
42	automorphism	automorphism	NOUN	NN	Number=Sing	40	pobj	_	_
43	of	of	ADP	IN	_	42	prep	_	_
44	the	the	DET	DT	Definite=Def|PronType=Art	46	det	_	_
45	free	free	ADJ	JJ	Degree=Pos	46	amod	_	_
46	group	group	NOUN	NN	Number=Sing	43	pobj	_	_
47	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	31	acl	_	_
48	an	an	DET	DT	Definite=Ind|PronType=Art	52	det	_	_
49	order	order	NOUN	NN	Number=Sing	51	npadvmod	_	_
50	-	-	PUNCT	HYPH	PunctType=Dash	51	punct	_	_
51	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	52	amod	_	_
52	action	action	NOUN	NN	Number=Sing	47	attr	_	SpaceAfter=No
53	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 127
# sent_id = 1
# text = In the present article we continue recent work in the direction of domain theory were certain (accessible) categories are used as generalized domains.
1	In	in	ADP	IN	_	6	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	present	present	ADJ	JJ	Degree=Pos	4	amod	_	_
4	article	article	NOUN	NN	Number=Sing	1	pobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	continue	continue	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	recent	recent	ADJ	JJ	Degree=Pos	8	amod	_	_
8	work	work	NOUN	NN	Number=Sing	6	dobj	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	direction	direction	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	domain	domain	NOUN	NN	Number=Sing	14	compound	_	_
14	theory	theory	NOUN	NN	Number=Sing	12	pobj	_	_
15	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	6	conj	_	_
16	certain	certain	ADJ	JJ	Degree=Pos	15	acomp	_	_
17	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	20	punct	_	SpaceAfter=No
18	accessible	accessible	ADJ	JJ	Degree=Pos	20	amod	_	SpaceAfter=No
19	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	20	punct	_	_
20	categories	category	NOUN	NNS	Number=Plur	22	nsubjpass	_	_
21	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	22	auxpass	_	_
22	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	conj	_	_
23	as	as	ADP	IN	_	22	prep	_	_
24	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	amod	_	_
25	domains	domain	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# sent_id = 2
# text = We discuss the possibility of using certain presheaf toposes as generalizations of the Scott topology at this level.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	discuss	discuss	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	possibility	possibility	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	certain	certain	ADJ	JJ	Degree=Pos	9	amod	_	_
8	presheaf	presheaf	NOUN	NN	Number=Sing	9	compound	_	_
9	toposes	topos	NOUN	NNS	Number=Plur	6	dobj	_	_
10	as	as	ADP	IN	_	6	prep	_	_
11	generalizations	generalization	NOUN	NNS	Number=Plur	10	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	Scott	Scott	PROPN	NNP	Number=Sing	15	compound	_	_
15	topology	topology	NOUN	NN	Number=Sing	12	pobj	_	_
16	at	at	ADP	IN	_	6	prep	_	_
17	this	this	DET	DT	Number=Sing|PronType=Dem	18	det	_	_
18	level	level	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that the toposes associated with Scott complete categories are injective with respect to dense inclusions of toposes.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	11	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	toposes	topos	NOUN	NNS	Number=Plur	11	nsubj	_	_
6	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	acl	_	_
7	with	with	ADP	IN	_	6	prep	_	_
8	Scott	Scott	PROPN	NNP	Number=Sing	10	nmod	_	_
9	complete	complete	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
12	injective	injective	ADJ	JJ	Degree=Pos	11	acomp	_	_
13	with	with	ADP	IN	_	12	prep	_	_
14	respect	respect	NOUN	NN	Number=Sing	13	pobj	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	dense	dense	ADJ	JJ	Degree=Pos	17	amod	_	_
17	inclusions	inclusion	NOUN	NNS	Number=Plur	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	toposes	topos	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We propose analogues of the upper and lower powerdomain in terms of the Scott topology at the level of categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	propose	propose	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	analogues	analogue	NOUN	NNS	Number=Plur	2	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
6	upper	upper	ADJ	JJ	Degree=Pos	9	amod	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	lower	low	ADJ	JJR	Degree=Cmp	6	conj	_	_
9	powerdomain	powerdomain	NOUN	NN	Number=Sing	4	pobj	_	_
10	in	in	ADP	IN	_	2	prep	_	_
11	terms	term	NOUN	NNS	Number=Plur	10	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	Scott	Scott	PROPN	NNP	Number=Sing	15	compound	_	_
15	topology	topology	NOUN	NN	Number=Sing	12	pobj	_	_
16	at	at	ADP	IN	_	2	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	level	level	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	categories	category	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = We show that the class of finitely accessible categories is closed under this generalized upper powerdomain construction (the respective result about the lower powerdomain construction is essentially known).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	11	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	class	class	NOUN	NN	Number=Sing	11	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	finitely	finitely	ADV	RB	_	8	advmod	_	_
8	accessible	accessible	ADJ	JJ	Degree=Pos	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
12	under	under	ADP	IN	_	11	prep	_	_
13	this	this	DET	DT	Number=Sing|PronType=Dem	17	det	_	_
14	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
15	upper	upper	ADJ	JJ	Degree=Pos	17	amod	_	_
16	powerdomain	powerdomain	NOUN	NN	Number=Sing	17	compound	_	_
17	construction	construction	NOUN	NN	Number=Sing	12	pobj	_	_
18	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	21	punct	_	SpaceAfter=No
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	respective	respective	ADJ	JJ	Degree=Pos	21	amod	_	_
21	result	result	NOUN	NN	Number=Sing	29	nsubjpass	_	_
22	about	about	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
24	lower	low	ADJ	JJR	Degree=Cmp	25	amod	_	_
25	powerdomain	powerdomain	NOUN	NN	Number=Sing	26	compound	_	_
26	construction	construction	NOUN	NN	Number=Sing	22	pobj	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	auxpass	_	_
28	essentially	essentially	ADV	RB	_	29	advmod	_	_
29	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	advcl	_	SpaceAfter=No
30	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	29	punct	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = We also treat the notion of ``coherent domain'' by introducing two possible notions of coherence for a finitely accessible category (qua generalized domain).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	treat	treat	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	notion	notion	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	10	punct	_	SpaceAfter=No
8	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	10	punct	_	SpaceAfter=No
9	coherent	coherent	ADJ	JJ	Degree=Pos	10	amod	_	_
10	domain	domain	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
11	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	3	punct	_	_
12	by	by	ADP	IN	_	3	prep	_	_
13	introducing	introduce	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	pcomp	_	_
14	two	two	NUM	CD	NumType=Card	16	nummod	_	_
15	possible	possible	ADJ	JJ	Degree=Pos	16	amod	_	_
16	notions	notion	NOUN	NNS	Number=Plur	13	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	coherence	coherence	NOUN	NN	Number=Sing	17	pobj	_	_
19	for	for	ADP	IN	_	13	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
21	finitely	finitely	ADV	RB	_	22	advmod	_	_
22	accessible	accessible	ADJ	JJ	Degree=Pos	23	amod	_	_
23	category	category	NOUN	NN	Number=Sing	19	pobj	_	_
24	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	23	punct	_	SpaceAfter=No
25	qua	qua	CCONJ	CC	ConjType=Cmp	23	cc	_	_
26	generalized	generalized	ADJ	JJ	Degree=Pos	27	amod	_	_
27	domain	domain	NOUN	NN	Number=Sing	23	conj	_	SpaceAfter=No
28	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	3	punct	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = The one of them imitates the stability of the compact saturated sets under intersection and the other one imitates the so - called ``2/3 SFP'' property.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	one	one	NUM	CD	NumType=Card	5	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	3	pobj	_	_
5	imitates	imitate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	stability	stability	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
10	compact	compact	ADJ	JJ	Degree=Pos	12	amod	_	_
11	saturated	saturate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
12	sets	set	NOUN	NNS	Number=Plur	8	pobj	_	_
13	under	under	ADP	IN	_	12	prep	_	_
14	intersection	intersection	NOUN	NN	Number=Sing	13	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	other	other	ADJ	JJ	Degree=Pos	18	amod	_	_
18	one	one	NOUN	NN	Number=Sing	19	nsubj	_	_
19	imitates	imitate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	conj	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
21	so	so	ADV	RB	_	23	advmod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	amod	_	_
24	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	29	punct	_	SpaceAfter=No
25	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	29	punct	_	SpaceAfter=No
26	2/3	2/3	NUM	CD	NumType=Card	27	nummod	_	_
27	SFP	SFP	PROPN	NNP	Number=Sing	29	nmod	_	SpaceAfter=No
28	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	29	punct	_	_
29	property	property	NOUN	NN	Number=Sing	19	dobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 8
# text = We show that the two notions are equivalent.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	two	two	NUM	CD	NumType=Card	6	nummod	_	_
6	notions	notion	NOUN	NNS	Number=Plur	7	nsubj	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	equivalent	equivalent	ADJ	JJ	Degree=Pos	7	acomp	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 9
# text = This amounts to characterizing the small categories whose free cocompletion under finite colimits has finite limits.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	amounts	amount	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	characterizing	characterize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	pcomp	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	small	small	ADJ	JJ	Degree=Pos	7	amod	_	_
7	categories	category	NOUN	NNS	Number=Plur	4	dobj	_	_
8	whose	whose	DET	WP$	Poss=Yes	10	poss	_	_
9	free	free	ADJ	JJ	Degree=Pos	10	amod	_	_
10	cocompletion	cocompletion	NOUN	NN	Number=Sing	14	nsubj	_	_
11	under	under	ADP	IN	_	10	prep	_	_
12	finite	finite	PROPN	NNP	Number=Sing	13	compound	_	_
13	colimits	colimit	NOUN	NNS	Number=Plur	11	pobj	_	_
14	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	relcl	_	_
15	finite	finite	ADJ	JJ	Degree=Pos	16	amod	_	_
16	limits	limit	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 128
# sent_id = 1
# text = In this paper we show how collapsing schemes can give us information on the homotopy type of the classifying space of a small category, when this category is presented by a complete rewrite system.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	how	how	SCONJ	WRB	_	7	advmod	_	_
7	collapsing	collapse	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	amod	_	_
8	schemes	scheme	NOUN	NNS	Number=Plur	10	nsubj	_	_
9	can	can	AUX	MD	VerbForm=Fin	10	aux	_	_
10	give	give	VERB	VB	VerbForm=Inf	5	ccomp	_	_
11	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	10	dative	_	_
12	information	information	NOUN	NN	Number=Sing	10	dobj	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	homotopy	homotopy	NOUN	NN	Number=Sing	16	compound	_	_
16	type	type	NOUN	NN	Number=Sing	13	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	classifying	classify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	amod	_	_
20	space	space	NOUN	NN	Number=Sing	17	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
23	small	small	ADJ	JJ	Degree=Pos	24	amod	_	_
24	category	category	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
26	when	when	SCONJ	WRB	_	30	advmod	_	_
27	this	this	DET	DT	Number=Sing|PronType=Dem	28	det	_	_
28	category	category	NOUN	NN	Number=Sing	30	nsubjpass	_	_
29	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	auxpass	_	_
30	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	advcl	_	_
31	by	by	ADP	IN	_	30	agent	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
33	complete	complete	ADJ	JJ	Degree=Pos	35	amod	_	_
34	rewrite	rewrite	NOUN	NN	Number=Sing	35	compound	_	_
35	system	system	NOUN	NN	Number=Sing	31	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 129
# sent_id = 1
# text = An action $ * : cal V times cal A to cal A $ of a monoidal category $ cal V $ on a category $ cal A $ corresponds to a strong monoidal functor $ F : cal V to [cal A, cal A] $ into the monoidal category of endofunctors of $ cal A $ .
1	An	an	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	action	action	NOUN	NN	Number=Sing	13	nsubj	_	_
3	$ * : cal V times cal A to cal A $	$ * : cal v times cal a to cal a $	SYM	$	_	2	appos	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	monoidal	monoidal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
8	$ cal V $	$ cal v $	SYM	$	_	2	appos	_	_
9	on	on	ADP	IN	_	2	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
12	$ cal A $	$ cal a $	SYM	$	_	13	nummod	_	_
13	corresponds	correspond	NOUN	NNS	Number=Plur	0	ROOT	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
16	strong	strong	ADJ	JJ	Degree=Pos	18	amod	_	_
17	monoidal	monoidal	NOUN	NN	Number=Sing	18	amod	_	_
18	functor	functor	NOUN	NN	Number=Sing	14	pobj	_	_
19	$ F : cal V to [cal A, cal A] $	$ f : cal v to [cal a, cal a] $	SYM	$	_	18	appos	_	_
20	into	into	ADP	IN	_	13	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	monoidal	monoidal	ADJ	JJ	Degree=Pos	23	amod	_	_
23	category	category	NOUN	NN	Number=Sing	20	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	endofunctors	endofunctor	NOUN	NNS	Number=Plur	24	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	$ cal A $	$ cal a $	SYM	$	_	26	pobj	_	_
28	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 2
# text = In many practical cases, the ordinary functor $ f : cal V to [cal A, cal A] $ underlying the monoidal $ F $ has a right adjoint $ g $ ; and when this is so, $ F $ itself has a right adjoint $ G $ as a monoidal functor - so that, passing to the categories of monoids (also called ``algebras'') in $ cal V $ and in $ [cal A, cal A] $ , we have an adjunction $ Mon F $ left adjoint to $ Mon G $ between the category $ Mon cal V $ of monoids in $ cal V $ and the category $ Mon [cal A, cal A] = Mnd cal A $ of monads on $ cal A $ .
1	In	in	ADP	IN	_	10	prep	_	_
2	many	many	ADJ	JJ	Degree=Pos	4	amod	_	_
3	practical	practical	ADJ	JJ	Degree=Pos	4	amod	_	_
4	cases	case	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	ordinary	ordinary	ADJ	JJ	Degree=Pos	8	amod	_	_
8	functor	functor	NOUN	NN	Number=Sing	10	nsubj	_	_
9	$ f : cal V to [cal A, cal A] $	$ f : cal v to [cal a, cal a] $	SYM	$	_	10	nsubj	_	_
10	underlying	underlie	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	csubj	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	monoidal	monoidal	NOUN	NN	Number=Sing	10	dobj	_	_
13	$ F $	$ f $	SYM	$	_	10	npadvmod	_	_
14	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	right	right	ADJ	JJ	Degree=Pos	17	amod	_	_
17	adjoint	adjoint	NOUN	NN	Number=Sing	14	dobj	_	_
18	$ g $	$ g $	SYM	$	_	17	appos	_	_
19	;	;	PUNCT	:	_	14	punct	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
21	when	when	SCONJ	WRB	_	23	advmod	_	_
22	this	this	PRON	DT	Number=Sing|PronType=Dem	23	nsubj	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	28	advcl	_	_
24	so	so	ADV	RB	_	23	advmod	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
26	$ F $	$ f $	SYM	$	_	27	nmod	_	_
27	itself	itself	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs|Reflex=Yes	28	nsubj	_	_
28	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	conj	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	right	right	ADJ	JJ	Degree=Pos	31	amod	_	_
31	adjoint	adjoint	NOUN	NN	Number=Sing	28	dobj	_	_
32	$ G $	$ g $	SYM	$	_	31	appos	_	_
33	as	as	ADP	IN	_	28	prep	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
35	monoidal	monoidal	ADJ	JJ	Degree=Pos	36	amod	_	_
36	functor	functor	NOUN	NN	Number=Sing	33	pobj	_	_
37	-	-	PUNCT	:	_	28	punct	_	_
38	so	so	SCONJ	IN	_	49	mark	_	_
39	that	that	SCONJ	IN	_	49	mark	_	SpaceAfter=No
40	,	,	PUNCT	,	PunctType=Comm	49	punct	_	_
41	passing	pass	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	49	advcl	_	_
42	to	to	ADP	IN	_	41	prep	_	_
43	the	the	DET	DT	Definite=Def|PronType=Art	44	det	_	_
44	categories	category	NOUN	NNS	Number=Plur	42	pobj	_	_
45	of	of	ADP	IN	_	44	prep	_	_
46	monoids	monoid	NOUN	NNS	Number=Plur	45	pobj	_	_
47	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	49	punct	_	SpaceAfter=No
48	also	also	ADV	RB	_	49	advmod	_	_
49	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	advcl	_	_
50	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	52	punct	_	SpaceAfter=No
51	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	52	punct	_	SpaceAfter=No
52	algebras	algebra	NOUN	NNS	Number=Plur	49	oprd	_	SpaceAfter=No
53	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	52	punct	_	SpaceAfter=No
54	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	49	punct	_	_
55	in	in	ADP	IN	_	49	prep	_	_
56	$ cal V $	$ cal v $	SYM	$	_	55	pobj	_	_
57	and	and	CCONJ	CC	ConjType=Cmp	55	cc	_	_
58	in	in	ADP	IN	_	62	prep	_	_
59	$ [cal A, cal A] $	$ [cal a, cal a] $	SYM	$	_	58	pobj	_	_
60	,	,	PUNCT	,	PunctType=Comm	62	punct	_	_
61	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	62	nsubj	_	_
62	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	49	conj	_	_
63	an	an	DET	DT	Definite=Ind|PronType=Art	64	det	_	_
64	adjunction	adjunction	NOUN	NN	Number=Sing	62	dobj	_	_
65	$ Mon F $	$ mon f $	SYM	$	_	66	nsubj	_	_
66	left	leave	VERB	VBD	Tense=Past|VerbForm=Fin	28	conj	_	_
67	adjoint	adjoint	NOUN	NN	Number=Sing	66	dobj	_	_
68	to	to	ADP	IN	_	66	prep	_	_
69	$ Mon G $	$ mon g $	SYM	$	_	68	pobj	_	_
70	between	between	ADP	IN	_	66	prep	_	_
71	the	the	DET	DT	Definite=Def|PronType=Art	72	det	_	_
72	category	category	NOUN	NN	Number=Sing	70	pobj	_	_
73	$ Mon cal V $	$ mon cal v $	SYM	$	_	72	appos	_	_
74	of	of	ADP	IN	_	73	prep	_	_
75	monoids	monoid	NOUN	NNS	Number=Plur	74	pobj	_	_
76	in	in	ADP	IN	_	72	prep	_	_
77	$ cal V $	$ cal v $	SYM	$	_	76	pobj	_	_
78	and	and	CCONJ	CC	ConjType=Cmp	72	cc	_	_
79	the	the	DET	DT	Definite=Def|PronType=Art	80	det	_	_
80	category	category	NOUN	NN	Number=Sing	72	conj	_	_
81	$ Mon [cal A, cal A] = Mnd cal A $	$ mon [cal a, cal a] = mnd cal a $	SYM	$	_	80	appos	_	_
82	of	of	ADP	IN	_	81	prep	_	_
83	monads	monad	NOUN	NNS	Number=Plur	82	pobj	_	_
84	on	on	ADP	IN	_	80	prep	_	_
85	$ cal A $	$ cal a $	SYM	$	_	84	pobj	_	_
86	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 3
# text = We give sufficient conditions for the existence of the right adjoint $ g $ , which involve the existence of right adjoints for the functors $ X * - $ and $ * A $ , and make $ cal A $ (at least when $ cal V $ is symmetric and closed) into a tensored and cotensored $ cal V $ - category $ {bf A} $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	sufficient	sufficient	ADJ	JJ	Degree=Pos	4	amod	_	_
4	conditions	condition	NOUN	NNS	Number=Plur	2	dobj	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	existence	existence	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	right	right	ADJ	JJ	Degree=Pos	11	amod	_	_
11	adjoint	adjoint	NOUN	NN	Number=Sing	8	pobj	_	_
12	$ g $	$ g $	SYM	$	_	11	appos	_	_
13	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
14	which	which	PRON	WDT	_	15	nsubj	_	_
15	involve	involve	VERB	VBP	Tense=Pres|VerbForm=Fin	11	relcl	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	existence	existence	NOUN	NN	Number=Sing	15	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	right	right	ADJ	JJ	Degree=Pos	20	amod	_	_
20	adjoints	adjoint	NOUN	NNS	Number=Plur	18	pobj	_	_
21	for	for	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	functors	functor	NOUN	NNS	Number=Plur	21	pobj	_	_
24	$ X * - $	$ x * - $	SYM	$	_	2	dobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	$ * A $	$ * a $	SYM	$	_	24	conj	_	_
27	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
29	make	make	VERB	VB	VerbForm=Inf	2	conj	_	_
30	$ cal A $	$ cal a $	SYM	$	_	29	dobj	_	_
31	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	30	punct	_	SpaceAfter=No
32	at	at	ADP	IN	_	33	advmod	_	_
33	least	least	ADJ	JJS	Degree=Sup	34	advmod	_	_
34	when	when	SCONJ	WRB	_	36	advmod	_	_
35	$ cal V $	$ cal v $	SYM	$	_	36	nsubj	_	_
36	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	advcl	_	_
37	symmetric	symmetric	ADJ	JJ	Degree=Pos	36	acomp	_	_
38	and	and	CCONJ	CC	ConjType=Cmp	37	cc	_	_
39	closed	closed	ADJ	JJ	Degree=Pos	37	conj	_	SpaceAfter=No
40	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	36	punct	_	_
41	into	into	ADP	IN	_	36	prep	_	_
42	a	a	DET	DT	Definite=Ind|PronType=Art	43	det	_	_
43	tensored	tensored	NOUN	NN	Number=Sing	41	pobj	_	_
44	and	and	CCONJ	CC	ConjType=Cmp	36	cc	_	_
45	cotensored	cotensore	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	36	conj	_	_
46	$ cal V $	$ cal v $	SYM	$	_	48	nummod	_	_
47	-	-	PUNCT	HYPH	PunctType=Dash	48	punct	_	_
48	category	category	NOUN	NN	Number=Sing	49	nmod	_	_
49	$ {bf A} $	$ {bf a} $	NOUN	NN	Number=Sing	45	dobj	_	_
50	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We give explicit formulae, as large ends, for the right adjoints $ g $ and $ Mon G $ , and also for some related right adjoints, when they exist; as well as another explicit expression for $ Mon G $ as a large limit, which uses a new representation of any (large) limit of monads of two special kinds, and an analogous result for general endofunctors.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	explicit	explicit	ADJ	JJ	Degree=Pos	4	amod	_	_
4	formulae	formulae	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
6	as	as	ADP	IN	_	2	prep	_	_
7	large	large	ADJ	JJ	Degree=Pos	8	amod	_	_
8	ends	end	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
10	for	for	ADP	IN	_	2	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	right	right	ADJ	JJ	Degree=Pos	13	amod	_	_
13	adjoints	adjoint	NOUN	NNS	Number=Plur	10	pobj	_	_
14	$ g $	$ g $	SYM	$	_	13	appos	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	$ Mon G $	$ mon g $	SYM	$	_	14	conj	_	_
17	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
19	also	also	ADV	RB	_	20	advmod	_	_
20	for	for	ADP	IN	_	10	conj	_	_
21	some	some	DET	DT	_	24	det	_	_
22	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
23	right	right	ADJ	JJ	Degree=Pos	24	amod	_	_
24	adjoints	adjoint	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	when	when	SCONJ	WRB	_	28	advmod	_	_
27	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	28	nsubj	_	_
28	exist	exist	VERB	VBP	Tense=Pres|VerbForm=Fin	24	relcl	_	SpaceAfter=No
29	;	;	PUNCT	:	_	24	punct	_	_
30	as	as	ADV	RB	_	32	advmod	_	_
31	well	well	ADV	RB	Degree=Pos	32	advmod	_	_
32	as	as	ADP	IN	_	24	cc	_	_
33	another	another	DET	DT	_	35	det	_	_
34	explicit	explicit	ADJ	JJ	Degree=Pos	35	amod	_	_
35	expression	expression	NOUN	NN	Number=Sing	24	conj	_	_
36	for	for	ADP	IN	_	35	prep	_	_
37	$ Mon G $	$ mon g $	SYM	$	_	36	pobj	_	_
38	as	as	ADP	IN	_	35	prep	_	_
39	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
40	large	large	ADJ	JJ	Degree=Pos	41	amod	_	_
41	limit	limit	NOUN	NN	Number=Sing	38	pobj	_	SpaceAfter=No
42	,	,	PUNCT	,	PunctType=Comm	41	punct	_	_
43	which	which	PRON	WDT	_	44	nsubj	_	_
44	uses	use	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	41	relcl	_	_
45	a	a	DET	DT	Definite=Ind|PronType=Art	47	det	_	_
46	new	new	ADJ	JJ	Degree=Pos	47	amod	_	_
47	representation	representation	NOUN	NN	Number=Sing	44	dobj	_	_
48	of	of	ADP	IN	_	47	prep	_	_
49	any	any	DET	DT	_	53	det	_	_
50	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	53	punct	_	SpaceAfter=No
51	large	large	ADJ	JJ	Degree=Pos	53	amod	_	SpaceAfter=No
52	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	53	punct	_	_
53	limit	limit	NOUN	NN	Number=Sing	48	pobj	_	_
54	of	of	ADP	IN	_	53	prep	_	_
55	monads	monad	NOUN	NNS	Number=Plur	54	pobj	_	_
56	of	of	ADP	IN	_	55	prep	_	_
57	two	two	NUM	CD	NumType=Card	59	nummod	_	_
58	special	special	ADJ	JJ	Degree=Pos	59	amod	_	_
59	kinds	kind	NOUN	NNS	Number=Plur	56	pobj	_	SpaceAfter=No
60	,	,	PUNCT	,	PunctType=Comm	41	punct	_	_
61	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
62	an	an	DET	DT	Definite=Ind|PronType=Art	64	det	_	_
63	analogous	analogous	ADJ	JJ	Degree=Pos	64	amod	_	_
64	result	result	NOUN	NN	Number=Sing	35	conj	_	_
65	for	for	ADP	IN	_	64	prep	_	_
66	general	general	ADJ	JJ	Degree=Pos	67	amod	_	_
67	endofunctors	endofunctor	NOUN	NNS	Number=Plur	65	pobj	_	SpaceAfter=No
68	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 130
# sent_id = 1
# text = The interpretation by Duskin and Glenn of abelian sheaf cohomology as connected components of a category of torsors is extended to homotopy classes.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	interpretation	interpretation	NOUN	NN	Number=Sing	20	nsubjpass	_	_
3	by	by	ADP	IN	_	2	prep	_	_
4	Duskin	Duskin	PROPN	NNP	Number=Sing	3	pobj	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	Glenn	Glenn	PROPN	NNP	Number=Sing	4	conj	_	_
7	of	of	ADP	IN	_	4	prep	_	_
8	abelian	abelian	PROPN	NNP	Number=Sing	10	compound	_	_
9	sheaf	sheaf	PROPN	NNP	Number=Sing	10	compound	_	_
10	cohomology	cohomology	NOUN	NN	Number=Sing	7	pobj	_	_
11	as	as	ADP	IN	_	2	prep	_	_
12	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
13	components	component	NOUN	NNS	Number=Plur	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	category	category	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	torsors	torsor	NOUN	NNS	Number=Plur	17	pobj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	auxpass	_	_
20	extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
21	to	to	PART	TO	_	22	aux	_	_
22	homotopy	homotopy	VERB	VB	VerbForm=Inf	20	xcomp	_	_
23	classes	class	NOUN	NNS	Number=Plur	22	dobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 2
# text = This is simultaneously an extension of Verdier's version of Cech cohomology to homotopy.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	simultaneously	simultaneously	ADV	RB	_	2	advmod	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	extension	extension	NOUN	NN	Number=Sing	2	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Verdier	verdier	NOUN	NN	Number=Sing	9	poss	_	SpaceAfter=No
8	's	's	PART	POS	_	7	case	_	_
9	version	version	NOUN	NN	Number=Sing	6	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	Cech	Cech	PROPN	NNP	Number=Sing	12	compound	_	_
12	cohomology	cohomology	NOUN	NN	Number=Sing	10	pobj	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	homotopy	homotopy	VERB	VB	VerbForm=Inf	5	acl	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 131
# sent_id = 1
# text = Exact sequences are a well known notion in homological algebra.
1	Exact	exact	ADJ	JJ	Degree=Pos	2	amod	_	_
2	sequences	sequence	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	well	well	ADV	RB	Degree=Pos	6	advmod	_	_
6	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
7	notion	notion	NOUN	NN	Number=Sing	3	attr	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	homological	homological	ADJ	JJ	Degree=Pos	10	amod	_	_
10	algebra	algebra	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = We investigate here the more vague properties of `homotopical exactness', appearing for instance in the fibre or cofibre sequence of a map.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	here	here	ADV	RB	PronType=Dem	2	advmod	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	more	more	ADV	RBR	Degree=Cmp	6	advmod	_	_
6	vague	vague	ADJ	JJ	Degree=Pos	7	amod	_	_
7	properties	property	NOUN	NNS	Number=Plur	2	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	8	punct	_	SpaceAfter=No
10	homotopical	homotopical	ADJ	JJ	Degree=Pos	11	amod	_	_
11	exactness	exactness	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
12	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	7	punct	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
14	appearing	appear	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	acl	_	_
15	for	for	ADP	IN	_	14	prep	_	_
16	instance	instance	NOUN	NN	Number=Sing	15	pobj	_	_
17	in	in	ADP	IN	_	14	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	fibre	fibre	NOUN	NN	Number=Sing	17	pobj	_	_
20	or	or	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	cofibre	cofibre	PROPN	NNP	Number=Sing	22	compound	_	_
22	sequence	sequence	NOUN	NN	Number=Sing	19	conj	_	_
23	of	of	ADP	IN	_	19	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
25	map	map	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Such notions of exactness can be given for very general `categories with homotopies' having homotopy kernels and cokernels, but become more interesting under suitable `stability' hypotheses, satisfied - in particular - by chain complexes.
1	Such	such	ADJ	JJ	Degree=Pos	2	amod	_	_
2	notions	notion	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	exactness	exactness	NOUN	NN	Number=Sing	3	pobj	_	_
5	can	can	AUX	MD	VerbForm=Fin	7	aux	_	_
6	be	be	AUX	VB	VerbForm=Inf	7	auxpass	_	_
7	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	very	very	ADV	RB	_	10	advmod	_	_
10	general	general	ADJ	JJ	Degree=Pos	12	amod	_	_
11	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	12	punct	_	SpaceAfter=No
12	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	_
13	with	with	ADP	IN	_	12	prep	_	_
14	homotopies	homotopie	NOUN	NNS	Number=Plur	16	nsubj	_	SpaceAfter=No
15	'	'	PART	POS	_	14	case	_	_
16	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	pcomp	_	_
17	homotopy	homotopy	NOUN	NN	Number=Sing	18	compound	_	_
18	kernels	kernel	NOUN	NNS	Number=Plur	16	dobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	cokernels	cokernel	NOUN	NNS	Number=Plur	18	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
22	but	but	CCONJ	CC	ConjType=Cmp	7	cc	_	_
23	become	become	VERB	VB	VerbForm=Inf	7	conj	_	_
24	more	more	ADV	RBR	Degree=Cmp	25	advmod	_	_
25	interesting	interesting	ADJ	JJ	Degree=Pos	23	acomp	_	_
26	under	under	ADP	IN	_	23	prep	_	_
27	suitable	suitable	ADJ	JJ	Degree=Pos	31	amod	_	_
28	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	31	punct	_	SpaceAfter=No
29	stability	stability	NOUN	NN	Number=Sing	31	nmod	_	SpaceAfter=No
30	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	31	punct	_	_
31	hypotheses	hypothesis	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
33	satisfied	satisfied	ADJ	JJ	Degree=Pos	31	amod	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
35	in	in	ADP	RP	_	33	prt	_	_
36	particular	particular	ADJ	JJ	Degree=Pos	35	amod	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
38	by	by	ADP	IN	_	33	prep	_	_
39	chain	chain	NOUN	NN	Number=Sing	40	compound	_	_
40	complexes	complex	NOUN	NNS	Number=Plur	38	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = It is then possible to measure the default of homotopical exactness of a sequence by the homotopy type of a certain object, a sort of `homotopical homology'.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	then	then	ADV	RB	PronType=Dem	2	advmod	_	_
4	possible	possible	ADJ	JJ	Degree=Pos	2	acomp	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	measure	measure	VERB	VB	VerbForm=Inf	2	xcomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	default	default	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	homotopical	homotopical	ADJ	JJ	Degree=Pos	11	amod	_	_
11	exactness	exactness	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	sequence	sequence	NOUN	NN	Number=Sing	12	pobj	_	_
15	by	by	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	homotopy	homotopy	NOUN	NN	Number=Sing	18	compound	_	_
18	type	type	NOUN	NN	Number=Sing	15	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	certain	certain	ADJ	JJ	Degree=Pos	22	amod	_	_
22	object	object	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
25	sort	sort	NOUN	NN	Number=Sing	2	attr	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	SpaceAfter=No
28	homotopical	homotopical	ADJ	JJ	Degree=Pos	29	amod	_	_
29	homology	homology	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
30	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	2	punct	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 132
# sent_id = 1
# text = We give a unified proof of Gabriel - Ulmer duality for locally finitely presentable categories, Adamek - Lawvere - Rosicky duality for varieties and Morita duality for presheaf categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	unified	unified	ADJ	JJ	Degree=Pos	5	amod	_	_
5	proof	proof	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Gabriel	Gabriel	PROPN	NNP	Number=Sing	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	Ulmer	Ulmer	PROPN	NNP	Number=Sing	10	compound	_	_
10	duality	duality	NOUN	NN	Number=Sing	6	pobj	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	locally	locally	ADV	RB	_	13	advmod	_	_
13	finitely	finitely	ADV	RB	_	15	amod	_	_
14	presentable	presentable	ADJ	JJ	Degree=Pos	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	Adamek	Adamek	PROPN	NNP	Number=Sing	22	nmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
19	Lawvere	Lawvere	PROPN	NNP	Number=Sing	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	Rosicky	rosicky	ADJ	JJ	Degree=Pos	22	amod	_	_
22	duality	duality	NOUN	NN	Number=Sing	15	appos	_	_
23	for	for	ADP	IN	_	22	prep	_	_
24	varieties	variety	NOUN	NNS	Number=Plur	23	pobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	Morita	Morita	PROPN	NNP	Number=Sing	27	compound	_	_
27	duality	duality	NOUN	NN	Number=Sing	24	conj	_	_
28	for	for	ADP	IN	_	27	prep	_	_
29	presheaf	presheaf	ADJ	JJ	Degree=Pos	30	amod	_	_
30	categories	category	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = As an application, we compare presheaf categories and varieties.
1	As	as	ADP	IN	_	6	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	compare	compare	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	presheaf	presheaf	ADJ	JJ	Degree=Pos	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	6	dobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	varieties	variety	NOUN	NNS	Number=Plur	8	conj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 133
# sent_id = 1
# text = In the context of synthetic differential geometry, we study the Laplace operator an a Riemannian manifold.
1	In	in	ADP	IN	_	10	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	context	context	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	synthetic	synthetic	ADJ	JJ	Degree=Pos	7	amod	_	_
6	differential	differential	ADJ	JJ	Degree=Pos	7	amod	_	_
7	geometry	geometry	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
9	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
10	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	Laplace	Laplace	PROPN	NNP	Number=Sing	13	compound	_	_
13	operator	operator	NOUN	NN	Number=Sing	10	dobj	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	Riemannian	riemannian	ADJ	JJ	Degree=Pos	17	amod	_	_
17	manifold	manifold	NOUN	NN	Number=Sing	13	appos	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = The main new aspect is a neighbourhood of the diagonal, smaller than the second neighbourhood usually required as support for second order differential operators.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	4	amod	_	_
3	new	new	ADJ	JJ	Degree=Pos	4	amod	_	_
4	aspect	aspect	NOUN	NN	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	neighbourhood	neighbourhood	NOUN	NN	Number=Sing	5	attr	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	diagonal	diagonal	ADJ	JJ	Degree=Pos	12	amod	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
12	smaller	small	ADJ	JJR	Degree=Cmp	8	pobj	_	_
13	than	than	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	second	second	ADJ	JJ	Degree=Pos	16	amod	_	_
16	neighbourhood	neighbourhood	NOUN	NN	Number=Sing	13	pobj	_	_
17	usually	usually	ADV	RB	_	18	advmod	_	_
18	required	require	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	acl	_	_
19	as	as	ADP	IN	_	18	prep	_	_
20	support	support	NOUN	NN	Number=Sing	19	pobj	_	_
21	for	for	ADP	IN	_	20	prep	_	_
22	second	second	ADJ	JJ	Degree=Pos	23	amod	_	_
23	order	order	NOUN	NN	Number=Sing	25	nmod	_	_
24	differential	differential	NOUN	NN	Number=Sing	25	amod	_	_
25	operators	operator	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = The new neighbourhood has the property that a function is affine on it if and only if it is harmonic.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	new	new	ADJ	JJ	Degree=Pos	3	amod	_	_
3	neighbourhood	neighbourhood	NOUN	NN	Number=Sing	4	nsubj	_	_
4	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	property	property	NOUN	NN	Number=Sing	4	dobj	_	_
7	that	that	PRON	WDT	PronType=Rel	10	mark	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	function	function	NOUN	NN	Number=Sing	10	nsubj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	relcl	_	_
11	affine	affine	NOUN	NN	Number=Sing	10	attr	_	_
12	on	on	ADP	IN	_	11	prep	_	_
13	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	12	pobj	_	_
14	if	if	SCONJ	IN	_	19	advmod	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	only	only	ADV	RB	_	19	advmod	_	_
17	if	if	SCONJ	IN	_	19	mark	_	_
18	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	19	nsubj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	advcl	_	_
20	harmonic	harmonic	ADJ	JJ	Degree=Pos	19	acomp	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 134
# sent_id = 1
# text = Let $ V $ be a symmetric monoidal closed category with a suitably compatible simplicial model category structure.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ V $	$ v $	SYM	$	_	1	ccomp	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	symmetric	symmetric	ADJ	JJ	Degree=Pos	6	amod	_	_
6	monoidal	monoidal	NOUN	NN	Number=Sing	3	attr	_	_
7	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	1	ccomp	_	_
8	category	category	NOUN	NN	Number=Sing	7	dobj	_	_
9	with	with	ADP	IN	_	7	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
11	suitably	suitably	ADV	RB	_	12	advmod	_	_
12	compatible	compatible	ADJ	JJ	Degree=Pos	16	amod	_	_
13	simplicial	simplicial	ADJ	JJ	Degree=Pos	14	amod	_	_
14	model	model	NOUN	NN	Number=Sing	16	compound	_	_
15	category	category	NOUN	NN	Number=Sing	16	compound	_	_
16	structure	structure	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show how to extend Dwyer and Kan's notion of simplicial localization to $ V $ - categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	how	how	SCONJ	WRB	_	5	advmod	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	extend	extend	VERB	VB	VerbForm=Inf	2	xcomp	_	_
6	Dwyer	Dwyer	PROPN	NNP	Number=Sing	5	dobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	Kan	Kan	PROPN	NNP	Number=Sing	10	poss	_	SpaceAfter=No
9	's	's	PART	POS	_	8	case	_	_
10	notion	notion	NOUN	NN	Number=Sing	6	conj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	simplicial	simplicial	ADJ	JJ	Degree=Pos	13	amod	_	_
13	localization	localization	NOUN	NN	Number=Sing	11	pobj	_	_
14	to	to	ADP	IN	_	5	prep	_	_
15	$ V $	$ v $	SYM	$	_	17	nummod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	categories	category	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = This may for instance be applied to the case where our categories are enriched in suitable models for spectra.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	6	nsubjpass	_	_
2	may	may	AUX	MD	VerbForm=Fin	6	aux	_	_
3	for	for	ADP	IN	_	6	prep	_	_
4	instance	instance	NOUN	NN	Number=Sing	3	pobj	_	_
5	be	be	AUX	VB	VerbForm=Inf	6	auxpass	_	_
6	applied	apply	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	to	to	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	case	case	NOUN	NN	Number=Sing	7	pobj	_	_
10	where	where	SCONJ	WRB	_	14	advmod	_	_
11	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	12	poss	_	_
12	categories	category	NOUN	NNS	Number=Plur	14	nsubjpass	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	relcl	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	suitable	suitable	ADJ	JJ	Degree=Pos	17	amod	_	_
17	models	model	NOUN	NNS	Number=Plur	15	pobj	_	_
18	for	for	ADP	IN	_	17	prep	_	_
19	spectra	spectra	PROPN	NNP	Number=Sing	18	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 135
# sent_id = 1
# text = Hopf monads are identified with monads in the 2 - category Opmon of monoidal categories, opmonoidal functors and transformations.
1	Hopf	hopf	NOUN	NN	Number=Sing	2	compound	_	_
2	monads	monad	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	identified	identify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	with	with	ADP	IN	_	4	prep	_	_
6	monads	monad	NOUN	NNS	Number=Plur	5	pobj	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
9	2	2	NUM	CD	NumType=Card	11	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	category	category	NOUN	NN	Number=Sing	12	compound	_	_
12	Opmon	Opmon	PROPN	NNP	Number=Sing	7	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	monoidal	monoidal	ADJ	JJ	Degree=Pos	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
17	opmonoidal	opmonoidal	ADJ	JJ	Degree=Pos	18	amod	_	_
18	functors	functor	NOUN	NNS	Number=Plur	12	conj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	transformations	transformation	NOUN	NNS	Number=Plur	18	conj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = Using Eilenberg - Moore objects, it is shown that for a Hopf monad $ S $ , the categories $ Alg(Coalg(S)) $ and $ Coalg(Alg(S)) $ are canonically isomorphic.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	advcl	_	_
2	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	4	compound	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	Moore	Moore	PROPN	NNP	Number=Sing	5	compound	_	_
5	objects	object	NOUN	NNS	Number=Plur	1	dobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
7	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	9	nsubjpass	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	that	that	SCONJ	IN	_	9	dobj	_	_
11	for	for	ADP	IN	_	9	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	Hopf	Hopf	PROPN	NNP	Number=Sing	14	compound	_	_
14	monad	monad	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	pobj	_	_
15	$ S $	$ s $	SYM	$	_	14	dobj	_	_
16	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	categories	category	NOUN	NNS	Number=Plur	22	nsubj	_	_
19	$ Alg(Coalg(S)) $	$ alg(coalg(s)) $	SYM	$	_	22	nsubj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	$ Coalg(Alg(S)) $	$ coalg(alg(s)) $	SYM	$	_	19	conj	_	_
22	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	ccomp	_	_
23	canonically	canonically	ADV	RB	_	24	advmod	_	_
24	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	22	acomp	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 3
# text = The monadic arrows Opmon are then characterized.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	monadic	monadic	ADJ	JJ	Degree=Pos	3	amod	_	_
3	arrows	arrow	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
4	Opmon	Opmon	PROPN	NNP	Number=Sing	7	nsubjpass	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
6	then	then	ADV	RB	PronType=Dem	7	advmod	_	_
7	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = Finally, the theory of multicategories and a generalization of structure and semantics are used to identify the categories of algebras of Hopf monads.
1	Finally	finally	ADV	RB	_	15	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	theory	theory	NOUN	NN	Number=Sing	15	nsubjpass	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	multicategories	multicategorie	NOUN	NNS	Number=Plur	5	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	generalization	generalization	NOUN	NN	Number=Sing	4	conj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	structure	structure	NOUN	NN	Number=Sing	10	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
13	semantics	semantic	NOUN	NNS	Number=Plur	9	conj	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
16	to	to	PART	TO	_	17	aux	_	_
17	identify	identify	VERB	VB	VerbForm=Inf	15	xcomp	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	categories	category	NOUN	NNS	Number=Plur	17	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	algebras	algebra	NOUN	NNS	Number=Plur	20	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	Hopf	Hopf	PROPN	NNP	Number=Sing	24	compound	_	_
24	monads	monad	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# doc_id = 136
# sent_id = 1
# text = Given a triple $ T $ on a complete category $ C $ and a factorization system $ E/M $ on the category of algebras, we show there is a one - to - one correspondence between full subcategories of the category of algebras that are closed under $ U $ - split epimorphisms, products, and $ M $ - subobjects and triple morphisms $ T - > S $ for which the induced natural transformation between free functors belongs to $ E $ .
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	triple	triple	ADJ	JJ	Degree=Pos	4	amod	_	_
4	$ T $	$ t $	SYM	$	_	1	pobj	_	_
5	on	on	ADP	IN	_	1	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	complete	complete	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
9	$ C $	$ c $	SYM	$	_	8	appos	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	factorization	factorization	NOUN	NN	Number=Sing	13	compound	_	_
13	system	system	NOUN	NN	Number=Sing	8	conj	_	_
14	$ E/M $	$ e/m $	SYM	$	_	1	dep	_	_
15	on	on	ADP	IN	_	1	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	algebras	algebras	PROPN	NNP	Number=Sing	18	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
21	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	22	nsubj	_	_
22	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
23	there	there	PRON	EX	_	24	expl	_	_
24	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	ccomp	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
26	one	one	NUM	CD	NumType=Card	31	nummod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
28	to	to	ADP	IN	_	26	prep	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
30	one	one	NUM	CD	NumType=Card	28	pobj	_	_
31	correspondence	correspondence	NOUN	NN	Number=Sing	24	attr	_	_
32	between	between	ADP	IN	_	31	prep	_	_
33	full	full	ADJ	JJ	Degree=Pos	34	amod	_	_
34	subcategories	subcategorie	NOUN	NNS	Number=Plur	32	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	category	category	NOUN	NN	Number=Sing	35	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	algebras	algebra	NOUN	NNS	Number=Plur	38	pobj	_	_
40	that	that	PRON	WDT	PronType=Rel	42	nsubjpass	_	_
41	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	42	auxpass	_	_
42	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	37	relcl	_	_
43	under	under	ADP	IN	_	42	prep	_	_
44	$ U $	$ u $	SYM	$	_	46	advmod	_	_
45	-	-	PUNCT	HYPH	PunctType=Dash	46	punct	_	_
46	split	split	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	47	amod	_	_
47	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	43	pobj	_	SpaceAfter=No
48	,	,	PUNCT	,	PunctType=Comm	47	punct	_	_
49	products	product	NOUN	NNS	Number=Plur	47	conj	_	SpaceAfter=No
50	,	,	PUNCT	,	PunctType=Comm	49	punct	_	_
51	and	and	CCONJ	CC	ConjType=Cmp	49	cc	_	_
52	$ M $	$ m $	SYM	$	_	54	compound	_	_
53	-	-	PUNCT	HYPH	PunctType=Dash	54	punct	_	_
54	subobjects	subobject	NOUN	NNS	Number=Plur	49	conj	_	_
55	and	and	CCONJ	CC	ConjType=Cmp	54	cc	_	_
56	triple	triple	ADJ	JJ	Degree=Pos	57	amod	_	_
57	morphisms	morphism	NOUN	NNS	Number=Plur	54	conj	_	_
58	$ T - > S $	$ t - > s $	SYM	$	_	47	appos	_	_
59	for	for	ADP	IN	_	68	prep	_	_
60	which	which	PRON	WDT	_	59	pobj	_	_
61	the	the	DET	DT	Definite=Def|PronType=Art	64	det	_	_
62	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	64	amod	_	_
63	natural	natural	ADJ	JJ	Degree=Pos	64	amod	_	_
64	transformation	transformation	NOUN	NN	Number=Sing	68	nsubj	_	_
65	between	between	ADP	IN	_	64	prep	_	_
66	free	free	ADJ	JJ	Degree=Pos	67	amod	_	_
67	functors	functor	NOUN	NNS	Number=Plur	65	pobj	_	_
68	belongs	belong	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	47	relcl	_	_
69	to	to	ADP	IN	_	68	prep	_	_
70	$ E $	$ e $	SYM	$	_	69	pobj	_	_
71	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# doc_id = 137
# sent_id = 1
# text = We give a definition of categorical model for the multiplicative fragment of non - commutative logic.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	definition	definition	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	categorical	categorical	ADJ	JJ	Degree=Pos	7	amod	_	_
7	model	model	NOUN	NN	Number=Sing	5	pobj	_	_
8	for	for	ADP	IN	_	2	dative	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	multiplicative	multiplicative	ADJ	JJ	Degree=Pos	11	amod	_	_
11	fragment	fragment	NOUN	NN	Number=Sing	8	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	non	non	ADJ	JJ	Degree=Pos	15	amod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	commutative	commutative	ADJ	JJ	Degree=Pos	16	amod	_	_
16	logic	logic	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We call such structures entropic categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	such	such	ADJ	JJ	Degree=Pos	4	amod	_	_
4	structures	structure	NOUN	NNS	Number=Plur	6	compound	_	_
5	entropic	entropic	NOUN	NN	Number=Sing	6	compound	_	_
6	categories	category	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
7	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We demonstrate the soundness and completeness of our axiomatization with respect to cut - elimination.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	demonstrate	demonstrate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	soundness	soundness	NOUN	NN	Number=Sing	2	dobj	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	completeness	completeness	NOUN	NN	Number=Sing	4	conj	_	_
7	of	of	ADP	IN	_	4	prep	_	_
8	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	9	poss	_	_
9	axiomatization	axiomatization	NOUN	NN	Number=Sing	7	pobj	_	_
10	with	with	ADP	IN	_	4	prep	_	_
11	respect	respect	NOUN	NN	Number=Sing	10	pobj	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	cut	cut	VERB	VB	VerbForm=Inf	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	elimination	elimination	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We then focus on several methods of building entropic categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	focus	focus	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	on	on	ADP	IN	_	3	prep	_	_
5	several	several	ADJ	JJ	Degree=Pos	6	amod	_	_
6	methods	method	NOUN	NNS	Number=Plur	4	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	building	build	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	pcomp	_	_
9	entropic	entropic	NOUN	NN	Number=Sing	10	compound	_	_
10	categories	category	NOUN	NNS	Number=Plur	8	dobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = Our first models are constructed via the notion of a partial bimonoid acting on a cocomplete category.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	3	poss	_	_
2	first	first	ADJ	JJ	Degree=Pos	3	amod	_	_
3	models	model	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	via	via	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	notion	notion	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	partial	partial	ADJ	JJ	Degree=Pos	12	amod	_	_
12	bimonoid	bimonoid	NOUN	NN	Number=Sing	9	pobj	_	_
13	acting	act	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	acl	_	_
14	on	on	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	cocomplete	cocomplete	ADJ	JJ	Degree=Pos	17	amod	_	_
17	category	category	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 6
# text = We also explore an entropic version of the Chu construction, and apply it in this setting.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	explore	explore	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	entropic	entropic	ADJ	JJ	Degree=Pos	6	amod	_	_
6	version	version	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	Chu	Chu	PROPN	NNP	Number=Sing	10	compound	_	_
10	construction	construction	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
13	apply	apply	VERB	VB	VerbForm=Inf	3	conj	_	_
14	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	13	dobj	_	_
15	in	in	ADP	IN	_	13	prep	_	_
16	this	this	DET	DT	Number=Sing|PronType=Dem	17	det	_	_
17	setting	setting	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = It has recently been demonstrated that Hopf algebras provide an excellent framework for modeling a number of variants of multiplicative linear logic, such as commutative, braided and cyclic.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	5	nsubjpass	_	_
2	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	aux	_	_
3	recently	recently	ADV	RB	_	5	advmod	_	_
4	been	be	AUX	VBN	Tense=Past|VerbForm=Part	5	auxpass	_	_
5	demonstrated	demonstrate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	that	that	SCONJ	IN	_	9	mark	_	_
7	Hopf	Hopf	PROPN	NNP	Number=Sing	8	compound	_	_
8	algebras	algebra	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	5	ccomp	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	excellent	excellent	ADJ	JJ	Degree=Pos	12	amod	_	_
12	framework	framework	NOUN	NN	Number=Sing	9	dobj	_	_
13	for	for	ADP	IN	_	12	prep	_	_
14	modeling	model	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	pcomp	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	number	number	NOUN	NN	Number=Sing	14	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	variants	variant	NOUN	NNS	Number=Plur	17	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	multiplicative	multiplicative	ADJ	JJ	Degree=Pos	22	amod	_	_
21	linear	linear	ADJ	JJ	Degree=Pos	22	compound	_	_
22	logic	logic	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	such	such	ADJ	JJ	Degree=Pos	25	amod	_	_
25	as	as	ADP	IN	_	22	prep	_	_
26	commutative	commutative	ADJ	JJ	Degree=Pos	25	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
28	braided	braid	VERB	VBD	Tense=Past|VerbForm=Fin	26	conj	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	cyclic	cyclic	NOUN	NN	Number=Sing	28	conj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 8
# text = We extend these ideas to the entropic setting by developing a new type of Hopf algebra, which we call entropic Hopf algebras.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	extend	extend	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	these	these	DET	DT	Number=Plur|PronType=Dem	4	det	_	_
4	ideas	idea	NOUN	NNS	Number=Plur	2	dobj	_	_
5	to	to	ADP	IN	_	2	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	entropic	entropic	NOUN	NN	Number=Sing	8	amod	_	_
8	setting	setting	NOUN	NN	Number=Sing	5	pobj	_	_
9	by	by	ADP	IN	_	2	prep	_	_
10	developing	develop	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	pcomp	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	new	new	ADJ	JJ	Degree=Pos	13	amod	_	_
13	type	type	NOUN	NN	Number=Sing	10	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	Hopf	Hopf	PROPN	NNP	Number=Sing	16	compound	_	_
16	algebra	algebra	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	which	which	PRON	WDT	_	20	dobj	_	_
19	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	20	nsubj	_	_
20	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	16	relcl	_	_
21	entropic	entropic	ADJ	JJ	Degree=Pos	23	amod	_	_
22	Hopf	Hopf	PROPN	NNP	Number=Sing	23	compound	_	_
23	algebras	algebra	NOUN	NNS	Number=Plur	20	dobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 9
# text = We show that the category of modules over an entropic Hopf algebra is an entropic category (possibly after application of the Chu construction).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	13	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	13	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	modules	module	NOUN	NNS	Number=Plur	6	pobj	_	_
8	over	over	ADP	IN	_	5	prep	_	_
9	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
10	entropic	entropic	NOUN	NN	Number=Sing	12	amod	_	_
11	Hopf	hopf	NOUN	NN	Number=Sing	12	compound	_	_
12	algebra	algebra	NOUN	NN	Number=Sing	8	pobj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	entropic	entropic	ADJ	JJ	Degree=Pos	16	amod	_	_
16	category	category	NOUN	NN	Number=Sing	13	attr	_	_
17	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	16	punct	_	SpaceAfter=No
18	possibly	possibly	ADV	RB	_	19	advmod	_	_
19	after	after	ADP	IN	_	13	prep	_	_
20	application	application	NOUN	NN	Number=Sing	19	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	Chu	Chu	PROPN	NNP	Number=Sing	24	compound	_	_
24	construction	construction	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
25	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	13	punct	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 10
# text = Several examples are discussed, based first on the notion of a bigroup.
1	Several	several	ADJ	JJ	Degree=Pos	2	amod	_	_
2	examples	example	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	discussed	discuss	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
6	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	advcl	_	_
7	first	first	ADV	RB	_	6	advmod	_	_
8	on	on	ADP	IN	_	6	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	notion	notion	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	bigroup	bigroup	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 11
# text = Finally the Tannaka - Krein reconstruction theorem is extended to the entropic setting.
1	Finally	finally	ADV	RB	_	7	advmod	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
3	Tannaka	Tannaka	PROPN	NNP	Number=Sing	5	compound	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	Krein	Krein	PROPN	NNP	Number=Sing	6	compound	_	_
6	reconstruction	reconstruction	NOUN	NN	Number=Sing	7	nsubj	_	_
7	theorem	theorem	ADJ	JJ	Degree=Pos	9	nsubjpass	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	entropic	entropic	NOUN	NN	Number=Sing	13	amod	_	_
13	setting	setting	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 138
# sent_id = 1
# text = By abstract Stone duality we mean that the topology or contravariant powerset functor, seen as a self - adjoint exponential $ Sigma^{( - )} $ on some category, is monadic.
1	By	by	ADP	IN	_	6	prep	_	_
2	abstract	abstract	ADJ	JJ	Degree=Pos	4	amod	_	_
3	Stone	Stone	PROPN	NNP	Number=Sing	4	compound	_	_
4	duality	duality	NOUN	NN	Number=Sing	1	pobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	mean	mean	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	27	mark	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	topology	topology	NOUN	NN	Number=Sing	22	nsubj	_	_
10	or	or	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	contravariant	contravariant	ADJ	JJ	Degree=Pos	13	amod	_	_
12	powerset	powerset	NOUN	NN	Number=Sing	13	compound	_	_
13	functor	functor	NOUN	NN	Number=Sing	9	conj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
15	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	acl	_	_
16	as	as	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
18	self	self	NOUN	NN	Number=Sing	20	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	adjoint	adjoint	NOUN	NN	Number=Sing	21	compound	_	_
21	exponential	exponential	NOUN	NN	Number=Sing	16	pobj	_	_
22	$ Sigma^{( - )} $	$ sigma^{( - )} $	SYM	$	_	27	nsubj	_	_
23	on	on	ADP	IN	_	22	prep	_	_
24	some	some	DET	DT	_	25	det	_	_
25	category	category	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
28	monadic	monadic	ADJ	JJ	Degree=Pos	27	acomp	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = Using Beck's theorem, this means that certain equalisers exist and carry the subspace topology.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	advcl	_	_
2	Beck	Beck	PROPN	NNP	Number=Sing	4	poss	_	SpaceAfter=No
3	's	's	PART	POS	_	2	case	_	_
4	theorem	theorem	ADJ	JJ	Degree=Pos	1	dobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	this	this	PRON	DT	Number=Sing|PronType=Dem	7	nsubj	_	_
7	means	mean	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	that	that	SCONJ	IN	_	11	mark	_	_
9	certain	certain	ADJ	JJ	Degree=Pos	10	amod	_	_
10	equalisers	equaliser	NOUN	NNS	Number=Plur	11	nsubj	_	_
11	exist	exist	VERB	VBP	Tense=Pres|VerbForm=Fin	7	ccomp	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	carry	carry	VERB	VB	VerbForm=Inf	11	conj	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	subspace	subspace	NOUN	NN	Number=Sing	16	compound	_	_
16	topology	topology	NOUN	NN	Number=Sing	13	dobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = These subspaces are encoded by idempotents that play a role similar to that of nuclei in locale theory.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	subspaces	subspace	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	encoded	encode	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	by	by	ADP	IN	_	4	agent	_	_
6	idempotents	idempotent	NOUN	NNS	Number=Plur	5	pobj	_	_
7	that	that	PRON	WDT	PronType=Rel	8	nsubj	_	_
8	play	play	VERB	VBP	Tense=Pres|VerbForm=Fin	6	relcl	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	role	role	NOUN	NN	Number=Sing	8	dobj	_	_
11	similar	similar	ADJ	JJ	Degree=Pos	10	amod	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	that	that	PRON	DT	Number=Sing|PronType=Dem	12	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	nuclei	nucleus	NOUN	NNS	Number=Plur	14	pobj	_	_
16	in	in	ADP	IN	_	8	prep	_	_
17	locale	locale	NOUN	NN	Number=Sing	18	compound	_	_
18	theory	theory	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = Paré showed that any elementary topos has this duality, and we prove it intuitionistically for the category of locally compact locales.
1	Paré	Paré	PROPN	NNP	Number=Sing	2	nsubj	_	_
2	showed	show	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	any	any	DET	DT	_	6	det	_	_
5	elementary	elementary	ADJ	JJ	Degree=Pos	6	amod	_	_
6	topos	topos	NOUN	NN	Number=Sing	7	nsubj	_	_
7	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	this	this	DET	DT	Number=Sing|PronType=Dem	9	det	_	_
9	duality	duality	NOUN	NN	Number=Sing	7	dobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
14	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	13	dobj	_	_
15	intuitionistically	intuitionistically	ADV	RB	_	13	advmod	_	_
16	for	for	ADP	IN	_	13	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	category	category	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	locally	locally	ADV	RB	_	21	advmod	_	_
21	compact	compact	ADJ	JJ	Degree=Pos	22	amod	_	_
22	locales	locale	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 5
# text = The paper is largely concerned with the construction of such a category out of one that merely has powers of some fixed object $ Sigma $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	largely	largely	ADV	RB	_	5	advmod	_	_
5	concerned	concerned	ADJ	JJ	Degree=Pos	3	acomp	_	_
6	with	with	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	construction	construction	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	such	such	DET	PDT	_	12	predet	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
13	out	out	ADP	IN	_	8	prep	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	one	one	NUM	CD	NumType=Card	14	pobj	_	_
16	that	that	PRON	WDT	PronType=Rel	18	nsubj	_	_
17	merely	merely	ADV	RB	_	18	advmod	_	_
18	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	relcl	_	_
19	powers	power	NOUN	NNS	Number=Plur	18	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	some	some	DET	DT	_	23	det	_	_
22	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	amod	_	_
23	object	object	NOUN	NN	Number=Sing	20	pobj	_	_
24	$ Sigma $	$ sigma $	SYM	$	_	5	dep	_	_
25	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = It builds on Sober Spaces and Continuations, where the related but weaker notion of abstract sobriety was considered.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	builds	build	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	on	on	ADP	IN	_	2	prep	_	_
4	Sober	Sober	PROPN	NNP	Number=Sing	5	compound	_	_
5	Spaces	Spaces	PROPN	NNPS	Number=Plur	3	pobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	Continuations	Continuations	PROPN	NNP	Number=Sing	5	conj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
9	where	where	SCONJ	WRB	_	19	advmod	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
11	related	related	ADJ	JJ	Degree=Pos	14	amod	_	_
12	but	but	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	weaker	weak	ADJ	JJR	Degree=Cmp	11	conj	_	_
14	notion	notion	NOUN	NN	Number=Sing	19	nsubjpass	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	abstract	abstract	ADJ	JJ	Degree=Pos	17	amod	_	_
17	sobriety	sobriety	NOUN	NN	Number=Sing	15	pobj	_	_
18	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	19	auxpass	_	_
19	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	relcl	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = The construction is done first by formally adjoining certain equalisers that $ Sigma^{( - )} $ takes to coequalisers, then using Eilenberg - Moore algebras, and finally presented as a lambda calculus similar to the axiom of comprehension in set theory.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	construction	construction	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	done	do	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	first	first	ADV	RB	_	4	advmod	_	_
6	by	by	ADP	IN	_	4	agent	_	_
7	formally	formally	ADV	RB	_	8	advmod	_	_
8	adjoining	adjoin	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	amod	_	_
9	certain	certain	ADJ	JJ	Degree=Pos	10	amod	_	_
10	equalisers	equaliser	NOUN	NNS	Number=Plur	6	pobj	_	_
11	that	that	SCONJ	IN	_	13	dobj	_	_
12	$ Sigma^{( - )} $	$ sigma^{( - )} $	SYM	$	_	13	nsubj	_	_
13	takes	take	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	relcl	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	coequalisers	coequaliser	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
17	then	then	ADV	RB	PronType=Dem	4	advmod	_	_
18	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	advcl	_	_
19	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	Moore	Moore	PROPN	NNP	Number=Sing	22	compound	_	_
22	algebras	algebra	NOUN	NNS	Number=Plur	18	dobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
25	finally	finally	ADV	RB	_	26	advmod	_	_
26	presented	present	VERB	VBD	Tense=Past|VerbForm=Fin	4	conj	_	_
27	as	as	ADP	IN	_	26	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
29	lambda	lambda	ADJ	JJ	Degree=Pos	30	amod	_	_
30	calculus	calculus	NOUN	NN	Number=Sing	27	pobj	_	_
31	similar	similar	ADJ	JJ	Degree=Pos	30	amod	_	_
32	to	to	ADP	IN	_	31	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
34	axiom	axiom	NOUN	NN	Number=Sing	32	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	comprehension	comprehension	NOUN	NN	Number=Sing	35	pobj	_	_
37	in	in	ADP	IN	_	36	prep	_	_
38	set	set	ADJ	JJ	Degree=Pos	39	amod	_	_
39	theory	theory	NOUN	NN	Number=Sing	37	pobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 8
# text = The comprehension calculus has a normalisation theorem, by which every type can be embedded as a subspace of a type formed without comprehension, and terms also normalise in a simple way.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	comprehension	comprehension	NOUN	NN	Number=Sing	3	compound	_	_
3	calculus	calculus	NOUN	NN	Number=Sing	4	nsubj	_	_
4	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	normalisation	normalisation	NOUN	NN	Number=Sing	4	dobj	_	_
7	theorem	theorem	ADJ	JJ	Degree=Pos	6	acl	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
9	by	by	ADP	IN	_	15	prep	_	_
10	which	which	PRON	WDT	_	9	pobj	_	_
11	every	every	DET	DT	_	12	det	_	_
12	type	type	NOUN	NN	Number=Sing	15	nsubjpass	_	_
13	can	can	AUX	MD	VerbForm=Fin	15	aux	_	_
14	be	be	AUX	VB	VerbForm=Inf	15	auxpass	_	_
15	embedded	embed	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	relcl	_	_
16	as	as	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	subspace	subspace	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	type	type	NOUN	NN	Number=Sing	19	pobj	_	_
22	formed	form	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	acl	_	_
23	without	without	ADP	IN	_	22	prep	_	_
24	comprehension	comprehension	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
27	terms	term	NOUN	NNS	Number=Plur	29	nsubj	_	_
28	also	also	ADV	RB	_	29	advmod	_	_
29	normalise	normalise	VERB	VBP	Tense=Pres|VerbForm=Fin	15	conj	_	_
30	in	in	ADP	IN	_	29	prep	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
32	simple	simple	ADJ	JJ	Degree=Pos	33	amod	_	_
33	way	way	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	29	punct	_	SpaceAfter=No

# sent_id = 9
# text = The symbolic and categorical structures are thereby shown to be equivalent.
1	The	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
2	symbolic	symbolic	ADJ	JJ	Degree=Pos	5	amod	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	categorical	categorical	ADJ	JJ	Degree=Pos	2	conj	_	_
5	structures	structure	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
7	thereby	thereby	ADV	RB	_	8	advmod	_	_
8	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	be	be	AUX	VB	VerbForm=Inf	8	xcomp	_	_
11	equivalent	equivalent	ADJ	JJ	Degree=Pos	10	acomp	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 10
# text = Finally, sums and certain quotients are constructed using the comprehension calculus, giving an extensive category.
1	Finally	finally	ADV	RB	_	8	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
3	sums	sum	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	certain	certain	ADJ	JJ	Degree=Pos	6	amod	_	_
6	quotients	quotient	NOUN	NNS	Number=Plur	3	conj	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	advcl	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	comprehension	comprehension	NOUN	NN	Number=Sing	12	compound	_	_
12	calculus	calculus	NOUN	NN	Number=Sing	9	dobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
14	giving	give	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	advcl	_	_
15	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	extensive	extensive	ADJ	JJ	Degree=Pos	17	amod	_	_
17	category	category	NOUN	NN	Number=Sing	14	dobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 139
# sent_id = 1
# text = It is proved that any category $ cal{K} $ which is equivalent to a simultaneously reflective and coreflective full subcategory of presheaves $ [cal{A}^{op}, Set] $ , is itself equivalent to the category of the form $ [cal{B}^{op}, Set] $ and the inclusion is induced by a functor $ cal{A} to cal{B} $ which is surjective on objects.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	SCONJ	IN	_	23	mark	_	_
5	any	any	DET	DT	_	6	det	_	_
6	category	category	NOUN	NN	Number=Sing	23	nsubj	_	_
7	$ cal{K} $	$ cal{k} $	SYM	$	_	6	appos	_	_
8	which	which	PRON	WDT	_	9	nsubj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	relcl	_	_
10	equivalent	equivalent	ADJ	JJ	Degree=Pos	9	acomp	_	_
11	to	to	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
13	simultaneously	simultaneously	ADV	RB	_	14	advmod	_	_
14	reflective	reflective	ADJ	JJ	Degree=Pos	18	amod	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	coreflective	coreflective	ADJ	JJ	Degree=Pos	14	conj	_	_
17	full	full	ADJ	JJ	Degree=Pos	18	amod	_	_
18	subcategory	subcategory	NOUN	NN	Number=Sing	11	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	presheaves	presheave	NOUN	NNS	Number=Plur	19	pobj	_	_
21	$ [cal{A}^{op}, Set] $	$ [cal{a}^{op}, set] $	SYM	$	_	20	appos	_	_
22	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
24	itself	itself	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs|Reflex=Yes	23	attr	_	_
25	equivalent	equivalent	ADJ	JJ	Degree=Pos	23	acomp	_	_
26	to	to	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	category	category	NOUN	NN	Number=Sing	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	form	form	NOUN	NN	Number=Sing	29	pobj	_	_
32	$ [cal{B}^{op}, Set] $	$ [cal{b}^{op}, set] $	SYM	$	_	23	dep	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	inclusion	inclusion	NOUN	NN	Number=Sing	37	nsubjpass	_	_
36	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	37	auxpass	_	_
37	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	conj	_	_
38	by	by	ADP	IN	_	37	agent	_	_
39	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
40	functor	functor	NOUN	NN	Number=Sing	41	compound	_	_
41	$ cal{A} to cal{B} $	$ cal{a} to cal{b} $	SYM	$	_	38	pobj	_	_
42	which	which	PRON	WDT	_	43	nsubj	_	_
43	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	41	relcl	_	_
44	surjective	surjective	ADJ	JJ	Degree=Pos	43	acomp	_	_
45	on	on	ADP	IN	_	44	prep	_	_
46	objects	object	NOUN	NNS	Number=Plur	45	pobj	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = We obtain a characterization of such functors.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	characterization	characterization	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	such	such	ADJ	JJ	Degree=Pos	7	amod	_	_
7	functors	functor	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Moreover, the base category $ Set $ can be replaced with any symmetric monoidal closed category $ V $ which is complete and cocomplete, and then analogy of the above result holds if we replace categories by $ V $ - categories and functors by $ V $ - functors.
1	Moreover	moreover	ADV	RB	_	9	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	base	base	NOUN	NN	Number=Sing	5	compound	_	_
5	category	category	NOUN	NN	Number=Sing	9	nsubjpass	_	_
6	$ Set $	$ set $	SYM	$	_	5	appos	_	_
7	can	can	AUX	MD	VerbForm=Fin	9	aux	_	_
8	be	be	AUX	VB	VerbForm=Inf	9	auxpass	_	_
9	replaced	replace	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	any	any	DET	DT	_	13	det	_	_
12	symmetric	symmetric	ADJ	JJ	Degree=Pos	13	amod	_	_
13	monoidal	monoidal	NOUN	NN	Number=Sing	14	nsubj	_	_
14	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	10	pcomp	_	_
15	category	category	NOUN	NN	Number=Sing	14	dobj	_	_
16	$ V $	$ v $	SYM	$	_	14	dep	_	_
17	which	which	PRON	WDT	_	18	nsubj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	advcl	_	_
19	complete	complete	ADJ	JJ	Degree=Pos	18	acomp	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	cocomplete	cocomplete	ADJ	JJ	Degree=Pos	19	conj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
24	then	then	ADV	RB	PronType=Dem	30	advmod	_	_
25	analogy	analogy	NOUN	NN	Number=Sing	30	nsubj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	above	above	ADJ	JJ	Degree=Pos	29	amod	_	_
29	result	result	NOUN	NN	Number=Sing	26	pobj	_	_
30	holds	hold	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	conj	_	_
31	if	if	SCONJ	IN	_	33	mark	_	_
32	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	33	nsubj	_	_
33	replace	replace	VERB	VBP	Tense=Pres|VerbForm=Fin	30	ccomp	_	_
34	categories	category	NOUN	NNS	Number=Plur	33	dobj	_	_
35	by	by	ADP	IN	_	33	prep	_	_
36	$ V $	$ v $	SYM	$	_	38	compound	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	38	punct	_	_
38	categories	category	NOUN	NNS	Number=Plur	35	pobj	_	_
39	and	and	CCONJ	CC	ConjType=Cmp	38	cc	_	_
40	functors	functor	NOUN	NNS	Number=Plur	38	conj	_	_
41	by	by	ADP	IN	_	33	prep	_	_
42	$ V $	$ v $	SYM	$	_	44	compound	_	_
43	-	-	PUNCT	HYPH	PunctType=Dash	44	punct	_	_
44	functors	functor	NOUN	NNS	Number=Plur	41	pobj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 4
# text = As a consequence we are able to derive well - known results on simultaneously reflective and coreflective categories of sets, Abelian groups, et cetera.
1	As	as	ADP	IN	_	5	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	consequence	consequence	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	able	able	ADJ	JJ	Degree=Pos	5	acomp	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	derive	derive	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	well	well	ADV	RB	Degree=Pos	11	advmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
12	results	result	NOUN	NNS	Number=Plur	8	dobj	_	_
13	on	on	ADP	IN	_	8	prep	_	_
14	simultaneously	simultaneously	ADV	RB	_	15	advmod	_	_
15	reflective	reflective	ADJ	JJ	Degree=Pos	18	amod	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	coreflective	coreflective	ADJ	JJ	Degree=Pos	15	conj	_	_
18	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	sets	set	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
22	Abelian	abelian	ADJ	JJ	Degree=Pos	23	amod	_	_
23	groups	group	NOUN	NNS	Number=Plur	4	appos	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
25	et	et	NOUN	NN	Number=Sing	26	compound	_	_
26	cetera	cetera	NOUN	NN	Number=Sing	23	appos	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 140
# sent_id = 1
# text = This paper defines flows (or discrete dynamical systems) and cyclic flows in a category and investigates how the trajectories of a point might approach a cycle.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	defines	define	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	flows	flow	NOUN	NNS	Number=Plur	3	dobj	_	_
5	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	4	punct	_	SpaceAfter=No
6	or	or	CCONJ	CC	ConjType=Cmp	4	cc	_	_
7	discrete	discrete	ADJ	JJ	Degree=Pos	9	amod	_	_
8	dynamical	dynamical	ADJ	JJ	Degree=Pos	9	amod	_	_
9	systems	system	NOUN	NNS	Number=Plur	4	conj	_	SpaceAfter=No
10	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	9	punct	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
12	cyclic	cyclic	ADJ	JJ	Degree=Pos	13	amod	_	_
13	flows	flow	NOUN	NNS	Number=Plur	4	conj	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	category	category	NOUN	NN	Number=Sing	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
18	investigates	investigate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	conj	_	_
19	how	how	SCONJ	WRB	_	26	advmod	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	trajectories	trajectory	NOUN	NNS	Number=Plur	26	nsubj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	point	point	NOUN	NN	Number=Sing	22	pobj	_	_
25	might	might	AUX	MD	VerbForm=Fin	26	aux	_	_
26	approach	approach	VERB	VB	VerbForm=Inf	18	ccomp	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	cycle	cycle	NOUN	NN	Number=Sing	26	dobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = The paper considers cyclic flows in the categories of Sets and of Boolean algebras and their duals and characterizes the Stone representation of a cyclic flow in Boolean algebras.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	considers	consider	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	cyclic	cyclic	ADJ	JJ	Degree=Pos	5	amod	_	_
5	flows	flow	NOUN	NNS	Number=Plur	3	dobj	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Sets	Sets	PROPN	NNPS	Number=Plur	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
12	of	of	ADP	IN	_	9	conj	_	_
13	Boolean	boolean	ADJ	JJ	Degree=Pos	14	amod	_	_
14	algebras	algebra	NOUN	NNS	Number=Plur	12	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	17	poss	_	_
17	duals	dual	NOUN	NNS	Number=Plur	14	conj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
19	characterizes	characterize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	Stone	Stone	PROPN	NNP	Number=Sing	22	compound	_	_
22	representation	representation	NOUN	NN	Number=Sing	19	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
25	cyclic	cyclic	ADJ	JJ	Degree=Pos	26	amod	_	_
26	flow	flow	NOUN	NN	Number=Sing	23	pobj	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	Boolean	Boolean	PROPN	NNP	Number=Sing	29	amod	_	_
29	algebras	algebra	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = A cyclic spectrum is constructed for Boolean flows.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	cyclic	cyclic	ADJ	JJ	Degree=Pos	3	amod	_	_
3	spectrum	spectrum	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	Boolean	boolean	ADJ	JJ	Degree=Pos	8	amod	_	_
8	flows	flow	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = Examples include attractive fixpoints, repulsive fixpoints, strange attractors and the logistic equation.
1	Examples	example	NOUN	NNS	Number=Plur	2	nsubj	_	_
2	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	attractive	attractive	ADJ	JJ	Degree=Pos	4	amod	_	_
4	fixpoints	fixpoint	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
6	repulsive	repulsive	ADJ	JJ	Degree=Pos	7	amod	_	_
7	fixpoints	fixpoint	NOUN	NNS	Number=Plur	4	conj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	strange	strange	ADJ	JJ	Degree=Pos	10	amod	_	_
10	attractors	attractor	NOUN	NNS	Number=Plur	7	conj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	logistic	logistic	ADJ	JJ	Degree=Pos	14	amod	_	_
14	equation	equation	NOUN	NN	Number=Sing	10	conj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 141
# sent_id = 1
# text = Directed Algebraic Topology studies phenomena where privileged directions appear, derived from the analysis of concurrency, traffic networks, space - time models, et cetera.
1	Directed	Directed	PROPN	NNP	Number=Sing	4	amod	_	_
2	Algebraic	Algebraic	PROPN	NNP	Number=Sing	3	compound	_	_
3	Topology	Topology	PROPN	NNP	Number=Sing	4	compound	_	_
4	studies	study	NOUN	NNS	Number=Plur	5	nsubj	_	_
5	phenomena	phenomena	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	where	where	SCONJ	WRB	_	9	advmod	_	_
7	privileged	privileged	ADJ	JJ	Degree=Pos	8	amod	_	_
8	directions	direction	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	appear	appear	VERB	VBP	Tense=Pres|VerbForm=Fin	5	relcl	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	derived	derive	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	acl	_	_
12	from	from	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	analysis	analysis	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	concurrency	concurrency	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	traffic	traffic	NOUN	NN	Number=Sing	19	compound	_	_
19	networks	network	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	space	space	NOUN	NN	Number=Sing	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	time	time	NOUN	NN	Number=Sing	24	compound	_	_
24	models	model	NOUN	NNS	Number=Plur	19	conj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	et	et	NOUN	NN	Number=Sing	27	compound	_	_
27	cetera	cetera	NOUN	NN	Number=Sing	16	appos	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = This is the sequel of a paper, where we introduced directed spaces, their non reversible homotopies and their fundamental category.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	sequel	sequel	NOUN	NN	Number=Sing	2	attr	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	paper	paper	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	where	where	SCONJ	WRB	_	11	advmod	_	_
10	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	11	nsubj	_	_
11	introduced	introduce	VERB	VBD	Tense=Past|VerbForm=Fin	7	relcl	_	_
12	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
13	spaces	space	NOUN	NNS	Number=Plur	11	dobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	18	poss	_	_
16	non	non	ADJ	JJ	Degree=Pos	17	amod	_	_
17	reversible	reversible	ADJ	JJ	Degree=Pos	18	amod	_	_
18	homotopies	homotopie	NOUN	NNS	Number=Plur	13	conj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	22	poss	_	_
21	fundamental	fundamental	ADJ	JJ	Degree=Pos	22	amod	_	_
22	category	category	NOUN	NN	Number=Sing	18	conj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Here we study some basic constructs of homotopy, like homotopy pushouts and pullbacks, mapping cones and homotopy fibres, suspensions and loops, cofibre and fibre sequences.
1	Here	here	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	some	some	DET	DT	_	6	det	_	_
5	basic	basic	ADJ	JJ	Degree=Pos	6	amod	_	_
6	constructs	construct	NOUN	NNS	Number=Plur	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	homotopy	homotopy	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
10	like	like	ADP	IN	_	3	prep	_	_
11	homotopy	homotopy	NOUN	NN	Number=Sing	12	compound	_	_
12	pushouts	pushout	NOUN	NNS	Number=Plur	10	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	pullbacks	pullback	NOUN	NNS	Number=Plur	12	conj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
16	mapping	mapping	NOUN	NN	Number=Sing	17	compound	_	_
17	cones	cone	NOUN	NNS	Number=Plur	12	conj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	homotopy	homotopy	NOUN	NN	Number=Sing	20	compound	_	_
20	fibres	fibre	NOUN	NNS	Number=Plur	17	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	suspensions	suspension	NOUN	NNS	Number=Plur	20	conj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	loops	loop	NOUN	NNS	Number=Plur	22	conj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	cofibre	cofibre	PROPN	NNP	Number=Sing	24	conj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	fibre	fibre	PROPN	NNP	Number=Sing	29	compound	_	_
29	sequences	sequence	NOUN	NNS	Number=Plur	26	conj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 142
# sent_id = 1
# text = A topological space is sober if it has exactly the points that are dictated by its open sets.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	topological	topological	ADJ	JJ	Degree=Pos	3	amod	_	_
3	space	space	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	sober	sober	ADJ	JJ	Degree=Pos	4	acomp	_	_
6	if	if	SCONJ	IN	_	8	mark	_	_
7	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	8	nsubj	_	_
8	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	advcl	_	_
9	exactly	exactly	ADV	RB	_	11	advmod	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	points	point	NOUN	NNS	Number=Plur	8	dobj	_	_
12	that	that	PRON	WDT	PronType=Rel	14	nsubjpass	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	dictated	dictate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	relcl	_	_
15	by	by	ADP	IN	_	14	agent	_	_
16	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	18	poss	_	_
17	open	open	ADJ	JJ	Degree=Pos	18	amod	_	_
18	sets	set	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = We explain the analogy with the way in which computational values are determined by the observations that can be made of them.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	explain	explain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	analogy	analogy	NOUN	NN	Number=Sing	2	dobj	_	_
5	with	with	ADP	IN	_	2	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	way	way	NOUN	NN	Number=Sing	5	pobj	_	_
8	in	in	ADP	IN	_	13	prep	_	_
9	which	which	PRON	WDT	_	8	pobj	_	_
10	computational	computational	ADJ	JJ	Degree=Pos	11	amod	_	_
11	values	value	NOUN	NNS	Number=Plur	13	nsubjpass	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	determined	determine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	relcl	_	_
14	by	by	ADP	IN	_	13	agent	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	observations	observation	NOUN	NNS	Number=Plur	14	pobj	_	_
17	that	that	PRON	WDT	PronType=Rel	20	nsubjpass	_	_
18	can	can	AUX	MD	VerbForm=Fin	20	aux	_	_
19	be	be	AUX	VB	VerbForm=Inf	20	auxpass	_	_
20	made	make	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	relcl	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	21	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = A new definition of sobriety is formulated in terms of lambda calculus and elementary category theory, with no reference to lattice structure, but, for topological spaces, this coincides with the standard lattice - theoretic definition.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	new	new	ADJ	JJ	Degree=Pos	3	amod	_	_
3	definition	definition	NOUN	NN	Number=Sing	7	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	sobriety	sobriety	NOUN	NN	Number=Sing	4	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	formulated	formulate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	terms	term	NOUN	NNS	Number=Plur	8	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	lambda	lambda	PROPN	NNP	Number=Sing	12	compound	_	_
12	calculus	calculus	PROPN	NNP	Number=Sing	10	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	elementary	elementary	ADJ	JJ	Degree=Pos	15	amod	_	_
15	category	category	NOUN	NN	Number=Sing	16	compound	_	_
16	theory	theory	NOUN	NN	Number=Sing	12	conj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
18	with	with	ADP	IN	_	7	prep	_	_
19	no	no	DET	DT	_	20	det	_	_
20	reference	reference	NOUN	NN	Number=Sing	18	pobj	_	_
21	to	to	PART	TO	_	22	aux	_	_
22	lattice	lattice	VERB	VB	VerbForm=Inf	20	acl	_	_
23	structure	structure	NOUN	NN	Number=Sing	22	dobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
25	but	but	CCONJ	CC	ConjType=Cmp	7	cc	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
27	for	for	ADP	IN	_	32	prep	_	_
28	topological	topological	ADJ	JJ	Degree=Pos	29	amod	_	_
29	spaces	space	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
31	this	this	PRON	DT	Number=Sing|PronType=Dem	32	nsubj	_	_
32	coincides	coincide	NOUN	NNS	Number=Plur	7	conj	_	_
33	with	with	ADP	IN	_	32	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
35	standard	standard	ADJ	JJ	Degree=Pos	39	amod	_	_
36	lattice	lattice	NOUN	NN	Number=Sing	38	npadvmod	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	38	punct	_	_
38	theoretic	theoretic	ADJ	JJ	Degree=Pos	39	amod	_	_
39	definition	definition	NOUN	NN	Number=Sing	33	pobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	32	punct	_	SpaceAfter=No

# sent_id = 4
# text = The primitive symbolic and categorical structures are extended to make their types sober.
1	The	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
2	primitive	primitive	ADJ	JJ	Degree=Pos	6	amod	_	_
3	symbolic	symbolic	ADJ	JJ	Degree=Pos	6	amod	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	categorical	categorical	ADJ	JJ	Degree=Pos	3	conj	_	_
6	structures	structure	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	make	make	VERB	VB	VerbForm=Inf	8	xcomp	_	_
11	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	12	poss	_	_
12	types	type	NOUN	NNS	Number=Plur	13	nsubj	_	_
13	sober	sober	ADJ	JJ	Degree=Pos	10	ccomp	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 5
# text = For the natural numbers, the additional structure provides definition by description and general recursion.
1	For	for	ADP	IN	_	9	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	natural	natural	ADJ	JJ	Degree=Pos	4	amod	_	_
4	numbers	number	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	additional	additional	ADJ	JJ	Degree=Pos	8	amod	_	_
8	structure	structure	NOUN	NN	Number=Sing	9	nsubj	_	_
9	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	definition	definition	NOUN	NN	Number=Sing	9	dobj	_	_
11	by	by	ADP	IN	_	9	prep	_	_
12	description	description	NOUN	NN	Number=Sing	11	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	general	general	ADJ	JJ	Degree=Pos	15	amod	_	_
15	recursion	recursion	NOUN	NN	Number=Sing	12	conj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 6
# text = We use the same basic categorical construction that Thielecke, Fuhrmann and Selinger use to study continuations, but our emphasis is completely different: we concentrate on the fragment of their calculus that excludes computational effects, but show how it nevertheless defines new denotational values.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
4	same	same	ADJ	JJ	Degree=Pos	7	amod	_	_
5	basic	basic	ADJ	JJ	Degree=Pos	7	amod	_	_
6	categorical	categorical	ADJ	JJ	Degree=Pos	7	amod	_	_
7	construction	construction	NOUN	NN	Number=Sing	2	dobj	_	_
8	that	that	PRON	WDT	PronType=Rel	14	dobj	_	_
9	Thielecke	Thielecke	PROPN	NNP	Number=Sing	14	nsubj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	Fuhrmann	Fuhrmann	PROPN	NNP	Number=Sing	9	conj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	Selinger	Selinger	PROPN	NNP	Number=Sing	11	conj	_	_
14	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	7	relcl	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	study	study	VERB	VB	VerbForm=Inf	14	xcomp	_	_
17	continuations	continuation	NOUN	NNS	Number=Plur	16	dobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
19	but	but	CCONJ	CC	ConjType=Cmp	2	cc	_	_
20	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	21	poss	_	_
21	emphasis	emphasis	NOUN	NN	Number=Sing	22	nsubj	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	ccomp	_	_
23	completely	completely	ADV	RB	_	24	advmod	_	_
24	different	different	ADJ	JJ	Degree=Pos	22	acomp	_	SpaceAfter=No
25	:	:	PUNCT	:	_	27	punct	_	_
26	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	27	nsubj	_	_
27	concentrate	concentrate	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
28	on	on	ADP	IN	_	27	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	fragment	fragment	NOUN	NN	Number=Sing	28	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	33	poss	_	_
33	calculus	calculus	NOUN	NN	Number=Sing	31	pobj	_	_
34	that	that	PRON	WDT	PronType=Rel	35	nsubj	_	_
35	excludes	exclude	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	relcl	_	_
36	computational	computational	ADJ	JJ	Degree=Pos	37	amod	_	_
37	effects	effect	NOUN	NNS	Number=Plur	35	dobj	_	SpaceAfter=No
38	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
39	but	but	CCONJ	CC	ConjType=Cmp	27	cc	_	_
40	show	show	VERB	VB	VerbForm=Inf	27	conj	_	_
41	how	how	SCONJ	WRB	_	44	advmod	_	_
42	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	44	nsubj	_	_
43	nevertheless	nevertheless	ADV	RB	_	44	advmod	_	_
44	defines	define	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	40	ccomp	_	_
45	new	new	ADJ	JJ	Degree=Pos	47	amod	_	_
46	denotational	denotational	ADJ	JJ	Degree=Pos	47	amod	_	_
47	values	value	NOUN	NNS	Number=Plur	44	dobj	_	SpaceAfter=No
48	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = Nor is this ``denotational semantics of continuations using sober spaces'', though that could easily be derived.
1	Nor	nor	CCONJ	CC	ConjType=Cmp	2	cc	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
4	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	7	punct	_	SpaceAfter=No
5	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	7	punct	_	SpaceAfter=No
6	denotational	denotational	ADJ	JJ	Degree=Pos	7	amod	_	_
7	semantics	semantic	NOUN	NNS	Number=Plur	2	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	continuations	continuation	NOUN	NNS	Number=Plur	8	pobj	_	_
10	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	acl	_	_
11	sober	sober	ADJ	JJ	Degree=Pos	12	amod	_	_
12	spaces	space	NOUN	NNS	Number=Plur	10	dobj	_	SpaceAfter=No
13	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	7	punct	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
15	though	though	SCONJ	IN	_	20	mark	_	_
16	that	that	PRON	DT	Number=Sing|PronType=Dem	20	nsubjpass	_	_
17	could	could	AUX	MD	VerbForm=Fin	20	aux	_	_
18	easily	easily	ADV	RB	_	20	advmod	_	_
19	be	be	AUX	VB	VerbForm=Inf	20	auxpass	_	_
20	derived	derive	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	advcl	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 8
# text = On the contrary, this paper provides the underlying $ lambda $ - calculus on the basis of which abstract Stone duality will re - axiomatise general topology.
1	On	on	ADP	IN	_	7	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	contrary	contrary	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	paper	paper	NOUN	NN	Number=Sing	7	nsubj	_	_
7	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
9	underlying	underlie	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	amod	_	_
10	$ lambda $	$ lambda $	SYM	$	_	12	compound	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	calculus	calculus	NOUN	NN	Number=Sing	7	dobj	_	_
13	on	on	ADP	IN	_	7	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	basis	basis	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	22	prep	_	_
17	which	which	PRON	WDT	_	16	pobj	_	_
18	abstract	abstract	ADJ	JJ	Degree=Pos	20	amod	_	_
19	Stone	Stone	PROPN	NNP	Number=Sing	20	compound	_	_
20	duality	duality	NOUN	NN	Number=Sing	22	nsubj	_	_
21	will	will	AUX	MD	VerbForm=Fin	22	aux	_	_
22	re	re	VERB	VB	VerbForm=Inf	15	relcl	_	_
23	-	-	VERB	VB	VerbForm=Inf	22	punct	_	_
24	axiomatise	axiomatise	VERB	VB	VerbForm=Inf	22	xcomp	_	_
25	general	general	ADJ	JJ	Degree=Pos	26	amod	_	_
26	topology	topology	NOUN	NN	Number=Sing	24	dobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 9
# text = The leading model of the new axioms is the category of locally compact locales and continuous maps.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	leading	lead	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	amod	_	_
3	model	model	NOUN	NN	Number=Sing	8	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	new	new	ADJ	JJ	Degree=Pos	7	amod	_	_
7	axioms	axiom	NOUN	NNS	Number=Plur	4	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	category	category	NOUN	NN	Number=Sing	8	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	locally	locally	ADV	RB	_	13	advmod	_	_
13	compact	compact	ADJ	JJ	Degree=Pos	14	amod	_	_
14	locales	locale	NOUN	NNS	Number=Plur	11	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	continuous	continuous	ADJ	JJ	Degree=Pos	17	amod	_	_
17	maps	map	NOUN	NNS	Number=Plur	14	conj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 143
# sent_id = 1
# text = Goguen categories were introduced in as a suitable categorical description of $ {mathcal L} $ - fuzzy relations, that is, of relations taking values from an arbitrary complete Brouwerian lattice $ {mathcal L} $ instead of the unit interval $ [0, 1] $ of the real numbers.
1	Goguen	Goguen	PROPN	NNP	Number=Sing	2	compound	_	_
2	categories	category	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	4	auxpass	_	_
4	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	in	in	ADP	RP	_	4	prt	_	_
6	as	as	ADP	IN	_	4	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	suitable	suitable	ADJ	JJ	Degree=Pos	10	amod	_	_
9	categorical	categorical	ADJ	JJ	Degree=Pos	10	amod	_	_
10	description	description	NOUN	NN	Number=Sing	6	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	$ {mathcal L} $	$ {mathcal l} $	SYM	$	_	14	quantmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	fuzzy	fuzzy	ADJ	JJ	Degree=Pos	15	amod	_	_
15	relations	relation	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
17	that	that	ADV	RB	_	18	advmod	_	_
18	is	is	ADV	RB	_	30	advmod	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	of	of	ADP	IN	_	18	prep	_	_
21	relations	relation	NOUN	NNS	Number=Plur	20	pobj	_	_
22	taking	take	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	21	acl	_	_
23	values	value	NOUN	NNS	Number=Plur	22	dobj	_	_
24	from	from	ADP	IN	_	22	prep	_	_
25	an	an	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
26	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	29	amod	_	_
27	complete	complete	ADJ	JJ	Degree=Pos	29	amod	_	_
28	Brouwerian	brouwerian	ADJ	JJ	Degree=Pos	29	amod	_	_
29	lattice	lattice	NOUN	NN	Number=Sing	24	pobj	_	_
30	$ {mathcal L} $	$ {mathcal l} $	SYM	$	_	2	appos	_	_
31	instead	instead	ADV	RB	_	32	advmod	_	_
32	of	of	ADP	IN	_	30	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
34	unit	unit	NOUN	NN	Number=Sing	35	compound	_	_
35	interval	interval	NOUN	NN	Number=Sing	32	pobj	_	_
36	$ [0, 1] $	$ [0, 1] $	SYM	$	_	30	conj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
39	real	real	ADJ	JJ	Degree=Pos	40	amod	_	_
40	numbers	number	NOUN	NNS	Number=Plur	37	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper we want to study operations on morphisms of a Goguen category which are derived from suitable binary functions on the underlying lattice of scalar elements, that is, on the abstract counterpart of $ {mathcal L} $ .
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	want	want	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	study	study	VERB	VB	VerbForm=Inf	5	xcomp	_	_
8	operations	operation	NOUN	NNS	Number=Plur	7	dobj	_	_
9	on	on	ADP	IN	_	7	prep	_	_
10	morphisms	morphism	NOUN	NNS	Number=Plur	9	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	Goguen	Goguen	PROPN	NNP	Number=Sing	14	compound	_	_
14	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
15	which	which	PRON	WDT	_	17	nsubjpass	_	_
16	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	17	auxpass	_	_
17	derived	derive	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	relcl	_	_
18	from	from	ADP	IN	_	17	prep	_	_
19	suitable	suitable	ADJ	JJ	Degree=Pos	21	amod	_	_
20	binary	binary	ADJ	JJ	Degree=Pos	21	amod	_	_
21	functions	function	NOUN	NNS	Number=Plur	18	pobj	_	_
22	on	on	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	underlying	underlie	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	25	amod	_	_
25	lattice	lattice	NOUN	NN	Number=Sing	22	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	scalar	scalar	ADJ	JJ	Degree=Pos	28	amod	_	_
28	elements	element	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
30	that	that	ADV	RB	_	31	advmod	_	_
31	is	is	ADV	RB	_	33	advmod	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
33	on	on	ADP	IN	_	7	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
35	abstract	abstract	ADJ	JJ	Degree=Pos	36	amod	_	_
36	counterpart	counterpart	NOUN	NN	Number=Sing	33	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	$ {mathcal L} $	$ {mathcal l} $	SYM	$	_	37	pobj	_	_
39	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 144
# sent_id = 1
# text = Injectivity with respect to morphisms having $ lambda $ - presentable domains and codomains is characterized: such injectivity classes are precisely those closed under products, $ lambda $ - directed colimits, and $ lambda $ - pure subobjects.
1	Injectivity	injectivity	VERB	VB	VerbForm=Inf	14	nsubjpass	_	_
2	with	with	ADP	IN	_	1	prep	_	_
3	respect	respect	NOUN	NN	Number=Sing	2	pobj	_	_
4	to	to	ADP	IN	_	3	prep	_	_
5	morphisms	morphism	NOUN	NNS	Number=Plur	4	pobj	_	_
6	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	1	advcl	_	_
7	$ lambda $	$ lambda $	SYM	$	_	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	presentable	presentable	ADJ	JJ	Degree=Pos	10	amod	_	_
10	domains	domain	NOUN	NNS	Number=Plur	6	dobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	codomains	codomain	NOUN	NNS	Number=Plur	10	conj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	ccomp	_	SpaceAfter=No
15	:	:	PUNCT	:	_	19	punct	_	_
16	such	such	ADJ	JJ	Degree=Pos	18	amod	_	_
17	injectivity	injectivity	NOUN	NN	Number=Sing	18	compound	_	_
18	classes	class	NOUN	NNS	Number=Plur	19	nsubj	_	_
19	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	precisely	precisely	ADV	RB	_	21	advmod	_	_
21	those	those	PRON	DT	Number=Plur|PronType=Dem	19	attr	_	_
22	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	acl	_	_
23	under	under	ADP	IN	_	22	prep	_	_
24	products	product	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
26	$ lambda $	$ lambda $	SYM	$	_	28	advmod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	amod	_	_
29	colimits	colimit	NOUN	NNS	Number=Plur	21	conj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
32	$ lambda $	$ lambda $	SYM	$	_	34	advmod	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	pure	pure	ADJ	JJ	Degree=Pos	35	amod	_	_
35	subobjects	subobject	NOUN	NNS	Number=Plur	19	conj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 2
# text = This sharpens the result of the first two authors.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	sharpens	sharpen	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	result	result	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
7	first	first	ADJ	JJ	Degree=Pos	9	amod	_	_
8	two	two	NUM	CD	NumType=Card	9	nummod	_	_
9	authors	author	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = In contrast, for geometric logic an example is found of a class closed under directed colimits and pure subobjects, but not axiomatizable by a geometric theory.
1	In	in	ADP	IN	_	10	prep	_	_
2	contrast	contrast	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
4	for	for	ADP	IN	_	10	prep	_	_
5	geometric	geometric	ADJ	JJ	Degree=Pos	6	amod	_	_
6	logic	logic	NOUN	NN	Number=Sing	4	pobj	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	example	example	NOUN	NN	Number=Sing	10	nsubjpass	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	found	find	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	class	class	NOUN	NN	Number=Sing	11	pobj	_	_
14	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	13	acl	_	_
15	under	under	ADP	IN	_	14	prep	_	_
16	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	colimits	colimit	NOUN	NNS	Number=Plur	15	pobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	pure	pure	ADJ	JJ	Degree=Pos	20	amod	_	_
20	subobjects	subobject	NOUN	NNS	Number=Plur	17	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
22	but	but	CCONJ	CC	ConjType=Cmp	14	cc	_	_
23	not	not	PART	RB	Polarity=Neg	24	neg	_	_
24	axiomatizable	axiomatizable	ADJ	JJ	Degree=Pos	14	conj	_	_
25	by	by	ADP	IN	_	24	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
27	geometric	geometric	ADJ	JJ	Degree=Pos	28	amod	_	_
28	theory	theory	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 4
# text = A more technical characterization of axiomatizable classes in geometric logic is presented.
1	A	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
2	more	more	ADV	RBR	Degree=Cmp	3	advmod	_	_
3	technical	technical	ADJ	JJ	Degree=Pos	4	amod	_	_
4	characterization	characterization	NOUN	NN	Number=Sing	12	nsubjpass	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	axiomatizable	axiomatizable	ADJ	JJ	Degree=Pos	7	amod	_	_
7	classes	class	NOUN	NNS	Number=Plur	5	pobj	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	geometric	geometric	ADJ	JJ	Degree=Pos	10	amod	_	_
10	logic	logic	NOUN	NN	Number=Sing	8	pobj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# doc_id = 145
# sent_id = 1
# text = We prove that pure morphisms of commutative rings are effective $ A $ - descent morphisms where $ A $ is a $ (COMMUTATIVE RINGS)^op $ - indexed category given by (i) finitely generated modules, or (ii) flat modules, or (iii) finitely generated flat modules, or (iv) finitely generated projective modules.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	9	mark	_	_
4	pure	pure	ADJ	JJ	Degree=Pos	5	amod	_	_
5	morphisms	morphism	NOUN	NNS	Number=Plur	9	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	commutative	commutative	ADJ	JJ	Degree=Pos	8	amod	_	_
8	rings	ring	NOUN	NNS	Number=Plur	6	pobj	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
10	effective	effective	ADJ	JJ	Degree=Pos	14	amod	_	_
11	$ A $	$ a $	SYM	$	_	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	descent	descent	NOUN	NN	Number=Sing	14	compound	_	_
14	morphisms	morphism	NOUN	NNS	Number=Plur	9	attr	_	_
15	where	where	SCONJ	WRB	_	17	advmod	_	_
16	$ A $	$ a $	SYM	$	_	17	nsubj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
19	$ (COMMUTATIVE RINGS)^op $	$ (commutative rings)^op $	NUM	CD	NumType=Card	21	advmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	amod	_	_
22	category	category	NOUN	NN	Number=Sing	17	attr	_	_
23	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	acl	_	_
24	by	by	ADP	IN	_	23	agent	_	_
25	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
26	i	i	NOUN	NN	Case=Acc|Number=Sing|Person=1|PronType=Prs	24	pobj	_	SpaceAfter=No
27	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	24	punct	_	_
28	finitely	finitely	ADV	RB	_	29	advmod	_	_
29	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	30	amod	_	_
30	modules	module	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
32	or	or	CCONJ	CC	ConjType=Cmp	30	cc	_	_
33	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	37	punct	_	SpaceAfter=No
34	ii	ii	PROPN	NNP	Number=Sing	37	nmod	_	SpaceAfter=No
35	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	37	punct	_	_
36	flat	flat	ADJ	JJ	Degree=Pos	37	amod	_	_
37	modules	module	NOUN	NNS	Number=Plur	30	conj	_	SpaceAfter=No
38	,	,	PUNCT	,	PunctType=Comm	37	punct	_	_
39	or	or	CCONJ	CC	ConjType=Cmp	37	cc	_	_
40	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	41	punct	_	SpaceAfter=No
41	iii	iii	PROPN	NNP	Number=Sing	37	conj	_	SpaceAfter=No
42	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	41	punct	_	_
43	finitely	finitely	ADV	RB	_	44	advmod	_	_
44	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	46	amod	_	_
45	flat	flat	ADJ	JJ	Degree=Pos	46	amod	_	_
46	modules	module	NOUN	NNS	Number=Plur	22	appos	_	SpaceAfter=No
47	,	,	PUNCT	,	PunctType=Comm	46	punct	_	_
48	or	or	CCONJ	CC	ConjType=Cmp	46	cc	_	_
49	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	50	punct	_	SpaceAfter=No
50	iv	iv	ADV	RB	_	53	dep	_	SpaceAfter=No
51	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	53	punct	_	_
52	finitely	finitely	ADV	RB	_	53	advmod	_	_
53	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	55	amod	_	_
54	projective	projective	ADJ	JJ	Degree=Pos	55	amod	_	_
55	modules	module	NOUN	NNS	Number=Plur	46	conj	_	SpaceAfter=No
56	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 146
# sent_id = 1
# text = We investigate the effect on Cauchy complete objects of the change of base 2 - functor $ {cal V} - Cat rightarrow {cal W} - Cat $ induced by a two - sided enrichment $ {cal V} rightarrow {cal W} $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	effect	effect	NOUN	NN	Number=Sing	2	dobj	_	_
5	on	on	ADP	IN	_	4	prep	_	_
6	Cauchy	Cauchy	PROPN	NNP	Number=Sing	8	amod	_	_
7	complete	complete	ADJ	JJ	Degree=Pos	8	amod	_	_
8	objects	object	NOUN	NNS	Number=Plur	5	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	change	change	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	base	base	NOUN	NN	Number=Sing	12	pobj	_	_
14	2	2	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	functor	functor	NOUN	NN	Number=Sing	17	nmod	_	_
17	$ {cal V} - Cat rightarrow {cal W} - Cat $	$ {cal v} - cat rightarrow {cal w} - cat $	SYM	$	_	11	appos	_	_
18	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acl	_	_
19	by	by	ADP	IN	_	18	agent	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
21	two	two	NUM	CD	NumType=Card	23	advmod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	sided	sided	ADJ	JJ	Degree=Pos	24	amod	_	_
24	enrichment	enrichment	NOUN	NN	Number=Sing	19	pobj	_	_
25	$ {cal V} rightarrow {cal W} $	$ {cal v} rightarrow {cal w} $	SYM	$	_	18	dobj	_	_
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We restrict our study to the case of locally partially ordered bases.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	restrict	restrict	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	4	poss	_	_
4	study	study	NOUN	NN	Number=Sing	2	dobj	_	_
5	to	to	ADP	IN	_	2	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	case	case	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	locally	locally	ADV	RB	_	11	advmod	_	_
10	partially	partially	ADV	RB	_	11	advmod	_	_
11	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
12	bases	basis	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The reversibility notion introduced by Walters is extended to two - sided enrichments and Cauchy completion.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	reversibility	reversibility	NOUN	NN	Number=Sing	3	compound	_	_
3	notion	notion	NOUN	NN	Number=Sing	8	nsubjpass	_	_
4	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	acl	_	_
5	by	by	ADP	IN	_	4	agent	_	_
6	Walters	Walters	PROPN	NNP	Number=Sing	5	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	two	two	NUM	CD	NumType=Card	12	advmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	sided	side	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
13	enrichments	enrichment	NOUN	NNS	Number=Plur	9	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	Cauchy	Cauchy	PROPN	NNP	Number=Sing	16	compound	_	_
16	completion	completion	NOUN	NN	Number=Sing	13	conj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show that a reversible left adjoint two - sided enrichment $ F: {cal V} rightarrow {cal W} $ between locally partially ordered reversible bicategories induces an adjunction $ F_{sim} dashv F^{sim}: VSkCRcCat rightharpoonup WSkCRcCat $ between sub - categories of skeletal and Cauchy - reversible complete enrichments.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	19	mark	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	reversible	reversible	ADJ	JJ	Degree=Pos	7	amod	_	_
6	left	left	ADJ	JJ	Degree=Pos	7	amod	_	_
7	adjoint	adjoint	NOUN	NN	Number=Sing	11	nmod	_	_
8	two	two	NUM	CD	NumType=Card	10	advmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	sided	sided	ADJ	JJ	Degree=Pos	11	amod	_	_
11	enrichment	enrichment	NOUN	NN	Number=Sing	19	nsubj	_	_
12	$ F: {cal V} rightarrow {cal W} $	$ f: {cal v} rightarrow {cal w} $	SYM	$	_	11	appos	_	_
13	between	between	ADP	IN	_	11	prep	_	_
14	locally	locally	ADV	RB	_	16	advmod	_	_
15	partially	partially	ADV	RB	_	16	advmod	_	_
16	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
17	reversible	reversible	ADJ	JJ	Degree=Pos	18	amod	_	_
18	bicategories	bicategorie	NOUN	NNS	Number=Plur	13	pobj	_	_
19	induces	induce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
20	an	an	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	adjunction	adjunction	NOUN	NN	Number=Sing	19	dobj	_	_
22	$ F_{sim} dashv F^{sim}: VSkCRcCat rightharpoonup WSkCRcCat $	$ f_{sim} dashv f^{sim}: vskcrccat rightharpoonup wskcrccat $	SYM	$	_	21	dep	_	_
23	between	between	ADP	IN	_	21	prep	_	_
24	sub	sub	NOUN	NN	Number=Sing	26	compound	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	categories	category	NOUN	NNS	Number=Plur	23	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	skeletal	skeletal	ADJ	JJ	Degree=Pos	34	amod	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	Cauchy	cauchy	NOUN	NN	Number=Sing	32	npadvmod	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	reversible	reversible	ADJ	JJ	Degree=Pos	28	conj	_	_
33	complete	complete	ADJ	JJ	Degree=Pos	34	amod	_	_
34	enrichments	enrichment	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = We give two applications: sheaves over locales and group actions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	two	two	NUM	CD	NumType=Card	4	nummod	_	_
4	applications	application	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
5	:	:	PUNCT	:	_	4	punct	_	_
6	sheaves	sheaf	NOUN	NNS	Number=Plur	2	dobj	_	_
7	over	over	ADP	IN	_	6	prep	_	_
8	locales	locale	NOUN	NNS	Number=Plur	7	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	group	group	NOUN	NN	Number=Sing	11	compound	_	_
11	actions	action	NOUN	NNS	Number=Plur	8	conj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 147
# sent_id = 1
# text = Every chain functor $ A_* $ , admits a $ L $ - colocalization $ A^L_* $ which (in contrast to the case of $ L $ - localizations) in general does not allow a realization as a spectrum (even if $ A_* $ stems from a spectrum itself).
1	Every	every	DET	DT	_	2	det	_	_
2	chain	chain	NOUN	NN	Number=Sing	3	nsubj	_	_
3	functor	functor	VERB	VBP	Tense=Pres|VerbForm=Fin	6	nsubj	_	_
4	$ A_* $	$ a_* $	SYM	$	_	3	nummod	_	_
5	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
6	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	$ L $	$ l $	SYM	$	_	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	colocalization	colocalization	NOUN	NN	Number=Sing	6	dobj	_	_
11	$ A^L_* $	$ a^l_* $	SYM	$	_	10	nmod	_	_
12	which	which	PRON	WDT	_	28	nsubj	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	28	punct	_	SpaceAfter=No
14	in	in	ADP	IN	_	28	prep	_	_
15	contrast	contrast	NOUN	NN	Number=Sing	14	pobj	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	case	case	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	$ L $	$ l $	SYM	$	_	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	localizations	localization	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	28	punct	_	_
24	in	in	ADP	IN	_	28	prep	_	_
25	general	general	ADJ	JJ	Degree=Pos	24	amod	_	_
26	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	28	aux	_	_
27	not	not	PART	RB	Polarity=Neg	28	neg	_	_
28	allow	allow	VERB	VB	VerbForm=Inf	6	advcl	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
30	realization	realization	NOUN	NN	Number=Sing	28	dobj	_	_
31	as	as	ADP	IN	_	30	prep	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
33	spectrum	spectrum	NOUN	NN	Number=Sing	31	pobj	_	_
34	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	33	punct	_	SpaceAfter=No
35	even	even	ADV	RB	_	38	advmod	_	_
36	if	if	SCONJ	IN	_	38	mark	_	_
37	$ A_* $	$ a_* $	SYM	$	_	38	nsubj	_	_
38	stems	stem	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	28	advcl	_	_
39	from	from	ADP	IN	_	38	prep	_	_
40	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
41	spectrum	spectrum	NOUN	NN	Number=Sing	39	pobj	_	_
42	itself	itself	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs|Reflex=Yes	41	appos	_	SpaceAfter=No
43	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	28	punct	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = The $ [E, ]_* $ - colocalization of A. K. Bousfield is retrieved as a special case of a general colocalization process for chain functors.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	$ [E, ]_* $	$ [e, ]_* $	SYM	$	_	4	quantmod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	colocalization	colocalization	NOUN	NN	Number=Sing	10	nsubjpass	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	A.	A.	PROPN	NNP	Number=Sing	8	compound	_	_
7	K.	K.	PROPN	NNP	Number=Sing	8	compound	_	_
8	Bousfield	Bousfield	PROPN	NNP	Number=Sing	5	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	retrieved	retrieve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	as	as	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	special	special	ADJ	JJ	Degree=Pos	14	amod	_	_
14	case	case	NOUN	NN	Number=Sing	11	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
17	general	general	ADJ	JJ	Degree=Pos	19	amod	_	_
18	colocalization	colocalization	NOUN	NN	Number=Sing	19	compound	_	_
19	process	process	NOUN	NN	Number=Sing	15	pobj	_	_
20	for	for	ADP	IN	_	19	prep	_	_
21	chain	chain	NOUN	NN	Number=Sing	22	compound	_	_
22	functors	functor	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# doc_id = 148
# sent_id = 1
# text = For the 2 - monad $ (( - )^2, I, C) $ on CAT, with unit $ I $ described by identities and multiplication $ C $ described by composition, we show that a functor $ F : {cal K}^2 rightarrow cal K $ satisfying $ FI_{cal K} = 1_{cal K} $ admits a unique, normal, pseudo - algebra structure for $ ( - )^2 $ if and only if there is a mere natural isomorphism $ F F^2 rightarrow F C_{cal K} $ .
1	For	for	ADP	IN	_	24	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
3	2	2	NUM	CD	NumType=Card	5	nummod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	monad	monad	NOUN	NNS	Number=Plur	6	compound	_	_
6	$ (( - )^2, I, C) $	$ (( - )^2, i, c) $	SYM	$	_	1	pobj	_	_
7	on	on	ADP	IN	_	6	prep	_	_
8	CAT	CAT	PROPN	NNP	Number=Sing	7	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
10	with	with	ADP	IN	_	13	prep	_	_
11	unit	unit	NOUN	NN	Number=Sing	10	pobj	_	_
12	$ I $	$ i $	SYM	$	_	10	dep	_	_
13	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	advcl	_	_
14	by	by	ADP	IN	_	13	agent	_	_
15	identities	identity	NOUN	NNS	Number=Plur	14	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	multiplication	multiplication	NOUN	NN	Number=Sing	15	conj	_	_
18	$ C $	$ c $	SYM	$	_	13	dep	_	_
19	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	xcomp	_	_
20	by	by	ADP	IN	_	19	agent	_	_
21	composition	composition	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
23	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	24	nsubj	_	_
24	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
25	that	that	SCONJ	IN	_	31	mark	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	functor	functor	NOUN	NN	Number=Sing	31	nsubj	_	_
28	$ F : {cal K}^2 rightarrow cal K $	$ f : {cal k}^2 rightarrow cal k $	SYM	$	_	27	appos	_	_
29	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	27	acl	_	_
30	$ FI_{cal K} = 1_{cal K} $	$ fi_{cal k} = 1_{cal k} $	SYM	$	_	31	nsubj	_	_
31	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	ccomp	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	40	det	_	_
33	unique	unique	ADJ	JJ	Degree=Pos	40	amod	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	40	punct	_	_
35	normal	normal	ADJ	JJ	Degree=Pos	40	amod	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	40	punct	_	_
37	pseudo	pseudo	NOUN	NN	Number=Sing	39	compound	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	algebra	algebra	NOUN	NN	Number=Sing	40	compound	_	_
40	structure	structure	NOUN	NN	Number=Sing	31	dobj	_	_
41	for	for	ADP	IN	_	31	prep	_	_
42	$ ( - )^2 $	$ ( - )^2 $	SYM	$	_	43	nummod	_	_
43	if	if	SCONJ	IN	_	41	pobj	_	_
44	and	and	CCONJ	CC	ConjType=Cmp	43	cc	_	_
45	only	only	ADV	RB	_	48	advmod	_	_
46	if	if	SCONJ	IN	_	48	mark	_	_
47	there	there	PRON	EX	_	48	expl	_	_
48	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	31	advcl	_	_
49	a	a	DET	DT	Definite=Ind|PronType=Art	52	det	_	_
50	mere	mere	ADJ	JJ	Degree=Pos	52	amod	_	_
51	natural	natural	ADJ	JJ	Degree=Pos	52	amod	_	_
52	isomorphism	isomorphism	NOUN	NN	Number=Sing	48	attr	_	_
53	$ F F^2 rightarrow F C_{cal K} $	$ f f^2 rightarrow f c_{cal k} $	SYM	$	_	52	appos	_	_
54	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that when this is the case the set of all natural transformations $ F F^2 rightarrow F C_{cal K} $ forms a commutative monoid isomorphic to the centre of $ cal K $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	16	mark	_	_
4	when	when	SCONJ	WRB	_	6	advmod	_	_
5	this	this	PRON	DT	Number=Sing|PronType=Dem	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	advcl	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	case	case	NOUN	NN	Number=Sing	6	attr	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	set	set	NOUN	NN	Number=Sing	16	nsubj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	all	all	DET	DT	_	14	det	_	_
13	natural	natural	ADJ	JJ	Degree=Pos	14	amod	_	_
14	transformations	transformation	NOUN	NNS	Number=Plur	11	pobj	_	_
15	$ F F^2 rightarrow F C_{cal K} $	$ f f^2 rightarrow f c_{cal k} $	SYM	$	_	16	nsubj	_	_
16	forms	form	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
18	commutative	commutative	ADJ	JJ	Degree=Pos	20	amod	_	_
19	monoid	monoid	NOUN	NN	Number=Sing	20	amod	_	_
20	isomorphic	isomorphic	NOUN	NN	Number=Sing	16	dobj	_	_
21	to	to	ADP	IN	_	16	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	centre	centre	NOUN	NN	Number=Sing	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	$ cal K $	$ cal k $	SYM	$	_	24	pobj	_	_
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 149
# sent_id = 1
# text = In this paper we describe a deductive system for categories with finite products and coproducts, prove decidability of equality of morphisms via cut elimination, and prove a ``Whitman theorem'' for the free such categories over arbitrary base categories.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	deductive	deductive	ADJ	JJ	Degree=Pos	8	amod	_	_
8	system	system	NOUN	NN	Number=Sing	5	dobj	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	_
11	with	with	ADP	IN	_	10	prep	_	_
12	finite	finite	ADJ	JJ	Degree=Pos	13	amod	_	_
13	products	product	NOUN	NNS	Number=Plur	11	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	coproducts	coproduct	NOUN	NNS	Number=Plur	13	conj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
17	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	5	conj	_	_
18	decidability	decidability	NOUN	NN	Number=Sing	17	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	equality	equality	NOUN	NN	Number=Sing	19	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	morphisms	morphism	NOUN	NNS	Number=Plur	21	pobj	_	_
23	via	via	ADP	IN	_	17	prep	_	_
24	cut	cut	NOUN	NN	Number=Sing	25	compound	_	_
25	elimination	elimination	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
28	prove	prove	VERB	VB	VerbForm=Inf	17	conj	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
30	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	33	punct	_	SpaceAfter=No
31	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	33	punct	_	SpaceAfter=No
32	Whitman	Whitman	PROPN	NNP	Number=Sing	33	compound	_	_
33	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	28	oprd	_	SpaceAfter=No
34	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	33	punct	_	_
35	for	for	ADP	IN	_	33	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
37	free	free	ADJ	JJ	Degree=Pos	39	amod	_	_
38	such	such	ADJ	JJ	Degree=Pos	39	amod	_	_
39	categories	category	NOUN	NNS	Number=Plur	35	pobj	_	_
40	over	over	ADP	IN	_	39	prep	_	_
41	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	43	amod	_	_
42	base	base	NOUN	NN	Number=Sing	43	compound	_	_
43	categories	category	NOUN	NNS	Number=Plur	40	pobj	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = This result provides a nice illustration of some basic techniques in categorical proof theory, and also seems to have slipped past unproved in previous work in this field.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	result	result	NOUN	NN	Number=Sing	3	nsubj	_	_
3	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	nice	nice	ADJ	JJ	Degree=Pos	6	amod	_	_
6	illustration	illustration	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	some	some	DET	DT	_	10	det	_	_
9	basic	basic	ADJ	JJ	Degree=Pos	10	amod	_	_
10	techniques	technique	NOUN	NNS	Number=Plur	7	pobj	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	categorical	categorical	ADJ	JJ	Degree=Pos	13	amod	_	_
13	proof	proof	NOUN	NN	Number=Sing	14	compound	_	_
14	theory	theory	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
17	also	also	ADV	RB	_	18	advmod	_	_
18	seems	seem	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
19	to	to	PART	TO	_	21	aux	_	_
20	have	have	AUX	VB	VerbForm=Inf	21	aux	_	_
21	slipped	slip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	xcomp	_	_
22	past	past	ADV	RB	_	23	advmod	_	_
23	unproved	unprove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	advcl	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	previous	previous	ADJ	JJ	Degree=Pos	26	amod	_	_
26	work	work	NOUN	NN	Number=Sing	24	pobj	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	this	this	DET	DT	Number=Sing|PronType=Dem	29	det	_	_
29	field	field	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Furthermore, it suggests a type - theoretic approach to 2 - player input - output games.
1	Furthermore	furthermore	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	4	nsubj	_	_
4	suggests	suggest	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
6	type	type	NOUN	NN	Number=Sing	8	npadvmod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	theoretic	theoretic	ADJ	JJ	Degree=Pos	9	amod	_	_
9	approach	approach	NOUN	NN	Number=Sing	4	dobj	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	player	player	NOUN	NN	Number=Sing	17	compound	_	_
14	input	input	NOUN	NN	Number=Sing	16	compound	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	output	output	NOUN	NN	Number=Sing	17	compound	_	_
17	games	game	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 150
# sent_id = 1
# text = Two proofs of the exponentiability of perfect maps are presented and compared to two other recent approaches.
1	Two	two	NUM	CD	NumType=Card	2	nummod	_	_
2	proofs	proof	NOUN	NNS	Number=Plur	10	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	exponentiability	exponentiability	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	perfect	perfect	ADJ	JJ	Degree=Pos	8	amod	_	_
8	maps	map	NOUN	NNS	Number=Plur	6	pobj	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	compared	compare	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	conj	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	two	two	NUM	CD	NumType=Card	17	nummod	_	_
15	other	other	ADJ	JJ	Degree=Pos	17	amod	_	_
16	recent	recent	ADJ	JJ	Degree=Pos	17	amod	_	_
17	approaches	approach	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = One of the proofs is an elementary approach including a direct construction of the exponentials.
1	One	one	NUM	CD	NumType=Card	5	nsubj	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	proofs	proof	NOUN	NNS	Number=Plur	2	pobj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	elementary	elementary	ADJ	JJ	Degree=Pos	8	amod	_	_
8	approach	approach	NOUN	NN	Number=Sing	5	attr	_	_
9	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	direct	direct	ADJ	JJ	Degree=Pos	12	amod	_	_
12	construction	construction	NOUN	NN	Number=Sing	9	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	exponentials	exponential	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = The other, implicit in the literature, uses internal locales in the topos of set - valued sheaves on a topological space.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	other	other	ADJ	JJ	Degree=Pos	4	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
4	implicit	implicit	ADJ	JJ	Degree=Pos	9	nsubj	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	literature	literature	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
9	uses	use	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	internal	internal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	locales	locale	NOUN	NNS	Number=Plur	9	dobj	_	_
12	in	in	ADP	IN	_	9	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	topos	topos	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	set	set	NOUN	NN	Number=Sing	18	npadvmod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
19	sheaves	sheaf	NOUN	NNS	Number=Plur	15	pobj	_	_
20	on	on	ADP	IN	_	9	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	topological	topological	ADJ	JJ	Degree=Pos	23	amod	_	_
23	space	space	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 151
# sent_id = 1
# text = Using the long exact sequence of nonabelian derived functors, an eight term exact sequence of Lie algebra homology with $ Lambda/qLambda $ coefficients is obtained, where $ Lambda $ is a ground ring and $ q $ is a nonnegative integer.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	34	csubj	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
3	long	long	ADJ	JJ	Degree=Pos	5	amod	_	_
4	exact	exact	ADJ	JJ	Degree=Pos	5	amod	_	_
5	sequence	sequence	NOUN	NN	Number=Sing	1	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	nonabelian	nonabelian	ADJ	JJ	Degree=Pos	8	amod	_	_
8	derived	derive	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	compound	_	_
9	functors	functor	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
12	eight	eight	NUM	CD	NumType=Card	13	nummod	_	_
13	term	term	NOUN	NN	Number=Sing	15	nmod	_	_
14	exact	exact	ADJ	JJ	Degree=Pos	15	amod	_	_
15	sequence	sequence	NOUN	NN	Number=Sing	9	appos	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	Lie	Lie	PROPN	NNP	Number=Sing	19	compound	_	_
18	algebra	algebra	PROPN	NNP	Number=Sing	19	compound	_	_
19	homology	homology	NOUN	NN	Number=Sing	16	pobj	_	_
20	with	with	ADP	IN	_	15	prep	_	_
21	$ Lambda/qLambda $	$ lambda/qlambda $	SYM	$	_	22	poss	_	_
22	coefficients	coefficient	NOUN	NNS	Number=Plur	24	nsubjpass	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	auxpass	_	_
24	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	relcl	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	where	where	SCONJ	WRB	_	28	advmod	_	_
27	$ Lambda $	$ lambda $	SYM	$	_	28	nsubj	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	relcl	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	ground	ground	NOUN	NN	Number=Sing	31	compound	_	_
31	ring	ring	NOUN	NN	Number=Sing	28	attr	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	$ q $	$ q $	SYM	$	_	15	appos	_	_
34	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
35	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
36	nonnegative	nonnegative	ADJ	JJ	Degree=Pos	37	amod	_	_
37	integer	integer	NOUN	NN	Number=Sing	34	attr	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	34	punct	_	SpaceAfter=No

# sent_id = 2
# text = Hopf formulas for the second and third homology of a Lie algebra are proved.
1	Hopf	hopf	NOUN	NN	Number=Sing	2	compound	_	_
2	formulas	formula	NOUN	NNS	Number=Plur	14	nsubjpass	_	_
3	for	for	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
5	second	second	ADJ	JJ	Degree=Pos	8	amod	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	third	third	ADJ	JJ	Degree=Pos	5	conj	_	_
8	homology	homology	NOUN	NN	Number=Sing	3	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	Lie	lie	NOUN	NN	Number=Sing	12	compound	_	_
12	algebra	algebra	NOUN	NNS	Number=Plur	9	pobj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 3
# text = The condition for the existence and the description of the universal $ q $ - central relative extension of a Lie epimorphism in terms of relative homologies are given.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	condition	condition	NOUN	NN	Number=Sing	27	nsubjpass	_	_
3	for	for	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	existence	existence	NOUN	NN	Number=Sing	3	pobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	description	description	NOUN	NN	Number=Sing	5	conj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
11	universal	universal	ADJ	JJ	Degree=Pos	16	amod	_	_
12	$ q $	$ q $	SYM	$	_	14	advmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	central	central	ADJ	JJ	Degree=Pos	16	amod	_	_
15	relative	relative	ADJ	JJ	Degree=Pos	16	amod	_	_
16	extension	extension	NOUN	NN	Number=Sing	9	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	Lie	lie	NOUN	NN	Number=Sing	20	compound	_	_
20	epimorphism	epimorphism	NOUN	NN	Number=Sing	17	pobj	_	_
21	in	in	ADP	IN	_	8	prep	_	_
22	terms	term	NOUN	NNS	Number=Plur	21	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	relative	relative	ADJ	JJ	Degree=Pos	25	amod	_	_
25	homologies	homology	NOUN	NNS	Number=Plur	23	pobj	_	_
26	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	27	auxpass	_	_
27	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	27	punct	_	SpaceAfter=No

# doc_id = 152
# sent_id = 1
# text = Entity - Relationship - Attribute ideas are commonly used to specify and design information systems.
1	Entity	entity	NOUN	NN	Number=Sing	3	compound	_	_
2	-	-	PUNCT	HYPH	PunctType=Dash	3	punct	_	_
3	Relationship	Relationship	PROPN	NNP	Number=Sing	5	compound	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	Attribute	Attribute	PROPN	NNP	Number=Sing	6	compound	_	_
6	ideas	idea	NOUN	NNS	Number=Plur	9	nsubjpass	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
8	commonly	commonly	ADV	RB	_	9	advmod	_	_
9	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	specify	specify	VERB	VB	VerbForm=Inf	9	xcomp	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	design	design	NOUN	NN	Number=Sing	11	conj	_	_
14	information	information	NOUN	NN	Number=Sing	15	compound	_	_
15	systems	system	NOUN	NNS	Number=Plur	13	dobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 2
# text = They use a graphical technique for displaying the objects of the system and relationships among them.
1	They	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	2	nsubj	_	_
2	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	graphical	graphical	ADJ	JJ	Degree=Pos	5	amod	_	_
5	technique	technique	NOUN	NN	Number=Sing	2	dobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	displaying	display	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	pcomp	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	objects	object	NOUN	NNS	Number=Plur	7	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	system	system	NOUN	NN	Number=Sing	10	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	relationships	relationship	NOUN	NNS	Number=Plur	12	conj	_	_
15	among	among	ADP	IN	_	9	prep	_	_
16	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	15	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The design process can be enhanced by specifying constraints of the system and the natural environment for these is the categorical notion of sketch.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	design	design	NOUN	NN	Number=Sing	3	compound	_	_
3	process	process	NOUN	NN	Number=Sing	6	nsubjpass	_	_
4	can	can	AUX	MD	VerbForm=Fin	6	aux	_	_
5	be	be	AUX	VB	VerbForm=Inf	6	auxpass	_	_
6	enhanced	enhance	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	by	by	ADP	IN	_	6	agent	_	_
8	specifying	specify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	amod	_	_
9	constraints	constraint	NOUN	NNS	Number=Plur	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	system	system	NOUN	NN	Number=Sing	10	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	natural	natural	ADJ	JJ	Degree=Pos	16	amod	_	_
16	environment	environment	NOUN	NN	Number=Sing	19	nsubj	_	_
17	for	for	ADP	IN	_	16	prep	_	_
18	these	these	PRON	DT	Number=Plur|PronType=Dem	17	pobj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	conj	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	categorical	categorical	ADJ	JJ	Degree=Pos	22	amod	_	_
22	notion	notion	NOUN	NN	Number=Sing	19	attr	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	sketch	sketch	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 4
# text = Here we argue that the finite - limit, finite - sum sketches with a terminal node are the appropriate class and call them EA sketches.
1	Here	here	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	argue	argue	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	18	mark	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
6	finite	finite	PROPN	NNP	Number=Sing	8	compound	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	limit	limit	NOUN	NN	Number=Sing	13	nmod	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
10	finite	finite	ADJ	JJ	Degree=Pos	12	compound	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	sum	sum	NOUN	NN	Number=Sing	13	compound	_	_
13	sketches	sketch	NOUN	NNS	Number=Plur	18	nsubj	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	terminal	terminal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	node	node	NOUN	NN	Number=Sing	14	pobj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	appropriate	appropriate	ADJ	JJ	Degree=Pos	21	amod	_	_
21	class	class	NOUN	NN	Number=Sing	18	attr	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
23	call	call	VERB	VB	VerbForm=Inf	18	conj	_	_
24	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	23	dobj	_	_
25	EA	EA	PROPN	NNP	Number=Sing	26	compound	_	_
26	sketches	sketch	NOUN	NNS	Number=Plur	23	oprd	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = A model for an EA sketch in a lextensive category is a `snapshot' of a database with values in that category.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	model	model	NOUN	NN	Number=Sing	11	nsubj	_	_
3	for	for	ADP	IN	_	2	prep	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	EA	EA	PROPN	NNP	Number=Sing	6	compound	_	_
6	sketch	sketch	NOUN	NN	Number=Sing	3	pobj	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	lextensive	lextensive	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	14	punct	_	SpaceAfter=No
14	snapshot	snapshot	NOUN	NN	Number=Sing	11	attr	_	SpaceAfter=No
15	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	14	punct	_	_
16	of	of	ADP	IN	_	14	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	database	database	NOUN	NN	Number=Sing	16	pobj	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	values	value	NOUN	NNS	Number=Plur	19	pobj	_	_
21	in	in	ADP	IN	_	20	prep	_	_
22	that	that	DET	DT	Number=Sing|PronType=Dem	23	det	_	_
23	category	category	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 6
# text = The category of models of an EA sketch is an object of models of the sketch in a 2 - category of lextensive categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	9	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	models	model	NOUN	NNS	Number=Plur	3	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	EA	EA	PROPN	NNP	Number=Sing	8	compound	_	_
8	sketch	sketch	NOUN	NN	Number=Sing	5	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	object	object	NOUN	NN	Number=Sing	9	attr	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	models	model	NOUN	NNS	Number=Plur	12	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	sketch	sketch	NOUN	NN	Number=Sing	14	pobj	_	_
17	in	in	ADP	IN	_	11	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
19	2	2	NUM	CD	NumType=Card	21	nummod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	category	category	NOUN	NN	Number=Sing	17	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	lextensive	lextensive	ADJ	JJ	Degree=Pos	24	amod	_	_
24	categories	category	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 7
# text = Moreover, modelling the same sketch in certain objects in other 2 - categories defines both the query language for the database and the updates (the dynamics) for the database.
1	Moreover	moreover	ADV	RB	_	15	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
3	modelling	model	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	csubj	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	same	same	ADJ	JJ	Degree=Pos	6	amod	_	_
6	sketch	sketch	NOUN	NN	Number=Sing	3	dobj	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	certain	certain	ADJ	JJ	Degree=Pos	9	amod	_	_
9	objects	object	NOUN	NNS	Number=Plur	7	pobj	_	_
10	in	in	ADP	IN	_	6	prep	_	_
11	other	other	ADJ	JJ	Degree=Pos	14	amod	_	_
12	2	2	NUM	CD	NumType=Card	14	nummod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
15	defines	define	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	both	both	CCONJ	CC	ConjType=Cmp	19	preconj	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	query	query	NOUN	NN	Number=Sing	19	compound	_	_
19	language	language	NOUN	NN	Number=Sing	15	dobj	_	_
20	for	for	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	database	database	NOUN	NN	Number=Sing	20	pobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	updates	update	NOUN	NNS	Number=Plur	19	conj	_	_
26	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	25	punct	_	SpaceAfter=No
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	dynamics	dynamic	NOUN	NNS	Number=Plur	25	appos	_	SpaceAfter=No
29	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	25	punct	_	_
30	for	for	ADP	IN	_	25	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	database	database	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# doc_id = 153
# sent_id = 1
# text = We associate to a Hausdorff space, $ X $ , a double groupoid, $ mbox{boldmath rho }^{square}_{2} (X) $ , the homotopy double groupoid of $ X $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	associate	associate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	6	compound	_	_
6	space	space	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	$ X $	$ x $	SYM	$	_	6	appos	_	_
9	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	double	double	ADJ	JJ	Degree=Pos	12	amod	_	_
12	groupoid	groupoid	NOUN	NN	Number=Sing	6	appos	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	$ mbox{boldmath rho }^{square}_{2} (X) $	$ mbox{boldmath rho }^{square}_{2} (x) $	SYM	$	_	12	appos	_	_
15	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	homotopy	homotopy	NOUN	NN	Number=Sing	12	conj	_	_
18	double	double	ADJ	JJ	Degree=Pos	19	amod	_	_
19	groupoid	groupoid	NOUN	NN	Number=Sing	17	appos	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	$ X $	$ x $	SYM	$	_	20	pobj	_	_
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The construction is based on the geometric notion of thin square.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	construction	construction	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	on	on	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	geometric	geometric	ADJ	JJ	Degree=Pos	8	amod	_	_
8	notion	notion	NOUN	NN	Number=Sing	5	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	thin	thin	ADJ	JJ	Degree=Pos	11	amod	_	_
11	square	square	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = Under the equivalence of categories between small $ 2 $ - categories and double categories with connection the homotopy double groupoid corresponds to the homotopy 2 - groupoid, $ {bf G}_{2} (X) $ .
1	Under	under	ADP	IN	_	20	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	equivalence	equivalence	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	_
6	between	between	ADP	IN	_	3	prep	_	_
7	small	small	ADJ	JJ	Degree=Pos	10	amod	_	_
8	$ 2 $	$ 2 $	SYM	$	_	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	double	double	ADJ	JJ	Degree=Pos	13	amod	_	_
13	categories	category	NOUN	NNS	Number=Plur	10	conj	_	_
14	with	with	ADP	IN	_	3	prep	_	_
15	connection	connection	NOUN	NN	Number=Sing	14	pobj	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	homotopy	homotopy	NOUN	NN	Number=Sing	15	appos	_	_
18	double	double	ADJ	JJ	Degree=Pos	20	amod	_	_
19	groupoid	groupoid	NOUN	NN	Number=Sing	20	compound	_	_
20	corresponds	correspond	NOUN	NNS	Number=Plur	0	ROOT	_	_
21	to	to	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	homotopy	homotopy	NOUN	NN	Number=Sing	21	pobj	_	_
24	2	2	NUM	CD	NumType=Card	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	groupoid	groupoid	NOUN	NN	Number=Sing	23	npadvmod	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
28	$ {bf G}_{2} (X) $	$ {bf g}_{2} (x) $	SYM	$	_	23	appos	_	_
29	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 4
# text = The cubical nature of $ mbox{boldmath rho }^{square}_{2} (X) $ as opposed to the globular nature of $ {bf G}_{2} (X) $ should provide a convenient tool when handling `local - to - global' problems as encountered in a generalised van Kampen theorem and dealing with tensor products and enrichments of the category of compactly generated Hausdorff spaces.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	cubical	cubical	ADJ	JJ	Degree=Pos	3	amod	_	_
3	nature	nature	NOUN	NN	Number=Sing	15	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	$ mbox{boldmath rho }^{square}_{2} (X) $	$ mbox{boldmath rho }^{square}_{2} (x) $	SYM	$	_	4	pobj	_	_
6	as	as	SCONJ	IN	_	7	mark	_	_
7	opposed	oppose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	advcl	_	_
8	to	to	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	globular	globular	ADJ	JJ	Degree=Pos	11	amod	_	_
11	nature	nature	NOUN	NN	Number=Sing	8	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	$ {bf G}_{2} (X) $	$ {bf g}_{2} (x) $	SYM	$	_	12	pobj	_	_
14	should	should	AUX	MD	VerbForm=Fin	15	aux	_	_
15	provide	provide	VERB	VB	VerbForm=Inf	0	ROOT	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	convenient	convenient	ADJ	JJ	Degree=Pos	18	amod	_	_
18	tool	tool	NOUN	NN	Number=Sing	15	dobj	_	_
19	when	when	SCONJ	WRB	_	20	advmod	_	_
20	handling	handle	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	36	csubj	_	_
21	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	28	punct	_	SpaceAfter=No
22	local	local	ADJ	JJ	Degree=Pos	28	amod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
24	to	to	ADP	IN	_	22	prep	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	global	global	ADJ	JJ	Degree=Pos	24	pobj	_	SpaceAfter=No
27	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	22	punct	_	_
28	problems	problem	NOUN	NNS	Number=Plur	20	dobj	_	_
29	as	as	SCONJ	IN	_	30	mark	_	_
30	encountered	encounter	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	advcl	_	_
31	in	in	ADP	IN	_	30	prep	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
33	generalised	generalise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	35	amod	_	_
34	van	van	PROPN	NNP	Number=Sing	35	compound	_	_
35	Kampen	Kampen	PROPN	NNP	Number=Sing	31	pobj	_	_
36	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	15	advcl	_	_
37	and	and	CCONJ	CC	ConjType=Cmp	36	cc	_	_
38	dealing	deal	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	36	conj	_	_
39	with	with	ADP	IN	_	38	prep	_	_
40	tensor	tensor	NOUN	NN	Number=Sing	41	compound	_	_
41	products	product	NOUN	NNS	Number=Plur	39	pobj	_	_
42	and	and	CCONJ	CC	ConjType=Cmp	41	cc	_	_
43	enrichments	enrichment	NOUN	NNS	Number=Plur	41	conj	_	_
44	of	of	ADP	IN	_	41	prep	_	_
45	the	the	DET	DT	Definite=Def|PronType=Art	46	det	_	_
46	category	category	NOUN	NN	Number=Sing	44	pobj	_	_
47	of	of	ADP	IN	_	46	prep	_	_
48	compactly	compactly	ADV	RB	_	49	advmod	_	_
49	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	51	amod	_	_
50	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	51	compound	_	_
51	spaces	space	NOUN	NNS	Number=Plur	47	pobj	_	SpaceAfter=No
52	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# doc_id = 154
# sent_id = 1
# text = Many people have proposed definitions of `weak $ n $ - category'.
1	Many	many	ADJ	JJ	Degree=Pos	2	amod	_	_
2	people	people	NOUN	NNS	Number=Plur	4	nsubj	_	_
3	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	aux	_	_
4	proposed	propose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	definitions	definition	NOUN	NNS	Number=Plur	4	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	6	punct	_	SpaceAfter=No
8	weak	weak	ADJ	JJ	Degree=Pos	11	amod	_	_
9	$ n $	$ n $	SYM	$	_	11	compound	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	category	category	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
12	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	4	punct	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = Ten of them are presented here.
1	Ten	ten	NUM	CD	NumType=Card	5	nsubjpass	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	2	pobj	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	here	here	ADV	RB	PronType=Dem	5	advmod	_	SpaceAfter=No
7	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = Each definition is given in two pages, with a further two pages on what happens when $ nleq 2 $ .
1	Each	each	DET	DT	_	2	det	_	_
2	definition	definition	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	two	two	NUM	CD	NumType=Card	7	nummod	_	_
7	pages	page	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
9	with	with	ADP	IN	_	4	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	further	further	ADJ	JJ	Degree=Pos	13	amod	_	_
12	two	two	NUM	CD	NumType=Card	13	nummod	_	_
13	pages	page	NOUN	NNS	Number=Plur	9	pobj	_	_
14	on	on	ADP	IN	_	13	prep	_	_
15	what	what	PRON	WP	_	16	nsubj	_	_
16	happens	happen	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	pcomp	_	_
17	when	when	SCONJ	WRB	_	18	advmod	_	_
18	$ nleq 2 $	$ nleq 2 $	SYM	$	_	16	advcl	_	_
19	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = The definitions can be read independently.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	definitions	definition	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
3	can	can	AUX	MD	VerbForm=Fin	5	aux	_	_
4	be	be	AUX	VB	VerbForm=Inf	5	auxpass	_	_
5	read	read	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	independently	independently	ADV	RB	_	5	advmod	_	SpaceAfter=No
7	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = Chatty bibliography follows.
1	Chatty	chatty	ADJ	JJ	Degree=Pos	2	amod	_	_
2	bibliography	bibliography	NOUN	NN	Number=Sing	3	nsubj	_	_
3	follows	follow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
4	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 155
# sent_id = 1
# text = Codescent morphisms are described in regular categories which satisfy the so - called strong amalgamation property.
1	Codescent	codescent	NOUN	NN	Number=Sing	2	compound	_	_
2	morphisms	morphism	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	regular	regular	ADJ	JJ	Degree=Pos	7	amod	_	_
7	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
8	which	which	PRON	WDT	_	9	nsubj	_	_
9	satisfy	satisfy	VERB	VBP	Tense=Pres|VerbForm=Fin	7	relcl	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
11	so	so	ADV	RB	_	13	advmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
14	strong	strong	ADJ	JJ	Degree=Pos	16	amod	_	_
15	amalgamation	amalgamation	NOUN	NN	Number=Sing	16	compound	_	_
16	property	property	NOUN	NN	Number=Sing	9	dobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = Among varieties of universal algebras possessing this property are, as is known, categories of groups, not necessarily associative rings, $ M $ - sets (for a monoid $ M $ ), Lie algebras (over a field), quasi - groups, commutative quasi - groups, Steiner quasi - groups, medial quasi - groups, semilattice $ lattices, weakly associative lattices, Boolean algebras, Heyting algebras.
1	Among	among	ADP	IN	_	61	prep	_	_
2	varieties	variety	NOUN	NNS	Number=Plur	1	pobj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	universal	universal	ADJ	JJ	Degree=Pos	5	amod	_	_
5	algebras	algebra	NOUN	NNS	Number=Plur	3	pobj	_	_
6	possessing	possess	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	csubj	_	_
7	this	this	DET	DT	Number=Sing|PronType=Dem	8	det	_	_
8	property	property	NOUN	NN	Number=Sing	6	dobj	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	relcl	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	61	punct	_	_
11	as	as	SCONJ	IN	_	13	mark	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	61	advcl	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	61	punct	_	_
15	categories	category	NOUN	NNS	Number=Plur	61	nsubj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	groups	group	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
19	not	not	PART	RB	Polarity=Neg	20	neg	_	_
20	necessarily	necessarily	ADV	RB	_	22	advmod	_	_
21	associative	associative	ADJ	JJ	Degree=Pos	22	amod	_	_
22	rings	ring	NOUN	NNS	Number=Plur	15	appos	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	$ M $	$ m $	SYM	$	_	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	sets	set	NOUN	NNS	Number=Plur	22	appos	_	_
27	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	15	punct	_	SpaceAfter=No
28	for	for	ADP	IN	_	15	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
30	monoid	monoid	NOUN	NN	Number=Sing	28	pobj	_	_
31	$ M $	$ m $	SYM	$	_	28	pobj	_	_
32	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	15	punct	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
34	Lie	Lie	PROPN	NNP	Number=Sing	35	compound	_	_
35	algebras	algebras	PROPN	NNPS	Number=Plur	15	appos	_	_
36	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	35	punct	_	SpaceAfter=No
37	over	over	ADP	IN	_	35	prep	_	_
38	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
39	field	field	NOUN	NN	Number=Sing	37	pobj	_	SpaceAfter=No
40	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	35	punct	_	SpaceAfter=No
41	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
42	quasi	quasi	PROPN	NNPS	Number=Plur	35	conj	_	_
43	-	-	NOUN	NNS	Number=Plur	35	conj	_	_
44	groups	group	NOUN	NNS	Number=Plur	35	conj	_	SpaceAfter=No
45	,	,	PUNCT	,	PunctType=Comm	44	punct	_	_
46	commutative	commutative	ADJ	JJ	Degree=Pos	47	amod	_	_
47	quasi	quasi	NOUN	NNS	Number=Plur	44	conj	_	_
48	-	-	PUNCT	:	_	44	conj	_	_
49	groups	group	NOUN	NNS	Number=Plur	44	conj	_	SpaceAfter=No
50	,	,	PUNCT	,	PunctType=Comm	49	punct	_	_
51	Steiner	Steiner	PROPN	NNP	Number=Sing	52	compound	_	_
52	quasi	quasi	NOUN	NNS	Number=Plur	49	conj	_	_
53	-	-	PUNCT	:	_	49	conj	_	_
54	groups	group	NOUN	NNS	Number=Plur	49	conj	_	SpaceAfter=No
55	,	,	PUNCT	,	PunctType=Comm	54	punct	_	_
56	medial	medial	ADJ	JJ	Degree=Pos	57	amod	_	_
57	quasi	quasi	NOUN	NNS	Number=Plur	54	conj	_	_
58	-	-	NOUN	NNS	Number=Plur	54	conj	_	_
59	groups	group	NOUN	NNS	Number=Plur	54	conj	_	SpaceAfter=No
60	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
61	semilattice	semilattice	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
62	$	$	SYM	$	_	63	nmod	_	_
63	lattices	lattice	NOUN	NNS	Number=Plur	61	dobj	_	SpaceAfter=No
64	,	,	PUNCT	,	PunctType=Comm	63	punct	_	_
65	weakly	weakly	ADJ	JJ	Degree=Pos	67	amod	_	_
66	associative	associative	ADJ	JJ	Degree=Pos	67	amod	_	_
67	lattices	lattice	NOUN	NNS	Number=Plur	63	appos	_	SpaceAfter=No
68	,	,	PUNCT	,	PunctType=Comm	67	punct	_	_
69	Boolean	boolean	ADJ	JJ	Degree=Pos	70	amod	_	_
70	algebras	algebra	NOUN	NNS	Number=Plur	67	conj	_	SpaceAfter=No
71	,	,	PUNCT	,	PunctType=Comm	70	punct	_	_
72	Heyting	heyte	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	73	compound	_	_
73	algebras	algebra	NOUN	NNS	Number=Plur	70	conj	_	SpaceAfter=No
74	.	.	PUNCT	.	PunctType=Peri	61	punct	_	SpaceAfter=No

# sent_id = 3
# text = It is shown that every codescent morphism of groups is effective.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	SCONJ	IN	_	10	mark	_	_
5	every	every	DET	DT	_	7	det	_	_
6	codescent	codescent	NOUN	NN	Number=Sing	7	compound	_	_
7	morphism	morphism	NOUN	NN	Number=Sing	10	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	groups	group	NOUN	NNS	Number=Plur	8	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
11	effective	effective	ADJ	JJ	Degree=Pos	10	acomp	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 156
# sent_id = 1
# text = We generalize Dress and Müller's main result on decomposable functors and the exponential principle.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	Dress	Dress	PROPN	NNP	Number=Sing	8	nmod	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	Müller	Müller	PROPN	NNP	Number=Sing	8	poss	_	SpaceAfter=No
6	's	's	PART	POS	_	5	case	_	_
7	main	main	ADJ	JJ	Degree=Pos	8	amod	_	_
8	result	result	NOUN	NN	Number=Sing	2	dobj	_	_
9	on	on	ADP	IN	_	8	prep	_	_
10	decomposable	decomposable	ADJ	JJ	Degree=Pos	11	amod	_	_
11	functors	functor	NOUN	NNS	Number=Plur	9	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	exponential	exponential	ADJ	JJ	Degree=Pos	15	amod	_	_
15	principle	principle	NOUN	NN	Number=Sing	11	conj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We observe that their result can be seen as a characterization of free algebras for certain monad on the category of species.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	observe	observe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	8	mark	_	_
4	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	5	poss	_	_
5	result	result	NOUN	NN	Number=Sing	8	nsubjpass	_	_
6	can	can	AUX	MD	VerbForm=Fin	8	aux	_	_
7	be	be	AUX	VB	VerbForm=Inf	8	auxpass	_	_
8	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
9	as	as	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	characterization	characterization	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	free	free	ADJ	JJ	Degree=Pos	14	amod	_	_
14	algebras	algebra	NOUN	NNS	Number=Plur	12	pobj	_	_
15	for	for	ADP	IN	_	11	prep	_	_
16	certain	certain	ADJ	JJ	Degree=Pos	17	amod	_	_
17	monad	monad	NOUN	NNS	Number=Plur	15	pobj	_	_
18	on	on	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	species	specie	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = This perspective allows to formulate a general exponential principle in a symmetric monoidal category.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	perspective	perspective	NOUN	NN	Number=Sing	3	nsubj	_	_
3	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	formulate	formulate	VERB	VB	VerbForm=Inf	3	xcomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	general	general	ADJ	JJ	Degree=Pos	9	amod	_	_
8	exponential	exponential	ADJ	JJ	Degree=Pos	9	amod	_	_
9	principle	principle	NOUN	NN	Number=Sing	5	dobj	_	_
10	in	in	ADP	IN	_	5	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
12	symmetric	symmetric	ADJ	JJ	Degree=Pos	14	amod	_	_
13	monoidal	monoidal	ADJ	JJ	Degree=Pos	14	amod	_	_
14	category	category	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show that for any groupoid $ G $ , the category of presheaves on the symmetric monoidal completion $ clikG $ of $ G $ satisfies the exponential principle.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	21	mark	_	_
4	for	for	ADP	IN	_	21	prep	_	_
5	any	any	DET	DT	_	6	det	_	_
6	groupoid	groupoid	NOUN	NN	Number=Sing	4	pobj	_	_
7	$ G $	$ g $	SYM	$	_	6	nummod	_	_
8	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	category	category	NOUN	NN	Number=Sing	21	nsubj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	presheaves	presheave	NOUN	NNS	Number=Plur	11	pobj	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
15	symmetric	symmetric	ADJ	JJ	Degree=Pos	17	amod	_	_
16	monoidal	monoidal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	completion	completion	NOUN	NN	Number=Sing	13	pobj	_	_
18	$ clikG $	$ clikg $	SYM	$	_	17	nmod	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	$ G $	$ g $	SYM	$	_	19	pobj	_	_
21	satisfies	satisfie	NOUN	NNS	Number=Plur	2	ccomp	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	exponential	exponential	ADJ	JJ	Degree=Pos	24	amod	_	_
24	principle	principle	NOUN	NN	Number=Sing	21	dobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = The main result in Dress and Müller reduces to the case $ G = 1 $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	result	result	NOUN	NN	Number=Sing	8	nsubj	_	_
4	in	in	ADP	IN	_	3	prep	_	_
5	Dress	Dress	PROPN	NNP	Number=Sing	4	pobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	Müller	Müller	PROPN	NNP	Number=Sing	5	conj	_	_
8	reduces	reduce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	case	case	NOUN	NN	Number=Sing	9	pobj	_	_
12	$ G = 1 $	$ g = 1 $	SYM	$	_	8	dobj	_	_
13	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 6
# text = We discuss two notions of functor between categories satisfying the exponential principle and express some well known combinatorial identities as instances of the preservation properties of these functors.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	discuss	discuss	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	two	two	NUM	CD	NumType=Card	4	nummod	_	_
4	notions	notion	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	functor	functor	NOUN	NN	Number=Sing	5	pobj	_	_
7	between	between	ADP	IN	_	4	prep	_	_
8	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
9	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	acl	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	exponential	exponential	ADJ	JJ	Degree=Pos	12	amod	_	_
12	principle	principle	NOUN	NN	Number=Sing	9	dobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
14	express	express	VERB	VB	VerbForm=Inf	9	conj	_	_
15	some	some	DET	DT	_	19	det	_	_
16	well	well	ADV	RB	Degree=Pos	17	advmod	_	_
17	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
18	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	19	amod	_	_
19	identities	identity	NOUN	NNS	Number=Plur	14	dobj	_	_
20	as	as	ADP	IN	_	14	prep	_	_
21	instances	instance	NOUN	NNS	Number=Plur	20	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	preservation	preservation	NOUN	NN	Number=Sing	25	compound	_	_
25	properties	property	NOUN	NNS	Number=Plur	22	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	these	these	DET	DT	Number=Plur|PronType=Dem	28	det	_	_
28	functors	functor	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = Finally, we give a characterization of $ G $ as a subcategory of presheaves on $ clikG $ .
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	characterization	characterization	NOUN	NN	Number=Sing	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	$ G $	$ g $	SYM	$	_	7	pobj	_	_
9	as	as	ADP	IN	_	4	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	subcategory	subcategory	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	presheaves	presheave	NOUN	NNS	Number=Plur	12	pobj	_	_
14	on	on	ADP	IN	_	13	prep	_	_
15	$ clikG $	$ clikg $	SYM	$	_	14	pobj	_	_
16	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 157
# sent_id = 1
# text = A specific property applicable to subsets of a hom - set in any small category is defined.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	specific	specific	ADJ	JJ	Degree=Pos	3	amod	_	_
3	property	property	NOUN	NN	Number=Sing	17	nsubjpass	_	_
4	applicable	applicable	ADJ	JJ	Degree=Pos	3	amod	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	subsets	subset	NOUN	NNS	Number=Plur	5	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	hom	hom	ADV	RB	_	11	advmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	pobj	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	any	any	DET	DT	_	15	det	_	_
14	small	small	ADJ	JJ	Degree=Pos	15	amod	_	_
15	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	auxpass	_	_
17	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 2
# text = Subsets with this property are called composition - representative.
1	Subsets	subset	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
2	with	with	ADP	IN	_	1	prep	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	property	property	NOUN	NN	Number=Sing	2	pobj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	composition	composition	NOUN	NN	Number=Sing	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	representative	representative	NOUN	NN	Number=Sing	6	oprd	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = The notion of composition - representability is motivated both by the representability of a linear functional on an associative algebra, and, by the recognizability of a subset of a monoid.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	notion	notion	NOUN	NN	Number=Sing	8	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	composition	composition	NOUN	NN	Number=Sing	6	compound	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	representability	representability	NOUN	NN	Number=Sing	3	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	both	both	PRON	DT	_	10	preconj	_	_
10	by	by	ADP	IN	_	8	agent	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	representability	representability	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	linear	linear	ADJ	JJ	Degree=Pos	16	amod	_	_
16	functional	functional	NOUN	NN	Number=Sing	13	pobj	_	_
17	on	on	ADP	IN	_	12	prep	_	_
18	an	an	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	associative	associative	ADJ	JJ	Degree=Pos	20	amod	_	_
20	algebra	algebra	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
24	by	by	ADP	IN	_	8	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	recognizability	recognizability	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
29	subset	subset	NOUN	NN	Number=Sing	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
32	monoid	monoid	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 4
# text = Various characterizations are provided which therefore may be regarded as analogs of certain characterizations for representability and recognizablity.
1	Various	various	ADJ	JJ	Degree=Pos	2	amod	_	_
2	characterizations	characterization	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	provided	provide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	which	which	PRON	WDT	_	9	nsubjpass	_	_
6	therefore	therefore	ADV	RB	_	9	advmod	_	_
7	may	may	AUX	MD	VerbForm=Fin	9	aux	_	_
8	be	be	AUX	VB	VerbForm=Inf	9	auxpass	_	_
9	regarded	regard	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	ccomp	_	_
10	as	as	ADP	IN	_	9	prep	_	_
11	analogs	analog	NOUN	NNS	Number=Plur	10	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	certain	certain	ADJ	JJ	Degree=Pos	14	amod	_	_
14	characterizations	characterization	NOUN	NNS	Number=Plur	12	pobj	_	_
15	for	for	ADP	IN	_	14	prep	_	_
16	representability	representability	NOUN	NN	Number=Sing	15	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	recognizablity	recognizablity	NOUN	NN	Number=Sing	16	conj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = As an application, the special case of an algebraic theory $ T $ is considered and simple characterizations for a recognizable forest are given.
1	As	as	ADP	IN	_	14	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	special	special	ADJ	JJ	Degree=Pos	7	amod	_	_
7	case	case	NOUN	NN	Number=Sing	14	nsubjpass	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	algebraic	algebraic	ADJ	JJ	Degree=Pos	11	amod	_	_
11	theory	theory	NOUN	NN	Number=Sing	8	pobj	_	_
12	$ T $	$ t $	SYM	$	_	11	appos	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	simple	simple	ADJ	JJ	Degree=Pos	17	amod	_	_
17	characterizations	characterization	NOUN	NNS	Number=Plur	23	nsubjpass	_	_
18	for	for	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	recognizable	recognizable	ADJ	JJ	Degree=Pos	21	amod	_	_
21	forest	forest	NOUN	NN	Number=Sing	18	pobj	_	_
22	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	23	auxpass	_	_
23	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	conj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# sent_id = 6
# text = In particular, it is shown that the composition - representative subsets of the hom - set $ T([1], [0]) $ , the set of all trees, are the recognizable forests and that they, in turn, are characterized by a corresponding finite `syntactic congruence.'
1	In	in	ADP	IN	_	6	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
4	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	6	nsubjpass	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	that	that	SCONJ	IN	_	26	mark	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
9	composition	composition	NOUN	NN	Number=Sing	11	npadvmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	representative	representative	NOUN	NN	Number=Sing	12	amod	_	_
12	subsets	subset	NOUN	NNS	Number=Plur	26	nsubj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
15	hom	hom	ADV	RB	_	17	advmod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
18	$ T([1], [0]) $	$ t([1], [0]) $	SYM	$	_	13	pobj	_	_
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	set	set	NOUN	NN	Number=Sing	18	appos	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	all	all	DET	DT	_	24	det	_	_
24	trees	tree	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
26	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	recognizable	recognizable	ADJ	JJ	Degree=Pos	29	amod	_	_
29	forests	forest	NOUN	NNS	Number=Plur	26	attr	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
31	that	that	SCONJ	IN	_	38	mark	_	_
32	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	38	nsubjpass	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	38	punct	_	_
34	in	in	ADP	IN	_	38	prep	_	_
35	turn	turn	NOUN	NN	Number=Sing	34	pobj	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	38	punct	_	_
37	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	38	auxpass	_	_
38	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	conj	_	_
39	by	by	ADP	IN	_	38	agent	_	_
40	a	a	DET	DT	Definite=Ind|PronType=Art	45	det	_	_
41	corresponding	corresponding	ADJ	JJ	Degree=Pos	45	amod	_	_
42	finite	finite	ADJ	JJ	Degree=Pos	45	nmod	_	_
43	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	45	punct	_	SpaceAfter=No
44	syntactic	syntactic	ADJ	JJ	Degree=Pos	45	amod	_	_
45	congruence	congruence	NOUN	NN	Number=Sing	39	pobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No
47	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	6	punct	_	SpaceAfter=No

# sent_id = 7
# text = Using a decomposition result (proved here), the composition - representative subsets of the hom - set $ T([m], [0]) $ for $ (0 leq m) $ are shown to be finite unions of $ m $ - fold (cartesian) products of recognizable forests.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	24	advcl	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	decomposition	decomposition	NOUN	NN	Number=Sing	4	compound	_	_
4	result	result	NOUN	NN	Number=Sing	1	dobj	_	_
5	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	6	punct	_	SpaceAfter=No
6	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	acl	_	_
7	here	here	ADV	RB	PronType=Dem	6	advmod	_	SpaceAfter=No
8	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	6	punct	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
11	composition	composition	NOUN	NN	Number=Sing	13	npadvmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	representative	representative	NOUN	NN	Number=Sing	14	amod	_	_
14	subsets	subset	NOUN	NNS	Number=Plur	24	nsubjpass	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
17	hom	hom	ADV	RB	_	19	advmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	amod	_	_
20	$ T([m], [0]) $	$ t([m], [0]) $	SYM	$	_	15	pobj	_	_
21	for	for	ADP	IN	_	20	prep	_	_
22	$ (0 leq m) $	$ (0 leq m) $	SYM	$	_	21	pobj	_	_
23	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	24	auxpass	_	_
24	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
25	to	to	PART	TO	_	26	aux	_	_
26	be	be	AUX	VB	VerbForm=Inf	24	xcomp	_	_
27	finite	finite	ADJ	JJ	Degree=Pos	28	amod	_	_
28	unions	union	NOUN	NNS	Number=Plur	26	attr	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	$ m $	$ m $	SYM	$	_	36	nmod	_	_
31	-	-	ADJ	JJ	Degree=Pos	30	advmod	_	_
32	fold	fold	ADJ	JJ	Degree=Pos	36	amod	_	_
33	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	36	punct	_	SpaceAfter=No
34	cartesian	cartesian	NOUN	NN	Number=Sing	36	nmod	_	SpaceAfter=No
35	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	36	punct	_	_
36	products	product	NOUN	NNS	Number=Plur	29	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	recognizable	recognizable	ADJ	JJ	Degree=Pos	39	amod	_	_
39	forests	forest	NOUN	NNS	Number=Plur	37	pobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# doc_id = 158
# sent_id = 1
# text = This paper studies lax higher dimensional structure over bicategories.
1	This	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	compound	_	_
3	studies	study	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	lax	lax	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	higher	high	ADJ	JJR	Degree=Cmp	7	amod	_	_
6	dimensional	dimensional	ADJ	JJ	Degree=Pos	7	amod	_	_
7	structure	structure	NOUN	NN	Number=Sing	4	dobj	_	_
8	over	over	ADP	IN	_	7	prep	_	_
9	bicategories	bicategorie	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = The general notion of a module between two morphisms of bicategories is described.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	general	general	ADJ	JJ	Degree=Pos	3	amod	_	_
3	notion	notion	NOUN	NN	Number=Sing	13	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	module	module	NOUN	NN	Number=Sing	4	pobj	_	_
7	between	between	ADP	IN	_	6	prep	_	_
8	two	two	NUM	CD	NumType=Card	9	nummod	_	_
9	morphisms	morphism	NOUN	NNS	Number=Plur	13	nsubjpass	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	bicategories	bicategorie	NOUN	NNS	Number=Plur	10	pobj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 3
# text = These modules together with their (multi - )2 - cells, which we call modulations, organize themselves into a multi - bicategory.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	modules	module	NOUN	NNS	Number=Plur	19	nsubj	_	_
3	together	together	ADV	RB	_	4	advmod	_	_
4	with	with	ADP	IN	_	2	prep	_	_
5	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	12	poss	_	_
6	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
7	multi	multi	NOUN	NN	Number=Sing	12	nmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
9	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	12	punct	_	SpaceAfter=No
10	2	2	NUM	CD	NumType=Card	12	nummod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	cells	cell	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	which	which	PRON	WDT	_	16	dobj	_	_
15	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	16	nsubj	_	_
16	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	12	relcl	_	_
17	modulations	modulation	NOUN	NNS	Number=Plur	16	dobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
19	organize	organize	VERB	VB	VerbForm=Inf	0	ROOT	_	_
20	themselves	themselves	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs|Reflex=Yes	19	dobj	_	_
21	into	into	ADP	IN	_	19	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
23	multi	multi	ADJ	JJ	Degree=Pos	25	amod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	bicategory	bicategory	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 4
# text = The usual notion of a module can be recovered from this general notion by simply choosing the domain bicategory to be the terminal or final bicategory.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	usual	usual	ADJ	JJ	Degree=Pos	3	amod	_	_
3	notion	notion	NOUN	NN	Number=Sing	9	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	module	module	NOUN	NN	Number=Sing	4	pobj	_	_
7	can	can	AUX	MD	VerbForm=Fin	9	aux	_	_
8	be	be	AUX	VB	VerbForm=Inf	9	auxpass	_	_
9	recovered	recover	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	from	from	ADP	IN	_	9	prep	_	_
11	this	this	DET	DT	Number=Sing|PronType=Dem	13	det	_	_
12	general	general	ADJ	JJ	Degree=Pos	13	amod	_	_
13	notion	notion	NOUN	NN	Number=Sing	10	pobj	_	_
14	by	by	ADP	IN	_	9	prep	_	_
15	simply	simply	ADV	RB	_	16	advmod	_	_
16	choosing	choose	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	pcomp	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	domain	domain	NOUN	NN	Number=Sing	19	compound	_	_
19	bicategory	bicategory	NOUN	NN	Number=Sing	16	dobj	_	_
20	to	to	PART	TO	_	21	aux	_	_
21	be	be	AUX	VB	VerbForm=Inf	16	advcl	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
23	terminal	terminal	ADJ	JJ	Degree=Pos	26	amod	_	_
24	or	or	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	final	final	ADJ	JJ	Degree=Pos	23	conj	_	_
26	bicategory	bicategory	NOUN	NN	Number=Sing	21	attr	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 5
# text = The composite of two such modules need not exist.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	composite	composite	NOUN	NN	Number=Sing	9	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	two	two	NUM	CD	NumType=Card	6	nummod	_	_
5	such	such	ADJ	JJ	Degree=Pos	6	amod	_	_
6	modules	module	NOUN	NNS	Number=Plur	3	pobj	_	_
7	need	need	AUX	MD	VerbType=Mod	9	aux	_	_
8	not	not	PART	RB	Polarity=Neg	9	neg	_	_
9	exist	exist	VERB	VB	VerbForm=Inf	0	ROOT	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 6
# text = However, when the domain bicategory is small and the codomain bicategory is locally cocomplete then the composite of any two modules does exist and has a simple construction using the local colimits.
1	However	however	ADV	RB	_	7	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
3	when	when	SCONJ	WRB	_	7	advmod	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	domain	domain	NOUN	NN	Number=Sing	6	compound	_	_
6	bicategory	bicategory	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	small	small	ADJ	JJ	Degree=Pos	7	acomp	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	codomain	codomain	ADJ	JJ	Degree=Pos	12	amod	_	_
12	bicategory	bicategory	NOUN	NN	Number=Sing	13	nsubj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	conj	_	_
14	locally	locally	ADV	RB	_	15	advmod	_	_
15	cocomplete	cocomplete	ADJ	JJ	Degree=Pos	13	acomp	_	_
16	then	then	ADV	RB	PronType=Dem	18	advmod	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	composite	composite	NOUN	NN	Number=Sing	24	nsubj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	any	any	DET	DT	_	22	det	_	_
21	two	two	NUM	CD	NumType=Card	22	nummod	_	_
22	modules	module	NOUN	NNS	Number=Plur	19	pobj	_	_
23	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	aux	_	_
24	exist	exist	VERB	VB	VerbForm=Inf	13	conj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	conj	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	simple	simple	ADJ	JJ	Degree=Pos	29	amod	_	_
29	construction	construction	NOUN	NN	Number=Sing	26	dobj	_	_
30	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	29	acl	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	local	local	ADJ	JJ	Degree=Pos	33	amod	_	_
33	colimits	colimit	NOUN	NNS	Number=Plur	30	dobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 7
# text = These modules and their modulations then give rise to a bicategory.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	modules	module	NOUN	NNS	Number=Plur	7	nsubj	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	5	poss	_	_
5	modulations	modulation	NOUN	NNS	Number=Plur	2	conj	_	_
6	then	then	ADV	RB	PronType=Dem	7	advmod	_	_
7	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	rise	rise	NOUN	NN	Number=Sing	7	dobj	_	_
9	to	to	ADP	IN	_	7	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	bicategory	bicategory	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 8
# text = Recall that neither transformations nor optransformations (respectively lax natural transformations and oplax natural transformations) between morphisms of bicategories give rise to a smooth 3 - dimensional structure.
1	Recall	recall	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	that	that	SCONJ	IN	_	21	mark	_	_
3	neither	neither	CCONJ	CC	ConjType=Cmp	4	preconj	_	_
4	transformations	transformation	NOUN	NNS	Number=Plur	21	nsubj	_	_
5	nor	nor	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	optransformations	optransformation	NOUN	NNS	Number=Plur	4	conj	_	_
7	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	4	punct	_	SpaceAfter=No
8	respectively	respectively	ADV	RB	_	9	advmod	_	_
9	lax	lax	ADJ	JJ	Degree=Pos	11	amod	_	_
10	natural	natural	ADJ	JJ	Degree=Pos	11	amod	_	_
11	transformations	transformation	NOUN	NNS	Number=Plur	4	conj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	oplax	oplax	NOUN	NN	Number=Sing	11	conj	_	_
14	natural	natural	ADJ	JJ	Degree=Pos	15	amod	_	_
15	transformations	transformation	NOUN	NNS	Number=Plur	11	conj	_	SpaceAfter=No
16	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	4	punct	_	_
17	between	between	ADP	IN	_	4	prep	_	_
18	morphisms	morphism	NOUN	NNS	Number=Plur	17	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	bicategories	bicategorie	NOUN	NNS	Number=Plur	19	pobj	_	_
21	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	1	ccomp	_	_
22	rise	rise	NOUN	NN	Number=Sing	21	dobj	_	_
23	to	to	ADP	IN	_	22	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
25	smooth	smooth	ADJ	JJ	Degree=Pos	29	amod	_	_
26	3	3	NUM	CD	NumType=Card	28	advmod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	dimensional	dimensional	ADJ	JJ	Degree=Pos	29	amod	_	_
29	structure	structure	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 9
# text = However, there is a smooth 3 - dimensional structure for modules, and both transformations and optransformations give rise to associated modules.
1	However	however	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	there	there	PRON	EX	_	4	expl	_	_
4	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
6	smooth	smooth	ADJ	JJ	Degree=Pos	10	amod	_	_
7	3	3	NUM	CD	NumType=Card	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	dimensional	dimensional	ADJ	JJ	Degree=Pos	10	amod	_	_
10	structure	structure	NOUN	NN	Number=Sing	4	attr	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	modules	module	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
15	both	both	DET	DT	_	16	det	_	_
16	transformations	transformation	NOUN	NNS	Number=Plur	19	nsubj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	optransformations	optransformation	NOUN	NNS	Number=Plur	16	conj	_	_
19	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	4	conj	_	_
20	rise	rise	NOUN	NN	Number=Sing	19	dobj	_	_
21	to	to	ADP	IN	_	20	prep	_	_
22	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	amod	_	_
23	modules	module	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 10
# text = Furthermore, the modulations between two modules associated with transformations can then be described directly as a new sort of modification between the transformations.
1	Furthermore	furthermore	ADV	RB	_	14	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	modulations	modulation	NOUN	NNS	Number=Plur	14	nsubjpass	_	_
5	between	between	ADP	IN	_	4	prep	_	_
6	two	two	NUM	CD	NumType=Card	7	nummod	_	_
7	modules	module	NOUN	NNS	Number=Plur	5	pobj	_	_
8	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	acl	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	transformations	transformation	NOUN	NNS	Number=Plur	9	pobj	_	_
11	can	can	AUX	MD	VerbForm=Fin	14	aux	_	_
12	then	then	ADV	RB	PronType=Dem	14	advmod	_	_
13	be	be	AUX	VB	VerbForm=Inf	14	auxpass	_	_
14	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
15	directly	directly	ADV	RB	_	14	advmod	_	_
16	as	as	ADP	IN	_	14	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	new	new	ADJ	JJ	Degree=Pos	19	amod	_	_
19	sort	sort	NOUN	NN	Number=Sing	16	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	modification	modification	NOUN	NN	Number=Sing	20	pobj	_	_
22	between	between	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	transformations	transformation	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 11
# text = This provides a locally full and faithful homomorphism from transformations and modifications into the bicategory of modules.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
4	locally	locally	ADV	RB	_	5	advmod	_	_
5	full	full	ADJ	JJ	Degree=Pos	8	amod	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	faithful	faithful	ADJ	JJ	Degree=Pos	5	conj	_	_
8	homomorphism	homomorphism	NOUN	NN	Number=Sing	2	dobj	_	_
9	from	from	ADP	IN	_	8	prep	_	_
10	transformations	transformation	NOUN	NNS	Number=Plur	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	modifications	modification	NOUN	NNS	Number=Plur	10	conj	_	_
13	into	into	ADP	IN	_	2	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	bicategory	bicategory	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	modules	module	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 12
# text = Finally, if each 1 - cell component of a transformation is a left - adjoint then the right - adjoints provide an optransformation.
1	Finally	finally	ADV	RB	_	22	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
3	if	if	SCONJ	IN	_	12	mark	_	_
4	each	each	DET	DT	_	8	det	_	_
5	1	1	NUM	CD	NumType=Card	7	nummod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	cell	cell	NOUN	NN	Number=Sing	8	compound	_	_
8	component	component	NOUN	NN	Number=Sing	12	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	transformation	transformation	NOUN	NN	Number=Sing	9	pobj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	advcl	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
14	left	left	ADJ	JJ	Degree=Pos	16	amod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	adjoint	adjoint	NOUN	NN	Number=Sing	12	attr	_	_
17	then	then	ADV	RB	PronType=Dem	22	advmod	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
19	right	right	ADJ	JJ	Degree=Pos	21	amod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	adjoints	adjoint	NOUN	NNS	Number=Plur	22	nsubj	_	_
22	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
23	an	an	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	optransformation	optransformation	NOUN	NN	Number=Sing	22	dobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# sent_id = 13
# text = In the module bicategory the module associated with this optransformation is right - adjoint to the module associated with the transformation.
1	In	in	ADP	IN	_	11	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	module	module	NOUN	NN	Number=Sing	4	compound	_	_
4	bicategory	bicategory	NOUN	NN	Number=Sing	1	pobj	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	module	module	NOUN	NN	Number=Sing	11	nsubj	_	_
7	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
8	with	with	ADP	IN	_	7	prep	_	_
9	this	this	DET	DT	Number=Sing|PronType=Dem	10	det	_	_
10	optransformation	optransformation	NOUN	NN	Number=Sing	8	pobj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	right	right	ADJ	JJ	Degree=Pos	14	amod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	adjoint	adjoint	NOUN	NN	Number=Sing	11	acomp	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	module	module	NOUN	NN	Number=Sing	15	pobj	_	_
18	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	transformation	transformation	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 14
# text = Therefore the inclusion of transformations whose 1 - cells have left adjoints into the (multi - )bicategory of modules provides a source of proarrow equipment.
1	Therefore	therefore	ADV	RB	_	22	advmod	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	inclusion	inclusion	NOUN	NN	Number=Sing	22	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	transformations	transformation	NOUN	NNS	Number=Plur	4	pobj	_	_
6	whose	whose	DET	WP$	Poss=Yes	9	poss	_	_
7	1	1	NUM	CD	NumType=Card	9	nummod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	cells	cell	NOUN	NNS	Number=Plur	11	nsubj	_	_
10	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	11	aux	_	_
11	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	relcl	_	_
12	adjoints	adjoint	NOUN	NNS	Number=Plur	11	dobj	_	_
13	into	into	ADP	IN	_	11	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
15	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	19	punct	_	SpaceAfter=No
16	multi	multi	ADJ	JJ	Degree=Pos	19	nmod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
18	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	19	punct	_	SpaceAfter=No
19	bicategory	bicategory	NOUN	NN	Number=Sing	13	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	modules	module	NOUN	NNS	Number=Plur	20	pobj	_	_
22	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	source	source	NOUN	NN	Number=Sing	22	dobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	proarrow	proarrow	NOUN	NN	Number=Sing	27	compound	_	_
27	equipment	equipment	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# doc_id = 159
# sent_id = 1
# text = We give an explicit construction of the category $ Opetope $ of opetopes.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	explicit	explicit	ADJ	JJ	Degree=Pos	5	amod	_	_
5	construction	construction	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
9	$ Opetope $	$ opetope $	SYM	$	_	8	appos	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	opetopes	opetope	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We prove that the category of opetopic sets is equivalent to the category of presheaves over Opetope.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	9	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	9	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	opetopic	opetopic	ADJ	JJ	Degree=Pos	8	amod	_	_
8	sets	set	NOUN	NNS	Number=Plur	6	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
10	equivalent	equivalent	ADJ	JJ	Degree=Pos	9	acomp	_	_
11	to	to	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	presheaves	presheave	NOUN	NNS	Number=Plur	14	pobj	_	_
16	over	over	ADP	IN	_	15	prep	_	_
17	Opetope	Opetope	PROPN	NNP	Number=Sing	16	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 160
# sent_id = 1
# text = For a complete cartesian - closed category $ V $ with coproducts, and for any pointed endofunctor $ T $ of the category of sets satisfying a suitable Beck - Chevalley - type condition, it is shown that the category of lax reflexive $ (T, V) $ - algebras is a quasitopos.
1	For	for	ADP	IN	_	35	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
3	complete	complete	ADJ	JJ	Degree=Pos	7	amod	_	_
4	cartesian	cartesian	NOUN	NN	Number=Sing	6	npadvmod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	closed	closed	ADJ	JJ	Degree=Pos	7	amod	_	_
7	category	category	NOUN	NN	Number=Sing	1	pobj	_	_
8	$ V $	$ v $	SYM	$	_	1	dep	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	coproducts	coproduct	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	1	cc	_	_
13	for	for	ADP	IN	_	35	prep	_	_
14	any	any	DET	DT	_	16	det	_	_
15	pointed	pointed	ADJ	JJ	Degree=Pos	16	amod	_	_
16	endofunctor	endofunctor	NOUN	NN	Number=Sing	13	pobj	_	_
17	$ T $	$ t $	SYM	$	_	16	appos	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	sets	set	NOUN	NNS	Number=Plur	21	pobj	_	_
23	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	acl	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
25	suitable	suitable	ADJ	JJ	Degree=Pos	31	amod	_	_
26	Beck	Beck	PROPN	NNP	Number=Sing	30	compound	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
28	Chevalley	Chevalley	PROPN	NNP	Number=Sing	30	compound	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	type	type	NOUN	NN	Number=Sing	31	compound	_	_
31	condition	condition	NOUN	NN	Number=Sing	23	dobj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
33	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	35	nsubjpass	_	_
34	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	35	auxpass	_	_
35	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
36	that	that	SCONJ	IN	_	45	mark	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	category	category	NOUN	NN	Number=Sing	45	nsubj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	lax	lax	PROPN	NNP	Number=Sing	44	amod	_	_
41	reflexive	reflexive	ADJ	JJ	Degree=Pos	44	amod	_	_
42	$ (T, V) $	$ (t, v) $	SYM	$	_	44	compound	_	_
43	-	-	PUNCT	HYPH	PunctType=Dash	44	punct	_	_
44	algebras	algebras	PROPN	NNP	Number=Sing	39	pobj	_	_
45	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	35	ccomp	_	_
46	a	a	DET	DT	Definite=Ind|PronType=Art	47	det	_	_
47	quasitopos	quasitopos	NOUN	NN	Number=Sing	45	attr	_	SpaceAfter=No
48	.	.	PUNCT	.	PunctType=Peri	35	punct	_	SpaceAfter=No

# sent_id = 2
# text = This result encompasses many known and new examples of quasitopoi.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	result	result	NOUN	NN	Number=Sing	3	nsubj	_	_
3	encompasses	encompass	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	many	many	ADJ	JJ	Degree=Pos	5	advmod	_	_
5	known	known	ADJ	JJ	Degree=Pos	8	amod	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	new	new	ADJ	JJ	Degree=Pos	5	conj	_	_
8	examples	example	NOUN	NNS	Number=Plur	3	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	quasitopoi	quasitopoi	PROPN	NNP	Number=Sing	9	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 161
# sent_id = 1
# text = We take some first steps in providing a synthetic theory of distributions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	take	take	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	some	some	DET	DT	_	5	det	_	_
4	first	first	ADJ	JJ	Degree=Pos	5	amod	_	_
5	steps	step	NOUN	NNS	Number=Plur	2	dobj	_	_
6	in	in	ADP	IN	_	2	prep	_	_
7	providing	provide	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	pcomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	synthetic	synthetic	ADJ	JJ	Degree=Pos	10	amod	_	_
10	theory	theory	NOUN	NN	Number=Sing	7	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	distributions	distribution	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In particular, we are interested in the use of distribution theory as foundation, not just as tool, in the study of the wave equation.
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	interested	interested	ADJ	JJ	Degree=Pos	5	acomp	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	use	use	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	distribution	distribution	NOUN	NN	Number=Sing	12	compound	_	_
12	theory	theory	NOUN	NN	Number=Sing	10	pobj	_	_
13	as	as	ADP	IN	_	9	prep	_	_
14	foundation	foundation	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
16	not	not	PART	RB	Polarity=Neg	19	neg	_	_
17	just	just	ADV	RB	_	19	advmod	_	_
18	as	as	SCONJ	IN	_	19	mark	_	_
19	tool	tool	NOUN	NN	Number=Sing	6	conj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	in	in	ADP	IN	_	19	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	study	study	NOUN	NN	Number=Sing	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	wave	wave	NOUN	NN	Number=Sing	27	compound	_	_
27	equation	equation	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 162
# sent_id = 1
# text = We introduce various notions of partial topos, that is, `topos without terminal object'.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	various	various	ADJ	JJ	Degree=Pos	4	amod	_	_
4	notions	notion	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	partial	partial	ADJ	JJ	Degree=Pos	7	amod	_	_
7	topos	topos	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
9	that	that	ADV	RB	_	10	advmod	_	_
10	is	is	ADV	RB	_	13	advmod	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
12	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	13	punct	_	SpaceAfter=No
13	topos	topos	NOUN	NN	Number=Sing	2	dobj	_	_
14	without	without	ADP	IN	_	13	prep	_	_
15	terminal	terminal	ADJ	JJ	Degree=Pos	16	amod	_	_
16	object	object	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
17	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	13	punct	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The strongest one, called local topos, is motivated by the key examples of finite trees and sheaves with compact support.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	strongest	strong	ADJ	JJS	Degree=Sup	3	amod	_	_
3	one	one	NUM	CD	NumType=Card	10	nsubjpass	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	acl	_	_
6	local	local	ADJ	JJ	Degree=Pos	7	amod	_	_
7	topos	topos	NOUN	NN	Number=Sing	5	oprd	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	by	by	ADP	IN	_	10	agent	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	key	key	ADJ	JJ	Degree=Pos	14	amod	_	_
14	examples	example	NOUN	NNS	Number=Plur	11	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	finite	finite	ADJ	JJ	Degree=Pos	17	amod	_	_
17	trees	tree	NOUN	NNS	Number=Plur	15	pobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	sheaves	sheaf	NOUN	NNS	Number=Plur	17	conj	_	_
20	with	with	ADP	IN	_	14	prep	_	_
21	compact	compact	ADJ	JJ	Degree=Pos	22	amod	_	_
22	support	support	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 3
# text = Local toposes satisfy all the usual exactness properties of toposes but are neither cartesian closed nor have a subobject classifier.
1	Local	local	ADJ	JJ	Degree=Pos	2	amod	_	_
2	toposes	topos	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	satisfy	satisfy	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	all	all	DET	PDT	_	8	predet	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
6	usual	usual	ADJ	JJ	Degree=Pos	8	amod	_	_
7	exactness	exactness	NOUN	NN	Number=Sing	8	compound	_	_
8	properties	property	NOUN	NNS	Number=Plur	3	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	toposes	topos	NOUN	NNS	Number=Plur	9	pobj	_	_
11	but	but	CCONJ	CC	ConjType=Cmp	3	cc	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	conj	_	_
13	neither	neither	DET	DT	_	14	det	_	_
14	cartesian	cartesian	NOUN	NN	Number=Sing	12	attr	_	_
15	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	12	acomp	_	_
16	nor	nor	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	have	have	VERB	VB	VerbForm=Inf	15	conj	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	subobject	subobject	NOUN	NN	Number=Sing	20	compound	_	_
20	classifier	classifier	NOUN	NN	Number=Sing	17	dobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = Examples for the weaker notions are local homeomorphisms and discrete fibrations.
1	Examples	example	NOUN	NNS	Number=Plur	6	nsubj	_	_
2	for	for	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	weaker	weak	ADJ	JJR	Degree=Cmp	5	amod	_	_
5	notions	notion	NOUN	NNS	Number=Plur	2	pobj	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	local	local	ADJ	JJ	Degree=Pos	8	amod	_	_
8	homeomorphisms	homeomorphism	NOUN	NNS	Number=Plur	6	attr	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	discrete	discrete	ADJ	JJ	Degree=Pos	11	amod	_	_
11	fibrations	fibration	NOUN	NNS	Number=Plur	8	conj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = Finally, for partial toposes with supports we show how they can be completed to toposes via an inverse limit construction.
1	Finally	finally	ADV	RB	_	9	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
3	for	for	ADP	IN	_	9	prep	_	_
4	partial	partial	ADJ	JJ	Degree=Pos	5	amod	_	_
5	toposes	topos	NOUN	NNS	Number=Plur	3	pobj	_	_
6	with	with	ADP	IN	_	5	prep	_	_
7	supports	support	NOUN	NNS	Number=Plur	6	pobj	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	how	how	SCONJ	WRB	_	14	advmod	_	_
11	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	14	nsubjpass	_	_
12	can	can	AUX	MD	VerbForm=Fin	14	aux	_	_
13	be	be	AUX	VB	VerbForm=Inf	14	auxpass	_	_
14	completed	complete	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	ccomp	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	toposes	topos	NOUN	NNS	Number=Plur	14	advcl	_	_
17	via	via	ADP	IN	_	16	prep	_	_
18	an	an	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
19	inverse	inverse	ADJ	JJ	Degree=Pos	20	amod	_	_
20	limit	limit	NOUN	NN	Number=Sing	21	compound	_	_
21	construction	construction	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 163
# sent_id = 1
# text = This paper studies the homomorphism of rings of continuous functions $ rho : C(X)to C(Y) $ , $ Y $ a subspace of a Tychonoff space $ X $ , induced by restriction.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	studies	study	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	homomorphism	homomorphism	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	rings	ring	NOUN	NNS	Number=Plur	6	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	continuous	continuous	ADJ	JJ	Degree=Pos	10	amod	_	_
10	functions	function	NOUN	NNS	Number=Plur	8	pobj	_	_
11	$ rho : C(X)to C(Y) $	$ rho : c(x)to c(y) $	SYM	$	_	3	dep	_	_
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	$ Y $	$ y $	SYM	$	_	15	quantmod	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	subspace	subspace	NOUN	NN	Number=Sing	3	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	Tychonoff	Tychonoff	PROPN	NNP	Number=Sing	19	compound	_	_
19	space	space	NOUN	NN	Number=Sing	16	pobj	_	_
20	$ X $	$ x $	SYM	$	_	19	appos	_	_
21	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
22	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
23	by	by	ADP	IN	_	22	agent	_	_
24	restriction	restriction	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = We ask when $ rho $ is an epimorphism in the categorical sense.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	ask	ask	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	when	when	SCONJ	WRB	_	5	advmod	_	_
4	$ rho $	$ rho $	SYM	$	_	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	epimorphism	epimorphism	NOUN	NN	Number=Sing	5	attr	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	categorical	categorical	ADJ	JJ	Degree=Pos	11	amod	_	_
11	sense	sense	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = There are several appropriate categories: we look at CR, all commutative rings, and $ R/N $ , all reduced commutative rings.
1	There	there	PRON	EX	_	2	expl	_	_
2	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	ccomp	_	_
3	several	several	ADJ	JJ	Degree=Pos	5	amod	_	_
4	appropriate	appropriate	ADJ	JJ	Degree=Pos	5	amod	_	_
5	categories	category	NOUN	NNS	Number=Plur	2	attr	_	SpaceAfter=No
6	:	:	PUNCT	:	_	8	punct	_	_
7	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	8	nsubj	_	_
8	look	look	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	at	at	ADP	IN	_	8	prep	_	_
10	CR	CR	PROPN	NNP	Number=Sing	9	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	all	all	DET	DT	_	14	det	_	_
13	commutative	commutative	ADJ	JJ	Degree=Pos	14	amod	_	_
14	rings	ring	NOUN	NNS	Number=Plur	10	conj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
17	$ R/N $	$ r/n $	SYM	$	_	14	conj	_	_
18	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
19	all	all	DET	DT	_	22	det	_	_
20	reduced	reduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	amod	_	_
21	commutative	commutative	ADJ	JJ	Degree=Pos	22	amod	_	_
22	rings	ring	NOUN	NNS	Number=Plur	8	npadvmod	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 4
# text = When $ X $ is first countable and perfectly normal (for example, a metric space), $ rho $ is a $ CR $ - epimorphism if and only if it is an $ R/N $ - epimorphism if and only if $ Y $ is locally closed in $ X $ .
1	When	when	SCONJ	WRB	_	3	advmod	_	_
2	$ X $	$ x $	SYM	$	_	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	advcl	_	_
4	first	first	ADV	RB	_	5	advmod	_	_
5	countable	countable	ADJ	JJ	Degree=Pos	3	acomp	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	perfectly	perfectly	ADV	RB	_	8	advmod	_	_
8	normal	normal	ADJ	JJ	Degree=Pos	5	conj	_	_
9	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	3	punct	_	SpaceAfter=No
10	for	for	ADP	IN	_	3	prep	_	_
11	example	example	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	metric	metric	ADJ	JJ	Degree=Pos	15	amod	_	_
15	space	space	NOUN	NN	Number=Sing	3	attr	_	SpaceAfter=No
16	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	15	punct	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
18	$ rho $	$ rho $	SYM	$	_	19	nsubj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
21	$ CR $	$ cr $	SYM	$	_	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	epimorphism	epimorphism	NOUN	NN	Number=Sing	19	attr	_	_
24	if	if	SCONJ	IN	_	29	mark	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
26	only	only	ADV	RB	_	29	advmod	_	_
27	if	if	SCONJ	IN	_	29	mark	_	_
28	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	29	nsubj	_	_
29	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	advcl	_	_
30	an	an	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
31	$ R/N $	$ r/n $	SYM	$	_	33	nmod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	epimorphism	epimorphism	NOUN	NN	Number=Sing	29	attr	_	_
34	if	if	SCONJ	IN	_	41	mark	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	34	cc	_	_
36	only	only	ADV	RB	_	41	advmod	_	_
37	if	if	SCONJ	IN	_	41	mark	_	_
38	$ Y $	$ y $	SYM	$	_	41	nsubjpass	_	_
39	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	41	auxpass	_	_
40	locally	locally	ADV	RB	_	41	advmod	_	_
41	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	advcl	_	_
42	in	in	ADP	IN	_	41	prep	_	_
43	$ X $	$ x $	SYM	$	_	42	pobj	_	_
44	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 5
# text = It is also shown that the restriction of $ rho $ to $ C^*(X)to C^*(Y) $ , when $ X $ is normal, is a $ CR $ - epimorphism if and only if it is a surjection.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	4	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
3	also	also	ADV	RB	_	4	advmod	_	_
4	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	that	that	SCONJ	IN	_	18	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	restriction	restriction	NOUN	NN	Number=Sing	18	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	$ rho $	$ rho $	SYM	$	_	8	pobj	_	_
10	to	to	ADP	IN	_	7	prep	_	_
11	$ C^*(X)to C^*(Y) $	$ c^*(x)to c^*(y) $	SYM	$	_	10	pobj	_	_
12	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
13	when	when	SCONJ	WRB	_	15	advmod	_	_
14	$ X $	$ x $	SYM	$	_	15	nsubj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	relcl	_	_
16	normal	normal	ADJ	JJ	Degree=Pos	15	acomp	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
20	$ CR $	$ cr $	SYM	$	_	22	nmod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	epimorphism	epimorphism	NOUN	NN	Number=Sing	18	attr	_	_
23	if	if	SCONJ	IN	_	28	mark	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
25	only	only	ADV	RB	_	28	advmod	_	_
26	if	if	SCONJ	IN	_	28	mark	_	_
27	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	28	nsubj	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	advcl	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
30	surjection	surjection	NOUN	NN	Number=Sing	28	attr	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 6
# text = In general spaces the picture is more complicated, as is shown by various examples.
1	In	in	ADP	IN	_	6	prep	_	_
2	general	general	ADJ	JJ	Degree=Pos	3	amod	_	_
3	spaces	space	NOUN	NNS	Number=Plur	1	pobj	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	picture	picture	NOUN	NN	Number=Sing	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	more	more	ADV	RBR	Degree=Cmp	8	advmod	_	_
8	complicated	complicated	ADJ	JJ	Degree=Pos	6	acomp	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
10	as	as	SCONJ	IN	_	12	mark	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	advcl	_	_
13	by	by	ADP	IN	_	12	agent	_	_
14	various	various	ADJ	JJ	Degree=Pos	15	amod	_	_
15	examples	example	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 7
# text = Information about $ Spec rho $ and $ Spec rho $ restricted to the proconstructible set of prime $ z $ - ideals is given.
1	Information	information	NOUN	NN	Number=Sing	6	nsubj	_	_
2	about	about	ADP	IN	_	3	advmod	_	_
3	$ Spec rho $	$ spec rho $	SYM	$	_	1	appos	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	$ Spec rho $	$ spec rho $	SYM	$	_	6	nsubj	_	_
6	restricted	restrict	VERB	VBD	Tense=Past|VerbForm=Fin	17	nsubjpass	_	_
7	to	to	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	proconstructible	proconstructible	ADJ	JJ	Degree=Pos	7	pobj	_	_
10	set	set	NOUN	NN	Number=Sing	9	acl	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	prime	prime	ADJ	JJ	Degree=Pos	15	amod	_	_
13	$ z $	$ z $	SYM	$	_	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	ideals	ideal	NOUN	NNS	Number=Plur	11	pobj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	auxpass	_	_
17	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# doc_id = 164
# sent_id = 1
# text = Generalizing the fact that Scott's continuous lattices form the equational hull of the class of all algebraic lattices, we describe an equational hull of $ LFP $ , the category of locally finitely presentable categories, over $ CAT $ .
1	Generalizing	generalize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	advcl	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	fact	fact	NOUN	NN	Number=Sing	1	dobj	_	_
4	that	that	SCONJ	IN	_	9	mark	_	_
5	Scott	Scott	PROPN	NNP	Number=Sing	8	poss	_	SpaceAfter=No
6	's	's	PART	POS	_	5	case	_	_
7	continuous	continuous	ADJ	JJ	Degree=Pos	8	amod	_	_
8	lattices	lattice	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	form	form	VERB	VBP	Tense=Pres|VerbForm=Fin	3	acl	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	equational	equational	ADJ	JJ	Degree=Pos	12	amod	_	_
12	hull	hull	NOUN	NN	Number=Sing	9	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	class	class	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	all	all	DET	DT	_	19	det	_	_
18	algebraic	algebraic	ADJ	JJ	Degree=Pos	19	amod	_	_
19	lattices	lattice	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
21	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	22	nsubj	_	_
22	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
23	an	an	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	equational	equational	ADJ	JJ	Degree=Pos	25	amod	_	_
25	hull	hull	NOUN	NN	Number=Sing	22	dobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	$ LFP $	$ lfp $	SYM	$	_	26	pobj	_	_
28	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	category	category	NOUN	NN	Number=Sing	25	appos	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	locally	locally	ADV	RB	_	33	advmod	_	_
33	finitely	finitely	ADV	RB	_	35	amod	_	_
34	presentable	presentable	ADJ	JJ	Degree=Pos	35	amod	_	_
35	categories	category	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
37	over	over	ADP	IN	_	25	prep	_	_
38	$ CAT $	$ cat $	SYM	$	_	37	pobj	_	_
39	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# sent_id = 2
# text = Up to a set - theoretical hypothesis this hull is formed by the category of all precontinuous categories, that is, categories in which limits and filtered colimits distribute.
1	Up	up	ADP	IN	_	23	prep	_	_
2	to	to	ADP	IN	_	1	prep	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
4	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	amod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	theoretical	theoretical	ADJ	JJ	Degree=Pos	7	amod	_	_
7	hypothesis	hypothesis	NOUN	NN	Number=Sing	2	pobj	_	_
8	this	this	DET	DT	Number=Sing|PronType=Dem	9	det	_	_
9	hull	hull	NOUN	NN	Number=Sing	11	nsubjpass	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	formed	form	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	relcl	_	_
12	by	by	ADP	IN	_	11	agent	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	all	all	DET	DT	_	18	det	_	_
17	precontinuous	precontinuous	ADJ	JJ	Degree=Pos	18	amod	_	_
18	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	that	that	ADV	RB	_	21	advmod	_	_
21	is	is	ADV	RB	_	23	advmod	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	categories	category	NOUN	NNS	Number=Plur	0	ROOT	_	_
24	in	in	ADP	IN	_	28	prep	_	_
25	which	which	PRON	WDT	_	24	pobj	_	_
26	limits	limit	NOUN	NNS	Number=Plur	24	pobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	filtered	filter	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	relcl	_	_
29	colimits	colimits	PROPN	NNPS	Number=Plur	28	dobj	_	_
30	distribute	distribute	VERB	VB	VerbForm=Inf	28	oprd	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# sent_id = 3
# text = This concept is closely related to the continuous categories of Johnstone and Joyal.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	concept	concept	NOUN	NN	Number=Sing	5	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
4	closely	closely	ADV	RB	_	5	advmod	_	_
5	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	continuous	continuous	ADJ	JJ	Degree=Pos	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	Johnstone	Johnstone	PROPN	NNP	Number=Sing	10	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	Joyal	Joyal	PROPN	NNP	Number=Sing	11	conj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 165
# sent_id = 1
# text = The homotopy classification of graded categorical groups and their homomorphisms is applied, in this paper, to obtain appropriate treatments for diverse crossed product constructions with operators which appear in several algebraic contexts.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	homotopy	homotopy	NOUN	NN	Number=Sing	3	compound	_	_
3	classification	classification	NOUN	NN	Number=Sing	12	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	graded	grade	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
6	categorical	categorical	ADJ	JJ	Degree=Pos	7	amod	_	_
7	groups	group	NOUN	NNS	Number=Plur	4	pobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
9	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	10	poss	_	_
10	homomorphisms	homomorphism	NOUN	NNS	Number=Plur	3	conj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	applied	apply	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	in	in	ADP	IN	_	12	prep	_	_
15	this	this	DET	DT	Number=Sing|PronType=Dem	16	det	_	_
16	paper	paper	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
18	to	to	PART	TO	_	19	aux	_	_
19	obtain	obtain	VERB	VB	VerbForm=Inf	12	advcl	_	_
20	appropriate	appropriate	ADJ	JJ	Degree=Pos	21	amod	_	_
21	treatments	treatment	NOUN	NNS	Number=Plur	19	dobj	_	_
22	for	for	ADP	IN	_	21	prep	_	_
23	diverse	diverse	ADJ	JJ	Degree=Pos	26	amod	_	_
24	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
25	product	product	NOUN	NN	Number=Sing	26	compound	_	_
26	constructions	construction	NOUN	NNS	Number=Plur	22	pobj	_	_
27	with	with	ADP	IN	_	26	prep	_	_
28	operators	operator	NOUN	NNS	Number=Plur	27	pobj	_	_
29	which	which	PRON	WDT	_	30	nsubj	_	_
30	appear	appear	VERB	VBP	Tense=Pres|VerbForm=Fin	28	relcl	_	_
31	in	in	ADP	IN	_	30	prep	_	_
32	several	several	ADJ	JJ	Degree=Pos	34	amod	_	_
33	algebraic	algebraic	ADJ	JJ	Degree=Pos	34	amod	_	_
34	contexts	context	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 2
# text = Precise classification theorems are therefore stated for equivariant extensions by groups either of monoids, or groups, or rings, or rings - groups or algebras as well as for graded Clifford systems with operators, equivariant Azumaya algebras over Galois extensions of commutative rings and for strongly graded bialgebras and Hopf algebras with operators.
1	Precise	precise	ADJ	JJ	Degree=Pos	3	amod	_	_
2	classification	classification	NOUN	NN	Number=Sing	3	compound	_	_
3	theorems	theorem	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
5	therefore	therefore	ADV	RB	_	6	advmod	_	_
6	stated	state	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	40	ccomp	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	equivariant	equivariant	ADJ	JJ	Degree=Pos	9	amod	_	_
9	extensions	extension	NOUN	NNS	Number=Plur	7	pobj	_	_
10	by	by	ADP	IN	_	9	prep	_	_
11	groups	group	NOUN	NNS	Number=Plur	10	pobj	_	_
12	either	either	CCONJ	CC	ConjType=Cmp	13	preconj	_	_
13	of	of	ADP	IN	_	6	prep	_	_
14	monoids	monoid	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	or	or	CCONJ	CC	ConjType=Cmp	14	cc	_	_
17	groups	group	NOUN	NNS	Number=Plur	14	conj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	or	or	CCONJ	CC	ConjType=Cmp	17	cc	_	_
20	rings	ring	NOUN	NNS	Number=Plur	17	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	or	or	CCONJ	CC	ConjType=Cmp	20	cc	_	_
23	rings	ring	NOUN	NNS	Number=Plur	25	compound	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	groups	group	NOUN	NNS	Number=Plur	20	conj	_	_
26	or	or	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	algebras	algebra	NOUN	NNS	Number=Plur	25	conj	_	_
28	as	as	ADV	RB	_	30	advmod	_	_
29	well	well	ADV	RB	Degree=Pos	30	advmod	_	_
30	as	as	ADP	IN	_	13	cc	_	_
31	for	for	ADP	IN	_	13	conj	_	_
32	graded	grade	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	pcomp	_	_
33	Clifford	Clifford	PROPN	NNP	Number=Sing	34	compound	_	_
34	systems	system	NOUN	NNS	Number=Plur	32	dobj	_	_
35	with	with	ADP	IN	_	32	prep	_	_
36	operators	operator	NOUN	NNS	Number=Plur	35	pobj	_	SpaceAfter=No
37	,	,	PUNCT	,	PunctType=Comm	40	punct	_	_
38	equivariant	equivariant	ADJ	JJ	Degree=Pos	40	amod	_	_
39	Azumaya	Azumaya	PROPN	NNP	Number=Sing	40	compound	_	_
40	algebras	algebra	NOUN	NNS	Number=Plur	0	ROOT	_	_
41	over	over	ADP	IN	_	40	prep	_	_
42	Galois	Galois	PROPN	NNP	Number=Sing	43	compound	_	_
43	extensions	extension	NOUN	NNS	Number=Plur	41	pobj	_	_
44	of	of	ADP	IN	_	43	prep	_	_
45	commutative	commutative	ADJ	JJ	Degree=Pos	46	amod	_	_
46	rings	ring	NOUN	NNS	Number=Plur	44	pobj	_	_
47	and	and	CCONJ	CC	ConjType=Cmp	41	cc	_	_
48	for	for	ADP	IN	_	41	conj	_	_
49	strongly	strongly	ADV	RB	_	50	advmod	_	_
50	graded	grade	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	51	amod	_	_
51	bialgebras	bialgebra	NOUN	NNS	Number=Plur	48	pobj	_	_
52	and	and	CCONJ	CC	ConjType=Cmp	51	cc	_	_
53	Hopf	Hopf	PROPN	NNP	Number=Sing	54	compound	_	_
54	algebras	algebra	NOUN	NNS	Number=Plur	51	conj	_	_
55	with	with	ADP	IN	_	51	prep	_	_
56	operators	operator	NOUN	NNS	Number=Plur	55	pobj	_	SpaceAfter=No
57	.	.	PUNCT	.	PunctType=Peri	40	punct	_	SpaceAfter=No

# sent_id = 3
# text = These specialized classifications follow from the theory of graded categorical groups after identifying, in each case, adequate systems of factor sets with graded monoidal functors to suitable graded categorical groups associated to the structure dealt with.
1	These	these	DET	DT	Number=Plur|PronType=Dem	3	det	_	_
2	specialized	specialized	ADJ	JJ	Degree=Pos	3	amod	_	_
3	classifications	classification	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	follow	follow	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	from	from	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	theory	theory	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	graded	grade	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
10	categorical	categorical	ADJ	JJ	Degree=Pos	11	amod	_	_
11	groups	group	NOUN	NNS	Number=Plur	8	pobj	_	_
12	after	after	ADP	IN	_	4	prep	_	_
13	identifying	identify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	pcomp	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
15	in	in	ADP	IN	_	37	prep	_	_
16	each	each	DET	DT	_	17	det	_	_
17	case	case	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	37	punct	_	_
19	adequate	adequate	ADJ	JJ	Degree=Pos	20	amod	_	_
20	systems	system	NOUN	NNS	Number=Plur	37	nsubj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	factor	factor	NOUN	NN	Number=Sing	23	compound	_	_
23	sets	set	NOUN	NNS	Number=Plur	21	pobj	_	_
24	with	with	ADP	IN	_	23	prep	_	_
25	graded	grade	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	amod	_	_
26	monoidal	monoidal	ADJ	JJ	Degree=Pos	27	amod	_	_
27	functors	functor	NOUN	NNS	Number=Plur	24	pobj	_	_
28	to	to	ADP	IN	_	20	prep	_	_
29	suitable	suitable	ADJ	JJ	Degree=Pos	32	amod	_	_
30	graded	grade	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	amod	_	_
31	categorical	categorical	ADJ	JJ	Degree=Pos	32	amod	_	_
32	groups	group	NOUN	NNS	Number=Plur	28	pobj	_	_
33	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	acl	_	_
34	to	to	ADP	IN	_	33	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	structure	structure	NOUN	NN	Number=Sing	34	pobj	_	_
37	dealt	deal	VERB	VBD	Tense=Past|VerbForm=Fin	4	conj	_	_
38	with	with	ADP	IN	_	37	prep	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 166
# sent_id = 1
# text = We characterize pointed varieties of universal algebras in which $ (Atimes B)/A approx B $ , that is, all product projections are normal epimorphisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	pointed	point	VERB	VBD	Tense=Past|VerbForm=Fin	2	ccomp	_	_
4	varieties	variety	NOUN	NNS	Number=Plur	3	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	universal	universal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	algebras	algebra	NOUN	NNS	Number=Plur	5	pobj	_	_
8	in	in	ADP	IN	_	10	prep	_	_
9	which	which	PRON	WDT	_	8	pobj	_	_
10	$ (Atimes B)/A approx B $	$ (atimes b)/a approx b $	DET	WP$	Poss=Yes	2	dep	_	_
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	that	that	ADV	RB	_	13	advmod	_	_
13	is	is	ADV	RB	_	18	advmod	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
15	all	all	DET	DT	_	17	det	_	_
16	product	product	NOUN	NN	Number=Sing	17	compound	_	_
17	projections	projection	NOUN	NNS	Number=Plur	18	nsubj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
19	normal	normal	ADJ	JJ	Degree=Pos	20	amod	_	_
20	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	18	attr	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 167
# sent_id = 1
# text = A notion of resolution for higher - dimensional categories is defined, by using polygraphs, and basic invariance theorems are proved.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	notion	notion	NOUN	NN	Number=Sing	11	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	resolution	resolution	NOUN	NN	Number=Sing	3	pobj	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	higher	high	ADJ	JJR	Degree=Cmp	8	advmod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	dimensional	dimensional	ADJ	JJ	Degree=Pos	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	by	by	ADP	IN	_	11	prep	_	_
14	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	pcomp	_	_
15	polygraphs	polygraph	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
18	basic	basic	ADJ	JJ	Degree=Pos	20	amod	_	_
19	invariance	invariance	NOUN	NN	Number=Sing	20	compound	_	_
20	theorems	theorem	NOUN	NNS	Number=Plur	22	nsubjpass	_	_
21	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	22	auxpass	_	_
22	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	conj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# doc_id = 168
# sent_id = 1
# text = Extended cubical sets (with connections and interchanges) are presheaves on a ground category, the extended cubical site $ K $ , corresponding to the (augmented) simplicial site, the category of finite ordinals.
1	Extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	amod	_	_
2	cubical	cubical	ADJ	JJ	Degree=Pos	3	amod	_	_
3	sets	set	NOUN	NNS	Number=Plur	10	nsubj	_	_
4	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	3	punct	_	SpaceAfter=No
5	with	with	ADP	IN	_	3	prep	_	_
6	connections	connection	NOUN	NNS	Number=Plur	5	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	interchanges	interchange	NOUN	NNS	Number=Plur	6	conj	_	SpaceAfter=No
9	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	3	punct	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	presheaves	presheave	NOUN	NNS	Number=Plur	10	attr	_	_
12	on	on	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	ground	ground	NOUN	NN	Number=Sing	15	compound	_	_
15	category	category	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
18	extended	extended	ADJ	JJ	Degree=Pos	20	amod	_	_
19	cubical	cubical	ADJ	JJ	Degree=Pos	20	amod	_	_
20	site	site	NOUN	NN	Number=Sing	10	npadvmod	_	_
21	$ K $	$ k $	SYM	$	_	20	appos	_	_
22	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
23	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	amod	_	_
24	to	to	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
26	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	30	punct	_	SpaceAfter=No
27	augmented	augmented	ADJ	JJ	Degree=Pos	30	amod	_	SpaceAfter=No
28	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	30	punct	_	_
29	simplicial	simplicial	ADJ	JJ	Degree=Pos	30	amod	_	_
30	site	site	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
33	category	category	NOUN	NN	Number=Sing	30	appos	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	finite	finite	ADJ	JJ	Degree=Pos	36	compound	_	_
36	ordinals	ordinal	NOUN	NNS	Number=Plur	34	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = We prove here that $ K $ has characterisations similar to the classical ones for the simplicial analogue, by generators and relations, or by the existence of a universal symmetric cubical monoid; in fact, $ K $ is the classifying category of a monoidal algebraic theory of such monoids.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	38	ccomp	_	_
3	here	here	ADV	RB	PronType=Dem	2	advmod	_	_
4	that	that	SCONJ	IN	_	6	mark	_	_
5	$ K $	$ k $	SYM	$	_	6	nsubj	_	_
6	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
7	characterisations	characterisation	NOUN	NNS	Number=Plur	6	dobj	_	_
8	similar	similar	ADJ	JJ	Degree=Pos	7	amod	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	classical	classical	ADJ	JJ	Degree=Pos	12	amod	_	_
12	ones	one	NOUN	NNS	Number=Plur	9	pobj	_	_
13	for	for	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	simplicial	simplicial	ADJ	JJ	Degree=Pos	16	amod	_	_
16	analogue	analogue	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
18	by	by	ADP	IN	_	6	prep	_	_
19	generators	generator	NOUN	NNS	Number=Plur	18	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	relations	relation	NOUN	NNS	Number=Plur	19	conj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
23	or	or	CCONJ	CC	ConjType=Cmp	18	cc	_	_
24	by	by	ADP	IN	_	18	conj	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	existence	existence	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
29	universal	universal	ADJ	JJ	Degree=Pos	32	amod	_	_
30	symmetric	symmetric	ADJ	JJ	Degree=Pos	32	amod	_	_
31	cubical	cubical	ADJ	JJ	Degree=Pos	32	amod	_	_
32	monoid	monoid	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
33	;	;	PUNCT	:	_	38	punct	_	_
34	in	in	ADP	IN	_	38	prep	_	_
35	fact	fact	NOUN	NN	Number=Sing	34	pobj	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	38	punct	_	_
37	$ K $	$ k $	SYM	$	_	38	nsubj	_	_
38	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
40	classifying	classify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	41	amod	_	_
41	category	category	NOUN	NN	Number=Sing	38	attr	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	a	a	DET	DT	Definite=Ind|PronType=Art	46	det	_	_
44	monoidal	monoidal	ADJ	JJ	Degree=Pos	46	amod	_	_
45	algebraic	algebraic	ADJ	JJ	Degree=Pos	46	amod	_	_
46	theory	theory	NOUN	NN	Number=Sing	42	pobj	_	_
47	of	of	ADP	IN	_	46	prep	_	_
48	such	such	ADJ	JJ	Degree=Pos	49	amod	_	_
49	monoids	monoid	NOUN	NNS	Number=Plur	47	pobj	_	SpaceAfter=No
50	.	.	PUNCT	.	PunctType=Peri	38	punct	_	SpaceAfter=No

# sent_id = 3
# text = Analogous results are given for the restricted cubical site $ I $ , of ordinary cubical sets (just faces and degeneracies) and for the intermediate site $ J $ (including connections).
1	Analogous	analogous	ADJ	JJ	Degree=Pos	2	amod	_	_
2	results	result	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	for	for	ADP	IN	_	4	dative	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
7	restricted	restricted	ADJ	JJ	Degree=Pos	9	amod	_	_
8	cubical	cubical	ADJ	JJ	Degree=Pos	9	amod	_	_
9	site	site	NOUN	NN	Number=Sing	5	pobj	_	_
10	$ I $	$ i $	SYM	$	_	9	appos	_	_
11	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
12	of	of	ADP	IN	_	9	prep	_	_
13	ordinary	ordinary	ADJ	JJ	Degree=Pos	15	amod	_	_
14	cubical	cubical	ADJ	JJ	Degree=Pos	15	amod	_	_
15	sets	set	NOUN	NNS	Number=Plur	12	pobj	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	15	punct	_	SpaceAfter=No
17	just	just	ADV	RB	_	18	advmod	_	_
18	faces	face	NOUN	NNS	Number=Plur	15	appos	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	degeneracies	degeneracy	NOUN	NNS	Number=Plur	18	conj	_	SpaceAfter=No
21	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	15	punct	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
23	for	for	ADP	IN	_	4	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	intermediate	intermediate	ADJ	JJ	Degree=Pos	26	amod	_	_
26	site	site	NOUN	NN	Number=Sing	23	pobj	_	_
27	$ J $	$ j $	SYM	$	_	26	appos	_	_
28	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	26	punct	_	SpaceAfter=No
29	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	26	prep	_	_
30	connections	connection	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
31	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	4	punct	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = We also consider briefly the reversible analogue, $ clikK $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	briefly	briefly	ADV	RB	_	3	advmod	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	reversible	reversible	ADJ	JJ	Degree=Pos	7	amod	_	_
7	analogue	analogue	NOUN	NN	Number=Sing	3	dobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	$ clikK $	$ clikk $	SYM	$	_	7	appos	_	_
10	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 169
# sent_id = 1
# text = Protomodular categories were introduced by the first author more than ten years ago.
1	Protomodular	protomodular	ADJ	JJ	Degree=Pos	2	amod	_	_
2	categories	category	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	4	auxpass	_	_
4	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	by	by	ADP	IN	_	4	agent	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	first	first	ADJ	JJ	Degree=Pos	8	amod	_	_
8	author	author	NOUN	NN	Number=Sing	5	pobj	_	_
9	more	more	ADJ	JJR	Degree=Cmp	11	amod	_	_
10	than	than	ADP	IN	_	11	quantmod	_	_
11	ten	ten	NUM	CD	NumType=Card	12	nummod	_	_
12	years	year	NOUN	NNS	Number=Plur	13	npadvmod	_	_
13	ago	ago	ADV	RB	_	8	advmod	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that a variety $ mathcal V $ of universal algebras is protomodular if and only if it has 0 - ary terms $ e_1, ..., e_n $ , binary terms $ t_1, ..., t_n $ , and (n+1) - ary term $ t $ satisfying the identities $ t(x, t_1(x, y), ..., t_n(x, y)) = y $ and $ t_i(x, x) = e_i $ for each $ i = 1, ..., n $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	10	mark	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	variety	variety	NOUN	NN	Number=Sing	10	nsubj	_	_
6	$ mathcal V $	$ mathcal v $	SYM	$	_	5	prep	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	universal	universal	ADJ	JJ	Degree=Pos	9	amod	_	_
9	algebras	algebra	NOUN	NNS	Number=Plur	7	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
11	protomodular	protomodular	ADJ	JJ	Degree=Pos	10	acomp	_	_
12	if	if	SCONJ	IN	_	10	prep	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	only	only	ADV	RB	_	17	advmod	_	_
15	if	if	SCONJ	IN	_	17	mark	_	_
16	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	17	nsubj	_	_
17	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	advcl	_	_
18	0	0	NUM	CD	NumType=Card	20	nummod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	ary	ary	ADJ	JJ	Degree=Pos	21	amod	_	_
21	terms	term	NOUN	NNS	Number=Plur	17	dobj	_	_
22	$ e_1, ..., e_n $	$ e_1, ..., e_n $	SYM	$	_	25	nmod	_	_
23	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
24	binary	binary	ADJ	JJ	Degree=Pos	25	amod	_	_
25	terms	term	NOUN	NNS	Number=Plur	2	dobj	_	_
26	$ t_1, ..., t_n $	$ t_1, ..., t_n $	SYM	$	_	34	nmod	_	_
27	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
29	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	30	punct	_	SpaceAfter=No
30	n+1	n+1	X	XX	_	26	conj	_	SpaceAfter=No
31	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	26	punct	_	_
32	-	-	PUNCT	:	_	33	punct	_	_
33	ary	ary	PROPN	NNP	Number=Sing	34	compound	_	_
34	term	term	NOUN	NN	Number=Sing	25	appos	_	_
35	$ t $	$ t $	SYM	$	_	34	appos	_	_
36	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	34	acl	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	identities	identity	NOUN	NNS	Number=Plur	36	dobj	_	_
39	$ t(x, t_1(x, y), ..., t_n(x, y)) = y $	$ t(x, t_1(x, y), ..., t_n(x, y)) = y $	SYM	$	_	34	appos	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	34	cc	_	_
41	$ t_i(x, x) = e_i $	$ t_i(x, x) = e_i $	SYM	$	_	25	conj	_	_
42	for	for	ADP	IN	_	41	prep	_	_
43	each	each	DET	DT	_	44	det	_	_
44	$ i = 1, ..., n $	$ i = 1, ..., n $	SYM	$	_	42	pobj	_	_
45	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 170
# sent_id = 1
# text = One can associate to any strict globular $ omega $ - category three augmented simplicial nerves called the globular nerve, the branching and the merging semi - cubical nerves.
1	One	one	PRON	PRP	PronType=Prs	3	nsubj	_	_
2	can	can	AUX	MD	VerbForm=Fin	3	aux	_	_
3	associate	associate	VERB	VB	VerbForm=Inf	0	ROOT	_	_
4	to	to	ADP	IN	_	3	prep	_	_
5	any	any	DET	DT	_	14	det	_	_
6	strict	strict	ADJ	JJ	Degree=Pos	14	amod	_	_
7	globular	globular	ADJ	JJ	Degree=Pos	14	amod	_	_
8	$ omega $	$ omega $	SYM	$	_	10	nmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	category	category	NOUN	NN	Number=Sing	14	nmod	_	_
11	three	three	NUM	CD	NumType=Card	10	nummod	_	_
12	augmented	augmented	ADJ	JJ	Degree=Pos	14	amod	_	_
13	simplicial	simplicial	ADJ	JJ	Degree=Pos	14	amod	_	_
14	nerves	nerve	NOUN	NNS	Number=Plur	4	pobj	_	_
15	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	14	acl	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	globular	globular	ADJ	JJ	Degree=Pos	18	amod	_	_
18	nerve	nerve	NOUN	NN	Number=Sing	15	oprd	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	branching	branching	NOUN	NN	Number=Sing	18	conj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
24	merging	merge	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	28	amod	_	_
25	semi	semi	ADJ	JJ	Degree=Pos	28	amod	_	_
26	-	-	ADJ	JJ	Degree=Pos	28	amod	_	_
27	cubical	cubical	ADJ	JJ	Degree=Pos	28	amod	_	_
28	nerves	nerve	NOUN	NNS	Number=Plur	21	conj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = If this strict globular $ omega $ - category is freely generated by a precubical set, then the corresponding homology theories contain different informations about the geometry of the higher dimensional automaton modeled by the precubical set.
1	If	if	SCONJ	IN	_	10	mark	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
3	strict	strict	ADJ	JJ	Degree=Pos	7	amod	_	_
4	globular	globular	ADJ	JJ	Degree=Pos	7	amod	_	_
5	$ omega $	$ omega $	SYM	$	_	7	compound	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	category	category	NOUN	NN	Number=Sing	10	nsubjpass	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
9	freely	freely	ADV	RB	_	10	advmod	_	_
10	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	advcl	_	_
11	by	by	ADP	IN	_	10	agent	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	precubical	precubical	ADJ	JJ	Degree=Pos	14	amod	_	_
14	set	set	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
16	then	then	ADV	RB	PronType=Dem	21	advmod	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
18	corresponding	corresponding	ADJ	JJ	Degree=Pos	20	amod	_	_
19	homology	homology	NOUN	NN	Number=Sing	20	compound	_	_
20	theories	theory	NOUN	NNS	Number=Plur	21	nsubj	_	_
21	contain	contain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
22	different	different	ADJ	JJ	Degree=Pos	23	amod	_	_
23	informations	information	NOUN	NNS	Number=Plur	21	dobj	_	_
24	about	about	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	geometry	geometry	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
29	higher	high	ADJ	JJR	Degree=Cmp	31	amod	_	_
30	dimensional	dimensional	ADJ	JJ	Degree=Pos	31	amod	_	_
31	automaton	automaton	NOUN	NN	Number=Sing	27	pobj	_	_
32	modeled	model	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	acl	_	_
33	by	by	ADP	IN	_	32	agent	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
35	precubical	precubical	ADJ	JJ	Degree=Pos	36	compound	_	_
36	set	set	NOUN	NN	Number=Sing	33	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# sent_id = 3
# text = Adding inverses in this $ omega $ - category to any morphism of dimension greater than 2 and with respect to any composition laws of dimension greater than 1 does not change these homology theories.
1	Adding	add	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	30	csubj	_	_
2	inverses	inverse	NOUN	NNS	Number=Plur	1	dobj	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
5	$ omega $	$ omega $	SYM	$	_	7	compound	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	category	category	NOUN	NN	Number=Sing	3	pobj	_	_
8	to	to	ADP	IN	_	1	prep	_	_
9	any	any	DET	DT	_	10	det	_	_
10	morphism	morphism	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	dimension	dimension	NOUN	NN	Number=Sing	11	pobj	_	_
13	greater	great	ADJ	JJR	Degree=Cmp	10	amod	_	_
14	than	than	ADP	IN	_	13	prep	_	_
15	2	2	NUM	CD	NumType=Card	14	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
17	with	with	ADP	IN	_	30	prep	_	_
18	respect	respect	NOUN	NN	Number=Sing	17	pobj	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	any	any	DET	DT	_	22	det	_	_
21	composition	composition	NOUN	NN	Number=Sing	22	compound	_	_
22	laws	law	NOUN	NNS	Number=Plur	19	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	dimension	dimension	NOUN	NN	Number=Sing	23	pobj	_	_
25	greater	great	ADJ	JJR	Degree=Cmp	22	amod	_	_
26	than	than	ADP	IN	_	25	prep	_	_
27	1	1	NUM	CD	NumType=Card	26	pobj	_	_
28	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	aux	_	_
29	not	not	PART	RB	Polarity=Neg	30	neg	_	_
30	change	change	VERB	VB	VerbForm=Inf	0	ROOT	_	_
31	these	these	DET	DT	Number=Plur|PronType=Dem	33	det	_	_
32	homology	homology	NOUN	NN	Number=Sing	33	compound	_	_
33	theories	theory	NOUN	NNS	Number=Plur	30	dobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	30	punct	_	SpaceAfter=No

# sent_id = 4
# text = In such a framework, the globular nerve always satisfies the Kan condition.
1	In	in	ADP	IN	_	10	prep	_	_
2	such	such	DET	PDT	_	4	predet	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	framework	framework	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	globular	globular	ADJ	JJ	Degree=Pos	8	amod	_	_
8	nerve	nerve	NOUN	NN	Number=Sing	10	nsubj	_	_
9	always	always	ADV	RB	_	10	advmod	_	_
10	satisfies	satisfy	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	Kan	Kan	PROPN	NNP	Number=Sing	13	compound	_	_
13	condition	condition	NOUN	NN	Number=Sing	10	dobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 5
# text = On the other hand, both branching and merging nerves never satisfy it, except in some very particular and uninteresting situations.
1	On	on	ADP	IN	_	12	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	other	other	ADJ	JJ	Degree=Pos	4	amod	_	_
4	hand	hand	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
6	both	both	PRON	DT	_	7	nsubj	_	_
7	branching	branch	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	csubj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	merging	merge	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	conj	_	_
10	nerves	nerve	NOUN	NNS	Number=Plur	9	dobj	_	_
11	never	never	ADV	RB	_	12	neg	_	_
12	satisfy	satisfy	VERB	VB	VerbForm=Inf	0	ROOT	_	_
13	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	12	dobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
15	except	except	SCONJ	IN	_	12	prep	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	some	some	DET	DT	_	22	det	_	_
18	very	very	ADV	RB	_	19	advmod	_	_
19	particular	particular	ADJ	JJ	Degree=Pos	22	amod	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	uninteresting	uninteresting	NOUN	NN	Number=Sing	19	conj	_	_
22	situations	situation	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 6
# text = In this paper, we introduce two new nerves (the branching and merging semi - globular nerves) satisfying the Kan condition and having conjecturally the same simplicial homology as the branching and merging semi - cubical nerves respectively in such framework.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	two	two	NUM	CD	NumType=Card	9	nummod	_	_
8	new	new	ADJ	JJ	Degree=Pos	9	amod	_	_
9	nerves	nerve	NOUN	NNS	Number=Plur	6	dobj	_	_
10	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	9	punct	_	SpaceAfter=No
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	branching	branching	NOUN	NN	Number=Sing	9	appos	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	merging	merge	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	conj	_	_
15	semi	semi	ADJ	JJ	Degree=Pos	18	amod	_	_
16	-	-	ADJ	JJ	Degree=Pos	15	nmod	_	_
17	globular	globular	ADJ	JJ	Degree=Pos	18	amod	_	_
18	nerves	nerve	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
19	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	9	punct	_	_
20	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	advcl	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	Kan	Kan	PROPN	NNP	Number=Sing	23	compound	_	_
23	condition	condition	NOUN	NN	Number=Sing	20	dobj	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
25	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	conj	_	_
26	conjecturally	conjecturally	ADV	RB	_	25	advmod	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
28	same	same	ADJ	JJ	Degree=Pos	30	amod	_	_
29	simplicial	simplicial	ADJ	JJ	Degree=Pos	30	amod	_	_
30	homology	homology	NOUN	NN	Number=Sing	25	dobj	_	_
31	as	as	ADP	IN	_	25	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
33	branching	branching	NOUN	NN	Number=Sing	31	pobj	_	_
34	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
35	merging	merge	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	25	conj	_	_
36	semi	semi	ADJ	JJ	Degree=Pos	39	amod	_	_
37	-	-	ADJ	JJ	Degree=Pos	39	amod	_	_
38	cubical	cubical	ADJ	JJ	Degree=Pos	39	amod	_	_
39	nerves	nerve	NOUN	NNS	Number=Plur	35	dobj	_	_
40	respectively	respectively	ADV	RB	_	35	advmod	_	_
41	in	in	ADP	IN	_	35	prep	_	_
42	such	such	ADJ	JJ	Degree=Pos	43	amod	_	_
43	framework	framework	NOUN	NN	Number=Sing	41	pobj	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 7
# text = The latter conjecture is related to the thin elements conjecture already introduced in our previous papers.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	latter	latter	ADJ	JJ	Degree=Pos	3	amod	_	_
3	conjecture	conjecture	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	thin	thin	ADJ	JJ	Degree=Pos	9	amod	_	_
9	elements	element	NOUN	NNS	Number=Plur	10	compound	_	_
10	conjecture	conjecture	NOUN	NN	Number=Sing	6	pobj	_	_
11	already	already	ADV	RB	_	12	advmod	_	_
12	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acl	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	16	poss	_	_
15	previous	previous	ADJ	JJ	Degree=Pos	16	amod	_	_
16	papers	paper	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 171
# sent_id = 1
# text = We show how the formal Wirthmuller isomorphism theorem simplifies the proof of the Wirthmuller isomorphism in equivariant stable homotopy theory.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	how	how	SCONJ	WRB	_	8	advmod	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	formal	formal	ADJ	JJ	Degree=Pos	7	amod	_	_
6	Wirthmuller	Wirthmuller	PROPN	NNP	Number=Sing	7	compound	_	_
7	isomorphism	isomorphism	NOUN	NN	Number=Sing	8	nsubj	_	_
8	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	2	ccomp	_	_
9	simplifies	simplifie	NOUN	NNS	Number=Plur	8	dobj	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	proof	proof	NOUN	NN	Number=Sing	9	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	Wirthmuller	Wirthmuller	PROPN	NNP	Number=Sing	15	compound	_	_
15	isomorphism	isomorphism	NOUN	NN	Number=Sing	12	pobj	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	equivariant	equivariant	ADJ	JJ	Degree=Pos	20	amod	_	_
18	stable	stable	ADJ	JJ	Degree=Pos	19	amod	_	_
19	homotopy	homotopy	NOUN	NN	Number=Sing	20	compound	_	_
20	theory	theory	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Other examples from equivariant stable homotopy theory show that the hypotheses of the formal Wirthmuller and formal Grothendieck isomorphism theorems cannot be weakened.
1	Other	other	ADJ	JJ	Degree=Pos	2	amod	_	_
2	examples	example	NOUN	NNS	Number=Plur	8	nsubj	_	_
3	from	from	ADP	IN	_	2	prep	_	_
4	equivariant	equivariant	ADJ	JJ	Degree=Pos	7	amod	_	_
5	stable	stable	ADJ	JJ	Degree=Pos	6	amod	_	_
6	homotopy	homotopy	NOUN	NN	Number=Sing	7	compound	_	_
7	theory	theory	NOUN	NN	Number=Sing	3	pobj	_	_
8	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	that	that	SCONJ	IN	_	24	mark	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	hypotheses	hypothesis	NOUN	NNS	Number=Plur	24	nsubjpass	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	formal	formal	ADJ	JJ	Degree=Pos	15	amod	_	_
15	Wirthmuller	wirthmuller	NOUN	NN	Number=Sing	12	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	formal	formal	ADJ	JJ	Degree=Pos	18	amod	_	_
18	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	20	compound	_	_
19	isomorphism	isomorphism	NOUN	NN	Number=Sing	20	compound	_	_
20	theorems	theorem	NOUN	NNS	Number=Plur	15	conj	_	_
21	can	can	AUX	MD	VerbForm=Fin	24	aux	_	SpaceAfter=No
22	not	not	PART	RB	Polarity=Neg	24	neg	_	_
23	be	be	AUX	VB	VerbForm=Inf	24	auxpass	_	_
24	weakened	weaken	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	ccomp	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 172
# sent_id = 1
# text = There are many contexts in algebraic geometry, algebraic topology, and homological algebra where one encounters a functor that has both a left and right adjoint, with the right adjoint being isomorphic to a shift of the left adjoint specified by an appropriate `dualizing object'.
1	There	there	PRON	EX	_	2	expl	_	_
2	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	many	many	ADJ	JJ	Degree=Pos	4	amod	_	_
4	contexts	context	NOUN	NNS	Number=Plur	2	attr	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	algebraic	algebraic	ADJ	JJ	Degree=Pos	7	amod	_	_
7	geometry	geometry	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
9	algebraic	algebraic	ADJ	JJ	Degree=Pos	10	amod	_	_
10	topology	topology	NOUN	NN	Number=Sing	4	conj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
13	homological	homological	ADJ	JJ	Degree=Pos	14	amod	_	_
14	algebra	algebra	NOUN	NN	Number=Sing	10	conj	_	_
15	where	where	SCONJ	WRB	_	17	advmod	_	_
16	one	one	PRON	PRP	PronType=Prs	17	nsubj	_	_
17	encounters	encounter	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	functor	functor	NOUN	NN	Number=Sing	17	dobj	_	_
20	that	that	PRON	WDT	PronType=Rel	21	nsubj	_	_
21	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	relcl	_	_
22	both	both	CCONJ	CC	ConjType=Cmp	27	preconj	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
24	left	left	ADJ	JJ	Degree=Pos	27	amod	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	right	right	ADJ	JJ	Degree=Pos	24	conj	_	_
27	adjoint	adjoint	NOUN	NN	Number=Sing	21	dobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
29	with	with	ADP	IN	_	21	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	right	right	ADJ	JJ	Degree=Pos	32	amod	_	_
32	adjoint	adjoint	NOUN	NN	Number=Sing	33	nsubj	_	_
33	being	be	AUX	VBG	VerbForm=Ger	29	pcomp	_	_
34	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	33	acomp	_	_
35	to	to	ADP	IN	_	34	prep	_	_
36	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
37	shift	shift	NOUN	NN	Number=Sing	35	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
40	left	left	ADJ	JJ	Degree=Pos	41	amod	_	_
41	adjoint	adjoint	NOUN	NN	Number=Sing	38	pobj	_	_
42	specified	specify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	41	acl	_	_
43	by	by	ADP	IN	_	42	agent	_	_
44	an	an	DET	DT	Definite=Ind|PronType=Art	48	det	_	_
45	appropriate	appropriate	ADJ	JJ	Degree=Pos	48	amod	_	_
46	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	48	punct	_	SpaceAfter=No
47	dualizing	dualize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	48	amod	_	_
48	object	object	NOUN	NN	Number=Sing	43	pobj	_	SpaceAfter=No
49	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	2	punct	_	SpaceAfter=No
50	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Typically the left adjoint is well understood while the right adjoint is more mysterious, and the result identifies the right adjoint in familiar terms.
1	Typically	typically	ADV	RB	_	7	advmod	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	left	left	ADJ	JJ	Degree=Pos	4	amod	_	_
4	adjoint	adjoint	NOUN	NN	Number=Sing	7	nsubjpass	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
6	well	well	ADV	RB	Degree=Pos	7	advmod	_	_
7	understood	understand	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	while	while	SCONJ	IN	_	12	mark	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	right	right	ADJ	JJ	Degree=Pos	11	amod	_	_
11	adjoint	adjoint	NOUN	NN	Number=Sing	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	advcl	_	_
13	more	more	ADV	RBR	Degree=Cmp	14	advmod	_	_
14	mysterious	mysterious	ADJ	JJ	Degree=Pos	12	acomp	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	result	result	NOUN	NN	Number=Sing	19	nsubj	_	_
19	identifies	identify	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	conj	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	right	right	ADJ	JJ	Degree=Pos	22	amod	_	_
22	adjoint	adjoint	NOUN	NN	Number=Sing	19	dobj	_	_
23	in	in	ADP	IN	_	22	prep	_	_
24	familiar	familiar	ADJ	JJ	Degree=Pos	25	amod	_	_
25	terms	term	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 3
# text = We give a categorical discussion of such results.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	categorical	categorical	ADJ	JJ	Degree=Pos	5	amod	_	_
5	discussion	discussion	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	such	such	ADJ	JJ	Degree=Pos	8	amod	_	_
8	results	result	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = One essential point is to differentiate between the classical framework that arises in algebraic geometry and a deceptively similar, but genuinely different, framework that arises in algebraic topology.
1	One	one	NUM	CD	NumType=Card	3	nummod	_	_
2	essential	essential	ADJ	JJ	Degree=Pos	3	amod	_	_
3	point	point	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	differentiate	differentiate	VERB	VB	VerbForm=Inf	4	xcomp	_	_
7	between	between	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	classical	classical	ADJ	JJ	Degree=Pos	10	amod	_	_
10	framework	framework	NOUN	NN	Number=Sing	7	pobj	_	_
11	that	that	PRON	WDT	PronType=Rel	12	nsubj	_	_
12	arises	arise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	relcl	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	algebraic	algebraic	ADJ	JJ	Degree=Pos	15	amod	_	_
15	geometry	geometry	NOUN	NN	Number=Sing	13	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
18	deceptively	deceptively	ADV	RB	_	19	advmod	_	_
19	similar	similar	ADJ	JJ	Degree=Pos	25	amod	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	but	but	CCONJ	CC	ConjType=Cmp	19	cc	_	_
22	genuinely	genuinely	ADV	RB	_	23	advmod	_	_
23	different	different	ADJ	JJ	Degree=Pos	19	conj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
25	framework	framework	NOUN	NN	Number=Sing	15	conj	_	_
26	that	that	PRON	WDT	PronType=Rel	27	nsubj	_	_
27	arises	arise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	relcl	_	_
28	in	in	ADP	IN	_	27	prep	_	_
29	algebraic	algebraic	ADJ	JJ	Degree=Pos	30	amod	_	_
30	topology	topology	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = Another is to make clear which parts of the proofs of such results are formal.
1	Another	another	PRON	DT	_	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	to	to	PART	TO	_	4	aux	_	_
4	make	make	VERB	VB	VerbForm=Inf	2	xcomp	_	_
5	clear	clear	ADJ	JJ	Degree=Pos	4	ccomp	_	_
6	which	which	DET	WDT	_	7	det	_	_
7	parts	part	NOUN	NNS	Number=Plur	14	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	proofs	proof	NOUN	NNS	Number=Plur	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	such	such	ADJ	JJ	Degree=Pos	13	amod	_	_
13	results	result	NOUN	NNS	Number=Plur	11	pobj	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
15	formal	formal	ADJ	JJ	Degree=Pos	14	acomp	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = The analysis significantly simplifies the proofs of particular cases, as we illustrate in a sequel discussing applications to equivariant stable homotopy theory.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	analysis	analysis	NOUN	NN	Number=Sing	4	nsubj	_	_
3	significantly	significantly	ADV	RB	_	4	advmod	_	_
4	simplifies	simplify	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	proofs	proof	NOUN	NNS	Number=Plur	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	particular	particular	ADJ	JJ	Degree=Pos	9	amod	_	_
9	cases	case	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
11	as	as	SCONJ	IN	_	13	mark	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	illustrate	illustrate	VERB	VBP	Tense=Pres|VerbForm=Fin	4	advcl	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	sequel	sequel	NOUN	NN	Number=Sing	14	pobj	_	_
17	discussing	discuss	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	acl	_	_
18	applications	application	NOUN	NNS	Number=Plur	17	dobj	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	equivariant	equivariant	ADJ	JJ	Degree=Pos	23	amod	_	_
21	stable	stable	ADJ	JJ	Degree=Pos	22	amod	_	_
22	homotopy	homotopy	NOUN	NN	Number=Sing	23	compound	_	_
23	theory	theory	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 173
# sent_id = 1
# text = Linear bicategories are a generalization of ordinary bicategories in which there are two horizontal (1 - cell) compositions corresponding to the ``tensor'' and ``par'' of linear logic.
1	Linear	Linear	PROPN	NNP	Number=Sing	2	compound	_	_
2	bicategories	bicategorie	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	generalization	generalization	NOUN	NN	Number=Sing	3	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	ordinary	ordinary	ADJ	JJ	Degree=Pos	8	amod	_	_
8	bicategories	bicategorie	NOUN	NNS	Number=Plur	6	pobj	_	_
9	in	in	ADP	IN	_	12	prep	_	_
10	which	which	PRON	WDT	_	9	pobj	_	_
11	there	there	PRON	EX	_	12	expl	_	_
12	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	relcl	_	_
13	two	two	NUM	CD	NumType=Card	20	nummod	_	_
14	horizontal	horizontal	ADJ	JJ	Degree=Pos	18	amod	_	_
15	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	18	punct	_	SpaceAfter=No
16	1	1	NUM	CD	NumType=Card	18	nummod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	cell	cell	NOUN	NN	Number=Sing	20	nmod	_	SpaceAfter=No
19	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	20	punct	_	_
20	compositions	composition	NOUN	NNS	Number=Plur	12	attr	_	_
21	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	amod	_	_
22	to	to	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
24	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	SpaceAfter=No
25	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	SpaceAfter=No
26	tensor	tensor	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
27	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	26	punct	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
29	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	31	punct	_	SpaceAfter=No
30	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	31	punct	_	SpaceAfter=No
31	par	par	NOUN	NN	Number=Sing	26	conj	_	SpaceAfter=No
32	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	31	punct	_	_
33	of	of	ADP	IN	_	31	prep	_	_
34	linear	linear	ADJ	JJ	Degree=Pos	35	amod	_	_
35	logic	logic	NOUN	NN	Number=Sing	33	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = Benabou's notion of a morphism (lax 2 - functor) of bicategories may be generalized to linear bicategories, where they are called linear functors.
1	Benabou	Benabou	PROPN	NNP	Number=Sing	3	poss	_	SpaceAfter=No
2	's	's	PART	POS	_	1	case	_	_
3	notion	notion	NOUN	NN	Number=Sing	17	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	morphism	morphism	NOUN	NN	Number=Sing	4	pobj	_	_
7	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	17	punct	_	SpaceAfter=No
8	lax	lax	PROPN	NNP	Number=Sing	17	nsubjpass	_	_
9	2	2	NUM	CD	NumType=Card	11	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	functor	functor	NOUN	NN	Number=Sing	8	npadvmod	_	SpaceAfter=No
12	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	8	punct	_	_
13	of	of	ADP	IN	_	8	prep	_	_
14	bicategories	bicategorie	NOUN	NNS	Number=Plur	13	pobj	_	_
15	may	may	AUX	MD	VerbForm=Fin	17	aux	_	_
16	be	be	AUX	VB	VerbForm=Inf	17	auxpass	_	_
17	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	linear	linear	ADJ	JJ	Degree=Pos	20	amod	_	_
20	bicategories	bicategorie	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	where	where	SCONJ	WRB	_	25	advmod	_	_
23	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	25	nsubjpass	_	_
24	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	25	auxpass	_	_
25	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	relcl	_	_
26	linear	linear	PROPN	NNP	Number=Sing	27	compound	_	_
27	functors	functor	NOUN	NNS	Number=Plur	25	oprd	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 3
# text = Unfortunately, as for the bicategorical case, it is not obvious how to organize linear functors smoothly into a higher dimensional structure.
1	Unfortunately	unfortunately	ADV	RB	_	10	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
3	as	as	ADP	IN	_	10	prep	_	_
4	for	for	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	bicategorical	bicategorical	ADJ	JJ	Degree=Pos	7	amod	_	_
7	case	case	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
9	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	10	nsubj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	not	not	PART	RB	Polarity=Neg	10	neg	_	_
12	obvious	obvious	ADJ	JJ	Degree=Pos	10	acomp	_	_
13	how	how	SCONJ	WRB	_	15	advmod	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	organize	organize	VERB	VB	VerbForm=Inf	10	xcomp	_	_
16	linear	linear	ADJ	JJ	Degree=Pos	17	amod	_	_
17	functors	functor	NOUN	NNS	Number=Plur	15	dobj	_	_
18	smoothly	smoothly	ADV	RB	_	15	advmod	_	_
19	into	into	ADP	IN	_	15	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
21	higher	high	ADJ	JJR	Degree=Cmp	22	advmod	_	_
22	dimensional	dimensional	ADJ	JJ	Degree=Pos	23	amod	_	_
23	structure	structure	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 4
# text = Not only do linear functors seem to lack the two compositions expected for a linear bicategory but, even worse, they inherit from the bicategorical level the failure to combine well with the obvious notion of transformation.
1	Not	not	PART	RB	Polarity=Neg	6	preconj	_	_
2	only	only	ADV	RB	_	1	advmod	_	_
3	do	do	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	aux	_	_
4	linear	linear	ADJ	JJ	Degree=Pos	5	compound	_	_
5	functors	functor	NOUN	NNS	Number=Plur	6	nsubj	_	_
6	seem	seem	VERB	VBP	Tense=Pres|VerbForm=Fin	23	ccomp	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	lack	lack	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	two	two	NUM	CD	NumType=Card	11	nummod	_	_
11	compositions	composition	NOUN	NNS	Number=Plur	8	dobj	_	_
12	expected	expect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acl	_	_
13	for	for	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	linear	linear	ADJ	JJ	Degree=Pos	16	amod	_	_
16	bicategory	bicategory	NOUN	NN	Number=Sing	13	pobj	_	_
17	but	but	CCONJ	CC	ConjType=Cmp	6	cc	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
19	even	even	ADV	RB	_	20	advmod	_	_
20	worse	bad	ADJ	JJR	Degree=Cmp	6	advmod	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
22	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	23	nsubj	_	_
23	inherit	inherit	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
24	from	from	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	bicategorical	bicategorical	ADJ	JJ	Degree=Pos	27	amod	_	_
27	level	level	NOUN	NN	Number=Sing	24	pobj	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	failure	failure	NOUN	NN	Number=Sing	23	dobj	_	_
30	to	to	PART	TO	_	31	aux	_	_
31	combine	combine	VERB	VB	VerbForm=Inf	29	acl	_	_
32	well	well	ADV	RB	Degree=Pos	31	advmod	_	_
33	with	with	ADP	IN	_	31	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
35	obvious	obvious	ADJ	JJ	Degree=Pos	36	amod	_	_
36	notion	notion	NOUN	NN	Number=Sing	33	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	transformation	transformation	NOUN	NN	Number=Sing	37	pobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# sent_id = 5
# text = As we shall see, there are also problems with lifting the notion of lax transformation to the linear setting.
1	As	as	SCONJ	IN	_	4	mark	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
3	shall	shall	AUX	MD	VerbType=Mod	4	aux	_	_
4	see	see	VERB	VB	VerbForm=Inf	7	advcl	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	there	there	PRON	EX	_	7	expl	_	_
7	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	also	also	ADV	RB	_	7	advmod	_	_
9	problems	problem	NOUN	NNS	Number=Plur	7	attr	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	lifting	lift	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	pcomp	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	notion	notion	NOUN	NN	Number=Sing	11	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	lax	lax	ADJ	JJ	Degree=Pos	16	amod	_	_
16	transformation	transformation	NOUN	NN	Number=Sing	14	pobj	_	_
17	to	to	ADP	IN	_	13	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	linear	linear	ADJ	JJ	Degree=Pos	20	compound	_	_
20	setting	setting	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 6
# text = One possible resolution is to step up one dimension, taking morphisms as the 0 - cell level.
1	One	one	NUM	CD	NumType=Card	3	nummod	_	_
2	possible	possible	ADJ	JJ	Degree=Pos	3	amod	_	_
3	resolution	resolution	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	step	step	VERB	VB	VerbForm=Inf	4	xcomp	_	_
7	up	up	ADP	RP	_	6	prt	_	_
8	one	one	NUM	CD	NumType=Card	9	nummod	_	_
9	dimension	dimension	NOUN	NN	Number=Sing	6	dobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
11	taking	take	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	advcl	_	_
12	morphisms	morphism	NOUN	NNS	Number=Plur	11	dobj	_	_
13	as	as	ADP	IN	_	11	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
15	0	0	NUM	CD	NumType=Card	17	nummod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	cell	cell	NOUN	NN	Number=Sing	18	compound	_	_
18	level	level	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 7
# text = In the linear setting, this suggests making linear functors 0 - cells, but what structure should sit above them?
1	In	in	ADP	IN	_	7	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	linear	linear	ADJ	JJ	Degree=Pos	4	compound	_	_
4	setting	setting	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	this	this	PRON	DT	Number=Sing|PronType=Dem	7	nsubj	_	_
7	suggests	suggest	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	making	make	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	xcomp	_	_
9	linear	linear	ADJ	JJ	Degree=Pos	10	compound	_	_
10	functors	functor	NOUN	NNS	Number=Plur	13	nsubj	_	_
11	0	0	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	cells	cell	NOUN	NNS	Number=Plur	8	dobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
15	but	but	CCONJ	CC	ConjType=Cmp	7	cc	_	_
16	what	what	DET	WDT	_	17	det	_	_
17	structure	structure	NOUN	NN	Number=Sing	19	nsubj	_	_
18	should	should	AUX	MD	VerbForm=Fin	19	aux	_	_
19	sit	sit	VERB	VB	VerbForm=Inf	7	conj	_	_
20	above	above	ADP	IN	_	19	prep	_	_
21	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	20	pobj	_	SpaceAfter=No
22	?	?	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 8
# text = Lax transformations in a suitable sense just do not seem to work very well for this purpose.
1	Lax	lax	NOUN	NN	Number=Sing	2	compound	_	_
2	transformations	transformation	NOUN	NNS	Number=Plur	10	nsubj	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	suitable	suitable	ADJ	JJ	Degree=Pos	6	amod	_	_
6	sense	sense	NOUN	NN	Number=Sing	3	pobj	_	_
7	just	just	ADV	RB	_	10	advmod	_	_
8	do	do	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	10	aux	_	_
9	not	not	PART	RB	Polarity=Neg	10	neg	_	_
10	seem	seem	VERB	VB	VerbForm=Inf	0	ROOT	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	work	work	VERB	VB	VerbForm=Inf	10	xcomp	_	_
13	very	very	ADV	RB	_	14	advmod	_	_
14	well	well	ADV	RB	Degree=Pos	12	advmod	_	_
15	for	for	ADP	IN	_	12	prep	_	_
16	this	this	DET	DT	Number=Sing|PronType=Dem	17	det	_	_
17	purpose	purpose	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 9
# text = Modules provide a more promising direction, but raise a number of technical issues concerning the composability of both the modules and their transformations.
1	Modules	module	NOUN	NNS	Number=Plur	2	nsubj	_	_
2	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
4	more	more	ADV	RBR	Degree=Cmp	5	advmod	_	_
5	promising	promising	ADJ	JJ	Degree=Pos	6	amod	_	_
6	direction	direction	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
8	but	but	CCONJ	CC	ConjType=Cmp	2	cc	_	_
9	raise	raise	VERB	VB	VerbForm=Inf	2	conj	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	number	number	NOUN	NN	Number=Sing	9	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	technical	technical	ADJ	JJ	Degree=Pos	14	amod	_	_
14	issues	issue	NOUN	NNS	Number=Plur	12	pobj	_	_
15	concerning	concern	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	composability	composability	NOUN	NN	Number=Sing	15	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	both	both	CCONJ	CC	ConjType=Cmp	21	preconj	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	modules	module	NOUN	NNS	Number=Plur	18	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	24	poss	_	_
24	transformations	transformation	NOUN	NNS	Number=Plur	21	conj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 10
# text = In general the required composites will not exist in either the linear bicategorical or ordinary bicategorical setting.
1	In	in	ADP	IN	_	8	prep	_	_
2	general	general	ADJ	JJ	Degree=Pos	1	amod	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	required	require	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	amod	_	_
5	composites	composite	NOUN	NNS	Number=Plur	8	nsubj	_	_
6	will	will	AUX	MD	VerbForm=Fin	8	aux	_	_
7	not	not	PART	RB	Polarity=Neg	8	neg	_	_
8	exist	exist	VERB	VB	VerbForm=Inf	0	ROOT	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	either	either	CCONJ	CC	ConjType=Cmp	17	preconj	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
12	linear	linear	ADJ	JJ	Degree=Pos	17	amod	_	_
13	bicategorical	bicategorical	ADJ	JJ	Degree=Pos	17	amod	_	_
14	or	or	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	ordinary	ordinary	ADJ	JJ	Degree=Pos	13	conj	_	_
16	bicategorical	bicategorical	ADJ	JJ	Degree=Pos	17	amod	_	_
17	setting	setting	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 11
# text = However, when these composites do exist modules between linear functors do combine to form a linear bicategory.
1	However	however	ADV	RB	_	13	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
3	when	when	SCONJ	WRB	_	7	advmod	_	_
4	these	these	DET	DT	Number=Plur|PronType=Dem	5	det	_	_
5	composites	composite	NOUN	NNS	Number=Plur	7	nsubj	_	_
6	do	do	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	aux	_	_
7	exist	exist	VERB	VB	VerbForm=Inf	13	advcl	_	_
8	modules	module	NOUN	NNS	Number=Plur	7	dobj	_	_
9	between	between	ADP	IN	_	8	prep	_	_
10	linear	linear	ADJ	JJ	Degree=Pos	11	amod	_	_
11	functors	functor	NOUN	NNS	Number=Plur	9	pobj	_	_
12	do	do	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	aux	_	_
13	combine	combine	VERB	VB	VerbForm=Inf	0	ROOT	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	form	form	VERB	VB	VerbForm=Inf	13	advcl	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	linear	linear	ADJ	JJ	Degree=Pos	18	amod	_	_
18	bicategory	bicategory	NOUN	NN	Number=Sing	15	dobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 12
# text = In order to better understand the conditions for the existence of composites, we have found it convenient, particularly in the linear setting, to develop the theory of ``poly - bicategories''.
1	In	in	ADP	IN	_	16	prep	_	_
2	order	order	NOUN	NN	Number=Sing	1	pobj	_	_
3	to	to	PART	TO	_	5	aux	_	_
4	better	well	ADV	RBR	Degree=Cmp	5	advmod	_	_
5	understand	understand	VERB	VB	VerbForm=Inf	2	acl	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	conditions	condition	NOUN	NNS	Number=Plur	5	dobj	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	existence	existence	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	composites	composite	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
14	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	16	nsubj	_	_
15	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	16	aux	_	_
16	found	find	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
17	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	18	nsubj	_	_
18	convenient	convenient	ADJ	JJ	Degree=Pos	16	ccomp	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
20	particularly	particularly	ADV	RB	_	21	advmod	_	_
21	in	in	ADP	IN	_	16	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	linear	linear	ADJ	JJ	Degree=Pos	24	compound	_	_
24	setting	setting	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
26	to	to	PART	TO	_	27	aux	_	_
27	develop	develop	VERB	VB	VerbForm=Inf	16	advcl	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	theory	theory	NOUN	NN	Number=Sing	27	dobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	35	punct	_	SpaceAfter=No
32	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	35	punct	_	SpaceAfter=No
33	poly	poly	ADJ	JJ	Degree=Pos	35	amod	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	bicategories	bicategorie	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
36	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	16	punct	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 13
# text = In this setting we can develop the theory so as to extract the answers to these problems not only for linear bicategories but also for ordinary bicategories.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	setting	setting	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
5	can	can	AUX	MD	VerbForm=Fin	6	aux	_	_
6	develop	develop	VERB	VB	VerbForm=Inf	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	theory	theory	NOUN	NN	Number=Sing	6	dobj	_	_
9	so	so	SCONJ	IN	_	12	mark	_	_
10	as	as	SCONJ	IN	_	12	mark	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	extract	extract	VERB	VB	VerbForm=Inf	6	advcl	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	answers	answer	NOUN	NNS	Number=Plur	12	dobj	_	_
15	to	to	ADP	IN	_	12	prep	_	_
16	these	these	DET	DT	Number=Plur|PronType=Dem	17	det	_	_
17	problems	problem	NOUN	NNS	Number=Plur	15	pobj	_	_
18	not	not	PART	RB	Polarity=Neg	20	preconj	_	_
19	only	only	ADV	RB	_	18	advmod	_	_
20	for	for	ADP	IN	_	12	prep	_	_
21	linear	linear	ADJ	JJ	Degree=Pos	22	amod	_	_
22	bicategories	bicategorie	NOUN	NNS	Number=Plur	20	pobj	_	_
23	but	but	CCONJ	CC	ConjType=Cmp	20	cc	_	_
24	also	also	ADV	RB	_	23	advmod	_	_
25	for	for	ADP	IN	_	20	conj	_	_
26	ordinary	ordinary	ADJ	JJ	Degree=Pos	27	amod	_	_
27	bicategories	bicategorie	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 14
# text = Poly - bicategories are 2 - dimensional generalizations of Szabo's poly - categories, consisting of objects, 1 - cells, and poly - 2 - cells.
1	Poly	poly	ADJ	JJ	Degree=Pos	3	amod	_	_
2	-	-	PUNCT	HYPH	PunctType=Dash	3	punct	_	_
3	bicategories	bicategorie	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	2	2	NUM	CD	NumType=Card	7	advmod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	dimensional	dimensional	ADJ	JJ	Degree=Pos	8	amod	_	_
8	generalizations	generalization	NOUN	NNS	Number=Plur	4	attr	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Szabo	Szabo	PROPN	NNP	Number=Sing	14	poss	_	SpaceAfter=No
11	's	's	PART	POS	_	10	case	_	_
12	poly	poly	ADJ	JJ	Degree=Pos	14	amod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
16	consisting	consist	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	acl	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	objects	object	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
20	1	1	NUM	CD	NumType=Card	22	nummod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	cells	cell	NOUN	NNS	Number=Plur	8	conj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
25	poly	poly	ADJ	JJ	Degree=Pos	29	amod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
27	2	2	NUM	CD	NumType=Card	29	nummod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	cells	cell	NOUN	NNS	Number=Plur	22	conj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 15
# text = The latter may have several 1 - cells as input and as output and can be composed by means of cutting along a single 1 - cell.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	latter	latter	ADJ	JJ	Degree=Pos	4	nsubj	_	_
3	may	may	AUX	MD	VerbForm=Fin	4	aux	_	_
4	have	have	VERB	VB	VerbForm=Inf	0	ROOT	_	_
5	several	several	ADJ	JJ	Degree=Pos	8	amod	_	_
6	1	1	NUM	CD	NumType=Card	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	cells	cell	NOUN	NNS	Number=Plur	4	dobj	_	_
9	as	as	ADP	IN	_	4	prep	_	_
10	input	input	NOUN	NN	Number=Sing	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
12	as	as	ADP	IN	_	9	conj	_	_
13	output	output	NOUN	NN	Number=Sing	12	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
15	can	can	AUX	MD	VerbForm=Fin	17	aux	_	_
16	be	be	AUX	VB	VerbForm=Inf	17	auxpass	_	_
17	composed	compose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	conj	_	_
18	by	by	ADP	IN	_	17	agent	_	_
19	means	mean	NOUN	NNS	Number=Plur	18	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	cutting	cut	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	pcomp	_	_
22	along	along	ADP	RP	_	21	prt	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
24	single	single	ADJ	JJ	Degree=Pos	27	amod	_	_
25	1	1	NUM	CD	NumType=Card	27	nummod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	cell	cell	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 16
# text = While a poly - bicategory does not require that there be any compositions for the 1 - cells, such composites are determined (up to 1 - cell isomorphism) by their universal properties.
1	While	while	SCONJ	IN	_	8	mark	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
3	poly	poly	ADJ	JJ	Degree=Pos	5	amod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	bicategory	bicategory	NOUN	NN	Number=Sing	8	nsubj	_	_
6	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	aux	_	_
7	not	not	PART	RB	Polarity=Neg	8	neg	_	_
8	require	require	VERB	VB	VerbForm=Inf	23	advcl	_	_
9	that	that	SCONJ	IN	_	11	mark	_	_
10	there	there	PRON	EX	_	11	expl	_	_
11	be	be	VERB	VBP	Tense=Pres|VerbForm=Fin	8	ccomp	_	_
12	any	any	DET	DT	_	13	det	_	_
13	compositions	composition	NOUN	NNS	Number=Plur	11	attr	_	_
14	for	for	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
16	1	1	NUM	CD	NumType=Card	18	nummod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	cells	cell	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
20	such	such	ADJ	JJ	Degree=Pos	21	amod	_	_
21	composites	composite	NOUN	NNS	Number=Plur	23	nsubjpass	_	_
22	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	23	auxpass	_	_
23	determined	determine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
24	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	30	punct	_	SpaceAfter=No
25	up	up	ADP	IN	_	30	nmod	_	_
26	to	to	PART	TO	_	25	prep	_	_
27	1	1	NUM	CD	NumType=Card	29	nummod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	cell	cell	NOUN	NN	Number=Sing	26	pobj	_	_
30	isomorphism	isomorphism	NOUN	NN	Number=Sing	23	dobj	_	SpaceAfter=No
31	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	30	punct	_	_
32	by	by	ADP	IN	_	30	prep	_	_
33	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	35	poss	_	_
34	universal	universal	ADJ	JJ	Degree=Pos	35	amod	_	_
35	properties	property	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# sent_id = 17
# text = We say a poly - bicategory is representable when there is a representing 1 - cell for each of the two possible 1 - cell compositions geared towards the domains and codomains of the poly 2 - cells.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	say	say	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
4	poly	poly	ADJ	JJ	Degree=Pos	6	amod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	bicategory	bicategory	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	representable	representable	ADJ	JJ	Degree=Pos	7	acomp	_	_
9	when	when	SCONJ	WRB	_	11	advmod	_	_
10	there	there	PRON	EX	_	11	expl	_	_
11	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	advcl	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
13	representing	represent	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	amod	_	_
14	1	1	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	cell	cell	NOUN	NN	Number=Sing	11	attr	_	_
17	for	for	ADP	IN	_	16	prep	_	_
18	each	each	PRON	DT	_	17	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
21	two	two	NUM	CD	NumType=Card	26	nummod	_	_
22	possible	possible	ADJ	JJ	Degree=Pos	26	amod	_	_
23	1	1	NUM	CD	NumType=Card	25	nummod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	cell	cell	NOUN	NN	Number=Sing	26	compound	_	_
26	compositions	composition	NOUN	NNS	Number=Plur	19	pobj	_	_
27	geared	gear	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	acl	_	_
28	towards	towards	ADP	IN	_	27	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	domains	domain	NOUN	NNS	Number=Plur	28	pobj	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
32	codomains	codomain	NOUN	NNS	Number=Plur	30	conj	_	_
33	of	of	ADP	IN	_	30	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
35	poly	poly	ADJ	JJ	Degree=Pos	38	amod	_	_
36	2	2	NUM	CD	NumType=Card	38	nummod	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	38	punct	_	_
38	cells	cell	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 18
# text = In this case we recover the notion of a linear bicategory.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	case	case	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	recover	recover	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	notion	notion	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	linear	linear	ADJ	JJ	Degree=Pos	11	amod	_	_
11	bicategory	bicategory	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 19
# text = The poly notions of functors, modules and their transformations are introduced as well.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	poly	poly	ADJ	JJ	Degree=Pos	3	amod	_	_
3	notions	notion	NOUN	NNS	Number=Plur	12	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	functors	functor	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	modules	module	NOUN	NNS	Number=Plur	12	nsubjpass	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	10	poss	_	_
10	transformations	transformation	NOUN	NNS	Number=Plur	7	conj	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
13	as	as	ADV	RB	_	14	advmod	_	_
14	well	well	ADV	RB	Degree=Pos	12	advmod	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 20
# text = The poly - functors between two given poly - bicategories $ P $ and $ P' $ together with poly - modules between poly - functors and their transformations form a new poly - bicategory provided $ P $ is representable and closed in the sense that every 1 - cell has both a left and a right adjoint (in the appropriate linear sense).
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	poly	poly	ADJ	JJ	Degree=Pos	4	amod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	functors	functor	NOUN	NNS	Number=Plur	26	nsubj	_	_
5	between	between	ADP	IN	_	4	prep	_	_
6	two	two	NUM	CD	NumType=Card	10	nummod	_	_
7	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
8	poly	poly	ADJ	JJ	Degree=Pos	10	amod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	bicategories	bicategorie	NOUN	NNS	Number=Plur	5	pobj	_	_
11	$ P $	$ p $	SYM	$	_	10	advmod	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
13	$ P' $	$ p' $	SYM	$	_	14	nmod	_	_
14	together	together	ADV	RB	_	26	advmod	_	_
15	with	with	ADP	IN	_	14	prep	_	_
16	poly	poly	NOUN	NN	Number=Sing	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	modules	module	NOUN	NNS	Number=Plur	15	pobj	_	_
19	between	between	ADP	IN	_	18	prep	_	_
20	poly	poly	ADJ	JJ	Degree=Pos	22	amod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	functors	functor	NOUN	NNS	Number=Plur	19	pobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	25	poss	_	_
25	transformations	transformation	NOUN	NNS	Number=Plur	22	conj	_	_
26	form	form	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
28	new	new	ADJ	JJ	Degree=Pos	31	amod	_	_
29	poly	poly	ADJ	JJ	Degree=Pos	31	amod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	bicategory	bicategory	NOUN	NN	Number=Sing	26	dobj	_	_
32	provided	provide	VERB	VBD	Tense=Past|VerbForm=Fin	31	acl	_	_
33	$ P $	$ p $	SYM	$	_	32	dobj	_	_
34	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	conj	_	_
35	representable	representable	ADJ	JJ	Degree=Pos	34	acomp	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	34	cc	_	_
37	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	34	conj	_	_
38	in	in	ADP	IN	_	37	prep	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
40	sense	sense	NOUN	NN	Number=Sing	38	pobj	_	_
41	that	that	SCONJ	IN	_	46	mark	_	_
42	every	every	DET	DT	_	45	det	_	_
43	1	1	NUM	CD	NumType=Card	45	nummod	_	_
44	-	-	PUNCT	HYPH	PunctType=Dash	45	punct	_	_
45	cell	cell	NOUN	NN	Number=Sing	46	nsubj	_	_
46	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	40	acl	_	_
47	both	both	CCONJ	CC	ConjType=Cmp	49	preconj	_	_
48	a	a	DET	DT	Definite=Ind|PronType=Art	49	det	_	_
49	left	left	NOUN	NN	Number=Sing	46	dobj	_	_
50	and	and	CCONJ	CC	ConjType=Cmp	49	cc	_	_
51	a	a	DET	DT	Definite=Ind|PronType=Art	53	det	_	_
52	right	right	ADJ	JJ	Degree=Pos	53	amod	_	_
53	adjoint	adjoint	NOUN	NN	Number=Sing	49	conj	_	_
54	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	49	punct	_	SpaceAfter=No
55	in	in	ADP	IN	_	49	prep	_	_
56	the	the	DET	DT	Definite=Def|PronType=Art	59	det	_	_
57	appropriate	appropriate	ADJ	JJ	Degree=Pos	59	amod	_	_
58	linear	linear	ADJ	JJ	Degree=Pos	59	amod	_	_
59	sense	sense	NOUN	NN	Number=Sing	55	pobj	_	SpaceAfter=No
60	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	46	punct	_	SpaceAfter=No
61	.	.	PUNCT	.	PunctType=Peri	26	punct	_	SpaceAfter=No

# sent_id = 21
# text = Finally we revisit the notion of linear (or lax) natural transformations, which can only be defined for representable poly - bicategories.
1	Finally	finally	ADV	RB	_	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	revisit	revisit	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	notion	notion	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	linear	linear	PROPN	NNP	Number=Sing	13	nmod	_	_
8	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	7	punct	_	SpaceAfter=No
9	or	or	CCONJ	CC	ConjType=Cmp	7	cc	_	_
10	lax	lax	ADJ	JJ	Degree=Pos	7	conj	_	SpaceAfter=No
11	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	13	punct	_	_
12	natural	natural	ADJ	JJ	Degree=Pos	13	amod	_	_
13	transformations	transformation	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	which	which	PRON	WDT	_	19	nsubjpass	_	_
16	can	can	AUX	MD	VerbForm=Fin	19	aux	_	_
17	only	only	ADV	RB	_	19	advmod	_	_
18	be	be	AUX	VB	VerbForm=Inf	19	auxpass	_	_
19	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	relcl	_	_
20	for	for	ADP	IN	_	19	prep	_	_
21	representable	representable	ADJ	JJ	Degree=Pos	24	amod	_	_
22	poly	poly	ADJ	JJ	Degree=Pos	24	amod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	bicategories	bicategorie	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 22
# text = These in fact correspond to modules having special properties.
1	These	these	PRON	DT	Number=Plur|PronType=Dem	4	nsubj	_	_
2	in	in	ADP	IN	_	4	prep	_	_
3	fact	fact	NOUN	NN	Number=Sing	2	pobj	_	_
4	correspond	correspond	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	modules	module	NOUN	NNS	Number=Plur	5	pobj	_	_
7	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	advcl	_	_
8	special	special	ADJ	JJ	Degree=Pos	9	amod	_	_
9	properties	property	NOUN	NNS	Number=Plur	7	dobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 174
# sent_id = 1
# text = In many applications of quasigroups isotopies and homotopies are more important than isomorphisms and homomorphisms.
1	In	in	ADP	IN	_	9	prep	_	_
2	many	many	ADJ	JJ	Degree=Pos	3	amod	_	_
3	applications	application	NOUN	NNS	Number=Plur	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	quasigroups	quasigroup	NOUN	NNS	Number=Plur	6	compound	_	_
6	isotopies	isotopie	NOUN	NNS	Number=Plur	4	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	homotopies	homotopie	NOUN	NNS	Number=Plur	6	conj	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	more	more	ADV	RBR	Degree=Cmp	11	advmod	_	_
11	important	important	ADJ	JJ	Degree=Pos	9	acomp	_	_
12	than	than	ADP	IN	_	11	prep	_	_
13	isomorphisms	isomorphism	NOUN	NNS	Number=Plur	12	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	homomorphisms	homomorphism	NOUN	NNS	Number=Plur	13	conj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper, the way homotopies may arise in the context of categorical quasigroup model theory is investigated.
1	In	in	ADP	IN	_	19	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	way	way	NOUN	NN	Number=Sing	19	nsubjpass	_	_
7	homotopies	homotopie	NOUN	NNS	Number=Plur	9	nsubj	_	_
8	may	may	AUX	MD	VerbForm=Fin	9	aux	_	_
9	arise	arise	VERB	VB	VerbForm=Inf	6	relcl	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	context	context	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	categorical	categorical	ADJ	JJ	Degree=Pos	16	amod	_	_
15	quasigroup	quasigroup	NOUN	NN	Number=Sing	16	compound	_	_
16	model	model	NOUN	NN	Number=Sing	17	compound	_	_
17	theory	theory	NOUN	NN	Number=Sing	13	pobj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	auxpass	_	_
19	investigated	investigate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this context, the algebraic structures are specified by diagram - based logics, such as sketches, and categories of models become functor categories.
1	In	in	ADP	IN	_	9	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	context	context	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	algebraic	algebraic	ADJ	JJ	Degree=Pos	7	amod	_	_
7	structures	structure	NOUN	NNS	Number=Plur	9	nsubjpass	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	specified	specify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	by	by	ADP	IN	_	9	agent	_	_
11	diagram	diagram	NOUN	NN	Number=Sing	13	npadvmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
14	logics	logic	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	such	such	ADJ	JJ	Degree=Pos	17	amod	_	_
17	as	as	ADP	IN	_	14	prep	_	_
18	sketches	sketch	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
21	categories	category	NOUN	NNS	Number=Plur	18	conj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	models	model	NOUN	NNS	Number=Plur	22	pobj	_	_
24	become	become	VERB	VBP	Tense=Pres|VerbForm=Fin	9	conj	_	_
25	functor	functor	NOUN	NN	Number=Sing	26	compound	_	_
26	categories	category	NOUN	NNS	Number=Plur	24	attr	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 4
# text = An idea, pioneered by Gvaramiya and Plotkin, is used to give a construction of a model category naturally equivalent to the category of quasigroups with homotopies between them.
1	An	an	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	idea	idea	NOUN	NN	Number=Sing	11	nsubjpass	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
4	pioneered	pioneer	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acl	_	_
5	by	by	ADP	IN	_	4	agent	_	_
6	Gvaramiya	Gvaramiya	PROPN	NNP	Number=Sing	5	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	Plotkin	Plotkin	PROPN	NNP	Number=Sing	6	conj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
12	to	to	PART	TO	_	13	aux	_	_
13	give	give	VERB	VB	VerbForm=Inf	11	xcomp	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	construction	construction	NOUN	NN	Number=Sing	13	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	model	model	NOUN	NN	Number=Sing	19	compound	_	_
19	category	category	NOUN	NN	Number=Sing	16	pobj	_	_
20	naturally	naturally	ADV	RB	_	21	advmod	_	_
21	equivalent	equivalent	ADJ	JJ	Degree=Pos	19	amod	_	_
22	to	to	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	category	category	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	quasigroups	quasigroup	NOUN	NNS	Number=Plur	25	pobj	_	_
27	with	with	ADP	IN	_	26	prep	_	_
28	homotopies	homotopie	NOUN	NNS	Number=Plur	27	pobj	_	_
29	between	between	ADP	IN	_	28	prep	_	_
30	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	29	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# doc_id = 175
# sent_id = 1
# text = A 2 - group is a `categorified' version of a group, in which the underlying set $ G $ has been replaced by a category and the multiplication map $ m ; G x G - > G $ has been replaced by a functor.
1	A	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
2	2	2	NUM	CD	NumType=Card	4	nummod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	group	group	NOUN	NN	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
7	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	10	punct	_	SpaceAfter=No
8	categorified	categorified	ADJ	JJ	Degree=Pos	10	amod	_	SpaceAfter=No
9	'	'	PART	POS	_	8	punct	_	_
10	version	version	NOUN	NN	Number=Sing	5	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	group	group	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	in	in	ADP	IN	_	23	prep	_	_
16	which	which	PRON	WDT	_	15	pobj	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	underlying	underlie	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	amod	_	_
19	set	set	VERB	VBD	Tense=Past|VerbForm=Fin	23	nsubjpass	_	_
20	$ G $	$ g $	SYM	$	_	19	npadvmod	_	_
21	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	aux	_	_
22	been	be	AUX	VBN	Tense=Past|VerbForm=Part	23	auxpass	_	_
23	replaced	replace	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	relcl	_	_
24	by	by	ADP	IN	_	23	agent	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
26	category	category	NOUN	NN	Number=Sing	24	pobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
29	multiplication	multiplication	NOUN	NN	Number=Sing	30	compound	_	_
30	map	map	VERB	VBP	Tense=Pres|VerbForm=Fin	23	conj	_	_
31	$ m ; G x G - > G $	$ m ; g x g - > g $	SYM	$	_	34	nsubjpass	_	_
32	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	34	aux	_	_
33	been	be	AUX	VBN	Tense=Past|VerbForm=Part	34	auxpass	_	_
34	replaced	replace	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	conj	_	_
35	by	by	ADP	IN	_	34	agent	_	_
36	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
37	functor	functor	NOUN	NN	Number=Sing	35	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	34	punct	_	SpaceAfter=No

# sent_id = 2
# text = Various versions of this notion have already been explored; our goal here is to provide a detailed introduction to two, which we call `weak' and `coherent' 2 - groups.
1	Various	various	ADJ	JJ	Degree=Pos	2	amod	_	_
2	versions	version	NOUN	NNS	Number=Plur	9	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	notion	notion	NOUN	NN	Number=Sing	3	pobj	_	_
6	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	aux	_	_
7	already	already	ADV	RB	_	9	advmod	_	_
8	been	be	AUX	VBN	Tense=Past|VerbForm=Part	9	auxpass	_	_
9	explored	explore	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	ccomp	_	SpaceAfter=No
10	;	;	PUNCT	:	_	14	punct	_	_
11	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	12	poss	_	_
12	goal	goal	NOUN	NN	Number=Sing	14	nsubj	_	_
13	here	here	ADV	RB	PronType=Dem	12	advmod	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	provide	provide	VERB	VB	VerbForm=Inf	14	xcomp	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	detailed	detailed	ADJ	JJ	Degree=Pos	19	amod	_	_
19	introduction	introduction	NOUN	NN	Number=Sing	16	dobj	_	_
20	to	to	ADP	IN	_	19	prep	_	_
21	two	two	NUM	CD	NumType=Card	20	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	which	which	PRON	WDT	_	25	dobj	_	_
24	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	25	nsubj	_	_
25	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	21	relcl	_	_
26	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	27	punct	_	SpaceAfter=No
27	weak	weak	ADJ	JJ	Degree=Pos	25	oprd	_	SpaceAfter=No
28	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	27	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
30	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	31	punct	_	SpaceAfter=No
31	coherent	coherent	ADJ	JJ	Degree=Pos	27	conj	_	SpaceAfter=No
32	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	31	punct	_	_
33	2	2	NUM	CD	NumType=Card	35	nummod	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	groups	group	NOUN	NNS	Number=Plur	25	oprd	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 3
# text = A weak 2 - group is a weak monoidal category in which every morphism has an inverse and every object x has a `weak inverse': an object $ y $ such that $ x tensor y iso 1 iso y tensor x $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
2	weak	weak	ADJ	JJ	Degree=Pos	5	amod	_	_
3	2	2	NUM	CD	NumType=Card	5	nummod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	group	group	NOUN	NN	Number=Sing	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	weak	weak	ADJ	JJ	Degree=Pos	10	amod	_	_
9	monoidal	monoidal	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	6	attr	_	_
11	in	in	ADP	IN	_	15	prep	_	_
12	which	which	PRON	WDT	_	11	pobj	_	_
13	every	every	DET	DT	_	14	det	_	_
14	morphism	morphism	NOUN	NN	Number=Sing	15	nsubj	_	_
15	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	relcl	_	_
16	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	inverse	inverse	NOUN	NN	Number=Sing	15	dobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
19	every	every	DET	DT	_	20	det	_	_
20	object	object	NOUN	NN	Number=Sing	22	nsubj	_	_
21	x	x	PUNCT	:	_	20	punct	_	_
22	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	conj	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
24	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	SpaceAfter=No
25	weak	weak	ADJ	JJ	Degree=Pos	26	amod	_	_
26	inverse	inverse	NOUN	NN	Number=Sing	22	dobj	_	SpaceAfter=No
27	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	26	punct	_	SpaceAfter=No
28	:	:	PUNCT	:	_	26	punct	_	_
29	an	an	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
30	object	object	NOUN	NN	Number=Sing	26	appos	_	_
31	$ y $	$ y $	SYM	$	_	30	appos	_	_
32	such	such	ADJ	JJ	Degree=Pos	33	amod	_	_
33	that	that	SCONJ	IN	_	34	nsubj	_	_
34	$ x tensor y iso 1 iso y tensor x $	$ x tensor y iso 1 iso y tensor x $	SYM	$	_	30	appos	_	_
35	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# sent_id = 4
# text = A coherent 2 - group is a weak 2 - group in which every object $ x $ is equipped with a specified weak inverse $ x' $ and isomorphisms $ i_x : 1 - > x tensor x', e_x : x' tensor x - > 1 $ forming an adjunction.
1	A	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
2	coherent	coherent	ADJ	JJ	Degree=Pos	5	amod	_	_
3	2	2	NUM	CD	NumType=Card	5	nummod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	group	group	NOUN	NN	Number=Sing	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	weak	weak	ADJ	JJ	Degree=Pos	11	amod	_	_
9	2	2	NUM	CD	NumType=Card	11	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	group	group	NOUN	NN	Number=Sing	6	attr	_	_
12	in	in	ADP	IN	_	18	prep	_	_
13	which	which	PRON	WDT	_	12	pobj	_	_
14	every	every	DET	DT	_	15	det	_	_
15	object	object	NOUN	NN	Number=Sing	18	nsubjpass	_	_
16	$ x $	$ x $	SYM	$	_	15	prep	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	auxpass	_	_
18	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	relcl	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
21	specified	specify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	amod	_	_
22	weak	weak	ADJ	JJ	Degree=Pos	23	amod	_	_
23	inverse	inverse	NOUN	NN	Number=Sing	24	compound	_	_
24	$ x' $	$ x' $	SYM	$	_	19	pobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
26	isomorphisms	isomorphism	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	conj	_	_
27	$ i_x : 1 - > x tensor x', e_x : x' tensor x - > 1 $	$ i_x : 1 - > x tensor x', e_x : x' tensor x - > 1 $	SYM	$	_	28	nsubj	_	_
28	forming	form	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	advcl	_	_
29	an	an	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
30	adjunction	adjunction	NOUN	NN	Number=Sing	28	dobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = We describe 2 - categories of weak and coherent 2 - groups and an `improvement' 2 - functor that turns weak 2 - groups into coherent ones, and prove that this 2 - functor is a 2 - equivalence of 2 - categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	2	2	NUM	CD	NumType=Card	5	nummod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	categories	category	NOUN	NNS	Number=Plur	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	weak	weak	ADJ	JJ	Degree=Pos	12	amod	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	coherent	coherent	ADJ	JJ	Degree=Pos	7	conj	_	_
10	2	2	NUM	CD	NumType=Card	12	nummod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	groups	group	NOUN	NNS	Number=Plur	6	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	16	punct	_	SpaceAfter=No
16	improvement	improvement	NOUN	NN	Number=Sing	5	conj	_	SpaceAfter=No
17	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	16	punct	_	_
18	2	2	NUM	CD	NumType=Card	20	nummod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	functor	functor	NOUN	NN	Number=Sing	16	appos	_	_
21	that	that	PRON	WDT	PronType=Rel	22	nsubj	_	_
22	turns	turn	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	relcl	_	_
23	weak	weak	ADJ	JJ	Degree=Pos	26	amod	_	_
24	2	2	NUM	CD	NumType=Card	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	groups	group	NOUN	NNS	Number=Plur	22	dobj	_	_
27	into	into	ADP	IN	_	22	prep	_	_
28	coherent	coherent	ADJ	JJ	Degree=Pos	29	amod	_	_
29	ones	one	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
32	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
33	that	that	SCONJ	IN	_	38	mark	_	_
34	this	this	DET	DT	Number=Sing|PronType=Dem	37	det	_	_
35	2	2	NUM	CD	NumType=Card	37	nummod	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	functor	functor	NOUN	NN	Number=Sing	38	nsubj	_	_
38	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	32	ccomp	_	_
39	a	a	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
40	2	2	NUM	CD	NumType=Card	42	nummod	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	equivalence	equivalence	NOUN	NN	Number=Sing	38	attr	_	_
43	of	of	ADP	IN	_	42	prep	_	_
44	2	2	NUM	CD	NumType=Card	46	nummod	_	_
45	-	-	PUNCT	HYPH	PunctType=Dash	46	punct	_	_
46	categories	category	NOUN	NNS	Number=Plur	43	pobj	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = We internalize the concept of coherent 2 - group, which gives a quick way to define Lie 2 - groups.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	internalize	internalize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	concept	concept	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	coherent	coherent	ADJ	JJ	Degree=Pos	9	amod	_	_
7	2	2	NUM	CD	NumType=Card	9	nummod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	group	group	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	which	which	PRON	WDT	_	12	nsubj	_	_
12	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	relcl	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	quick	quick	ADJ	JJ	Degree=Pos	15	amod	_	_
15	way	way	NOUN	NN	Number=Sing	12	dobj	_	_
16	to	to	PART	TO	_	17	aux	_	_
17	define	define	VERB	VB	VerbForm=Inf	15	relcl	_	_
18	Lie	Lie	PROPN	NNP	Number=Sing	17	dobj	_	_
19	2	2	NUM	CD	NumType=Card	21	nummod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	groups	group	NOUN	NNS	Number=Plur	17	dobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = We give a tour of examples, including the `fundamental 2 - group' of a space and various Lie 2 - groups.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	tour	tour	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	examples	example	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
8	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
10	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	14	punct	_	SpaceAfter=No
11	fundamental	fundamental	ADJ	JJ	Degree=Pos	14	amod	_	_
12	2	2	NUM	CD	NumType=Card	14	nummod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	group	group	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
15	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	14	punct	_	_
16	of	of	ADP	IN	_	14	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	space	space	NOUN	NN	Number=Sing	16	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	various	various	ADJ	JJ	Degree=Pos	21	amod	_	_
21	Lie	lie	NOUN	NN	Number=Sing	18	conj	_	_
22	2	2	NUM	CD	NumType=Card	24	nummod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	groups	group	NOUN	NNS	Number=Plur	14	appos	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 8
# text = We also explain how coherent 2 - groups can be classified in terms of 3rd cohomology classes in group cohomology.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	explain	explain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	how	how	SCONJ	WRB	_	5	advmod	_	_
5	coherent	coherent	ADJ	JJ	Degree=Pos	11	nsubjpass	_	_
6	2	2	NUM	CD	NumType=Card	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	groups	group	NOUN	NNS	Number=Plur	11	nsubjpass	_	_
9	can	can	AUX	MD	VerbForm=Fin	11	aux	_	_
10	be	be	AUX	VB	VerbForm=Inf	11	auxpass	_	_
11	classified	classify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	ccomp	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	terms	term	NOUN	NNS	Number=Plur	12	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	3rd	3rd	ADJ	JJ	Degree=Pos	17	amod	_	_
16	cohomology	cohomology	NOUN	NN	Number=Sing	17	compound	_	_
17	classes	class	NOUN	NNS	Number=Plur	14	pobj	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	group	group	NOUN	NN	Number=Sing	20	compound	_	_
20	cohomology	cohomology	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 9
# text = Finally, using this classification, we construct for any connected and simply - connected compact simple Lie group $ G $ a family of 2 - groups $ G_h (h in Z) $ having $ G $ as its group of objects and $ U(1) $ as the group of automorphisms of its identity object.
1	Finally	finally	ADV	RB	_	8	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
3	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	advcl	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	classification	classification	NOUN	NN	Number=Sing	3	dobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
7	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	8	nsubj	_	_
8	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	any	any	DET	DT	_	19	det	_	_
11	connected	connected	ADJ	JJ	Degree=Pos	19	amod	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	simply	simply	ADV	RB	_	15	advmod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	conj	_	_
16	compact	compact	ADJ	JJ	Degree=Pos	17	amod	_	_
17	simple	simple	ADJ	JJ	Degree=Pos	19	amod	_	_
18	Lie	lie	NOUN	NN	Number=Sing	19	compound	_	_
19	group	group	NOUN	NN	Number=Sing	9	pobj	_	_
20	$ G $	$ g $	SYM	$	_	22	nmod	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	family	family	NOUN	NN	Number=Sing	8	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	2	2	NUM	CD	NumType=Card	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	groups	group	NOUN	NNS	Number=Plur	23	pobj	_	_
27	$ G_h (h in Z) $	$ g_h (h in z) $	SYM	$	_	28	nsubj	_	_
28	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	advcl	_	_
29	$ G $	$ g $	SYM	$	_	28	dobj	_	_
30	as	as	ADP	IN	_	28	prep	_	_
31	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	32	poss	_	_
32	group	group	NOUN	NN	Number=Sing	30	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	objects	object	NOUN	NNS	Number=Plur	33	pobj	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
36	$ U(1) $	$ u(1) $	SYM	$	_	32	conj	_	_
37	as	as	ADP	IN	_	32	prep	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
39	group	group	NOUN	NN	Number=Sing	37	pobj	_	_
40	of	of	ADP	IN	_	39	prep	_	_
41	automorphisms	automorphism	NOUN	NNS	Number=Plur	40	pobj	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	45	poss	_	_
44	identity	identity	NOUN	NN	Number=Sing	45	compound	_	_
45	object	object	NOUN	NN	Number=Sing	42	pobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 10
# text = These 2 - groups are built using Chern - Simons theory, and are closely related to the Lie 2 - algebras $ g_h (h in R) $ described in a companion paper.
1	These	these	DET	DT	Number=Plur|PronType=Dem	4	det	_	_
2	2	2	NUM	CD	NumType=Card	4	nummod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	groups	group	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	built	build	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	advcl	_	_
8	Chern	Chern	PROPN	NNP	Number=Sing	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	Simons	Simons	PROPN	NNPS	Number=Plur	11	compound	_	_
11	theory	theory	NOUN	NN	Number=Sing	7	dobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	16	auxpass	_	_
15	closely	closely	ADV	RB	_	16	advmod	_	_
16	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	conj	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	Lie	lie	NOUN	NN	Number=Sing	17	pobj	_	_
20	2	2	NUM	CD	NumType=Card	22	nummod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	algebras	algebra	NOUN	NNS	Number=Plur	19	appos	_	_
23	$ g_h (h in R) $	$ g_h (h in r) $	SYM	$	_	24	nsubj	_	_
24	described	describe	VERB	VBD	Tense=Past|VerbForm=Fin	6	conj	_	_
25	in	in	ADP	IN	_	24	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
27	companion	companion	NOUN	NN	Number=Sing	28	compound	_	_
28	paper	paper	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 176
# sent_id = 1
# text = The theory of Lie algebras can be categorified starting from a new notion of `2 - vector space', which we define as an internal category in Vect.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	theory	theory	NOUN	NN	Number=Sing	8	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	Lie	Lie	PROPN	NNP	Number=Sing	5	compound	_	_
5	algebras	algebra	NOUN	NNS	Number=Plur	3	pobj	_	_
6	can	can	AUX	MD	VerbForm=Fin	8	aux	_	_
7	be	be	AUX	VB	VerbForm=Inf	8	auxpass	_	_
8	categorified	categorifie	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	starting	start	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	xcomp	_	_
10	from	from	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	new	new	ADJ	JJ	Degree=Pos	13	amod	_	_
13	notion	notion	NOUN	NN	Number=Sing	10	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	19	punct	_	SpaceAfter=No
16	2	2	NUM	CD	NumType=Card	18	nummod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	vector	vector	NOUN	NN	Number=Sing	19	compound	_	_
19	space	space	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
20	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	19	punct	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
22	which	which	PRON	WDT	_	24	dobj	_	_
23	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	24	nsubj	_	_
24	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	19	relcl	_	_
25	as	as	ADP	IN	_	24	prep	_	_
26	an	an	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
27	internal	internal	ADJ	JJ	Degree=Pos	28	amod	_	_
28	category	category	NOUN	NN	Number=Sing	25	pobj	_	_
29	in	in	ADP	IN	_	28	prep	_	_
30	Vect	Vect	PROPN	NNP	Number=Sing	29	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = There is a 2 - category 2Vect having these 2 - vector spaces as objects, `linear functors' as morphisms and `linear natural transformations' as 2 - morphisms.
1	There	there	PRON	EX	_	2	expl	_	_
2	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
4	2	2	NUM	CD	NumType=Card	6	nummod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	category	category	NOUN	NN	Number=Sing	7	compound	_	_
7	2Vect	2vect	NOUN	NN	Number=Sing	2	attr	_	_
8	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	acl	_	_
9	these	these	DET	DT	Number=Plur|PronType=Dem	13	det	_	_
10	2	2	NUM	CD	NumType=Card	12	nummod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	vector	vector	NOUN	NN	Number=Sing	13	compound	_	_
13	spaces	space	NOUN	NNS	Number=Plur	8	dobj	_	_
14	as	as	ADP	IN	_	13	prep	_	_
15	objects	object	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	15	punct	_	SpaceAfter=No
18	linear	linear	PROPN	NNP	Number=Sing	19	compound	_	_
19	functors	functor	NOUN	NNS	Number=Plur	15	appos	_	SpaceAfter=No
20	'	'	PART	POS	_	19	case	_	_
21	as	as	ADP	IN	_	19	prep	_	_
22	morphisms	morphism	NOUN	NNS	Number=Plur	21	pobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	27	punct	_	SpaceAfter=No
25	linear	linear	ADJ	JJ	Degree=Pos	27	amod	_	_
26	natural	natural	ADJ	JJ	Degree=Pos	27	amod	_	_
27	transformations	transformation	NOUN	NNS	Number=Plur	22	conj	_	SpaceAfter=No
28	'	'	PART	POS	_	19	punct	_	_
29	as	as	ADP	IN	_	19	prep	_	_
30	2	2	NUM	CD	NumType=Card	32	nummod	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	morphisms	morphism	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We define a `semistrict Lie 2 - algebra' to be a 2 - vector space $ L $ equipped with a skew - symmetric bilinear functor $ [ . , . ] : L x L - > L $ satisfying the Jacobi identity up to a completely antisymmetric trilinear natural transformation called the `Jacobiator', which in turn must satisfy a certain law of its own.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
4	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	6	punct	_	SpaceAfter=No
5	semistrict	semistrict	ADJ	JJ	Degree=Pos	6	nmod	_	_
6	Lie	Lie	PROPN	NNP	Number=Sing	9	nmod	_	_
7	2	2	NUM	CD	NumType=Card	9	nummod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	algebra	algebra	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
10	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	9	punct	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	be	be	AUX	VB	VerbForm=Inf	2	xcomp	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
14	2	2	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	vector	vector	NOUN	NN	Number=Sing	17	compound	_	_
17	space	space	NOUN	NN	Number=Sing	12	attr	_	_
18	$ L $	$ l $	SYM	$	_	17	appos	_	_
19	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
22	skew	skew	NOUN	NN	Number=Sing	24	advmod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	symmetric	symmetric	ADJ	JJ	Degree=Pos	26	amod	_	_
25	bilinear	bilinear	PROPN	NNP	Number=Sing	26	compound	_	_
26	functor	functor	NOUN	NN	Number=Sing	20	pobj	_	_
27	$ [ . , . ] : L x L - > L $	$ [ . , . ] : l x l - > l $	SYM	$	_	12	advmod	_	_
28	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	advcl	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
30	Jacobi	Jacobi	PROPN	NNP	Number=Sing	31	compound	_	_
31	identity	identity	NOUN	NN	Number=Sing	28	dobj	_	_
32	up	up	ADP	IN	_	28	prep	_	_
33	to	to	ADP	IN	_	32	prep	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
35	completely	completely	ADV	RB	_	36	advmod	_	_
36	antisymmetric	antisymmetric	ADJ	JJ	Degree=Pos	39	amod	_	_
37	trilinear	trilinear	ADJ	JJ	Degree=Pos	39	nmod	_	_
38	natural	natural	ADJ	JJ	Degree=Pos	39	amod	_	_
39	transformation	transformation	NOUN	NN	Number=Sing	33	pobj	_	_
40	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	39	acl	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
42	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	43	punct	_	SpaceAfter=No
43	Jacobiator	Jacobiator	PROPN	NNP	Number=Sing	40	oprd	_	SpaceAfter=No
44	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	43	punct	_	SpaceAfter=No
45	,	,	PUNCT	,	PunctType=Comm	43	punct	_	_
46	which	which	PRON	WDT	_	50	nsubj	_	_
47	in	in	ADP	IN	_	50	prep	_	_
48	turn	turn	NOUN	NN	Number=Sing	47	pobj	_	_
49	must	must	AUX	MD	VerbForm=Fin	50	aux	_	_
50	satisfy	satisfy	VERB	VB	VerbForm=Inf	43	relcl	_	_
51	a	a	DET	DT	Definite=Ind|PronType=Art	53	det	_	_
52	certain	certain	ADJ	JJ	Degree=Pos	53	amod	_	_
53	law	law	NOUN	NN	Number=Sing	50	dobj	_	_
54	of	of	ADP	IN	_	53	prep	_	_
55	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	56	poss	_	_
56	own	own	ADJ	JJ	Degree=Pos	54	pobj	_	SpaceAfter=No
57	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = This law is closely related to the Zamolodchikov tetrahedron equation, and indeed we prove that any semistrict Lie 2 - algebra gives a solution of this equation, just as any Lie algebra gives a solution of the Yang - Baxter equation.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	law	law	NOUN	NN	Number=Sing	5	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
4	closely	closely	ADV	RB	_	5	advmod	_	_
5	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	Zamolodchikov	Zamolodchikov	PROPN	NNP	Number=Sing	10	compound	_	_
9	tetrahedron	tetrahedron	NOUN	NN	Number=Sing	10	compound	_	_
10	equation	equation	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
13	indeed	indeed	ADV	RB	_	15	advmod	_	_
14	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	15	nsubj	_	_
15	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	5	conj	_	_
16	that	that	SCONJ	IN	_	23	mark	_	_
17	any	any	DET	DT	_	19	det	_	_
18	semistrict	semistrict	ADJ	JJ	Degree=Pos	19	amod	_	_
19	Lie	lie	NOUN	NN	Number=Sing	23	nsubj	_	_
20	2	2	NUM	CD	NumType=Card	22	nummod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	algebra	algebra	PROPN	NNP	Number=Sing	23	nsubj	_	_
23	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	ccomp	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
25	solution	solution	NOUN	NN	Number=Sing	23	dobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	this	this	DET	DT	Number=Sing|PronType=Dem	28	det	_	_
28	equation	equation	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
30	just	just	ADV	RB	_	35	advmod	_	_
31	as	as	SCONJ	IN	_	35	mark	_	_
32	any	any	DET	DT	_	34	det	_	_
33	Lie	lie	NOUN	NN	Number=Sing	34	compound	_	_
34	algebra	algebra	NOUN	NN	Number=Sing	35	nsubj	_	_
35	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	advcl	_	_
36	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
37	solution	solution	NOUN	NN	Number=Sing	35	dobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
40	Yang	Yang	PROPN	NNP	Number=Sing	42	compound	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	Baxter	Baxter	PROPN	NNP	Number=Sing	43	compound	_	_
43	equation	equation	NOUN	NN	Number=Sing	38	pobj	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 5
# text = We construct a 2 - category of semistrict Lie 2 - algebras and prove that it is 2 - equivalent to the 2 - category of 2 - term $ L_infty $ - algebras in the sense of Stasheff.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
4	2	2	NUM	CD	NumType=Card	6	nummod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	category	category	NOUN	NN	Number=Sing	12	nmod	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	semistrict	semistrict	ADJ	JJ	Degree=Pos	9	compound	_	_
9	Lie	Lie	PROPN	NNP	Number=Sing	7	pobj	_	_
10	2	2	NUM	CD	NumType=Card	12	nummod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	algebras	algebra	NOUN	NNS	Number=Plur	2	dobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
14	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
15	that	that	SCONJ	IN	_	17	mark	_	_
16	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	17	nsubj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	ccomp	_	_
18	2	2	NUM	CD	NumType=Card	20	npadvmod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	equivalent	equivalent	ADJ	JJ	Degree=Pos	17	acomp	_	_
21	to	to	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
23	2	2	NUM	CD	NumType=Card	25	nummod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	category	category	NOUN	NN	Number=Sing	21	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	2	2	NUM	CD	NumType=Card	29	nummod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	term	term	NOUN	NN	Number=Sing	32	compound	_	_
30	$ L_infty $	$ l_infty $	SYM	$	_	32	compound	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	algebras	algebra	NOUN	NNS	Number=Plur	26	pobj	_	_
33	in	in	ADP	IN	_	17	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	sense	sense	NOUN	NN	Number=Sing	33	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	Stasheff	Stasheff	PROPN	NNP	Number=Sing	36	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = We also study strict and skeletal Lie 2 - algebras, obtaining the former from strict Lie 2 - groups and using the latter to classify Lie 2 - algebras in terms of 3rd cohomology classes in Lie algebra cohomology.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	strict	strict	ADJ	JJ	Degree=Pos	7	amod	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	skeletal	skeletal	ADJ	JJ	Degree=Pos	4	conj	_	_
7	Lie	lie	NOUN	NN	Number=Sing	3	dobj	_	_
8	2	2	NUM	CD	NumType=Card	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	algebras	algebra	NOUN	NNS	Number=Plur	3	dobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
12	obtaining	obtain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	advcl	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	former	former	ADJ	JJ	Degree=Pos	12	dobj	_	_
15	from	from	ADP	IN	_	12	prep	_	_
16	strict	strict	ADJ	JJ	Degree=Pos	17	amod	_	_
17	Lie	lie	NOUN	NN	Number=Sing	20	nmod	_	_
18	2	2	NUM	CD	NumType=Card	20	nummod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	groups	group	NOUN	NNS	Number=Plur	15	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
22	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	conj	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	latter	latter	ADJ	JJ	Degree=Pos	22	dobj	_	_
25	to	to	PART	TO	_	26	aux	_	_
26	classify	classify	VERB	VB	VerbForm=Inf	22	xcomp	_	_
27	Lie	Lie	PROPN	NNP	Number=Sing	26	dobj	_	_
28	2	2	NUM	CD	NumType=Card	30	nummod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	algebras	algebra	NOUN	NNS	Number=Plur	26	dobj	_	_
31	in	in	ADP	IN	_	26	prep	_	_
32	terms	term	NOUN	NNS	Number=Plur	31	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	3rd	3rd	ADJ	JJ	Degree=Pos	36	amod	_	_
35	cohomology	cohomology	NOUN	NN	Number=Sing	36	compound	_	_
36	classes	class	NOUN	NNS	Number=Plur	33	pobj	_	_
37	in	in	ADP	IN	_	36	prep	_	_
38	Lie	Lie	PROPN	NNP	Number=Sing	40	compound	_	_
39	algebra	algebra	PROPN	NNP	Number=Sing	40	compound	_	_
40	cohomology	cohomology	NOUN	NN	Number=Sing	37	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = This classification allows us to construct for any finite - dimensional Lie algebra $ g $ a canonical 1 - parameter family of Lie 2 - algebras $ g_h $ which reduces to $ g $ at $ h = 0 $ .
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	classification	classification	NOUN	NN	Number=Sing	3	nsubj	_	_
3	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	construct	construct	VERB	VB	VerbForm=Inf	3	ccomp	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	any	any	DET	DT	_	13	det	_	_
9	finite	finite	ADJ	JJ	Degree=Pos	11	npadvmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	dimensional	dimensional	ADJ	JJ	Degree=Pos	12	amod	_	_
12	Lie	lie	NOUN	NN	Number=Sing	13	compound	_	_
13	algebra	algebra	PROPN	NNP	Number=Sing	7	pobj	_	_
14	$ g $	$ g $	SYM	$	_	20	nmod	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
16	canonical	canonical	ADJ	JJ	Degree=Pos	20	amod	_	_
17	1	1	NUM	CD	NumType=Card	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	parameter	parameter	NOUN	NN	Number=Sing	20	compound	_	_
20	family	family	NOUN	NN	Number=Sing	13	appos	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	Lie	Lie	PROPN	NNP	Number=Sing	21	pobj	_	_
23	2	2	NUM	CD	NumType=Card	25	nummod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	algebras	algebra	NOUN	NNS	Number=Plur	6	npadvmod	_	_
26	$ g_h $	$ g_h $	SYM	$	_	25	prep	_	_
27	which	which	PRON	WDT	_	28	nsubj	_	_
28	reduces	reduce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	relcl	_	_
29	to	to	ADP	IN	_	28	prep	_	_
30	$ g $	$ g $	SYM	$	_	29	pobj	_	_
31	at	at	ADP	IN	_	28	prep	_	_
32	$ h = 0 $	$ h = 0 $	SYM	$	_	31	pobj	_	_
33	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 8
# text = These are closely related to the 2 - groups $ G_h $ constructed in a companion paper.
1	These	these	PRON	DT	Number=Plur|PronType=Dem	2	nsubj	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	closely	closely	ADV	RB	_	4	advmod	_	_
4	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acomp	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
7	2	2	NUM	CD	NumType=Card	9	nummod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	groups	group	NOUN	NNS	Number=Plur	5	pobj	_	_
10	$ G_h $	$ g_h $	SYM	$	_	9	appos	_	_
11	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	acl	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	companion	companion	NOUN	NN	Number=Sing	15	compound	_	_
15	paper	paper	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 177
# sent_id = 1
# text = If $ X $ is a locale, then its double powerlocale $ PX $ is defined to be $ PU(PL(X)) $ where $ PU $ and $ PL $ are the upper and lower powerlocale constructions.
1	If	if	SCONJ	IN	_	3	mark	_	_
2	$ X $	$ x $	SYM	$	_	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	advcl	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	locale	locale	NOUN	NN	Number=Sing	3	attr	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
7	then	then	ADV	RB	PronType=Dem	13	advmod	_	_
8	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	10	poss	_	_
9	double	double	ADJ	JJ	Degree=Pos	10	amod	_	_
10	powerlocale	powerlocale	NOUN	NN	Number=Sing	13	nsubjpass	_	_
11	$ PX $	$ px $	SYM	$	_	10	appos	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	be	be	AUX	VB	VerbForm=Inf	13	xcomp	_	_
16	$ PU(PL(X)) $	$ pu(pl(x)) $	SYM	$	_	21	nsubj	_	_
17	where	where	SCONJ	WRB	_	18	advmod	_	_
18	$ PU $	$ pu $	SYM	$	_	16	relcl	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	$ PL $	$ pl $	SYM	$	_	18	conj	_	_
21	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	conj	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
23	upper	upper	ADJ	JJ	Degree=Pos	27	amod	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	lower	low	ADJ	JJR	Degree=Cmp	23	conj	_	_
26	powerlocale	powerlocale	NOUN	NN	Number=Sing	27	compound	_	_
27	constructions	construction	NOUN	NNS	Number=Plur	21	attr	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# sent_id = 2
# text = We prove various results relating it to exponentiation of locales, including the following.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	various	various	ADJ	JJ	Degree=Pos	4	amod	_	_
4	results	result	NOUN	NNS	Number=Plur	2	dobj	_	_
5	relating	relate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	acl	_	_
6	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	5	dobj	_	_
7	to	to	ADP	IN	_	5	prep	_	_
8	exponentiation	exponentiation	NOUN	NN	Number=Sing	7	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	locales	locale	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
12	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	following	following	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = First, if $ X $ is a locale for which the exponential $ S^X $ exists (where $ S $ is the Sierpinski locale), then $ PX $ is an exponential $ S^(S^X) $ .
1	First	first	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	if	if	SCONJ	IN	_	5	mark	_	_
4	$ X $	$ x $	SYM	$	_	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	ccomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	locale	locale	NOUN	NN	Number=Sing	5	attr	_	_
8	for	for	ADP	IN	_	13	prep	_	_
9	which	which	PRON	WDT	_	8	pobj	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
11	exponential	exponential	ADJ	JJ	Degree=Pos	13	amod	_	_
12	$ S^X $	$ s^x $	X	ADD	_	13	nmod	_	_
13	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	relcl	_	_
14	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	13	punct	_	SpaceAfter=No
15	where	where	SCONJ	WRB	_	17	advmod	_	_
16	$ S $	$ s $	SYM	$	_	17	nsubj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	Sierpinski	Sierpinski	PROPN	NNP	Number=Sing	20	compound	_	_
20	locale	locale	NOUN	NN	Number=Sing	17	attr	_	SpaceAfter=No
21	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	17	punct	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
23	then	then	ADV	RB	PronType=Dem	25	advmod	_	_
24	$ PX $	$ px $	SYM	$	_	25	nsubj	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
26	an	an	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	exponential	exponential	ADJ	JJ	Degree=Pos	25	attr	_	_
28	$ S^(S^X) $	$ s^(s^x) $	SYM	$	_	25	attr	_	_
29	.	.	PUNCT	.	PunctType=Peri	25	punct	_	SpaceAfter=No

# sent_id = 4
# text = Second, if in addition $ W $ is a locale for which $ PW $ is homeomorphic to $ S^X $ , then $ X $ is an exponential $ S^W $ .
1	Second	second	ADJ	JJ	Degree=Pos	7	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
3	if	if	SCONJ	IN	_	7	mark	_	_
4	in	in	ADP	IN	_	7	prep	_	_
5	addition	addition	NOUN	NN	Number=Sing	4	pobj	_	_
6	$ W $	$ w $	SYM	$	_	4	dep	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	ccomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	locale	locale	NOUN	NN	Number=Sing	7	attr	_	_
10	for	for	ADP	IN	_	13	prep	_	_
11	which	which	PRON	WDT	_	10	pobj	_	_
12	$ PW $	$ pw $	SYM	$	_	13	nsubj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	relcl	_	_
14	homeomorphic	homeomorphic	ADJ	JJ	Degree=Pos	13	acomp	_	_
15	to	to	ADP	IN	_	13	prep	_	_
16	$ S^X $	$ s^x $	SYM	$	_	7	dep	_	_
17	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
18	then	then	ADV	RB	PronType=Dem	19	advmod	_	_
19	$ X $	$ x $	SYM	$	_	20	nsubj	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	exponential	exponential	ADJ	JJ	Degree=Pos	23	amod	_	_
23	$ S^W $	$ s^w $	SYM	$	_	20	attr	_	_
24	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 5
# text = The work uses geometric reasoning, that is, reasoning stable under pullback along geometric morphisms, and this enables the locales to be discussed in terms of their points as though they were spaces.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	work	work	NOUN	NN	Number=Sing	3	nsubj	_	_
3	uses	use	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	geometric	geometric	ADJ	JJ	Degree=Pos	5	amod	_	_
5	reasoning	reasoning	NOUN	NN	Number=Sing	3	dobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
7	that	that	ADV	RB	_	8	advmod	_	_
8	is	is	ADV	RB	_	10	advmod	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
10	reasoning	reasoning	NOUN	NN	Number=Sing	3	advcl	_	_
11	stable	stable	ADJ	JJ	Degree=Pos	10	advmod	_	_
12	under	under	ADP	IN	_	11	prep	_	_
13	pullback	pullback	NOUN	NN	Number=Sing	12	pobj	_	_
14	along	along	ADP	IN	_	10	prep	_	_
15	geometric	geometric	ADJ	JJ	Degree=Pos	16	amod	_	_
16	morphisms	morphism	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
19	this	this	PRON	DT	Number=Sing|PronType=Dem	20	nsubj	_	_
20	enables	enable	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	locales	locale	NOUN	NNS	Number=Plur	25	nsubjpass	_	_
23	to	to	PART	TO	_	25	aux	_	_
24	be	be	AUX	VB	VerbForm=Inf	25	auxpass	_	_
25	discussed	discuss	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	ccomp	_	_
26	in	in	ADP	IN	_	25	prep	_	_
27	terms	term	NOUN	NNS	Number=Plur	26	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	30	poss	_	_
30	points	point	NOUN	NNS	Number=Plur	28	pobj	_	_
31	as	as	SCONJ	IN	_	34	mark	_	_
32	though	though	SCONJ	IN	_	34	mark	_	_
33	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	34	nsubj	_	_
34	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	25	advcl	_	_
35	spaces	space	NOUN	NNS	Number=Plur	34	attr	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 6
# text = It relies on a number of geometricity results including those for locale presentations and for powerlocales.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	relies	rely	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	on	on	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	number	number	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	geometricity	geometricity	NOUN	NN	Number=Sing	8	compound	_	_
8	results	result	NOUN	NNS	Number=Plur	6	pobj	_	_
9	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	prep	_	_
10	those	those	PRON	DT	Number=Plur|PronType=Dem	9	pobj	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	locale	locale	NOUN	NN	Number=Sing	13	compound	_	_
13	presentations	presentation	NOUN	NNS	Number=Plur	11	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
15	for	for	ADP	IN	_	11	conj	_	_
16	powerlocales	powerlocale	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 178
# sent_id = 1
# text = Adamek and Sousa recently solved the problem of characterizing the subcategories $ K $ of a locally $ lambda $ - presentable category C which are $ lambda $ - orthogonal in $ C $ , using their concept of $ Klambda $ - pure morphism.
1	Adamek	Adamek	PROPN	NNP	Number=Sing	5	nsubj	_	_
2	and	and	CCONJ	CC	ConjType=Cmp	1	cc	_	_
3	Sousa	Sousa	PROPN	NNP	Number=Sing	1	conj	_	_
4	recently	recently	ADV	RB	_	5	advmod	_	_
5	solved	solve	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	problem	problem	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	characterizing	characterize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	pcomp	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	subcategories	subcategorie	NOUN	NNS	Number=Plur	9	dobj	_	_
12	$ K $	$ k $	SYM	$	_	9	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
15	locally	locally	ADV	RB	_	18	advmod	_	_
16	$ lambda $	$ lambda $	SYM	$	_	18	advmod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	presentable	presentable	ADJ	JJ	Degree=Pos	20	amod	_	_
19	category	category	NOUN	NN	Number=Sing	20	compound	_	_
20	C	c	NOUN	NN	Number=Sing	13	pobj	_	_
21	which	which	PRON	WDT	_	22	nsubj	_	_
22	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	20	relcl	_	_
23	$ lambda $	$ lambda $	SYM	$	_	25	advmod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	orthogonal	orthogonal	ADJ	JJ	Degree=Pos	22	acomp	_	_
26	in	in	ADP	IN	_	25	prep	_	_
27	$ C $	$ c $	SYM	$	_	26	pobj	_	_
28	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
29	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	advcl	_	_
30	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	31	poss	_	_
31	concept	concept	NOUN	NN	Number=Sing	29	dobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	$ Klambda $	$ klambda $	SYM	$	_	35	advmod	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	pure	pure	ADJ	JJ	Degree=Pos	36	amod	_	_
36	morphism	morphism	NOUN	NN	Number=Sing	32	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = We strengthen the latter definition, in order to obtain a characterization of the classes defined by orthogonality with respect to $ lambda $ - presentable morphisms (where $ f : A rightarrow B $ is called $ lambda $ - presentable if it is a $ lambda $ - presentable object of the comma category $ A/C $ ).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	strengthen	strengthen	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	latter	latter	ADJ	JJ	Degree=Pos	5	amod	_	_
5	definition	definition	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
7	in	in	ADP	IN	_	2	prep	_	_
8	order	order	NOUN	NN	Number=Sing	7	pobj	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	obtain	obtain	VERB	VB	VerbForm=Inf	8	acl	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	characterization	characterization	NOUN	NN	Number=Sing	10	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	classes	class	NOUN	NNS	Number=Plur	13	pobj	_	_
16	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
17	by	by	ADP	IN	_	16	agent	_	_
18	orthogonality	orthogonality	NOUN	NN	Number=Sing	17	pobj	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	respect	respect	NOUN	NN	Number=Sing	19	pobj	_	_
21	to	to	ADP	IN	_	20	prep	_	_
22	$ lambda $	$ lambda $	SYM	$	_	24	advmod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	presentable	presentable	ADJ	JJ	Degree=Pos	25	amod	_	_
25	morphisms	morphism	NOUN	NNS	Number=Plur	21	pobj	_	_
26	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	25	punct	_	SpaceAfter=No
27	where	where	SCONJ	WRB	_	30	advmod	_	_
28	$ f : A rightarrow B $	$ f : a rightarrow b $	SYM	$	_	30	nsubjpass	_	_
29	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	auxpass	_	_
30	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	relcl	_	_
31	$ lambda $	$ lambda $	SYM	$	_	33	advmod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	presentable	presentable	ADJ	JJ	Degree=Pos	30	oprd	_	_
34	if	if	SCONJ	IN	_	36	mark	_	_
35	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	36	nsubj	_	_
36	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	advcl	_	_
37	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
38	$ lambda $	$ lambda $	SYM	$	_	40	advmod	_	_
39	-	-	PUNCT	HYPH	PunctType=Dash	40	punct	_	_
40	presentable	presentable	ADJ	JJ	Degree=Pos	41	amod	_	_
41	object	object	NOUN	NN	Number=Sing	36	attr	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	the	the	DET	DT	Definite=Def|PronType=Art	45	det	_	_
44	comma	comma	ADJ	JJ	Degree=Pos	45	amod	_	_
45	category	category	NOUN	NN	Number=Sing	42	pobj	_	_
46	$ A/C $	$ a/c $	SYM	$	_	36	npadvmod	_	_
47	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	2	punct	_	SpaceAfter=No
48	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Those classes are natural examples of reflective subcategories defined by proper classes of morphisms.
1	Those	those	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	classes	class	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	natural	natural	ADJ	JJ	Degree=Pos	5	amod	_	_
5	examples	example	NOUN	NNS	Number=Plur	3	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	reflective	reflective	ADJ	JJ	Degree=Pos	8	amod	_	_
8	subcategories	subcategorie	NOUN	NNS	Number=Plur	6	pobj	_	_
9	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	by	by	ADP	IN	_	9	agent	_	_
11	proper	proper	ADJ	JJ	Degree=Pos	12	amod	_	_
12	classes	class	NOUN	NNS	Number=Plur	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	morphisms	morphism	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = Adamek and Sousa's result follows from ours.
1	Adamek	Adamek	PROPN	NNP	Number=Sing	6	nsubj	_	_
2	and	and	CCONJ	CC	ConjType=Cmp	1	cc	_	_
3	Sousa	Sousa	PROPN	NNP	Number=Sing	5	poss	_	SpaceAfter=No
4	's	's	PART	POS	_	3	case	_	_
5	result	result	NOUN	NN	Number=Sing	1	conj	_	_
6	follows	follow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	from	from	ADP	IN	_	6	prep	_	_
8	ours	ours	PRON	PRP	Number=Plur|Person=1|Poss=Yes|PronType=Prs	7	pobj	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = We also prove that $ lambda $ - presentable morphisms are precisely the pushouts of morphisms between $ lambda $ - presentable objects of $ C $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	9	mark	_	_
5	$ lambda $	$ lambda $	SYM	$	_	7	advmod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	presentable	presentable	ADJ	JJ	Degree=Pos	8	amod	_	_
8	morphisms	morphism	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
10	precisely	precisely	ADV	RB	_	9	advmod	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	pushouts	pushout	NOUN	NNS	Number=Plur	9	attr	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	morphisms	morphism	NOUN	NNS	Number=Plur	13	pobj	_	_
15	between	between	ADP	IN	_	12	prep	_	_
16	$ lambda $	$ lambda $	SYM	$	_	18	advmod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	presentable	presentable	ADJ	JJ	Degree=Pos	19	amod	_	_
19	objects	object	NOUN	NNS	Number=Plur	15	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	$ C $	$ c $	SYM	$	_	20	pobj	_	_
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 179
# sent_id = 1
# text = The paper develops the previously proposed approach to constructing factorization systems in general categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	develops	develop	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	previously	previously	ADV	RB	_	6	advmod	_	_
6	proposed	propose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
7	approach	approach	NOUN	NN	Number=Sing	3	dobj	_	_
8	to	to	ADP	IN	_	7	prep	_	_
9	constructing	construct	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	pcomp	_	_
10	factorization	factorization	NOUN	NN	Number=Sing	11	compound	_	_
11	systems	system	NOUN	NNS	Number=Plur	9	dobj	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	general	general	ADJ	JJ	Degree=Pos	14	amod	_	_
14	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = This approach is applied to the problem of finding conditions under which a functor (not necessarily admitting a right adjoint) `reflects' factorization systems.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	approach	approach	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	applied	apply	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	problem	problem	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	finding	find	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	pcomp	_	_
10	conditions	condition	NOUN	NNS	Number=Plur	9	dobj	_	_
11	under	under	ADP	IN	_	24	prep	_	_
12	which	which	PRON	WDT	_	11	pobj	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	functor	functor	NOUN	NN	Number=Sing	24	nsubj	_	_
15	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	18	punct	_	SpaceAfter=No
16	not	not	PART	RB	Polarity=Neg	18	neg	_	_
17	necessarily	necessarily	ADV	RB	_	18	advmod	_	_
18	admitting	admit	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	acl	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	right	right	ADJ	JJ	Degree=Pos	21	amod	_	_
21	adjoint	adjoint	NOUN	NN	Number=Sing	18	dobj	_	SpaceAfter=No
22	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	18	punct	_	_
23	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	24	punct	_	SpaceAfter=No
24	reflects	reflect	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	relcl	_	SpaceAfter=No
25	'	'	PART	POS	_	24	case	_	_
26	factorization	factorization	NOUN	NN	Number=Sing	27	compound	_	_
27	systems	system	NOUN	NNS	Number=Plur	24	dobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = In particular, a generalization of the well - known Cassidy - Héebert - Kelly factorization theorem is given.
1	In	in	ADP	IN	_	19	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	generalization	generalization	NOUN	NN	Number=Sing	19	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
8	well	well	ADV	RB	Degree=Pos	10	advmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
11	Cassidy	Cassidy	PROPN	NNP	Number=Sing	15	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
13	Héebert	Héebert	PROPN	NNP	Number=Sing	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	Kelly	Kelly	PROPN	NNP	Number=Sing	16	compound	_	_
16	factorization	factorization	NOUN	NN	Number=Sing	6	pobj	_	_
17	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	5	amod	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	auxpass	_	_
19	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 4
# text = The problem of relating a factorization system to a pointed endofunctor is considered.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	problem	problem	NOUN	NN	Number=Sing	13	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	relating	relate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	pcomp	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	factorization	factorization	NOUN	NN	Number=Sing	7	compound	_	_
7	system	system	NOUN	NN	Number=Sing	4	dobj	_	_
8	to	to	ADP	IN	_	4	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	pointed	point	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
11	endofunctor	endofunctor	NOUN	NN	Number=Sing	8	pobj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 5
# text = Some relevant examples in concrete categories are given.
1	Some	some	DET	DT	_	3	det	_	_
2	relevant	relevant	ADJ	JJ	Degree=Pos	3	amod	_	_
3	examples	example	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
4	in	in	ADP	IN	_	3	prep	_	_
5	concrete	concrete	ADJ	JJ	Degree=Pos	6	amod	_	_
6	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 180
# sent_id = 1
# text = Lyubashenko has described enriched 2 - categories as categories enriched over $ V $ - Cat, the 2 - category of categories enriched over a symmetric monoidal $ V $ .
1	Lyubashenko	Lyubashenko	PROPN	NNP	Number=Sing	3	nsubj	_	_
2	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	aux	_	_
3	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
5	2	2	NUM	CD	NumType=Card	7	nummod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	categories	category	NOUN	NNS	Number=Plur	3	dobj	_	_
8	as	as	SCONJ	IN	_	10	mark	_	_
9	categories	category	NOUN	NNS	Number=Plur	10	nsubj	_	_
10	enriched	enrich	VERB	VBD	Tense=Past|VerbForm=Fin	3	advcl	_	_
11	over	over	ADP	IN	_	10	prep	_	_
12	$ V $	$ v $	SYM	$	_	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	Cat	Cat	PROPN	NNP	Number=Sing	11	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
17	2	2	NUM	CD	NumType=Card	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	category	category	NOUN	NN	Number=Sing	10	npadvmod	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	categories	category	NOUN	NNS	Number=Plur	20	pobj	_	_
22	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	acl	_	_
23	over	over	ADP	IN	_	22	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
25	symmetric	symmetric	ADJ	JJ	Degree=Pos	26	amod	_	_
26	monoidal	monoidal	NOUN	NN	Number=Sing	23	pobj	_	_
27	$ V $	$ v $	SYM	$	_	22	npadvmod	_	_
28	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = This construction is the strict analogue for $ V $ - functors in $ V $ - Cat of Brian Day's probicategories for $ V $ - modules in $ V - Mod $ .
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	construction	construction	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	strict	strict	ADJ	JJ	Degree=Pos	6	amod	_	_
6	analogue	analogue	NOUN	NN	Number=Sing	3	attr	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	$ V $	$ v $	SYM	$	_	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	functors	functor	NOUN	NNS	Number=Plur	7	pobj	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	$ V $	$ v $	SYM	$	_	14	nmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	Cat	cat	NOUN	NN	Number=Sing	11	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	Brian	Brian	PROPN	NNP	Number=Sing	17	compound	_	_
17	Day	Day	PROPN	NNP	Number=Sing	19	poss	_	SpaceAfter=No
18	's	's	PART	POS	_	17	case	_	_
19	probicategories	probicategorie	NOUN	NNS	Number=Plur	15	pobj	_	_
20	for	for	ADP	IN	_	14	prep	_	_
21	$ V $	$ v $	SYM	$	_	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	modules	module	NOUN	NNS	Number=Plur	20	pobj	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	$ V - Mod $	$ v - mod $	SYM	$	_	24	pobj	_	_
26	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Here I generalize the strict version to enriched $ n $ - categories for $ k $ - fold monoidal $ V $ .
1	Here	here	ADV	RB	PronType=Dem	3	advmod	_	_
2	I	I	PRON	PRP	Case=Nom|Number=Sing|Person=1|PronType=Prs	3	nsubj	_	_
3	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	strict	strict	ADJ	JJ	Degree=Pos	6	amod	_	_
6	version	version	NOUN	NN	Number=Sing	3	dobj	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
9	$ n $	$ n $	SYM	$	_	11	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	categories	category	NOUN	NNS	Number=Plur	8	dobj	_	_
12	for	for	ADP	IN	_	8	prep	_	_
13	$ k $	$ k $	SYM	$	_	14	nmod	_	_
14	-	-	ADJ	JJ	Degree=Pos	16	amod	_	_
15	fold	fold	ADJ	JJ	Degree=Pos	16	amod	_	_
16	monoidal	monoidal	NOUN	NN	Number=Sing	12	pobj	_	_
17	$ V $	$ v $	SYM	$	_	3	dobj	_	_
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = The latter is defined as by Balteanu, Fiedorowicz, Schwanzl and Vogt but with the addition of making visible the coherent associators.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	latter	latter	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	as	as	ADP	IN	_	4	prep	_	_
6	by	by	ADP	IN	_	5	prep	_	_
7	Balteanu	Balteanu	PROPN	NNP	Number=Sing	6	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	Fiedorowicz	Fiedorowicz	PROPN	NNP	Number=Sing	7	conj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	Schwanzl	Schwanzl	PROPN	NNP	Number=Sing	9	conj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	Vogt	Vogt	PROPN	NNP	Number=Sing	11	conj	_	_
14	but	but	CCONJ	CC	ConjType=Cmp	4	cc	_	_
15	with	with	ADP	IN	_	4	conj	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	addition	addition	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	making	make	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	18	pcomp	_	_
20	visible	visible	ADJ	JJ	Degree=Pos	19	ccomp	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	coherent	coherent	ADJ	JJ	Degree=Pos	23	amod	_	_
23	associators	associator	NOUN	NNS	Number=Plur	20	dobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = The symmetric case can easily be recovered.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	symmetric	symmetric	ADJ	JJ	Degree=Pos	3	amod	_	_
3	case	case	NOUN	NN	Number=Sing	7	nsubjpass	_	_
4	can	can	AUX	MD	VerbForm=Fin	7	aux	_	_
5	easily	easily	ADV	RB	_	7	advmod	_	_
6	be	be	AUX	VB	VerbForm=Inf	7	auxpass	_	_
7	recovered	recover	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 6
# text = This paper proposes a recursive definition of $ V - n $ - categories and their morphisms.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	proposes	propose	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	recursive	recursive	ADJ	JJ	Degree=Pos	6	amod	_	_
6	definition	definition	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	$ V - n $	$ v - n $	SYM	$	_	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	13	poss	_	_
13	morphisms	morphism	NOUN	NNS	Number=Plur	10	conj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = We show that for $ V k $ - fold monoidal the structure of a $ (k - n) $ - fold monoidal strict $ (n+1) $ - category is possessed by $ V - n - Cat $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	22	mark	_	_
4	for	for	ADP	IN	_	22	prep	_	_
5	$ V k $	$ v k $	SYM	$	_	6	nmod	_	_
6	-	-	ADJ	JJ	Degree=Pos	8	amod	_	_
7	fold	fold	ADJ	JJ	Degree=Pos	8	amod	_	_
8	monoidal	monoidal	NOUN	NN	Number=Sing	4	pobj	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	structure	structure	NOUN	NN	Number=Sing	22	nsubjpass	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	$ (k - n) $	$ (k - n) $	SYM	$	_	14	nmod	_	_
14	-	-	PUNCT	:	_	11	pobj	_	_
15	fold	fold	VERB	VB	VerbForm=Inf	11	pcomp	_	_
16	monoidal	monoidal	NOUN	NN	Number=Sing	15	dobj	_	_
17	strict	strict	ADJ	JJ	Degree=Pos	20	amod	_	_
18	$ (n+1) $	$ (n+1) $	SYM	$	_	20	nmod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	category	category	NOUN	NN	Number=Sing	22	nsubjpass	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	auxpass	_	_
22	possessed	possess	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
23	by	by	ADP	IN	_	22	agent	_	_
24	$ V - n - Cat $	$ v - n - cat $	SYM	$	_	23	pobj	_	_
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 8
# text = This article is a completion of the work begun by the author in the preprint entitled Higher dimensional enrichment, and the initial sections duplicate the .
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	article	article	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	completion	completion	NOUN	NN	Number=Sing	3	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	work	work	NOUN	NN	Number=Sing	6	pobj	_	_
9	begun	begin	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	by	by	ADP	IN	_	9	agent	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	author	author	NOUN	NN	Number=Sing	10	pobj	_	_
13	in	in	ADP	IN	_	9	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	preprint	preprint	NOUN	NN	Number=Sing	13	pobj	_	_
16	entitled	entitle	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
17	Higher	high	ADJ	JJR	Degree=Cmp	19	amod	_	_
18	dimensional	dimensional	ADJ	JJ	Degree=Pos	19	amod	_	_
19	enrichment	enrichment	NOUN	NN	Number=Sing	16	oprd	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	initial	initial	ADJ	JJ	Degree=Pos	24	amod	_	_
24	sections	section	NOUN	NNS	Number=Plur	25	nsubj	_	_
25	duplicate	duplicate	VERB	VBP	Tense=Pres|VerbForm=Fin	3	conj	_	_
26	the	the	PRON	DT	Definite=Def|PronType=Art	25	dobj	_	_
27	.	.	PUNCT	.	PunctType=Peri	25	punct	_	SpaceAfter=No

# doc_id = 181
# sent_id = 1
# text = We investigate categorical versions of algebraically closed (that is, pure) embeddings, existentially closed embeddings, and the like, in the context of locally presentable categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	categorical	categorical	ADJ	JJ	Degree=Pos	4	amod	_	_
4	versions	version	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	algebraically	algebraically	ADV	RB	_	7	advmod	_	_
7	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
8	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
9	that	that	ADV	RB	_	10	advmod	_	_
10	is	is	ADV	RB	_	14	advmod	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
12	pure	pure	ADJ	JJ	Degree=Pos	14	amod	_	SpaceAfter=No
13	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	14	punct	_	_
14	embeddings	embedding	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	existentially	existentially	ADV	RB	_	17	advmod	_	_
17	closed	closed	ADJ	JJ	Degree=Pos	18	amod	_	_
18	embeddings	embedding	NOUN	NNS	Number=Plur	14	conj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	like	like	ADJ	JJ	Degree=Pos	2	conj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	in	in	ADP	IN	_	22	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	context	context	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	locally	locally	ADV	RB	_	29	advmod	_	_
29	presentable	presentable	ADJ	JJ	Degree=Pos	30	amod	_	_
30	categories	category	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The definitions of Fakir, as well as some of his results, are revisited and extended.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	definitions	definition	NOUN	NNS	Number=Plur	15	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	Fakir	Fakir	PROPN	NNP	Number=Sing	3	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
6	as	as	ADV	RB	_	8	advmod	_	_
7	well	well	ADV	RB	Degree=Pos	8	advmod	_	_
8	as	as	ADP	IN	_	4	cc	_	_
9	some	some	PRON	DT	_	4	conj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	his	his	PRON	PRP$	Gender=Masc|Number=Sing|Person=3|Poss=Yes|PronType=Prs	12	poss	_	_
12	results	result	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	revisited	revisit	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	conj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 3
# text = Related preservation theorems are obtained, and a new proof of the main result of Rosicky, Adamek and Borceux, characterizing $ lambda $ - injectivity classes in locally $ lambda $ - presentable categories, is given.
1	Related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	amod	_	_
2	preservation	preservation	NOUN	NN	Number=Sing	3	compound	_	_
3	theorems	theorem	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	new	new	ADJ	JJ	Degree=Pos	10	amod	_	_
10	proof	proof	NOUN	NN	Number=Sing	35	nsubjpass	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	main	main	ADJ	JJ	Degree=Pos	14	amod	_	_
14	result	result	NOUN	NN	Number=Sing	11	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	Rosicky	rosicky	ADJ	JJ	Degree=Pos	15	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	Adamek	Adamek	PROPN	NNP	Number=Sing	16	conj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	Borceux	Borceux	PROPN	NNP	Number=Sing	18	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
22	characterizing	characterize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	acl	_	_
23	$ lambda $	$ lambda $	SYM	$	_	25	amod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	injectivity	injectivity	NOUN	NN	Number=Sing	26	compound	_	_
26	classes	class	NOUN	NNS	Number=Plur	22	dobj	_	_
27	in	in	ADP	IN	_	22	prep	_	_
28	locally	locally	ADV	RB	_	32	advmod	_	_
29	$ lambda $	$ lambda $	SYM	$	_	31	advmod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	presentable	presentable	ADJ	JJ	Degree=Pos	32	amod	_	_
32	categories	category	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
34	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	35	auxpass	_	_
35	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	conj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	35	punct	_	SpaceAfter=No

# doc_id = 182
# sent_id = 1
# text = Following Ghilardi and Meloni, a relational variable set on a category $ B $ is a lax functor $ B $ to $ Rel $ , where $ Rel $ is the category of sets and relations.
1	Following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	prep	_	_
2	Ghilardi	Ghilardi	PROPN	NNP	Number=Sing	1	pobj	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	Meloni	Meloni	PROPN	NNP	Number=Sing	2	conj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	relational	relational	ADJ	JJ	Degree=Pos	8	amod	_	_
8	variable	variable	NOUN	NN	Number=Sing	14	nsubj	_	_
9	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	on	on	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	category	category	NOUN	NN	Number=Sing	13	compound	_	_
13	$ B $	$ b $	SYM	$	_	10	pobj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	lax	lax	ADJ	JJ	Degree=Pos	17	amod	_	_
17	functor	functor	NOUN	NN	Number=Sing	14	attr	_	_
18	$ B $	$ b $	SYM	$	_	17	nmod	_	_
19	to	to	PART	TO	_	17	prep	_	_
20	$ Rel $	$ rel $	SYM	$	_	19	pobj	_	_
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	where	where	SCONJ	WRB	_	24	advmod	_	_
23	$ Rel $	$ rel $	SYM	$	_	24	nsubj	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	relcl	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	category	category	NOUN	NN	Number=Sing	24	attr	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	sets	set	NOUN	NNS	Number=Plur	27	pobj	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	relations	relation	NOUN	NNS	Number=Plur	28	conj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 2
# text = Change - of - base functors and their adjoints are considered for certain categories of relational variable sets and applied to construct the simplification of a dynamic set (in the sense of Stell).
1	Change	change	NOUN	NN	Number=Sing	6	nmod	_	_
2	-	-	PUNCT	HYPH	PunctType=Dash	1	punct	_	_
3	of	of	ADP	IN	_	1	prep	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	3	punct	_	_
5	base	base	NOUN	NN	Number=Sing	3	pobj	_	_
6	functors	functor	NOUN	NNS	Number=Plur	11	nsubjpass	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	9	poss	_	_
9	adjoints	adjoint	NOUN	NNS	Number=Plur	6	conj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	certain	certain	ADJ	JJ	Degree=Pos	14	amod	_	_
14	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	relational	relational	ADJ	JJ	Degree=Pos	18	amod	_	_
17	variable	variable	ADJ	JJ	Degree=Pos	18	amod	_	_
18	sets	set	NOUN	NNS	Number=Plur	15	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
20	applied	apply	VERB	VBD	Tense=Past|VerbForm=Fin	11	conj	_	_
21	to	to	PART	TO	_	22	aux	_	_
22	construct	construct	VERB	VB	VerbForm=Inf	20	xcomp	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	simplification	simplification	NOUN	NN	Number=Sing	22	dobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
27	dynamic	dynamic	ADJ	JJ	Degree=Pos	28	amod	_	_
28	set	set	NOUN	NN	Number=Sing	25	pobj	_	_
29	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	28	punct	_	SpaceAfter=No
30	in	in	ADP	IN	_	22	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	sense	sense	NOUN	NN	Number=Sing	30	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	Stell	Stell	PROPN	NNP	Number=Sing	33	pobj	_	SpaceAfter=No
35	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	20	punct	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# doc_id = 183
# sent_id = 1
# text = In 1970, Gerstenhaber introduced a list of axioms defining Moore categories in order to develop the Baer Extension Theory.
1	In	in	ADP	IN	_	5	prep	_	_
2	1970	1970	NUM	CD	NumType=Card	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	Gerstenhaber	Gerstenhaber	PROPN	NNP	Number=Sing	5	nsubj	_	_
5	introduced	introduce	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	list	list	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	axioms	axiom	NOUN	NNS	Number=Plur	8	pobj	_	_
10	defining	define	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	acl	_	_
11	Moore	Moore	PROPN	NNP	Number=Sing	12	compound	_	_
12	categories	category	NOUN	NNS	Number=Plur	10	dobj	_	_
13	in	in	ADP	IN	_	5	prep	_	_
14	order	order	NOUN	NN	Number=Sing	13	pobj	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	develop	develop	VERB	VB	VerbForm=Inf	14	acl	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
18	Baer	Baer	PROPN	NNP	Number=Sing	19	compound	_	_
19	Extension	Extension	PROPN	NNP	Number=Sing	20	compound	_	_
20	Theory	Theory	PROPN	NNP	Number=Sing	16	dobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper, we study some implications between the axioms and compare them with more recent notions, showing that, apart from size restrictions, a Moore category is a pointed, strongly protomodular and Barr - exact category with cokernels.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	some	some	DET	DT	_	8	det	_	_
8	implications	implication	NOUN	NNS	Number=Plur	6	dobj	_	_
9	between	between	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	axioms	axiom	NOUN	NNS	Number=Plur	9	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
13	compare	compare	VERB	VB	VerbForm=Inf	6	conj	_	_
14	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	13	dobj	_	_
15	with	with	ADP	IN	_	13	prep	_	_
16	more	more	ADV	RBR	Degree=Cmp	17	advmod	_	_
17	recent	recent	ADJ	JJ	Degree=Pos	18	amod	_	_
18	notions	notion	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
20	showing	show	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	advcl	_	_
21	that	that	SCONJ	IN	_	31	mark	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
23	apart	apart	ADV	RB	_	31	advmod	_	_
24	from	from	ADP	IN	_	23	prep	_	_
25	size	size	NOUN	NN	Number=Sing	26	compound	_	_
26	restrictions	restriction	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
29	Moore	Moore	PROPN	NNP	Number=Sing	30	compound	_	_
30	category	category	NOUN	NN	Number=Sing	31	nsubj	_	_
31	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	ccomp	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
33	pointed	point	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	36	amod	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
35	strongly	strongly	ADV	RB	_	36	advmod	_	_
36	protomodular	protomodular	ADJ	JJ	Degree=Pos	41	amod	_	_
37	and	and	CCONJ	CC	ConjType=Cmp	36	cc	_	_
38	Barr	Barr	PROPN	NNP	Number=Sing	40	npadvmod	_	_
39	-	-	PUNCT	HYPH	PunctType=Dash	40	punct	_	_
40	exact	exact	ADJ	JJ	Degree=Pos	41	amod	_	_
41	category	category	NOUN	NN	Number=Sing	31	attr	_	_
42	with	with	ADP	IN	_	41	prep	_	_
43	cokernels	cokernel	NOUN	NNS	Number=Plur	42	pobj	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 184
# sent_id = 1
# text = Completions of (small) categories under certain kinds of colimits and exactness conditions have been studied extensively in the literature.
1	Completions	completion	NOUN	NNS	Number=Plur	17	nsubjpass	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	6	punct	_	SpaceAfter=No
4	small	small	ADJ	JJ	Degree=Pos	6	amod	_	SpaceAfter=No
5	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	6	punct	_	_
6	categories	category	NOUN	NNS	Number=Plur	2	pobj	_	_
7	under	under	ADP	IN	_	6	prep	_	_
8	certain	certain	ADJ	JJ	Degree=Pos	9	amod	_	_
9	kinds	kind	NOUN	NNS	Number=Plur	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	colimits	colimit	NOUN	NNS	Number=Plur	14	nmod	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	exactness	exactness	ADJ	JJ	Degree=Pos	14	compound	_	_
14	conditions	condition	NOUN	NNS	Number=Plur	10	pobj	_	_
15	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	17	aux	_	_
16	been	be	AUX	VBN	Tense=Past|VerbForm=Part	17	auxpass	_	_
17	studied	study	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
18	extensively	extensively	ADV	RB	_	17	advmod	_	_
19	in	in	ADP	IN	_	17	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	literature	literature	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 2
# text = When the category that we complete is not left exact but has some weaker kind of limit for finite diagrams, the universal property of the completion is usually stated with respect to functors that enjoy a property reminiscent of flatness.
1	When	when	SCONJ	WRB	_	9	advmod	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	category	category	NOUN	NN	Number=Sing	9	nsubjpass	_	_
4	that	that	PRON	WDT	PronType=Rel	6	dobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	complete	complete	VERB	VBP	Tense=Pres|VerbForm=Fin	3	relcl	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
8	not	not	PART	RB	Polarity=Neg	9	neg	_	_
9	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	30	advcl	_	_
10	exact	exact	ADJ	JJ	Degree=Pos	9	oprd	_	_
11	but	but	CCONJ	CC	ConjType=Cmp	9	cc	_	_
12	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	conj	_	_
13	some	some	DET	DT	_	15	det	_	_
14	weaker	weak	ADJ	JJR	Degree=Cmp	15	amod	_	_
15	kind	kind	NOUN	NN	Number=Sing	12	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	limit	limit	NOUN	NN	Number=Sing	16	pobj	_	_
18	for	for	ADP	IN	_	17	prep	_	_
19	finite	finite	PROPN	NNP	Number=Sing	20	compound	_	_
20	diagrams	diagram	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	universal	universal	ADJ	JJ	Degree=Pos	24	amod	_	_
24	property	property	NOUN	NN	Number=Sing	30	nsubjpass	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	completion	completion	NOUN	NN	Number=Sing	25	pobj	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	auxpass	_	_
29	usually	usually	ADV	RB	_	30	advmod	_	_
30	stated	state	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
31	with	with	ADP	IN	_	30	prep	_	_
32	respect	respect	NOUN	NN	Number=Sing	31	pobj	_	_
33	to	to	ADP	IN	_	32	prep	_	_
34	functors	functor	NOUN	NNS	Number=Plur	33	pobj	_	_
35	that	that	PRON	WDT	PronType=Rel	36	nsubj	_	_
36	enjoy	enjoy	VERB	VBP	Tense=Pres|VerbForm=Fin	34	relcl	_	_
37	a	a	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
38	property	property	NOUN	NN	Number=Sing	36	dobj	_	_
39	reminiscent	reminiscent	ADJ	JJ	Degree=Pos	38	amod	_	_
40	of	of	ADP	IN	_	39	prep	_	_
41	flatness	flatness	NOUN	NN	Number=Sing	40	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	30	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this fashion notions like that of a left covering or a multilimit merging functor have appeared in the literature.
1	In	in	ADP	IN	_	17	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
3	fashion	fashion	NOUN	NN	Number=Sing	4	compound	_	_
4	notions	notion	NOUN	NNS	Number=Plur	17	nsubj	_	_
5	like	like	ADP	IN	_	4	prep	_	_
6	that	that	PRON	DT	Number=Sing|PronType=Dem	5	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	left	left	ADJ	JJ	Degree=Pos	10	amod	_	_
10	covering	covering	NOUN	NN	Number=Sing	7	pobj	_	_
11	or	or	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	multilimit	multilimit	NOUN	NN	Number=Sing	15	compound	_	_
14	merging	merging	NOUN	NN	Number=Sing	15	compound	_	_
15	functor	functor	NOUN	NN	Number=Sing	10	conj	_	_
16	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	17	aux	_	_
17	appeared	appear	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	literature	literature	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show here that such notions coincide with flatness when the latter is interpreted relative to (the internal logic of) a site structure associated to the target category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	here	here	ADV	RB	PronType=Dem	2	advmod	_	_
4	that	that	SCONJ	IN	_	7	mark	_	_
5	such	such	ADJ	JJ	Degree=Pos	6	amod	_	_
6	notions	notion	NOUN	NNS	Number=Plur	7	nsubj	_	_
7	coincide	coincide	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	with	with	ADP	IN	_	7	prep	_	_
9	flatness	flatness	NOUN	NN	Number=Sing	8	pobj	_	_
10	when	when	SCONJ	WRB	_	14	advmod	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	latter	latter	NOUN	NN	Number=Sing	14	nsubjpass	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	interpreted	interpret	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	advcl	_	_
15	relative	relative	ADJ	JJ	Degree=Pos	14	advmod	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	16	punct	_	SpaceAfter=No
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	internal	internal	ADJ	JJ	Degree=Pos	20	amod	_	_
20	logic	logic	NOUN	NN	Number=Sing	16	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	SpaceAfter=No
22	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	21	punct	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	site	site	NOUN	NN	Number=Sing	25	compound	_	_
25	structure	structure	NOUN	NN	Number=Sing	21	pobj	_	_
26	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	acl	_	_
27	to	to	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
29	target	target	NOUN	NN	Number=Sing	30	compound	_	_
30	category	category	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = We exploit this in order to show that the left Kan extensions of such functors, along the inclusion of their domain into its completion, are left exact.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	exploit	exploit	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	this	this	PRON	DT	Number=Sing|PronType=Dem	2	dobj	_	_
4	in	in	ADP	IN	_	2	prep	_	_
5	order	order	NOUN	NN	Number=Sing	4	pobj	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	show	show	VERB	VB	VerbForm=Inf	5	acl	_	_
8	that	that	SCONJ	IN	_	28	mark	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
10	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
11	Kan	Kan	PROPN	NNP	Number=Sing	12	compound	_	_
12	extensions	extension	NOUN	NNS	Number=Plur	28	nsubjpass	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	such	such	ADJ	JJ	Degree=Pos	15	amod	_	_
15	functors	functor	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
17	along	along	ADP	IN	_	12	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	inclusion	inclusion	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	22	poss	_	_
22	domain	domain	NOUN	NN	Number=Sing	20	pobj	_	_
23	into	into	ADP	IN	_	19	prep	_	_
24	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	25	poss	_	_
25	completion	completion	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
27	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	28	auxpass	_	_
28	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	ccomp	_	_
29	exact	exact	ADJ	JJ	Degree=Pos	28	oprd	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = This gives in a very economical and uniform manner the universal property of such completions.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	in	in	ADP	IN	_	2	prt	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
5	very	very	ADV	RB	_	6	advmod	_	_
6	economical	economical	ADJ	JJ	Degree=Pos	9	amod	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	uniform	uniform	ADJ	JJ	Degree=Pos	6	conj	_	_
9	manner	manner	NOUN	NN	Number=Sing	2	dobj	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	universal	universal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	property	property	NOUN	NN	Number=Sing	2	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	such	such	ADJ	JJ	Degree=Pos	15	amod	_	_
15	completions	completion	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = Our result relies heavily on some unpublished work of Kock from 1989.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	result	result	NOUN	NN	Number=Sing	3	nsubj	_	_
3	relies	rely	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	heavily	heavily	ADV	RB	_	3	advmod	_	_
5	on	on	ADP	IN	_	3	prep	_	_
6	some	some	DET	DT	_	8	det	_	_
7	unpublished	unpublished	ADJ	JJ	Degree=Pos	8	amod	_	_
8	work	work	NOUN	NN	Number=Sing	5	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Kock	Kock	PROPN	NNP	Number=Sing	9	pobj	_	_
11	from	from	ADP	IN	_	8	prep	_	_
12	1989	1989	NUM	CD	NumType=Card	11	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 8
# text = We further apply this to give a pretopos completion process for small categories having a weak finite limit property.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	further	far	ADV	RB	_	3	advmod	_	_
3	apply	apply	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	this	this	PRON	DT	Number=Sing|PronType=Dem	3	dobj	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	give	give	VERB	VB	VerbForm=Inf	3	advcl	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	pretopos	pretopos	NOUN	NN	Number=Sing	10	compound	_	_
9	completion	completion	NOUN	NN	Number=Sing	10	compound	_	_
10	process	process	NOUN	NN	Number=Sing	6	dobj	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	small	small	ADJ	JJ	Degree=Pos	13	amod	_	_
13	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
14	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	acl	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
16	weak	weak	ADJ	JJ	Degree=Pos	19	amod	_	_
17	finite	finite	ADJ	JJ	Degree=Pos	18	compound	_	_
18	limit	limit	NOUN	NN	Number=Sing	19	compound	_	_
19	property	property	NOUN	NN	Number=Sing	14	dobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 185
# sent_id = 1
# text = The purpose of this paper is to set up a theory of generalized operads and multicategories and to use it as a language in which to propose a definition of weak $ n $ - category.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	purpose	purpose	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	paper	paper	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	set	set	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	up	up	ADP	RP	_	8	prt	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	theory	theory	NOUN	NN	Number=Sing	8	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
14	operads	operad	NOUN	NNS	Number=Plur	12	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	multicategories	multicategorie	NOUN	NNS	Number=Plur	14	conj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
18	to	to	PART	TO	_	19	aux	_	_
19	use	use	VERB	VB	VerbForm=Inf	8	conj	_	_
20	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	19	dobj	_	_
21	as	as	ADP	IN	_	19	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
23	language	language	NOUN	NN	Number=Sing	21	pobj	_	_
24	in	in	ADP	IN	_	27	prep	_	_
25	which	which	PRON	WDT	_	24	pobj	_	_
26	to	to	PART	TO	_	27	aux	_	_
27	propose	propose	VERB	VB	VerbForm=Inf	23	relcl	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
29	definition	definition	NOUN	NN	Number=Sing	27	dobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	weak	weak	ADJ	JJ	Degree=Pos	34	amod	_	_
32	$ n $	$ n $	SYM	$	_	34	compound	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	category	category	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = Included is a full explanation of why the proposed definition of $ n $ - category is a reasonable one, and of what happens when $ n $ is less than or equal to 2.
1	Included	include	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	csubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	full	full	ADJ	JJ	Degree=Pos	5	amod	_	_
5	explanation	explanation	NOUN	NN	Number=Sing	2	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	why	why	SCONJ	WRB	_	15	advmod	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	proposed	propose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	definition	definition	NOUN	NN	Number=Sing	15	nsubj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	$ n $	$ n $	SYM	$	_	14	nummod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	pcomp	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	reasonable	reasonable	ADJ	JJ	Degree=Pos	18	amod	_	_
18	one	one	NOUN	NN	Number=Sing	15	attr	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
21	of	of	ADP	IN	_	6	conj	_	_
22	what	what	PRON	WP	_	23	nsubj	_	_
23	happens	happen	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	21	pcomp	_	_
24	when	when	SCONJ	WRB	_	26	advmod	_	_
25	$ n $	$ n $	SYM	$	_	26	nsubj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	advcl	_	_
27	less	less	ADJ	JJR	Degree=Cmp	26	acomp	_	_
28	than	than	ADP	IN	_	27	prep	_	_
29	or	or	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	equal	equal	ADJ	JJ	Degree=Pos	28	conj	_	_
31	to	to	ADP	IN	_	30	prep	_	_
32	2	2	NUM	CD	NumType=Card	31	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Generalized operads and multicategories play other parts in higher - dimensional algebra too, some of which are outlined here: for instance, they can be used to simplify the opetopic approach to $ n $ - categories expounded by Baez, Dolan and others, and are a natural language in which to discuss enrichment of categorical structures.
1	Generalized	generalized	ADJ	JJ	Degree=Pos	2	amod	_	_
2	operads	operad	NOUN	NNS	Number=Plur	5	nsubj	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	multicategories	multicategorie	NOUN	NNS	Number=Plur	2	conj	_	_
5	play	play	VERB	VBP	Tense=Pres|VerbForm=Fin	28	ccomp	_	_
6	other	other	ADJ	JJ	Degree=Pos	7	amod	_	_
7	parts	part	NOUN	NNS	Number=Plur	5	dobj	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	higher	high	ADJ	JJR	Degree=Cmp	11	amod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	dimensional	dimensional	ADJ	JJ	Degree=Pos	12	amod	_	_
12	algebra	algebra	NOUN	NNS	Number=Plur	8	pobj	_	_
13	too	too	ADV	RB	_	5	advmod	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
15	some	some	PRON	DT	_	19	nsubjpass	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	which	which	PRON	WDT	_	16	pobj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	19	auxpass	_	_
19	outlined	outline	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	conj	_	_
20	here	here	ADV	RB	PronType=Dem	19	advmod	_	SpaceAfter=No
21	:	:	PUNCT	:	_	28	punct	_	_
22	for	for	ADP	IN	_	28	prep	_	_
23	instance	instance	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
25	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	28	nsubjpass	_	_
26	can	can	AUX	MD	VerbForm=Fin	28	aux	_	_
27	be	be	AUX	VB	VerbForm=Inf	28	auxpass	_	_
28	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
29	to	to	PART	TO	_	30	aux	_	_
30	simplify	simplify	VERB	VB	VerbForm=Inf	28	xcomp	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	opetopic	opetopic	ADJ	JJ	Degree=Pos	33	amod	_	_
33	approach	approach	NOUN	NN	Number=Sing	30	dobj	_	_
34	to	to	ADP	IN	_	33	prep	_	_
35	$ n $	$ n $	SYM	$	_	37	nummod	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	categories	category	NOUN	NNS	Number=Plur	34	pobj	_	_
38	expounded	expound	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	37	acl	_	_
39	by	by	ADP	IN	_	38	agent	_	_
40	Baez	Baez	PROPN	NNP	Number=Sing	39	pobj	_	SpaceAfter=No
41	,	,	PUNCT	,	PunctType=Comm	40	punct	_	_
42	Dolan	Dolan	PROPN	NNP	Number=Sing	40	conj	_	_
43	and	and	CCONJ	CC	ConjType=Cmp	42	cc	_	_
44	others	other	NOUN	NNS	Number=Plur	42	conj	_	SpaceAfter=No
45	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
46	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
47	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	28	conj	_	_
48	a	a	DET	DT	Definite=Ind|PronType=Art	50	det	_	_
49	natural	natural	ADJ	JJ	Degree=Pos	50	amod	_	_
50	language	language	NOUN	NN	Number=Sing	47	attr	_	_
51	in	in	ADP	IN	_	54	prep	_	_
52	which	which	PRON	WDT	_	51	pobj	_	_
53	to	to	PART	TO	_	54	aux	_	_
54	discuss	discuss	VERB	VB	VerbForm=Inf	50	relcl	_	_
55	enrichment	enrichment	NOUN	NN	Number=Sing	54	dobj	_	_
56	of	of	ADP	IN	_	55	prep	_	_
57	categorical	categorical	ADJ	JJ	Degree=Pos	58	amod	_	_
58	structures	structure	NOUN	NNS	Number=Plur	56	pobj	_	SpaceAfter=No
59	.	.	PUNCT	.	PunctType=Peri	28	punct	_	SpaceAfter=No

# doc_id = 186
# sent_id = 1
# text = This paper displays an approach to the construction of the homotopy theory of simplicial sets and the corresponding equivalence with the homotopy theory of topological spaces which is based on simplicial approximation techniques.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	displays	display	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	approach	approach	NOUN	NN	Number=Sing	3	dobj	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	construction	construction	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	homotopy	homotopy	NOUN	NN	Number=Sing	12	compound	_	_
12	theory	theory	NOUN	NN	Number=Sing	9	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	simplicial	simplicial	ADJ	JJ	Degree=Pos	15	amod	_	_
15	sets	set	NOUN	NNS	Number=Plur	13	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	corresponding	corresponding	ADJ	JJ	Degree=Pos	19	amod	_	_
19	equivalence	equivalence	NOUN	NN	Number=Sing	8	conj	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	homotopy	homotopy	NOUN	NN	Number=Sing	23	compound	_	_
23	theory	theory	NOUN	NN	Number=Sing	20	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	topological	topological	ADJ	JJ	Degree=Pos	26	amod	_	_
26	spaces	space	NOUN	NNS	Number=Plur	24	pobj	_	_
27	which	which	PRON	WDT	_	29	nsubjpass	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	auxpass	_	_
29	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	relcl	_	_
30	on	on	ADP	IN	_	29	prep	_	_
31	simplicial	simplicial	ADJ	JJ	Degree=Pos	33	amod	_	_
32	approximation	approximation	NOUN	NN	Number=Sing	33	compound	_	_
33	techniques	technique	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = The required simplicial approximation results for simplicial sets and their proofs are given in full.
1	The	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
2	required	require	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	amod	_	_
3	simplicial	simplicial	ADJ	JJ	Degree=Pos	5	amod	_	_
4	approximation	approximation	NOUN	NN	Number=Sing	5	compound	_	_
5	results	result	NOUN	NNS	Number=Plur	13	nsubjpass	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	simplicial	simplicial	ADJ	JJ	Degree=Pos	8	amod	_	_
8	sets	set	NOUN	NNS	Number=Plur	6	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
10	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	11	poss	_	_
11	proofs	proof	NOUN	NNS	Number=Plur	13	nsubjpass	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	full	full	ADJ	JJ	Degree=Pos	14	amod	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 3
# text = Subdivision behaves like a covering in the context of the techniques displayed here.
1	Subdivision	subdivision	NOUN	NN	Number=Sing	2	nsubj	_	_
2	behaves	behave	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	like	like	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	covering	covering	NOUN	NN	Number=Sing	3	pobj	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	context	context	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	techniques	technique	NOUN	NNS	Number=Plur	9	pobj	_	_
12	displayed	display	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acl	_	_
13	here	here	ADV	RB	PronType=Dem	12	advmod	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 187
# sent_id = 1
# text = This article treats the problem of deriving the reflector of a semi - abelian category $ cal A $ onto a Birkhoff subcategory $ cal B $ of $ cal A $ .
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	article	article	NOUN	NN	Number=Sing	3	nsubj	_	_
3	treats	treat	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	problem	problem	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	deriving	derive	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	pcomp	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	reflector	reflector	NOUN	NN	Number=Sing	7	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
12	semi	semi	ADJ	JJ	Degree=Pos	15	amod	_	_
13	-	-	ADJ	JJ	Degree=Pos	15	amod	_	_
14	abelian	abelian	ADJ	JJ	Degree=Pos	15	amod	_	_
15	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
16	$ cal A $	$ cal a $	SYM	$	_	15	appos	_	_
17	onto	onto	ADP	IN	_	7	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	Birkhoff	Birkhoff	PROPN	NNP	Number=Sing	20	compound	_	_
20	subcategory	subcategory	ADJ	JJ	Degree=Pos	17	pobj	_	_
21	$ cal B $	$ cal b $	SYM	$	_	3	dep	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	$ cal A $	$ cal a $	SYM	$	_	22	pobj	_	_
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = Basing ourselves on Carrasco, Cegarra and Grandjean's homology theory for crossed modules, we establish a connection between our theory of Baer invariants with a generalization—to semi - abelian categories—of Barr and Beck's cotriple homology theory.
1	Basing	base	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	advcl	_	_
2	ourselves	ourselves	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs|Reflex=Yes	1	dobj	_	_
3	on	on	ADP	IN	_	1	prep	_	_
4	Carrasco	Carrasco	PROPN	NNP	Number=Sing	3	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
6	Cegarra	Cegarra	PROPN	NNP	Number=Sing	4	conj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	Grandjean	Grandjean	PROPN	NNP	Number=Sing	11	poss	_	SpaceAfter=No
9	's	's	PART	POS	_	8	case	_	_
10	homology	homology	NOUN	NN	Number=Sing	11	compound	_	_
11	theory	theory	NOUN	NN	Number=Sing	6	conj	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	crossed	crossed	ADJ	JJ	Degree=Pos	14	amod	_	_
14	modules	module	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
16	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	17	nsubj	_	_
17	establish	establish	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	connection	connection	NOUN	NN	Number=Sing	17	dobj	_	_
20	between	between	ADP	IN	_	19	prep	_	_
21	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	22	poss	_	_
22	theory	theory	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	Baer	Baer	PROPN	NNP	Number=Sing	25	compound	_	_
25	invariants	invariant	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	pobj	_	_
26	with	with	ADP	IN	_	25	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	generalization	generalization	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
29	—	—	PUNCT	:	_	28	punct	_	SpaceAfter=No
30	to	to	ADP	IN	_	28	prep	_	_
31	semi	semi	ADJ	JJ	Degree=Pos	34	amod	_	_
32	-	-	ADJ	JJ	Degree=Pos	34	punct	_	_
33	abelian	abelian	ADJ	JJ	Degree=Pos	34	amod	_	_
34	categories	category	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
35	—	—	PUNCT	:	_	34	punct	_	SpaceAfter=No
36	of	of	ADP	IN	_	34	prep	_	_
37	Barr	Barr	PROPN	NNP	Number=Sing	36	pobj	_	_
38	and	and	CCONJ	CC	ConjType=Cmp	37	cc	_	_
39	Beck	Beck	PROPN	NNP	Number=Sing	43	poss	_	SpaceAfter=No
40	's	's	PART	POS	_	39	case	_	_
41	cotriple	cotriple	NOUN	NN	Number=Sing	42	compound	_	_
42	homology	homology	NOUN	NN	Number=Sing	43	compound	_	_
43	theory	theory	NOUN	NN	Number=Sing	37	conj	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 3
# text = This results in a semi - abelian version of Hopf's formula and the Stallings - Stammbach sequence from group homology.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	results	result	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
5	semi	semi	ADJ	JJ	Degree=Pos	7	amod	_	_
6	-	-	ADJ	JJ	Degree=Pos	7	punct	_	_
7	abelian	abelian	ADJ	JJ	Degree=Pos	8	amod	_	_
8	version	version	NOUN	NN	Number=Sing	3	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Hopf	Hopf	PROPN	NNP	Number=Sing	12	poss	_	SpaceAfter=No
11	's	's	PART	POS	_	10	case	_	_
12	formula	formula	NOUN	NN	Number=Sing	9	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
15	Stallings	Stallings	PROPN	NNP	Number=Sing	17	compound	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	Stammbach	Stammbach	PROPN	NNP	Number=Sing	18	compound	_	_
18	sequence	sequence	NOUN	NN	Number=Sing	12	conj	_	_
19	from	from	ADP	IN	_	18	prep	_	_
20	group	group	NOUN	NN	Number=Sing	21	compound	_	_
21	homology	homology	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 188
# sent_id = 1
# text = Extending the work of Fröhlich, Lue and Furtado - Coelho, we consider the theory of Baer invariants in the context of semi - abelian categories.
1	Extending	extend	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	advcl	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	work	work	NOUN	NN	Number=Sing	1	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	Fröhlich	Fröhlich	PROPN	NNP	Number=Sing	4	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	Lue	Lue	PROPN	NNP	Number=Sing	5	conj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	Furtado	Furtado	PROPN	NNP	Number=Sing	11	compound	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	Coelho	Coelho	PROPN	NNP	Number=Sing	7	conj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	theory	theory	NOUN	NN	Number=Sing	14	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	Baer	Baer	PROPN	NNP	Number=Sing	19	compound	_	_
19	invariants	invariant	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	pobj	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	context	context	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	semi	semi	ADJ	JJ	Degree=Pos	27	amod	_	_
25	-	-	ADJ	JJ	Degree=Pos	27	amod	_	_
26	abelian	abelian	ADJ	JJ	Degree=Pos	27	amod	_	_
27	categories	category	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 2
# text = Several exact sequences, relative to a subfunctor of the identity functor, are obtained.
1	Several	several	ADJ	JJ	Degree=Pos	3	amod	_	_
2	exact	exact	ADJ	JJ	Degree=Pos	3	amod	_	_
3	sequences	sequence	NOUN	NNS	Number=Plur	15	nsubjpass	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	relative	relative	ADJ	JJ	Degree=Pos	3	amod	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	subfunctor	subfunctor	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	identity	identity	NOUN	NN	Number=Sing	12	compound	_	_
12	functor	functor	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 3
# text = We consider a notion of commutator which, in the case of abelianization, corresponds to Smith's.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	commutator	commutator	NOUN	NN	Number=Sing	5	pobj	_	_
7	which	which	PRON	WDT	_	15	nsubj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
9	in	in	ADP	IN	_	15	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	case	case	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	abelianization	abelianization	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
15	corresponds	correspond	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	relcl	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	Smith	Smith	PROPN	NNP	Number=Sing	16	pobj	_	SpaceAfter=No
18	's	's	PART	POS	_	17	case	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = The resulting notion of centrality fits into Janelidze and Kelly's theory of central extensions.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	amod	_	_
3	notion	notion	NOUN	NN	Number=Sing	6	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	centrality	centrality	NOUN	NN	Number=Sing	4	pobj	_	_
6	fits	fit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	into	into	ADP	IN	_	6	prep	_	_
8	Janelidze	Janelidze	PROPN	NNP	Number=Sing	7	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	Kelly	Kelly	PROPN	NNP	Number=Sing	12	poss	_	SpaceAfter=No
11	's	's	PART	POS	_	10	case	_	_
12	theory	theory	NOUN	NN	Number=Sing	8	conj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	central	central	ADJ	JJ	Degree=Pos	15	amod	_	_
15	extensions	extension	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = Finally we propose a notion of nilpotency, relative to a Birkhoff subcategory of a semi - abelian category.
1	Finally	finally	ADV	RB	_	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	propose	propose	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	notion	notion	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	nilpotency	nilpotency	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	relative	relative	ADJ	JJ	Degree=Pos	7	amod	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	Birkhoff	Birkhoff	PROPN	NNP	Number=Sing	13	compound	_	_
13	subcategory	subcategory	NOUN	NN	Number=Sing	10	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
16	semi	semi	ADJ	JJ	Degree=Pos	19	amod	_	_
17	-	-	ADJ	JJ	Degree=Pos	19	amod	_	_
18	abelian	abelian	ADJ	JJ	Degree=Pos	19	amod	_	_
19	category	category	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 189
# sent_id = 1
# text = It is shown that, for a finitely - complete category $ C $ with coequalizers of kernel pairs, if every product - regular epi is also stably - regular then there exist the reflections $ (R)Grphs(C) - - > (R)Rel(C) $ , from (reflexive) graphs into (reflexive) relations in $ C $ , and $ Cat(C) - - > Preord(C) $ , from categories into preorders in $ C $ .
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	SCONJ	IN	_	32	mark	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
6	for	for	ADP	IN	_	32	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	finitely	finitely	ADV	RB	_	10	advmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	complete	complete	ADJ	JJ	Degree=Pos	11	amod	_	_
11	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
12	$ C $	$ c $	SYM	$	_	6	dep	_	_
13	with	with	ADP	IN	_	6	prep	_	_
14	coequalizers	coequalizer	NOUN	NNS	Number=Plur	13	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	kernel	kernel	NOUN	NN	Number=Sing	17	compound	_	_
17	pairs	pair	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
19	if	if	SCONJ	IN	_	25	mark	_	_
20	every	every	DET	DT	_	24	det	_	_
21	product	product	NOUN	NN	Number=Sing	23	npadvmod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	regular	regular	ADJ	JJ	Degree=Pos	24	amod	_	_
24	epi	epi	NOUN	NN	Number=Sing	25	nsubj	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	32	advcl	_	_
26	also	also	ADV	RB	_	25	advmod	_	_
27	stably	stably	ADV	RB	_	29	advmod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	regular	regular	ADJ	JJ	Degree=Pos	25	acomp	_	_
30	then	then	ADV	RB	PronType=Dem	32	advmod	_	_
31	there	there	PRON	EX	_	32	expl	_	_
32	exist	exist	VERB	VBP	Tense=Pres|VerbForm=Fin	3	ccomp	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
34	reflections	reflection	NOUN	NNS	Number=Plur	32	dobj	_	_
35	$ (R)Grphs(C) - - > (R)Rel(C) $	$ (R)Grphs(C) - - > (R)Rel(C) $	PROPN	NNP	Number=Sing	34	appos	_	_
36	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
37	from	from	ADP	IN	_	32	prep	_	_
38	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	41	punct	_	SpaceAfter=No
39	reflexive	reflexive	ADJ	JJ	Degree=Pos	41	amod	_	SpaceAfter=No
40	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	41	punct	_	_
41	graphs	graph	NOUN	NNS	Number=Plur	37	pobj	_	_
42	into	into	ADP	IN	_	41	prep	_	_
43	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	46	punct	_	SpaceAfter=No
44	reflexive	reflexive	ADJ	JJ	Degree=Pos	46	amod	_	SpaceAfter=No
45	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	46	punct	_	_
46	relations	relation	NOUN	NNS	Number=Plur	42	pobj	_	_
47	in	in	ADP	IN	_	46	prep	_	_
48	$ C $	$ c $	SYM	$	_	47	pobj	_	_
49	,	,	PUNCT	,	PunctType=Comm	41	punct	_	_
50	and	and	CCONJ	CC	ConjType=Cmp	41	cc	_	_
51	$ Cat(C) - - > Preord(C) $	$ cat(c) - - > preord(c) $	SYM	$	_	41	conj	_	_
52	,	,	PUNCT	,	PunctType=Comm	41	punct	_	_
53	from	from	ADP	IN	_	37	prep	_	_
54	categories	category	NOUN	NNS	Number=Plur	53	pobj	_	_
55	into	into	ADP	IN	_	54	prep	_	_
56	preorders	preorder	NOUN	NNS	Number=Plur	55	pobj	_	_
57	in	in	ADP	IN	_	56	prep	_	_
58	$ C $	$ c $	SYM	$	_	57	pobj	_	_
59	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = Furthermore, such a sufficient condition ensures as well that these reflections do have stable units.
1	Furthermore	furthermore	ADV	RB	_	7	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
3	such	such	DET	PDT	_	6	predet	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	sufficient	sufficient	ADJ	JJ	Degree=Pos	6	amod	_	_
6	condition	condition	NOUN	NN	Number=Sing	7	nsubj	_	_
7	ensures	ensure	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	as	as	ADV	RB	_	9	advmod	_	_
9	well	well	ADV	RB	Degree=Pos	7	advmod	_	_
10	that	that	SCONJ	IN	_	14	mark	_	_
11	these	these	DET	DT	Number=Plur|PronType=Dem	12	det	_	_
12	reflections	reflection	NOUN	NNS	Number=Plur	14	nsubj	_	_
13	do	do	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	aux	_	_
14	have	have	VERB	VB	VerbForm=Inf	7	ccomp	_	_
15	stable	stable	ADJ	JJ	Degree=Pos	16	amod	_	_
16	units	unit	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = This last property is equivalent to the existence of a monotone - light factorization system, provided there are sufficiently many effective descent morphisms with domain in the respective full subcategory.
1	This	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
2	last	last	ADJ	JJ	Degree=Pos	3	amod	_	_
3	property	property	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	equivalent	equivalent	ADJ	JJ	Degree=Pos	4	acomp	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	existence	existence	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
11	monotone	monotone	NOUN	NN	Number=Sing	13	amod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	light	light	ADJ	JJ	Degree=Pos	15	amod	_	_
14	factorization	factorization	NOUN	NN	Number=Sing	15	compound	_	_
15	system	system	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
17	provided	provide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	prep	_	_
18	there	there	PRON	EX	_	19	expl	_	_
19	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	conj	_	_
20	sufficiently	sufficiently	ADV	RB	_	21	advmod	_	_
21	many	many	ADJ	JJ	Degree=Pos	24	amod	_	_
22	effective	effective	ADJ	JJ	Degree=Pos	24	amod	_	_
23	descent	descent	NOUN	NN	Number=Sing	24	compound	_	_
24	morphisms	morphism	NOUN	NNS	Number=Plur	19	attr	_	_
25	with	with	ADP	IN	_	19	prep	_	_
26	domain	domain	NOUN	NN	Number=Sing	25	pobj	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
29	respective	respective	ADJ	JJ	Degree=Pos	31	amod	_	_
30	full	full	ADJ	JJ	Degree=Pos	31	amod	_	_
31	subcategory	subcategory	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = In this way, we have internalized the monotone - light factorization for small categories via preordered sets, associated with the reflection $ Cat - - > Preord $ , which is now just the special case $ C = Set $ .
1	In	in	ADP	IN	_	7	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	way	way	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
6	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	aux	_	_
7	internalized	internalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
9	monotone	monotone	NOUN	NN	Number=Sing	11	amod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	light	light	ADJ	JJ	Degree=Pos	12	amod	_	_
12	factorization	factorization	NOUN	NN	Number=Sing	7	dobj	_	_
13	for	for	ADP	IN	_	12	prep	_	_
14	small	small	ADJ	JJ	Degree=Pos	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	_
16	via	via	ADP	IN	_	7	prep	_	_
17	preordered	preordere	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
18	sets	set	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
20	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	advcl	_	_
21	with	with	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	reflection	reflection	NOUN	NN	Number=Sing	21	pobj	_	_
24	$ Cat - - > Preord $	$ cat - - > preord $	SYM	$	_	20	npadvmod	_	_
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	which	which	PRON	WDT	_	27	nsubj	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	relcl	_	_
28	now	now	ADV	RB	_	27	advmod	_	_
29	just	just	ADV	RB	_	32	advmod	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	special	special	ADJ	JJ	Degree=Pos	32	amod	_	_
32	case	case	NOUN	NN	Number=Sing	27	attr	_	_
33	$ C = Set $	$ c = set $	SYM	$	_	27	attr	_	_
34	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 190
# sent_id = 1
# text = Two notions, generic morphisms and parametric representations, useful for the analysis of endofunctors arising in enumerative combinatorics, higher dimensional category theory, and logic, are defined and examined.
1	Two	two	NUM	CD	NumType=Card	2	nummod	_	_
2	notions	notion	NOUN	NNS	Number=Plur	30	nsubjpass	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
4	generic	generic	ADJ	JJ	Degree=Pos	5	amod	_	_
5	morphisms	morphism	NOUN	NNS	Number=Plur	2	conj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	parametric	parametric	ADJ	JJ	Degree=Pos	8	amod	_	_
8	representations	representation	NOUN	NNS	Number=Plur	5	conj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
10	useful	useful	ADJ	JJ	Degree=Pos	2	amod	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	analysis	analysis	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	endofunctors	endofunctor	NOUN	NNS	Number=Plur	14	pobj	_	_
16	arising	arise	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	acl	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	enumerative	enumerative	ADJ	JJ	Degree=Pos	19	amod	_	_
19	combinatorics	combinatoric	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
21	higher	high	ADJ	JJR	Degree=Cmp	24	amod	_	_
22	dimensional	dimensional	ADJ	JJ	Degree=Pos	24	amod	_	_
23	category	category	NOUN	NN	Number=Sing	24	compound	_	_
24	theory	theory	NOUN	NN	Number=Sing	2	appos	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
27	logic	logic	NOUN	NN	Number=Sing	24	conj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
29	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	30	auxpass	_	_
30	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
32	examined	examine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	30	conj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	30	punct	_	SpaceAfter=No

# sent_id = 2
# text = Applications to the Batanin approach to higher category theory, Joyal species and operads are provided.
1	Applications	application	NOUN	NNS	Number=Plur	16	nsubjpass	_	_
2	to	to	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	Batanin	Batanin	PROPN	NNP	Number=Sing	5	amod	_	_
5	approach	approach	NOUN	NN	Number=Sing	2	pobj	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	higher	high	ADJ	JJR	Degree=Cmp	9	amod	_	_
8	category	category	NOUN	NN	Number=Sing	9	compound	_	_
9	theory	theory	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
11	Joyal	joyal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	species	specie	NOUN	NNS	Number=Plur	16	nsubjpass	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	operads	operad	NOUN	NNS	Number=Plur	12	conj	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	16	auxpass	_	_
16	provided	provide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# doc_id = 191
# sent_id = 1
# text = The centre of a monoidal category is a braided monoidal category.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	centre	centre	NOUN	NN	Number=Sing	7	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	monoidal	monoidal	ADJ	JJ	Degree=Pos	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	3	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	braided	braid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
10	monoidal	monoidal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	category	category	NOUN	NN	Number=Sing	7	attr	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 2
# text = Monoidal categories are monoidal objects (or pseudomonoids) in the monoidal bicategory of categories.
1	Monoidal	monoidal	ADJ	JJ	Degree=Pos	2	amod	_	_
2	categories	category	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	monoidal	monoidal	ADJ	JJ	Degree=Pos	5	amod	_	_
5	objects	object	NOUN	NNS	Number=Plur	3	attr	_	_
6	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	5	punct	_	SpaceAfter=No
7	or	or	CCONJ	CC	ConjType=Cmp	5	cc	_	_
8	pseudomonoids	pseudomonoid	NOUN	NNS	Number=Plur	5	conj	_	SpaceAfter=No
9	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	5	punct	_	_
10	in	in	ADP	IN	_	3	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	monoidal	monoidal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	bicategory	bicategory	NOUN	NN	Number=Sing	10	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	categories	category	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = This paper provides a universal construction in a braided monoidal bicategory that produces a braided monoidal object from any monoidal object.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	universal	universal	ADJ	JJ	Degree=Pos	6	amod	_	_
6	construction	construction	NOUN	NN	Number=Sing	3	dobj	_	_
7	in	in	ADP	IN	_	3	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	braided	braid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
10	monoidal	monoidal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	bicategory	bicategory	NOUN	NN	Number=Sing	7	pobj	_	_
12	that	that	PRON	WDT	PronType=Rel	13	nsubj	_	_
13	produces	produce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	relcl	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	braided	braid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
16	monoidal	monoidal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	object	object	NOUN	NN	Number=Sing	13	dobj	_	_
18	from	from	ADP	IN	_	17	prep	_	_
19	any	any	DET	DT	_	21	det	_	_
20	monoidal	monoidal	ADJ	JJ	Degree=Pos	21	amod	_	_
21	object	object	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = Some properties and sufficient conditions for existence of the construction are examined.
1	Some	some	DET	DT	_	2	det	_	_
2	properties	property	NOUN	NNS	Number=Plur	12	nsubjpass	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	sufficient	sufficient	ADJ	JJ	Degree=Pos	5	amod	_	_
5	conditions	condition	NOUN	NNS	Number=Plur	2	conj	_	_
6	for	for	ADP	IN	_	2	prep	_	_
7	existence	existence	NOUN	NN	Number=Sing	6	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	construction	construction	NOUN	NN	Number=Sing	8	pobj	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	examined	examine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# doc_id = 192
# sent_id = 1
# text = In the early 1990's the authors proved that the full subcategory of `sup - lattices' determined by the constructively completely distributive (CCD) lattices is equivalent to the idempotent splitting completion of the bicategory of sets and relations.
1	In	in	ADP	IN	_	8	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	early	early	ADJ	JJ	Degree=Pos	4	amod	_	_
4	1990	1990	NUM	CD	NumType=Card	7	poss	_	SpaceAfter=No
5	's	's	PART	POS	_	4	case	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	authors	author	NOUN	NNS	Number=Plur	8	nsubj	_	_
8	proved	prove	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
9	that	that	SCONJ	IN	_	29	mark	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	full	full	ADJ	JJ	Degree=Pos	12	amod	_	_
12	subcategory	subcategory	NOUN	NN	Number=Sing	29	nsubj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	13	punct	_	SpaceAfter=No
15	sup	sup	NOUN	NN	Number=Sing	17	compound	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	lattices	lattice	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
18	'	'	PART	POS	_	17	case	_	_
19	determined	determine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
20	by	by	ADP	IN	_	19	agent	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
22	constructively	constructively	ADV	RB	_	23	advmod	_	_
23	completely	completely	ADV	RB	_	24	advmod	_	_
24	distributive	distributive	ADJ	JJ	Degree=Pos	28	amod	_	_
25	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	28	punct	_	SpaceAfter=No
26	CCD	CCD	PROPN	NNP	Number=Sing	28	nmod	_	SpaceAfter=No
27	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	28	punct	_	_
28	lattices	lattice	NOUN	NNS	Number=Plur	20	pobj	_	_
29	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	ccomp	_	_
30	equivalent	equivalent	ADJ	JJ	Degree=Pos	29	acomp	_	_
31	to	to	ADP	IN	_	30	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
33	idempotent	idempotent	ADJ	JJ	Degree=Pos	35	amod	_	_
34	splitting	splitting	NOUN	NN	Number=Sing	35	amod	_	_
35	completion	completion	NOUN	NN	Number=Sing	31	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	bicategory	bicategory	NOUN	NN	Number=Sing	36	pobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	sets	set	NOUN	NNS	Number=Plur	39	pobj	_	_
41	and	and	CCONJ	CC	ConjType=Cmp	40	cc	_	_
42	relations	relation	NOUN	NNS	Number=Plur	40	conj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = Having many corollaries, this was an extremely useful result.
1	Having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	advcl	_	_
2	many	many	ADJ	JJ	Degree=Pos	3	amod	_	_
3	corollaries	corollary	NOUN	NNS	Number=Plur	1	dobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	this	this	PRON	DT	Number=Sing|PronType=Dem	6	nsubj	_	_
6	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	0	ROOT	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	extremely	extremely	ADV	RB	_	9	advmod	_	_
9	useful	useful	ADJ	JJ	Degree=Pos	10	amod	_	_
10	result	result	NOUN	NN	Number=Sing	6	attr	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = Moreover, as the authors soon suspected, it specializes a much more general result.
1	Moreover	moreover	ADV	RB	_	10	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
3	as	as	SCONJ	IN	_	7	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	authors	author	NOUN	NNS	Number=Plur	7	nsubj	_	_
6	soon	soon	ADV	RB	_	7	advmod	_	_
7	suspected	suspect	VERB	VBD	Tense=Past|VerbForm=Fin	10	advcl	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
9	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	10	nsubj	_	_
10	specializes	specialize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
12	much	much	ADV	RB	_	13	advmod	_	_
13	more	more	ADJ	JJR	Degree=Cmp	15	amod	_	_
14	general	general	ADJ	JJ	Degree=Pos	15	amod	_	_
15	result	result	NOUN	NN	Number=Sing	10	dobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 4
# text = Let $ D $ be a monad on a category $ C $ in which idempotents split.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ D $	$ d $	SYM	$	_	3	nsubj	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	monad	monad	NOUN	NNS	Number=Plur	3	attr	_	_
6	on	on	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
9	$ C $	$ c $	SYM	$	_	8	appos	_	_
10	in	in	ADP	IN	_	13	prep	_	_
11	which	which	PRON	WDT	_	10	pobj	_	_
12	idempotents	idempotent	NOUN	NNS	Number=Plur	13	nsubj	_	_
13	split	split	VERB	VBP	Tense=Pres|VerbForm=Fin	9	relcl	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 5
# text = Write $ kar(C_D) $ for the idempotent splitting completion of the Kleisli category.
1	Write	write	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ kar(C_D) $	$ kar(c_d) $	SYM	$	_	1	dobj	_	_
3	for	for	ADP	IN	_	1	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	idempotent	idempotent	ADJ	JJ	Degree=Pos	7	amod	_	_
6	splitting	splitting	NOUN	NN	Number=Sing	7	amod	_	_
7	completion	completion	NOUN	NN	Number=Sing	3	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	Kleisli	Kleisli	PROPN	NNP	Number=Sing	11	compound	_	_
11	category	category	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 6
# text = Write $ spl(C^D) $ for the category whose objects are pairs $ ((L, s), t) $ , where $ (L, s) $ is an object of the Eilenberg - Moore category for $ D $ , and $ t $ is a homomorphism that splits $ s $ , with $ spl(C^D)(((L, s), t), ((L', s'), t'))=C^D((L, s)(L', s')) $ .
1	Write	write	VERB	VB	VerbForm=Inf	28	csubj	_	_
2	$ spl(C^D) $	$ spl(c^d) $	SYM	$	_	28	nsubj	_	_
3	for	for	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	3	pobj	_	_
6	whose	whose	DET	WP$	Poss=Yes	7	poss	_	_
7	objects	object	NOUN	NNS	Number=Plur	8	nsubj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	relcl	_	_
9	pairs	pair	NOUN	NNS	Number=Plur	8	attr	_	_
10	$ ((L, s), t) $	$ ((l, s), t) $	NUM	CD	NumType=Card	8	attr	_	_
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	where	where	SCONJ	WRB	_	14	advmod	_	_
13	$ (L, s) $	$ (l, s) $	SYM	$	_	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	relcl	_	_
15	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	object	object	NOUN	NN	Number=Sing	14	attr	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
19	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	Moore	Moore	PROPN	NNP	Number=Sing	22	compound	_	_
22	category	category	NOUN	NN	Number=Sing	17	pobj	_	_
23	for	for	ADP	IN	_	16	prep	_	_
24	$ D $	$ d $	SYM	$	_	23	pobj	_	_
25	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
27	$ t $	$ t $	SYM	$	_	10	appos	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
30	homomorphism	homomorphism	NOUN	NN	Number=Sing	28	attr	_	_
31	that	that	PRON	WDT	PronType=Rel	32	nsubj	_	_
32	splits	split	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	relcl	_	_
33	$ s $	$ s $	SYM	$	_	32	dobj	_	_
34	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
35	with	with	ADP	IN	_	32	prep	_	_
36	$ spl(C^D)(((L, s), t), ((L', s'), t'))=C^D((L, s)(L', s')) $	$ spl(c^d)(((l, s), t), ((l', s'), t'))=c^d((l, s)(l', s')) $	SYM	$	_	35	pobj	_	_
37	.	.	PUNCT	.	PunctType=Peri	28	punct	_	SpaceAfter=No

# sent_id = 7
# text = The main result is that $ kar(C_D) $ is isomorphic to $ spl(C^D) $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	result	result	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	7	mark	_	_
6	$ kar(C_D) $	$ kar(c_d) $	SYM	$	_	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
8	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	7	acomp	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	$ spl(C^D) $	$ spl(c^d) $	SYM	$	_	9	pobj	_	_
11	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 8
# text = We also show how this implies the CCD lattice characterization theorem and consider a more general context.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	how	how	SCONJ	WRB	_	6	advmod	_	_
5	this	this	PRON	DT	Number=Sing|PronType=Dem	6	nsubj	_	_
6	implies	imply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	CCD	CCD	PROPN	NNP	Number=Sing	9	compound	_	_
9	lattice	lattice	NOUN	NN	Number=Sing	10	compound	_	_
10	characterization	characterization	NOUN	NN	Number=Sing	11	nsubj	_	_
11	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	6	ccomp	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
13	consider	consider	VERB	VB	VerbForm=Inf	6	conj	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	more	more	ADV	RBR	Degree=Cmp	16	advmod	_	_
16	general	general	ADJ	JJ	Degree=Pos	17	amod	_	_
17	context	context	NOUN	NN	Number=Sing	13	dobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 193
# sent_id = 1
# text = Some unsolved problems about the classifying topos for Boolean algebras, as well as about the axiomatic arithmetic of finite combinatorial toposes, are closely connected with some simple distinctions between finite automata.
1	Some	some	DET	DT	_	3	det	_	_
2	unsolved	unsolved	ADJ	JJ	Degree=Pos	3	amod	_	_
3	problems	problem	NOUN	NNS	Number=Plur	26	nsubjpass	_	_
4	about	about	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	classifying	classify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	amod	_	_
7	topos	topos	NOUN	NN	Number=Sing	4	pobj	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	Boolean	Boolean	PROPN	NNP	Number=Sing	10	amod	_	_
10	algebras	algebra	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
12	as	as	ADV	RB	_	14	advmod	_	_
13	well	well	ADV	RB	Degree=Pos	14	advmod	_	_
14	as	as	ADP	IN	_	3	cc	_	_
15	about	about	ADP	IN	_	3	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	axiomatic	axiomatic	ADJ	JJ	Degree=Pos	18	amod	_	_
18	arithmetic	arithmetic	NOUN	NN	Number=Sing	15	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	finite	finite	ADJ	JJ	Degree=Pos	22	amod	_	_
21	combinatorial	combinatorial	PROPN	NNP	Number=Sing	22	compound	_	_
22	toposes	topos	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
24	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	26	auxpass	_	_
25	closely	closely	ADV	RB	_	26	advmod	_	_
26	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
27	with	with	ADP	IN	_	26	prep	_	_
28	some	some	DET	DT	_	30	det	_	_
29	simple	simple	ADJ	JJ	Degree=Pos	30	amod	_	_
30	distinctions	distinction	NOUN	NNS	Number=Plur	27	pobj	_	_
31	between	between	ADP	IN	_	30	prep	_	_
32	finite	finite	PROPN	NNP	Number=Sing	33	compound	_	_
33	automata	automata	PROPN	NNP	Number=Sing	31	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	26	punct	_	SpaceAfter=No

# doc_id = 194
# sent_id = 1
# text = We show that every small category enriched over $ Sl $ —the symmetric monoidal closed category of sup - lattices and sup - preserving morphisms—is Morita equivalent to an $ Sl $ - monoid.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	26	ccomp	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	every	every	DET	DT	_	6	det	_	_
5	small	small	ADJ	JJ	Degree=Pos	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	7	nsubj	_	_
7	enriched	enrich	VERB	VBD	Tense=Past|VerbForm=Fin	14	ccomp	_	_
8	over	over	ADP	IN	_	7	prep	_	_
9	$ Sl $	$ sl $	SYM	$	_	8	pobj	_	_
10	—	—	PUNCT	:	_	14	punct	_	SpaceAfter=No
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	symmetric	symmetric	ADJ	JJ	Degree=Pos	13	amod	_	_
13	monoidal	monoidal	NOUN	NN	Number=Sing	14	nsubj	_	_
14	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	2	ccomp	_	_
15	category	category	NOUN	NN	Number=Sing	14	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	sup	sup	NOUN	NN	Number=Sing	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	lattices	lattice	NOUN	NNS	Number=Plur	16	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	sup	sup	NOUN	NN	Number=Sing	23	npadvmod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	24	amod	_	_
24	morphisms	morphism	NOUN	NNS	Number=Plur	19	conj	_	SpaceAfter=No
25	—	—	PUNCT	:	_	26	punct	_	SpaceAfter=No
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
27	Morita	Morita	PROPN	NNP	Number=Sing	28	compound	_	_
28	equivalent	equivalent	ADJ	JJ	Degree=Pos	26	attr	_	_
29	to	to	ADP	IN	_	28	prep	_	_
30	an	an	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
31	$ Sl $	$ sl $	SYM	$	_	33	compound	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	monoid	monoid	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	26	punct	_	SpaceAfter=No

# sent_id = 2
# text = As a corollary, we obtain a result of Borceux and Vitale asserting that every separable $ Sl $ - category is Morita equivalent to a separable $ Sl $ - monoid.
1	As	as	ADP	IN	_	6	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	corollary	corollary	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	result	result	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Borceux	Borceux	PROPN	NNP	Number=Sing	13	nsubj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	Vitale	Vitale	PROPN	NNP	Number=Sing	10	conj	_	_
13	asserting	assert	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	pcomp	_	_
14	that	that	SCONJ	IN	_	20	mark	_	_
15	every	every	DET	DT	_	19	det	_	_
16	separable	separable	ADJ	JJ	Degree=Pos	19	amod	_	_
17	$ Sl $	$ sl $	SYM	$	_	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	category	category	NOUN	NN	Number=Sing	20	nsubj	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
21	Morita	Morita	PROPN	NNP	Number=Sing	22	compound	_	_
22	equivalent	equivalent	ADJ	JJ	Degree=Pos	20	acomp	_	_
23	to	to	ADP	IN	_	22	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
25	separable	separable	ADJ	JJ	Degree=Pos	28	amod	_	_
26	$ Sl $	$ sl $	SYM	$	_	28	compound	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	monoid	monoid	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 195
# sent_id = 1
# text = A PROP is a way of encoding structure borne by an object of a symmetric monoidal category.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	PROP	prop	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	way	way	NOUN	NN	Number=Sing	3	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	encoding	encode	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	pcomp	_	_
8	structure	structure	NOUN	NN	Number=Sing	7	dobj	_	_
9	borne	bear	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	by	by	ADP	IN	_	9	agent	_	_
11	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	object	object	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	symmetric	symmetric	ADJ	JJ	Degree=Pos	17	amod	_	_
16	monoidal	monoidal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	category	category	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = We describe a notion of distributive law for PROPs, based on Beck's distributive laws for monads.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	distributive	distributive	ADJ	JJ	Degree=Pos	7	amod	_	_
7	law	law	NOUN	NN	Number=Sing	5	pobj	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	PROPs	prop	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
11	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	acl	_	_
12	on	on	ADP	IN	_	11	prep	_	_
13	Beck	Beck	PROPN	NNP	Number=Sing	16	poss	_	SpaceAfter=No
14	's	's	PART	POS	_	13	case	_	_
15	distributive	distributive	ADJ	JJ	Degree=Pos	16	amod	_	_
16	laws	law	NOUN	NNS	Number=Plur	12	pobj	_	_
17	for	for	ADP	IN	_	16	prep	_	_
18	monads	monad	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = A distributive law between PROPs allows them to be composed, and an algebra for the composite PROP consists of a single object with an algebra structure for each of the original PROPs, subject to compatibility conditions encoded by the distributive law.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	distributive	distributive	ADJ	JJ	Degree=Pos	3	amod	_	_
3	law	law	NOUN	NN	Number=Sing	6	nsubj	_	_
4	between	between	ADP	IN	_	3	prep	_	_
5	PROPs	prop	NOUN	NNS	Number=Plur	4	pobj	_	_
6	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	10	nsubjpass	_	_
8	to	to	PART	TO	_	10	aux	_	_
9	be	be	AUX	VB	VerbForm=Inf	10	auxpass	_	_
10	composed	compose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	ccomp	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	algebra	algebra	NOUN	NN	Number=Sing	19	nsubj	_	_
15	for	for	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	composite	composite	ADJ	JJ	Degree=Pos	18	amod	_	_
18	PROP	prop	NOUN	NN	Number=Sing	15	pobj	_	_
19	consists	consist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	conj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	single	single	ADJ	JJ	Degree=Pos	23	amod	_	_
23	object	object	NOUN	NN	Number=Sing	20	pobj	_	_
24	with	with	ADP	IN	_	23	prep	_	_
25	an	an	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
26	algebra	algebra	NOUN	NN	Number=Sing	27	compound	_	_
27	structure	structure	NOUN	NN	Number=Sing	24	pobj	_	_
28	for	for	ADP	IN	_	27	prep	_	_
29	each	each	PRON	DT	_	28	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	original	original	ADJ	JJ	Degree=Pos	33	amod	_	_
33	PROPs	prop	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
35	subject	subject	ADJ	JJ	Degree=Pos	27	amod	_	_
36	to	to	ADP	IN	_	35	prep	_	_
37	compatibility	compatibility	NOUN	NN	Number=Sing	38	compound	_	_
38	conditions	condition	NOUN	NNS	Number=Plur	36	pobj	_	_
39	encoded	encode	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	38	acl	_	_
40	by	by	ADP	IN	_	39	agent	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
42	distributive	distributive	ADJ	JJ	Degree=Pos	43	amod	_	_
43	law	law	NOUN	NN	Number=Sing	40	pobj	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = An example is the PROP for bialgebras, which is a composite of the PROP for coalgebras and that for algebras.
1	An	an	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	example	example	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	PROP	prop	NOUN	NN	Number=Sing	3	attr	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	bialgebras	bialgebra	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	which	which	PRON	WDT	_	10	nsubj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	relcl	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	composite	composite	NOUN	NN	Number=Sing	10	attr	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	PROP	prop	NOUN	NN	Number=Sing	13	pobj	_	_
16	for	for	ADP	IN	_	15	prep	_	_
17	coalgebras	coalgebra	NOUN	NNS	Number=Plur	16	pobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
19	that	that	SCONJ	IN	_	10	conj	_	_
20	for	for	ADP	IN	_	19	prep	_	_
21	algebras	algebra	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 196
# sent_id = 1
# text = We show, for a monad $ T $ , that coalgebra structures on a $ T $ - algebra can be described in terms of "braidings", provided that the monad is equipped with an invertible distributive law satisfying the Yang - Baxter equation.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
4	for	for	ADP	IN	_	2	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	monad	monad	NOUN	NNS	Number=Plur	4	pobj	_	_
7	$ T $	$ t $	SYM	$	_	6	appos	_	_
8	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
9	that	that	SCONJ	IN	_	19	mark	_	_
10	coalgebra	coalgebra	NOUN	NNS	Number=Plur	11	compound	_	_
11	structures	structure	NOUN	NNS	Number=Plur	19	nsubjpass	_	_
12	on	on	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
14	$ T $	$ t $	SYM	$	_	16	compound	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	algebra	algebra	PROPN	NNP	Number=Sing	12	pobj	_	_
17	can	can	AUX	MD	VerbForm=Fin	19	aux	_	_
18	be	be	AUX	VB	VerbForm=Inf	19	auxpass	_	_
19	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	terms	term	NOUN	NNS	Number=Plur	20	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	24	punct	_	SpaceAfter=No
24	braidings	braiding	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	24	punct	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
27	provided	provide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	prep	_	_
28	that	that	SCONJ	IN	_	32	mark	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	monad	monad	NOUN	NNS	Number=Plur	32	nsubjpass	_	_
31	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	32	auxpass	_	_
32	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	ccomp	_	_
33	with	with	ADP	IN	_	32	prep	_	_
34	an	an	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
35	invertible	invertible	ADJ	JJ	Degree=Pos	37	amod	_	_
36	distributive	distributive	ADJ	JJ	Degree=Pos	37	amod	_	_
37	law	law	NOUN	NN	Number=Sing	33	pobj	_	_
38	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	37	acl	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
40	Yang	Yang	PROPN	NNP	Number=Sing	42	compound	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	Baxter	Baxter	PROPN	NNP	Number=Sing	43	compound	_	_
43	equation	equation	NOUN	NN	Number=Sing	38	dobj	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 197
# sent_id = 1
# text = Cubical sets have a directed homology, studied in a previous paper and consisting of preordered abelian groups, with a positive cone generated by the structural cubes.
1	Cubical	cubical	ADJ	JJ	Degree=Pos	2	amod	_	_
2	sets	set	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	amod	_	_
6	homology	homology	NOUN	NN	Number=Sing	3	dobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	studied	study	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	previous	previous	ADJ	JJ	Degree=Pos	12	amod	_	_
12	paper	paper	NOUN	NN	Number=Sing	9	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
14	consisting	consist	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	conj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	preordered	preordere	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
17	abelian	abelian	ADJ	JJ	Degree=Pos	18	compound	_	_
18	groups	group	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
20	with	with	ADP	IN	_	3	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	positive	positive	ADJ	JJ	Degree=Pos	23	amod	_	_
23	cone	cone	NOUN	NN	Number=Sing	20	pobj	_	_
24	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	acl	_	_
25	by	by	ADP	IN	_	24	agent	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	structural	structural	ADJ	JJ	Degree=Pos	28	amod	_	_
28	cubes	cube	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = By this additional information, cubical sets can provide a sort of `noncommutative topology', agreeing with some results of noncommutative geometry but lacking the metric aspects of $ C* $ - algebras.
1	By	by	ADP	IN	_	9	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
3	additional	additional	ADJ	JJ	Degree=Pos	4	amod	_	_
4	information	information	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
6	cubical	cubical	ADJ	JJ	Degree=Pos	7	amod	_	_
7	sets	set	NOUN	NNS	Number=Plur	9	nsubj	_	_
8	can	can	AUX	MD	VerbForm=Fin	9	aux	_	_
9	provide	provide	VERB	VB	VerbForm=Inf	0	ROOT	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	sort	sort	NOUN	NN	Number=Sing	9	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	12	punct	_	SpaceAfter=No
14	noncommutative	noncommutative	ADJ	JJ	Degree=Pos	15	amod	_	_
15	topology	topology	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	9	punct	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
18	agreeing	agree	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	advcl	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	some	some	DET	DT	_	21	det	_	_
21	results	result	NOUN	NNS	Number=Plur	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	noncommutative	noncommutative	ADJ	JJ	Degree=Pos	24	amod	_	_
24	geometry	geometry	NOUN	NN	Number=Sing	22	pobj	_	_
25	but	but	CCONJ	CC	ConjType=Cmp	18	cc	_	_
26	lacking	lack	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	18	conj	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	metric	metric	ADJ	JJ	Degree=Pos	29	amod	_	_
29	aspects	aspect	NOUN	NNS	Number=Plur	26	dobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	$ C* $	$ c* $	SYM	$	_	30	pobj	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	algebras	algebra	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 3
# text = Here, we make such similarity stricter by introducing normed cubical sets and their normed directed homology, formed of normed preordered abelian groups.
1	Here	here	ADV	RB	PronType=Dem	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	make	make	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	such	such	ADJ	JJ	Degree=Pos	7	amod	_	_
6	similarity	similarity	NOUN	NN	Number=Sing	7	compound	_	_
7	stricter	strict	ADJ	JJR	Degree=Cmp	4	dobj	_	_
8	by	by	ADP	IN	_	4	prep	_	_
9	introducing	introduce	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	pcomp	_	_
10	normed	normed	ADJ	JJ	Degree=Pos	12	amod	_	_
11	cubical	cubical	ADJ	JJ	Degree=Pos	12	amod	_	_
12	sets	set	NOUN	NNS	Number=Plur	9	dobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	17	poss	_	_
15	normed	normed	ADJ	JJ	Degree=Pos	17	amod	_	_
16	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	homology	homology	NOUN	NN	Number=Sing	12	conj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	formed	form	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	normed	normed	PROPN	NNP	Number=Sing	24	amod	_	_
22	preordered	preordere	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
23	abelian	abelian	ADJ	JJ	Degree=Pos	24	compound	_	_
24	groups	group	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = The normed cubical sets $ NC_theta $ associated with `irrational' rotations have thus the same classification up to isomorphism as the well - known irrational rotation $ C* $ - algebras $ A_theta $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	normed	normed	ADJ	JJ	Degree=Pos	4	amod	_	_
3	cubical	cubical	ADJ	JJ	Degree=Pos	4	amod	_	_
4	sets	set	NOUN	NNS	Number=Plur	12	nsubj	_	_
5	$ NC_theta $	$ nc_theta $	SYM	$	_	4	appos	_	_
6	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	acl	_	_
7	with	with	ADP	IN	_	6	prep	_	_
8	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	11	punct	_	SpaceAfter=No
9	irrational	irrational	ADJ	JJ	Degree=Pos	11	amod	_	SpaceAfter=No
10	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	11	punct	_	_
11	rotations	rotation	NOUN	NNS	Number=Plur	7	pobj	_	_
12	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	thus	thus	ADV	RB	_	16	advmod	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	same	same	ADJ	JJ	Degree=Pos	16	amod	_	_
16	classification	classification	NOUN	NN	Number=Sing	12	dobj	_	_
17	up	up	ADP	IN	_	16	prep	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	isomorphism	isomorphism	NOUN	NN	Number=Sing	18	pobj	_	_
20	as	as	ADP	IN	_	16	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
22	well	well	ADV	RB	Degree=Pos	24	advmod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
25	irrational	irrational	ADJ	JJ	Degree=Pos	26	amod	_	_
26	rotation	rotation	NOUN	NN	Number=Sing	20	pobj	_	_
27	$ C* $	$ c* $	SYM	$	_	29	dep	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	algebras	algebras	PROPN	NNP	Number=Sing	26	appos	_	_
30	$ A_theta $	$ a_theta $	SYM	$	_	29	appos	_	_
31	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# doc_id = 198
# sent_id = 1
# text = We characterize semi - abelian monadic categories and their localizations.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	semi	semi	ADJ	JJ	Degree=Pos	7	amod	_	_
4	-	-	ADV	RB	_	7	amod	_	_
5	abelian	abelian	ADJ	JJ	Degree=Pos	7	amod	_	_
6	monadic	monadic	ADJ	JJ	Degree=Pos	7	amod	_	_
7	categories	category	NOUN	NNS	Number=Plur	2	dobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	10	poss	_	_
10	localizations	localization	NOUN	NNS	Number=Plur	7	conj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = These results are then used to obtain a characterization of pointed protomodular quasimonadic categories, and in particular of protomodular quasivarieties.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	results	result	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
4	then	then	ADV	RB	PronType=Dem	5	advmod	_	_
5	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	obtain	obtain	VERB	VB	VerbForm=Inf	5	xcomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	characterization	characterization	NOUN	NN	Number=Sing	7	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	pointed	pointed	ADJ	JJ	Degree=Pos	14	amod	_	_
12	protomodular	protomodular	ADJ	JJ	Degree=Pos	14	amod	_	_
13	quasimonadic	quasimonadic	ADJ	JJ	Degree=Pos	14	amod	_	_
14	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
17	in	in	ADP	IN	_	5	prep	_	_
18	particular	particular	ADJ	JJ	Degree=Pos	17	amod	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	protomodular	protomodular	ADJ	JJ	Degree=Pos	21	amod	_	_
21	quasivarieties	quasivarietie	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 199
# sent_id = 1
# text = A pregroup is a partially ordered monoid in which every element has a left and a right adjoint.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	pregroup	pregroup	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	partially	partially	ADV	RB	_	6	advmod	_	_
6	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
7	monoid	monoid	NOUN	NN	Number=Sing	3	attr	_	_
8	in	in	ADP	IN	_	12	prep	_	_
9	which	which	PRON	WDT	_	8	pobj	_	_
10	every	every	DET	DT	_	11	det	_	_
11	element	element	NOUN	NN	Number=Sing	12	nsubj	_	_
12	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	relcl	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	left	left	NOUN	NN	Number=Sing	12	dobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	right	right	ADJ	JJ	Degree=Pos	18	amod	_	_
18	adjoint	adjoint	NOUN	NN	Number=Sing	14	conj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = The main result is that for some well - behaved subgroups of the group of diffeomorphisms of the real numbers, the set of all endofunctions of the integers that are asymptotic at $ pminfty $ to (the restriction to the integers of) a function in the subgroup is a pregroup.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	result	result	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	49	mark	_	_
6	for	for	ADP	IN	_	49	prep	_	_
7	some	some	DET	DT	_	11	det	_	_
8	well	well	ADV	RB	Degree=Pos	10	advmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	behaved	behave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
11	subgroups	subgroup	NOUN	NNS	Number=Plur	6	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	group	group	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	diffeomorphisms	diffeomorphism	NOUN	NNS	Number=Plur	15	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	real	real	ADJ	JJ	Degree=Pos	20	amod	_	_
20	numbers	number	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	49	punct	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	set	set	NOUN	NN	Number=Sing	49	nsubj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	all	all	DET	DT	_	26	det	_	_
26	endofunctions	endofunction	NOUN	NNS	Number=Plur	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	integers	integer	NOUN	NNS	Number=Plur	27	pobj	_	_
30	that	that	PRON	WDT	PronType=Rel	31	nsubj	_	_
31	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	29	relcl	_	_
32	asymptotic	asymptotic	ADJ	JJ	Degree=Pos	31	acomp	_	_
33	at	at	ADP	IN	_	31	prep	_	_
34	$ pminfty $	$ pminfty $	SYM	$	_	33	pobj	_	_
35	to	to	PART	TO	_	23	prep	_	_
36	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	38	punct	_	SpaceAfter=No
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	restriction	restriction	NOUN	NN	Number=Sing	35	pobj	_	_
39	to	to	ADP	IN	_	38	prep	_	_
40	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
41	integers	integer	NOUN	NNS	Number=Plur	39	pobj	_	_
42	of	of	ADP	IN	_	41	prep	_	SpaceAfter=No
43	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	42	punct	_	_
44	a	a	DET	DT	Definite=Ind|PronType=Art	45	det	_	_
45	function	function	NOUN	NN	Number=Sing	23	appos	_	_
46	in	in	ADP	IN	_	45	prep	_	_
47	the	the	DET	DT	Definite=Def|PronType=Art	48	det	_	_
48	subgroup	subgroup	NOUN	NN	Number=Sing	46	pobj	_	_
49	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
50	a	a	DET	DT	Definite=Ind|PronType=Art	51	det	_	_
51	pregroup	pregroup	NOUN	NN	Number=Sing	49	attr	_	SpaceAfter=No
52	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 200
# sent_id = 1
# text = In this paper we introduce and study the categorical group of derivations, $ Der(G, A) $ , from a categorical group $ G $ into a braided categorical group $ (A, c) $ equipped with a given coherent left action of $ G $ .
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	study	study	VERB	VB	VerbForm=Inf	5	conj	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	categorical	categorical	ADJ	JJ	Degree=Pos	10	amod	_	_
10	group	group	NOUN	NN	Number=Sing	7	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	derivations	derivation	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
14	$ Der(G, A) $	$ der(g, a) $	SYM	$	_	7	dobj	_	_
15	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
16	from	from	ADP	IN	_	7	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	categorical	categorical	ADJ	JJ	Degree=Pos	19	amod	_	_
19	group	group	NOUN	NN	Number=Sing	16	pobj	_	_
20	$ G $	$ g $	SYM	$	_	16	dep	_	_
21	into	into	ADP	IN	_	7	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
23	braided	braid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	amod	_	_
24	categorical	categorical	ADJ	JJ	Degree=Pos	25	amod	_	_
25	group	group	NOUN	NN	Number=Sing	21	pobj	_	_
26	$ (A, c) $	$ (a, c) $	SYM	$	_	27	nsubj	_	_
27	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	conj	_	_
28	with	with	ADP	IN	_	27	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
30	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	amod	_	_
31	coherent	coherent	ADJ	JJ	Degree=Pos	33	amod	_	_
32	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	amod	_	_
33	action	action	NOUN	NN	Number=Sing	28	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	$ G $	$ g $	SYM	$	_	34	pobj	_	_
36	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = Categorical groups provide a 2 - dimensional vision of groups and so this object is a sort of 0 - cohomology at a higher level for categorical groups.
1	Categorical	categorical	ADJ	JJ	Degree=Pos	2	amod	_	_
2	groups	group	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
5	2	2	NUM	CD	NumType=Card	7	advmod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	dimensional	dimensional	ADJ	JJ	Degree=Pos	8	amod	_	_
8	vision	vision	NOUN	NN	Number=Sing	3	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	groups	group	NOUN	NNS	Number=Plur	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
12	so	so	ADV	RB	_	15	advmod	_	_
13	this	this	DET	DT	Number=Sing|PronType=Dem	14	det	_	_
14	object	object	NOUN	NN	Number=Sing	15	nsubj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	sort	sort	NOUN	NN	Number=Sing	15	attr	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	0	0	NUM	CD	NumType=Card	21	nummod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	cohomology	cohomology	NOUN	NN	Number=Sing	18	pobj	_	_
22	at	at	ADP	IN	_	17	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	higher	high	ADJ	JJR	Degree=Cmp	25	amod	_	_
25	level	level	NOUN	NN	Number=Sing	22	pobj	_	_
26	for	for	ADP	IN	_	25	prep	_	_
27	categorical	categorical	ADJ	JJ	Degree=Pos	28	amod	_	_
28	groups	group	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that the functor $ Der( - , A) $ is corepresentable by the semidirect product of $ A $ with $ G $ and that $ Der(G, - ) $ preserves homotopy kernels.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	functor	functor	NOUN	NN	Number=Sing	7	nsubj	_	_
6	$ Der( - , A) $	$ der( - , a) $	SYM	$	_	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	corepresentable	corepresentable	ADJ	JJ	Degree=Pos	7	acomp	_	_
9	by	by	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	semidirect	semidirect	NOUN	NN	Number=Sing	12	compound	_	_
12	product	product	NOUN	NN	Number=Sing	9	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	$ A $	$ a $	SYM	$	_	13	pobj	_	_
15	with	with	ADP	IN	_	12	prep	_	_
16	$ G $	$ g $	SYM	$	_	15	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
18	that	that	SCONJ	IN	_	20	mark	_	_
19	$ Der(G, - ) $	$ der(g, - ) $	SYM	$	_	20	nsubj	_	_
20	preserves	preserve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	conj	_	_
21	homotopy	homotopy	PROPN	NNP	Number=Sing	22	compound	_	_
22	kernels	kernels	PROPN	NNP	Number=Sing	20	dobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = Well - known cohomology groups, and exact sequences relating these groups, in several different contexts are then obtained as examples of this general theory.
1	Well	well	ADV	RB	Degree=Pos	3	advmod	_	_
2	-	-	PUNCT	HYPH	PunctType=Dash	3	punct	_	_
3	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	amod	_	_
4	cohomology	cohomology	NOUN	NN	Number=Sing	5	compound	_	_
5	groups	group	NOUN	NNS	Number=Plur	20	nsubjpass	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
8	exact	exact	ADJ	JJ	Degree=Pos	9	amod	_	_
9	sequences	sequence	NOUN	NNS	Number=Plur	5	conj	_	_
10	relating	relate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	acl	_	_
11	these	these	DET	DT	Number=Plur|PronType=Dem	12	det	_	_
12	groups	group	NOUN	NNS	Number=Plur	10	dobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
14	in	in	ADP	IN	_	20	prep	_	_
15	several	several	ADJ	JJ	Degree=Pos	17	amod	_	_
16	different	different	ADJ	JJ	Degree=Pos	17	amod	_	_
17	contexts	context	NOUN	NNS	Number=Plur	14	pobj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	20	auxpass	_	_
19	then	then	ADV	RB	PronType=Dem	20	advmod	_	_
20	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
21	as	as	ADP	IN	_	20	prep	_	_
22	examples	example	NOUN	NNS	Number=Plur	21	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	this	this	DET	DT	Number=Sing|PronType=Dem	26	det	_	_
25	general	general	ADJ	JJ	Degree=Pos	26	amod	_	_
26	theory	theory	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# doc_id = 201
# sent_id = 1
# text = In this paper we construct extensions of $ Set $ - monads—and, more generally, of lax $ Rel $ - monads—into lax monads of the bicategory $ Mat(V) $ of generalized $ V $ - matrices, whenever $ V $ is a well - behaved lattice equipped with a tensor product.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	extensions	extension	NOUN	NNS	Number=Plur	5	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	$ Set $	$ set $	SYM	$	_	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	monads	monad	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
11	—	—	PUNCT	:	_	6	punct	_	SpaceAfter=No
12	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
14	more	more	ADV	RBR	Degree=Cmp	15	advmod	_	_
15	generally	generally	ADV	RB	_	5	advmod	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	of	of	ADP	IN	_	15	prep	_	_
18	lax	lax	ADJ	JJ	Degree=Pos	21	amod	_	_
19	$ Rel $	$ rel $	SYM	$	_	21	nmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	monads	monad	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
22	—	—	PUNCT	:	_	17	punct	_	SpaceAfter=No
23	into	into	ADP	IN	_	5	prep	_	_
24	lax	lax	ADJ	JJ	Degree=Pos	25	amod	_	_
25	monads	monad	NOUN	NNS	Number=Plur	23	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	bicategory	bicategory	NOUN	NN	Number=Sing	26	pobj	_	_
29	$ Mat(V) $	$ mat(v) $	SYM	$	_	38	nsubj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	34	amod	_	_
32	$ V $	$ v $	SYM	$	_	34	compound	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	matrices	matrix	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
35	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
36	whenever	whenever	SCONJ	WRB	_	37	advmod	_	_
37	$ V $	$ v $	SYM	$	_	38	nsubj	_	_
38	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	conj	_	_
39	a	a	DET	DT	Definite=Ind|PronType=Art	43	det	_	_
40	well	well	ADV	RB	Degree=Pos	42	advmod	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	behaved	behave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	43	amod	_	_
43	lattice	lattice	NOUN	NN	Number=Sing	38	attr	_	_
44	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	43	acl	_	_
45	with	with	ADP	IN	_	44	prep	_	_
46	a	a	DET	DT	Definite=Ind|PronType=Art	48	det	_	_
47	tensor	tensor	NOUN	NN	Number=Sing	48	compound	_	_
48	product	product	NOUN	NN	Number=Sing	45	pobj	_	SpaceAfter=No
49	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = We add some guiding examples.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	add	add	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	some	some	DET	DT	_	5	det	_	_
4	guiding	guide	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	amod	_	_
5	examples	example	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
6	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 202
# sent_id = 1
# text = We show that strongly protomodular categories (as the category of groups for instance) provide an appropriate framework in which the commutator of two equivalence relations do coincide with the commutator of their associated normal subobjects, whereas it is not the case in any semi - abelian category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	16	mark	_	_
4	strongly	strongly	ADV	RB	_	5	advmod	_	_
5	protomodular	protomodular	ADJ	JJ	Degree=Pos	6	amod	_	_
6	categories	category	NOUN	NNS	Number=Plur	16	nsubj	_	_
7	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	6	punct	_	SpaceAfter=No
8	as	as	ADP	IN	_	6	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	groups	group	NOUN	NNS	Number=Plur	11	pobj	_	_
13	for	for	ADP	IN	_	12	prep	_	_
14	instance	instance	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
15	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	6	punct	_	_
16	provide	provide	VERB	VB	VerbForm=Inf	2	ccomp	_	_
17	an	an	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	appropriate	appropriate	ADJ	JJ	Degree=Pos	19	amod	_	_
19	framework	framework	NOUN	NN	Number=Sing	16	dobj	_	_
20	in	in	ADP	IN	_	29	prep	_	_
21	which	which	PRON	WDT	_	20	pobj	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	commutator	commutator	NOUN	NN	Number=Sing	29	nsubj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	two	two	NUM	CD	NumType=Card	27	nummod	_	_
26	equivalence	equivalence	NOUN	NN	Number=Sing	27	compound	_	_
27	relations	relation	NOUN	NNS	Number=Plur	24	pobj	_	_
28	do	do	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	29	aux	_	_
29	coincide	coincide	VERB	VB	VerbForm=Inf	19	relcl	_	_
30	with	with	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	commutator	commutator	NOUN	NN	Number=Sing	30	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	37	poss	_	_
35	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	37	amod	_	_
36	normal	normal	ADJ	JJ	Degree=Pos	37	amod	_	_
37	subobjects	subobject	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
38	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
39	whereas	whereas	SCONJ	IN	_	41	mark	_	_
40	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	41	nsubj	_	_
41	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	advcl	_	_
42	not	not	PART	RB	Polarity=Neg	41	neg	_	_
43	the	the	DET	DT	Definite=Def|PronType=Art	44	det	_	_
44	case	case	NOUN	NN	Number=Sing	41	attr	_	_
45	in	in	ADP	IN	_	44	prep	_	_
46	any	any	DET	DT	_	50	det	_	_
47	semi	semi	ADJ	JJ	Degree=Pos	50	amod	_	_
48	-	-	ADJ	JJ	Degree=Pos	50	amod	_	_
49	abelian	abelian	ADJ	JJ	Degree=Pos	50	amod	_	_
50	category	category	NOUN	NN	Number=Sing	45	pobj	_	SpaceAfter=No
51	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 203
# sent_id = 1
# text = We generalize to an arbitrary variety the von Neumann axiom for a ring.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	6	amod	_	_
6	variety	variety	NOUN	NN	Number=Sing	3	pobj	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	von	von	PROPN	NNP	Number=Sing	9	compound	_	_
9	Neumann	Neumann	PROPN	NNP	Number=Sing	10	nsubj	_	_
10	axiom	axiom	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	ring	ring	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = We study its implications on the purity of monomorphisms and the flatness of algebras.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	4	poss	_	_
4	implications	implication	NOUN	NNS	Number=Plur	2	dobj	_	_
5	on	on	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	purity	purity	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	8	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	flatness	flatness	NOUN	NN	Number=Sing	7	conj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	algebras	algebra	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 204
# sent_id = 1
# text = Brown representability approximates the homotopy category of spectra by means of cohomology functors defined on finite spectra.
1	Brown	brown	ADJ	JJ	Degree=Pos	2	amod	_	_
2	representability	representability	NOUN	NN	Number=Sing	3	nsubj	_	_
3	approximates	approximate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	homotopy	homotopy	NOUN	NN	Number=Sing	6	compound	_	_
6	category	category	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	spectra	spectra	PROPN	NNP	Number=Sing	7	pobj	_	_
9	by	by	ADP	IN	_	3	prep	_	_
10	means	mean	NOUN	NNS	Number=Plur	9	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	cohomology	cohomology	NOUN	NN	Number=Sing	13	compound	_	_
13	functors	functor	NOUN	NNS	Number=Plur	11	pobj	_	_
14	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	acl	_	_
15	on	on	ADP	IN	_	14	prep	_	_
16	finite	finite	PROPN	NNP	Number=Sing	17	compound	_	_
17	spectra	spectra	PROPN	NNP	Number=Sing	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = We will show that if a model category $ cal K $ is suitably determined by $ lambda $ - small objects then its homotopy category $ Ho(cal K) $ is approximated by cohomology functors defined on those $ lambda $ - small objects.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	will	will	AUX	MD	VerbForm=Fin	3	aux	_	_
3	show	show	VERB	VB	VerbForm=Inf	0	ROOT	_	_
4	that	that	SCONJ	IN	_	24	mark	_	_
5	if	if	SCONJ	IN	_	12	mark	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	model	model	NOUN	NN	Number=Sing	8	compound	_	_
8	category	category	NOUN	NN	Number=Sing	10	nsubj	_	_
9	$ cal K $	$ cal k $	SYM	$	_	8	appos	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
11	suitably	suitably	ADV	RB	_	12	advmod	_	_
12	determined	determine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	advcl	_	_
13	by	by	ADP	IN	_	12	agent	_	_
14	$ lambda $	$ lambda $	SYM	$	_	16	advmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	small	small	ADJ	JJ	Degree=Pos	17	amod	_	_
17	objects	object	NOUN	NNS	Number=Plur	13	pobj	_	_
18	then	then	ADV	RB	PronType=Dem	17	advmod	_	_
19	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	21	poss	_	_
20	homotopy	homotopy	NOUN	NN	Number=Sing	21	compound	_	_
21	category	category	NOUN	NN	Number=Sing	24	nsubjpass	_	_
22	$ Ho(cal K) $	$ ho(cal k) $	SYM	$	_	21	appos	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	auxpass	_	_
24	approximated	approximate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	ccomp	_	_
25	by	by	ADP	IN	_	24	agent	_	_
26	cohomology	cohomology	NOUN	NN	Number=Sing	27	compound	_	_
27	functors	functor	NOUN	NNS	Number=Plur	25	pobj	_	_
28	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	acl	_	_
29	on	on	ADP	IN	_	28	prep	_	_
30	those	those	DET	DT	Number=Plur|PronType=Dem	34	det	_	_
31	$ lambda $	$ lambda $	SYM	$	_	33	advmod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	small	small	ADJ	JJ	Degree=Pos	34	amod	_	_
34	objects	object	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = In the case of simplicial sets, we have $ lambda = omega_1 $ , that is, $ lambda $ - small means countable.
1	In	in	ADP	IN	_	9	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	case	case	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	simplicial	simplicial	ADJ	JJ	Degree=Pos	6	amod	_	_
6	sets	set	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	$ lambda = omega_1 $	$ lambda = omega_1 $	SYM	$	_	9	dobj	_	_
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	that	that	ADV	RB	_	13	advmod	_	_
13	is	is	ADV	RB	_	18	advmod	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
15	$ lambda $	$ lambda $	SYM	$	_	17	advmod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	small	small	ADJ	JJ	Degree=Pos	18	amod	_	_
18	means	mean	NOUN	NNS	Number=Plur	19	nsubj	_	_
19	countable	countable	ADJ	JJ	Degree=Pos	9	ccomp	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 205
# sent_id = 1
# text = For large signatures $ Sigma $ we prove that Birkhoff's Variety Theorem holds (that is, equationally presentable collections of $ Sigma $ - algebras are precisely those closed under limits, subalgebras, and quotient algebras)
1	For	for	ADP	IN	_	6	prep	_	_
2	large	large	ADJ	JJ	Degree=Pos	3	amod	_	_
3	signatures	signature	NOUN	NNS	Number=Plur	1	pobj	_	_
4	$ Sigma $	$ sigma $	SYM	$	_	1	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	12	mark	_	_
8	Birkhoff	Birkhoff	PROPN	NNP	Number=Sing	11	poss	_	SpaceAfter=No
9	's	's	PART	POS	_	8	case	_	_
10	Variety	Variety	PROPN	NNP	Number=Sing	11	compound	_	_
11	Theorem	Theorem	PROPN	NNP	Number=Sing	12	nsubj	_	_
12	holds	hold	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
14	that	that	ADV	RB	_	15	nsubj	_	_
15	is	is	ADV	RB	_	19	advmod	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
17	equationally	equationally	ADV	RB	_	18	advmod	_	_
18	presentable	presentable	ADJ	JJ	Degree=Pos	19	amod	_	_
19	collections	collection	NOUN	NNS	Number=Plur	24	nsubj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	$ Sigma $	$ sigma $	SYM	$	_	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	algebras	algebra	NOUN	NNS	Number=Plur	20	pobj	_	_
24	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
25	precisely	precisely	ADV	RB	_	26	advmod	_	_
26	those	those	PRON	DT	Number=Plur|PronType=Dem	24	attr	_	_
27	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	acl	_	_
28	under	under	ADP	IN	_	27	prep	_	_
29	limits	limit	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
31	subalgebras	subalgebras	PROPN	NNP	Number=Sing	29	conj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
34	quotient	quotient	ADJ	JJ	Degree=Pos	35	compound	_	_
35	algebras	algebra	NOUN	NNS	Number=Plur	31	conj	_	SpaceAfter=No
36	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	24	punct	_	SpaceAfter=No

# sent_id = 2
# text = iff the universe of small sets is not measurable.
1	iff	iff	PROPN	NNP	Number=Sing	7	nsubj	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	universe	universe	NOUN	NN	Number=Sing	7	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	small	small	ADJ	JJ	Degree=Pos	6	amod	_	_
6	sets	set	NOUN	NNS	Number=Plur	4	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	not	not	PART	RB	Polarity=Neg	7	neg	_	_
9	measurable	measurable	ADJ	JJ	Degree=Pos	7	acomp	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = Under that limitation Birkhoff's Variety Theorem holds in fact for $ F $ - algebras of an arbitrary endofunctor $ F $ of the category $ Class $ of classes and functions.
1	Under	under	ADP	IN	_	8	prep	_	_
2	that	that	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	limitation	limitation	NOUN	NN	Number=Sing	1	pobj	_	_
4	Birkhoff	Birkhoff	PROPN	NNP	Number=Sing	7	poss	_	SpaceAfter=No
5	's	's	PART	POS	_	4	case	_	_
6	Variety	Variety	PROPN	NNP	Number=Sing	7	compound	_	_
7	Theorem	Theorem	PROPN	NNP	Number=Sing	8	nsubj	_	_
8	holds	hold	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	fact	fact	NOUN	NN	Number=Sing	9	pobj	_	_
11	for	for	ADP	IN	_	8	prep	_	_
12	$ F $	$ f $	SYM	$	_	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	algebras	algebra	NOUN	NNS	Number=Plur	11	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	an	an	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	18	amod	_	_
18	endofunctor	endofunctor	NOUN	NN	Number=Sing	15	pobj	_	_
19	$ F $	$ f $	SYM	$	_	18	appos	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	category	category	NOUN	NN	Number=Sing	20	pobj	_	_
23	$ Class $	$ class $	SYM	$	_	22	nummod	_	_
24	of	of	ADP	IN	_	22	prep	_	_
25	classes	class	NOUN	NNS	Number=Plur	24	pobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	functions	function	NOUN	NNS	Number=Plur	25	conj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 4
# text = For endofunctors $ F $ of $ Set $ , the category of small sets, Jan Reiterman proved that if $ F $ is a varietor (that is, if free $ F $ - algebras exist) then Birkhoff's Variety Theorem holds for $ F $ - algebras.
1	For	for	ADP	IN	_	15	prep	_	_
2	endofunctors	endofunctor	NOUN	NNS	Number=Plur	1	pobj	_	_
3	$ F $	$ f $	SYM	$	_	2	prep	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	$ Set $	$ set $	SYM	$	_	4	pobj	_	_
6	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	15	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	small	small	ADJ	JJ	Degree=Pos	11	amod	_	_
11	sets	set	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
13	Jan	Jan	PROPN	NNP	Number=Sing	14	compound	_	_
14	Reiterman	Reiterman	PROPN	NNP	Number=Sing	15	nsubj	_	_
15	proved	prove	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
16	that	that	SCONJ	IN	_	38	mark	_	_
17	if	if	SCONJ	IN	_	19	mark	_	_
18	$ F $	$ f $	SYM	$	_	19	nsubj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	38	advcl	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	varietor	varietor	NOUN	NN	Number=Sing	19	attr	_	_
22	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	21	punct	_	SpaceAfter=No
23	that	that	ADV	RB	_	24	nsubj	_	_
24	is	is	ADV	RB	_	31	advmod	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	if	if	SCONJ	IN	_	27	mark	_	_
27	free	free	ADJ	JJ	Degree=Pos	31	amod	_	_
28	$ F $	$ f $	SYM	$	_	30	compound	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	algebras	algebra	NOUN	NNS	Number=Plur	31	nsubj	_	_
31	exist	exist	VERB	VBP	Tense=Pres|VerbForm=Fin	21	appos	_	SpaceAfter=No
32	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	21	punct	_	_
33	then	then	ADV	RB	PronType=Dem	38	advmod	_	_
34	Birkhoff	Birkhoff	PROPN	NNP	Number=Sing	37	poss	_	SpaceAfter=No
35	's	's	PART	POS	_	34	case	_	_
36	Variety	Variety	PROPN	NNP	Number=Sing	37	compound	_	_
37	Theorem	Theorem	PROPN	NNP	Number=Sing	38	nsubj	_	_
38	holds	hold	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	ccomp	_	_
39	for	for	ADP	IN	_	38	prep	_	_
40	$ F $	$ f $	SYM	$	_	42	compound	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	algebras	algebra	NOUN	NNS	Number=Plur	39	pobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 5
# text = We prove the converse, whenever $ F $ preserves preimages: if $ F $ is not a varietor, Birkhoff's Variety Theorem does not hold.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	converse	converse	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
6	whenever	whenever	SCONJ	WRB	_	7	advmod	_	_
7	$ F $	$ f $	SYM	$	_	8	nsubj	_	_
8	preserves	preserve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
9	preimages	preimage	NOUN	NNS	Number=Plur	8	dobj	_	SpaceAfter=No
10	:	:	PUNCT	:	_	8	punct	_	_
11	if	if	SCONJ	IN	_	13	mark	_	_
12	$ F $	$ f $	SYM	$	_	13	nsubj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	advcl	_	_
14	not	not	PART	RB	Polarity=Neg	13	neg	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	varietor	varietor	NOUN	NN	Number=Sing	13	attr	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
18	Birkhoff	Birkhoff	PROPN	NNP	Number=Sing	21	poss	_	SpaceAfter=No
19	's	's	PART	POS	_	18	case	_	_
20	Variety	Variety	PROPN	NNP	Number=Sing	21	compound	_	_
21	Theorem	Theorem	PROPN	NNP	Number=Sing	24	nsubj	_	_
22	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	aux	_	_
23	not	not	PART	RB	Polarity=Neg	24	neg	_	_
24	hold	hold	VERB	VB	VerbForm=Inf	2	ccomp	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = However, we also present a non - varietor satisfying Birkhoff's Variety Theorem.
1	However	however	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
4	also	also	ADV	RB	_	5	advmod	_	_
5	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	non	non	ADJ	JJ	Degree=Pos	9	amod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	varietor	varietor	NOUN	NN	Number=Sing	5	dobj	_	_
10	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	advcl	_	_
11	Birkhoff	Birkhoff	PROPN	NNP	Number=Sing	14	poss	_	SpaceAfter=No
12	's	's	PART	POS	_	11	case	_	_
13	Variety	Variety	PROPN	NNP	Number=Sing	14	compound	_	_
14	Theorem	Theorem	PROPN	NNP	Number=Sing	10	dobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 7
# text = Our most surprising example is two varietors whose coproduct does not satisfy Birkhoff's Variety Theorem.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	4	poss	_	_
2	most	most	ADV	RBS	Degree=Sup	3	advmod	_	_
3	surprising	surprising	ADJ	JJ	Degree=Pos	4	amod	_	_
4	example	example	NOUN	NN	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	two	two	NUM	CD	NumType=Card	7	nummod	_	_
7	varietors	varietor	NOUN	NNS	Number=Plur	5	attr	_	_
8	whose	whose	DET	WP$	Poss=Yes	9	poss	_	_
9	coproduct	coproduct	NOUN	NN	Number=Sing	12	nsubj	_	_
10	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	aux	_	_
11	not	not	PART	RB	Polarity=Neg	12	neg	_	_
12	satisfy	satisfy	VERB	VB	VerbForm=Inf	7	relcl	_	_
13	Birkhoff	Birkhoff	PROPN	NNP	Number=Sing	16	poss	_	SpaceAfter=No
14	's	's	PART	POS	_	13	case	_	_
15	Variety	Variety	PROPN	NNP	Number=Sing	16	compound	_	_
16	Theorem	Theorem	PROPN	NNP	Number=Sing	12	dobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 206
# sent_id = 1
# text = The paper is in essence a survey of categories having $ phi $ - weighted colimits for all the weights $ phi $ in some class $ Phi $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	in	in	ADP	IN	_	3	prep	_	_
5	essence	essence	NOUN	NN	Number=Sing	4	pobj	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	survey	survey	NOUN	NN	Number=Sing	3	attr	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	_
10	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	acl	_	_
11	$ phi $	$ phi $	SYM	$	_	13	advmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	weighted	weight	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
14	colimits	colimit	NOUN	NNS	Number=Plur	10	dobj	_	_
15	for	for	ADP	IN	_	14	prep	_	_
16	all	all	DET	PDT	_	18	predet	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	weights	weight	NOUN	NNS	Number=Plur	15	pobj	_	_
19	$ phi $	$ phi $	SYM	$	_	7	appos	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	some	some	DET	DT	_	22	det	_	_
22	class	class	NOUN	NN	Number=Sing	20	pobj	_	_
23	$ Phi $	$ phi $	SYM	$	_	3	dep	_	_
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = We introduce the class $ Phi^+ $ of $ Phi $ - flat weights which are those $ psi $ for which $ psi $ - colimits commute in the base $ cal V $ with limits having weights in $ Phi $ ; and the class $ Phi^ - $ of $ Phi $ - atomic weights, which are those $ psi $ for which $ psi $ - limits commute in the base $ cal V $ with colimits having weights in $ Phi $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	class	class	NOUN	NN	Number=Sing	2	dobj	_	_
5	$ Phi^+ $	$ phi^+ $	SYM	$	_	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	$ Phi $	$ phi $	SYM	$	_	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	flat	flat	ADJ	JJ	Degree=Pos	10	amod	_	_
10	weights	weight	NOUN	NNS	Number=Plur	6	pobj	_	_
11	which	which	PRON	WDT	_	12	nsubj	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	10	relcl	_	_
13	those	those	PRON	DT	Number=Plur|PronType=Dem	12	attr	_	_
14	$ psi $	$ psi $	SYM	$	_	12	attr	_	_
15	for	for	ADP	IN	_	20	prep	_	_
16	which	which	PRON	WDT	_	15	pobj	_	_
17	$ psi $	$ psi $	SYM	$	_	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	colimits	colimit	NOUN	NNS	Number=Plur	20	compound	_	_
20	commute	commute	NOUN	NN	Number=Sing	14	relcl	_	_
21	in	in	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	base	base	NOUN	NN	Number=Sing	21	pobj	_	_
24	$ cal V $	$ cal v $	SYM	$	_	12	attr	_	_
25	with	with	ADP	IN	_	12	prep	_	_
26	limits	limit	NOUN	NNS	Number=Plur	25	pobj	_	_
27	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	26	acl	_	_
28	weights	weight	NOUN	NNS	Number=Plur	27	dobj	_	_
29	in	in	ADP	IN	_	28	prep	_	_
30	$ Phi $	$ phi $	SYM	$	_	29	pobj	_	_
31	;	;	PUNCT	:	_	2	punct	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
34	class	class	NOUN	NN	Number=Sing	35	compound	_	_
35	$ Phi^ - $	$ phi^ - $	SYM	$	_	2	conj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	$ Phi $	$ phi $	SYM	$	_	39	amod	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	atomic	atomic	ADJ	JJ	Degree=Pos	40	amod	_	_
40	weights	weight	NOUN	NNS	Number=Plur	36	pobj	_	SpaceAfter=No
41	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
42	which	which	PRON	WDT	_	43	nsubj	_	_
43	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	35	relcl	_	_
44	those	those	DET	DT	Number=Plur|PronType=Dem	45	det	_	_
45	$ psi $	$ psi $	SYM	$	_	43	attr	_	_
46	for	for	ADP	IN	_	51	prep	_	_
47	which	which	PRON	WDT	_	46	pobj	_	_
48	$ psi $	$ psi $	SYM	$	_	50	nummod	_	_
49	-	-	PUNCT	HYPH	PunctType=Dash	50	punct	_	_
50	limits	limit	NOUN	NNS	Number=Plur	51	compound	_	_
51	commute	commute	NOUN	NN	Number=Sing	45	relcl	_	_
52	in	in	ADP	IN	_	51	prep	_	_
53	the	the	DET	DT	Definite=Def|PronType=Art	54	det	_	_
54	base	base	NOUN	NN	Number=Sing	52	pobj	_	_
55	$ cal V $	$ cal v $	SYM	$	_	43	dep	_	_
56	with	with	ADP	IN	_	43	prep	_	_
57	colimits	colimit	NOUN	NNS	Number=Plur	56	pobj	_	_
58	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	57	acl	_	_
59	weights	weight	NOUN	NNS	Number=Plur	58	dobj	_	_
60	in	in	ADP	IN	_	59	prep	_	_
61	$ Phi $	$ phi $	SYM	$	_	60	pobj	_	_
62	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that both these classes are saturated (that is, what was called closed in the terminology of Albert and Kelly).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	8	mark	_	_
4	both	both	CCONJ	CC	ConjType=Cmp	6	predet	_	_
5	these	these	DET	DT	Number=Plur|PronType=Dem	6	det	_	_
6	classes	class	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	saturated	saturate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
9	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	15	punct	_	SpaceAfter=No
10	that	that	ADV	RB	_	11	advmod	_	_
11	is	is	ADV	RB	_	15	advmod	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
13	what	what	PRON	WP	_	15	nsubjpass	_	_
14	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	15	auxpass	_	_
15	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	parataxis	_	_
16	closed	closed	ADJ	JJ	Degree=Pos	15	oprd	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	terminology	terminology	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	Albert	Albert	PROPN	NNP	Number=Sing	20	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	Kelly	Kelly	PROPN	NNP	Number=Sing	21	conj	_	SpaceAfter=No
24	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	15	punct	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We prove that for the class $ cal P $ of all weights, the classes $ cal P^+ $ and $ cal P^ - $ both coincide with the class $ Q $ of absolute weights.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	18	mark	_	_
4	for	for	ADP	IN	_	18	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	class	class	NOUN	NN	Number=Sing	4	pobj	_	_
7	$ cal P $	$ cal p $	SYM	$	_	4	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	all	all	DET	DT	_	10	det	_	_
10	weights	weight	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	classes	class	NOUN	NNS	Number=Plur	18	nsubj	_	_
14	$ cal P^+ $	$ cal p^+ $	SYM	$	_	13	appos	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	$ cal P^ - $	$ cal p^ - $	SYM	$	_	14	conj	_	_
17	both	both	PRON	DT	_	16	appos	_	_
18	coincide	coincide	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	class	class	NOUN	NN	Number=Sing	19	pobj	_	_
22	$ Q $	$ q $	SYM	$	_	21	appos	_	_
23	of	of	ADP	IN	_	21	prep	_	_
24	absolute	absolute	ADJ	JJ	Degree=Pos	25	amod	_	_
25	weights	weight	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = For any class $ Phi $ and any category $ cal A $ , we have the free $ Phi $ - cocompletion $ Phi(cal A) $ of $ cal A $ ; and we recognize $ cal Q(cal A) $ as the Cauchy - completion of $ cal A $ .
1	For	for	ADP	IN	_	11	prep	_	_
2	any	any	DET	DT	_	3	det	_	_
3	class	class	NOUN	NN	Number=Sing	1	pobj	_	_
4	$ Phi $	$ phi $	SYM	$	_	1	pobj	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	1	cc	_	_
6	any	any	DET	DT	_	7	det	_	_
7	category	category	NOUN	NN	Number=Sing	1	pobj	_	_
8	$ cal A $	$ cal a $	SYM	$	_	7	nummod	_	_
9	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
10	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	11	nsubj	_	_
11	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
13	free	free	ADJ	JJ	Degree=Pos	16	amod	_	_
14	$ Phi $	$ phi $	SYM	$	_	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	cocompletion	cocompletion	NOUN	NN	Number=Sing	11	dobj	_	_
17	$ Phi(cal A) $	$ phi(cal a) $	SYM	$	_	16	appos	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	$ cal A $	$ cal a $	SYM	$	_	18	pobj	_	_
20	;	;	PUNCT	:	_	11	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
22	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	23	nsubj	_	_
23	recognize	recognize	VERB	VBP	Tense=Pres|VerbForm=Fin	11	conj	_	_
24	$ cal Q(cal A) $	$ cal q(cal a) $	SYM	$	_	23	dobj	_	_
25	as	as	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
27	Cauchy	Cauchy	PROPN	NNP	Number=Sing	29	compound	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	completion	completion	NOUN	NN	Number=Sing	25	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	$ cal A $	$ cal a $	SYM	$	_	30	pobj	_	_
32	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# sent_id = 6
# text = We study the equivalence between $ {(cal Q(cal A^{op}))}^{op} $ and $ cal Q(cal A) $ , which we exhibit as the restriction of the Isbell adjunction between $ {[cal A, cal V]}^{op} $ and $ [cal A^{op}, cal V] $ when $ cal A $ is small; and we give a new Morita theorem for any class $ Phi $ containing $ cal Q $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	equivalence	equivalence	NOUN	NN	Number=Sing	2	dobj	_	_
5	between	between	ADP	IN	_	4	prep	_	_
6	$ {(cal Q(cal A^{op}))}^{op} $	$ {(cal q(cal a^{op}))}^{op} $	SYM	$	_	5	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	$ cal Q(cal A) $	$ cal q(cal a) $	SYM	$	_	6	conj	_	_
9	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
10	which	which	PRON	WDT	_	12	dobj	_	_
11	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	12	nsubj	_	_
12	exhibit	exhibit	VERB	VBP	Tense=Pres|VerbForm=Fin	4	relcl	_	_
13	as	as	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	restriction	restriction	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	Isbell	Isbell	PROPN	NNP	Number=Sing	19	compound	_	_
19	adjunction	adjunction	NOUN	NN	Number=Sing	16	pobj	_	_
20	between	between	ADP	IN	_	19	prep	_	_
21	$ {[cal A, cal V]}^{op} $	$ {[cal a, cal v]}^{op} $	SYM	$	_	20	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	$ [cal A^{op}, cal V] $	$ [cal a^{op}, cal v] $	SYM	$	_	21	conj	_	_
24	when	when	SCONJ	WRB	_	25	advmod	_	_
25	$ cal A $	$ cal a $	SYM	$	_	26	nsubj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
27	small	small	ADJ	JJ	Degree=Pos	26	acomp	_	SpaceAfter=No
28	;	;	PUNCT	:	_	2	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
30	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	31	nsubj	_	_
31	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
33	new	new	ADJ	JJ	Degree=Pos	35	amod	_	_
34	Morita	Morita	PROPN	NNP	Number=Sing	35	compound	_	_
35	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	31	dobj	_	_
36	for	for	ADP	IN	_	35	prep	_	_
37	any	any	DET	DT	_	38	det	_	_
38	class	class	NOUN	NN	Number=Sing	36	pobj	_	_
39	$ Phi $	$ phi $	SYM	$	_	31	dobj	_	_
40	containing	contain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	31	advcl	_	_
41	$ cal Q $	$ cal q $	SYM	$	_	40	dep	_	_
42	.	.	PUNCT	.	PunctType=Peri	31	punct	_	SpaceAfter=No

# sent_id = 7
# text = We end with the study of $ Phi $ - continuous weights and their relation to the $ Phi $ - flat weights.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	end	end	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	with	with	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	study	study	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	$ Phi $	$ phi $	SYM	$	_	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	continuous	continuous	ADJ	JJ	Degree=Pos	10	amod	_	_
10	weights	weight	NOUN	NNS	Number=Plur	6	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	13	poss	_	_
13	relation	relation	NOUN	NN	Number=Sing	10	conj	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
16	$ Phi $	$ phi $	SYM	$	_	18	advmod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	flat	flat	ADJ	JJ	Degree=Pos	19	amod	_	_
19	weights	weight	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 207
# sent_id = 1
# text = In order to apply nonstandard methods to modern algebraic geometry, as a first step in this paper we study the applications of nonstandard constructions to category theory.
1	In	in	ADP	IN	_	20	prep	_	_
2	order	order	NOUN	NN	Number=Sing	1	pobj	_	_
3	to	to	PART	TO	_	4	aux	_	_
4	apply	apply	VERB	VB	VerbForm=Inf	2	acl	_	_
5	nonstandard	nonstandard	ADJ	JJ	Degree=Pos	6	amod	_	_
6	methods	method	NOUN	NNS	Number=Plur	4	dobj	_	_
7	to	to	ADP	IN	_	4	prep	_	_
8	modern	modern	ADJ	JJ	Degree=Pos	10	amod	_	_
9	algebraic	algebraic	ADJ	JJ	Degree=Pos	10	amod	_	_
10	geometry	geometry	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
12	as	as	ADP	IN	_	20	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	first	first	ADJ	JJ	Degree=Pos	15	amod	_	_
15	step	step	NOUN	NN	Number=Sing	12	pobj	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	this	this	DET	DT	Number=Sing|PronType=Dem	18	det	_	_
18	paper	paper	NOUN	NN	Number=Sing	16	pobj	_	_
19	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	20	nsubj	_	_
20	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	applications	application	NOUN	NNS	Number=Plur	20	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	nonstandard	nonstandard	ADJ	JJ	Degree=Pos	25	amod	_	_
25	constructions	construction	NOUN	NNS	Number=Plur	23	pobj	_	_
26	to	to	ADP	IN	_	20	prep	_	_
27	category	category	NOUN	NN	Number=Sing	28	compound	_	_
28	theory	theory	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 2
# text = It turns out that many categorical properties are well behaved under enlargements.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	turns	turn	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	out	out	ADP	RP	_	2	prt	_	_
4	that	that	SCONJ	IN	_	8	mark	_	_
5	many	many	ADJ	JJ	Degree=Pos	7	amod	_	_
6	categorical	categorical	ADJ	JJ	Degree=Pos	7	amod	_	_
7	properties	property	NOUN	NNS	Number=Plur	8	nsubj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
9	well	well	ADV	RB	Degree=Pos	10	advmod	_	_
10	behaved	behave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
11	under	under	ADP	IN	_	10	prep	_	_
12	enlargements	enlargement	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 208
# sent_id = 1
# text = Following Lawvere, a generalized metric space is a set $ X $ equipped with a metric map from $ X^{2} $ to the interval of upper reals (approximated from above but not from below) from 0 to $ infty $ inclusive, and satisfying the zero self - distance law and the triangle inequality.
1	Following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	csubj	_	_
2	Lawvere	Lawvere	PROPN	NNP	Number=Sing	1	dobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
6	metric	metric	ADJ	JJ	Degree=Pos	7	amod	_	_
7	space	space	NOUN	NN	Number=Sing	2	appos	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	set	set	NOUN	NN	Number=Sing	8	attr	_	_
11	$ X $	$ x $	SYM	$	_	10	appos	_	_
12	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acl	_	_
13	with	with	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	metric	metric	ADJ	JJ	Degree=Pos	16	amod	_	_
16	map	map	NOUN	NN	Number=Sing	13	pobj	_	_
17	from	from	ADP	IN	_	16	prep	_	_
18	$ X^{2} $	$ x^{2} $	SYM	$	_	17	pobj	_	_
19	to	to	ADP	IN	_	10	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	interval	interval	NOUN	NN	Number=Sing	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	upper	upper	ADJ	JJ	Degree=Pos	24	amod	_	_
24	reals	real	NOUN	NNS	Number=Plur	22	pobj	_	_
25	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
26	approximated	approximate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	acl	_	_
27	from	from	ADP	IN	_	26	prep	_	_
28	above	above	ADV	RB	_	27	pcomp	_	_
29	but	but	CCONJ	CC	ConjType=Cmp	27	cc	_	_
30	not	not	PART	RB	Polarity=Neg	31	neg	_	_
31	from	from	ADP	IN	_	26	prep	_	_
32	below	below	ADV	RB	_	31	pcomp	_	SpaceAfter=No
33	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	24	punct	_	_
34	from	from	ADP	IN	_	10	prep	_	_
35	0	0	NUM	CD	NumType=Card	34	pobj	_	_
36	to	to	PART	TO	_	34	prep	_	_
37	$ infty $	$ infty $	SYM	$	_	38	nmod	_	_
38	inclusive	inclusive	ADJ	JJ	Degree=Pos	36	pobj	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
41	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	conj	_	_
42	the	the	DET	DT	Definite=Def|PronType=Art	47	det	_	_
43	zero	zero	NUM	CD	NumType=Card	47	nummod	_	_
44	self	self	NOUN	NN	Number=Sing	46	compound	_	_
45	-	-	PUNCT	HYPH	PunctType=Dash	46	punct	_	_
46	distance	distance	NOUN	NN	Number=Sing	47	compound	_	_
47	law	law	NOUN	NN	Number=Sing	41	dobj	_	_
48	and	and	CCONJ	CC	ConjType=Cmp	47	cc	_	_
49	the	the	DET	DT	Definite=Def|PronType=Art	51	det	_	_
50	triangle	triangle	NOUN	NN	Number=Sing	51	compound	_	_
51	inequality	inequality	NOUN	NN	Number=Sing	47	conj	_	SpaceAfter=No
52	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = We describe a completion of generalized metric spacees by Cauchy filters of formal balls.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	completion	completion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
7	metric	metric	ADJ	JJ	Degree=Pos	8	amod	_	_
8	spacees	spacee	NOUN	NNS	Number=Plur	5	pobj	_	_
9	by	by	ADP	IN	_	2	prep	_	_
10	Cauchy	Cauchy	PROPN	NNP	Number=Sing	11	compound	_	_
11	filters	filter	NOUN	NNS	Number=Plur	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	formal	formal	ADJ	JJ	Degree=Pos	14	amod	_	_
14	balls	ball	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = In terms of Lawvere's approach using categories enriched over $ [0, infty] $ , the Cauchy filters are equivalent to flat left modules.
1	In	in	ADP	IN	_	16	prep	_	_
2	terms	term	NOUN	NNS	Number=Plur	1	pobj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	Lawvere	Lawvere	PROPN	NNP	Number=Sing	6	poss	_	SpaceAfter=No
5	's	's	PART	POS	_	4	case	_	_
6	approach	approach	NOUN	NN	Number=Sing	3	pobj	_	_
7	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	acl	_	_
8	categories	category	NOUN	NNS	Number=Plur	7	dobj	_	_
9	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	over	over	ADP	IN	_	9	prep	_	_
11	$ [0, infty] $	$ [0, infty] $	SYM	$	_	1	nmod	_	_
12	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	Cauchy	Cauchy	PROPN	NNP	Number=Sing	15	compound	_	_
15	filters	filter	NOUN	NNS	Number=Plur	16	nsubj	_	_
16	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
17	equivalent	equivalent	ADJ	JJ	Degree=Pos	16	acomp	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	flat	flat	ADJ	JJ	Degree=Pos	21	amod	_	_
20	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	amod	_	_
21	modules	module	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 4
# text = The completion generalizes the usual one for metric spaces.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	completion	completion	NOUN	NN	Number=Sing	3	nsubj	_	_
3	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	usual	usual	ADJ	JJ	Degree=Pos	6	amod	_	_
6	one	one	NOUN	NN	Number=Sing	3	dobj	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	metric	metric	ADJ	JJ	Degree=Pos	9	amod	_	_
9	spaces	space	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = For quasimetrics it is equivalent to the Yoneda completion in its netwise form due to Kunzi and Schellekens and thereby gives a new and explicit characterization of the points of the Yoneda completion.
1	For	for	ADP	IN	_	4	prep	_	_
2	quasimetrics	quasimetric	NOUN	NNS	Number=Plur	1	pobj	_	_
3	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	equivalent	equivalent	ADJ	JJ	Degree=Pos	4	acomp	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	Yoneda	Yoneda	PROPN	NNP	Number=Sing	9	compound	_	_
9	completion	completion	NOUN	NN	Number=Sing	6	pobj	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	13	poss	_	_
12	netwise	netwise	NOUN	NN	Number=Sing	13	compound	_	_
13	form	form	NOUN	NN	Number=Sing	10	pobj	_	_
14	due	due	ADP	IN	_	4	prep	_	_
15	to	to	ADP	IN	_	14	pcomp	_	_
16	Kunzi	Kunzi	PROPN	NNP	Number=Sing	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	Schellekens	Schellekens	PROPN	NNP	Number=Sing	16	conj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
20	thereby	thereby	ADV	RB	_	21	advmod	_	_
21	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	conj	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
23	new	new	ADJ	JJ	Degree=Pos	26	amod	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	explicit	explicit	ADJ	JJ	Degree=Pos	23	conj	_	_
26	characterization	characterization	NOUN	NN	Number=Sing	21	dobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	points	point	NOUN	NNS	Number=Plur	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	Yoneda	Yoneda	PROPN	NNP	Number=Sing	33	compound	_	_
33	completion	completion	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 6
# text = Non - expansive functions between gms's lift to continuous maps between the completions.
1	Non	non	ADJ	JJ	Degree=Pos	3	amod	_	_
2	-	-	PUNCT	HYPH	PunctType=Dash	3	punct	_	_
3	expansive	expansive	ADJ	JJ	Degree=Pos	4	amod	_	_
4	functions	function	NOUN	NNS	Number=Plur	0	ROOT	_	_
5	between	between	ADP	IN	_	4	prep	_	_
6	gms	gms	NOUN	NN	Number=Sing	8	poss	_	SpaceAfter=No
7	's	's	PART	POS	_	6	case	_	_
8	lift	lift	NOUN	NN	Number=Sing	5	pobj	_	_
9	to	to	ADP	IN	_	4	prep	_	_
10	continuous	continuous	ADJ	JJ	Degree=Pos	11	amod	_	_
11	maps	map	NOUN	NNS	Number=Plur	9	pobj	_	_
12	between	between	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	completions	completion	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 7
# text = Various examples and constructions are given, including finite products.
1	Various	various	ADJ	JJ	Degree=Pos	2	amod	_	_
2	examples	example	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	constructions	construction	NOUN	NNS	Number=Plur	2	conj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	prep	_	_
9	finite	finite	ADJ	JJ	Degree=Pos	10	amod	_	_
10	products	product	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 8
# text = The completion is easily adapted to produce a locale, and that part of the work is constructively valid.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	completion	completion	NOUN	NN	Number=Sing	5	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
4	easily	easily	ADV	RB	_	5	advmod	_	_
5	adapted	adapt	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	produce	produce	VERB	VB	VerbForm=Inf	5	xcomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	locale	locale	NOUN	NN	Number=Sing	7	dobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
12	that	that	DET	DT	Number=Sing|PronType=Dem	13	det	_	_
13	part	part	NOUN	NN	Number=Sing	17	nsubj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	work	work	NOUN	NN	Number=Sing	14	pobj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	conj	_	_
18	constructively	constructively	ADV	RB	_	19	advmod	_	_
19	valid	valid	ADJ	JJ	Degree=Pos	17	acomp	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 9
# text = The exposition illustrates the use of geometric logic to enable point - based reasoning for locales.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	exposition	exposition	NOUN	NN	Number=Sing	3	nsubj	_	_
3	illustrates	illustrate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	use	use	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	geometric	geometric	ADJ	JJ	Degree=Pos	8	amod	_	_
8	logic	logic	NOUN	NN	Number=Sing	6	pobj	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	enable	enable	VERB	VB	VerbForm=Inf	5	acl	_	_
11	point	point	NOUN	NN	Number=Sing	13	npadvmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
14	reasoning	reasoning	NOUN	NN	Number=Sing	10	dobj	_	_
15	for	for	ADP	IN	_	14	prep	_	_
16	locales	locale	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 209
# sent_id = 1
# text = A precise concept of concrete geometrical category is introduced in an axiomatic way.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	precise	precise	ADJ	JJ	Degree=Pos	3	amod	_	_
3	concept	concept	NOUN	NN	Number=Sing	9	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	concrete	concrete	ADJ	JJ	Degree=Pos	7	amod	_	_
6	geometrical	geometrical	ADJ	JJ	Degree=Pos	7	amod	_	_
7	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	axiomatic	axiomatic	ADJ	JJ	Degree=Pos	13	amod	_	_
13	way	way	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 2
# text = To any algebra $ L $ for an many - sorted infinitary algebraic theory $ T $ is associated a concrete geometrical category $ Geo(L) $ , the so - called classifying concrete geometrical category of $ L $ , satisfying a universal property.
1	To	to	ADP	IN	_	15	prep	_	_
2	any	any	DET	DT	_	3	det	_	_
3	algebra	algebra	NOUN	NN	Number=Sing	1	pobj	_	_
4	$ L $	$ l $	SYM	$	_	1	pcomp	_	_
5	for	for	ADP	IN	_	1	prep	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
7	many	many	ADJ	JJ	Degree=Pos	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	sorted	sort	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
10	infinitary	infinitary	ADJ	JJ	Degree=Pos	12	amod	_	_
11	algebraic	algebraic	ADJ	JJ	Degree=Pos	12	amod	_	_
12	theory	theory	NOUN	NN	Number=Sing	5	pobj	_	_
13	$ T $	$ t $	SYM	$	_	12	appos	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
17	concrete	concrete	ADJ	JJ	Degree=Pos	19	amod	_	_
18	geometrical	geometrical	ADJ	JJ	Degree=Pos	19	amod	_	_
19	category	category	NOUN	NN	Number=Sing	15	dobj	_	_
20	$ Geo(L) $	$ geo(l) $	SYM	$	_	19	appos	_	_
21	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
23	so	so	ADV	RB	_	25	advmod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
26	classifying	classify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	appos	_	_
27	concrete	concrete	ADJ	JJ	Degree=Pos	29	amod	_	_
28	geometrical	geometrical	ADJ	JJ	Degree=Pos	29	amod	_	_
29	category	category	NOUN	NN	Number=Sing	26	dobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	$ L $	$ l $	SYM	$	_	30	pobj	_	_
32	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
33	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	advcl	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
35	universal	universal	ADJ	JJ	Degree=Pos	36	amod	_	_
36	property	property	NOUN	NN	Number=Sing	33	dobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 3
# text = The terminology "geometrical" is justified firstly for $ Geo(L) $ and secondly for any concrete geometrical category by proving that they are all classifying ones.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	terminology	terminology	NOUN	NN	Number=Sing	4	nmod	_	_
3	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	4	punct	_	SpaceAfter=No
4	geometrical	geometrical	ADJ	JJ	Degree=Pos	7	nsubjpass	_	SpaceAfter=No
5	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	7	punct	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	justified	justify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	firstly	firstly	ADV	RB	_	7	advmod	_	_
9	for	for	ADP	IN	_	7	prep	_	_
10	$ Geo(L) $	$ geo(l) $	SYM	$	_	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	secondly	secondly	ADV	RB	_	13	advmod	_	_
13	for	for	ADP	IN	_	10	conj	_	_
14	any	any	DET	DT	_	17	det	_	_
15	concrete	concrete	ADJ	JJ	Degree=Pos	17	amod	_	_
16	geometrical	geometrical	ADJ	JJ	Degree=Pos	17	amod	_	_
17	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
18	by	by	ADP	IN	_	7	prep	_	_
19	proving	prove	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	18	pcomp	_	_
20	that	that	SCONJ	IN	_	24	mark	_	_
21	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	24	nsubj	_	_
22	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	24	aux	_	_
23	all	all	PRON	DT	_	24	dep	_	_
24	classifying	classify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	ccomp	_	_
25	ones	one	NOUN	NNS	Number=Plur	24	dobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = The legitimate category $ CGC $ of concrete geometrical categories is build up and proved to be the dual of the legitimate category $ TGC $ of topological geometrical categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	legitimate	legitimate	ADJ	JJ	Degree=Pos	3	amod	_	_
3	category	category	NOUN	NN	Number=Sing	10	nsubjpass	_	_
4	$ CGC $	$ cgc $	SYM	$	_	3	appos	_	_
5	of	of	ADP	IN	_	3	prep	_	_
6	concrete	concrete	ADJ	JJ	Degree=Pos	8	amod	_	_
7	geometrical	geometrical	ADJ	JJ	Degree=Pos	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	build	build	VERB	VB	VerbForm=Inf	0	ROOT	_	_
11	up	up	ADP	RP	_	10	prt	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
13	proved	prove	VERB	VBD	Tense=Past|VerbForm=Fin	10	conj	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	be	be	AUX	VB	VerbForm=Inf	13	xcomp	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	dual	dual	ADJ	JJ	Degree=Pos	15	attr	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	legitimate	legitimate	ADJ	JJ	Degree=Pos	21	amod	_	_
21	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
22	$ TGC $	$ tgc $	SYM	$	_	21	appos	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	topological	topological	ADJ	JJ	Degree=Pos	26	amod	_	_
25	geometrical	geometrical	ADJ	JJ	Degree=Pos	26	amod	_	_
26	categories	category	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# doc_id = 210
# sent_id = 1
# text = For every group $ G $ , we construct a functor $ F : SET - - > SET $ (finitary for a finite group $ G $ ) such that the monoid of all natural endotransformations of $ F $ is a group isomorphic to $ G $ .
1	For	for	ADP	IN	_	7	prep	_	_
2	every	every	DET	DT	_	3	det	_	_
3	group	group	NOUN	NN	Number=Sing	1	pobj	_	_
4	$ G $	$ g $	SYM	$	_	1	pobj	_	_
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	functor	functor	NOUN	NN	Number=Sing	7	dobj	_	_
10	$ F : SET - - > SET $	$ f : set - - > set $	SYM	$	_	9	nummod	_	_
11	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	9	punct	_	SpaceAfter=No
12	finitary	finitary	ADJ	JJ	Degree=Pos	9	amod	_	_
13	for	for	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	finite	finite	ADJ	JJ	Degree=Pos	16	compound	_	_
16	group	group	NOUN	NN	Number=Sing	13	pobj	_	_
17	$ G $	$ g $	SYM	$	_	9	appos	_	_
18	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	9	punct	_	_
19	such	such	ADJ	JJ	Degree=Pos	29	acomp	_	_
20	that	that	SCONJ	IN	_	29	mark	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	monoid	monoid	NOUN	NN	Number=Sing	29	nsubj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	all	all	DET	DT	_	26	det	_	_
25	natural	natural	ADJ	JJ	Degree=Pos	26	amod	_	_
26	endotransformations	endotransformation	NOUN	NNS	Number=Plur	23	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	$ F $	$ f $	SYM	$	_	27	pobj	_	_
29	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	ccomp	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
31	group	group	NOUN	NN	Number=Sing	29	attr	_	_
32	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	31	amod	_	_
33	to	to	ADP	IN	_	29	prep	_	_
34	$ G $	$ g $	SYM	$	_	33	pobj	_	_
35	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 211
# sent_id = 1
# text = We consider a semi - abelian category $ V $
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
4	semi	semi	ADJ	JJ	Degree=Pos	7	amod	_	_
5	-	-	ADJ	JJ	Degree=Pos	7	amod	_	_
6	abelian	abelian	ADJ	JJ	Degree=Pos	7	amod	_	_
7	category	category	NOUN	NN	Number=Sing	2	dobj	_	_
8	$ V $	$ v $	SYM	$	_	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = and we write $ Act(G, X) $ for the set of actions of the object $ G $ on the object $ X $ , in the sense of the theory of semi - direct products in $ V $ .
1	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	write	write	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	$ Act(G, X) $	$ act(g, x) $	SYM	$	_	3	dobj	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	set	set	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	actions	action	NOUN	NNS	Number=Plur	8	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	object	object	NOUN	NN	Number=Sing	10	pobj	_	_
13	$ G $	$ g $	SYM	$	_	4	appos	_	_
14	on	on	ADP	IN	_	3	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	object	object	NOUN	NN	Number=Sing	14	pobj	_	_
17	$ X $	$ x $	SYM	$	_	16	appos	_	_
18	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
19	in	in	ADP	IN	_	3	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	sense	sense	NOUN	NN	Number=Sing	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	theory	theory	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	semi	semi	ADJ	JJ	Degree=Pos	28	advmod	_	_
27	-	-	ADJ	JJ	Degree=Pos	28	punct	_	_
28	direct	direct	ADJ	JJ	Degree=Pos	29	amod	_	_
29	products	product	NOUN	NNS	Number=Plur	25	pobj	_	_
30	in	in	ADP	IN	_	29	prep	_	_
31	$ V $	$ v $	SYM	$	_	30	pobj	_	_
32	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = We investigate the representability of the functor $ Act( - , X) $ in the case where $ V $ is locally presentable, with finite limits commuting with filtered colimits.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	representability	representability	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	functor	functor	PROPN	NNP	Number=Sing	5	pobj	_	_
8	$ Act( - , X) $	$ Act( - , X) $	PROPN	NNP	Number=Sing	7	appos	_	_
9	in	in	ADP	IN	_	4	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	case	case	NOUN	NN	Number=Sing	9	pobj	_	_
12	where	where	SCONJ	WRB	_	14	advmod	_	_
13	$ V $	$ v $	SYM	$	_	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	relcl	_	_
15	locally	locally	ADV	RB	_	16	advmod	_	_
16	presentable	presentable	ADJ	JJ	Degree=Pos	14	acomp	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
18	with	with	ADP	IN	_	14	prep	_	_
19	finite	finite	ADJ	JJ	Degree=Pos	20	amod	_	_
20	limits	limit	NOUN	NNS	Number=Plur	18	pobj	_	_
21	commuting	commute	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	acl	_	_
22	with	with	ADP	IN	_	21	prep	_	_
23	filtered	filter	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
24	colimits	colimit	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = This contains all categories of models of a semi - abelian theory in a Grothendieck topos, thus in particular all semi - abelian varieties of universal algebra.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	contains	contain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	all	all	DET	DT	_	4	det	_	_
4	categories	category	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	models	model	NOUN	NNS	Number=Plur	5	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
9	semi	semi	ADJ	JJ	Degree=Pos	11	amod	_	_
10	-	-	ADJ	JJ	Degree=Pos	11	punct	_	_
11	abelian	abelian	ADJ	JJ	Degree=Pos	12	amod	_	_
12	theory	theory	NOUN	NN	Number=Sing	7	pobj	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	16	compound	_	_
16	topos	topos	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
18	thus	thus	ADV	RB	_	25	advmod	_	_
19	in	in	ADP	IN	_	25	prep	_	_
20	particular	particular	ADJ	JJ	Degree=Pos	19	amod	_	_
21	all	all	DET	DT	_	25	det	_	_
22	semi	semi	ADJ	JJ	Degree=Pos	25	amod	_	_
23	-	-	ADJ	JJ	Degree=Pos	25	amod	_	_
24	abelian	abelian	ADJ	JJ	Degree=Pos	25	amod	_	_
25	varieties	variety	NOUN	NNS	Number=Plur	2	dep	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	universal	universal	ADJ	JJ	Degree=Pos	28	amod	_	_
28	algebra	algebra	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = For such categories, we prove first that the representability of $ Act( - , X) $ reduces to the preservation of binary coproducts.
1	For	for	ADP	IN	_	6	prep	_	_
2	such	such	ADJ	JJ	Degree=Pos	3	amod	_	_
3	categories	category	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	first	first	ADV	RB	_	6	advmod	_	_
8	that	that	SCONJ	IN	_	13	mark	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	representability	representability	NOUN	NN	Number=Sing	13	nsubj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	$ Act( - , X) $	$ act( - , x) $	SYM	$	_	13	nmod	_	_
13	reduces	reduce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	preservation	preservation	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	binary	binary	ADJ	JJ	Degree=Pos	19	amod	_	_
19	coproducts	coproduct	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 6
# text = Next we give both a very simple necessary condition and a very simple sufficient condition, in terms of amalgamation properties, for the preservation of binary coproducts by the functor $ Act( - , X) $ in a general semi - abelian category.
1	Next	next	ADV	RB	_	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	both	both	CCONJ	CC	ConjType=Cmp	9	preconj	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
6	very	very	ADV	RB	_	7	advmod	_	_
7	simple	simple	ADJ	JJ	Degree=Pos	9	amod	_	_
8	necessary	necessary	ADJ	JJ	Degree=Pos	9	amod	_	_
9	condition	condition	NOUN	NN	Number=Sing	3	dobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
12	very	very	ADV	RB	_	13	advmod	_	_
13	simple	simple	ADJ	JJ	Degree=Pos	15	amod	_	_
14	sufficient	sufficient	ADJ	JJ	Degree=Pos	15	amod	_	_
15	condition	condition	NOUN	NN	Number=Sing	9	conj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
17	in	in	ADP	IN	_	3	prep	_	_
18	terms	term	NOUN	NNS	Number=Plur	17	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	amalgamation	amalgamation	NOUN	NN	Number=Sing	21	compound	_	_
21	properties	property	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
23	for	for	ADP	IN	_	3	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	preservation	preservation	NOUN	NN	Number=Sing	23	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	binary	binary	ADJ	JJ	Degree=Pos	28	amod	_	_
28	coproducts	coproduct	NOUN	NNS	Number=Plur	26	pobj	_	_
29	by	by	ADP	IN	_	25	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	functor	functor	PROPN	NNP	Number=Sing	29	pobj	_	_
32	$ Act( - , X) $	$ Act( - , X) $	PROPN	NNP	Number=Sing	29	pobj	_	_
33	in	in	ADP	IN	_	25	prep	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
35	general	general	ADJ	JJ	Degree=Pos	39	amod	_	_
36	semi	semi	ADJ	JJ	Degree=Pos	39	amod	_	_
37	-	-	ADJ	JJ	Degree=Pos	39	amod	_	_
38	abelian	abelian	ADJ	JJ	Degree=Pos	39	amod	_	_
39	category	category	NOUN	NN	Number=Sing	33	pobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = Finally, we exhibit the precise form of the more involved ``if and only if'' amalgamation property corresponding to the representability of actions: this condition is in particular related to a new notion of ``normalization of a morphism''.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	exhibit	exhibit	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	precise	precise	ADJ	JJ	Degree=Pos	7	amod	_	_
7	form	form	NOUN	NN	Number=Sing	4	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	PRON	DT	Definite=Def|PronType=Art	11	advmod	_	_
10	more	more	ADV	RBR	Degree=Cmp	11	advmod	_	_
11	involved	involved	ADJ	JJ	Degree=Pos	8	pobj	_	_
12	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	11	punct	_	SpaceAfter=No
13	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	11	punct	_	SpaceAfter=No
14	if	if	SCONJ	IN	_	11	dep	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	only	only	ADV	RB	_	14	conj	_	_
17	if	if	SCONJ	IN	_	30	mark	_	SpaceAfter=No
18	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	17	punct	_	_
19	amalgamation	amalgamation	NOUN	NN	Number=Sing	20	compound	_	_
20	property	property	NOUN	NN	Number=Sing	17	pobj	_	_
21	corresponding	corresponding	NOUN	NN	Number=Sing	20	amod	_	_
22	to	to	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	representability	representability	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	actions	action	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
27	:	:	PUNCT	:	_	30	punct	_	_
28	this	this	DET	DT	Number=Sing|PronType=Dem	29	det	_	_
29	condition	condition	NOUN	NN	Number=Sing	30	nsubj	_	_
30	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	advcl	_	_
31	in	in	ADP	IN	_	33	prep	_	_
32	particular	particular	ADJ	JJ	Degree=Pos	31	amod	_	_
33	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	30	acomp	_	_
34	to	to	ADP	IN	_	33	prep	_	_
35	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
36	new	new	ADJ	JJ	Degree=Pos	37	amod	_	_
37	notion	notion	NOUN	NN	Number=Sing	34	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	38	punct	_	SpaceAfter=No
40	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	38	punct	_	SpaceAfter=No
41	normalization	normalization	NOUN	NN	Number=Sing	38	pobj	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	a	a	DET	DT	Definite=Ind|PronType=Art	44	det	_	_
44	morphism	morphism	NOUN	NN	Number=Sing	42	pobj	_	SpaceAfter=No
45	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	30	punct	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 8
# text = We provide also a wide supply of algebraic examples and counter - examples, giving in particular evidence of the relevance of the object representing $ Act( - , X) $ , when it turns out to exist.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	also	also	ADV	RB	_	2	advmod	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	wide	wide	ADJ	JJ	Degree=Pos	6	amod	_	_
6	supply	supply	NOUN	NN	Number=Sing	2	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	algebraic	algebraic	ADJ	JJ	Degree=Pos	9	amod	_	_
9	examples	example	NOUN	NNS	Number=Plur	7	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	counter	counter	NOUN	NN	Number=Sing	9	conj	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
13	examples	example	NOUN	NNS	Number=Plur	9	conj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
15	giving	give	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
16	in	in	ADP	RP	_	15	prt	_	_
17	particular	particular	ADJ	JJ	Degree=Pos	18	amod	_	_
18	evidence	evidence	NOUN	NN	Number=Sing	15	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	relevance	relevance	NOUN	NN	Number=Sing	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	object	object	NOUN	NN	Number=Sing	22	pobj	_	_
25	representing	represent	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	24	acl	_	_
26	$ Act( - , X) $	$ act( - , x) $	SYM	$	_	25	dobj	_	_
27	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
28	when	when	SCONJ	WRB	_	30	advmod	_	_
29	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	30	nsubj	_	_
30	turns	turn	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	advcl	_	_
31	out	out	ADP	RP	_	30	prt	_	_
32	to	to	PART	TO	_	33	aux	_	_
33	exist	exist	VERB	VB	VerbForm=Inf	30	xcomp	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 212
# sent_id = 1
# text = We generalize the Baues - Jibladze descent theorem to a large class of groupoid enriched categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
4	Baues	Baues	PROPN	NNPS	Number=Plur	6	compound	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	Jibladze	Jibladze	PROPN	NNP	Number=Sing	7	compound	_	_
7	descent	descent	NOUN	NN	Number=Sing	8	nsubj	_	_
8	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	2	ccomp	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	large	large	ADJ	JJ	Degree=Pos	12	amod	_	_
12	class	class	NOUN	NN	Number=Sing	9	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	groupoid	groupoid	NOUN	NN	Number=Sing	15	npadvmod	_	_
15	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
16	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 213
# sent_id = 1
# text = The definition of a category of $ (T, V) $ - algebras, where $ V $ is a unital commutative quantale and $ T $ is a $ Set $ - monad, requires the existence of a certain lax extension of $ T $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	definition	definition	NOUN	NN	Number=Sing	20	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	$ (T, V) $	$ (t, v) $	SYM	$	_	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	algebras	algebra	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	where	where	SCONJ	WRB	_	13	advmod	_	_
12	$ V $	$ v $	SYM	$	_	13	nsubj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	relcl	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	unital	unital	ADJ	JJ	Degree=Pos	17	amod	_	_
16	commutative	commutative	ADJ	JJ	Degree=Pos	17	amod	_	_
17	quantale	quantale	NOUN	NN	Number=Sing	13	attr	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	$ T $	$ t $	SYM	$	_	20	nsubj	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
22	$ Set $	$ set $	SYM	$	_	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	monad	monad	NOUN	NNS	Number=Plur	20	attr	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
26	requires	require	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	conj	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	existence	existence	NOUN	NN	Number=Sing	26	dobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
31	certain	certain	ADJ	JJ	Degree=Pos	33	amod	_	_
32	lax	lax	ADJ	JJ	Degree=Pos	33	amod	_	_
33	extension	extension	NOUN	NN	Number=Sing	29	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	$ T $	$ t $	SYM	$	_	34	pobj	_	_
36	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this article, we present a general construction of such an extension.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	article	article	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	general	general	ADJ	JJ	Degree=Pos	9	amod	_	_
9	construction	construction	NOUN	NN	Number=Sing	6	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	such	such	DET	PDT	_	13	predet	_	_
12	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	extension	extension	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = This leads to the formation of two categories of $ (T, V) $ - algebras: the category $ Alg(T, V) $ of canonical $ (T, V) $ - algebras, and the category $ Alg(T', V) $ of op - canonical $ (T, V) $ - algebras.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	leads	lead	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	formation	formation	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	two	two	NUM	CD	NumType=Card	8	nummod	_	_
8	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	$ (T, V) $	$ (t, v) $	SYM	$	_	9	pobj	_	_
11	-	-	PUNCT	:	_	12	punct	_	_
12	algebras	algebra	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
13	:	:	PUNCT	:	_	2	punct	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	category	category	NOUN	NN	Number=Sing	1	appos	_	_
16	$ Alg(T, V) $	$ alg(t, v) $	SYM	$	_	15	appos	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	canonical	canonical	ADJ	JJ	Degree=Pos	21	amod	_	_
19	$ (T, V) $	$ (T, V) $	PROPN	NNP	Number=Sing	18	nmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	algebras	algebra	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	category	category	NOUN	NN	Number=Sing	15	conj	_	_
26	$ Alg(T', V) $	$ alg(t', v) $	SYM	$	_	25	appos	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	op	op	NOUN	NN	Number=Sing	27	pobj	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	canonical	canonical	NOUN	NN	Number=Sing	15	appos	_	_
31	$ (T, V) $	$ (t, v) $	SYM	$	_	33	compound	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	algebras	algebra	NOUN	NNS	Number=Plur	15	conj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = The usual topological - like examples of categories of $ (T, V) $ - algebras (preordered sets, topological, metric and approach spaces) are obtained in this way, and the category of closure spaces appears as a category of canonical $ (P, V) $ - algebras, where $ P $ is the powerset monad.
1	The	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
2	usual	usual	ADJ	JJ	Degree=Pos	6	amod	_	_
3	topological	topological	ADJ	JJ	Degree=Pos	5	amod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	like	like	ADJ	JJ	Degree=Pos	6	amod	_	_
6	examples	example	NOUN	NNS	Number=Plur	25	nsubjpass	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	$ (T, V) $	$ (t, v) $	SYM	$	_	12	nmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	algebras	algebras	PROPN	NNP	Number=Sing	9	pobj	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
14	preordered	preordere	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
15	sets	set	NOUN	NNS	Number=Plur	12	appos	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	topological	topological	ADJ	JJ	Degree=Pos	22	amod	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	metric	metric	ADJ	JJ	Degree=Pos	17	conj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	approach	approach	NOUN	NN	Number=Sing	19	conj	_	_
22	spaces	space	NOUN	NNS	Number=Plur	12	appos	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	12	punct	_	_
24	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	25	auxpass	_	_
25	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
26	in	in	ADP	IN	_	25	prep	_	_
27	this	this	DET	DT	Number=Sing|PronType=Dem	28	det	_	_
28	way	way	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	category	category	NOUN	NN	Number=Sing	36	nsubj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	closure	closure	NOUN	NN	Number=Sing	35	compound	_	_
35	spaces	space	NOUN	NNS	Number=Plur	33	pobj	_	_
36	appears	appear	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	conj	_	_
37	as	as	ADP	IN	_	36	prep	_	_
38	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
39	category	category	NOUN	NN	Number=Sing	37	pobj	_	_
40	of	of	ADP	IN	_	39	prep	_	_
41	canonical	canonical	ADJ	JJ	Degree=Pos	44	amod	_	_
42	$ (P, V) $	$ (P, V) $	PROPN	NNP	Number=Sing	44	compound	_	_
43	-	-	PUNCT	HYPH	PunctType=Dash	44	punct	_	_
44	algebras	algebra	NOUN	NNS	Number=Plur	40	pobj	_	SpaceAfter=No
45	,	,	PUNCT	,	PunctType=Comm	44	punct	_	_
46	where	where	SCONJ	WRB	_	48	advmod	_	_
47	$ P $	$ p $	SYM	$	_	48	nsubj	_	_
48	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	44	relcl	_	_
49	the	the	DET	DT	Definite=Def|PronType=Art	51	det	_	_
50	powerset	powerset	NOUN	NN	Number=Sing	51	compound	_	_
51	monad	monad	NOUN	NNS	Number=Plur	48	attr	_	SpaceAfter=No
52	.	.	PUNCT	.	PunctType=Peri	36	punct	_	SpaceAfter=No

# sent_id = 5
# text = This unified presentation allows us to study how these categories are related, and it is shown that under suitable hypotheses both $ Alg(T, V) $ and $ Alg(T', V) $ embed coreflectively into $ Alg(P, V) $ .
1	This	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
2	unified	unified	ADJ	JJ	Degree=Pos	3	amod	_	_
3	presentation	presentation	NOUN	NN	Number=Sing	4	nsubj	_	_
4	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	study	study	VERB	VB	VerbForm=Inf	4	ccomp	_	_
8	how	how	SCONJ	WRB	_	12	advmod	_	_
9	these	these	DET	DT	Number=Plur|PronType=Dem	10	det	_	_
10	categories	category	NOUN	NNS	Number=Plur	12	nsubjpass	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	ccomp	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
15	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	17	nsubjpass	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	auxpass	_	_
17	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	conj	_	_
18	that	that	SCONJ	IN	_	26	mark	_	_
19	under	under	ADP	IN	_	26	prep	_	_
20	suitable	suitable	ADJ	JJ	Degree=Pos	21	amod	_	_
21	hypotheses	hypothesis	NOUN	NNS	Number=Plur	19	pobj	_	_
22	both	both	CCONJ	CC	ConjType=Cmp	23	preconj	_	_
23	$ Alg(T, V) $	$ alg(t, v) $	SYM	$	_	21	appos	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	$ Alg(T', V) $	$ alg(t', v) $	SYM	$	_	26	nsubj	_	_
26	embed	embe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	ccomp	_	_
27	coreflectively	coreflectively	ADV	RB	_	26	advmod	_	_
28	into	into	ADP	IN	_	26	prep	_	_
29	$ Alg(P, V) $	$ alg(p, v) $	SYM	$	_	28	pobj	_	_
30	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# doc_id = 214
# sent_id = 1
# text = This paper is the second in a series exploring the properties of a functor which assigns a homotopy double groupoid with connections to a Hausdorff space.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	second	second	ADJ	JJ	Degree=Pos	3	attr	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	series	series	NOUN	NN	Number=Sing	6	pobj	_	_
9	exploring	explore	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	acl	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	properties	property	NOUN	NNS	Number=Plur	9	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	functor	functor	NOUN	NN	Number=Sing	12	pobj	_	_
15	which	which	PRON	WDT	_	16	nsubj	_	_
16	assigns	assign	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	homotopy	homotopy	NOUN	NN	Number=Sing	16	dobj	_	_
19	double	double	ADJ	JJ	Degree=Pos	20	amod	_	_
20	groupoid	groupoid	NOUN	NN	Number=Sing	16	dobj	_	_
21	with	with	ADP	IN	_	16	prep	_	_
22	connections	connection	NOUN	NNS	Number=Plur	21	pobj	_	_
23	to	to	ADP	IN	_	22	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
25	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	26	compound	_	_
26	space	space	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that this functor satisfies a version of the van Kampen theorem, and so is a suitable tool for nonabelian, 2 - dimensional, local - to - global problems.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	6	mark	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	functor	functor	NOUN	NN	Number=Sing	6	nsubj	_	_
6	satisfies	satisfy	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	version	version	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	van	van	PROPN	NNP	Number=Sing	12	compound	_	_
12	Kampen	Kampen	PROPN	NNP	Number=Sing	9	pobj	_	_
13	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	6	ccomp	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
16	so	so	ADV	RB	_	17	advmod	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	conj	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	suitable	suitable	ADJ	JJ	Degree=Pos	20	amod	_	_
20	tool	tool	NOUN	NN	Number=Sing	17	attr	_	_
21	for	for	ADP	IN	_	20	prep	_	_
22	nonabelian	nonabelian	PROPN	NNP	Number=Sing	33	amod	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	2	2	NUM	CD	NumType=Card	26	npadvmod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	dimensional	dimensional	ADJ	JJ	Degree=Pos	33	amod	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
28	local	local	ADJ	JJ	Degree=Pos	33	amod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
30	to	to	ADP	IN	_	28	prep	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
32	global	global	ADJ	JJ	Degree=Pos	30	pobj	_	_
33	problems	problem	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The methods are analogous to those developed by Brown and Higgins for similar theorems for other higher homotopy groupoids.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	methods	method	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	analogous	analogous	ADJ	JJ	Degree=Pos	3	acomp	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	those	those	PRON	DT	Number=Plur|PronType=Dem	5	pobj	_	_
7	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
8	by	by	ADP	IN	_	7	agent	_	_
9	Brown	Brown	PROPN	NNP	Number=Sing	8	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	Higgins	Higgins	PROPN	NNP	Number=Sing	9	conj	_	_
12	for	for	ADP	IN	_	7	prep	_	_
13	similar	similar	ADJ	JJ	Degree=Pos	14	amod	_	_
14	theorems	theorem	NOUN	NNS	Number=Plur	12	pobj	_	_
15	for	for	ADP	IN	_	14	prep	_	_
16	other	other	ADJ	JJ	Degree=Pos	19	amod	_	_
17	higher	high	ADJ	JJR	Degree=Cmp	19	amod	_	_
18	homotopy	homotopy	NOUN	NN	Number=Sing	19	compound	_	_
19	groupoids	groupoid	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = An integral part of the proof is a detailed discussion of commutative cubes in a double category with connections, and a proof of the key result that any composition of commutative cubes is commutative.
1	An	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	integral	integral	ADJ	JJ	Degree=Pos	3	amod	_	_
3	part	part	NOUN	NN	Number=Sing	7	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	proof	proof	NOUN	NN	Number=Sing	4	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	detailed	detailed	ADJ	JJ	Degree=Pos	10	amod	_	_
10	discussion	discussion	NOUN	NN	Number=Sing	7	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	commutative	commutative	ADJ	JJ	Degree=Pos	13	amod	_	_
13	cubes	cube	NOUN	NNS	Number=Plur	11	pobj	_	_
14	in	in	ADP	IN	_	10	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	double	double	ADJ	JJ	Degree=Pos	17	amod	_	_
17	category	category	NOUN	NN	Number=Sing	14	pobj	_	_
18	with	with	ADP	IN	_	10	prep	_	_
19	connections	connection	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
23	proof	proof	NOUN	NN	Number=Sing	10	conj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	key	key	ADJ	JJ	Degree=Pos	27	amod	_	_
27	result	result	NOUN	NN	Number=Sing	24	pobj	_	_
28	that	that	SCONJ	IN	_	34	mark	_	_
29	any	any	DET	DT	_	30	det	_	_
30	composition	composition	NOUN	NN	Number=Sing	34	nsubj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	commutative	commutative	ADJ	JJ	Degree=Pos	33	amod	_	_
33	cubes	cube	NOUN	NNS	Number=Plur	31	pobj	_	_
34	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	acl	_	_
35	commutative	commutative	ADJ	JJ	Degree=Pos	34	acomp	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 5
# text = These results have recently been generalised to all dimensions by Philip Higgins.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	results	result	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
3	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	aux	_	_
4	recently	recently	ADV	RB	_	6	advmod	_	_
5	been	be	AUX	VBN	Tense=Past|VerbForm=Part	6	auxpass	_	_
6	generalised	generalise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	to	to	ADP	IN	_	6	prep	_	_
8	all	all	DET	DT	_	9	det	_	_
9	dimensions	dimension	NOUN	NNS	Number=Plur	7	pobj	_	_
10	by	by	ADP	IN	_	9	prep	_	_
11	Philip	Philip	PROPN	NNP	Number=Sing	12	compound	_	_
12	Higgins	Higgins	PROPN	NNP	Number=Sing	10	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 215
# sent_id = 1
# text = A survey of parts of General Coalgebra is presented with applications to the theory of systems.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	survey	survey	NOUN	NN	Number=Sing	9	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	parts	part	NOUN	NNS	Number=Plur	3	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	General	General	PROPN	NNP	Number=Sing	7	compound	_	_
7	Coalgebra	Coalgebra	PROPN	NNP	Number=Sing	5	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	applications	application	NOUN	NNS	Number=Plur	10	pobj	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	theory	theory	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	systems	system	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 2
# text = Stress is laid on terminal coalgebras and coinduction as well as iterative algebras and iterative theories.
1	Stress	stress	NOUN	NN	Number=Sing	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	laid	lay	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	on	on	ADP	IN	_	3	prep	_	_
5	terminal	terminal	ADJ	JJ	Degree=Pos	6	amod	_	_
6	coalgebras	coalgebra	NOUN	NNS	Number=Plur	4	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	coinduction	coinduction	NOUN	NN	Number=Sing	6	conj	_	_
9	as	as	ADV	RB	_	11	advmod	_	_
10	well	well	ADV	RB	Degree=Pos	11	advmod	_	_
11	as	as	ADP	IN	_	6	cc	_	_
12	iterative	iterative	ADJ	JJ	Degree=Pos	13	amod	_	_
13	algebras	algebra	NOUN	NNS	Number=Plur	6	conj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	iterative	iterative	ADJ	JJ	Degree=Pos	16	amod	_	_
16	theories	theory	NOUN	NNS	Number=Plur	13	conj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 216
# sent_id = 1
# text = In the quest for an elegant formulation of the notion of ``polycategory'' we develop a more symmetric counterpart to Burroni's notion of `` $ T $ - category'', where $ T $ is a cartesian monad on a category $ X $ with pullbacks.
1	In	in	ADP	IN	_	0	ROOT	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	quest	quest	NOUN	NN	Number=Sing	1	pobj	_	_
4	for	for	ADP	IN	_	3	prep	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	elegant	elegant	ADJ	JJ	Degree=Pos	7	amod	_	_
7	formulation	formulation	NOUN	NN	Number=Sing	4	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	notion	notion	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	14	punct	_	SpaceAfter=No
13	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	14	punct	_	SpaceAfter=No
14	polycategory	polycategory	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
15	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	14	punct	_	_
16	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	17	nsubj	_	_
17	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	14	relcl	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
19	more	more	ADV	RBR	Degree=Cmp	20	advmod	_	_
20	symmetric	symmetric	ADJ	JJ	Degree=Pos	21	amod	_	_
21	counterpart	counterpart	NOUN	NN	Number=Sing	17	dobj	_	_
22	to	to	ADP	IN	_	21	prep	_	_
23	Burroni	Burroni	PROPN	NNP	Number=Sing	25	poss	_	SpaceAfter=No
24	's	's	PART	POS	_	23	case	_	_
25	notion	notion	NOUN	NN	Number=Sing	22	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	SpaceAfter=No
28	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	_
29	$ T $	$ t $	SYM	$	_	31	nummod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	category	category	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
32	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	25	punct	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
34	where	where	SCONJ	WRB	_	36	advmod	_	_
35	$ T $	$ t $	SYM	$	_	36	nsubj	_	_
36	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	relcl	_	_
37	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
38	cartesian	cartesian	ADJ	JJ	Degree=Pos	39	amod	_	_
39	monad	monad	NOUN	NNS	Number=Plur	36	attr	_	_
40	on	on	ADP	IN	_	39	prep	_	_
41	a	a	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
42	category	category	NOUN	NN	Number=Sing	40	pobj	_	_
43	$ X $	$ x $	SYM	$	_	42	appos	_	_
44	with	with	ADP	IN	_	39	prep	_	_
45	pullbacks	pullback	NOUN	NNS	Number=Plur	44	pobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = Our approach involves two such monads, $ S $ and $ T $ , that are linked by a suitable generalization of a distributive law in the sense of Beck.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	approach	approach	NOUN	NN	Number=Sing	3	nsubj	_	_
3	involves	involve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	two	two	NUM	CD	NumType=Card	6	nummod	_	_
5	such	such	ADJ	JJ	Degree=Pos	6	amod	_	_
6	monads	monad	NOUN	NNS	Number=Plur	3	dobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	$ S $	$ s $	SYM	$	_	6	appos	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	$ T $	$ t $	SYM	$	_	8	conj	_	_
11	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
12	that	that	PRON	WDT	PronType=Rel	14	nsubjpass	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	linked	link	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	relcl	_	_
15	by	by	ADP	IN	_	14	agent	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	suitable	suitable	ADJ	JJ	Degree=Pos	18	amod	_	_
18	generalization	generalization	NOUN	NN	Number=Sing	15	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	distributive	distributive	ADJ	JJ	Degree=Pos	22	amod	_	_
22	law	law	NOUN	NN	Number=Sing	19	pobj	_	_
23	in	in	ADP	IN	_	14	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	sense	sense	NOUN	NN	Number=Sing	23	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	Beck	Beck	PROPN	NNP	Number=Sing	26	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = This takes the form of a span $ omega : TS ST $ in the functor category $ [X, X] $ and guarantees essential associativity for a canonical pullback - induced composition of $ S - T $ - spans over $ X $ , identifying them as the 1 - cells of a bicategory, whose (internal) monoids then qualify as `` $ omega $ - categories''.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	takes	take	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	form	form	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	span	span	NOUN	NN	Number=Sing	5	pobj	_	_
8	$ omega : TS ST $	$ omega : ts st $	SYM	$	_	7	appos	_	_
9	in	in	ADP	IN	_	2	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	functor	functor	NOUN	NN	Number=Sing	12	compound	_	_
12	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
13	$ [X, X] $	$ [x, x] $	SYM	$	_	12	appos	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
15	guarantees	guarantee	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
16	essential	essential	ADJ	JJ	Degree=Pos	17	amod	_	_
17	associativity	associativity	NOUN	NN	Number=Sing	15	dobj	_	_
18	for	for	ADP	IN	_	15	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
20	canonical	canonical	ADJ	JJ	Degree=Pos	24	amod	_	_
21	pullback	pullback	NOUN	NN	Number=Sing	23	npadvmod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
24	composition	composition	NOUN	NN	Number=Sing	18	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	$ S - T $	$ s - t $	SYM	$	_	28	nmod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	spans	span	NOUN	NNS	Number=Plur	25	pobj	_	_
29	over	over	ADP	IN	_	24	prep	_	_
30	$ X $	$ x $	SYM	$	_	29	pobj	_	_
31	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
32	identifying	identify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	advcl	_	_
33	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	32	dobj	_	_
34	as	as	ADP	IN	_	32	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
36	1	1	NUM	CD	NumType=Card	38	nummod	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	38	punct	_	_
38	cells	cell	NOUN	NNS	Number=Plur	34	pobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
41	bicategory	bicategory	NOUN	NN	Number=Sing	39	pobj	_	SpaceAfter=No
42	,	,	PUNCT	,	PunctType=Comm	41	punct	_	_
43	whose	whose	DET	WP$	Poss=Yes	47	poss	_	_
44	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	47	punct	_	SpaceAfter=No
45	internal	internal	ADJ	JJ	Degree=Pos	47	amod	_	SpaceAfter=No
46	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	47	punct	_	_
47	monoids	monoid	NOUN	NNS	Number=Plur	49	nsubj	_	_
48	then	then	ADV	RB	PronType=Dem	49	advmod	_	_
49	qualify	qualify	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
50	as	as	ADP	IN	_	49	prep	_	_
51	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	50	punct	_	SpaceAfter=No
52	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	50	punct	_	_
53	$ omega $	$ omega $	SYM	$	_	55	compound	_	_
54	-	-	PUNCT	HYPH	PunctType=Dash	55	punct	_	_
55	categories	category	NOUN	NNS	Number=Plur	50	pobj	_	SpaceAfter=No
56	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	49	punct	_	SpaceAfter=No
57	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = In case that $ S $ and $ T $ both are the free monoid monad on set, we construct an omega utilizing an apparently new classical distributive law linking the free semigroup monad with itself.
1	In	in	ADP	IN	_	17	prep	_	_
2	case	case	NOUN	NN	Number=Sing	1	pobj	_	_
3	that	that	SCONJ	IN	_	8	mark	_	_
4	$ S $	$ s $	SYM	$	_	3	nmod	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	$ T $	$ t $	SYM	$	_	7	nmod	_	_
7	both	both	PRON	DT	_	8	nsubj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	acl	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
10	free	free	ADJ	JJ	Degree=Pos	12	amod	_	_
11	monoid	monoid	NOUN	NN	Number=Sing	12	compound	_	_
12	monad	monad	NOUN	NNS	Number=Plur	8	attr	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	set	set	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
16	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	17	nsubj	_	_
17	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
18	an	an	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	omega	omega	NOUN	NN	Number=Sing	17	dobj	_	_
20	utilizing	utilize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	acl	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
22	apparently	apparently	ADV	RB	_	23	advmod	_	_
23	new	new	ADJ	JJ	Degree=Pos	26	amod	_	_
24	classical	classical	ADJ	JJ	Degree=Pos	26	amod	_	_
25	distributive	distributive	ADJ	JJ	Degree=Pos	26	amod	_	_
26	law	law	NOUN	NN	Number=Sing	20	dobj	_	_
27	linking	link	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	26	acl	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
29	free	free	ADJ	JJ	Degree=Pos	30	amod	_	_
30	semigroup	semigroup	NOUN	NN	Number=Sing	31	compound	_	_
31	monad	monad	NOUN	NNS	Number=Plur	27	dobj	_	_
32	with	with	ADP	IN	_	31	prep	_	_
33	itself	itself	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs|Reflex=Yes	32	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 5
# text = Our construction then gives rise to so - called ``planar polycategories'', which nowadays seem to be of more intrinsic interest than Szabo's original polycategories.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	construction	construction	NOUN	NN	Number=Sing	4	nsubj	_	_
3	then	then	ADV	RB	PronType=Dem	4	advmod	_	_
4	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	rise	rise	NOUN	NN	Number=Sing	4	dobj	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	so	so	ADV	RB	_	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
10	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	13	punct	_	SpaceAfter=No
11	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	13	punct	_	SpaceAfter=No
12	planar	planar	ADJ	JJ	Degree=Pos	13	amod	_	_
13	polycategories	polycategorie	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
14	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	13	punct	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
16	which	which	PRON	WDT	_	18	nsubj	_	_
17	nowadays	nowadays	ADV	RB	_	18	advmod	_	_
18	seem	seem	VERB	VBP	Tense=Pres|VerbForm=Fin	13	relcl	_	_
19	to	to	PART	TO	_	20	aux	_	_
20	be	be	AUX	VB	VerbForm=Inf	18	xcomp	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	more	more	ADV	RBR	Degree=Cmp	23	advmod	_	_
23	intrinsic	intrinsic	ADJ	JJ	Degree=Pos	24	amod	_	_
24	interest	interest	NOUN	NN	Number=Sing	21	pobj	_	_
25	than	than	ADP	IN	_	24	prep	_	_
26	Szabo	Szabo	PROPN	NNP	Number=Sing	29	poss	_	SpaceAfter=No
27	's	's	PART	POS	_	26	case	_	_
28	original	original	ADJ	JJ	Degree=Pos	29	amod	_	_
29	polycategories	polycategorie	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 6
# text = Weakly cartesian monads on $ X $ may be accommodated as well by first quotienting the bicategory of $ X $ - spans.
1	Weakly	weakly	ADJ	JJ	Degree=Pos	3	amod	_	_
2	cartesian	cartesian	ADJ	JJ	Degree=Pos	3	amod	_	_
3	monads	monad	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
4	on	on	ADP	IN	_	3	prep	_	_
5	$ X $	$ x $	SYM	$	_	4	pobj	_	_
6	may	may	AUX	MD	VerbForm=Fin	8	aux	_	_
7	be	be	AUX	VB	VerbForm=Inf	8	auxpass	_	_
8	accommodated	accommodate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	as	as	ADV	RB	_	10	advmod	_	_
10	well	well	ADV	RB	Degree=Pos	8	advmod	_	_
11	by	by	ADP	IN	_	8	agent	_	_
12	first	first	ADV	RB	_	13	advmod	_	_
13	quotienting	quotiente	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	pcomp	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	bicategory	bicategory	NOUN	NN	Number=Sing	13	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	$ X $	$ x $	SYM	$	_	19	nmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	spans	span	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 217
# sent_id = 1
# text = We revise our `Physical Traces' paper in the light of the results in another work.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	revise	revise	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	6	poss	_	_
4	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	6	punct	_	SpaceAfter=No
5	Physical	Physical	PROPN	NNP	Number=Sing	6	compound	_	_
6	Traces	Traces	PROPN	NNPS	Number=Plur	8	poss	_	SpaceAfter=No
7	'	'	PART	POS	_	6	case	_	_
8	paper	paper	NOUN	NN	Number=Sing	2	dobj	_	_
9	in	in	ADP	IN	_	2	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	light	light	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	results	result	NOUN	NNS	Number=Plur	12	pobj	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	another	another	DET	DT	_	17	det	_	_
17	work	work	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The key fact is that the notion of a strongly compact closed category allows abstract notions of adjoint, bipartite projector and inner product to be defined, and their key properties to be proved.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	key	key	ADJ	JJ	Degree=Pos	3	amod	_	_
3	fact	fact	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	14	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	notion	notion	NOUN	NN	Number=Sing	14	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
10	strongly	strongly	ADV	RB	_	11	advmod	_	_
11	compact	compact	ADJ	JJ	Degree=Pos	13	amod	_	_
12	closed	closed	ADJ	JJ	Degree=Pos	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
14	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
15	abstract	abstract	ADJ	JJ	Degree=Pos	16	amod	_	_
16	notions	notion	NOUN	NNS	Number=Plur	27	nsubjpass	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	adjoint	adjoint	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	bipartite	bipartite	ADJ	JJ	Degree=Pos	21	amod	_	_
21	projector	projector	NOUN	NN	Number=Sing	18	conj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	inner	inner	ADJ	JJ	Degree=Pos	24	amod	_	_
24	product	product	NOUN	NN	Number=Sing	21	conj	_	_
25	to	to	PART	TO	_	27	aux	_	_
26	be	be	AUX	VB	VerbForm=Inf	27	auxpass	_	_
27	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	ccomp	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
30	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	32	poss	_	_
31	key	key	ADJ	JJ	Degree=Pos	32	amod	_	_
32	properties	property	NOUN	NNS	Number=Plur	35	nsubjpass	_	_
33	to	to	PART	TO	_	35	aux	_	_
34	be	be	AUX	VB	VerbForm=Inf	35	auxpass	_	_
35	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	conj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this paper we improve on the definition of strong compact closure as compared to the one presented in the other work.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	improve	improve	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	on	on	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	definition	definition	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	strong	strong	ADJ	JJ	Degree=Pos	12	amod	_	_
11	compact	compact	ADJ	JJ	Degree=Pos	12	amod	_	_
12	closure	closure	NOUN	NN	Number=Sing	9	pobj	_	_
13	as	as	ADP	IN	_	5	prep	_	_
14	compared	compare	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	prep	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	one	one	NOUN	NN	Number=Sing	15	pobj	_	_
18	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
19	in	in	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	other	other	ADJ	JJ	Degree=Pos	22	amod	_	_
22	work	work	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = This modification enables an elegant characterization of strong compact closure in terms of adjoints and a Yanking axiom, and a better treatment of bipartite projectors.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	modification	modification	NOUN	NN	Number=Sing	3	nsubj	_	_
3	enables	enable	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	elegant	elegant	ADJ	JJ	Degree=Pos	6	amod	_	_
6	characterization	characterization	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	strong	strong	ADJ	JJ	Degree=Pos	10	amod	_	_
9	compact	compact	ADJ	JJ	Degree=Pos	10	amod	_	_
10	closure	closure	NOUN	NN	Number=Sing	7	pobj	_	_
11	in	in	ADP	IN	_	6	prep	_	_
12	terms	term	NOUN	NNS	Number=Plur	11	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	adjoints	adjoint	NOUN	NNS	Number=Plur	13	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	Yanking	Yanking	PROPN	NNP	Number=Sing	18	compound	_	_
18	axiom	axiom	NOUN	NN	Number=Sing	12	conj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	better	well	ADJ	JJR	Degree=Cmp	23	amod	_	_
23	treatment	treatment	NOUN	NN	Number=Sing	6	conj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	bipartite	bipartite	ADJ	JJ	Degree=Pos	26	amod	_	_
26	projectors	projector	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 218
# sent_id = 1
# text = We give two related universal properties of the span construction.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	two	two	NUM	CD	NumType=Card	6	nummod	_	_
4	related	related	ADJ	JJ	Degree=Pos	6	amod	_	_
5	universal	universal	ADJ	JJ	Degree=Pos	6	amod	_	_
6	properties	property	NOUN	NNS	Number=Plur	2	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	span	span	NOUN	NN	Number=Sing	10	compound	_	_
10	construction	construction	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The first involves sinister morphisms out of the base category and sinister transformations.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	first	first	ADJ	JJ	Degree=Pos	3	nsubj	_	_
3	involves	involve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	sinister	sinister	ADJ	JJ	Degree=Pos	5	amod	_	_
5	morphisms	morphism	NOUN	NNS	Number=Plur	3	dobj	_	_
6	out	out	ADP	IN	_	3	prep	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	base	base	NOUN	NN	Number=Sing	10	compound	_	_
10	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	sinister	sinister	ADJ	JJ	Degree=Pos	13	amod	_	_
13	transformations	transformation	NOUN	NNS	Number=Plur	10	conj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = The second involves oplax morphisms out of the bicategory of spans having an extra property; we call these `jointed' oplax morphisms.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	second	second	ADJ	JJ	Degree=Pos	3	nsubj	_	_
3	involves	involve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	ccomp	_	_
4	oplax	oplax	PROPN	NNP	Number=Sing	5	compound	_	_
5	morphisms	morphism	NOUN	NNS	Number=Plur	3	dobj	_	_
6	out	out	ADP	IN	_	3	prep	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	bicategory	bicategory	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	spans	span	NOUN	NNS	Number=Plur	10	pobj	_	_
12	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	acl	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	extra	extra	ADJ	JJ	Degree=Pos	15	amod	_	_
15	property	property	NOUN	NN	Number=Sing	12	dobj	_	SpaceAfter=No
16	;	;	PUNCT	:	_	18	punct	_	_
17	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	18	nsubj	_	_
18	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
19	these	these	DET	DT	Number=Plur|PronType=Dem	24	det	_	_
20	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	21	punct	_	SpaceAfter=No
21	jointed	joint	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	SpaceAfter=No
22	'	'	PART	POS	_	21	punct	_	_
23	oplax	oplax	PROPN	NNP	Number=Sing	24	compound	_	_
24	morphisms	morphism	NOUN	NNS	Number=Plur	18	dobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# doc_id = 219
# sent_id = 1
# text = The relationships between thin elements, commutative shells and connections in cubical $ omega $ - categories are explored by a method which does not involve the use of pasting theory or nerves of $ omega $ - categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	relationships	relationship	NOUN	NNS	Number=Plur	17	nsubjpass	_	_
3	between	between	ADP	IN	_	2	prep	_	_
4	thin	thin	ADJ	JJ	Degree=Pos	5	amod	_	_
5	elements	element	NOUN	NNS	Number=Plur	3	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	commutative	commutative	ADJ	JJ	Degree=Pos	8	amod	_	_
8	shells	shell	NOUN	NNS	Number=Plur	5	conj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	connections	connection	NOUN	NNS	Number=Plur	8	conj	_	_
11	in	in	ADP	IN	_	8	prep	_	_
12	cubical	cubical	ADJ	JJ	Degree=Pos	15	amod	_	_
13	$ omega $	$ omega $	SYM	$	_	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
16	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	17	auxpass	_	_
17	explored	explore	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
18	by	by	ADP	IN	_	17	agent	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	method	method	NOUN	NN	Number=Sing	18	pobj	_	_
21	which	which	PRON	WDT	_	24	nsubj	_	_
22	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	aux	_	_
23	not	not	PART	RB	Polarity=Neg	24	neg	_	_
24	involve	involve	VERB	VB	VerbForm=Inf	20	relcl	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	use	use	NOUN	NN	Number=Sing	24	dobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	pasting	paste	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	27	pcomp	_	_
29	theory	theory	NOUN	NN	Number=Sing	28	dobj	_	_
30	or	or	CCONJ	CC	ConjType=Cmp	29	cc	_	_
31	nerves	nerve	NOUN	NNS	Number=Plur	29	conj	_	_
32	of	of	ADP	IN	_	29	prep	_	_
33	$ omega $	$ omega $	SYM	$	_	35	compound	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	categories	category	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 2
# text = It is shown that composites of commutative shells are commutative and that thin structures are equivalent to appropriate sets of connections; this work extends to all dimensions the results proved in dimensions 2 and 3 in other work.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	ccomp	_	_
4	that	that	SCONJ	IN	_	9	mark	_	_
5	composites	composite	NOUN	NNS	Number=Plur	9	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	commutative	commutative	ADJ	JJ	Degree=Pos	8	amod	_	_
8	shells	shell	NOUN	NNS	Number=Plur	6	pobj	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
10	commutative	commutative	ADJ	JJ	Degree=Pos	9	acomp	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
12	that	that	SCONJ	IN	_	15	mark	_	_
13	thin	thin	ADJ	JJ	Degree=Pos	14	amod	_	_
14	structures	structure	NOUN	NNS	Number=Plur	15	nsubj	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	conj	_	_
16	equivalent	equivalent	ADJ	JJ	Degree=Pos	15	acomp	_	_
17	to	to	PART	TO	_	18	aux	_	_
18	appropriate	appropriate	ADJ	JJ	Degree=Pos	19	amod	_	_
19	sets	set	NOUN	NNS	Number=Plur	16	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	connections	connection	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
22	;	;	PUNCT	:	_	25	punct	_	_
23	this	this	DET	DT	Number=Sing|PronType=Dem	24	det	_	_
24	work	work	NOUN	NN	Number=Sing	25	nsubj	_	_
25	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
26	to	to	ADP	IN	_	25	prep	_	_
27	all	all	DET	DT	_	28	det	_	_
28	dimensions	dimension	NOUN	NNS	Number=Plur	26	pobj	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	results	result	NOUN	NNS	Number=Plur	31	nsubj	_	_
31	proved	prove	VERB	VBD	Tense=Past|VerbForm=Fin	28	relcl	_	_
32	in	in	ADP	IN	_	31	prep	_	_
33	dimensions	dimension	NOUN	NNS	Number=Plur	32	pobj	_	_
34	2	2	NUM	CD	NumType=Card	33	nummod	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
36	3	3	NUM	CD	NumType=Card	33	conj	_	_
37	in	in	ADP	IN	_	31	prep	_	_
38	other	other	ADJ	JJ	Degree=Pos	39	amod	_	_
39	work	work	NOUN	NN	Number=Sing	37	pobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	25	punct	_	SpaceAfter=No

# doc_id = 220
# sent_id = 1
# text = Call - by - push - value is a "semantic machine code", providing a set of simple primitives from which both the call - by - value and call - by - name paradigms are built.
1	Call	call	VERB	VB	VerbForm=Inf	7	nmod	_	_
2	-	-	PUNCT	HYPH	PunctType=Dash	1	punct	_	_
3	by	by	ADP	IN	_	1	prep	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	3	punct	_	_
5	push	push	NOUN	NN	Number=Sing	3	pobj	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	value	value	NOUN	NN	Number=Sing	8	nsubj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
10	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	13	punct	_	SpaceAfter=No
11	semantic	semantic	ADJ	JJ	Degree=Pos	13	amod	_	_
12	machine	machine	NOUN	NN	Number=Sing	13	compound	_	_
13	code	code	NOUN	NN	Number=Sing	8	attr	_	SpaceAfter=No
14	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	13	punct	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
16	providing	provide	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	advcl	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	set	set	NOUN	NN	Number=Sing	16	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	simple	simple	ADJ	JJ	Degree=Pos	21	amod	_	_
21	primitives	primitive	NOUN	NNS	Number=Plur	19	pobj	_	_
22	from	from	ADP	IN	_	39	prep	_	_
23	which	which	PRON	WDT	_	22	pobj	_	_
24	both	both	CCONJ	CC	ConjType=Cmp	37	det	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
26	call	call	NOUN	NN	Number=Sing	37	nmod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
28	by	by	ADP	IN	_	26	prep	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
30	value	value	NOUN	NN	Number=Sing	28	pobj	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
32	call	call	NOUN	NN	Number=Sing	26	conj	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
34	by	by	ADP	IN	_	32	prep	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	36	punct	_	_
36	name	name	NOUN	NN	Number=Sing	34	pobj	_	_
37	paradigms	paradigm	NOUN	NNS	Number=Plur	39	nsubjpass	_	_
38	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	39	auxpass	_	_
39	built	build	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	relcl	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = We present its operational semantics as a stack machine, suggesting a term judgement of stacks.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	5	poss	_	_
4	operational	operational	ADJ	JJ	Degree=Pos	5	amod	_	_
5	semantics	semantic	NOUN	NNS	Number=Plur	2	dobj	_	_
6	as	as	ADP	IN	_	2	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	stack	stack	NOUN	NN	Number=Sing	9	amod	_	_
9	machine	machine	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
11	suggesting	suggest	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	term	term	NOUN	NN	Number=Sing	14	compound	_	_
14	judgement	judgement	NOUN	NN	Number=Sing	11	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	stacks	stack	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We then see that $ CBPV $ , incorporating these stack terms, has a simple categorical semantics based on an adjunction between values and stacks.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	see	see	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	3	dobj	_	_
5	$ CBPV $	$ cbpv $	SYM	$	_	4	dep	_	_
6	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
7	incorporating	incorporate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	advcl	_	_
8	these	these	DET	DT	Number=Plur|PronType=Dem	10	det	_	_
9	stack	stack	ADJ	JJ	Degree=Pos	10	amod	_	_
10	terms	term	NOUN	NNS	Number=Plur	7	dobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
12	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
14	simple	simple	ADJ	JJ	Degree=Pos	16	amod	_	_
15	categorical	categorical	ADJ	JJ	Degree=Pos	16	amod	_	_
16	semantics	semantic	NOUN	NNS	Number=Plur	12	dobj	_	_
17	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	acl	_	_
18	on	on	ADP	IN	_	17	prep	_	_
19	an	an	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	adjunction	adjunction	NOUN	NN	Number=Sing	18	pobj	_	_
21	between	between	ADP	IN	_	20	prep	_	_
22	values	value	NOUN	NNS	Number=Plur	21	pobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	stacks	stack	NOUN	NNS	Number=Plur	22	conj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = There are no coherence requirements.
1	There	there	PRON	EX	_	2	expl	_	_
2	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	no	no	DET	DT	_	5	det	_	_
4	coherence	coherence	NOUN	NN	Number=Sing	5	compound	_	_
5	requirements	requirement	NOUN	NNS	Number=Plur	2	attr	_	SpaceAfter=No
6	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = We describe this semantics incrementally.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	semantics	semantic	NOUN	NNS	Number=Plur	2	dobj	_	_
5	incrementally	incrementally	ADV	RB	_	2	advmod	_	SpaceAfter=No
6	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = First, we introduce locally indexed categories and the op - Grothendieck construction, and use these to give the basic structure for interpreting the three judgements: values, stacks and computations.
1	First	first	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	locally	locally	ADV	RB	_	6	advmod	_	_
6	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
7	categories	category	NOUN	NNS	Number=Plur	4	dobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
10	op	op	NOUN	NN	Number=Sing	12	compound	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	13	compound	_	_
13	construction	construction	NOUN	NN	Number=Sing	7	conj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
16	use	use	VERB	VB	VerbForm=Inf	4	conj	_	_
17	these	these	PRON	DT	Number=Plur|PronType=Dem	16	dobj	_	_
18	to	to	PART	TO	_	19	aux	_	_
19	give	give	VERB	VB	VerbForm=Inf	16	xcomp	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	basic	basic	ADJ	JJ	Degree=Pos	22	amod	_	_
22	structure	structure	NOUN	NN	Number=Sing	19	dobj	_	_
23	for	for	ADP	IN	_	19	prep	_	_
24	interpreting	interpret	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	23	pcomp	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	three	three	NUM	CD	NumType=Card	27	nummod	_	_
27	judgements	judgement	NOUN	NNS	Number=Plur	24	dobj	_	SpaceAfter=No
28	:	:	PUNCT	:	_	27	punct	_	_
29	values	value	NOUN	NNS	Number=Plur	27	appos	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
31	stacks	stack	NOUN	NNS	Number=Plur	29	conj	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	computations	computation	NOUN	NNS	Number=Plur	31	conj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 7
# text = Then we look at the universal property required to interpret each type constructor.
1	Then	then	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	look	look	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	at	at	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	universal	universal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	property	property	NOUN	NN	Number=Sing	4	pobj	_	_
8	required	require	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	acl	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	interpret	interpret	VERB	VB	VerbForm=Inf	8	xcomp	_	_
11	each	each	DET	DT	_	13	det	_	_
12	type	type	NOUN	NN	Number=Sing	13	compound	_	_
13	constructor	constructor	NOUN	NN	Number=Sing	10	dobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 8
# text = We define a model to be a strong adjunction with countable coproducts, countable products and exponentials.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	model	model	NOUN	NN	Number=Sing	2	dobj	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	be	be	AUX	VB	VerbForm=Inf	4	relcl	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	strong	strong	ADJ	JJ	Degree=Pos	9	amod	_	_
9	adjunction	adjunction	NOUN	NN	Number=Sing	6	attr	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	countable	countable	ADJ	JJ	Degree=Pos	12	amod	_	_
12	coproducts	coproduct	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	countable	countable	ADJ	JJ	Degree=Pos	15	amod	_	_
15	products	product	NOUN	NNS	Number=Plur	12	conj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	exponentials	exponential	NOUN	NNS	Number=Plur	15	conj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 9
# text = We see a wide range of instances of this structure: we give examples for divergence, storage, erratic choice, continuations, possible worlds and games (with or without a bracketing condition), in each case resolving the strong monad from the literature into a strong adjunction.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	see	see	VERB	VBP	Tense=Pres|VerbForm=Fin	13	ccomp	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	wide	wide	ADJ	JJ	Degree=Pos	5	amod	_	_
5	range	range	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	instances	instance	NOUN	NNS	Number=Plur	6	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	this	this	DET	DT	Number=Sing|PronType=Dem	10	det	_	_
10	structure	structure	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
11	:	:	PUNCT	:	_	13	punct	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	examples	example	NOUN	NNS	Number=Plur	13	dobj	_	_
15	for	for	ADP	IN	_	13	prep	_	_
16	divergence	divergence	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	storage	storage	NOUN	NN	Number=Sing	16	conj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	erratic	erratic	ADJ	JJ	Degree=Pos	21	amod	_	_
21	choice	choice	NOUN	NN	Number=Sing	18	conj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	continuations	continuation	NOUN	NNS	Number=Plur	21	conj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
25	possible	possible	ADJ	JJ	Degree=Pos	26	amod	_	_
26	worlds	world	NOUN	NNS	Number=Plur	23	conj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	games	game	NOUN	NNS	Number=Plur	26	conj	_	_
29	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	16	punct	_	SpaceAfter=No
30	with	with	ADP	IN	_	13	prep	_	_
31	or	or	CCONJ	CC	ConjType=Cmp	30	cc	_	_
32	without	without	ADP	IN	_	30	conj	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
34	bracketing	bracket	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	35	amod	_	_
35	condition	condition	NOUN	NN	Number=Sing	32	pobj	_	SpaceAfter=No
36	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	13	punct	_	SpaceAfter=No
37	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
38	in	in	ADP	IN	_	13	prep	_	_
39	each	each	DET	DT	_	40	det	_	_
40	case	case	NOUN	NN	Number=Sing	38	pobj	_	_
41	resolving	resolve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	38	pcomp	_	_
42	the	the	DET	DT	Definite=Def|PronType=Art	44	det	_	_
43	strong	strong	ADJ	JJ	Degree=Pos	44	amod	_	_
44	monad	monad	NOUN	NNS	Number=Plur	41	dobj	_	_
45	from	from	ADP	IN	_	44	prep	_	_
46	the	the	DET	DT	Definite=Def|PronType=Art	47	det	_	_
47	literature	literature	NOUN	NN	Number=Sing	45	pobj	_	_
48	into	into	ADP	IN	_	41	prep	_	_
49	a	a	DET	DT	Definite=Ind|PronType=Art	51	det	_	_
50	strong	strong	ADJ	JJ	Degree=Pos	51	amod	_	_
51	adjunction	adjunction	NOUN	NN	Number=Sing	48	pobj	_	SpaceAfter=No
52	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 10
# text = And we give ways of constructing models from other models.
1	And	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	ways	way	NOUN	NNS	Number=Plur	3	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	constructing	construct	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	models	model	NOUN	NNS	Number=Plur	6	dobj	_	_
8	from	from	ADP	IN	_	6	prep	_	_
9	other	other	ADJ	JJ	Degree=Pos	10	amod	_	_
10	models	model	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 11
# text = Finally, we see that call - by - value and call - by - name are interpreted within the Kleisli and co - Kleisli parts, respectively, of a call - by - push - value adjunction.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	see	see	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	DET	DT	Number=Sing|PronType=Dem	16	det	_	_
6	call	call	NOUN	NN	Number=Sing	16	nmod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
8	by	by	ADP	IN	_	6	prep	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
10	value	value	NOUN	NN	Number=Sing	8	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
12	call	call	NOUN	NN	Number=Sing	6	conj	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
14	by	by	ADP	IN	_	12	prep	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	name	name	NOUN	NN	Number=Sing	18	nsubjpass	_	_
17	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	18	auxpass	_	_
18	interpreted	interpret	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	ccomp	_	_
19	within	within	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	Kleisli	Kleisli	PROPN	NNP	Number=Sing	26	nmod	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	co	co	NOUN	NN	Number=Sing	21	conj	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
25	Kleisli	Kleisli	PROPN	NNP	Number=Sing	26	amod	_	_
26	parts	part	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
28	respectively	respectively	ADV	RB	_	18	advmod	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
30	of	of	ADP	IN	_	18	prep	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
32	call	call	NOUN	NN	Number=Sing	39	nmod	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
34	by	by	ADP	IN	_	32	prep	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
36	push	push	NOUN	NN	Number=Sing	38	compound	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	38	punct	_	_
38	value	value	NOUN	NN	Number=Sing	34	pobj	_	_
39	adjunction	adjunction	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# doc_id = 221
# sent_id = 1
# text = Call two maps, $ f $ , $ g $ from $ C $ to $ C' $ , of chain complexes absolutely homologous if for any additive functor $ F $ , the induced $ Ff $ and $ Fg $ are homologous (induce the same map on homology).
1	Call	call	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	two	two	NUM	CD	NumType=Card	3	nummod	_	_
3	maps	map	NOUN	NNS	Number=Plur	1	dobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	$ f $	$ f $	SYM	$	_	3	appos	_	_
6	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
7	$ g $	$ g $	SYM	$	_	3	appos	_	_
8	from	from	ADP	IN	_	1	prep	_	_
9	$ C $	$ c $	SYM	$	_	8	pobj	_	_
10	to	to	ADP	IN	_	8	prep	_	_
11	$ C' $	$ c' $	SYM	$	_	10	pobj	_	_
12	,	,	PUNCT	,	PunctType=Comm	1	punct	_	_
13	of	of	ADP	IN	_	1	prep	_	_
14	chain	chain	NOUN	NN	Number=Sing	15	compound	_	_
15	complexes	complexe	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	pobj	_	_
16	absolutely	absolutely	ADV	RB	_	17	advmod	_	_
17	homologous	homologous	ADJ	JJ	Degree=Pos	15	amod	_	_
18	if	if	SCONJ	IN	_	26	mark	_	_
19	for	for	ADP	IN	_	26	prep	_	_
20	any	any	DET	DT	_	22	det	_	_
21	additive	additive	ADJ	JJ	Degree=Pos	22	amod	_	_
22	functor	functor	NOUN	NN	Number=Sing	19	pobj	_	_
23	$ F $	$ f $	SYM	$	_	22	appos	_	_
24	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
25	the	the	PRON	DT	Definite=Def|PronType=Art	26	nsubj	_	_
26	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	advcl	_	_
27	$ Ff $	$ ff $	SYM	$	_	26	dobj	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
29	$ Fg $	$ fg $	SYM	$	_	26	conj	_	_
30	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	1	conj	_	_
31	homologous	homologous	ADJ	JJ	Degree=Pos	30	acomp	_	_
32	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	33	punct	_	SpaceAfter=No
33	induce	induce	VERB	VB	VerbForm=Inf	1	conj	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
35	same	same	ADJ	JJ	Degree=Pos	36	amod	_	_
36	map	map	NOUN	NN	Number=Sing	33	dobj	_	_
37	on	on	ADP	IN	_	36	prep	_	_
38	homology	homology	NOUN	NN	Number=Sing	37	pobj	_	SpaceAfter=No
39	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	33	punct	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = It is known that the identity is absolutely homologous to 0 if and only if it is homotopic to 0 and tempting to conjecture that $ f $ and $ g $ are absolutely homologous if and only if they are homotopic.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	SCONJ	IN	_	7	mark	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	identity	identity	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
8	absolutely	absolutely	ADV	RB	_	9	advmod	_	_
9	homologous	homologous	ADJ	JJ	Degree=Pos	7	acomp	_	_
10	to	to	PART	TO	_	9	prep	_	_
11	0	0	NUM	CD	NumType=Card	10	pobj	_	_
12	if	if	SCONJ	IN	_	7	dep	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	only	only	ADV	RB	_	17	advmod	_	_
15	if	if	SCONJ	IN	_	17	mark	_	_
16	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	17	nsubj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	advcl	_	_
18	homotopic	homotopic	NOUN	NN	Number=Sing	17	acomp	_	_
19	to	to	ADP	IN	_	17	prep	_	_
20	0	0	NUM	CD	NumType=Card	19	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
22	tempting	tempting	ADJ	JJ	Degree=Pos	19	conj	_	_
23	to	to	PART	TO	_	24	aux	_	_
24	conjecture	conjecture	VERB	VB	VerbForm=Inf	22	xcomp	_	_
25	that	that	SCONJ	IN	_	29	mark	_	_
26	$ f $	$ f $	SYM	$	_	29	nsubj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	$ g $	$ g $	SYM	$	_	26	conj	_	_
29	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	24	ccomp	_	_
30	absolutely	absolutely	ADV	RB	_	31	advmod	_	_
31	homologous	homologous	ADJ	JJ	Degree=Pos	29	acomp	_	_
32	if	if	SCONJ	IN	_	29	prep	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
34	only	only	ADV	RB	_	37	advmod	_	_
35	if	if	SCONJ	IN	_	37	mark	_	_
36	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	37	nsubj	_	_
37	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	29	conj	_	_
38	homotopic	homotopic	NOUN	NN	Number=Sing	37	attr	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = This conjecture is false, but there is an equational characterization of absolute homology.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	conjecture	conjecture	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	false	false	ADJ	JJ	Degree=Pos	3	acomp	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
6	but	but	CCONJ	CC	ConjType=Cmp	3	cc	_	_
7	there	there	PRON	EX	_	8	expl	_	_
8	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
9	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	equational	equational	ADJ	JJ	Degree=Pos	11	amod	_	_
11	characterization	characterization	NOUN	NN	Number=Sing	8	attr	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	absolute	absolute	ADJ	JJ	Degree=Pos	14	amod	_	_
14	homology	homology	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 4
# text = I also characterize left absolute and right absolute (in which $ F $ is quantified over left or right exact functors).
1	I	I	PRON	PRP	Case=Nom|Number=Sing|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	ccomp	_	_
5	absolute	absolute	ADJ	JJ	Degree=Pos	4	oprd	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	right	right	ADV	RB	_	5	conj	_	_
8	absolute	absolute	ADJ	JJ	Degree=Pos	5	conj	_	_
9	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	4	punct	_	SpaceAfter=No
10	in	in	ADP	IN	_	14	prep	_	_
11	which	which	PRON	WDT	_	10	pobj	_	_
12	$ F $	$ f $	SYM	$	_	14	nsubjpass	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	quantified	quantify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	advcl	_	_
15	over	over	ADP	IN	_	14	prep	_	_
16	left	left	ADJ	JJ	Degree=Pos	20	amod	_	_
17	or	or	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	right	right	ADJ	JJ	Degree=Pos	16	conj	_	_
19	exact	exact	ADJ	JJ	Degree=Pos	20	amod	_	_
20	functors	functor	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
21	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	4	punct	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 222
# sent_id = 1
# text = We thoroughly treat several familiar and less familiar definitions and results concerning categories, functors and distributors enriched in a base quantaloid $ Q $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	thoroughly	thoroughly	ADV	RB	_	3	advmod	_	_
3	treat	treat	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	several	several	ADJ	JJ	Degree=Pos	9	amod	_	_
5	familiar	familiar	ADJ	JJ	Degree=Pos	9	amod	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	less	less	ADV	RBR	Degree=Cmp	8	advmod	_	_
8	familiar	familiar	ADJ	JJ	Degree=Pos	5	conj	_	_
9	definitions	definition	NOUN	NNS	Number=Plur	3	dobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	results	result	NOUN	NNS	Number=Plur	9	conj	_	_
12	concerning	concern	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	prep	_	_
13	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	functors	functor	NOUN	NNS	Number=Plur	13	conj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	distributors	distributor	NOUN	NNS	Number=Plur	15	conj	_	_
18	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	acl	_	_
19	in	in	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	base	base	NOUN	NN	Number=Sing	22	compound	_	_
22	quantaloid	quantaloid	NOUN	NN	Number=Sing	19	pobj	_	_
23	$ Q $	$ q $	SYM	$	_	3	dep	_	_
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = In analogy with $ V $ - category theory we discuss such things as adjoint functors, (pointwise) left Kan extensions, weighted (co)limits, presheaves and free (co)completion, Cauchy completion and Morita equivalence.
1	In	in	ADP	IN	_	9	prep	_	_
2	analogy	analogy	NOUN	NN	Number=Sing	1	pobj	_	_
3	with	with	ADP	IN	_	2	prep	_	_
4	$ V $	$ v $	SYM	$	_	6	nummod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	category	category	NOUN	NN	Number=Sing	7	compound	_	_
7	theory	theory	NOUN	NN	Number=Sing	3	pobj	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	discuss	discuss	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	such	such	ADJ	JJ	Degree=Pos	11	amod	_	_
11	things	thing	NOUN	NNS	Number=Plur	9	dobj	_	_
12	as	as	ADP	IN	_	11	prep	_	_
13	adjoint	adjoint	NOUN	NN	Number=Sing	14	compound	_	_
14	functors	functor	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	17	punct	_	SpaceAfter=No
17	pointwise	pointwise	NOUN	NN	Number=Sing	19	nsubj	_	SpaceAfter=No
18	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	17	punct	_	_
19	left	leave	VERB	VBD	Tense=Past|VerbForm=Fin	9	conj	_	_
20	Kan	Kan	PROPN	NNP	Number=Sing	21	compound	_	_
21	extensions	extension	NOUN	NNS	Number=Plur	19	dobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
23	weighted	weight	VERB	VBD	Tense=Past|VerbForm=Fin	19	conj	_	_
24	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	23	punct	_	SpaceAfter=No
25	co)limits	co)limit	NOUN	NNS	Number=Plur	23	dobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
27	presheaves	presheave	NOUN	NNS	Number=Plur	25	conj	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
29	free	free	ADJ	JJ	Degree=Pos	31	amod	_	_
30	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	31	punct	_	SpaceAfter=No
31	co)completion	co)completion	NOUN	NN	Number=Sing	27	conj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
33	Cauchy	Cauchy	PROPN	NNP	Number=Sing	34	compound	_	_
34	completion	completion	NOUN	NN	Number=Sing	31	conj	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	34	cc	_	_
36	Morita	Morita	PROPN	NNP	Number=Sing	37	compound	_	_
37	equivalence	equivalence	NOUN	NN	Number=Sing	34	conj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 3
# text = With an appendix on the universality of the quantaloid $ Dist(Q) $ of $ Q $ - enriched categories and distributors.
1	With	with	ADP	IN	_	0	ROOT	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	appendix	appendix	NOUN	NN	Number=Sing	1	pobj	_	_
4	on	on	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	universality	universality	NOUN	NN	Number=Sing	4	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	quantaloid	quantaloid	ADJ	JJ	Degree=Pos	10	amod	_	_
10	$ Dist(Q) $	$ dist(q) $	SYM	$	_	7	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	$ Q $	$ q $	SYM	$	_	14	advmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	distributors	distributor	NOUN	NNS	Number=Plur	15	conj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# doc_id = 223
# sent_id = 1
# text = We recall and reformulate certain known constructions, in order to make a convenient setting for obtaining generalized monotone - light factorizations in the sense of Carboni, Janelidze, Kelly and Paré.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	recall	recall	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	reformulate	reformulate	VERB	VB	VerbForm=Inf	2	conj	_	_
5	certain	certain	ADJ	JJ	Degree=Pos	7	amod	_	_
6	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
7	constructions	construction	NOUN	NNS	Number=Plur	4	dobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
9	in	in	ADP	IN	_	4	prep	_	_
10	order	order	NOUN	NN	Number=Sing	9	pobj	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	make	make	VERB	VB	VerbForm=Inf	10	acl	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	convenient	convenient	ADJ	JJ	Degree=Pos	15	amod	_	_
15	setting	setting	NOUN	NN	Number=Sing	12	dobj	_	_
16	for	for	ADP	IN	_	15	prep	_	_
17	obtaining	obtain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	pcomp	_	_
18	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	amod	_	_
19	monotone	monotone	NOUN	NN	Number=Sing	21	npadvmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	light	light	ADJ	JJ	Degree=Pos	22	amod	_	_
22	factorizations	factorization	NOUN	NNS	Number=Plur	17	dobj	_	_
23	in	in	ADP	IN	_	17	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	sense	sense	NOUN	NN	Number=Sing	23	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	Carboni	Carboni	PROPN	NNP	Number=Sing	26	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
29	Janelidze	Janelidze	PROPN	NNP	Number=Sing	27	conj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
31	Kelly	Kelly	PROPN	NNP	Number=Sing	29	conj	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	Paré	Paré	PROPN	NNP	Number=Sing	31	conj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This setting is used to study the existence of monotone - light factorizations both in categories of simplicial objects and in categories of internal categories.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	setting	setting	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	study	study	VERB	VB	VerbForm=Inf	4	xcomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	existence	existence	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	monotone	monotone	NOUN	NN	Number=Sing	12	npadvmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	light	light	ADJ	JJ	Degree=Pos	13	amod	_	_
13	factorizations	factorization	NOUN	NNS	Number=Plur	9	pobj	_	_
14	both	both	PRON	DT	_	15	preconj	_	_
15	in	in	ADP	IN	_	13	prep	_	_
16	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	simplicial	simplicial	ADJ	JJ	Degree=Pos	19	amod	_	_
19	objects	object	NOUN	NNS	Number=Plur	17	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
21	in	in	ADP	IN	_	15	conj	_	_
22	categories	category	NOUN	NNS	Number=Plur	21	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	internal	internal	ADJ	JJ	Degree=Pos	25	amod	_	_
25	categories	category	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = It is shown that there is a non - trivial monotone - light factorization for simplicial sets, such that the monotone - light factorization for reflexive graphs via reflexive relations is a special case of it, obtained by truncation.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	SCONJ	IN	_	6	mark	_	_
5	there	there	PRON	EX	_	6	expl	_	_
6	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
8	non	non	ADJ	JJ	Degree=Pos	10	amod	_	_
9	-	-	ADJ	JJ	Degree=Pos	10	punct	_	_
10	trivial	trivial	ADJ	JJ	Degree=Pos	14	amod	_	_
11	monotone	monotone	NOUN	NN	Number=Sing	13	npadvmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	light	light	ADJ	JJ	Degree=Pos	14	amod	_	_
14	factorization	factorization	NOUN	NN	Number=Sing	6	attr	_	_
15	for	for	ADP	IN	_	14	prep	_	_
16	simplicial	simplicial	ADJ	JJ	Degree=Pos	17	amod	_	_
17	sets	set	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
19	such	such	ADJ	JJ	Degree=Pos	32	acomp	_	_
20	that	that	SCONJ	IN	_	32	mark	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
22	monotone	monotone	NOUN	NN	Number=Sing	24	amod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	light	light	ADJ	JJ	Degree=Pos	25	amod	_	_
25	factorization	factorization	NOUN	NN	Number=Sing	32	nsubj	_	_
26	for	for	ADP	IN	_	25	prep	_	_
27	reflexive	reflexive	ADJ	JJ	Degree=Pos	28	amod	_	_
28	graphs	graph	NOUN	NNS	Number=Plur	26	pobj	_	_
29	via	via	ADP	IN	_	28	prep	_	_
30	reflexive	reflexive	ADJ	JJ	Degree=Pos	31	amod	_	_
31	relations	relation	NOUN	NNS	Number=Plur	29	pobj	_	_
32	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
34	special	special	ADJ	JJ	Degree=Pos	35	amod	_	_
35	case	case	NOUN	NN	Number=Sing	32	attr	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	36	pobj	_	SpaceAfter=No
38	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
39	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	advcl	_	_
40	by	by	ADP	IN	_	39	agent	_	_
41	truncation	truncation	NOUN	NN	Number=Sing	40	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = More generally, we will show that there exists a monotone - light factorization associated with every full subcategory $ Mono(F_n), n >= 0 $ , consisting of all simplicial sets whose unit morphisms are monic for the localization $ F_n:mathbf{Set}^{Delta^{op}}rightarrowmathbf{Set}^{Delta^{op}_n} $ , which truncates each simplicial set after the object of $ n $ - simplices.
1	More	more	ADV	RBR	Degree=Cmp	2	advmod	_	_
2	generally	generally	ADV	RB	_	6	advmod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
5	will	will	AUX	MD	VerbForm=Fin	6	aux	_	_
6	show	show	VERB	VB	VerbForm=Inf	0	ROOT	_	_
7	that	that	SCONJ	IN	_	9	mark	_	_
8	there	there	PRON	EX	_	9	expl	_	_
9	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
11	monotone	monotone	NOUN	NN	Number=Sing	13	amod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	light	light	ADJ	JJ	Degree=Pos	14	amod	_	_
14	factorization	factorization	NOUN	NN	Number=Sing	9	dobj	_	_
15	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	acl	_	_
16	with	with	ADP	IN	_	15	prep	_	_
17	every	every	DET	DT	_	20	det	_	_
18	full	full	ADJ	JJ	Degree=Pos	20	amod	_	_
19	subcategory	subcategory	ADJ	JJ	Degree=Pos	20	amod	_	_
20	$ Mono(F_n), n >= 0 $	$ mono(f_n), n >= 0 $	SYM	$	_	16	pobj	_	_
21	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
22	consisting	consist	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	advcl	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	all	all	DET	DT	_	26	det	_	_
25	simplicial	simplicial	ADJ	JJ	Degree=Pos	26	amod	_	_
26	sets	set	NOUN	NNS	Number=Plur	23	pobj	_	_
27	whose	whose	DET	WP$	Poss=Yes	28	poss	_	_
28	unit	unit	NOUN	NN	Number=Sing	29	compound	_	_
29	morphisms	morphism	NOUN	NNS	Number=Plur	30	nsubj	_	_
30	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	26	relcl	_	_
31	monic	monic	ADJ	JJ	Degree=Pos	30	acomp	_	_
32	for	for	ADP	IN	_	30	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
34	localization	localization	NOUN	NN	Number=Sing	32	pobj	_	_
35	$ F_n:mathbf{Set}^{Delta^{op}}rightarrowmathbf{Set}^{Delta^{op}_n} $	$ f_n:mathbf{set}^{delta^{op}}rightarrowmathbf{set}^{delta^{op}_n} $	SYM	$	_	34	appos	_	_
36	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
37	which	which	PRON	WDT	_	38	nsubj	_	_
38	truncates	truncate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	34	relcl	_	_
39	each	each	DET	DT	_	40	det	_	_
40	simplicial	simplicial	NOUN	NN	Number=Sing	41	nsubj	_	_
41	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	38	ccomp	_	_
42	after	after	ADP	IN	_	41	prep	_	_
43	the	the	DET	DT	Definite=Def|PronType=Art	44	det	_	_
44	object	object	NOUN	NN	Number=Sing	42	pobj	_	_
45	of	of	ADP	IN	_	44	prep	_	_
46	$ n $	$ n $	SYM	$	_	48	compound	_	_
47	-	-	PUNCT	HYPH	PunctType=Dash	48	punct	_	_
48	simplices	simplice	NOUN	NNS	Number=Plur	45	pobj	_	SpaceAfter=No
49	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = The monotone - light factorization for categories via preorders is as well derived from the proposed setting.
1	The	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
2	monotone	monotone	NOUN	NN	Number=Sing	4	amod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	light	light	ADJ	JJ	Degree=Pos	5	amod	_	_
5	factorization	factorization	NOUN	NN	Number=Sing	10	nsubj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
8	via	via	ADP	IN	_	5	prep	_	_
9	preorders	preorder	NOUN	NNS	Number=Plur	8	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	as	as	ADV	RB	_	12	advmod	_	_
12	well	well	ADV	RB	Degree=Pos	13	advmod	_	_
13	derived	derive	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acomp	_	_
14	from	from	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	proposed	propose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	setting	setting	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 6
# text = We also show that, for regular Maltsev categories, the reflection of internal groupoids into internal equivalence relations necessarily produces monotone - light factorizations.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	21	mark	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
6	for	for	ADP	IN	_	21	prep	_	_
7	regular	regular	ADJ	JJ	Degree=Pos	9	amod	_	_
8	Maltsev	Maltsev	PROPN	NNP	Number=Sing	9	compound	_	_
9	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	reflection	reflection	NOUN	NN	Number=Sing	21	nsubj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	internal	internal	ADJ	JJ	Degree=Pos	15	amod	_	_
15	groupoids	groupoid	NOUN	NNS	Number=Plur	13	pobj	_	_
16	into	into	ADP	IN	_	12	prep	_	_
17	internal	internal	ADJ	JJ	Degree=Pos	18	amod	_	_
18	equivalence	equivalence	NOUN	NN	Number=Sing	19	compound	_	_
19	relations	relation	NOUN	NNS	Number=Plur	16	pobj	_	_
20	necessarily	necessarily	ADV	RB	_	21	advmod	_	_
21	produces	produce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
22	monotone	monotone	NOUN	NN	Number=Sing	24	npadvmod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	light	light	ADJ	JJ	Degree=Pos	25	amod	_	_
25	factorizations	factorization	NOUN	NNS	Number=Plur	21	dobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = It turns out that all these reflections do have stable units, in the sense of Cassidy, Hébert and Kelly, giving rise to Galois theories.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	turns	turn	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	out	out	ADP	RP	_	2	prt	_	_
4	that	that	SCONJ	IN	_	9	mark	_	_
5	all	all	DET	PDT	_	7	predet	_	_
6	these	these	DET	DT	Number=Plur|PronType=Dem	7	det	_	_
7	reflections	reflection	NOUN	NNS	Number=Plur	9	nsubj	_	_
8	do	do	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	aux	_	_
9	have	have	VERB	VB	VerbForm=Inf	2	ccomp	_	_
10	stable	stable	ADJ	JJ	Degree=Pos	11	amod	_	_
11	units	unit	NOUN	NNS	Number=Plur	9	dobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
13	in	in	ADP	IN	_	9	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	sense	sense	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	Cassidy	Cassidy	PROPN	NNP	Number=Sing	16	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	Hébert	Hébert	PROPN	NNP	Number=Sing	17	conj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	Kelly	Kelly	PROPN	NNP	Number=Sing	19	conj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
23	giving	give	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	advcl	_	_
24	rise	rise	NOUN	NN	Number=Sing	23	dobj	_	_
25	to	to	ADP	IN	_	24	prep	_	_
26	Galois	Galois	PROPN	NNP	Number=Sing	27	compound	_	_
27	theories	theory	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 224
# sent_id = 1
# text = Storrer introduced the epimorphic hull of a commutative semiprime ring $ R $ and showed that it is (up to isomorphism) the unique essential epic von Neumann regular extension of $ R $ .
1	Storrer	Storrer	PROPN	NNP	Number=Sing	2	nsubj	_	_
2	introduced	introduce	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	epimorphic	epimorphic	ADJ	JJ	Degree=Pos	5	amod	_	_
5	hull	hull	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	commutative	commutative	ADJ	JJ	Degree=Pos	9	amod	_	_
9	semiprime	semiprime	NOUN	NN	Number=Sing	10	compound	_	_
10	ring	ring	VERB	VB	VerbForm=Inf	6	pobj	_	_
11	$ R $	$ r $	SYM	$	_	2	advmod	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
13	showed	show	VERB	VBD	Tense=Past|VerbForm=Fin	2	conj	_	_
14	that	that	SCONJ	IN	_	16	mark	_	_
15	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	16	nsubj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
17	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	16	punct	_	SpaceAfter=No
18	up	up	ADP	IN	_	16	acomp	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	isomorphism	isomorphism	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
21	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	16	punct	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
23	unique	unique	ADJ	JJ	Degree=Pos	29	amod	_	_
24	essential	essential	ADJ	JJ	Degree=Pos	27	nmod	_	_
25	epic	epic	ADJ	JJ	Degree=Pos	27	compound	_	_
26	von	von	PROPN	NNP	Number=Sing	27	compound	_	_
27	Neumann	Neumann	PROPN	NNP	Number=Sing	29	nmod	_	_
28	regular	regular	ADJ	JJ	Degree=Pos	29	amod	_	_
29	extension	extension	NOUN	NN	Number=Sing	16	attr	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	$ R $	$ r $	SYM	$	_	30	pobj	_	_
32	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In the case when $ R = C(X) $ with $ X $ a Tychonoff space, we show that the embedding induced by a dense subspace of $ X $ is always essential.
1	In	in	ADP	IN	_	13	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	case	case	NOUN	NN	Number=Sing	1	pobj	_	_
4	when	when	SCONJ	WRB	_	13	advmod	_	_
5	$ R = C(X) $	$ r = c(x) $	SYM	$	_	4	nmod	_	_
6	with	with	ADP	IN	_	4	prep	_	_
7	$ X $	$ x $	SYM	$	_	10	predet	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	Tychonoff	Tychonoff	PROPN	NNP	Number=Sing	10	compound	_	_
10	space	space	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	that	that	SCONJ	IN	_	24	mark	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	embedding	embed	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	24	nsubj	_	_
17	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	acl	_	_
18	by	by	ADP	IN	_	17	agent	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	dense	dense	ADJ	JJ	Degree=Pos	21	amod	_	_
21	subspace	subspace	NOUN	NN	Number=Sing	18	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	$ X $	$ x $	SYM	$	_	22	pobj	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
25	always	always	ADV	RB	_	24	advmod	_	_
26	essential	essential	ADJ	JJ	Degree=Pos	24	acomp	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 3
# text = This simplifies the search for spaces whose epimorphic hull is a full ring of continuous functions, and allows us to obtain new examples where this occurs.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	simplifies	simplify	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	search	search	NOUN	NN	Number=Sing	2	dobj	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	spaces	space	NOUN	NNS	Number=Plur	5	pobj	_	_
7	whose	whose	DET	WP$	Poss=Yes	9	poss	_	_
8	epimorphic	epimorphic	ADJ	JJ	Degree=Pos	9	amod	_	_
9	hull	hull	NOUN	NN	Number=Sing	10	nsubj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	relcl	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	full	full	ADJ	JJ	Degree=Pos	13	amod	_	_
13	ring	ring	NOUN	NN	Number=Sing	10	attr	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	continuous	continuous	ADJ	JJ	Degree=Pos	16	amod	_	_
16	functions	function	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
19	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	conj	_	_
20	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	22	nsubj	_	_
21	to	to	PART	TO	_	22	aux	_	_
22	obtain	obtain	VERB	VB	VerbForm=Inf	19	ccomp	_	_
23	new	new	ADJ	JJ	Degree=Pos	24	amod	_	_
24	examples	example	NOUN	NNS	Number=Plur	22	dobj	_	_
25	where	where	SCONJ	WRB	_	27	advmod	_	_
26	this	this	PRON	DT	Number=Sing|PronType=Dem	27	nsubj	_	_
27	occurs	occur	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	relcl	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = The main theorem comes close to a characterisation of this phenomenon.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	theorem	theorem	NOUN	NN	Number=Sing	4	nsubj	_	_
4	comes	come	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	close	close	ADV	RB	_	4	advmod	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	characterisation	characterisation	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	this	this	DET	DT	Number=Sing|PronType=Dem	11	det	_	_
11	phenomenon	phenomenon	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 225
# sent_id = 1
# text = We show that the generic symmetric monoidal category with a commutative separable algebra which has a $ Sigma $ - family of actions is the category of cospans of finite $ Sigma $ - labelled graphs restricted to finite sets as objects, thus providing a syntax for automata on the alphabet $ Sigma $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	22	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
5	generic	generic	ADJ	JJ	Degree=Pos	8	amod	_	_
6	symmetric	symmetric	ADJ	JJ	Degree=Pos	8	amod	_	_
7	monoidal	monoidal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	22	nsubj	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	commutative	commutative	ADJ	JJ	Degree=Pos	13	amod	_	_
12	separable	separable	ADJ	JJ	Degree=Pos	13	amod	_	_
13	algebra	algebra	NOUN	NN	Number=Sing	9	pobj	_	_
14	which	which	PRON	WDT	_	15	nsubj	_	_
15	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	relcl	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
17	$ Sigma $	$ sigma $	SYM	$	_	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	family	family	NOUN	NN	Number=Sing	15	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	actions	action	NOUN	NNS	Number=Plur	20	pobj	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	category	category	NOUN	NN	Number=Sing	22	attr	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	cospans	cospan	NOUN	NNS	Number=Plur	25	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	finite	finite	PROPN	NNP	Number=Sing	27	pobj	_	_
29	$ Sigma $	$ sigma $	SYM	$	_	31	advmod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	labelled	label	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	amod	_	_
32	graphs	graph	NOUN	NNS	Number=Plur	27	pobj	_	_
33	restricted	restrict	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	acl	_	_
34	to	to	ADP	IN	_	33	prep	_	_
35	finite	finite	ADJ	JJ	Degree=Pos	36	amod	_	_
36	sets	set	NOUN	NNS	Number=Plur	34	pobj	_	_
37	as	as	ADP	IN	_	33	prep	_	_
38	objects	object	NOUN	NNS	Number=Plur	37	pobj	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
40	thus	thus	ADV	RB	_	41	advmod	_	_
41	providing	provide	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	advcl	_	_
42	a	a	DET	DT	Definite=Ind|PronType=Art	43	det	_	_
43	syntax	syntax	NOUN	NN	Number=Sing	41	dobj	_	_
44	for	for	ADP	IN	_	43	prep	_	_
45	automata	automata	NOUN	NN	Number=Sing	44	pobj	_	_
46	on	on	ADP	IN	_	41	prep	_	_
47	the	the	DET	DT	Definite=Def|PronType=Art	48	det	_	_
48	alphabet	alphabet	NOUN	NN	Number=Sing	46	pobj	_	_
49	$ Sigma $	$ sigma $	SYM	$	_	41	dep	_	_
50	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We use this result to produce semantic functors for $ Sigma $ - automata.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	result	result	NOUN	NN	Number=Sing	2	dobj	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	produce	produce	VERB	VB	VerbForm=Inf	2	xcomp	_	_
7	semantic	semantic	ADJ	JJ	Degree=Pos	8	amod	_	_
8	functors	functor	NOUN	NNS	Number=Plur	6	dobj	_	_
9	for	for	ADP	IN	_	6	prep	_	_
10	$ Sigma $	$ sigma $	SYM	$	_	12	compound	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	automata	automata	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 226
# sent_id = 1
# text = This work is a contribution to a recent field, Directed Algebraic Topology.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	work	work	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	contribution	contribution	NOUN	NN	Number=Sing	3	attr	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	recent	recent	ADJ	JJ	Degree=Pos	9	amod	_	_
9	field	field	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
11	Directed	Directed	PROPN	NNP	Number=Sing	13	compound	_	_
12	Algebraic	Algebraic	PROPN	NNP	Number=Sing	13	compound	_	_
13	Topology	Topology	PROPN	NNP	Number=Sing	5	appos	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = Categories which appear as fundamental categories of `directed structures', for example ordered topological spaces, have to be studied up to appropriate notions of directed homotopy equivalence, which are more general than ordinary equivalence of categories.
1	Categories	category	NOUN	NNS	Number=Plur	15	nsubj	_	_
2	which	which	PRON	WDT	_	3	nsubj	_	_
3	appear	appear	VERB	VBP	Tense=Pres|VerbForm=Fin	1	relcl	_	_
4	as	as	ADP	IN	_	3	prep	_	_
5	fundamental	fundamental	ADJ	JJ	Degree=Pos	6	amod	_	_
6	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	10	punct	_	SpaceAfter=No
9	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	structures	structure	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
11	'	'	PART	POS	_	1	punct	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
13	for	for	ADP	IN	_	15	prep	_	_
14	example	example	NOUN	NN	Number=Sing	13	pobj	_	_
15	ordered	order	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
16	topological	topological	ADJ	JJ	Degree=Pos	17	amod	_	_
17	spaces	space	NOUN	NNS	Number=Plur	15	dobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	ccomp	_	_
20	to	to	PART	TO	_	22	aux	_	_
21	be	be	AUX	VB	VerbForm=Inf	22	auxpass	_	_
22	studied	study	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	xcomp	_	_
23	up	up	ADP	RP	_	22	prt	_	_
24	to	to	PART	TO	_	22	prep	_	_
25	appropriate	appropriate	ADJ	JJ	Degree=Pos	26	amod	_	_
26	notions	notion	NOUN	NNS	Number=Plur	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	30	amod	_	_
29	homotopy	homotopy	NOUN	NN	Number=Sing	30	compound	_	_
30	equivalence	equivalence	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
32	which	which	PRON	WDT	_	33	nsubj	_	_
33	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	30	relcl	_	_
34	more	more	ADV	RBR	Degree=Cmp	35	advmod	_	_
35	general	general	ADJ	JJ	Degree=Pos	33	acomp	_	_
36	than	than	ADP	IN	_	35	prep	_	_
37	ordinary	ordinary	ADJ	JJ	Degree=Pos	38	amod	_	_
38	equivalence	equivalence	NOUN	NN	Number=Sing	36	pobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	categories	category	NOUN	NNS	Number=Plur	39	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 3
# text = Here we introduce past and future equivalences of categories—sort of symmetric versions of an adjunction—and use them and their combinations to get `directed models' of a category; in the simplest case, these are the join of the least full reflective and the least full coreflective subcategory.
1	Here	here	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	41	ccomp	_	_
4	past	past	NOUN	NN	Number=Sing	7	amod	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	future	future	ADJ	JJ	Degree=Pos	4	conj	_	_
7	equivalences	equivalence	NOUN	NNS	Number=Plur	3	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
10	—	—	PUNCT	:	_	7	punct	_	SpaceAfter=No
11	sort	sort	ADV	RB	_	12	advmod	_	_
12	of	of	ADP	IN	_	3	prep	_	_
13	symmetric	symmetric	ADJ	JJ	Degree=Pos	14	amod	_	_
14	versions	version	NOUN	NNS	Number=Plur	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	adjunction	adjunction	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
18	—	—	PUNCT	:	_	3	punct	_	SpaceAfter=No
19	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
20	use	use	VERB	VB	VerbForm=Inf	3	conj	_	_
21	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	20	dobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	24	poss	_	_
24	combinations	combination	NOUN	NNS	Number=Plur	21	conj	_	_
25	to	to	PART	TO	_	26	aux	_	_
26	get	get	VERB	VB	VerbForm=Inf	20	xcomp	_	_
27	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	29	punct	_	SpaceAfter=No
28	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	amod	_	_
29	models	model	NOUN	NNS	Number=Plur	26	dobj	_	SpaceAfter=No
30	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	29	punct	_	_
31	of	of	ADP	IN	_	29	prep	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
33	category	category	NOUN	NN	Number=Sing	31	pobj	_	SpaceAfter=No
34	;	;	PUNCT	:	_	41	punct	_	_
35	in	in	ADP	IN	_	41	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
37	simplest	simple	ADJ	JJS	Degree=Sup	38	amod	_	_
38	case	case	NOUN	NN	Number=Sing	35	pobj	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	41	punct	_	_
40	these	these	PRON	DT	Number=Plur|PronType=Dem	41	nsubj	_	_
41	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
42	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
43	join	join	NOUN	NN	Number=Sing	41	attr	_	_
44	of	of	ADP	IN	_	43	prep	_	_
45	the	the	DET	DT	Definite=Def|PronType=Art	48	det	_	_
46	least	least	ADJ	JJS	Degree=Sup	48	amod	_	_
47	full	full	ADJ	JJ	Degree=Pos	48	amod	_	_
48	reflective	reflective	NOUN	NN	Number=Sing	44	pobj	_	_
49	and	and	CCONJ	CC	ConjType=Cmp	48	cc	_	_
50	the	the	DET	DT	Definite=Def|PronType=Art	54	det	_	_
51	least	least	ADJ	JJS	Degree=Sup	52	advmod	_	_
52	full	full	ADJ	JJ	Degree=Pos	54	amod	_	_
53	coreflective	coreflective	ADJ	JJ	Degree=Pos	54	amod	_	_
54	subcategory	subcategory	NOUN	NN	Number=Sing	48	conj	_	SpaceAfter=No
55	.	.	PUNCT	.	PunctType=Peri	41	punct	_	SpaceAfter=No

# doc_id = 227
# sent_id = 1
# text = This paper constructs models of intuitionistic set theory in suitable categories.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	constructs	construct	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	models	model	NOUN	NNS	Number=Plur	3	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	intuitionistic	intuitionistic	ADJ	JJ	Degree=Pos	7	amod	_	_
7	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
8	theory	theory	NOUN	NN	Number=Sing	5	pobj	_	_
9	in	in	ADP	IN	_	4	prep	_	_
10	suitable	suitable	ADJ	JJ	Degree=Pos	11	amod	_	_
11	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = First, a Basic Intuitionistic Set Theory (BIST) is stated, and the categorical semantics are given.
1	First	first	ADV	RB	_	12	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
4	Basic	Basic	PROPN	NNP	Number=Sing	7	compound	_	_
5	Intuitionistic	Intuitionistic	PROPN	NNP	Number=Sing	6	compound	_	_
6	Set	Set	PROPN	NNP	Number=Sing	7	compound	_	_
7	Theory	Theory	PROPN	NNP	Number=Sing	12	nsubjpass	_	_
8	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	7	punct	_	SpaceAfter=No
9	BIST	BIST	PROPN	NNP	Number=Sing	7	appos	_	SpaceAfter=No
10	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	7	punct	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	stated	state	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	categorical	categorical	ADJ	JJ	Degree=Pos	17	amod	_	_
17	semantics	semantic	NOUN	NNS	Number=Plur	19	nsubjpass	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	19	auxpass	_	_
19	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	conj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 3
# text = Second, we give a notion of an ideal over a category, using which one can build a model of BIST in which a given topos occurs as the sets.
1	Second	second	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	notion	notion	NOUN	NN	Number=Sing	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	ideal	ideal	NOUN	NN	Number=Sing	7	pobj	_	_
10	over	over	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	category	category	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
14	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	advcl	_	_
15	which	which	DET	WDT	_	16	det	_	_
16	one	one	PRON	PRP	PronType=Prs	18	nsubj	_	_
17	can	can	AUX	MD	VerbForm=Fin	18	aux	_	_
18	build	build	VERB	VB	VerbForm=Inf	14	ccomp	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	model	model	NOUN	NN	Number=Sing	18	dobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	BIST	BIST	PROPN	NNP	Number=Sing	21	pobj	_	_
23	in	in	ADP	IN	_	28	prep	_	_
24	which	which	PRON	WDT	_	23	pobj	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
26	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	amod	_	_
27	topos	topos	NOUN	NN	Number=Sing	28	nsubj	_	_
28	occurs	occur	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	relcl	_	_
29	as	as	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	sets	set	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = And third, a sheaf model is given of a Basic Intuitionistic Class Theory conservatively extending BIST.
1	And	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
2	third	third	ADV	RB	_	8	advmod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	sheaf	sheaf	NOUN	NN	Number=Sing	6	compound	_	_
6	model	model	NOUN	NN	Number=Sing	8	nsubjpass	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
11	Basic	Basic	PROPN	NNP	Number=Sing	14	compound	_	_
12	Intuitionistic	Intuitionistic	PROPN	NNP	Number=Sing	13	compound	_	_
13	Class	Class	PROPN	NNP	Number=Sing	14	compound	_	_
14	Theory	Theory	PROPN	NNP	Number=Sing	9	pobj	_	_
15	conservatively	conservatively	ADV	RB	_	16	advmod	_	_
16	extending	extend	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	acl	_	_
17	BIST	BIST	PROPN	NNP	Number=Sing	16	dobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 5
# text = The paper extends the results in work by Awodey, Butz, Simpson and Streicher by introducing a new and perhaps more natural notion of ideal, and in the class theory of part three.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	results	result	NOUN	NNS	Number=Plur	3	dobj	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	work	work	NOUN	NN	Number=Sing	6	pobj	_	_
8	by	by	ADP	IN	_	3	prep	_	_
9	Awodey	Awodey	PROPN	NNP	Number=Sing	8	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	Butz	Butz	PROPN	NNP	Number=Sing	9	conj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	Simpson	Simpson	PROPN	NNP	Number=Sing	11	conj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	Streicher	Streicher	PROPN	NNP	Number=Sing	13	conj	_	_
16	by	by	ADP	IN	_	3	prep	_	_
17	introducing	introduce	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	pcomp	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
19	new	new	ADJ	JJ	Degree=Pos	24	amod	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	perhaps	perhaps	ADV	RB	_	22	advmod	_	_
22	more	more	ADV	RBR	Degree=Cmp	23	advmod	_	_
23	natural	natural	ADJ	JJ	Degree=Pos	24	amod	_	_
24	notion	notion	NOUN	NN	Number=Sing	17	dobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	ideal	ideal	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
29	in	in	ADP	IN	_	3	conj	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	class	class	NOUN	NN	Number=Sing	32	compound	_	_
32	theory	theory	NOUN	NN	Number=Sing	29	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	part	part	NOUN	NN	Number=Sing	33	pobj	_	_
35	three	three	NUM	CD	NumType=Card	34	nummod	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 228
# sent_id = 1
# text = The aim of this paper is to describe Quillen model category structures on the category $ CatC $ of internal categories and functors in a given finitely complete category $ C $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	aim	aim	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	paper	paper	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	describe	describe	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	Quillen	quillen	ADJ	JJ	Degree=Pos	12	amod	_	_
10	model	model	NOUN	NN	Number=Sing	12	compound	_	_
11	category	category	NOUN	NN	Number=Sing	12	compound	_	_
12	structures	structure	NOUN	NNS	Number=Plur	8	dobj	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
16	$ CatC $	$ catc $	SYM	$	_	15	appos	_	_
17	of	of	ADP	IN	_	15	prep	_	_
18	internal	internal	ADJ	JJ	Degree=Pos	19	amod	_	_
19	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	functors	functor	NOUN	NNS	Number=Plur	19	conj	_	_
22	in	in	ADP	IN	_	8	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
24	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	amod	_	_
25	finitely	finitely	ADV	RB	_	26	advmod	_	_
26	complete	complete	ADJ	JJ	Degree=Pos	27	amod	_	_
27	category	category	NOUN	NN	Number=Sing	22	pobj	_	_
28	$ C $	$ c $	SYM	$	_	8	dobj	_	_
29	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = Several non - equivalent notions of internal equivalence exist; to capture these notions, the model structures are defined relative to a given Grothendieck topology on $ C $ .
1	Several	several	ADJ	JJ	Degree=Pos	5	amod	_	_
2	non	non	ADJ	JJ	Degree=Pos	4	amod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	equivalent	equivalent	ADJ	JJ	Degree=Pos	5	amod	_	_
5	notions	notion	NOUN	NNS	Number=Plur	9	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	internal	internal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	equivalence	equivalence	NOUN	NN	Number=Sing	6	pobj	_	_
9	exist	exist	VERB	VBP	Tense=Pres|VerbForm=Fin	20	ccomp	_	SpaceAfter=No
10	;	;	PUNCT	:	_	20	punct	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	capture	capture	VERB	VB	VerbForm=Inf	20	advcl	_	_
13	these	these	DET	DT	Number=Plur|PronType=Dem	14	det	_	_
14	notions	notion	NOUN	NNS	Number=Plur	12	dobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	model	model	NOUN	NN	Number=Sing	18	compound	_	_
18	structures	structure	NOUN	NNS	Number=Plur	20	nsubjpass	_	_
19	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	20	auxpass	_	_
20	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
21	relative	relative	ADJ	JJ	Degree=Pos	20	advmod	_	_
22	to	to	ADP	IN	_	21	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
24	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
25	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	26	compound	_	_
26	topology	topology	NOUN	NN	Number=Sing	22	pobj	_	_
27	on	on	ADP	IN	_	20	prep	_	_
28	$ C $	$ c $	SYM	$	_	27	pobj	_	_
29	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 3
# text = Under mild conditions on $ C $ , the regular epimorphism topology determines a model structure where we is the class of weak equivalences of internal categories (in the sense of Bunge and Pare).
1	Under	under	ADP	IN	_	11	prep	_	_
2	mild	mild	ADJ	JJ	Degree=Pos	3	amod	_	_
3	conditions	condition	NOUN	NNS	Number=Plur	1	pobj	_	_
4	on	on	ADP	IN	_	3	prep	_	_
5	$ C $	$ c $	SYM	$	_	4	pobj	_	_
6	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	regular	regular	ADJ	JJ	Degree=Pos	10	amod	_	_
9	epimorphism	epimorphism	NOUN	NN	Number=Sing	10	compound	_	_
10	topology	topology	NOUN	NN	Number=Sing	11	nsubj	_	_
11	determines	determine	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	model	model	NOUN	NN	Number=Sing	14	compound	_	_
14	structure	structure	NOUN	NN	Number=Sing	11	dobj	_	_
15	where	where	SCONJ	WRB	_	17	advmod	_	_
16	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	17	nsubj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	class	class	NOUN	NN	Number=Sing	17	attr	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	weak	weak	ADJ	JJ	Degree=Pos	22	amod	_	_
22	equivalences	equivalence	NOUN	NNS	Number=Plur	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	internal	internal	ADJ	JJ	Degree=Pos	25	amod	_	_
25	categories	category	NOUN	NNS	Number=Plur	23	pobj	_	_
26	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	27	punct	_	SpaceAfter=No
27	in	in	ADP	IN	_	11	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	sense	sense	NOUN	NN	Number=Sing	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	Bunge	Bunge	PROPN	NNP	Number=Sing	30	pobj	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	Pare	Pare	PROPN	NNP	Number=Sing	31	conj	_	SpaceAfter=No
34	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	27	punct	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 4
# text = For a Grothendieck topos $ C $ we get a structure that, though different from Joyal and Tierney's, has an equivalent homotopy category.
1	For	for	ADP	IN	_	7	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	4	compound	_	_
4	topos	topos	PROPN	NNP	Number=Sing	1	pobj	_	_
5	$ C $	$ c $	SYM	$	_	7	dep	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	get	get	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	structure	structure	NOUN	NN	Number=Sing	7	dobj	_	_
10	that	that	PRON	WDT	PronType=Rel	20	nsubj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
12	though	though	SCONJ	IN	_	13	mark	_	_
13	different	different	ADJ	JJ	Degree=Pos	20	advcl	_	_
14	from	from	ADP	IN	_	13	prep	_	_
15	Joyal	Joyal	PROPN	NNP	Number=Sing	14	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	Tierney	Tierney	PROPN	NNP	Number=Sing	15	conj	_	SpaceAfter=No
18	's	's	PART	POS	_	17	case	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
20	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	relcl	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
22	equivalent	equivalent	ADJ	JJ	Degree=Pos	24	amod	_	_
23	homotopy	homotopy	NOUN	NN	Number=Sing	24	compound	_	_
24	category	category	NOUN	NN	Number=Sing	20	dobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 5
# text = In case $ C $ is semi - abelian, these weak equivalences turn out to be homology isomorphisms, and the model structure on $ CatC $ induces a notion of homotopy of internal crossed modules.
1	In	in	ADP	IN	_	4	prep	_	_
2	case	case	NOUN	NN	Number=Sing	1	pobj	_	_
3	$ C $	$ c $	SYM	$	_	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	advcl	_	_
5	semi	semi	ADJ	JJ	Degree=Pos	4	acomp	_	_
6	-	-	ADJ	JJ	Degree=Pos	4	attr	_	_
7	abelian	abelian	ADJ	JJ	Degree=Pos	4	acomp	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
9	these	these	DET	DT	Number=Plur|PronType=Dem	11	det	_	_
10	weak	weak	ADJ	JJ	Degree=Pos	11	amod	_	_
11	equivalences	equivalence	NOUN	NNS	Number=Plur	12	nsubj	_	_
12	turn	turn	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	out	out	ADP	RP	_	12	prt	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	be	be	AUX	VB	VerbForm=Inf	12	xcomp	_	_
16	homology	homology	NOUN	NN	Number=Sing	17	compound	_	_
17	isomorphisms	isomorphism	NOUN	NNS	Number=Plur	15	attr	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	model	model	NOUN	NN	Number=Sing	22	compound	_	_
22	structure	structure	NOUN	NN	Number=Sing	25	nsubj	_	_
23	on	on	ADP	IN	_	22	prep	_	_
24	$ CatC $	$ catc $	SYM	$	_	23	pobj	_	_
25	induces	induce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	conj	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	notion	notion	NOUN	NN	Number=Sing	25	dobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	homotopy	homotopy	NOUN	NN	Number=Sing	28	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	internal	internal	ADJ	JJ	Degree=Pos	33	amod	_	_
32	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	amod	_	_
33	modules	module	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 6
# text = In case $ C $ is the category $ Gp $ of groups and homomorphisms, it reduces to the case of crossed modules of groups.
1	In	in	ADP	IN	_	4	prep	_	_
2	case	case	NOUN	NN	Number=Sing	1	pobj	_	_
3	$ C $	$ c $	SYM	$	_	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	ccomp	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	category	category	NOUN	NN	Number=Sing	4	attr	_	_
7	$ Gp $	$ gp $	SYM	$	_	6	appos	_	_
8	of	of	ADP	IN	_	6	prep	_	_
9	groups	group	NOUN	NNS	Number=Plur	8	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	homomorphisms	homomorphism	NOUN	NNS	Number=Plur	9	conj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
13	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	14	nsubj	_	_
14	reduces	reduce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	case	case	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	crossed	crossed	ADJ	JJ	Degree=Pos	20	amod	_	_
20	modules	module	NOUN	NNS	Number=Plur	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	groups	group	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 7
# text = The trivial topology on a category $ C $ determines a model structure on $ CatC $ where $ we $ is the class of strong equivalences (homotopy equivalences), $ fib $ the class of internal functors with the homotopy lifting property, and $ cof $ the class of functors with the homotopy extension property.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	trivial	trivial	ADJ	JJ	Degree=Pos	3	amod	_	_
3	topology	topology	NOUN	NN	Number=Sing	8	nsubj	_	_
4	on	on	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
7	$ C $	$ c $	SYM	$	_	3	appos	_	_
8	determines	determine	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	model	model	NOUN	NN	Number=Sing	11	compound	_	_
11	structure	structure	NOUN	NN	Number=Sing	8	dobj	_	_
12	on	on	ADP	IN	_	8	prep	_	_
13	$ CatC $	$ catc $	SYM	$	_	12	pobj	_	_
14	where	where	SCONJ	WRB	_	15	advmod	_	_
15	$ we $	$ we $	SYM	$	_	13	relcl	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	conj	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	class	class	NOUN	NN	Number=Sing	16	attr	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	strong	strong	ADJ	JJ	Degree=Pos	21	amod	_	_
21	equivalences	equivalence	NOUN	NNS	Number=Plur	19	pobj	_	_
22	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	21	punct	_	SpaceAfter=No
23	homotopy	homotopy	NOUN	NN	Number=Sing	24	compound	_	_
24	equivalences	equivalence	NOUN	NNS	Number=Plur	21	appos	_	SpaceAfter=No
25	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	21	punct	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
27	$ fib $	$ fib $	SYM	$	_	29	predet	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	class	class	NOUN	NN	Number=Sing	8	dobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	internal	internal	ADJ	JJ	Degree=Pos	32	amod	_	_
32	functors	functor	NOUN	NNS	Number=Plur	30	pobj	_	_
33	with	with	ADP	IN	_	29	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
35	homotopy	homotopy	NOUN	NN	Number=Sing	36	npadvmod	_	_
36	lifting	lifting	NOUN	NN	Number=Sing	37	amod	_	_
37	property	property	NOUN	NN	Number=Sing	33	pobj	_	SpaceAfter=No
38	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
39	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
40	$ cof $	$ cof $	SYM	$	_	42	nmod	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	42	det	_	_
42	class	class	NOUN	NN	Number=Sing	29	conj	_	_
43	of	of	ADP	IN	_	42	prep	_	_
44	functors	functor	NOUN	NNS	Number=Plur	43	pobj	_	_
45	with	with	ADP	IN	_	42	prep	_	_
46	the	the	DET	DT	Definite=Def|PronType=Art	49	det	_	_
47	homotopy	homotopy	NOUN	NN	Number=Sing	48	compound	_	_
48	extension	extension	NOUN	NN	Number=Sing	49	compound	_	_
49	property	property	NOUN	NN	Number=Sing	45	pobj	_	SpaceAfter=No
50	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 8
# text = As a special case, the ``folk'' Quillen model category structure on the category $ Cat = CatSet $ of small categories is recovered.
1	As	as	ADP	IN	_	23	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	special	special	ADJ	JJ	Degree=Pos	4	amod	_	_
4	case	case	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
7	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	9	punct	_	SpaceAfter=No
8	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	9	punct	_	SpaceAfter=No
9	folk	folk	NOUN	NN	Number=Sing	14	nmod	_	SpaceAfter=No
10	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	9	punct	_	_
11	Quillen	quillen	ADJ	JJ	Degree=Pos	14	amod	_	_
12	model	model	NOUN	NN	Number=Sing	14	compound	_	_
13	category	category	NOUN	NN	Number=Sing	14	compound	_	_
14	structure	structure	NOUN	NN	Number=Sing	23	nsubjpass	_	_
15	on	on	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
18	$ Cat = CatSet $	$ cat = catset $	SYM	$	_	23	nsubjpass	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	small	small	ADJ	JJ	Degree=Pos	21	amod	_	_
21	categories	category	NOUN	NNS	Number=Plur	19	pobj	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	auxpass	_	_
23	recovered	recover	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# doc_id = 229
# sent_id = 1
# text = It is well known that for any monad, the associated Kleisli category is embedded in the category of Eilenberg - Moore algebras as the free ones.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
3	well	well	ADV	RB	Degree=Pos	4	advmod	_	_
4	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	that	that	SCONJ	IN	_	15	mark	_	_
6	for	for	ADP	IN	_	15	prep	_	_
7	any	any	DET	DT	_	8	det	_	_
8	monad	monad	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
11	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
12	Kleisli	Kleisli	PROPN	NNP	Number=Sing	13	compound	_	_
13	category	category	NOUN	NN	Number=Sing	15	nsubjpass	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	embedded	embed	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	ccomp	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	category	category	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	Moore	Moore	PROPN	NNP	Number=Sing	23	compound	_	_
23	algebras	algebra	NOUN	NNS	Number=Plur	19	pobj	_	_
24	as	as	ADP	IN	_	15	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	free	free	ADJ	JJ	Degree=Pos	27	amod	_	_
27	ones	one	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = We discovered some interesting examples in which this embedding is reflective; that is, it has a left adjoint.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	discovered	discover	VERB	VBD	Tense=Past|VerbForm=Fin	17	ccomp	_	_
3	some	some	DET	DT	_	5	det	_	_
4	interesting	interesting	ADJ	JJ	Degree=Pos	5	amod	_	_
5	examples	example	NOUN	NNS	Number=Plur	2	dobj	_	_
6	in	in	ADP	IN	_	10	prep	_	_
7	which	which	PRON	WDT	_	6	pobj	_	_
8	this	this	DET	DT	Number=Sing|PronType=Dem	9	det	_	_
9	embedding	embed	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	nsubj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	relcl	_	_
11	reflective	reflective	ADJ	JJ	Degree=Pos	10	acomp	_	SpaceAfter=No
12	;	;	PUNCT	:	_	17	punct	_	_
13	that	that	PRON	DT	Number=Sing|PronType=Dem	14	advmod	_	_
14	is	is	ADV	RB	_	17	advmod	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
16	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	17	nsubj	_	_
17	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	left	left	ADJ	JJ	Degree=Pos	20	amod	_	_
20	adjoint	adjoint	NOUN	NN	Number=Sing	17	dobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 3
# text = To understand this phenomenon we introduce and study a class of monads arising from factorization systems, and thereby termed factorization monads.
1	To	to	PART	TO	_	2	aux	_	_
2	understand	understand	VERB	VB	VerbForm=Inf	20	advcl	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	phenomenon	phenomenon	NOUN	NN	Number=Sing	2	dobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	4	relcl	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	study	study	VERB	VB	VerbForm=Inf	6	conj	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	class	class	NOUN	NN	Number=Sing	8	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	monads	monad	NOUN	NNS	Number=Plur	11	pobj	_	_
13	arising	arise	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	acl	_	_
14	from	from	ADP	IN	_	13	prep	_	_
15	factorization	factorization	NOUN	NN	Number=Sing	16	compound	_	_
16	systems	system	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
19	thereby	thereby	ADV	RB	_	20	advmod	_	_
20	termed	term	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
21	factorization	factorization	NOUN	NN	Number=Sing	22	compound	_	_
22	monads	monad	NOUN	NNS	Number=Plur	20	dobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 4
# text = For them we show that under some simple conditions on the factorization system the free algebras are a full reflective subcategory of the algebras.
1	For	for	ADP	IN	_	4	prep	_	_
2	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	1	pobj	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	17	mark	_	_
6	under	under	ADP	IN	_	17	prep	_	_
7	some	some	DET	DT	_	9	det	_	_
8	simple	simple	ADJ	JJ	Degree=Pos	9	amod	_	_
9	conditions	condition	NOUN	NNS	Number=Plur	6	pobj	_	_
10	on	on	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	factorization	factorization	NOUN	NN	Number=Sing	13	compound	_	_
13	system	system	NOUN	NN	Number=Sing	10	pobj	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	free	free	ADJ	JJ	Degree=Pos	16	amod	_	_
16	algebras	algebra	NOUN	NNS	Number=Plur	17	nsubj	_	_
17	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
19	full	full	ADJ	JJ	Degree=Pos	21	amod	_	_
20	reflective	reflective	ADJ	JJ	Degree=Pos	21	amod	_	_
21	subcategory	subcategory	NOUN	NN	Number=Sing	17	attr	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	algebras	algebra	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = We provide various examples of this situation of a combinatorial nature.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	various	various	ADJ	JJ	Degree=Pos	4	amod	_	_
4	examples	example	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
7	situation	situation	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	11	amod	_	_
11	nature	nature	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 230
# sent_id = 1
# text = A generating family in a category $ C $ is a collection of objects $ {A_i|iin I} $ such that if for any subobject $ Y > - - > X $ , every $ f: A_i rightarrow X $ factors through $ m $ , then $ m $ is an isomorphism—that is, the functors $ C(A_i, - ) $ are collectively conservative.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	generating	generate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	amod	_	_
3	family	family	NOUN	NN	Number=Sing	8	nsubj	_	_
4	in	in	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
7	$ C $	$ c $	SYM	$	_	4	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	collection	collection	NOUN	NN	Number=Sing	8	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	objects	object	NOUN	NNS	Number=Plur	11	pobj	_	_
13	$ {A_i|iin I} $	$ {a_i|iin i} $	SYM	$	_	14	nmod	_	_
14	such	such	ADJ	JJ	Degree=Pos	24	amod	_	_
15	that	that	SCONJ	IN	_	24	mark	_	_
16	if	if	SCONJ	IN	_	17	mark	_	_
17	for	for	ADP	IN	_	24	prep	_	_
18	any	any	DET	DT	_	19	det	_	_
19	subobject	subobject	NOUN	NN	Number=Sing	17	pobj	_	_
20	$ Y > - - > X $	$ y > - - > x $	SYM	$	_	17	advmod	_	_
21	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
22	every	every	DET	DT	_	24	det	_	_
23	$ f: A_i rightarrow X $	$ f: a_i rightarrow x $	SYM	$	_	24	nmod	_	_
24	factors	factor	NOUN	NNS	Number=Plur	8	attr	_	_
25	through	through	ADP	IN	_	24	prep	_	_
26	$ m $	$ m $	SYM	$	_	25	pobj	_	_
27	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
28	then	then	ADV	RB	PronType=Dem	29	advmod	_	_
29	$ m $	$ m $	SYM	$	_	30	nsubj	_	_
30	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	conj	_	_
31	an	an	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
32	isomorphism	isomorphism	NOUN	NN	Number=Sing	30	attr	_	SpaceAfter=No
33	—	—	PUNCT	:	_	32	punct	_	SpaceAfter=No
34	that	that	PRON	WDT	PronType=Rel	35	nsubj	_	_
35	is	is	ADV	RB	_	8	advmod	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	functors	functor	NOUN	NNS	Number=Plur	35	attr	_	_
39	$ C(A_i, - ) $	$ c(a_i, - ) $	SYM	$	_	40	nsubj	_	_
40	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	conj	_	_
41	collectively	collectively	ADV	RB	_	42	advmod	_	_
42	conservative	conservative	ADJ	JJ	Degree=Pos	40	acomp	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	40	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper, we examine some circumstances under which subobjects of 1 form a generating family.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	examine	examine	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	some	some	DET	DT	_	8	det	_	_
8	circumstances	circumstance	NOUN	NNS	Number=Plur	6	dobj	_	_
9	under	under	ADP	IN	_	14	prep	_	_
10	which	which	PRON	WDT	_	9	pobj	_	_
11	subobjects	subobject	NOUN	NNS	Number=Plur	14	nsubj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	1	1	NUM	CD	NumType=Card	12	pobj	_	_
14	form	form	VERB	VB	VerbForm=Inf	8	relcl	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	generating	generate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	amod	_	_
17	family	family	NOUN	NN	Number=Sing	14	dobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = Objects for which subobjects of 1 do form a generating family are called partially well - pointed.
1	Objects	object	NOUN	NNS	Number=Plur	13	nsubjpass	_	_
2	for	for	ADP	IN	_	8	prep	_	_
3	which	which	PRON	WDT	_	2	pobj	_	_
4	subobjects	subobject	NOUN	NNS	Number=Plur	8	nsubj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	1	1	NUM	CD	NumType=Card	5	pobj	_	_
7	do	do	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	aux	_	_
8	form	form	VERB	VB	VerbForm=Inf	1	relcl	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	generating	generating	NOUN	NN	Number=Sing	11	amod	_	_
11	family	family	NOUN	NN	Number=Sing	8	dobj	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
14	partially	partially	ADV	RB	_	17	advmod	_	_
15	well	well	ADV	RB	Degree=Pos	17	advmod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	pointed	point	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	oprd	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 4
# text = For a Grothendieck topos, it is well known that subobjects of 1 form a generating family if and only if the topos is localic.
1	For	for	ADP	IN	_	9	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	4	compound	_	_
4	topos	topos	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
6	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	9	nsubjpass	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
8	well	well	ADV	RB	Degree=Pos	9	advmod	_	_
9	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	that	that	SCONJ	IN	_	14	mark	_	_
11	subobjects	subobject	NOUN	NNS	Number=Plur	14	nsubj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	1	1	NUM	CD	NumType=Card	12	pobj	_	_
14	form	form	VERB	VB	VerbForm=Inf	9	ccomp	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	generating	generating	NOUN	NN	Number=Sing	17	amod	_	_
17	family	family	NOUN	NN	Number=Sing	14	dobj	_	_
18	if	if	SCONJ	IN	_	24	mark	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	only	only	ADV	RB	_	24	advmod	_	_
21	if	if	SCONJ	IN	_	24	mark	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	topos	topos	NOUN	NN	Number=Sing	24	nsubj	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	advcl	_	_
25	localic	localic	ADJ	JJ	Degree=Pos	24	acomp	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 5
# text = For the elementary case, little more is known.
1	For	for	ADP	IN	_	9	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	elementary	elementary	ADJ	JJ	Degree=Pos	4	amod	_	_
4	case	case	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
6	little	little	ADJ	JJ	Degree=Pos	7	advmod	_	_
7	more	more	ADJ	JJR	Degree=Cmp	9	nsubjpass	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 6
# text = The problem is studied by Borceux, where it is shown that the result is internally true, an equivalent condition is found in the boolean case, and certain preservation properties are shown.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	problem	problem	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	studied	study	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	ccomp	_	_
5	by	by	ADP	IN	_	4	agent	_	_
6	Borceux	Borceux	PROPN	NNP	Number=Sing	5	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	where	where	SCONJ	WRB	_	11	advmod	_	_
9	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	11	nsubjpass	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	relcl	_	_
12	that	that	SCONJ	IN	_	15	mark	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	result	result	NOUN	NN	Number=Sing	15	nsubj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	ccomp	_	_
16	internally	internally	ADV	RB	_	17	advmod	_	_
17	true	true	ADJ	JJ	Degree=Pos	15	acomp	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
19	an	an	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	equivalent	equivalent	ADJ	JJ	Degree=Pos	21	amod	_	_
21	condition	condition	NOUN	NN	Number=Sing	23	nsubjpass	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	auxpass	_	_
23	found	find	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	boolean	boolean	ADJ	JJ	Degree=Pos	27	amod	_	_
27	case	case	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
30	certain	certain	ADJ	JJ	Degree=Pos	32	amod	_	_
31	preservation	preservation	NOUN	NN	Number=Sing	32	compound	_	_
32	properties	property	NOUN	NNS	Number=Plur	34	nsubjpass	_	_
33	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	34	auxpass	_	_
34	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	conj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# sent_id = 7
# text = We look at two different approaches to the problem, one based on a generalization of projectivity, and the other based on looking at the most extreme sorts of counterexamples.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	look	look	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	at	at	ADP	IN	_	2	prep	_	_
4	two	two	NUM	CD	NumType=Card	6	nummod	_	_
5	different	different	ADJ	JJ	Degree=Pos	6	amod	_	_
6	approaches	approach	NOUN	NNS	Number=Plur	3	pobj	_	_
7	to	to	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	problem	problem	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
11	one	one	NUM	CD	NumType=Card	2	npadvmod	_	_
12	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acl	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	generalization	generalization	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	projectivity	projectivity	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	other	other	ADJ	JJ	Degree=Pos	11	conj	_	_
22	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	acl	_	_
23	on	on	ADP	IN	_	22	prep	_	_
24	looking	look	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	23	pcomp	_	_
25	at	at	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
27	most	most	ADV	RBS	Degree=Sup	28	advmod	_	_
28	extreme	extreme	ADJ	JJ	Degree=Pos	29	amod	_	_
29	sorts	sort	NOUN	NNS	Number=Plur	25	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	counterexamples	counterexample	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 231
# sent_id = 1
# text = In this paper the machinery and results developed in other work are extended to the study of constructive set theories.
1	In	in	ADP	IN	_	13	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	machinery	machinery	NOUN	NN	Number=Sing	13	nsubjpass	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	results	result	NOUN	NNS	Number=Plur	5	conj	_	_
8	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	acl	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	other	other	ADJ	JJ	Degree=Pos	11	amod	_	_
11	work	work	NOUN	NN	Number=Sing	9	pobj	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	study	study	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	constructive	constructive	ADJ	JJ	Degree=Pos	20	amod	_	_
19	set	set	ADJ	JJ	Degree=Pos	20	amod	_	_
20	theories	theory	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 2
# text = Specifically, we introduce two constructive set theories BCST and CST and prove that they are sound and complete with respect to models in categories with certain structure.
1	Specifically	specifically	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	two	two	NUM	CD	NumType=Card	8	nummod	_	_
6	constructive	constructive	ADJ	JJ	Degree=Pos	8	amod	_	_
7	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
8	theories	theory	NOUN	NNS	Number=Plur	4	dobj	_	_
9	BCST	BCST	PROPN	NNP	Number=Sing	8	appos	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	CST	CST	PROPN	NNP	Number=Sing	9	conj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
13	prove	prove	VERB	VB	VerbForm=Inf	4	conj	_	_
14	that	that	SCONJ	IN	_	16	mark	_	_
15	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	16	nsubj	_	_
16	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
17	sound	sound	ADJ	JJ	Degree=Pos	16	acomp	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	complete	complete	ADJ	JJ	Degree=Pos	17	conj	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	respect	respect	NOUN	NN	Number=Sing	20	pobj	_	_
22	to	to	ADP	IN	_	21	prep	_	_
23	models	model	NOUN	NNS	Number=Plur	22	pobj	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	categories	category	NOUN	NNS	Number=Plur	24	pobj	_	_
26	with	with	ADP	IN	_	25	prep	_	_
27	certain	certain	ADJ	JJ	Degree=Pos	28	amod	_	_
28	structure	structure	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = Specifically, basic categories of classes and categories of classes are axiomatized and shown to provide models of the aforementioned set theories.
1	Specifically	specifically	ADV	RB	_	12	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
3	basic	basic	ADJ	JJ	Degree=Pos	4	amod	_	_
4	categories	category	NOUN	NNS	Number=Plur	12	nsubjpass	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	classes	class	NOUN	NNS	Number=Plur	5	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	categories	category	NOUN	NNS	Number=Plur	6	conj	_	_
9	of	of	ADP	IN	_	6	prep	_	_
10	classes	class	NOUN	NNS	Number=Plur	9	pobj	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	axiomatized	axiomatize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	conj	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	provide	provide	VERB	VB	VerbForm=Inf	14	xcomp	_	_
17	models	model	NOUN	NNS	Number=Plur	16	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
20	aforementioned	aforementioned	ADJ	JJ	Degree=Pos	22	amod	_	_
21	set	set	ADJ	JJ	Degree=Pos	22	amod	_	_
22	theories	theory	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 4
# text = Finally, models of these theories are constructed in the category of ideals.
1	Finally	finally	ADV	RB	_	8	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
3	models	model	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	these	these	DET	DT	Number=Plur|PronType=Dem	6	det	_	_
6	theories	theory	NOUN	NNS	Number=Plur	4	pobj	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	ideals	ideal	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 232
# sent_id = 1
# text = In this paper, we examine a new approach to topos theory—rather than considering subobjects, look at quotients.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	examine	examine	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	new	new	ADJ	JJ	Degree=Pos	9	amod	_	_
9	approach	approach	NOUN	NN	Number=Sing	6	dobj	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	topos	topos	NOUN	NN	Number=Sing	12	compound	_	_
12	theory	theory	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
13	—	—	PUNCT	:	_	12	punct	_	SpaceAfter=No
14	rather	rather	ADV	RB	_	15	advmod	_	_
15	than	than	ADP	IN	_	9	cc	_	_
16	considering	consider	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	pcomp	_	_
17	subobjects	subobject	NOUN	NNS	Number=Plur	16	dobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
19	look	look	VERB	VB	VerbForm=Inf	6	conj	_	_
20	at	at	ADP	IN	_	19	prep	_	_
21	quotients	quotient	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = This leads to the notion of a copower object, which is the object of quotients of a given object.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	leads	lead	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	notion	notion	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	copower	copower	NOUN	NN	Number=Sing	9	compound	_	_
9	object	object	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	which	which	PRON	WDT	_	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	relcl	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	object	object	NOUN	NN	Number=Sing	12	attr	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	quotients	quotient	NOUN	NNS	Number=Plur	15	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	amod	_	_
20	object	object	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We study some properties of copower objects, many of which are similar to the properties of power objects.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	some	some	DET	DT	_	4	det	_	_
4	properties	property	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	copower	copower	NOUN	NN	Number=Sing	7	compound	_	_
7	objects	object	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
9	many	many	ADJ	JJ	Degree=Pos	12	nsubj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	which	which	PRON	WDT	_	10	pobj	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	relcl	_	_
13	similar	similar	ADJ	JJ	Degree=Pos	12	acomp	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	properties	property	NOUN	NNS	Number=Plur	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	power	power	NOUN	NN	Number=Sing	19	compound	_	_
19	objects	object	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = Given enough categorical structure (that is, in a pretopos) it is possible to get power objects from copower objects, and vice versa.
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	prep	_	_
2	enough	enough	ADJ	JJ	Degree=Pos	4	amod	_	_
3	categorical	categorical	ADJ	JJ	Degree=Pos	4	amod	_	_
4	structure	structure	NOUN	NN	Number=Sing	1	pobj	_	_
5	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	4	punct	_	SpaceAfter=No
6	that	that	ADV	RB	_	7	advmod	_	_
7	is	is	ADV	RB	_	4	parataxis	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	in	in	ADP	IN	_	7	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	pretopos	pretopos	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	1	punct	_	_
13	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	possible	possible	ADJ	JJ	Degree=Pos	14	acomp	_	_
16	to	to	PART	TO	_	17	aux	_	_
17	get	get	VERB	VB	VerbForm=Inf	14	xcomp	_	_
18	power	power	NOUN	NN	Number=Sing	19	compound	_	_
19	objects	object	NOUN	NNS	Number=Plur	17	dobj	_	_
20	from	from	ADP	IN	_	17	prep	_	_
21	copower	copower	NOUN	NN	Number=Sing	22	amod	_	_
22	objects	object	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
25	vice	vice	ADV	RB	_	26	advmod	_	_
26	versa	versa	ADV	RB	_	17	conj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 5
# text = We then examine some new definitions of finiteness arising from the notion of a copower object.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	examine	examine	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	some	some	DET	DT	_	6	det	_	_
5	new	new	ADJ	JJ	Degree=Pos	6	amod	_	_
6	definitions	definition	NOUN	NNS	Number=Plur	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	finiteness	finiteness	NOUN	NN	Number=Sing	7	pobj	_	_
9	arising	arise	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	acl	_	_
10	from	from	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	notion	notion	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	copower	copower	NOUN	NN	Number=Sing	16	compound	_	_
16	object	object	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = We will see that the most naturally occurring such notions are equivalent to the standard notions, $ K $ - finiteness (at least for well - pointed objects) and $ tilde{K} $ - finiteness, but that this new way of looking at them gives new information, and in fact gives rise to another notion of finiteness, which is related to the classical notion of an amorphous set—that is, an infinite set that is not the disjoint union of two infinite sets.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	will	will	AUX	MD	VerbForm=Fin	3	aux	_	_
3	see	see	VERB	VB	VerbForm=Inf	0	ROOT	_	_
4	that	that	SCONJ	IN	_	11	mark	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
6	most	most	ADV	RBS	Degree=Sup	7	advmod	_	_
7	naturally	naturally	ADV	RB	_	8	advmod	_	_
8	occurring	occur	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	csubj	_	_
9	such	such	ADJ	JJ	Degree=Pos	10	amod	_	_
10	notions	notion	NOUN	NNS	Number=Plur	8	dobj	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
12	equivalent	equivalent	ADJ	JJ	Degree=Pos	11	acomp	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	standard	standard	ADJ	JJ	Degree=Pos	16	amod	_	_
16	notions	notion	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	$ K $	$ k $	SYM	$	_	20	nummod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	finiteness	finiteness	NOUN	NN	Number=Sing	16	appos	_	_
21	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	16	punct	_	SpaceAfter=No
22	at	at	ADP	IN	_	23	advmod	_	_
23	least	least	ADJ	JJS	Degree=Sup	24	advmod	_	_
24	for	for	ADP	IN	_	16	prep	_	_
25	well	well	ADV	RB	Degree=Pos	27	advmod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	pointed	point	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	amod	_	_
28	objects	object	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
29	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	16	punct	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
31	$ tilde{K} $	$ tilde{k} $	SYM	$	_	33	nummod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	finiteness	finiteness	NOUN	NN	Number=Sing	16	conj	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
35	but	but	CCONJ	CC	ConjType=Cmp	11	cc	_	_
36	that	that	SCONJ	IN	_	44	mark	_	_
37	this	this	DET	DT	Number=Sing|PronType=Dem	39	det	_	_
38	new	new	ADJ	JJ	Degree=Pos	39	amod	_	_
39	way	way	NOUN	NN	Number=Sing	44	nsubj	_	_
40	of	of	ADP	IN	_	39	prep	_	_
41	looking	look	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	40	pcomp	_	_
42	at	at	ADP	IN	_	41	prep	_	_
43	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	42	pobj	_	_
44	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	conj	_	_
45	new	new	ADJ	JJ	Degree=Pos	46	amod	_	_
46	information	information	NOUN	NN	Number=Sing	44	dobj	_	SpaceAfter=No
47	,	,	PUNCT	,	PunctType=Comm	44	punct	_	_
48	and	and	CCONJ	CC	ConjType=Cmp	44	cc	_	_
49	in	in	ADP	IN	_	51	prep	_	_
50	fact	fact	NOUN	NN	Number=Sing	49	pobj	_	_
51	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	44	conj	_	_
52	rise	rise	NOUN	NN	Number=Sing	51	dobj	_	_
53	to	to	ADP	IN	_	52	prep	_	_
54	another	another	DET	DT	_	55	det	_	_
55	notion	notion	NOUN	NN	Number=Sing	53	pobj	_	_
56	of	of	ADP	IN	_	55	prep	_	_
57	finiteness	finiteness	NOUN	NN	Number=Sing	56	pobj	_	SpaceAfter=No
58	,	,	PUNCT	,	PunctType=Comm	57	punct	_	_
59	which	which	PRON	WDT	_	61	nsubjpass	_	_
60	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	61	auxpass	_	_
61	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	57	relcl	_	_
62	to	to	ADP	IN	_	61	prep	_	_
63	the	the	DET	DT	Definite=Def|PronType=Art	65	det	_	_
64	classical	classical	ADJ	JJ	Degree=Pos	65	amod	_	_
65	notion	notion	NOUN	NN	Number=Sing	62	pobj	_	_
66	of	of	ADP	IN	_	65	prep	_	_
67	an	an	DET	DT	Definite=Ind|PronType=Art	69	det	_	_
68	amorphous	amorphous	ADJ	JJ	Degree=Pos	69	amod	_	_
69	set	set	NOUN	NN	Number=Sing	66	pobj	_	SpaceAfter=No
70	—	—	PUNCT	:	_	69	punct	_	SpaceAfter=No
71	that	that	PRON	DT	Number=Sing|PronType=Dem	72	nsubj	_	_
72	is	is	ADV	RB	_	69	relcl	_	SpaceAfter=No
73	,	,	PUNCT	,	PunctType=Comm	72	punct	_	_
74	an	an	DET	DT	Definite=Ind|PronType=Art	76	det	_	_
75	infinite	infinite	ADJ	JJ	Degree=Pos	76	amod	_	_
76	set	set	NOUN	NN	Number=Sing	72	attr	_	_
77	that	that	PRON	WDT	PronType=Rel	78	nsubj	_	_
78	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	76	relcl	_	_
79	not	not	PART	RB	Polarity=Neg	78	neg	_	_
80	the	the	DET	DT	Definite=Def|PronType=Art	82	det	_	_
81	disjoint	disjoint	NOUN	NN	Number=Sing	82	compound	_	_
82	union	union	NOUN	NN	Number=Sing	78	attr	_	_
83	of	of	ADP	IN	_	82	prep	_	_
84	two	two	NUM	CD	NumType=Card	86	nummod	_	_
85	infinite	infinite	ADJ	JJ	Degree=Pos	86	amod	_	_
86	sets	set	NOUN	NNS	Number=Plur	83	pobj	_	SpaceAfter=No
87	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = Finally, We look briefly at two similar notions: potency objects and per objects.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	look	look	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	briefly	briefly	ADV	RB	_	4	advmod	_	_
6	at	at	ADP	IN	_	4	prep	_	_
7	two	two	NUM	CD	NumType=Card	9	nummod	_	_
8	similar	similar	ADJ	JJ	Degree=Pos	9	amod	_	_
9	notions	notion	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
10	:	:	PUNCT	:	_	9	punct	_	_
11	potency	potency	NOUN	NN	Number=Sing	12	compound	_	_
12	objects	object	NOUN	NNS	Number=Plur	9	appos	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	per	per	ADP	IN	_	12	prep	_	_
15	objects	object	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 233
# sent_id = 1
# text = The process some call `categorification' consists of interpreting set - theoretic structures in mathematics as derived from category - theoretic structures.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	process	process	NOUN	NN	Number=Sing	8	nsubj	_	_
3	some	some	PRON	DT	_	4	nsubj	_	_
4	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	2	appos	_	_
5	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	6	punct	_	SpaceAfter=No
6	categorification	categorification	NOUN	NN	Number=Sing	4	dobj	_	SpaceAfter=No
7	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	6	punct	_	_
8	consists	consist	NOUN	NNS	Number=Plur	0	ROOT	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	interpreting	interpret	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	pcomp	_	_
11	set	set	NOUN	NN	Number=Sing	13	amod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	theoretic	theoretic	NOUN	NN	Number=Sing	14	amod	_	_
14	structures	structure	NOUN	NNS	Number=Plur	10	dobj	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	mathematics	mathematic	NOUN	NNS	Number=Plur	15	pobj	_	_
17	as	as	SCONJ	IN	_	18	mark	_	_
18	derived	derive	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	advcl	_	_
19	from	from	ADP	IN	_	18	prep	_	_
20	category	category	NOUN	NN	Number=Sing	22	npadvmod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	theoretic	theoretic	ADJ	JJ	Degree=Pos	23	amod	_	_
23	structures	structure	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = Examples include the interpretation of $ N $ as the Burnside rig of the category of finite sets with product and coproduct, and of $ N[x] $ in terms the category of combinatorial species.
1	Examples	example	NOUN	NNS	Number=Plur	2	nsubj	_	_
2	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	interpretation	interpretation	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	$ N $	$ n $	SYM	$	_	5	pobj	_	_
7	as	as	ADP	IN	_	4	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	Burnside	Burnside	PROPN	NNP	Number=Sing	10	compound	_	_
10	rig	rig	NOUN	NN	Number=Sing	7	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	finite	finite	ADJ	JJ	Degree=Pos	16	compound	_	_
16	sets	set	NOUN	NNS	Number=Plur	14	pobj	_	_
17	with	with	ADP	IN	_	13	prep	_	_
18	product	product	NOUN	NN	Number=Sing	17	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	coproduct	coproduct	NOUN	NN	Number=Sing	18	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
23	of	of	ADP	IN	_	4	prep	_	_
24	$ N[x] $	$ n[x] $	SYM	$	_	23	pobj	_	_
25	in	in	ADP	IN	_	2	prep	_	_
26	terms	term	NOUN	NNS	Number=Plur	25	pobj	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	category	category	NOUN	NN	Number=Sing	2	dobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	31	amod	_	_
31	species	specie	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = This has interesting applications to quantum mechanics, and in particular the quantum harmonic oscillator, via Joyal's `combinatorial species', and a new generalization called `stuff types' described by Baez and Dolan, which are a special case of Kelly's `clubs'.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	interesting	interesting	ADJ	JJ	Degree=Pos	4	amod	_	_
4	applications	application	NOUN	NNS	Number=Plur	2	dobj	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	quantum	quantum	ADJ	JJ	Degree=Pos	7	compound	_	_
7	mechanics	mechanic	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
10	in	in	ADP	IN	_	15	prep	_	_
11	particular	particular	ADJ	JJ	Degree=Pos	10	amod	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
13	quantum	quantum	PROPN	NNP	Number=Sing	15	amod	_	_
14	harmonic	harmonic	ADJ	JJ	Degree=Pos	15	compound	_	_
15	oscillator	oscillator	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	via	via	ADP	IN	_	15	prep	_	_
18	Joyal	Joyal	PROPN	NNP	Number=Sing	22	poss	_	SpaceAfter=No
19	's	's	PART	POS	_	18	case	_	_
20	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	22	punct	_	SpaceAfter=No
21	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	22	amod	_	_
22	species	specie	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
23	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	15	punct	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
27	new	new	ADJ	JJ	Degree=Pos	28	amod	_	_
28	generalization	generalization	NOUN	NN	Number=Sing	15	conj	_	_
29	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	acl	_	_
30	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	32	punct	_	SpaceAfter=No
31	stuff	stuff	NOUN	NN	Number=Sing	32	compound	_	_
32	types	type	NOUN	NNS	Number=Plur	29	oprd	_	SpaceAfter=No
33	'	'	PART	POS	_	32	case	_	_
34	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	acl	_	_
35	by	by	ADP	IN	_	34	agent	_	_
36	Baez	Baez	PROPN	NNP	Number=Sing	35	pobj	_	_
37	and	and	CCONJ	CC	ConjType=Cmp	36	cc	_	_
38	Dolan	Dolan	PROPN	NNP	Number=Sing	36	conj	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
40	which	which	PRON	WDT	_	41	nsubj	_	_
41	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	36	relcl	_	_
42	a	a	DET	DT	Definite=Ind|PronType=Art	44	det	_	_
43	special	special	ADJ	JJ	Degree=Pos	44	amod	_	_
44	case	case	NOUN	NN	Number=Sing	41	attr	_	_
45	of	of	ADP	IN	_	44	prep	_	_
46	Kelly	Kelly	PROPN	NNP	Number=Sing	49	poss	_	SpaceAfter=No
47	's	's	PART	POS	_	46	case	_	_
48	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	49	punct	_	SpaceAfter=No
49	clubs	club	NOUN	NNS	Number=Plur	45	pobj	_	SpaceAfter=No
50	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	28	punct	_	SpaceAfter=No
51	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = Operators between stuff types be represented as rudimentary Feynman diagrams for the oscillator.
1	Operators	operator	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
2	between	between	ADP	IN	_	1	prep	_	_
3	stuff	stuff	NOUN	NN	Number=Sing	4	compound	_	_
4	types	type	NOUN	NNS	Number=Plur	2	pobj	_	_
5	be	be	AUX	VB	VerbForm=Inf	6	auxpass	_	_
6	represented	represent	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	as	as	ADP	IN	_	6	prep	_	_
8	rudimentary	rudimentary	ADJ	JJ	Degree=Pos	10	amod	_	_
9	Feynman	Feynman	PROPN	NNP	Number=Sing	10	compound	_	_
10	diagrams	diagram	NOUN	NNS	Number=Plur	7	pobj	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	oscillator	oscillator	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = In quantum mechanics, we want to represent states in an algebra over the complex numbers, and also want our Feynman diagrams to carry more structure than these `stuff operators' can do, and these turn out to be closely related.
1	In	in	ADP	IN	_	6	prep	_	_
2	quantum	quantum	ADJ	JJ	Degree=Pos	3	amod	_	_
3	mechanics	mechanic	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	want	want	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	represent	represent	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	states	state	NOUN	NNS	Number=Plur	8	dobj	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	algebra	algebra	NOUN	NN	Number=Sing	10	pobj	_	_
13	over	over	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	complex	complex	ADJ	JJ	Degree=Pos	16	amod	_	_
16	numbers	number	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
19	also	also	ADV	RB	_	20	advmod	_	_
20	want	want	VERB	VBP	Tense=Pres|VerbForm=Fin	6	conj	_	_
21	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	23	poss	_	_
22	Feynman	Feynman	PROPN	NNP	Number=Sing	23	compound	_	_
23	diagrams	diagram	NOUN	NNS	Number=Plur	25	nsubj	_	_
24	to	to	PART	TO	_	25	aux	_	_
25	carry	carry	VERB	VB	VerbForm=Inf	20	ccomp	_	_
26	more	more	ADJ	JJR	Degree=Cmp	27	amod	_	_
27	structure	structure	NOUN	NN	Number=Sing	25	dobj	_	_
28	than	than	SCONJ	IN	_	35	mark	_	_
29	these	these	DET	DT	Number=Plur|PronType=Dem	32	det	_	_
30	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	32	punct	_	SpaceAfter=No
31	stuff	stuff	NOUN	NN	Number=Sing	32	compound	_	_
32	operators	operator	NOUN	NNS	Number=Plur	35	nsubj	_	SpaceAfter=No
33	'	'	PART	POS	_	32	punct	_	_
34	can	can	AUX	MD	VerbForm=Fin	35	aux	_	_
35	do	do	VERB	VB	VerbForm=Inf	27	advcl	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
37	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
38	these	these	PRON	DT	Number=Plur|PronType=Dem	39	nsubj	_	_
39	turn	turn	VERB	VBP	Tense=Pres|VerbForm=Fin	6	conj	_	_
40	out	out	ADP	RP	_	39	prt	_	_
41	to	to	PART	TO	_	44	aux	_	_
42	be	be	AUX	VB	VerbForm=Inf	44	auxpass	_	_
43	closely	closely	ADV	RB	_	44	advmod	_	_
44	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	39	xcomp	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	39	punct	_	SpaceAfter=No

# sent_id = 6
# text = We will describe a categorification of the quantum harmonic oscillator in which the group of `phases'—that is, $ U(1) $ , the circle group—plays a special role.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	will	will	AUX	MD	VerbForm=Fin	3	aux	_	_
3	describe	describe	VERB	VB	VerbForm=Inf	26	ccomp	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	categorification	categorification	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	quantum	quantum	PROPN	NNP	Number=Sing	10	amod	_	_
9	harmonic	harmonic	ADJ	JJ	Degree=Pos	10	compound	_	_
10	oscillator	oscillator	NOUN	NN	Number=Sing	6	pobj	_	_
11	in	in	ADP	IN	_	18	prep	_	_
12	which	which	PRON	WDT	_	11	pobj	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	group	group	NOUN	NN	Number=Sing	18	nsubj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	15	punct	_	SpaceAfter=No
17	phases'—that	phases'—that	ADV	RB	_	15	pobj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	relcl	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	$ U(1) $	$ u(1) $	SYM	$	_	18	attr	_	_
21	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	circle	circle	NOUN	NN	Number=Sing	24	compound	_	_
24	group	group	NOUN	NN	Number=Sing	5	appos	_	SpaceAfter=No
25	—	—	PUNCT	:	_	26	punct	_	SpaceAfter=No
26	plays	play	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	special	special	ADJ	JJ	Degree=Pos	29	amod	_	_
29	role	role	NOUN	NN	Number=Sing	26	dobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	26	punct	_	SpaceAfter=No

# sent_id = 7
# text = We describe a general notion of ` $ M $ - stuff types' for any monoid $ M $ , and see that the case $ M = U(1) $ provides an interpretation of time evolution in the combinatorial setting, as well as recovering the usual Feynman rules for the quantum harmonic oscillator.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	general	general	ADJ	JJ	Degree=Pos	5	amod	_	_
5	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	6	punct	_	_
8	$ M $	$ m $	SYM	$	_	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	stuff	stuff	NOUN	NN	Number=Sing	11	compound	_	_
11	types	type	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
12	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	5	punct	_	_
13	for	for	ADP	IN	_	2	prep	_	_
14	any	any	DET	DT	_	15	det	_	_
15	monoid	monoid	NOUN	NN	Number=Sing	13	pobj	_	_
16	$ M $	$ m $	SYM	$	_	2	dobj	_	_
17	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
19	see	see	VERB	VB	VerbForm=Inf	2	conj	_	_
20	that	that	SCONJ	IN	_	24	mark	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	case	case	NOUN	NN	Number=Sing	24	nsubj	_	_
23	$ M = U(1) $	$ m = u(1) $	SYM	$	_	24	nsubj	_	_
24	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	ccomp	_	_
25	an	an	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
26	interpretation	interpretation	NOUN	NN	Number=Sing	24	dobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	time	time	NOUN	NN	Number=Sing	29	compound	_	_
29	evolution	evolution	NOUN	NN	Number=Sing	27	pobj	_	_
30	in	in	ADP	IN	_	24	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	combinatorial	combinatorial	NOUN	NN	Number=Sing	33	compound	_	_
33	setting	setting	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
35	as	as	ADV	RB	_	37	advmod	_	_
36	well	well	ADV	RB	Degree=Pos	37	advmod	_	_
37	as	as	ADP	IN	_	24	cc	_	_
38	recovering	recover	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	37	pcomp	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	42	det	_	_
40	usual	usual	ADJ	JJ	Degree=Pos	42	amod	_	_
41	Feynman	Feynman	PROPN	NNP	Number=Sing	42	compound	_	_
42	rules	rule	NOUN	NNS	Number=Plur	38	dobj	_	_
43	for	for	ADP	IN	_	42	prep	_	_
44	the	the	DET	DT	Definite=Def|PronType=Art	47	det	_	_
45	quantum	quantum	PROPN	NNP	Number=Sing	47	amod	_	_
46	harmonic	harmonic	ADJ	JJ	Degree=Pos	47	compound	_	_
47	oscillator	oscillator	NOUN	NN	Number=Sing	43	pobj	_	SpaceAfter=No
48	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 234
# sent_id = 1
# text = Motivated by applications to Mackey functors, Serge Bouc characterized pullback and finite coproduct preserving functors between categories of permutation representations of finite groups.
1	Motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	advcl	_	_
2	by	by	ADP	IN	_	1	agent	_	_
3	applications	application	NOUN	NNS	Number=Plur	2	pobj	_	_
4	to	to	ADP	IN	_	3	prep	_	_
5	Mackey	Mackey	PROPN	NNP	Number=Sing	6	compound	_	_
6	functors	functor	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
8	Serge	Serge	PROPN	NNP	Number=Sing	9	compound	_	_
9	Bouc	Bouc	PROPN	NNP	Number=Sing	10	nsubj	_	_
10	characterized	characterize	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
11	pullback	pullback	NOUN	NN	Number=Sing	14	nmod	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	finite	finite	ADJ	JJ	Degree=Pos	11	conj	_	_
14	coproduct	coproduct	NOUN	NN	Number=Sing	15	npadvmod	_	_
15	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	amod	_	_
16	functors	functor	NOUN	NNS	Number=Plur	10	dobj	_	_
17	between	between	ADP	IN	_	16	prep	_	_
18	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	permutation	permutation	NOUN	NN	Number=Sing	21	compound	_	_
21	representations	representation	NOUN	NNS	Number=Plur	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	finite	finite	ADJ	JJ	Degree=Pos	24	amod	_	_
24	groups	group	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = Initially surprising to a category theorist, this result does have a categorical explanation which we provide.
1	Initially	initially	ADV	RB	_	2	advmod	_	_
2	surprising	surprising	ADJ	JJ	Degree=Pos	11	advcl	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	category	category	NOUN	NN	Number=Sing	6	compound	_	_
6	theorist	theorist	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
8	this	this	DET	DT	Number=Sing|PronType=Dem	9	det	_	_
9	result	result	NOUN	NN	Number=Sing	11	nsubj	_	_
10	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	aux	_	_
11	have	have	VERB	VB	VerbForm=Inf	0	ROOT	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	categorical	categorical	ADJ	JJ	Degree=Pos	14	amod	_	_
14	explanation	explanation	NOUN	NN	Number=Sing	11	dobj	_	_
15	which	which	PRON	WDT	_	17	dobj	_	_
16	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	17	nsubj	_	_
17	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	14	relcl	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# doc_id = 235
# sent_id = 1
# text = What remains of a geometrical notion like that of a principal bundle when the base space is not a manifold but a coarse graining of it, like the poset formed by a base for the topology ordered under inclusion?
1	What	what	PRON	WP	_	2	nsubj	_	_
2	remains	remain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	geometrical	geometrical	ADJ	JJ	Degree=Pos	6	amod	_	_
6	notion	notion	NOUN	NN	Number=Sing	3	pobj	_	_
7	like	like	ADP	IN	_	6	prep	_	_
8	that	that	PRON	DT	Number=Sing|PronType=Dem	7	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	principal	principal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	bundle	bundle	NOUN	NN	Number=Sing	9	pobj	_	_
13	when	when	SCONJ	WRB	_	17	advmod	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	base	base	NOUN	NN	Number=Sing	16	compound	_	_
16	space	space	NOUN	NN	Number=Sing	17	nsubj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	advcl	_	_
18	not	not	PART	RB	Polarity=Neg	17	neg	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	manifold	manifold	NOUN	NN	Number=Sing	17	attr	_	_
21	but	but	CCONJ	CC	ConjType=Cmp	17	cc	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
23	coarse	coarse	ADJ	JJ	Degree=Pos	24	amod	_	_
24	graining	graining	NOUN	NN	Number=Sing	2	npadvmod	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	25	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
28	like	like	ADP	IN	_	2	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	poset	poset	NOUN	NN	Number=Sing	28	pobj	_	_
31	formed	form	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	30	acl	_	_
32	by	by	ADP	IN	_	31	agent	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
34	base	base	NOUN	NN	Number=Sing	32	pobj	_	_
35	for	for	ADP	IN	_	34	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	topology	topology	NOUN	NN	Number=Sing	35	pobj	_	_
38	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	37	acl	_	_
39	under	under	ADP	IN	_	38	prep	_	_
40	inclusion	inclusion	NOUN	NN	Number=Sing	39	pobj	_	SpaceAfter=No
41	?	?	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Motivated by the search for a geometrical framework for developing gauge theories in algebraic quantum field theory, we give, in the present paper, a first answer to this question.
1	Motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	advcl	_	_
2	by	by	ADP	IN	_	1	agent	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	search	search	NOUN	NN	Number=Sing	2	pobj	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	geometrical	geometrical	ADJ	JJ	Degree=Pos	8	amod	_	_
8	framework	framework	NOUN	NN	Number=Sing	5	pobj	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	developing	develop	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	pcomp	_	_
11	gauge	gauge	NOUN	NN	Number=Sing	12	compound	_	_
12	theories	theory	NOUN	NNS	Number=Plur	10	dobj	_	_
13	in	in	ADP	IN	_	10	prep	_	_
14	algebraic	algebraic	ADJ	JJ	Degree=Pos	16	amod	_	_
15	quantum	quantum	PROPN	NNP	Number=Sing	16	compound	_	_
16	field	field	NOUN	NN	Number=Sing	17	compound	_	_
17	theory	theory	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
19	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	20	nsubj	_	_
20	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	in	in	ADP	IN	_	20	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	present	present	ADJ	JJ	Degree=Pos	25	amod	_	_
25	paper	paper	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	first	first	ADJ	JJ	Degree=Pos	29	amod	_	_
29	answer	answer	NOUN	NN	Number=Sing	20	dobj	_	_
30	to	to	ADP	IN	_	29	prep	_	_
31	this	this	DET	DT	Number=Sing|PronType=Dem	32	det	_	_
32	question	question	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 3
# text = The notions of transition function, connection form and curvature form find a nice description in terms of cohomology, in general non - Abelian, of a poset with values in a group $ G $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	notions	notion	NOUN	NNS	Number=Plur	12	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	transition	transition	NOUN	NN	Number=Sing	5	compound	_	_
5	function	function	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	connection	connection	NOUN	NN	Number=Sing	8	compound	_	_
8	form	form	NOUN	NN	Number=Sing	5	conj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	curvature	curvature	NOUN	NN	Number=Sing	11	compound	_	_
11	form	form	NOUN	NN	Number=Sing	8	conj	_	_
12	find	find	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	nice	nice	ADJ	JJ	Degree=Pos	15	amod	_	_
15	description	description	NOUN	NN	Number=Sing	12	dobj	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	terms	term	NOUN	NNS	Number=Plur	16	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	cohomology	cohomology	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
21	in	in	ADP	IN	_	12	prep	_	_
22	general	general	ADJ	JJ	Degree=Pos	25	amod	_	_
23	non	non	PROPN	NNP	Number=Sing	25	compound	_	_
24	-	-	PROPN	NNP	Number=Sing	25	punct	_	_
25	Abelian	Abelian	PROPN	NNP	Number=Sing	21	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
27	of	of	ADP	IN	_	12	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
29	poset	poset	NOUN	NN	Number=Sing	27	pobj	_	_
30	with	with	ADP	IN	_	29	prep	_	_
31	values	value	NOUN	NNS	Number=Plur	30	pobj	_	_
32	in	in	ADP	IN	_	31	prep	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
34	group	group	NOUN	NN	Number=Sing	32	pobj	_	_
35	$ G $	$ g $	SYM	$	_	12	dep	_	_
36	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 4
# text = Interpreting a 1 - cocycle as a principal bundle, a connection turns out to be a 1 - cochain associated in a suitable way with this 1 - cocycle; the curvature of a connection turns out to be its 2 - coboundary.
1	Interpreting	interpret	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	advcl	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
3	1	1	NUM	CD	NumType=Card	5	nummod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	cocycle	cocycle	NOUN	NN	Number=Sing	1	dobj	_	_
6	as	as	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	principal	principal	ADJ	JJ	Degree=Pos	9	amod	_	_
9	bundle	bundle	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	connection	connection	NOUN	NN	Number=Sing	13	nsubj	_	_
13	turns	turn	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	37	ccomp	_	_
14	out	out	ADP	RP	_	13	prt	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	be	be	AUX	VB	VerbForm=Inf	13	xcomp	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
18	1	1	NUM	CD	NumType=Card	20	nummod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	cochain	cochain	NOUN	NN	Number=Sing	16	attr	_	_
21	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	acl	_	_
22	in	in	ADP	IN	_	21	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	suitable	suitable	ADJ	JJ	Degree=Pos	25	amod	_	_
25	way	way	NOUN	NN	Number=Sing	22	pobj	_	_
26	with	with	ADP	IN	_	25	prep	_	_
27	this	this	DET	DT	Number=Sing|PronType=Dem	30	det	_	_
28	1	1	NUM	CD	NumType=Card	30	nummod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	cocycle	cocycle	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
31	;	;	PUNCT	:	_	37	punct	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
33	curvature	curvature	NOUN	NN	Number=Sing	37	nsubj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
36	connection	connection	NOUN	NN	Number=Sing	34	pobj	_	_
37	turns	turn	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
38	out	out	ADP	RP	_	37	prt	_	_
39	to	to	PART	TO	_	40	aux	_	_
40	be	be	AUX	VB	VerbForm=Inf	37	xcomp	_	_
41	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	44	poss	_	_
42	2	2	NUM	CD	NumType=Card	44	nummod	_	_
43	-	-	PUNCT	HYPH	PunctType=Dash	44	punct	_	_
44	coboundary	coboundary	NOUN	NN	Number=Sing	40	attr	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	37	punct	_	SpaceAfter=No

# sent_id = 5
# text = We show the existence of nonflat connections, and relate flat connections to homomorphisms of the fundamental group of the poset into $ G $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	existence	existence	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	nonflat	nonflat	NOUN	NN	Number=Sing	7	compound	_	_
7	connections	connection	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
10	relate	relate	VERB	VB	VerbForm=Inf	2	conj	_	_
11	flat	flat	ADJ	JJ	Degree=Pos	12	amod	_	_
12	connections	connection	NOUN	NNS	Number=Plur	10	dobj	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	homomorphisms	homomorphism	NOUN	NNS	Number=Plur	13	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	fundamental	fundamental	ADJ	JJ	Degree=Pos	18	amod	_	_
18	group	group	NOUN	NN	Number=Sing	15	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	poset	poset	NOUN	NN	Number=Sing	19	pobj	_	_
22	into	into	ADP	IN	_	10	prep	_	_
23	$ G $	$ g $	SYM	$	_	22	pobj	_	_
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = We discuss holonomy and prove an analogue of the Ambrose - Singer theorem.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	discuss	discuss	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	holonomy	holonomy	NOUN	NN	Number=Sing	2	dobj	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
5	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	analogue	analogue	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
10	Ambrose	Ambrose	PROPN	NNP	Number=Sing	12	compound	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	Singer	Singer	PROPN	NNP	Number=Sing	8	pobj	_	_
13	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	5	oprd	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 236
# sent_id = 1
# text = Given a groupoid $ G $ one has, in addition to the equivalence of categories $ E $ from $ G $ to its skeleton, a fibration $ F $ from $ G $ to its set of connected components (seen as a discrete category).
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	groupoid	groupoid	NOUN	NN	Number=Sing	1	pobj	_	_
4	$ G $	$ g $	SYM	$	_	5	nmod	_	_
5	one	one	NOUN	NN	Number=Sing	3	appos	_	_
6	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	1	auxpass	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	in	in	ADP	IN	_	1	prep	_	_
9	addition	addition	NOUN	NN	Number=Sing	8	pobj	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	equivalence	equivalence	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	_
15	$ E $	$ e $	SYM	$	_	12	appos	_	_
16	from	from	ADP	IN	_	12	prep	_	_
17	$ G $	$ g $	SYM	$	_	16	pobj	_	_
18	to	to	ADP	IN	_	16	prep	_	_
19	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	20	poss	_	_
20	skeleton	skeleton	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
23	fibration	fibration	NOUN	NN	Number=Sing	20	appos	_	_
24	$ F $	$ f $	SYM	$	_	20	appos	_	_
25	from	from	ADP	IN	_	16	prep	_	_
26	$ G $	$ g $	SYM	$	_	25	pobj	_	_
27	to	to	ADP	IN	_	25	prep	_	_
28	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	29	poss	_	_
29	set	set	NOUN	NN	Number=Sing	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	connected	connected	ADJ	JJ	Degree=Pos	32	amod	_	_
32	components	component	NOUN	NNS	Number=Plur	30	pobj	_	_
33	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	32	punct	_	SpaceAfter=No
34	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	acl	_	_
35	as	as	ADP	IN	_	34	prep	_	_
36	a	a	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
37	discrete	discrete	ADJ	JJ	Degree=Pos	38	amod	_	_
38	category	category	NOUN	NN	Number=Sing	35	pobj	_	SpaceAfter=No
39	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	1	punct	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = From the observation that $ E $ and $ F $ differ unless $ G[x, x]=id_x $ for every object $ x $ of $ G $ , we prove there is a fibered equivalence from $ C[Sigma^{ - 1}] $ to $ C/Sigma $ when $ Sigma $ is a Yoneda - system of a loop - free category $ C $ .
1	From	from	ADP	IN	_	31	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	observation	observation	NOUN	NN	Number=Sing	1	pobj	_	_
4	that	that	SCONJ	IN	_	8	mark	_	_
5	$ E $	$ e $	SYM	$	_	4	nmod	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	$ F $	$ f $	SYM	$	_	8	nsubj	_	_
8	differ	differ	VERB	VB	VerbForm=Inf	3	relcl	_	_
9	unless	unless	SCONJ	IN	_	19	mark	_	_
10	$ G[x, x]=id_x $	$ g[x, x]=id_x $	SYM	$	_	9	nmod	_	_
11	for	for	ADP	IN	_	19	prep	_	_
12	every	every	DET	DT	_	13	det	_	_
13	object	object	NOUN	NN	Number=Sing	11	pobj	_	_
14	$ x $	$ x $	SYM	$	_	13	prep	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	$ G $	$ g $	SYM	$	_	15	pobj	_	_
17	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	8	advcl	_	_
20	there	there	PRON	EX	_	21	expl	_	_
21	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	ccomp	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
23	fibered	fibere	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
24	equivalence	equivalence	NOUN	NN	Number=Sing	21	attr	_	_
25	from	from	ADP	IN	_	24	prep	_	_
26	$ C[Sigma^{ - 1}] $	$ c[sigma^{ - 1}] $	SYM	$	_	25	pobj	_	_
27	to	to	PART	TO	_	25	prep	_	_
28	$ C/Sigma $	$ c/sigma $	SYM	$	_	27	pobj	_	_
29	when	when	SCONJ	WRB	_	30	advmod	_	_
30	$ Sigma $	$ sigma $	SYM	$	_	31	nsubj	_	_
31	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
33	Yoneda	Yoneda	PROPN	NNP	Number=Sing	35	compound	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	system	system	NOUN	NN	Number=Sing	31	attr	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
38	loop	loop	NOUN	NN	Number=Sing	40	npadvmod	_	_
39	-	-	PUNCT	HYPH	PunctType=Dash	40	punct	_	_
40	free	free	ADJ	JJ	Degree=Pos	41	amod	_	_
41	category	category	NOUN	NN	Number=Sing	36	pobj	_	_
42	$ C $	$ c $	SYM	$	_	41	appos	_	_
43	.	.	PUNCT	.	PunctType=Peri	31	punct	_	SpaceAfter=No

# sent_id = 3
# text = In fact, all the equivalences from $ C[Sigma^{ - 1}] $ to $ C/Sigma $ are fibered.
1	In	in	ADP	IN	_	12	prep	_	_
2	fact	fact	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
4	all	all	DET	PDT	_	6	predet	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	equivalences	equivalence	NOUN	NNS	Number=Plur	12	nsubjpass	_	_
7	from	from	ADP	IN	_	6	prep	_	_
8	$ C[Sigma^{ - 1}] $	$ c[sigma^{ - 1}] $	SYM	$	_	7	pobj	_	_
9	to	to	PART	TO	_	7	prep	_	_
10	$ C/Sigma $	$ c/sigma $	SYM	$	_	6	nmod	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	fibered	fibere	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 4
# text = Furthermore, since the quotient $ C/Sigma $ shrinks as $ Sigma $ grows, we define the component category of a loop - free category as $ C/{overline{Sigma}} $ where $ overline{Sigma} $ is the greatest Yoneda - system of $ C $ .
1	Furthermore	furthermore	ADV	RB	_	7	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
3	since	since	SCONJ	IN	_	7	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	quotient	quotient	NOUN	NN	Number=Sing	7	nsubj	_	_
6	$ C/Sigma $	$ c/sigma $	SYM	$	_	7	nmod	_	_
7	shrinks	shrink	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	advcl	_	_
8	as	as	SCONJ	IN	_	10	mark	_	_
9	$ Sigma $	$ sigma $	SYM	$	_	10	nsubj	_	_
10	grows	grow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	advcl	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	component	component	NOUN	NN	Number=Sing	16	compound	_	_
16	category	category	NOUN	NN	Number=Sing	13	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
19	loop	loop	NOUN	NN	Number=Sing	21	npadvmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	free	free	ADJ	JJ	Degree=Pos	22	amod	_	_
22	category	category	NOUN	NN	Number=Sing	17	pobj	_	_
23	as	as	ADP	IN	_	13	prep	_	_
24	$ C/{overline{Sigma}} $	$ c/{overline{sigma}} $	SYM	$	_	23	pobj	_	_
25	where	where	SCONJ	WRB	_	27	advmod	_	_
26	$ overline{Sigma} $	$ overline{sigma} $	SYM	$	_	27	nsubj	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	relcl	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
29	greatest	great	ADJ	JJS	Degree=Sup	32	amod	_	_
30	Yoneda	Yoneda	PROPN	NNP	Number=Sing	32	compound	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	system	system	NOUN	NN	Number=Sing	27	attr	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	$ C $	$ c $	SYM	$	_	33	pobj	_	_
35	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# doc_id = 237
# sent_id = 1
# text = Directed Algebraic Topology is a recent field, deeply linked with ordinary and higher dimensional category theory.
1	Directed	Directed	PROPN	NNP	Number=Sing	3	compound	_	_
2	Algebraic	Algebraic	PROPN	NNP	Number=Sing	3	compound	_	_
3	Topology	Topology	PROPN	NNP	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	recent	recent	ADJ	JJ	Degree=Pos	7	amod	_	_
7	field	field	NOUN	NN	Number=Sing	4	attr	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
9	deeply	deeply	ADV	RB	_	10	advmod	_	_
10	linked	link	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	advcl	_	_
11	with	with	ADP	IN	_	10	prep	_	_
12	ordinary	ordinary	ADJ	JJ	Degree=Pos	17	amod	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	higher	high	ADJ	JJR	Degree=Cmp	12	conj	_	_
15	dimensional	dimensional	ADJ	JJ	Degree=Pos	17	amod	_	_
16	category	category	NOUN	NN	Number=Sing	17	compound	_	_
17	theory	theory	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = A `directed space', for example, an ordered topological space, has directed homotopies (which are generally non reversible) and a fundamental category (replacing the fundamental groupoid of the classical case).
1	A	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
2	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	4	punct	_	SpaceAfter=No
3	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	amod	_	_
4	space	space	NOUN	NN	Number=Sing	16	nsubj	_	SpaceAfter=No
5	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	4	punct	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
7	for	for	ADP	IN	_	4	prep	_	_
8	example	example	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	ordered	ordered	ADJ	JJ	Degree=Pos	13	amod	_	_
12	topological	topological	ADJ	JJ	Degree=Pos	13	amod	_	_
13	space	space	NOUN	NN	Number=Sing	4	appos	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
15	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	aux	_	_
16	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
17	homotopies	homotopie	NOUN	NNS	Number=Plur	16	dobj	_	_
18	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	17	punct	_	SpaceAfter=No
19	which	which	PRON	WDT	_	20	nsubj	_	_
20	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	17	relcl	_	_
21	generally	generally	ADV	RB	_	20	advmod	_	_
22	non	non	ADJ	JJ	Degree=Pos	23	advmod	_	_
23	reversible	reversible	ADJ	JJ	Degree=Pos	20	acomp	_	SpaceAfter=No
24	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	20	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
27	fundamental	fundamental	ADJ	JJ	Degree=Pos	28	amod	_	_
28	category	category	NOUN	NN	Number=Sing	17	conj	_	_
29	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	28	punct	_	SpaceAfter=No
30	replacing	replace	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	28	acl	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	fundamental	fundamental	ADJ	JJ	Degree=Pos	33	amod	_	_
33	groupoid	groupoid	NOUN	NN	Number=Sing	30	dobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
36	classical	classical	ADJ	JJ	Degree=Pos	37	amod	_	_
37	case	case	NOUN	NN	Number=Sing	34	pobj	_	SpaceAfter=No
38	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	28	punct	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 3
# text = Finding a simple—possibly finite—model of the latter is a non - trivial problem, whose solution gives relevant information on the given `space'; a problem which is of interest for applications as well as in general Category Theory.
1	Finding	find	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	csubj	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	simple	simple	ADJ	JJ	Degree=Pos	6	amod	_	SpaceAfter=No
4	—	—	PUNCT	:	_	6	punct	_	SpaceAfter=No
5	possibly	possibly	ADV	RB	_	6	advmod	_	_
6	finite	finite	ADJ	JJ	Degree=Pos	8	nmod	_	SpaceAfter=No
7	—	—	PUNCT	:	_	8	punct	_	SpaceAfter=No
8	model	model	NOUN	NN	Number=Sing	1	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	latter	latter	ADJ	JJ	Degree=Pos	9	pobj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
14	non	non	ADJ	JJ	Degree=Pos	17	amod	_	_
15	-	-	ADJ	JJ	Degree=Pos	17	punct	_	_
16	trivial	trivial	ADJ	JJ	Degree=Pos	17	amod	_	_
17	problem	problem	NOUN	NN	Number=Sing	12	attr	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	whose	whose	DET	WP$	Poss=Yes	20	poss	_	_
20	solution	solution	NOUN	NN	Number=Sing	21	nsubj	_	_
21	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
22	relevant	relevant	ADJ	JJ	Degree=Pos	23	amod	_	_
23	information	information	NOUN	NN	Number=Sing	21	dobj	_	_
24	on	on	ADP	IN	_	21	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
26	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	amod	_	_
27	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	28	punct	_	SpaceAfter=No
28	space	space	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
29	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	24	pobj	_	SpaceAfter=No
30	;	;	PUNCT	:	_	17	punct	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
32	problem	problem	NOUN	NN	Number=Sing	17	appos	_	_
33	which	which	PRON	WDT	_	34	nsubj	_	_
34	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	32	relcl	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	interest	interest	NOUN	NN	Number=Sing	35	pobj	_	_
37	for	for	ADP	IN	_	36	prep	_	_
38	applications	application	NOUN	NNS	Number=Plur	37	pobj	_	_
39	as	as	ADV	RB	_	41	advmod	_	_
40	well	well	ADV	RB	Degree=Pos	41	advmod	_	_
41	as	as	ADP	IN	_	37	cc	_	_
42	in	in	ADP	IN	_	36	prep	_	_
43	general	general	ADJ	JJ	Degree=Pos	45	amod	_	_
44	Category	Category	PROPN	NNP	Number=Sing	45	compound	_	_
45	Theory	Theory	PROPN	NNP	Number=Sing	42	pobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 4
# text = Here we continue the work ``The shape of a category up to directed homotopy", with a deeper analysis of `surjective models', motivated by studying the singularities of 3 - dimensional ordered spaces.
1	Here	here	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	continue	continue	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	work	work	NOUN	NN	Number=Sing	3	dobj	_	_
6	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	3	punct	_	SpaceAfter=No
7	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	3	punct	_	SpaceAfter=No
8	The	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	shape	shape	NOUN	NN	Number=Sing	3	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
13	up	up	ADP	RP	_	9	prep	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
16	homotopy	homotopy	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
17	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	9	punct	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
19	with	with	ADP	IN	_	9	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	deeper	deep	ADJ	JJR	Degree=Cmp	22	amod	_	_
22	analysis	analysis	NOUN	NN	Number=Sing	19	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	SpaceAfter=No
25	surjective	surjective	ADJ	JJ	Degree=Pos	26	amod	_	_
26	models	model	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
27	'	'	PART	POS	_	26	punct	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
29	motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	acl	_	_
30	by	by	ADP	IN	_	29	prep	_	_
31	studying	study	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	30	pcomp	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
33	singularities	singularity	NOUN	NNS	Number=Plur	31	dobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	3	3	NUM	CD	NumType=Card	37	advmod	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	dimensional	dimensional	ADJ	JJ	Degree=Pos	39	amod	_	_
38	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	39	amod	_	_
39	spaces	space	NOUN	NNS	Number=Plur	34	pobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 238
# sent_id = 1
# text = Given an additive equational category with a closed symmetric monoidal structure and a potential dualizing object, we find sufficient conditions that the category of topological objects over that category has a good notion of full subcategories of strong and weakly topologized objects and show that each is equivalent to the chu category of the original category with respect to the dualizing object.
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
3	additive	additive	ADJ	JJ	Degree=Pos	5	amod	_	_
4	equational	equational	ADJ	JJ	Degree=Pos	5	amod	_	_
5	category	category	NOUN	NN	Number=Sing	1	pobj	_	_
6	with	with	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	closed	closed	ADJ	JJ	Degree=Pos	11	amod	_	_
9	symmetric	symmetric	ADJ	JJ	Degree=Pos	11	amod	_	_
10	monoidal	monoidal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	structure	structure	NOUN	NN	Number=Sing	6	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
14	potential	potential	ADJ	JJ	Degree=Pos	16	amod	_	_
15	dualizing	dualizing	NOUN	NN	Number=Sing	16	amod	_	_
16	object	object	NOUN	NN	Number=Sing	11	conj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	find	find	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	sufficient	sufficient	ADJ	JJ	Degree=Pos	21	amod	_	_
21	conditions	condition	NOUN	NNS	Number=Plur	19	dobj	_	_
22	that	that	SCONJ	IN	_	31	mark	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	category	category	NOUN	NN	Number=Sing	31	nsubj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	topological	topological	ADJ	JJ	Degree=Pos	27	amod	_	_
27	objects	object	NOUN	NNS	Number=Plur	25	pobj	_	_
28	over	over	ADP	IN	_	24	prep	_	_
29	that	that	DET	DT	Number=Sing|PronType=Dem	30	det	_	_
30	category	category	NOUN	NN	Number=Sing	28	pobj	_	_
31	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	21	acl	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
33	good	good	ADJ	JJ	Degree=Pos	34	amod	_	_
34	notion	notion	NOUN	NN	Number=Sing	31	dobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	full	full	ADJ	JJ	Degree=Pos	37	amod	_	_
37	subcategories	subcategorie	NOUN	NNS	Number=Plur	35	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	strong	strong	ADJ	JJ	Degree=Pos	43	amod	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	39	cc	_	_
41	weakly	weakly	ADJ	JJ	Degree=Pos	39	conj	_	_
42	topologized	topologize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	39	conj	_	_
43	objects	object	NOUN	NNS	Number=Plur	38	pobj	_	_
44	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
45	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	31	conj	_	_
46	that	that	SCONJ	IN	_	48	mark	_	_
47	each	each	PRON	DT	_	48	nsubj	_	_
48	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	45	ccomp	_	_
49	equivalent	equivalent	ADJ	JJ	Degree=Pos	48	acomp	_	_
50	to	to	ADP	IN	_	49	prep	_	_
51	the	the	DET	DT	Definite=Def|PronType=Art	53	det	_	_
52	chu	chu	PROPN	NNP	Number=Sing	53	compound	_	_
53	category	category	NOUN	NN	Number=Sing	50	pobj	_	_
54	of	of	ADP	IN	_	53	prep	_	_
55	the	the	DET	DT	Definite=Def|PronType=Art	57	det	_	_
56	original	original	ADJ	JJ	Degree=Pos	57	amod	_	_
57	category	category	NOUN	NN	Number=Sing	54	pobj	_	_
58	with	with	ADP	IN	_	49	prep	_	_
59	respect	respect	NOUN	NN	Number=Sing	58	pobj	_	_
60	to	to	ADP	IN	_	59	prep	_	_
61	the	the	DET	DT	Definite=Def|PronType=Art	63	det	_	_
62	dualizing	dualize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	63	amod	_	_
63	object	object	NOUN	NN	Number=Sing	60	pobj	_	SpaceAfter=No
64	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# doc_id = 239
# sent_id = 1
# text = Motivated by a desire to gain a better understanding of the ``dimension - by - dimension'' decompositions of certain prominent monads in higher category theory, we investigate descent theory for endofunctors and monads.
1	Motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	advcl	_	_
2	by	by	ADP	IN	_	1	agent	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	desire	desire	NOUN	NN	Number=Sing	2	pobj	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	gain	gain	VERB	VB	VerbForm=Inf	4	acl	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	better	well	ADJ	JJR	Degree=Cmp	9	amod	_	_
9	understanding	understanding	NOUN	NN	Number=Sing	6	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
12	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	20	punct	_	SpaceAfter=No
13	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	20	punct	_	SpaceAfter=No
14	dimension	dimension	NOUN	NN	Number=Sing	20	nmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
16	by	by	ADP	IN	_	14	prep	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
18	dimension	dimension	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
19	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	20	punct	_	_
20	decompositions	decomposition	NOUN	NNS	Number=Plur	10	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	certain	certain	ADJ	JJ	Degree=Pos	24	amod	_	_
23	prominent	prominent	ADJ	JJ	Degree=Pos	24	amod	_	_
24	monads	monad	NOUN	NNS	Number=Plur	21	pobj	_	_
25	in	in	ADP	IN	_	24	prep	_	_
26	higher	high	ADJ	JJR	Degree=Cmp	28	amod	_	_
27	category	category	NOUN	NN	Number=Sing	28	compound	_	_
28	theory	theory	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
30	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	31	nsubj	_	_
31	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
32	descent	descent	NOUN	NN	Number=Sing	33	compound	_	_
33	theory	theory	NOUN	NN	Number=Sing	31	dobj	_	_
34	for	for	ADP	IN	_	33	prep	_	_
35	endofunctors	endofunctor	NOUN	NNS	Number=Plur	34	pobj	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
37	monads	monad	NOUN	NNS	Number=Plur	35	conj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	31	punct	_	SpaceAfter=No

# sent_id = 2
# text = After setting up a basic framework of indexed monoidal categories, we describe a suitable subcategory of $ Cat $ over which we can view the assignment $ C | - > Mnd(C) $ as an indexed category; on this base category, there is a natural topology.
1	After	after	ADP	IN	_	13	prep	_	_
2	setting	set	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	1	pcomp	_	_
3	up	up	ADP	RP	_	2	prt	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	basic	basic	ADJ	JJ	Degree=Pos	6	amod	_	_
6	framework	framework	NOUN	NN	Number=Sing	2	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
9	monoidal	monoidal	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	38	ccomp	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	suitable	suitable	ADJ	JJ	Degree=Pos	16	amod	_	_
16	subcategory	subcategory	NOUN	NN	Number=Sing	13	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	$ Cat $	$ cat $	SYM	$	_	17	pobj	_	_
19	over	over	ADP	IN	_	23	prep	_	_
20	which	which	PRON	WDT	_	19	pobj	_	_
21	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	23	nsubj	_	_
22	can	can	AUX	MD	VerbForm=Fin	23	aux	_	_
23	view	view	VERB	VB	VerbForm=Inf	16	relcl	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	assignment	assignment	NOUN	NN	Number=Sing	23	dobj	_	_
26	$ C | - > Mnd(C) $	$ c | - > mnd(c) $	SYM	$	_	23	dep	_	_
27	as	as	ADP	IN	_	23	prep	_	_
28	an	an	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
29	indexed	indexed	ADJ	JJ	Degree=Pos	30	amod	_	_
30	category	category	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
31	;	;	PUNCT	:	_	38	punct	_	_
32	on	on	ADP	IN	_	38	prep	_	_
33	this	this	DET	DT	Number=Sing|PronType=Dem	35	det	_	_
34	base	base	NOUN	NN	Number=Sing	35	compound	_	_
35	category	category	NOUN	NN	Number=Sing	32	pobj	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	38	punct	_	_
37	there	there	PRON	EX	_	38	expl	_	_
38	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
39	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
40	natural	natural	ADJ	JJ	Degree=Pos	41	amod	_	_
41	topology	topology	NOUN	NN	Number=Sing	38	attr	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	38	punct	_	SpaceAfter=No

# sent_id = 3
# text = Then we single out a class of monads which are well - behaved with respect to reindexing.
1	Then	then	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	single	single	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	out	out	ADP	RP	_	3	prt	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	class	class	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	monads	monad	NOUN	NNS	Number=Plur	7	pobj	_	_
9	which	which	PRON	WDT	_	10	nsubj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	relcl	_	_
11	well	well	ADV	RB	Degree=Pos	13	advmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	behaved	behave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acomp	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	respect	respect	NOUN	NN	Number=Sing	14	pobj	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	reindexing	reindexe	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	pcomp	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = The main result is now, that such monads form a stack.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	result	result	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	now	now	ADV	RB	_	4	advmod	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
7	that	that	SCONJ	IN	_	10	mark	_	_
8	such	such	ADJ	JJ	Degree=Pos	9	amod	_	_
9	monads	monad	NOUN	NNS	Number=Plur	10	nsubj	_	_
10	form	form	VERB	VBP	Tense=Pres|VerbForm=Fin	4	ccomp	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	stack	stack	NOUN	NN	Number=Sing	10	dobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = Using this, we can shed some light on the free strict $ omega $ - category monad on globular sets and the free operad - with - contraction monad on the category of collections.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	advcl	_	_
2	this	this	PRON	DT	Number=Sing|PronType=Dem	1	dobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
5	can	can	AUX	MD	VerbForm=Fin	6	aux	_	_
6	shed	shed	VERB	VB	VerbForm=Inf	0	ROOT	_	_
7	some	some	DET	DT	_	8	det	_	_
8	light	light	NOUN	NN	Number=Sing	6	dobj	_	_
9	on	on	ADP	IN	_	6	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
11	free	free	ADJ	JJ	Degree=Pos	16	amod	_	_
12	strict	strict	ADJ	JJ	Degree=Pos	16	amod	_	_
13	$ omega $	$ omega $	SYM	$	_	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	category	category	NOUN	NN	Number=Sing	16	compound	_	_
16	monad	monad	NOUN	NNS	Number=Plur	9	pobj	_	_
17	on	on	ADP	IN	_	16	prep	_	_
18	globular	globular	ADJ	JJ	Degree=Pos	19	amod	_	_
19	sets	set	NOUN	NNS	Number=Plur	17	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
22	free	free	ADJ	JJ	Degree=Pos	28	amod	_	_
23	operad	operad	NOUN	NN	Number=Sing	28	nmod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
25	with	with	ADP	IN	_	23	prep	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
27	contraction	contraction	NOUN	NN	Number=Sing	25	pobj	_	_
28	monad	monad	NOUN	NNS	Number=Plur	19	conj	_	_
29	on	on	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	category	category	NOUN	NN	Number=Sing	29	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	collections	collection	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 240
# sent_id = 1
# text = In this paper equivalence of the concepts of ana - bicategory and the 2D - multitopic category is proved.
1	In	in	ADP	IN	_	19	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	4	compound	_	_
4	equivalence	equivalence	NOUN	NN	Number=Sing	1	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	concepts	concept	NOUN	NNS	Number=Plur	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	ana	ana	NOUN	NN	Number=Sing	11	compound	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	bicategory	bicategory	PROPN	NNP	Number=Sing	8	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
14	2D	2D	PROPN	NNP	Number=Sing	16	compound	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	multitopic	multitopic	NOUN	NN	Number=Sing	17	compound	_	_
17	category	category	NOUN	NN	Number=Sing	19	nsubjpass	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	auxpass	_	_
19	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 2
# text = The equivalence is FOLDS equivalence of the FOLDS - Specifications of the two concepts.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	equivalence	equivalence	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	FOLDS	FOLDS	PROPN	NNP	Number=Sing	5	compound	_	_
5	equivalence	equivalence	NOUN	NN	Number=Sing	3	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	FOLDS	FOLDS	PROPN	NNP	Number=Sing	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	Specifications	specification	NOUN	NNS	Number=Plur	6	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	two	two	NUM	CD	NumType=Card	14	nummod	_	_
14	concepts	concept	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Two constructions for transforming one form of category to another are given and it is shown that we get a structure equivalent to the original one when we compose the two constructions.
1	Two	two	NUM	CD	NumType=Card	2	nummod	_	_
2	constructions	construction	NOUN	NNS	Number=Plur	12	nsubjpass	_	_
3	for	for	ADP	IN	_	2	prep	_	_
4	transforming	transform	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	pcomp	_	_
5	one	one	NUM	CD	NumType=Card	6	nummod	_	_
6	form	form	NOUN	NN	Number=Sing	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
9	to	to	ADP	IN	_	4	prep	_	_
10	another	another	PRON	DT	_	9	pobj	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	16	nsubjpass	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	auxpass	_	_
16	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	conj	_	_
17	that	that	SCONJ	IN	_	19	mark	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	get	get	VERB	VBP	Tense=Pres|VerbForm=Fin	16	ccomp	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	structure	structure	NOUN	NN	Number=Sing	19	dobj	_	_
22	equivalent	equivalent	ADJ	JJ	Degree=Pos	21	amod	_	_
23	to	to	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	original	original	ADJ	JJ	Degree=Pos	26	amod	_	_
26	one	one	NUM	CD	NumType=Card	23	pobj	_	_
27	when	when	SCONJ	WRB	_	29	advmod	_	_
28	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	29	nsubj	_	_
29	compose	compose	VERB	VBP	Tense=Pres|VerbForm=Fin	19	advcl	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	two	two	NUM	CD	NumType=Card	32	nummod	_	_
32	constructions	construction	NOUN	NNS	Number=Plur	29	dobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# doc_id = 241
# sent_id = 1
# text = The well - known notion of crossed module of groups is raised in this paper to the categorical level supported by the theory of categorical groups.
1	The	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
2	well	well	ADV	RB	Degree=Pos	4	advmod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	amod	_	_
5	notion	notion	NOUN	NN	Number=Sing	12	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	crossed	crossed	ADJ	JJ	Degree=Pos	8	amod	_	_
8	module	module	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	groups	group	NOUN	NNS	Number=Plur	9	pobj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	raised	raise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	this	this	DET	DT	Number=Sing|PronType=Dem	15	det	_	_
15	paper	paper	NOUN	NN	Number=Sing	13	pobj	_	_
16	to	to	ADP	IN	_	12	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	categorical	categorical	ADJ	JJ	Degree=Pos	19	amod	_	_
19	level	level	NOUN	NN	Number=Sing	16	pobj	_	_
20	supported	support	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	acl	_	_
21	by	by	ADP	IN	_	20	agent	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	theory	theory	NOUN	NN	Number=Sing	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	categorical	categorical	ADJ	JJ	Degree=Pos	26	amod	_	_
26	groups	group	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 2
# text = We construct the cokernel of a categorical crossed module and we establish the universal property of this categorical group.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	cokernel	cokernel	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	categorical	categorical	ADJ	JJ	Degree=Pos	9	amod	_	_
8	crossed	crossed	ADJ	JJ	Degree=Pos	9	amod	_	_
9	module	module	NOUN	NN	Number=Sing	5	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
11	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	12	nsubj	_	_
12	establish	establish	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	universal	universal	ADJ	JJ	Degree=Pos	15	amod	_	_
15	property	property	NOUN	NN	Number=Sing	12	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	this	this	DET	DT	Number=Sing|PronType=Dem	19	det	_	_
18	categorical	categorical	ADJ	JJ	Degree=Pos	19	amod	_	_
19	group	group	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also prove a suitable 2 - dimensional version of the kernel - cokernel lemma for a diagram of categorical crossed modules.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
5	suitable	suitable	ADJ	JJ	Degree=Pos	9	amod	_	_
6	2	2	NUM	CD	NumType=Card	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	dimensional	dimensional	ADJ	JJ	Degree=Pos	9	amod	_	_
9	version	version	NOUN	NN	Number=Sing	3	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
12	kernel	kernel	NOUN	NN	Number=Sing	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	cokernel	cokernel	NOUN	NN	Number=Sing	15	compound	_	_
15	lemma	lemma	NOUN	NN	Number=Sing	10	pobj	_	_
16	for	for	ADP	IN	_	9	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	diagram	diagram	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	categorical	categorical	ADJ	JJ	Degree=Pos	22	amod	_	_
21	crossed	crossed	ADJ	JJ	Degree=Pos	22	amod	_	_
22	modules	module	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = We then study derivations with coefficients in categorical crossed modules and show the existence of a categorical crossed module given by inner derivations.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	derivations	derivation	NOUN	NNS	Number=Plur	3	dobj	_	_
5	with	with	ADP	IN	_	3	prep	_	_
6	coefficients	coefficient	NOUN	NNS	Number=Plur	5	pobj	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	categorical	categorical	ADJ	JJ	Degree=Pos	10	amod	_	_
9	crossed	crossed	ADJ	JJ	Degree=Pos	10	amod	_	_
10	modules	module	NOUN	NNS	Number=Plur	7	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
12	show	show	VERB	VB	VerbForm=Inf	3	conj	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	existence	existence	NOUN	NN	Number=Sing	12	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
17	categorical	categorical	ADJ	JJ	Degree=Pos	19	amod	_	_
18	crossed	crossed	ADJ	JJ	Degree=Pos	19	amod	_	_
19	module	module	NOUN	NN	Number=Sing	15	pobj	_	_
20	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	acl	_	_
21	by	by	ADP	IN	_	20	agent	_	_
22	inner	inner	ADJ	JJ	Degree=Pos	23	amod	_	_
23	derivations	derivation	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = This allows us to define the low - dimensional cohomology categorical groups and, finally, these invariants are connected by a six - term 2 - exact sequence obtained by using the kernel - cokernel lemma.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	define	define	VERB	VB	VerbForm=Inf	2	ccomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
7	low	low	ADV	RB	_	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	dimensional	dimensional	ADJ	JJ	Degree=Pos	12	amod	_	_
10	cohomology	cohomology	NOUN	NN	Number=Sing	12	nmod	_	_
11	categorical	categorical	ADJ	JJ	Degree=Pos	12	amod	_	_
12	groups	group	NOUN	NNS	Number=Plur	5	dobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
15	finally	finally	ADV	RB	_	20	advmod	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
17	these	these	DET	DT	Number=Plur|PronType=Dem	18	det	_	_
18	invariants	invariant	NOUN	NNS	Number=Plur	20	nsubjpass	_	_
19	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	20	auxpass	_	_
20	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	conj	_	_
21	by	by	ADP	IN	_	20	agent	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
23	six	six	NUM	CD	NumType=Card	25	nummod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	term	term	NOUN	NN	Number=Sing	29	nmod	_	_
26	2	2	NUM	CD	NumType=Card	28	nummod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	exact	exact	ADJ	JJ	Degree=Pos	29	amod	_	_
29	sequence	sequence	NOUN	NN	Number=Sing	21	pobj	_	_
30	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	acl	_	_
31	by	by	ADP	IN	_	30	agent	_	_
32	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	31	pcomp	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
34	kernel	kernel	NOUN	NN	Number=Sing	36	compound	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	36	punct	_	_
36	cokernel	cokernel	NOUN	NN	Number=Sing	37	compound	_	_
37	lemma	lemma	NOUN	NN	Number=Sing	32	dobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 242
# sent_id = 1
# text = Given a topological space $ X $ , $ K(X) $ denotes the upper semi - lattice of its (Hausdorff) compactifications.
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	topological	topological	ADJ	JJ	Degree=Pos	4	amod	_	_
4	space	space	NOUN	NN	Number=Sing	1	pobj	_	_
5	$ X $	$ x $	SYM	$	_	4	appos	_	_
6	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
7	$ K(X) $	$ k(x) $	SYM	$	_	8	nsubj	_	_
8	denotes	denote	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
10	upper	upper	ADJ	JJ	Degree=Pos	13	amod	_	_
11	semi	semi	ADJ	JJ	Degree=Pos	13	amod	_	_
12	-	-	NOUN	NNS	Number=Plur	13	punct	_	_
13	lattice	lattice	NOUN	NN	Number=Sing	8	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	19	poss	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	19	punct	_	SpaceAfter=No
17	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	19	nmod	_	SpaceAfter=No
18	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	19	punct	_	_
19	compactifications	compactification	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = Recent studies have asked when, for $ alpha X in K(X) $ , the restriction homomorphism $ rho : C(alpha X) to C(X) $ is an epimorphism in the category of commutative rings.
1	Recent	recent	ADJ	JJ	Degree=Pos	2	amod	_	_
2	studies	study	NOUN	NNS	Number=Plur	4	nsubj	_	_
3	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	aux	_	_
4	asked	ask	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	when	when	SCONJ	WRB	_	14	advmod	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
7	for	for	ADP	IN	_	14	prep	_	_
8	$ alpha X in K(X) $	$ alpha x in k(x) $	SYM	$	_	7	pobj	_	_
9	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	restriction	restriction	NOUN	NN	Number=Sing	12	compound	_	_
12	homomorphism	homomorphism	NOUN	NN	Number=Sing	9	nmod	_	_
13	$ rho : C(alpha X) to C(X) $	$ rho : c(alpha x) to c(x) $	SYM	$	_	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
15	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	epimorphism	epimorphism	NOUN	NN	Number=Sing	14	attr	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	category	category	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	commutative	commutative	ADJ	JJ	Degree=Pos	22	amod	_	_
22	rings	ring	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = This article continues this study by examining the sub - semilattice, $ K_{epi}(X) $ , of those compactifications where $ rho $ is an epimorphism along with two of its subsets, and its complement $ K_{nepi}(X) $ .
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	article	article	NOUN	NN	Number=Sing	3	nsubj	_	_
3	continues	continue	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	study	study	NOUN	NN	Number=Sing	3	dobj	_	_
6	by	by	ADP	IN	_	3	prep	_	_
7	examining	examine	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	pcomp	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
9	sub	sub	NOUN	NN	Number=Sing	11	compound	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	semilattice	semilattice	PROPN	NNP	Number=Sing	7	dobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	$ K_{epi}(X) $	$ k_{epi}(x) $	SYM	$	_	11	appos	_	_
14	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
15	of	of	ADP	IN	_	11	prep	_	_
16	those	those	DET	DT	Number=Plur|PronType=Dem	17	det	_	_
17	compactifications	compactification	NOUN	NNS	Number=Plur	15	pobj	_	_
18	where	where	SCONJ	WRB	_	20	advmod	_	_
19	$ rho $	$ rho $	SYM	$	_	20	nsubj	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	epimorphism	epimorphism	NOUN	NN	Number=Sing	20	attr	_	_
23	along	along	ADP	IN	_	22	prep	_	_
24	with	with	ADP	IN	_	23	prep	_	_
25	two	two	NUM	CD	NumType=Card	24	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	28	poss	_	_
28	subsets	subset	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
31	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	33	poss	_	_
32	complement	complement	NOUN	NN	Number=Sing	33	amod	_	_
33	$ K_{nepi}(X) $	$ k_{nepi}(x) $	SYM	$	_	3	conj	_	_
34	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = The role of $ K_z(X)subseteq K(X) $ of those $ alpha X $ where $ X $ is $ z $ - embedded in $ alpha X $ , is also examined.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	role	role	NOUN	NN	Number=Sing	19	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	$ K_z(X)subseteq K(X) $	$ k_z(x)subseteq k(x) $	SYM	$	_	3	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	those	those	DET	DT	Number=Plur|PronType=Dem	7	det	_	_
7	$ alpha X $	$ alpha x $	SYM	$	_	5	pobj	_	_
8	where	where	SCONJ	WRB	_	10	advmod	_	_
9	$ X $	$ x $	SYM	$	_	10	nsubj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	relcl	_	_
11	$ z $	$ z $	SYM	$	_	13	dep	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	embedded	embed	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acomp	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	$ alpha X $	$ alpha x $	SYM	$	_	14	pobj	_	_
16	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	auxpass	_	_
18	also	also	ADV	RB	_	19	advmod	_	_
19	examined	examine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 5
# text = The cases where $ X $ is a $ P $ - space and, more particularly, where $ X $ is discrete, receive special attention.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	cases	case	NOUN	NNS	Number=Plur	0	ROOT	_	_
3	where	where	SCONJ	WRB	_	5	advmod	_	_
4	$ X $	$ x $	SYM	$	_	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	relcl	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	$ P $	$ p $	SYM	$	_	9	nmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	space	space	NOUN	NN	Number=Sing	5	attr	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
12	more	more	ADV	RBR	Degree=Cmp	13	advmod	_	_
13	particularly	particularly	ADV	RB	_	5	advmod	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	where	where	SCONJ	WRB	_	17	advmod	_	_
16	$ X $	$ x $	SYM	$	_	17	nsubj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
18	discrete	discrete	ADJ	JJ	Degree=Pos	17	acomp	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
20	receive	receive	VERB	VBP	Tense=Pres|VerbForm=Fin	17	conj	_	_
21	special	special	ADJ	JJ	Degree=Pos	22	amod	_	_
22	attention	attention	NOUN	NN	Number=Sing	20	dobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 243
# sent_id = 1
# text = This paper studies numerals, natural numbers objects and, more generally, free actions, in a topos.
1	This	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	compound	_	_
3	studies	study	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	numerals	numeral	NOUN	NNS	Number=Plur	0	ROOT	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
6	natural	natural	ADJ	JJ	Degree=Pos	7	amod	_	_
7	numbers	number	NOUN	NNS	Number=Plur	8	compound	_	_
8	objects	object	NOUN	NNS	Number=Plur	4	conj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
11	more	more	ADV	RBR	Degree=Cmp	12	advmod	_	_
12	generally	generally	ADV	RB	_	15	advmod	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
14	free	free	ADJ	JJ	Degree=Pos	15	amod	_	_
15	actions	action	NOUN	NNS	Number=Plur	8	conj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	in	in	ADP	IN	_	15	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	topos	topos	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = A pre - numeral is a poset with a constant, 0, and a unary operation, $ s $ , such that: $ xleq y $ implies $ sx leq sy xleq sx $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
2	pre	pre	ADJ	JJ	Degree=Pos	4	amod	_	_
3	-	-	ADJ	JJ	Degree=Pos	4	punct	_	_
4	numeral	numeral	ADJ	JJ	Degree=Pos	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	poset	poset	NOUN	NN	Number=Sing	5	attr	_	_
8	with	with	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
10	constant	constant	ADJ	JJ	Degree=Pos	12	amod	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
12	0	0	NUM	CD	NumType=Card	8	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	unary	unary	ADJ	JJ	Degree=Pos	17	amod	_	_
17	operation	operation	NOUN	NN	Number=Sing	5	conj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	$ s $	$ s $	SYM	$	_	17	appos	_	_
20	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
21	such	such	ADJ	JJ	Degree=Pos	22	amod	_	_
22	that	that	SCONJ	IN	_	25	mark	_	SpaceAfter=No
23	:	:	PUNCT	:	_	25	punct	_	_
24	$ xleq y $	$ xleq y $	SYM	$	_	25	nsubj	_	_
25	implies	imply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
26	$ sx leq sy xleq sx $	$ sx leq sy xleq sx $	SYM	$	_	25	advmod	_	_
27	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = A numeral is a minimal pre - numeral.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	numeral	numeral	ADJ	JJ	Degree=Pos	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
5	minimal	minimal	ADJ	JJ	Degree=Pos	8	amod	_	_
6	pre	pre	ADJ	JJ	Degree=Pos	8	amod	_	_
7	-	-	ADJ	JJ	Degree=Pos	8	punct	_	_
8	numeral	numeral	ADJ	JJ	Degree=Pos	3	acomp	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 244
# sent_id = 1
# text = A representation theory for (strict) categorical groups is constructed.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	representation	representation	NOUN	NN	Number=Sing	3	compound	_	_
3	theory	theory	NOUN	NN	Number=Sing	11	nsubjpass	_	_
4	for	for	ADP	IN	_	3	prep	_	_
5	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	9	punct	_	SpaceAfter=No
6	strict	strict	ADJ	JJ	Degree=Pos	9	amod	_	SpaceAfter=No
7	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	9	punct	_	_
8	categorical	categorical	ADJ	JJ	Degree=Pos	9	amod	_	_
9	groups	group	NOUN	NNS	Number=Plur	4	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 2
# text = Each categorical group determines a monoidal bicategory of representations.
1	Each	each	DET	DT	_	3	det	_	_
2	categorical	categorical	ADJ	JJ	Degree=Pos	3	amod	_	_
3	group	group	NOUN	NN	Number=Sing	4	nsubj	_	_
4	determines	determine	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	monoidal	monoidal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	bicategory	bicategory	NOUN	NN	Number=Sing	4	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	representations	representation	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = Typically, these bicategories contain representations which are indecomposable but not irreducible.
1	Typically	typically	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	these	these	DET	DT	Number=Plur|PronType=Dem	4	det	_	_
4	bicategories	bicategorie	NOUN	NNS	Number=Plur	5	nsubj	_	_
5	contain	contain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	representations	representation	NOUN	NNS	Number=Plur	5	dobj	_	_
7	which	which	PRON	WDT	_	8	nsubj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	relcl	_	_
9	indecomposable	indecomposable	ADJ	JJ	Degree=Pos	8	acomp	_	_
10	but	but	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	not	not	PART	RB	Polarity=Neg	12	neg	_	_
12	irreducible	irreducible	ADJ	JJ	Degree=Pos	9	conj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = A simple example is computed in explicit detail.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	simple	simple	ADJ	JJ	Degree=Pos	3	amod	_	_
3	example	example	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	computed	compute	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	explicit	explicit	ADJ	JJ	Degree=Pos	8	amod	_	_
8	detail	detail	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 245
# sent_id = 1
# text = Two constructions of paths in double categories are studied, providing algebraic versions of the homotopy groupoid of a space.
1	Two	two	NUM	CD	NumType=Card	2	nummod	_	_
2	constructions	construction	NOUN	NNS	Number=Plur	9	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	paths	path	NOUN	NNS	Number=Plur	3	pobj	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	double	double	ADJ	JJ	Degree=Pos	7	amod	_	_
7	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	studied	study	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	providing	provide	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	advcl	_	_
12	algebraic	algebraic	ADJ	JJ	Degree=Pos	13	amod	_	_
13	versions	version	NOUN	NNS	Number=Plur	11	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	homotopy	homotopy	NOUN	NN	Number=Sing	17	compound	_	_
17	groupoid	groupoid	NOUN	NN	Number=Sing	14	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	space	space	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 2
# text = Universal properties of these constructions are presented.
1	Universal	universal	ADJ	JJ	Degree=Pos	2	amod	_	_
2	properties	property	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	these	these	DET	DT	Number=Plur|PronType=Dem	5	det	_	_
5	constructions	construction	NOUN	NNS	Number=Plur	3	pobj	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = The first is seen as the codomain of the universal oplax morphism of double categories and the second, which is a quotient of the first, gives the universal normal oplax morphism.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	first	first	ADJ	JJ	Degree=Pos	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	ccomp	_	_
5	as	as	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	codomain	codomain	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
10	universal	universal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	oplax	oplax	PROPN	NNP	Number=Sing	12	compound	_	_
12	morphism	morphism	NOUN	NN	Number=Sing	8	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	double	double	ADJ	JJ	Degree=Pos	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	second	second	NOUN	NN	Number=Sing	7	conj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	which	which	PRON	WDT	_	21	nsubj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	relcl	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
23	quotient	quotient	NOUN	NN	Number=Sing	21	attr	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	first	first	ADJ	JJ	Degree=Pos	24	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
28	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
30	universal	universal	ADJ	JJ	Degree=Pos	33	amod	_	_
31	normal	normal	ADJ	JJ	Degree=Pos	33	amod	_	_
32	oplax	oplax	NOUN	NN	Number=Sing	33	compound	_	_
33	morphism	morphism	NOUN	NN	Number=Sing	28	dobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	28	punct	_	SpaceAfter=No

# sent_id = 4
# text = Normality forces an equivalence relation on cells, a special case of which was seen before in the free adjoint construction.
1	Normality	normality	ADJ	JJ	Degree=Pos	2	amod	_	_
2	forces	force	NOUN	NNS	Number=Plur	15	dep	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	equivalence	equivalence	NOUN	NN	Number=Sing	5	compound	_	_
5	relation	relation	NOUN	NN	Number=Sing	2	appos	_	_
6	on	on	ADP	IN	_	5	prep	_	_
7	cells	cell	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	special	special	ADJ	JJ	Degree=Pos	11	amod	_	_
11	case	case	NOUN	NN	Number=Sing	15	nsubjpass	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	which	which	PRON	WDT	_	12	pobj	_	_
14	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	15	auxpass	_	_
15	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
16	before	before	ADV	RB	_	15	advmod	_	_
17	in	in	ADP	IN	_	15	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
19	free	free	ADJ	JJ	Degree=Pos	20	amod	_	_
20	adjoint	adjoint	NOUN	NN	Number=Sing	21	compound	_	_
21	construction	construction	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 5
# text = These constructions are the object part of 2 - comonads which are shown to be oplax idempotent.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	constructions	construction	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	object	object	NOUN	NN	Number=Sing	6	compound	_	_
6	part	part	NOUN	NN	Number=Sing	3	attr	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	2	2	NUM	CD	NumType=Card	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	comonads	comonad	NOUN	NNS	Number=Plur	7	pobj	_	_
11	which	which	PRON	WDT	_	13	nsubjpass	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	relcl	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	be	be	AUX	VB	VerbForm=Inf	13	xcomp	_	_
16	oplax	oplax	PROPN	NNP	Number=Sing	15	attr	_	_
17	idempotent	idempotent	ADJ	JJ	Degree=Pos	15	acomp	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = The coalgebras for these comonads turn out to be Leinster's $ fc $ - multicategories, with representable identities in the second case.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	coalgebras	coalgebra	NOUN	NNS	Number=Plur	6	nsubj	_	_
3	for	for	ADP	IN	_	2	prep	_	_
4	these	these	DET	DT	Number=Plur|PronType=Dem	5	det	_	_
5	comonads	comonad	NOUN	NNS	Number=Plur	3	pobj	_	_
6	turn	turn	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	out	out	ADP	RP	_	6	prt	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	be	be	AUX	VB	VerbForm=Inf	6	xcomp	_	_
10	Leinster	Leinster	PROPN	NNP	Number=Sing	14	poss	_	SpaceAfter=No
11	's	's	PART	POS	_	10	case	_	_
12	$ fc $	$ fc $	SYM	$	_	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	multicategories	multicategorie	NOUN	NNS	Number=Plur	9	attr	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
16	with	with	ADP	IN	_	6	prep	_	_
17	representable	representable	ADJ	JJ	Degree=Pos	18	amod	_	_
18	identities	identity	NOUN	NNS	Number=Plur	16	pobj	_	_
19	in	in	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	second	second	ADJ	JJ	Degree=Pos	22	amod	_	_
22	case	case	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 246
# sent_id = 1
# text = A flow on a compact Hausdorff space $ X $ is given by a map $ t : X - - > X $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	flow	flow	NOUN	NN	Number=Sing	10	nsubjpass	_	_
3	on	on	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	compact	compact	ADJ	JJ	Degree=Pos	7	amod	_	_
6	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	7	compound	_	_
7	space	space	NOUN	NN	Number=Sing	3	pobj	_	_
8	$ X $	$ x $	SYM	$	_	2	appos	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	by	by	ADP	IN	_	10	agent	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	map	map	NOUN	NN	Number=Sing	11	pobj	_	_
14	$ t : X - - > X $	$ t : x - - > x $	SYM	$	_	13	appos	_	_
15	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = The general goal of this paper is to find the "cyclic parts" of such a flow.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	general	general	ADJ	JJ	Degree=Pos	3	amod	_	_
3	goal	goal	NOUN	NN	Number=Sing	7	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	paper	paper	NOUN	NN	Number=Sing	4	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	find	find	VERB	VB	VerbForm=Inf	7	xcomp	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
11	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	13	punct	_	SpaceAfter=No
12	cyclic	cyclic	ADJ	JJ	Degree=Pos	13	amod	_	_
13	parts	part	NOUN	NNS	Number=Plur	9	dobj	_	SpaceAfter=No
14	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	13	punct	_	_
15	of	of	ADP	IN	_	13	prep	_	_
16	such	such	DET	PDT	_	18	predet	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	flow	flow	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = To do this, we approximate $ (X, t) $ by a flow on a Stone space (that is, a totally disconnected, compact Hausdorff space).
1	To	to	PART	TO	_	2	aux	_	_
2	do	do	VERB	VB	VerbForm=Inf	6	advcl	_	_
3	this	this	PRON	DT	Number=Sing|PronType=Dem	2	dobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	approximate	approximate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	$ (X, t) $	$ (x, t) $	SYM	$	_	6	dobj	_	_
8	by	by	ADP	IN	_	7	agent	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	flow	flow	NOUN	NN	Number=Sing	8	pobj	_	_
11	on	on	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	Stone	Stone	PROPN	NNP	Number=Sing	14	compound	_	_
14	space	space	NOUN	NN	Number=Sing	11	pobj	_	_
15	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
16	that	that	ADV	RB	_	17	advmod	_	_
17	is	is	ADV	RB	_	25	advmod	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
20	totally	totally	ADV	RB	_	21	advmod	_	_
21	disconnected	disconnected	ADJ	JJ	Degree=Pos	25	amod	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
23	compact	compact	ADJ	JJ	Degree=Pos	25	amod	_	_
24	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	25	compound	_	_
25	space	space	NOUN	NN	Number=Sing	14	appos	_	SpaceAfter=No
26	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	6	punct	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = Such a flow can be examined by analyzing the resulting flow on the Boolean algebra of clopen subsets, using the spectrum defined in our previous paper, The cyclic spectrum of a Boolean flow.
1	Such	such	DET	PDT	_	3	predet	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	flow	flow	NOUN	NN	Number=Sing	6	nsubjpass	_	_
4	can	can	AUX	MD	VerbForm=Fin	6	aux	_	_
5	be	be	AUX	VB	VerbForm=Inf	6	auxpass	_	_
6	examined	examine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	ccomp	_	_
7	by	by	ADP	IN	_	6	prep	_	_
8	analyzing	analyze	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	pcomp	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	amod	_	_
11	flow	flow	NOUN	NN	Number=Sing	8	dobj	_	_
12	on	on	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	Boolean	boolean	ADJ	JJ	Degree=Pos	15	amod	_	_
15	algebra	algebra	NOUN	NN	Number=Sing	12	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	clopen	clopen	ADJ	JJ	Degree=Pos	18	amod	_	_
18	subsets	subset	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
20	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	conj	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	spectrum	spectrum	NOUN	NN	Number=Sing	20	dobj	_	_
23	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	acl	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	27	poss	_	_
26	previous	previous	ADJ	JJ	Degree=Pos	27	amod	_	_
27	paper	paper	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
29	The	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
30	cyclic	cyclic	ADJ	JJ	Degree=Pos	31	amod	_	_
31	spectrum	spectrum	NOUN	NN	Number=Sing	0	ROOT	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
34	Boolean	boolean	ADJ	JJ	Degree=Pos	35	amod	_	_
35	flow	flow	NOUN	NN	Number=Sing	32	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	31	punct	_	SpaceAfter=No

# sent_id = 5
# text = In this paper, we describe the cyclic spectrum in terms that do not rely on topos theory.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	cyclic	cyclic	NOUN	NN	Number=Sing	9	compound	_	_
9	spectrum	spectrum	NOUN	NN	Number=Sing	6	dobj	_	_
10	in	in	ADP	IN	_	6	prep	_	_
11	terms	term	NOUN	NNS	Number=Plur	10	pobj	_	_
12	that	that	PRON	WDT	PronType=Rel	15	nsubj	_	_
13	do	do	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	aux	_	_
14	not	not	PART	RB	Polarity=Neg	15	neg	_	_
15	rely	rely	VERB	VB	VerbForm=Inf	11	relcl	_	_
16	on	on	ADP	IN	_	15	prep	_	_
17	topos	topos	NOUN	NN	Number=Sing	18	compound	_	_
18	theory	theory	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 6
# text = We then compute the cyclic spectrum of any finitely generated Boolean flow.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	compute	compute	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	cyclic	cyclic	ADJ	JJ	Degree=Pos	6	compound	_	_
6	spectrum	spectrum	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	any	any	DET	DT	_	12	det	_	_
9	finitely	finitely	ADV	RB	_	10	advmod	_	_
10	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
11	Boolean	boolean	ADJ	JJ	Degree=Pos	12	amod	_	_
12	flow	flow	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = We define when a sheaf of Boolean flows can be regarded as cyclic and find necessary conditions for representing a Boolean flow using the global sections of such a sheaf.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	when	when	SCONJ	WRB	_	11	advmod	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	sheaf	sheaf	NOUN	NN	Number=Sing	11	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Boolean	boolean	ADJ	JJ	Degree=Pos	8	amod	_	_
8	flows	flow	NOUN	NNS	Number=Plur	6	pobj	_	_
9	can	can	AUX	MD	VerbForm=Fin	11	aux	_	_
10	be	be	AUX	VB	VerbForm=Inf	11	auxpass	_	_
11	regarded	regard	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	advcl	_	_
12	as	as	ADP	IN	_	11	prep	_	_
13	cyclic	cyclic	ADJ	JJ	Degree=Pos	12	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
15	find	find	VERB	VB	VerbForm=Inf	11	conj	_	_
16	necessary	necessary	ADJ	JJ	Degree=Pos	17	amod	_	_
17	conditions	condition	NOUN	NNS	Number=Plur	15	dobj	_	_
18	for	for	ADP	IN	_	17	prep	_	_
19	representing	represent	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	18	pcomp	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	Boolean	boolean	ADJ	JJ	Degree=Pos	22	amod	_	_
22	flow	flow	NOUN	NN	Number=Sing	19	dobj	_	_
23	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	acl	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	global	global	ADJ	JJ	Degree=Pos	26	amod	_	_
26	sections	section	NOUN	NNS	Number=Plur	23	dobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	such	such	DET	PDT	_	30	predet	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
30	sheaf	sheaf	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 8
# text = In the final section, we define and explore a related spectrum based on minimal subflows of Stone spaces.
1	In	in	ADP	IN	_	7	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	final	final	ADJ	JJ	Degree=Pos	4	amod	_	_
4	section	section	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	explore	explore	VERB	VB	VerbForm=Inf	7	conj	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	related	related	ADJ	JJ	Degree=Pos	12	amod	_	_
12	spectrum	spectrum	NOUN	NN	Number=Sing	9	dobj	_	_
13	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
14	on	on	ADP	IN	_	13	prep	_	_
15	minimal	minimal	ADJ	JJ	Degree=Pos	16	amod	_	_
16	subflows	subflow	NOUN	NNS	Number=Plur	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	Stone	Stone	PROPN	NNP	Number=Sing	19	compound	_	_
19	spaces	space	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 247
# sent_id = 1
# text = The correlators of two - dimensional rational conformal field theories that are obtained in the TFT construction of Fuchs, Runkel and Schweigert are shown to be invariant under the action of the relative modular group and to obey bulk and boundary factorisation constraints.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	correlators	correlator	NOUN	NNS	Number=Plur	25	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	two	two	NUM	CD	NumType=Card	6	advmod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	dimensional	dimensional	ADJ	JJ	Degree=Pos	10	amod	_	_
7	rational	rational	ADJ	JJ	Degree=Pos	10	amod	_	_
8	conformal	conformal	ADJ	JJ	Degree=Pos	9	amod	_	_
9	field	field	NOUN	NN	Number=Sing	10	compound	_	_
10	theories	theory	NOUN	NNS	Number=Plur	3	pobj	_	_
11	that	that	PRON	WDT	PronType=Rel	13	nsubjpass	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	relcl	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	TFT	TFT	PROPN	NNP	Number=Sing	17	compound	_	_
17	construction	construction	NOUN	NN	Number=Sing	14	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	Fuchs	Fuchs	PROPN	NNP	Number=Sing	18	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	Runkel	Runkel	PROPN	NNP	Number=Sing	19	conj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	Schweigert	Schweigert	PROPN	NNP	Number=Sing	21	conj	_	_
24	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	25	auxpass	_	_
25	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
26	to	to	PART	TO	_	27	aux	_	_
27	be	be	AUX	VB	VerbForm=Inf	25	xcomp	_	_
28	invariant	invariant	ADJ	JJ	Degree=Pos	27	acomp	_	_
29	under	under	ADP	IN	_	27	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	action	action	NOUN	NN	Number=Sing	29	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
34	relative	relative	ADJ	JJ	Degree=Pos	36	amod	_	_
35	modular	modular	ADJ	JJ	Degree=Pos	36	amod	_	_
36	group	group	NOUN	NN	Number=Sing	32	pobj	_	_
37	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
38	to	to	PART	TO	_	39	aux	_	_
39	obey	obey	VERB	VB	VerbForm=Inf	27	conj	_	_
40	bulk	bulk	ADJ	JJ	Degree=Pos	44	amod	_	_
41	and	and	CCONJ	CC	ConjType=Cmp	40	cc	_	_
42	boundary	boundary	ADJ	JJ	Degree=Pos	40	conj	_	_
43	factorisation	factorisation	NOUN	NN	Number=Sing	40	conj	_	_
44	constraints	constraint	NOUN	NNS	Number=Plur	39	dobj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	25	punct	_	SpaceAfter=No

# sent_id = 2
# text = We present results both for conformal field theories defined on oriented surfaces and for theories defined on unoriented surfaces.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	results	result	NOUN	NNS	Number=Plur	2	dobj	_	_
4	both	both	CCONJ	CC	ConjType=Cmp	5	preconj	_	_
5	for	for	ADP	IN	_	3	prep	_	_
6	conformal	conformal	ADJ	JJ	Degree=Pos	8	amod	_	_
7	field	field	NOUN	NN	Number=Sing	8	compound	_	_
8	theories	theory	NOUN	NNS	Number=Plur	5	pobj	_	_
9	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	on	on	ADP	IN	_	9	prep	_	_
11	oriented	orient	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
12	surfaces	surface	NOUN	NNS	Number=Plur	10	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
14	for	for	ADP	IN	_	9	conj	_	_
15	theories	theory	NOUN	NNS	Number=Plur	14	pobj	_	_
16	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
17	on	on	ADP	IN	_	16	prep	_	_
18	unoriented	unoriented	ADJ	JJ	Degree=Pos	19	amod	_	_
19	surfaces	surface	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = In the latter case, in particular the so - called cross cap constraint is included.
1	In	in	ADP	IN	_	16	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	latter	latter	ADJ	JJ	Degree=Pos	4	amod	_	_
4	case	case	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
6	in	in	ADP	IN	_	16	prep	_	_
7	particular	particular	ADJ	JJ	Degree=Pos	6	amod	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
9	so	so	ADV	RB	_	11	advmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
12	cross	cross	PROPN	NNP	Number=Sing	13	compound	_	_
13	cap	cap	NOUN	NN	Number=Sing	14	compound	_	_
14	constraint	constraint	NOUN	NN	Number=Sing	16	nsubjpass	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	auxpass	_	_
16	included	include	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# doc_id = 248
# sent_id = 1
# text = The construction of a free restriction category can be broken into two steps: the construction of a free stable semilattice fibration followed by the construction of a free restriction category for this fibration.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	construction	construction	NOUN	NN	Number=Sing	10	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	free	free	ADJ	JJ	Degree=Pos	6	amod	_	_
6	restriction	restriction	NOUN	NN	Number=Sing	7	compound	_	_
7	category	category	NOUN	NN	Number=Sing	3	pobj	_	_
8	can	can	AUX	MD	VerbForm=Fin	10	aux	_	_
9	be	be	AUX	VB	VerbForm=Inf	10	auxpass	_	_
10	broken	break	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	into	into	ADP	IN	_	10	prep	_	_
12	two	two	NUM	CD	NumType=Card	13	nummod	_	_
13	steps	step	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
14	:	:	PUNCT	:	_	13	punct	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	construction	construction	NOUN	NN	Number=Sing	13	appos	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
19	free	free	ADJ	JJ	Degree=Pos	22	amod	_	_
20	stable	stable	ADJ	JJ	Degree=Pos	22	amod	_	_
21	semilattice	semilattice	NOUN	NN	Number=Sing	22	compound	_	_
22	fibration	fibration	NOUN	NN	Number=Sing	17	pobj	_	_
23	followed	follow	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	acl	_	_
24	by	by	ADP	IN	_	23	agent	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	construction	construction	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
29	free	free	ADJ	JJ	Degree=Pos	30	amod	_	_
30	restriction	restriction	NOUN	NN	Number=Sing	31	compound	_	_
31	category	category	NOUN	NN	Number=Sing	27	pobj	_	_
32	for	for	ADP	IN	_	31	prep	_	_
33	this	this	DET	DT	Number=Sing|PronType=Dem	34	det	_	_
34	fibration	fibration	NOUN	NN	Number=Sing	32	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = Restriction categories produced from such fibrations are `unitary', in a sense which generalizes that from the theory of inverse semigroups.
1	Restriction	restriction	NOUN	NN	Number=Sing	2	compound	_	_
2	categories	category	NOUN	NNS	Number=Plur	7	nsubj	_	_
3	produced	produce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acl	_	_
4	from	from	ADP	IN	_	3	prep	_	_
5	such	such	ADJ	JJ	Degree=Pos	6	amod	_	_
6	fibrations	fibration	NOUN	NNS	Number=Plur	4	pobj	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	7	punct	_	SpaceAfter=No
9	unitary	unitary	ADJ	JJ	Degree=Pos	7	acomp	_	SpaceAfter=No
10	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	7	punct	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
12	in	in	ADP	IN	_	7	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	sense	sense	NOUN	NN	Number=Sing	12	pobj	_	_
15	which	which	PRON	WDT	_	16	nsubj	_	_
16	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
17	that	that	SCONJ	IN	_	16	dobj	_	_
18	from	from	ADP	IN	_	16	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	theory	theory	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	inverse	inverse	ADJ	JJ	Degree=Pos	23	amod	_	_
23	semigroups	semigroup	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = Characterization theorems for unitary restriction categories are derived.
1	Characterization	characterization	NOUN	NN	Number=Sing	2	compound	_	_
2	theorems	theorem	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
3	for	for	ADP	IN	_	2	prep	_	_
4	unitary	unitary	ADJ	JJ	Degree=Pos	6	amod	_	_
5	restriction	restriction	NOUN	NN	Number=Sing	6	compound	_	_
6	categories	category	NOUN	NNS	Number=Plur	3	pobj	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	derived	derive	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 4
# text = The paper ends with an explicit description of the free restriction category on a directed graph.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	ends	end	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	with	with	ADP	IN	_	3	prep	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	explicit	explicit	ADJ	JJ	Degree=Pos	7	amod	_	_
7	description	description	NOUN	NN	Number=Sing	4	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
10	free	free	ADJ	JJ	Degree=Pos	11	amod	_	_
11	restriction	restriction	NOUN	NN	Number=Sing	12	compound	_	_
12	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
13	on	on	ADP	IN	_	7	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
16	graph	graph	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 249
# sent_id = 1
# text = A quantaloid is a sup - lattice - enriched category; our subject is that of categories, functors and distributors enriched in a base quantaloid $ mathcal{Q} $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	quantaloid	quantaloid	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	ccomp	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
5	sup	sup	ADJ	JJ	Degree=Pos	7	amod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	lattice	lattice	NOUN	NN	Number=Sing	9	npadvmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	3	attr	_	SpaceAfter=No
11	;	;	PUNCT	:	_	14	punct	_	_
12	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	13	poss	_	_
13	subject	subject	NOUN	NN	Number=Sing	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	that	that	PRON	DT	Number=Sing|PronType=Dem	14	nsubj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	functors	functor	NOUN	NNS	Number=Plur	17	conj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	distributors	distributor	NOUN	NNS	Number=Plur	19	conj	_	_
22	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
23	in	in	ADP	IN	_	22	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
25	base	base	NOUN	NN	Number=Sing	26	compound	_	_
26	quantaloid	quantaloid	NOUN	NN	Number=Sing	23	pobj	_	_
27	$ mathcal{Q} $	$ mathcal{q} $	SYM	$	_	17	appos	_	_
28	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show how cocomplete $ mathcal{Q} $ - categories are precisely those which are tensored and conically cocomplete, or alternatively, those which are tensored, cotensored and `order - cocomplete'.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	how	how	SCONJ	WRB	_	4	advmod	_	_
4	cocomplete	cocomplete	ADJ	JJ	Degree=Pos	7	amod	_	_
5	$ mathcal{Q} $	$ mathcal{q} $	SYM	$	_	7	compound	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	categories	category	NOUN	NNS	Number=Plur	8	nsubj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
9	precisely	precisely	ADV	RB	_	10	advmod	_	_
10	those	those	PRON	DT	Number=Plur|PronType=Dem	8	attr	_	_
11	which	which	PRON	WDT	_	12	nsubj	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	10	relcl	_	_
13	tensored	tensored	ADJ	JJ	Degree=Pos	12	acomp	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	conically	conically	ADV	RB	_	16	advmod	_	_
16	cocomplete	cocomplete	ADJ	JJ	Degree=Pos	13	conj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
18	or	or	CCONJ	CC	ConjType=Cmp	13	cc	_	_
19	alternatively	alternatively	ADV	RB	_	13	conj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
21	those	those	PRON	DT	Number=Plur|PronType=Dem	10	conj	_	_
22	which	which	PRON	WDT	_	23	nsubj	_	_
23	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	21	relcl	_	_
24	tensored	tensored	ADJ	JJ	Degree=Pos	23	acomp	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	cotensored	cotensore	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	conj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	SpaceAfter=No
29	order	order	NOUN	NN	Number=Sing	31	npadvmod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	cocomplete	cocomplete	NOUN	NN	Number=Sing	26	conj	_	SpaceAfter=No
32	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	21	punct	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = In fact, tensors and cotensors in a $ mathcal{Q} $ - category determine, and are determined by, certain adjunctions in the category of $ mathcal{Q} $ - categories; some of these adjunctions can be reduced to adjuctions in the category of ordered sets.
1	In	in	ADP	IN	_	16	prep	_	_
2	fact	fact	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
4	tensors	tensor	NOUN	NNS	Number=Plur	16	nsubjpass	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	cotensors	cotensor	NOUN	NNS	Number=Plur	4	conj	_	_
7	in	in	ADP	IN	_	4	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
9	$ mathcal{Q} $	$ mathcal{q} $	SYM	$	_	11	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	category	category	NOUN	NN	Number=Sing	12	compound	_	_
12	determine	determine	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	16	auxpass	_	_
16	determined	determine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	35	advcl	_	_
17	by	by	ADP	IN	_	16	agent	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
19	certain	certain	ADJ	JJ	Degree=Pos	20	amod	_	_
20	adjunctions	adjunction	NOUN	NNS	Number=Plur	35	nsubjpass	_	_
21	in	in	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	category	category	NOUN	NN	Number=Sing	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	$ mathcal{Q} $	$ mathcal{q} $	SYM	$	_	27	nmod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	categories	category	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
28	;	;	PUNCT	:	_	35	punct	_	_
29	some	some	PRON	DT	_	35	nsubjpass	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	these	these	DET	DT	Number=Plur|PronType=Dem	32	det	_	_
32	adjunctions	adjunction	NOUN	NNS	Number=Plur	30	pobj	_	_
33	can	can	AUX	MD	VerbForm=Fin	35	aux	_	_
34	be	be	AUX	VB	VerbForm=Inf	35	auxpass	_	_
35	reduced	reduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
36	to	to	ADP	IN	_	35	prep	_	_
37	adjuctions	adjuction	NOUN	NNS	Number=Plur	36	pobj	_	_
38	in	in	ADP	IN	_	37	prep	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
40	category	category	NOUN	NN	Number=Sing	38	pobj	_	_
41	of	of	ADP	IN	_	40	prep	_	_
42	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	43	amod	_	_
43	sets	set	NOUN	NNS	Number=Plur	41	pobj	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	35	punct	_	SpaceAfter=No

# sent_id = 4
# text = Bearing this in mind, we explain how tensored $ mathcal{Q} $ - categories are equivalent to order - valued closed pseudofunctors on $ mathcal{Q}^{op} $ ; this result is then finetuned to obtain in particular that cocomplete $ mathcal{Q} $ - categories are equivalent to sup - lattice - valued homomorphisms on $ mathcal{Q}^{op} $ (a.k.a. $ mathcal{Q} $ - modules).
1	Bearing	bear	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	advcl	_	_
2	this	this	PRON	DT	Number=Sing|PronType=Dem	1	dobj	_	_
3	in	in	ADP	IN	_	1	prep	_	_
4	mind	mind	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	explain	explain	VERB	VBP	Tense=Pres|VerbForm=Fin	28	ccomp	_	_
8	how	how	SCONJ	WRB	_	9	advmod	_	_
9	tensored	tensore	VERB	VBD	Tense=Past|VerbForm=Fin	13	acomp	_	_
10	$ mathcal{Q} $	$ mathcal{q} $	SYM	$	_	12	compound	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	categories	category	NOUN	NNS	Number=Plur	13	nsubj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	ccomp	_	_
14	equivalent	equivalent	ADJ	JJ	Degree=Pos	13	acomp	_	_
15	to	to	PART	TO	_	18	aux	_	_
16	order	order	NOUN	NN	Number=Sing	18	npadvmod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	xcomp	_	_
19	closed	closed	ADJ	JJ	Degree=Pos	20	amod	_	_
20	pseudofunctors	pseudofunctor	NOUN	NNS	Number=Plur	18	dobj	_	_
21	on	on	ADP	IN	_	20	prep	_	_
22	$ mathcal{Q}^{op} $	$ mathcal{q}^{op} $	SYM	$	_	21	pobj	_	_
23	;	;	PUNCT	:	_	28	punct	_	_
24	this	this	DET	DT	Number=Sing|PronType=Dem	25	det	_	_
25	result	result	NOUN	NN	Number=Sing	28	nsubjpass	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	28	auxpass	_	_
27	then	then	ADV	RB	PronType=Dem	28	advmod	_	_
28	finetuned	finetune	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
29	to	to	PART	TO	_	30	aux	_	_
30	obtain	obtain	VERB	VB	VerbForm=Inf	28	xcomp	_	_
31	in	in	ADP	IN	_	30	prep	_	_
32	particular	particular	ADJ	JJ	Degree=Pos	31	amod	_	_
33	that	that	SCONJ	IN	_	38	mark	_	_
34	cocomplete	cocomplete	ADJ	JJ	Degree=Pos	37	amod	_	_
35	$ mathcal{Q} $	$ mathcal{q} $	SYM	$	_	37	compound	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	categories	category	NOUN	NNS	Number=Plur	38	nsubj	_	_
38	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	30	ccomp	_	_
39	equivalent	equivalent	ADJ	JJ	Degree=Pos	38	acomp	_	_
40	to	to	ADP	IN	_	39	prep	_	_
41	sup	sup	ADJ	JJ	Degree=Pos	43	amod	_	_
42	-	-	PUNCT	HYPH	PunctType=Dash	43	punct	_	_
43	lattice	lattice	NOUN	NN	Number=Sing	45	npadvmod	_	_
44	-	-	PUNCT	HYPH	PunctType=Dash	45	punct	_	_
45	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	46	amod	_	_
46	homomorphisms	homomorphism	NOUN	NNS	Number=Plur	40	pobj	_	_
47	on	on	ADP	IN	_	46	prep	_	_
48	$ mathcal{Q}^{op} $	$ mathcal{q}^{op} $	SYM	$	_	47	pobj	_	_
49	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	54	punct	_	SpaceAfter=No
50	a.k.a	a.k.a	ADJ	JJ	Degree=Pos	54	amod	_	SpaceAfter=No
51	.	.	PUNCT	.	PunctType=Peri	54	punct	_	_
52	$ mathcal{Q} $	$ mathcal{q} $	SYM	$	_	54	compound	_	_
53	-	-	PUNCT	HYPH	PunctType=Dash	54	punct	_	_
54	modules	module	NOUN	NNS	Number=Plur	48	appos	_	SpaceAfter=No
55	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	48	punct	_	SpaceAfter=No
56	.	.	PUNCT	.	PunctType=Peri	28	punct	_	SpaceAfter=No

# doc_id = 250
# sent_id = 1
# text = We say that a class $ mathbb{D} $ of categories is the Bourn localization of a class $ mathbb{C} $ of categories, and we write $ mathbb{D} = mathrm{Loc}mathbb{C} $ , if $ mathbb{D} $ is the class of all (finitely complete) categories $ mathcal{D} $ such that for each object $ A $ in $ mathcal{D} $ , $ mathrm{Pt}(mathcal{D}downarrow A) in mathbb{C} $ , where $ mathrm{Pt}(mathcal{D}downarrow A) $ denotes the category of all pointed objects in the comma - category $ (mathcal{D}downarrow A) $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	say	say	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	9	mark	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	class	class	NOUN	NN	Number=Sing	6	nmod	_	_
6	$ mathbb{D} $	$ mathbb{d} $	SYM	$	_	9	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	Bourn	Bourn	PROPN	NNP	Number=Sing	12	compound	_	_
12	localization	localization	NOUN	NN	Number=Sing	9	attr	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	class	class	NOUN	NN	Number=Sing	16	compound	_	_
16	$ mathbb{C} $	$ mathbb{c} $	SYM	$	_	13	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
21	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	22	nsubj	_	_
22	write	write	VERB	VBP	Tense=Pres|VerbForm=Fin	9	conj	_	_
23	$ mathbb{D} = mathrm{Loc}mathbb{C} $	$ mathbb{d} = mathrm{loc}mathbb{c} $	SYM	$	_	22	dobj	_	_
24	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
25	if	if	SCONJ	IN	_	27	mark	_	_
26	$ mathbb{D} $	$ mathbb{d} $	SYM	$	_	27	nsubj	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	advcl	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	class	class	NOUN	NN	Number=Sing	27	attr	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	all	all	DET	DT	_	36	det	_	_
32	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	36	punct	_	SpaceAfter=No
33	finitely	finitely	ADV	RB	_	34	advmod	_	_
34	complete	complete	ADJ	JJ	Degree=Pos	36	amod	_	SpaceAfter=No
35	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	36	punct	_	_
36	categories	category	NOUN	NNS	Number=Plur	30	pobj	_	_
37	$ mathcal{D} $	$ mathcal{d} $	SYM	$	_	39	predet	_	_
38	such	such	ADJ	JJ	Degree=Pos	39	amod	_	_
39	that	that	SCONJ	IN	_	47	nsubj	_	_
40	for	for	ADP	IN	_	47	prep	_	_
41	each	each	DET	DT	_	42	det	_	_
42	object	object	NOUN	NN	Number=Sing	40	pobj	_	_
43	$ A $	$ a $	SYM	$	_	47	nmod	_	_
44	in	in	ADP	IN	_	43	prep	_	_
45	$ mathcal{D} $	$ mathcal{d} $	SYM	$	_	44	pobj	_	_
46	,	,	PUNCT	,	PunctType=Comm	44	punct	_	_
47	$ mathrm{Pt}(mathcal{D}downarrow A) in mathbb{C} $	$ mathrm{pt}(mathcal{d}downarrow a) in mathbb{c} $	SYM	$	_	27	dep	_	_
48	,	,	PUNCT	,	PunctType=Comm	47	punct	_	_
49	where	where	SCONJ	WRB	_	51	advmod	_	_
50	$ mathrm{Pt}(mathcal{D}downarrow A) $	$ mathrm{pt}(mathcal{d}downarrow a) $	SYM	$	_	51	nsubj	_	_
51	denotes	denote	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	47	relcl	_	_
52	the	the	DET	DT	Definite=Def|PronType=Art	53	det	_	_
53	category	category	NOUN	NN	Number=Sing	51	dobj	_	_
54	of	of	ADP	IN	_	53	prep	_	_
55	all	all	DET	DT	_	57	det	_	_
56	pointed	point	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	57	amod	_	_
57	objects	object	NOUN	NNS	Number=Plur	54	pobj	_	_
58	in	in	ADP	IN	_	51	prep	_	_
59	the	the	DET	DT	Definite=Def|PronType=Art	63	det	_	_
60	comma	comma	NOUN	NN	Number=Sing	62	compound	_	_
61	-	-	PUNCT	HYPH	PunctType=Dash	62	punct	_	_
62	category	category	NOUN	NN	Number=Sing	63	compound	_	_
63	$ (mathcal{D}downarrow A) $	$ (mathcal{d}downarrow a) $	NUM	CD	NumType=Card	58	pobj	_	_
64	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = As Bourn showed, if we take $ mathbb{D} $ to be the class of Maltsev categories in the sense of Carboni, Lambek, and Pedicchio, and $ mathbb{C} $ to be the class of unital categories in the sense of Bourn, which generalize pointed Jónsson - Tarski varieties, then $ mathbb{D} = mathrm{Loc}(mathbb{C}) $ .
1	As	as	SCONJ	IN	_	3	mark	_	_
2	Bourn	Bourn	PROPN	NNP	Number=Sing	3	nsubj	_	_
3	showed	show	VERB	VBD	Tense=Past|VerbForm=Fin	51	advcl	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	if	if	SCONJ	IN	_	7	mark	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	take	take	VERB	VBP	Tense=Pres|VerbForm=Fin	51	advcl	_	_
8	$ mathbb{D} $	$ mathbb{d} $	SYM	$	_	7	dobj	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	be	be	AUX	VB	VerbForm=Inf	7	advcl	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	class	class	NOUN	NN	Number=Sing	10	attr	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	Maltsev	Maltsev	PROPN	NNP	Number=Sing	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	_
16	in	in	ADP	IN	_	12	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	sense	sense	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	Carboni	Carboni	PROPN	NNP	Number=Sing	19	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	Lambek	Lambek	PROPN	NNP	Number=Sing	20	conj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
25	Pedicchio	Pedicchio	PROPN	NNP	Number=Sing	22	conj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
28	$ mathbb{C} $	$ mathbb{c} $	SYM	$	_	7	dep	_	_
29	to	to	PART	TO	_	30	aux	_	_
30	be	be	AUX	VB	VerbForm=Inf	7	advcl	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	class	class	NOUN	NN	Number=Sing	30	attr	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	unital	unital	ADJ	JJ	Degree=Pos	35	amod	_	_
35	categories	category	NOUN	NNS	Number=Plur	33	pobj	_	_
36	in	in	ADP	IN	_	32	prep	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	sense	sense	NOUN	NN	Number=Sing	36	pobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	Bourn	Bourn	PROPN	NNP	Number=Sing	39	pobj	_	SpaceAfter=No
41	,	,	PUNCT	,	PunctType=Comm	40	punct	_	_
42	which	which	PRON	WDT	_	43	nsubj	_	_
43	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	40	relcl	_	_
44	pointed	point	VERB	VBD	Tense=Past|VerbForm=Fin	48	amod	_	_
45	Jónsson	Jónsson	PROPN	NNP	Number=Sing	47	compound	_	_
46	-	-	PUNCT	HYPH	PunctType=Dash	47	punct	_	_
47	Tarski	Tarski	PROPN	NNP	Number=Sing	48	compound	_	_
48	varieties	variety	NOUN	NNS	Number=Plur	43	dobj	_	SpaceAfter=No
49	,	,	PUNCT	,	PunctType=Comm	40	punct	_	_
50	then	then	ADV	RB	PronType=Dem	51	advmod	_	_
51	$ mathbb{D} = mathrm{Loc}(mathbb{C}) $	$ mathbb{d} = mathrm{loc}(mathbb{c}) $	SYM	$	_	0	ROOT	_	_
52	.	.	PUNCT	.	PunctType=Peri	51	punct	_	SpaceAfter=No

# sent_id = 3
# text = A similar result was obtained by the author: if $ mathbb{D} $ is as above and $ mathbb{C} $ is the class of subtractive categories, which generalize pointed subtractive varieties in the sense of Ursini, then $ mathbb{D} = mathrm{Loc}(mathbb{C}) $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	similar	similar	ADJ	JJ	Degree=Pos	3	amod	_	_
3	result	result	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	5	auxpass	_	_
5	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	ccomp	_	_
6	by	by	ADP	IN	_	5	agent	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	author	author	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
9	:	:	PUNCT	:	_	5	punct	_	_
10	if	if	SCONJ	IN	_	12	mark	_	_
11	$ mathbb{D} $	$ mathbb{d} $	SYM	$	_	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	advcl	_	_
13	as	as	ADV	RB	_	14	advmod	_	_
14	above	above	ADJ	JJ	Degree=Pos	12	advmod	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	$ mathbb{C} $	$ mathbb{c} $	SYM	$	_	17	nsubj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	class	class	NOUN	NN	Number=Sing	17	attr	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	subtractive	subtractive	ADJ	JJ	Degree=Pos	22	amod	_	_
22	categories	category	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	which	which	PRON	WDT	_	25	nsubj	_	_
25	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	22	relcl	_	_
26	pointed	point	VERB	VBD	Tense=Past|VerbForm=Fin	28	amod	_	_
27	subtractive	subtractive	ADJ	JJ	Degree=Pos	28	amod	_	_
28	varieties	variety	NOUN	NNS	Number=Plur	25	dobj	_	_
29	in	in	ADP	IN	_	25	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	sense	sense	NOUN	NN	Number=Sing	29	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	Ursini	Ursini	PROPN	NNP	Number=Sing	32	pobj	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
35	then	then	ADV	RB	PronType=Dem	33	advmod	_	_
36	$ mathbb{D} = mathrm{Loc}(mathbb{C}) $	$ mathbb{d} = mathrm{loc}(mathbb{c}) $	SYM	$	_	17	dep	_	_
37	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 4
# text = In the present paper we extend these results to abstract classes of categories obtained from classes of varieties.
1	In	in	ADP	IN	_	6	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	present	present	ADJ	JJ	Degree=Pos	4	amod	_	_
4	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	extend	extend	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	these	these	DET	DT	Number=Plur|PronType=Dem	8	det	_	_
8	results	result	NOUN	NNS	Number=Plur	6	dobj	_	_
9	to	to	ADP	IN	_	6	prep	_	_
10	abstract	abstract	ADJ	JJ	Degree=Pos	11	amod	_	_
11	classes	class	NOUN	NNS	Number=Plur	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	_
14	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	acl	_	_
15	from	from	ADP	IN	_	14	prep	_	_
16	classes	class	NOUN	NNS	Number=Plur	15	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	varieties	variety	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = We also show that the Bourn localization of the union of the classes of unital and subtractive categories is still the class of Maltsev categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	19	mark	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	Bourn	Bourn	PROPN	NNP	Number=Sing	7	compound	_	_
7	localization	localization	NOUN	NN	Number=Sing	19	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	union	union	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	classes	class	NOUN	NNS	Number=Plur	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	unital	unital	ADJ	JJ	Degree=Pos	18	amod	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	subtractive	subtractive	ADJ	JJ	Degree=Pos	15	conj	_	_
18	categories	category	NOUN	NNS	Number=Plur	14	pobj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
20	still	still	ADV	RB	_	19	advmod	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	class	class	NOUN	NN	Number=Sing	19	attr	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	Maltsev	Maltsev	PROPN	NNP	Number=Sing	25	amod	_	_
25	categories	category	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 251
# sent_id = 1
# text = Let $ L $ be an arbitrary orthomodular lattice.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ L $	$ l $	SYM	$	_	3	nsubj	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	7	amod	_	_
6	orthomodular	orthomodular	NOUN	NN	Number=Sing	7	compound	_	_
7	lattice	lattice	NOUN	NN	Number=Sing	3	attr	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = There is a one to one correspondence between orthomodular sublattices of L satisfying an extra condition and quantic quantifiers.
1	There	there	PRON	EX	_	2	expl	_	_
2	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
4	one	one	NUM	CD	NumType=Card	6	quantmod	_	_
5	to	to	ADP	IN	_	6	quantmod	_	_
6	one	one	NUM	CD	NumType=Card	7	nummod	_	_
7	correspondence	correspondence	NOUN	NN	Number=Sing	2	attr	_	_
8	between	between	ADP	IN	_	7	prep	_	_
9	orthomodular	orthomodular	ADJ	JJ	Degree=Pos	10	amod	_	_
10	sublattices	sublattice	NOUN	NNS	Number=Plur	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	L	L	PROPN	NNP	Number=Sing	11	pobj	_	_
13	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	acl	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	extra	extra	ADJ	JJ	Degree=Pos	16	amod	_	_
16	condition	condition	NOUN	NN	Number=Sing	13	dobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	quantic	quantic	ADJ	JJ	Degree=Pos	19	amod	_	_
19	quantifiers	quantifier	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The category of orthomodular lattices is equivalent to the category of posets having two families of endofunctors satisfying six conditions.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	orthomodular	orthomodular	ADJ	JJ	Degree=Pos	5	amod	_	_
5	lattices	lattice	NOUN	NNS	Number=Plur	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	equivalent	equivalent	ADJ	JJ	Degree=Pos	6	acomp	_	_
8	to	to	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	posets	poset	NOUN	NNS	Number=Plur	11	pobj	_	_
13	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	acl	_	_
14	two	two	NUM	CD	NumType=Card	15	nummod	_	_
15	families	family	NOUN	NNS	Number=Plur	13	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	endofunctors	endofunctor	NOUN	NNS	Number=Plur	16	pobj	_	_
18	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	acl	_	_
19	six	six	NUM	CD	NumType=Card	20	nummod	_	_
20	conditions	condition	NOUN	NNS	Number=Plur	18	dobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 252
# sent_id = 1
# text = We study closedness properties of internal relations in finitely complete categories, which leads to developing a unified approach to: Maltsev categories, in the sense of Carboni, Lambek and Pedicchio, that generalize Maltsev varieties of universal algebras; unital categories, in the sense of Bourn, that generalize pointed Jónsson - Tarski varieties; and subtractive categories, introduced by the author, that generalize pointed subtractive varieties in the sense of Ursini.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	54	ccomp	_	_
3	closedness	closedness	NOUN	NN	Number=Sing	4	amod	_	_
4	properties	property	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	internal	internal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	relations	relation	NOUN	NNS	Number=Plur	5	pobj	_	_
8	in	in	ADP	IN	_	2	prep	_	_
9	finitely	finitely	ADV	RB	_	10	advmod	_	_
10	complete	complete	ADJ	JJ	Degree=Pos	11	amod	_	_
11	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	which	which	PRON	WDT	_	14	nsubj	_	_
14	leads	lead	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	relcl	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	developing	develop	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	pcomp	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	unified	unified	ADJ	JJ	Degree=Pos	19	amod	_	_
19	approach	approach	NOUN	NN	Number=Sing	16	dobj	_	_
20	to	to	ADP	IN	_	19	prep	_	SpaceAfter=No
21	:	:	PUNCT	:	_	20	punct	_	_
22	Maltsev	maltsev	ADJ	JJ	Degree=Pos	23	amod	_	_
23	categories	category	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	54	punct	_	_
25	in	in	ADP	IN	_	54	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	sense	sense	NOUN	NN	Number=Sing	25	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	Carboni	Carboni	PROPN	NNP	Number=Sing	28	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
31	Lambek	Lambek	PROPN	NNP	Number=Sing	29	conj	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	Pedicchio	Pedicchio	PROPN	NNP	Number=Sing	31	conj	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
35	that	that	PRON	WDT	PronType=Rel	36	nsubj	_	_
36	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	27	relcl	_	_
37	Maltsev	Maltsev	PROPN	NNP	Number=Sing	38	compound	_	_
38	varieties	variety	NOUN	NNS	Number=Plur	36	dobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	universal	universal	ADJ	JJ	Degree=Pos	41	amod	_	_
41	algebras	algebra	NOUN	NNS	Number=Plur	39	pobj	_	SpaceAfter=No
42	;	;	PUNCT	:	_	54	punct	_	_
43	unital	unital	ADJ	JJ	Degree=Pos	44	amod	_	_
44	categories	category	NOUN	NNS	Number=Plur	54	nsubj	_	SpaceAfter=No
45	,	,	PUNCT	,	PunctType=Comm	54	punct	_	_
46	in	in	ADP	IN	_	54	prep	_	_
47	the	the	DET	DT	Definite=Def|PronType=Art	48	det	_	_
48	sense	sense	NOUN	NN	Number=Sing	46	pobj	_	_
49	of	of	ADP	IN	_	48	prep	_	_
50	Bourn	Bourn	PROPN	NNP	Number=Sing	49	pobj	_	SpaceAfter=No
51	,	,	PUNCT	,	PunctType=Comm	54	punct	_	_
52	that	that	PRON	WDT	PronType=Rel	54	nsubj	_	_
53	generalize	generalize	NOUN	NN	Number=Sing	52	nmod	_	_
54	pointed	point	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
55	Jónsson	Jónsson	PROPN	NNP	Number=Sing	57	compound	_	_
56	-	-	PUNCT	HYPH	PunctType=Dash	57	punct	_	_
57	Tarski	Tarski	PROPN	NNP	Number=Sing	58	compound	_	_
58	varieties	variety	NOUN	NNS	Number=Plur	54	dobj	_	SpaceAfter=No
59	;	;	PUNCT	:	_	58	punct	_	_
60	and	and	CCONJ	CC	ConjType=Cmp	58	cc	_	_
61	subtractive	subtractive	ADJ	JJ	Degree=Pos	62	amod	_	_
62	categories	category	NOUN	NNS	Number=Plur	71	nsubj	_	SpaceAfter=No
63	,	,	PUNCT	,	PunctType=Comm	62	punct	_	_
64	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	62	acl	_	_
65	by	by	ADP	IN	_	64	agent	_	_
66	the	the	DET	DT	Definite=Def|PronType=Art	67	det	_	_
67	author	author	NOUN	NN	Number=Sing	65	pobj	_	SpaceAfter=No
68	,	,	PUNCT	,	PunctType=Comm	62	punct	_	_
69	that	that	PRON	WDT	PronType=Rel	70	nsubj	_	_
70	generalize	generalize	NOUN	NN	Number=Sing	62	relcl	_	_
71	pointed	point	VERB	VBD	Tense=Past|VerbForm=Fin	58	conj	_	_
72	subtractive	subtractive	ADJ	JJ	Degree=Pos	73	amod	_	_
73	varieties	variety	NOUN	NNS	Number=Plur	71	dobj	_	_
74	in	in	ADP	IN	_	71	prep	_	_
75	the	the	DET	DT	Definite=Def|PronType=Art	76	det	_	_
76	sense	sense	NOUN	NN	Number=Sing	74	pobj	_	_
77	of	of	ADP	IN	_	76	prep	_	_
78	Ursini	Ursini	PROPN	NNP	Number=Sing	77	pobj	_	SpaceAfter=No
79	.	.	PUNCT	.	PunctType=Peri	54	punct	_	SpaceAfter=No

# doc_id = 253
# sent_id = 1
# text = We consider exponentiable objects in lax slices of $ Top $ with respect to the specialization order (and its opposite) on a base space $ B $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	exponentiable	exponentiable	ADJ	JJ	Degree=Pos	4	amod	_	_
4	objects	object	NOUN	NNS	Number=Plur	2	dobj	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	lax	lax	ADJ	JJ	Degree=Pos	7	amod	_	_
7	slices	slice	NOUN	NNS	Number=Plur	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	$ Top $	$ top $	SYM	$	_	8	pobj	_	_
10	with	with	ADP	IN	_	2	prep	_	_
11	respect	respect	NOUN	NN	Number=Sing	10	pobj	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	specialization	specialization	NOUN	NN	Number=Sing	15	compound	_	_
15	order	order	NOUN	NN	Number=Sing	12	pobj	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	15	punct	_	SpaceAfter=No
17	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
18	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	19	poss	_	_
19	opposite	opposite	NOUN	NN	Number=Sing	15	conj	_	SpaceAfter=No
20	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	19	punct	_	_
21	on	on	ADP	IN	_	19	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
23	base	base	NOUN	NN	Number=Sing	24	compound	_	_
24	space	space	NOUN	NN	Number=Sing	21	pobj	_	_
25	$ B $	$ b $	SYM	$	_	19	appos	_	_
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	0	ROOT	_	_
2	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# doc_id = 254
# sent_id = 1
# text = For a differential graded $ k $ - quiver $ Q $ we define the free $ A_infty $ - category $ FQ $ generated by $ Q $ .
1	For	for	ADP	IN	_	10	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	differential	differential	NOUN	NN	Number=Sing	1	pobj	_	_
4	graded	grade	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	acl	_	_
5	$ k $	$ k $	SYM	$	_	7	compound	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	quiver	quiver	NOUN	NN	Number=Sing	4	dobj	_	_
8	$ Q $	$ q $	SYM	$	_	4	dep	_	_
9	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
10	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
12	free	free	ADJ	JJ	Degree=Pos	15	amod	_	_
13	$ A_infty $	$ a_infty $	SYM	$	_	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	category	category	NOUN	NN	Number=Sing	10	dobj	_	_
16	$ FQ $	$ fq $	SYM	$	_	15	appos	_	_
17	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
18	by	by	ADP	IN	_	17	prep	_	_
19	$ Q $	$ q $	SYM	$	_	18	pobj	_	_
20	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = The main result is that the restriction $ A_infty $ - functor $ A_infty(FQ, A) to A_1(Q, A) $ is an equivalence, where objects of the last $ A_ $ - category are morphisms of differential graded $ k $ - quivers $ Q to A $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	result	result	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	12	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	restriction	restriction	NOUN	NN	Number=Sing	12	nsubj	_	_
8	$ A_infty $	$ a_infty $	SYM	$	_	10	det	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	functor	functor	NOUN	NN	Number=Sing	11	compound	_	_
11	$ A_infty(FQ, A) to A_1(Q, A) $	$ a_infty(fq, a) to a_1(q, a) $	SYM	$	_	7	appos	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	equivalence	equivalence	NOUN	NN	Number=Sing	12	attr	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	where	where	SCONJ	WRB	_	24	advmod	_	_
17	objects	object	NOUN	NNS	Number=Plur	24	nsubj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
20	last	last	ADJ	JJ	Degree=Pos	23	amod	_	_
21	$ A_ $	$ a_ $	SYM	$	_	23	nummod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
24	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	28	auxpass	_	_
25	morphisms	morphism	NOUN	NNS	Number=Plur	24	attr	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	differential	differential	NOUN	NN	Number=Sing	26	pobj	_	_
28	graded	grade	VERB	VBD	Tense=Past|VerbForm=Fin	14	relcl	_	_
29	$ k $	$ k $	SYM	$	_	31	nummod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	quivers	quiver	NOUN	NNS	Number=Plur	32	compound	_	_
32	$ Q to A $	$ q to a $	SYM	$	_	28	dobj	_	_
33	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 255
# sent_id = 1
# text = It is shown that the cubical nerve of a strict omega - category is a sequence of sets with cubical face operations and distinguished subclasses of thin elements satisfying certain thin filler conditions.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	SCONJ	IN	_	14	mark	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	cubical	cubical	ADJ	JJ	Degree=Pos	7	amod	_	_
7	nerve	nerve	NOUN	NN	Number=Sing	14	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
10	strict	strict	ADJ	JJ	Degree=Pos	13	amod	_	_
11	omega	omega	NOUN	NN	Number=Sing	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	sequence	sequence	NOUN	NN	Number=Sing	14	attr	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	sets	set	NOUN	NNS	Number=Plur	17	pobj	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	cubical	cubical	ADJ	JJ	Degree=Pos	21	amod	_	_
21	face	face	NOUN	NN	Number=Sing	22	compound	_	_
22	operations	operation	NOUN	NNS	Number=Plur	19	pobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	distinguished	distinguished	ADJ	JJ	Degree=Pos	25	amod	_	_
25	subclasses	subclass	NOUN	NNS	Number=Plur	22	conj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	thin	thin	ADJ	JJ	Degree=Pos	28	amod	_	_
28	elements	element	NOUN	NNS	Number=Plur	26	pobj	_	_
29	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	28	acl	_	_
30	certain	certain	ADJ	JJ	Degree=Pos	33	amod	_	_
31	thin	thin	ADJ	JJ	Degree=Pos	33	amod	_	_
32	filler	filler	NOUN	NN	Number=Sing	33	compound	_	_
33	conditions	condition	NOUN	NNS	Number=Plur	29	dobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = It is also shown that a sequence of this type is the cubical nerve of a strict omega - category unique up to isomorphism; the cubical nerve functor is therefore an equivalence of categories.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	4	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
3	also	also	ADV	RB	_	4	advmod	_	_
4	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	30	ccomp	_	_
5	that	that	SCONJ	IN	_	11	mark	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	sequence	sequence	NOUN	NN	Number=Sing	11	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	this	this	DET	DT	Number=Sing|PronType=Dem	10	det	_	_
10	type	type	NOUN	NN	Number=Sing	8	pobj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	cubical	cubical	ADJ	JJ	Degree=Pos	14	amod	_	_
14	nerve	nerve	NOUN	NN	Number=Sing	11	attr	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
17	strict	strict	ADJ	JJ	Degree=Pos	20	amod	_	_
18	omega	omega	NOUN	NN	Number=Sing	20	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
21	unique	unique	ADJ	JJ	Degree=Pos	14	acl	_	_
22	up	up	ADP	IN	_	21	prep	_	_
23	to	to	ADP	IN	_	22	prep	_	_
24	isomorphism	isomorphism	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
25	;	;	PUNCT	:	_	30	punct	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
27	cubical	cubical	ADJ	JJ	Degree=Pos	29	amod	_	_
28	nerve	nerve	NOUN	NN	Number=Sing	29	compound	_	_
29	functor	functor	NOUN	NN	Number=Sing	30	nsubj	_	_
30	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
31	therefore	therefore	ADV	RB	_	30	advmod	_	_
32	an	an	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
33	equivalence	equivalence	NOUN	NN	Number=Sing	30	attr	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	categories	category	NOUN	NNS	Number=Plur	34	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	30	punct	_	SpaceAfter=No

# sent_id = 3
# text = The sequences of sets involved are the analogues of cubical $ T $ - complexes appropriate for strict omega - categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	sequences	sequence	NOUN	NNS	Number=Plur	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	sets	set	NOUN	NNS	Number=Plur	3	pobj	_	_
5	involved	involve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	acl	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	analogues	analogue	NOUN	NNS	Number=Plur	6	attr	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	cubical	cubical	ADJ	JJ	Degree=Pos	13	amod	_	_
11	$ T $	$ t $	SYM	$	_	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	complexes	complex	NOUN	NNS	Number=Plur	9	pobj	_	_
14	appropriate	appropriate	ADJ	JJ	Degree=Pos	13	amod	_	_
15	for	for	ADP	IN	_	14	prep	_	_
16	strict	strict	ADJ	JJ	Degree=Pos	19	amod	_	_
17	omega	omega	NOUN	NN	Number=Sing	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = Degeneracies are not required in the definition of these sequences, but can in fact be constructed as thin fillers.
1	Degeneracies	degeneracy	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
3	not	not	PART	RB	Polarity=Neg	4	neg	_	_
4	required	require	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	definition	definition	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	these	these	DET	DT	Number=Plur|PronType=Dem	10	det	_	_
10	sequences	sequence	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
12	but	but	CCONJ	CC	ConjType=Cmp	4	cc	_	_
13	can	can	AUX	MD	VerbForm=Fin	17	aux	_	_
14	in	in	ADP	IN	_	17	prep	_	_
15	fact	fact	NOUN	NN	Number=Sing	14	pobj	_	_
16	be	be	AUX	VB	VerbForm=Inf	17	auxpass	_	_
17	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	conj	_	_
18	as	as	ADP	IN	_	17	prep	_	_
19	thin	thin	ADJ	JJ	Degree=Pos	20	amod	_	_
20	fillers	filler	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 5
# text = The proof of the thin filler conditions uses chain complexes and chain homotopies.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	proof	proof	NOUN	NN	Number=Sing	8	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	thin	thin	ADJ	JJ	Degree=Pos	7	amod	_	_
6	filler	filler	NOUN	NN	Number=Sing	7	compound	_	_
7	conditions	condition	NOUN	NNS	Number=Plur	3	pobj	_	_
8	uses	use	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	chain	chain	NOUN	NN	Number=Sing	10	compound	_	_
10	complexes	complex	NOUN	NNS	Number=Plur	8	dobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	chain	chain	NOUN	NN	Number=Sing	13	compound	_	_
13	homotopies	homotopie	NOUN	NNS	Number=Plur	10	conj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 256
# sent_id = 1
# text = We show, for an arbitrary adjunction $ F dashv U : cal B to cal A $ with $ cal B $ Cauchy complete, that the functor $ F $ is comonadic if and only if the monad $ T $ on $ cal A $ induced by the adjunction is of effective descent type, meaning that the free $ T $ - algebra functor $ F^{T}: cal A to cal A^{T} $ is comonadic.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
4	for	for	ADP	IN	_	2	prep	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	7	amod	_	_
7	adjunction	adjunction	NOUN	NN	Number=Sing	4	pobj	_	_
8	$ F dashv U : cal B to cal A $	$ f dashv u : cal b to cal a $	SYM	$	_	7	nmod	_	_
9	with	with	ADP	IN	_	7	prep	_	_
10	$ cal B $	$ cal b $	SYM	$	_	11	nmod	_	_
11	Cauchy	cauchy	NOUN	NN	Number=Sing	9	pobj	_	_
12	complete	complete	ADJ	JJ	Degree=Pos	7	amod	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
14	that	that	SCONJ	IN	_	18	mark	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	functor	functor	NOUN	NN	Number=Sing	18	nsubj	_	_
17	$ F $	$ f $	SYM	$	_	16	appos	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
19	comonadic	comonadic	ADJ	JJ	Degree=Pos	18	acomp	_	_
20	if	if	SCONJ	IN	_	33	mark	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
22	only	only	ADV	RB	_	33	advmod	_	_
23	if	if	SCONJ	IN	_	33	mark	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	monad	monad	NOUN	NNS	Number=Plur	33	nsubj	_	_
26	$ T $	$ t $	SYM	$	_	25	appos	_	_
27	on	on	ADP	IN	_	25	prep	_	_
28	$ cal A $	$ cal a $	SYM	$	_	27	pobj	_	_
29	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	acl	_	_
30	by	by	ADP	IN	_	29	agent	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	adjunction	adjunction	NOUN	NN	Number=Sing	30	pobj	_	_
33	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	advcl	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	effective	effective	ADJ	JJ	Degree=Pos	37	amod	_	_
36	descent	descent	NOUN	NN	Number=Sing	37	compound	_	_
37	type	type	NOUN	NN	Number=Sing	34	pobj	_	SpaceAfter=No
38	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
39	meaning	mean	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	33	advcl	_	_
40	that	that	SCONJ	IN	_	48	mark	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	46	det	_	_
42	free	free	ADJ	JJ	Degree=Pos	46	amod	_	_
43	$ T $	$ t $	SYM	$	_	45	nummod	_	_
44	-	-	PUNCT	HYPH	PunctType=Dash	45	punct	_	_
45	algebra	algebra	NOUN	NN	Number=Sing	46	compound	_	_
46	functor	functor	NOUN	NN	Number=Sing	48	nsubj	_	_
47	$ F^{T}: cal A to cal A^{T} $	$ f^{t}: cal a to cal a^{t} $	SYM	$	_	48	nsubj	_	_
48	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	39	ccomp	_	_
49	comonadic	comonadic	ADJ	JJ	Degree=Pos	48	acomp	_	SpaceAfter=No
50	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This result is applied to several situations: In Section 4 to give a sufficient condition for an exponential functor on a cartesian closed category to be monadic, in Sections 5 and 6 to settle the question of the comonadicity of those functors whose domain is Set, or Set $ _{star} $ , or the category of modules over a semisimple ring, in Section 7 to study the effectiveness of (co)monads on module categories.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	result	result	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	applied	apply	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	several	several	ADJ	JJ	Degree=Pos	7	amod	_	_
7	situations	situation	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	:	:	PUNCT	:	_	4	punct	_	_
9	In	in	ADP	IN	_	4	prep	_	_
10	Section	section	NOUN	NN	Number=Sing	9	pobj	_	_
11	4	4	NUM	CD	NumType=Card	10	nummod	_	_
12	to	to	PART	TO	_	13	aux	_	_
13	give	give	VERB	VB	VerbForm=Inf	10	relcl	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	sufficient	sufficient	ADJ	JJ	Degree=Pos	16	amod	_	_
16	condition	condition	NOUN	NN	Number=Sing	13	dobj	_	_
17	for	for	ADP	IN	_	16	prep	_	_
18	an	an	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	exponential	exponential	ADJ	JJ	Degree=Pos	20	amod	_	_
20	functor	functor	NOUN	NN	Number=Sing	17	pobj	_	_
21	on	on	ADP	IN	_	20	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
23	cartesian	cartesian	ADJ	JJ	Degree=Pos	24	advmod	_	_
24	closed	closed	ADJ	JJ	Degree=Pos	25	amod	_	_
25	category	category	NOUN	NN	Number=Sing	21	pobj	_	_
26	to	to	PART	TO	_	27	aux	_	_
27	be	be	AUX	VB	VerbForm=Inf	16	acl	_	_
28	monadic	monadic	ADJ	JJ	Degree=Pos	27	acomp	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
30	in	in	ADP	IN	_	13	prep	_	_
31	Sections	Sections	PROPN	NNP	Number=Sing	30	pobj	_	_
32	5	5	NUM	CD	NumType=Card	31	nummod	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
34	6	6	NUM	CD	NumType=Card	31	conj	_	_
35	to	to	PART	TO	_	36	aux	_	_
36	settle	settle	VERB	VB	VerbForm=Inf	13	advcl	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	question	question	NOUN	NN	Number=Sing	36	dobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
41	comonadicity	comonadicity	NOUN	NN	Number=Sing	39	pobj	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	those	those	DET	DT	Number=Plur|PronType=Dem	44	det	_	_
44	functors	functor	NOUN	NNS	Number=Plur	42	pobj	_	_
45	whose	whose	DET	WP$	Poss=Yes	46	poss	_	_
46	domain	domain	NOUN	NN	Number=Sing	47	nsubj	_	_
47	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	44	relcl	_	_
48	Set	set	NOUN	NN	Number=Sing	47	attr	_	SpaceAfter=No
49	,	,	PUNCT	,	PunctType=Comm	48	punct	_	_
50	or	or	CCONJ	CC	ConjType=Cmp	48	cc	_	_
51	Set	set	VERB	VB	VerbForm=Inf	48	conj	_	_
52	$ _{star} $	$ _{star} $	SYM	$	_	51	dobj	_	_
53	,	,	PUNCT	,	PunctType=Comm	52	punct	_	_
54	or	or	CCONJ	CC	ConjType=Cmp	52	cc	_	_
55	the	the	DET	DT	Definite=Def|PronType=Art	56	det	_	_
56	category	category	NOUN	NN	Number=Sing	52	conj	_	_
57	of	of	ADP	IN	_	56	prep	_	_
58	modules	module	NOUN	NNS	Number=Plur	57	pobj	_	_
59	over	over	ADP	IN	_	58	prep	_	_
60	a	a	DET	DT	Definite=Ind|PronType=Art	62	det	_	_
61	semisimple	semisimple	ADJ	JJ	Degree=Pos	62	amod	_	_
62	ring	ring	NOUN	NN	Number=Sing	59	pobj	_	SpaceAfter=No
63	,	,	PUNCT	,	PunctType=Comm	51	punct	_	_
64	in	in	ADP	IN	_	51	prep	_	_
65	Section	section	NOUN	NN	Number=Sing	64	pobj	_	_
66	7	7	NUM	CD	NumType=Card	65	nummod	_	_
67	to	to	PART	TO	_	68	aux	_	_
68	study	study	VERB	VB	VerbForm=Inf	51	advcl	_	_
69	the	the	DET	DT	Definite=Def|PronType=Art	70	det	_	_
70	effectiveness	effectiveness	NOUN	NN	Number=Sing	68	dobj	_	_
71	of	of	ADP	IN	_	70	prep	_	_
72	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	71	punct	_	SpaceAfter=No
73	co)monads	co)monad	NOUN	NNS	Number=Plur	71	pobj	_	_
74	on	on	ADP	IN	_	73	prep	_	_
75	module	module	NOUN	NN	Number=Sing	76	compound	_	_
76	categories	category	NOUN	NNS	Number=Plur	74	pobj	_	SpaceAfter=No
77	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = Our final application is a descent theorem for noncommutative rings from which we deduce an important result of Joyal and Tierney and of Olivier, asserting that the effective descent morphisms in the opposite of the category of commutative unital rings are precisely the pure monomorphisms.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	3	poss	_	_
2	final	final	ADJ	JJ	Degree=Pos	3	amod	_	_
3	application	application	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	descent	descent	NOUN	NN	Number=Sing	7	compound	_	_
7	theorem	theorem	ADJ	JJ	Degree=Pos	4	attr	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	noncommutative	noncommutative	ADJ	JJ	Degree=Pos	10	amod	_	_
10	rings	ring	NOUN	NNS	Number=Plur	8	pobj	_	_
11	from	from	ADP	IN	_	14	prep	_	_
12	which	which	PRON	WDT	_	11	pobj	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	deduce	deduce	VERB	VBP	Tense=Pres|VerbForm=Fin	10	relcl	_	_
15	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	important	important	ADJ	JJ	Degree=Pos	17	amod	_	_
17	result	result	NOUN	NN	Number=Sing	14	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	Joyal	Joyal	PROPN	NNP	Number=Sing	18	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	Tierney	Tierney	PROPN	NNP	Number=Sing	19	conj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
23	of	of	ADP	IN	_	19	conj	_	_
24	Olivier	Olivier	PROPN	NNP	Number=Sing	23	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
26	asserting	assert	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	advcl	_	_
27	that	that	SCONJ	IN	_	42	mark	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
29	effective	effective	ADJ	JJ	Degree=Pos	31	amod	_	_
30	descent	descent	NOUN	NN	Number=Sing	31	compound	_	_
31	morphisms	morphism	NOUN	NNS	Number=Plur	42	nsubj	_	_
32	in	in	ADP	IN	_	31	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
34	opposite	opposite	NOUN	NN	Number=Sing	32	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	category	category	NOUN	NN	Number=Sing	35	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	commutative	commutative	ADJ	JJ	Degree=Pos	41	amod	_	_
40	unital	unital	PROPN	NNP	Number=Sing	41	compound	_	_
41	rings	ring	NOUN	NNS	Number=Plur	38	pobj	_	_
42	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	26	ccomp	_	_
43	precisely	precisely	ADV	RB	_	42	advmod	_	_
44	the	the	DET	DT	Definite=Def|PronType=Art	46	det	_	_
45	pure	pure	ADJ	JJ	Degree=Pos	46	amod	_	_
46	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	42	attr	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 257
# sent_id = 1
# text = We give a Dialectica - style interpretation of first - order classical affine logic.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
4	Dialectica	Dialectica	PROPN	NNP	Number=Sing	6	compound	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	style	style	NOUN	NN	Number=Sing	7	compound	_	_
7	interpretation	interpretation	NOUN	NN	Number=Sing	2	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	first	first	ADJ	JJ	Degree=Pos	11	amod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	order	order	NOUN	NN	Number=Sing	14	nmod	_	_
12	classical	classical	ADJ	JJ	Degree=Pos	14	amod	_	_
13	affine	affine	NOUN	NN	Number=Sing	14	compound	_	_
14	logic	logic	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = By moving to a contraction - free logic, the translation (also known as $ D $ - translation) of a first - order formula into a higher - type $ existsforall $ - formula can be made symmetric with respect to duality, including exponentials.
1	By	by	ADP	IN	_	36	prep	_	_
2	moving	move	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	1	pcomp	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
5	contraction	contraction	NOUN	NN	Number=Sing	7	npadvmod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	free	free	ADJ	JJ	Degree=Pos	8	amod	_	_
8	logic	logic	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	translation	translation	NOUN	NN	Number=Sing	36	nsubjpass	_	_
12	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
13	also	also	ADV	RB	_	14	advmod	_	_
14	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acl	_	_
15	as	as	ADP	IN	_	14	prep	_	_
16	$ D $	$ d $	SYM	$	_	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	translation	translation	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
19	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	14	punct	_	_
20	of	of	ADP	IN	_	14	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
22	first	first	ADJ	JJ	Degree=Pos	24	amod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	order	order	NOUN	NN	Number=Sing	25	compound	_	_
25	formula	formula	NOUN	NN	Number=Sing	20	pobj	_	_
26	into	into	ADP	IN	_	25	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
28	higher	high	ADJ	JJR	Degree=Cmp	30	amod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	type	type	NOUN	NN	Number=Sing	33	nmod	_	_
31	$ existsforall $	$ existsforall $	SYM	$	_	33	nummod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	formula	formula	NOUN	NN	Number=Sing	26	pobj	_	_
34	can	can	AUX	MD	VerbForm=Fin	36	aux	_	_
35	be	be	AUX	VB	VerbForm=Inf	36	auxpass	_	_
36	made	make	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
37	symmetric	symmetric	ADJ	JJ	Degree=Pos	36	oprd	_	_
38	with	with	ADP	IN	_	37	prep	_	_
39	respect	respect	NOUN	NN	Number=Sing	38	pobj	_	_
40	to	to	ADP	IN	_	39	prep	_	_
41	duality	duality	NOUN	NN	Number=Sing	40	pobj	_	SpaceAfter=No
42	,	,	PUNCT	,	PunctType=Comm	41	punct	_	_
43	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	41	prep	_	_
44	exponentials	exponential	NOUN	NNS	Number=Plur	43	pobj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	36	punct	_	SpaceAfter=No

# sent_id = 3
# text = It turned out that the propositional part of our $ D $ - translation uses the same construction as de Paiva's dialectica category $ GC $ and we show how our $ D $ - translation extends $ GC $ to the first - order setting in terms of an indexed category.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	turned	turn	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
3	out	out	ADP	RP	_	2	prt	_	_
4	that	that	SCONJ	IN	_	13	mark	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	propositional	propositional	ADJ	JJ	Degree=Pos	7	amod	_	_
7	part	part	NOUN	NN	Number=Sing	13	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	12	poss	_	_
10	$ D $	$ d $	SYM	$	_	12	nummod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	translation	translation	NOUN	NN	Number=Sing	8	pobj	_	_
13	uses	use	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	same	same	ADJ	JJ	Degree=Pos	16	amod	_	_
16	construction	construction	NOUN	NN	Number=Sing	13	dobj	_	_
17	as	as	ADP	IN	_	16	prep	_	_
18	de	de	PROPN	NNP	Number=Sing	19	compound	_	_
19	Paiva	Paiva	PROPN	NNP	Number=Sing	22	poss	_	SpaceAfter=No
20	's	's	PART	POS	_	19	case	_	_
21	dialectica	dialectica	NOUN	NN	Number=Sing	22	compound	_	_
22	category	category	NOUN	NN	Number=Sing	17	pobj	_	_
23	$ GC $	$ gc $	SYM	$	_	13	dep	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
25	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	26	nsubj	_	_
26	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	13	conj	_	_
27	how	how	SCONJ	WRB	_	32	advmod	_	_
28	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	31	poss	_	_
29	$ D $	$ d $	SYM	$	_	31	compound	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	translation	translation	NOUN	NN	Number=Sing	32	nsubj	_	_
32	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	ccomp	_	_
33	$ GC $	$ gc $	SYM	$	_	32	dep	_	_
34	to	to	ADP	IN	_	32	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
36	first	first	ADJ	JJ	Degree=Pos	38	amod	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	38	punct	_	_
38	order	order	NOUN	NN	Number=Sing	39	compound	_	_
39	setting	setting	NOUN	NN	Number=Sing	34	pobj	_	_
40	in	in	ADP	IN	_	39	prep	_	_
41	terms	term	NOUN	NNS	Number=Plur	40	pobj	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	an	an	DET	DT	Definite=Ind|PronType=Art	45	det	_	_
44	indexed	indexed	ADJ	JJ	Degree=Pos	45	amod	_	_
45	category	category	NOUN	NN	Number=Sing	42	pobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = Furthermore the combination of Girard's $ ?clik $ - translation and our $ D $ - translation results in the essentially equivalent $ existsforall $ - formulas as the double - negation translation and Godel's original $ D $ - translation.
1	Furthermore	furthermore	ADV	RB	_	3	advmod	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	combination	combination	NOUN	NN	Number=Sing	0	ROOT	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	Girard	Girard	PROPN	NNP	Number=Sing	9	poss	_	SpaceAfter=No
6	's	's	PART	POS	_	5	case	_	_
7	$ ?clik $	$ ?clik $	NOUN	NN	Number=Sing	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	translation	translation	NOUN	NN	Number=Sing	4	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	15	poss	_	_
12	$ D $	$ d $	SYM	$	_	14	nummod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	translation	translation	NOUN	NN	Number=Sing	15	compound	_	_
15	results	result	NOUN	NNS	Number=Plur	9	conj	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
18	essentially	essentially	ADV	RB	_	19	advmod	_	_
19	equivalent	equivalent	ADJ	JJ	Degree=Pos	22	amod	_	_
20	$ existsforall $	$ existsforall $	SYM	$	_	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	formulas	formula	NOUN	NNS	Number=Plur	16	pobj	_	_
23	as	as	ADP	IN	_	3	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
25	double	double	ADJ	JJ	Degree=Pos	27	amod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	negation	negation	NOUN	NN	Number=Sing	28	compound	_	_
28	translation	translation	NOUN	NN	Number=Sing	23	pobj	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	Godel	Godel	PROPN	NNP	Number=Sing	35	poss	_	SpaceAfter=No
31	's	's	PART	POS	_	30	case	_	_
32	original	original	ADJ	JJ	Degree=Pos	35	amod	_	_
33	$ D $	$ d $	SYM	$	_	35	compound	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	translation	translation	NOUN	NN	Number=Sing	28	conj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 258
# sent_id = 1
# text = This note investigates two generic constructions used to produce categorical models of linear logic, the Chu construction and the Dialectica construction, in parallel.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	note	note	NOUN	NN	Number=Sing	3	nsubj	_	_
3	investigates	investigate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	two	two	NUM	CD	NumType=Card	6	nummod	_	_
5	generic	generic	ADJ	JJ	Degree=Pos	6	amod	_	_
6	constructions	construction	NOUN	NNS	Number=Plur	3	dobj	_	_
7	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	produce	produce	VERB	VB	VerbForm=Inf	7	xcomp	_	_
10	categorical	categorical	ADJ	JJ	Degree=Pos	11	amod	_	_
11	models	model	NOUN	NNS	Number=Plur	9	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	linear	linear	ADJ	JJ	Degree=Pos	14	amod	_	_
14	logic	logic	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	Chu	Chu	PROPN	NNP	Number=Sing	18	compound	_	_
18	construction	construction	NOUN	NN	Number=Sing	6	conj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	Dialectica	Dialectica	PROPN	NNP	Number=Sing	22	compound	_	_
22	construction	construction	NOUN	NN	Number=Sing	18	conj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
24	in	in	ADP	IN	_	3	prep	_	_
25	parallel	parallel	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = The constructions have the same objects, but are rather different in other ways.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	constructions	construction	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	same	same	ADJ	JJ	Degree=Pos	6	amod	_	_
6	objects	object	NOUN	NNS	Number=Plur	3	dobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
8	but	but	CCONJ	CC	ConjType=Cmp	3	cc	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	conj	_	_
10	rather	rather	ADV	RB	_	11	advmod	_	_
11	different	different	ADJ	JJ	Degree=Pos	9	acomp	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	other	other	ADJ	JJ	Degree=Pos	14	amod	_	_
14	ways	way	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = We discuss similarities and differences and prove that the Dialectica construction can be done over a symmetric monoidal closed basis.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	discuss	discuss	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	similarities	similarity	NOUN	NNS	Number=Plur	2	dobj	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	differences	difference	NOUN	NNS	Number=Plur	3	conj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
7	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
8	that	that	SCONJ	IN	_	14	mark	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	Dialectica	Dialectica	PROPN	NNP	Number=Sing	11	compound	_	_
11	construction	construction	NOUN	NN	Number=Sing	14	nsubjpass	_	_
12	can	can	AUX	MD	VerbForm=Fin	14	aux	_	_
13	be	be	AUX	VB	VerbForm=Inf	14	auxpass	_	_
14	done	do	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	ccomp	_	_
15	over	over	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	symmetric	symmetric	ADJ	JJ	Degree=Pos	18	amod	_	_
18	monoidal	monoidal	NOUN	NN	Number=Sing	15	pobj	_	_
19	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	20	amod	_	_
20	basis	basis	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We also point out interesting open problems concerning the Dialectica construction.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	point	point	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	out	out	ADP	RP	_	3	prt	_	_
5	interesting	interesting	ADJ	JJ	Degree=Pos	7	amod	_	_
6	open	open	ADJ	JJ	Degree=Pos	7	amod	_	_
7	problems	problem	NOUN	NNS	Number=Plur	3	dobj	_	_
8	concerning	concern	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	acl	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	Dialectica	Dialectica	PROPN	NNP	Number=Sing	11	compound	_	_
11	construction	construction	NOUN	NN	Number=Sing	8	dobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 259
# sent_id = 1
# text = The cyclic Chu - construction for closed bicategories with pullbacks, which generalizes the original Chu - construction for symmetric monoidal closed categories, turns out to have a non - cyclic counterpart.
1	The	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
2	cyclic	cyclic	ADJ	JJ	Degree=Pos	5	amod	_	_
3	Chu	Chu	PROPN	NNP	Number=Sing	5	compound	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	construction	construction	NOUN	NN	Number=Sing	25	nsubj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	closed	closed	ADJ	JJ	Degree=Pos	8	amod	_	_
8	bicategories	bicategorie	NOUN	NNS	Number=Plur	6	pobj	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	pullbacks	pullback	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	which	which	PRON	WDT	_	13	nsubj	_	_
13	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	relcl	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
15	original	original	ADJ	JJ	Degree=Pos	18	amod	_	_
16	Chu	Chu	PROPN	NNP	Number=Sing	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	construction	construction	NOUN	NN	Number=Sing	13	dobj	_	_
19	for	for	ADP	IN	_	18	prep	_	_
20	symmetric	symmetric	ADJ	JJ	Degree=Pos	23	amod	_	_
21	monoidal	monoidal	NOUN	NN	Number=Sing	23	amod	_	_
22	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	amod	_	_
23	categories	category	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
25	turns	turn	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
26	out	out	ADP	RP	_	25	prt	_	_
27	to	to	PART	TO	_	28	aux	_	_
28	have	have	VERB	VB	VerbForm=Inf	25	xcomp	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
30	non	non	ADJ	JJ	Degree=Pos	32	amod	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	cyclic	cyclic	ADJ	JJ	Degree=Pos	33	amod	_	_
33	counterpart	counterpart	NOUN	NN	Number=Sing	28	dobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	25	punct	_	SpaceAfter=No

# sent_id = 2
# text = Both use so - called Chu - spans as new 1 - cells between 1 - cells of the underlying bicategory, which form the new objects.
1	Both	both	PRON	DT	_	2	nsubj	_	_
2	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	so	so	ADV	RB	_	5	advmod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
6	Chu	Chu	PROPN	NNP	Number=Sing	8	compound	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	spans	span	NOUN	NNS	Number=Plur	2	dobj	_	_
9	as	as	ADP	IN	_	2	prep	_	_
10	new	new	ADJ	JJ	Degree=Pos	13	amod	_	_
11	1	1	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	cells	cell	NOUN	NNS	Number=Plur	9	pobj	_	_
14	between	between	ADP	IN	_	13	prep	_	_
15	1	1	NUM	CD	NumType=Card	17	nummod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	cells	cell	NOUN	NNS	Number=Plur	14	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	underlying	underlying	ADJ	JJ	Degree=Pos	21	amod	_	_
21	bicategory	bicategory	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	which	which	PRON	WDT	_	24	nsubj	_	_
24	form	form	VERB	VBP	Tense=Pres|VerbForm=Fin	21	relcl	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	new	new	ADJ	JJ	Degree=Pos	27	amod	_	_
27	objects	object	NOUN	NNS	Number=Plur	24	dobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Chu - spans may be seen as a natural generalization of 2 - cell - spans in the base bicategory that no longer are confined to a single hom - category.
1	Chu	Chu	PROPN	NNP	Number=Sing	3	compound	_	_
2	-	-	PUNCT	HYPH	PunctType=Dash	3	punct	_	_
3	spans	span	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
4	may	may	AUX	MD	VerbForm=Fin	6	aux	_	_
5	be	be	AUX	VB	VerbForm=Inf	6	auxpass	_	_
6	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	as	as	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	natural	natural	ADJ	JJ	Degree=Pos	10	amod	_	_
10	generalization	generalization	NOUN	NN	Number=Sing	7	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	2	2	NUM	CD	NumType=Card	14	nummod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	cell	cell	NOUN	NN	Number=Sing	16	compound	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	spans	span	NOUN	NNS	Number=Plur	11	pobj	_	_
17	in	in	ADP	IN	_	10	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	base	base	ADJ	JJ	Degree=Pos	20	compound	_	_
20	bicategory	bicategory	NOUN	NN	Number=Sing	17	pobj	_	_
21	that	that	PRON	WDT	PronType=Rel	25	nsubjpass	_	_
22	no	no	ADV	RB	_	23	neg	_	_
23	longer	long	ADV	RBR	Degree=Cmp	25	advmod	_	_
24	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	25	auxpass	_	_
25	confined	confine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	ccomp	_	_
26	to	to	ADP	IN	_	25	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
28	single	single	ADJ	JJ	Degree=Pos	31	amod	_	_
29	hom	hom	NOUN	NN	Number=Sing	31	amod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	category	category	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = This view helps to clarify the composition of Chu - spans.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	view	view	NOUN	NN	Number=Sing	3	nsubj	_	_
3	helps	help	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	clarify	clarify	VERB	VB	VerbForm=Inf	3	xcomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	composition	composition	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	Chu	Chu	PROPN	NNP	Number=Sing	11	compound	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	spans	span	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = We consider various approaches of linking the underlying bicategory with the newly constructed ones, for example by means of two - dimensional generalizations of bifibrations.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	various	various	ADJ	JJ	Degree=Pos	4	amod	_	_
4	approaches	approach	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	linking	link	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	underlying	underlying	ADJ	JJ	Degree=Pos	9	amod	_	_
9	bicategory	bicategory	NOUN	NN	Number=Sing	6	dobj	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
12	newly	newly	ADV	RB	_	13	advmod	_	_
13	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
14	ones	one	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
16	for	for	ADP	IN	_	2	prep	_	_
17	example	example	NOUN	NN	Number=Sing	16	pobj	_	_
18	by	by	ADP	IN	_	17	prep	_	_
19	means	mean	NOUN	NNS	Number=Plur	18	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	two	two	NUM	CD	NumType=Card	23	advmod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	dimensional	dimensional	ADJ	JJ	Degree=Pos	24	amod	_	_
24	generalizations	generalization	NOUN	NNS	Number=Plur	20	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	bifibrations	bifibration	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = In the quest for a better connection, we investigate, whether Chu - spans form a double category.
1	In	in	ADP	IN	_	10	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	quest	quest	NOUN	NN	Number=Sing	1	pobj	_	_
4	for	for	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	better	well	ADJ	JJR	Degree=Cmp	7	amod	_	_
7	connection	connection	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
9	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
10	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	whether	whether	SCONJ	IN	_	16	mark	_	_
13	Chu	Chu	PROPN	NNP	Number=Sing	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	spans	span	NOUN	NNS	Number=Plur	16	nsubj	_	_
16	form	form	VERB	VBP	Tense=Pres|VerbForm=Fin	10	ccomp	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	double	double	ADJ	JJ	Degree=Pos	19	amod	_	_
19	category	category	NOUN	NN	Number=Sing	16	dobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 7
# text = While this turns out not to be the case, we are led to considering a generalization of the construction to paths of 1 - cells in the base, leading to two hierarchies of closed bicategories, one for linear paths and one for loops.
1	While	while	SCONJ	IN	_	3	mark	_	_
2	this	this	PRON	DT	Number=Sing|PronType=Dem	3	nsubj	_	_
3	turns	turn	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	advcl	_	_
4	out	out	ADP	RP	_	3	prt	_	_
5	not	not	PART	RB	Polarity=Neg	7	neg	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	be	be	AUX	VB	VerbForm=Inf	3	xcomp	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	case	case	NOUN	NN	Number=Sing	7	attr	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
11	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubjpass	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	led	lead	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	considering	consider	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	pcomp	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	generalization	generalization	NOUN	NN	Number=Sing	15	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	construction	construction	NOUN	NN	Number=Sing	18	pobj	_	_
21	to	to	ADP	IN	_	15	prep	_	_
22	paths	path	NOUN	NNS	Number=Plur	21	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	1	1	NUM	CD	NumType=Card	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	cells	cell	NOUN	NNS	Number=Plur	23	pobj	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	base	base	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
31	leading	lead	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	advcl	_	_
32	to	to	ADP	IN	_	31	prep	_	_
33	two	two	NUM	CD	NumType=Card	34	nummod	_	_
34	hierarchies	hierarchy	NOUN	NNS	Number=Plur	32	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	closed	closed	ADJ	JJ	Degree=Pos	37	amod	_	_
37	bicategories	bicategorie	NOUN	NNS	Number=Plur	35	pobj	_	SpaceAfter=No
38	,	,	PUNCT	,	PunctType=Comm	34	punct	_	_
39	one	one	NUM	CD	NumType=Card	34	appos	_	_
40	for	for	ADP	IN	_	39	prep	_	_
41	linear	linear	ADJ	JJ	Degree=Pos	42	amod	_	_
42	paths	path	NOUN	NNS	Number=Plur	40	pobj	_	_
43	and	and	CCONJ	CC	ConjType=Cmp	39	cc	_	_
44	one	one	NUM	CD	NumType=Card	39	conj	_	_
45	for	for	ADP	IN	_	44	prep	_	_
46	loops	loop	NOUN	NNS	Number=Plur	45	pobj	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 8
# text = The possibility of moving beyond paths, respectively, loops of the same length is indicated.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	possibility	possibility	NOUN	NN	Number=Sing	16	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	moving	move	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	pcomp	_	_
5	beyond	beyond	ADP	IN	_	4	prep	_	_
6	paths	path	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
8	respectively	respectively	ADV	RB	_	10	advmod	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
10	loops	loop	NOUN	NNS	Number=Plur	16	nsubjpass	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	same	same	ADJ	JJ	Degree=Pos	14	amod	_	_
14	length	length	NOUN	NN	Number=Sing	11	pobj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	auxpass	_	_
16	indicated	indicate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 9
# text = Finally, Chu - spans in rel are identified as bipartite state transition systems.
1	Finally	finally	ADV	RB	_	9	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
3	Chu	Chu	PROPN	NNP	Number=Sing	5	compound	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	spans	spans	PROPN	NNPS	Number=Plur	9	nsubjpass	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	rel	rel	NOUN	NN	Number=Sing	6	pobj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	identified	identify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	as	as	ADP	IN	_	9	prep	_	_
11	bipartite	bipartite	ADJ	JJ	Degree=Pos	14	amod	_	_
12	state	state	NOUN	NN	Number=Sing	14	compound	_	_
13	transition	transition	NOUN	NN	Number=Sing	14	compound	_	_
14	systems	system	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 10
# text = Even though their composition may fail here due to the lack of pullbacks in $ rel $ , basic game - theoretic constructions can be performed on cyclic Chu - spans.
1	Even	even	ADV	RB	_	6	advmod	_	_
2	though	though	SCONJ	IN	_	6	mark	_	_
3	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	4	poss	_	_
4	composition	composition	NOUN	NN	Number=Sing	6	nsubj	_	_
5	may	may	AUX	MD	VerbForm=Fin	6	aux	_	_
6	fail	fail	VERB	VB	VerbForm=Inf	24	advcl	_	_
7	here	here	ADV	RB	PronType=Dem	6	advmod	_	_
8	due	due	ADP	IN	_	6	prep	_	_
9	to	to	ADP	IN	_	8	pcomp	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	lack	lack	NOUN	NN	Number=Sing	8	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	pullbacks	pullback	NOUN	NNS	Number=Plur	12	pobj	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	$ rel $	$ rel $	SYM	$	_	14	pobj	_	_
16	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
17	basic	basic	ADJ	JJ	Degree=Pos	21	amod	_	_
18	game	game	NOUN	NN	Number=Sing	20	npadvmod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	theoretic	theoretic	ADJ	JJ	Degree=Pos	21	amod	_	_
21	constructions	construction	NOUN	NNS	Number=Plur	24	nsubjpass	_	_
22	can	can	AUX	MD	VerbForm=Fin	24	aux	_	_
23	be	be	AUX	VB	VerbForm=Inf	24	auxpass	_	_
24	performed	perform	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
25	on	on	ADP	IN	_	24	prep	_	_
26	cyclic	cyclic	ADJ	JJ	Degree=Pos	29	compound	_	_
27	Chu	Chu	PROPN	NNP	Number=Sing	29	compound	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	spans	span	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# sent_id = 11
# text = These are available in all symmetric monoidal closed categories with finite products.
1	These	these	PRON	DT	Number=Plur|PronType=Dem	2	nsubj	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	available	available	ADJ	JJ	Degree=Pos	2	acomp	_	_
4	in	in	ADP	IN	_	3	prep	_	_
5	all	all	DET	DT	_	7	det	_	_
6	symmetric	symmetric	ADJ	JJ	Degree=Pos	7	amod	_	_
7	monoidal	monoidal	NOUN	NN	Number=Sing	4	pobj	_	_
8	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	2	conj	_	_
9	categories	category	NOUN	NNS	Number=Plur	8	dobj	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	finite	finite	ADJ	JJ	Degree=Pos	12	amod	_	_
12	products	product	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 12
# text = If pullbacks exist as well, the bicategory of cyclic Chu - spans inherits a monoidal structure that on objects coincides with the categorical product.
1	If	if	SCONJ	IN	_	3	mark	_	_
2	pullbacks	pullback	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	exist	exist	VERB	VBP	Tense=Pres|VerbForm=Fin	14	advcl	_	_
4	as	as	ADV	RB	_	5	advmod	_	_
5	well	well	ADV	RB	Degree=Pos	3	advmod	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	bicategory	bicategory	NOUN	NN	Number=Sing	14	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	cyclic	cyclic	ADJ	JJ	Degree=Pos	13	amod	_	_
11	Chu	Chu	PROPN	NNP	Number=Sing	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	spans	spans	PROPN	NNP	Number=Sing	9	pobj	_	_
14	inherits	inherit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	monoidal	monoidal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	structure	structure	NOUN	NN	Number=Sing	14	dobj	_	_
18	that	that	PRON	WDT	PronType=Rel	19	nsubj	_	_
19	on	on	ADP	IN	_	14	ccomp	_	_
20	objects	object	NOUN	NNS	Number=Plur	19	pobj	_	_
21	coincides	coincide	NOUN	NNS	Number=Plur	19	pobj	_	_
22	with	with	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	categorical	categorical	ADJ	JJ	Degree=Pos	25	amod	_	_
25	product	product	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# doc_id = 260
# sent_id = 1
# text = This paper serves to bring three independent but important areas of computer science to a common meeting point: Formal Concept Analysis, Chu Spaces, and Domain Theory.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	serves	serve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	bring	bring	VERB	VB	VerbForm=Inf	3	xcomp	_	_
6	three	three	NUM	CD	NumType=Card	10	nummod	_	_
7	independent	independent	ADJ	JJ	Degree=Pos	10	amod	_	_
8	but	but	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	important	important	ADJ	JJ	Degree=Pos	7	conj	_	_
10	areas	area	NOUN	NNS	Number=Plur	5	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	computer	computer	NOUN	NN	Number=Sing	13	compound	_	_
13	science	science	NOUN	NN	Number=Sing	11	pobj	_	_
14	to	to	ADP	IN	_	5	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
16	common	common	ADJ	JJ	Degree=Pos	18	amod	_	_
17	meeting	meeting	NOUN	NN	Number=Sing	18	compound	_	_
18	point	point	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
19	:	:	PUNCT	:	_	22	punct	_	_
20	Formal	Formal	PROPN	NNP	Number=Sing	22	compound	_	_
21	Concept	Concept	PROPN	NNP	Number=Sing	22	compound	_	_
22	Analysis	Analysis	PROPN	NNP	Number=Sing	3	dep	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	Chu	Chu	PROPN	NNP	Number=Sing	25	compound	_	_
25	Spaces	Spaces	PROPN	NNPS	Number=Plur	22	conj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
28	Domain	Domain	PROPN	NNP	Number=Sing	29	compound	_	_
29	Theory	Theory	PROPN	NNP	Number=Sing	25	conj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# sent_id = 2
# text = Each area is given a perspective or reformulation that is conducive to the flow of ideas and to the exploration of cross - disciplinary connections.
1	Each	each	DET	DT	_	2	det	_	_
2	area	area	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	perspective	perspective	NOUN	NN	Number=Sing	4	dobj	_	_
7	or	or	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	reformulation	reformulation	NOUN	NN	Number=Sing	6	conj	_	_
9	that	that	PRON	WDT	PronType=Rel	10	nsubj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	relcl	_	_
11	conducive	conducive	ADJ	JJ	Degree=Pos	10	acomp	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	flow	flow	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	ideas	idea	NOUN	NNS	Number=Plur	15	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
18	to	to	ADP	IN	_	12	conj	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	exploration	exploration	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	cross	cross	ADJ	JJ	Degree=Pos	25	amod	_	_
23	-	-	ADJ	JJ	Degree=Pos	25	amod	_	_
24	disciplinary	disciplinary	ADJ	JJ	Degree=Pos	25	amod	_	_
25	connections	connection	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = Among other results, we show that the notion of state in Scott's information system corresponds precisely to that of formal concepts in Formal Concept Analysis with respect to all finite Chu spaces, and the entailment relation corresponds to ``association rules".
1	Among	among	ADP	IN	_	6	prep	_	_
2	other	other	ADJ	JJ	Degree=Pos	3	amod	_	_
3	results	result	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	17	mark	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	notion	notion	NOUN	NN	Number=Sing	17	nsubj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	state	state	NOUN	NN	Number=Sing	10	pobj	_	_
12	in	in	ADP	IN	_	9	prep	_	_
13	Scott	Scott	PROPN	NNP	Number=Sing	16	poss	_	SpaceAfter=No
14	's	's	PART	POS	_	13	case	_	_
15	information	information	NOUN	NN	Number=Sing	16	compound	_	_
16	system	system	NOUN	NN	Number=Sing	12	pobj	_	_
17	corresponds	correspond	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
18	precisely	precisely	ADV	RB	_	19	advmod	_	_
19	to	to	ADP	IN	_	17	prep	_	_
20	that	that	PRON	DT	Number=Sing|PronType=Dem	19	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	formal	formal	ADJ	JJ	Degree=Pos	23	amod	_	_
23	concepts	concept	NOUN	NNS	Number=Plur	21	pobj	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	Formal	Formal	PROPN	NNP	Number=Sing	27	compound	_	_
26	Concept	Concept	PROPN	NNP	Number=Sing	27	compound	_	_
27	Analysis	Analysis	PROPN	NNP	Number=Sing	24	pobj	_	_
28	with	with	ADP	IN	_	23	prep	_	_
29	respect	respect	NOUN	NN	Number=Sing	28	pobj	_	_
30	to	to	ADP	IN	_	29	prep	_	_
31	all	all	DET	DT	_	34	det	_	_
32	finite	finite	PROPN	NNP	Number=Sing	34	compound	_	_
33	Chu	Chu	PROPN	NNP	Number=Sing	34	compound	_	_
34	spaces	space	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
35	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
38	entailment	entailment	ADJ	JJ	Degree=Pos	39	amod	_	_
39	relation	relation	NOUN	NN	Number=Sing	40	compound	_	_
40	corresponds	correspond	NOUN	NNS	Number=Plur	17	conj	_	_
41	to	to	ADP	IN	_	40	prep	_	_
42	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	41	punct	_	SpaceAfter=No
43	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	41	punct	_	SpaceAfter=No
44	association	association	NOUN	NN	Number=Sing	45	compound	_	_
45	rules	rule	NOUN	NNS	Number=Plur	41	pobj	_	SpaceAfter=No
46	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	40	punct	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = We introduce, moreover, the notion of approximable concept and show that approximable concepts represent algebraic lattices which are identical to Scott domains except the inclusion of a top element.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
4	moreover	moreover	ADV	RB	_	2	advmod	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	approximable	approximable	NOUN	NN	Number=Sing	10	compound	_	_
10	concept	concept	NOUN	NN	Number=Sing	8	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
12	show	show	VERB	VB	VerbForm=Inf	7	conj	_	_
13	that	that	SCONJ	IN	_	16	mark	_	_
14	approximable	approximable	NOUN	NN	Number=Sing	15	compound	_	_
15	concepts	concept	NOUN	NNS	Number=Plur	16	nsubj	_	_
16	represent	represent	VERB	VBP	Tense=Pres|VerbForm=Fin	12	ccomp	_	_
17	algebraic	algebraic	ADJ	JJ	Degree=Pos	18	amod	_	_
18	lattices	lattice	NOUN	NNS	Number=Plur	16	dobj	_	_
19	which	which	PRON	WDT	_	20	nsubj	_	_
20	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	18	relcl	_	_
21	identical	identical	ADJ	JJ	Degree=Pos	20	acomp	_	_
22	to	to	ADP	IN	_	21	prep	_	_
23	Scott	Scott	PROPN	NNP	Number=Sing	24	compound	_	_
24	domains	domain	NOUN	NNS	Number=Plur	22	pobj	_	_
25	except	except	SCONJ	IN	_	20	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	inclusion	inclusion	NOUN	NN	Number=Sing	25	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	top	top	ADJ	JJ	Degree=Pos	31	amod	_	_
31	element	element	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = This notion serves as a stepping stone in recent work in which a new notion of morphism on formal contexts results in a category equivalent to (i) the category of complete algebraic lattices and Scott continuous functions, and (ii) a category of information systems and approximable mappings.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	notion	notion	NOUN	NN	Number=Sing	3	nsubj	_	_
3	serves	serve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	as	as	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	stepping	stepping	ADJ	JJ	Degree=Pos	7	amod	_	_
7	stone	stone	NOUN	NN	Number=Sing	4	pobj	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	recent	recent	ADJ	JJ	Degree=Pos	10	amod	_	_
10	work	work	NOUN	NN	Number=Sing	8	pobj	_	_
11	in	in	ADP	IN	_	15	prep	_	_
12	which	which	PRON	WDT	_	11	pobj	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	new	new	ADJ	JJ	Degree=Pos	15	amod	_	_
15	notion	notion	NOUN	NN	Number=Sing	10	relcl	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	morphism	morphism	NOUN	NN	Number=Sing	16	pobj	_	_
18	on	on	ADP	IN	_	17	prep	_	_
19	formal	formal	ADJ	JJ	Degree=Pos	20	amod	_	_
20	contexts	context	NOUN	NNS	Number=Plur	18	pobj	_	_
21	results	result	NOUN	NNS	Number=Plur	18	pobj	_	_
22	in	in	ADP	IN	_	21	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	category	category	NOUN	NN	Number=Sing	22	pobj	_	_
25	equivalent	equivalent	ADJ	JJ	Degree=Pos	24	amod	_	_
26	to	to	ADP	IN	_	25	prep	_	_
27	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	26	punct	_	SpaceAfter=No
28	i	i	NOUN	NN	Case=Acc|Number=Sing|Person=1|PronType=Prs	26	pobj	_	SpaceAfter=No
29	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	28	punct	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	category	category	NOUN	NN	Number=Sing	15	appos	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	complete	complete	ADJ	JJ	Degree=Pos	35	amod	_	_
34	algebraic	algebraic	ADJ	JJ	Degree=Pos	35	amod	_	_
35	lattices	lattice	NOUN	NNS	Number=Plur	32	pobj	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
37	Scott	Scott	PROPN	NNP	Number=Sing	39	nmod	_	_
38	continuous	continuous	ADJ	JJ	Degree=Pos	39	amod	_	_
39	functions	function	NOUN	NNS	Number=Plur	35	conj	_	SpaceAfter=No
40	,	,	PUNCT	,	PunctType=Comm	39	punct	_	_
41	and	and	CCONJ	CC	ConjType=Cmp	39	cc	_	_
42	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	43	punct	_	SpaceAfter=No
43	ii	ii	PROPN	NNP	Number=Sing	39	conj	_	SpaceAfter=No
44	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	39	punct	_	_
45	a	a	DET	DT	Definite=Ind|PronType=Art	46	det	_	_
46	category	category	NOUN	NN	Number=Sing	39	appos	_	_
47	of	of	ADP	IN	_	46	prep	_	_
48	information	information	NOUN	NN	Number=Sing	49	compound	_	_
49	systems	system	NOUN	NNS	Number=Plur	47	pobj	_	_
50	and	and	CCONJ	CC	ConjType=Cmp	49	cc	_	_
51	approximable	approximable	NOUN	NN	Number=Sing	52	compound	_	_
52	mappings	mapping	NOUN	NNS	Number=Plur	49	conj	_	SpaceAfter=No
53	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 261
# sent_id = 1
# text = This paper describes a natural deduction formulation for Full Intuitionistic Linear Logic, an intriguing variation of multiplicative linear logic, due to Hyland and de Paiva.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	describes	describe	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	natural	natural	ADJ	JJ	Degree=Pos	6	amod	_	_
6	deduction	deduction	NOUN	NN	Number=Sing	7	compound	_	_
7	formulation	formulation	NOUN	NN	Number=Sing	3	dobj	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	Full	Full	PROPN	NNP	Number=Sing	12	compound	_	_
10	Intuitionistic	Intuitionistic	PROPN	NNP	Number=Sing	12	compound	_	_
11	Linear	Linear	PROPN	NNP	Number=Sing	12	compound	_	_
12	Logic	Logic	PROPN	NNP	Number=Sing	8	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	intriguing	intriguing	ADJ	JJ	Degree=Pos	16	amod	_	_
16	variation	variation	NOUN	NN	Number=Sing	12	appos	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	multiplicative	multiplicative	ADJ	JJ	Degree=Pos	20	amod	_	_
19	linear	linear	ADJ	JJ	Degree=Pos	20	compound	_	_
20	logic	logic	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
22	due	due	ADP	IN	_	3	prep	_	_
23	to	to	ADP	IN	_	22	pcomp	_	_
24	Hyland	Hyland	PROPN	NNP	Number=Sing	22	pobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	de	de	PROPN	NNP	Number=Sing	27	compound	_	_
27	Paiva	Paiva	PROPN	NNP	Number=Sing	24	conj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = Full Intuitionistic Linear Logic resembles intuitionistic logic, in that all its connectives are independent, but resembles classical logic in that its sequent - calculus formulation has intrinsic multiple conclusions.
1	Full	full	ADJ	JJ	Degree=Pos	4	amod	_	_
2	Intuitionistic	Intuitionistic	PROPN	NNP	Number=Sing	4	compound	_	_
3	Linear	Linear	PROPN	NNP	Number=Sing	4	compound	_	_
4	Logic	Logic	PROPN	NNP	Number=Sing	5	nsubj	_	_
5	resembles	resemble	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	intuitionistic	intuitionistic	ADJ	JJ	Degree=Pos	7	amod	_	_
7	logic	logic	NOUN	NN	Number=Sing	5	dobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
9	in	in	SCONJ	IN	_	14	mark	_	_
10	that	that	SCONJ	IN	_	14	mark	_	_
11	all	all	DET	PDT	_	13	predet	_	_
12	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	13	poss	_	_
13	connectives	connective	NOUN	NNS	Number=Plur	14	nsubj	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	advcl	_	_
15	independent	independent	ADJ	JJ	Degree=Pos	14	acomp	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
17	but	but	CCONJ	CC	ConjType=Cmp	14	cc	_	_
18	resembles	resemble	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	conj	_	_
19	classical	classical	ADJ	JJ	Degree=Pos	20	amod	_	_
20	logic	logic	NOUN	NN	Number=Sing	18	dobj	_	_
21	in	in	ADP	IN	_	18	prep	_	_
22	that	that	SCONJ	IN	_	28	mark	_	_
23	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	27	poss	_	_
24	sequent	sequent	ADJ	JJ	Degree=Pos	26	amod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	calculus	calculus	NOUN	NN	Number=Sing	27	compound	_	_
27	formulation	formulation	NOUN	NN	Number=Sing	28	nsubj	_	_
28	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	ccomp	_	_
29	intrinsic	intrinsic	ADJ	JJ	Degree=Pos	31	amod	_	_
30	multiple	multiple	ADJ	JJ	Degree=Pos	31	amod	_	_
31	conclusions	conclusion	NOUN	NNS	Number=Plur	28	dobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = From the intrinsic multiple conclusions comes the inspiration to modify Parigot's natural deduction systems for classical logic, to produce a natural deduction formulation and a term assignment system for FILL.
1	From	from	ADP	IN	_	6	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
3	intrinsic	intrinsic	ADJ	JJ	Degree=Pos	5	amod	_	_
4	multiple	multiple	ADJ	JJ	Degree=Pos	5	amod	_	_
5	conclusions	conclusion	NOUN	NNS	Number=Plur	1	pobj	_	_
6	comes	come	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	inspiration	inspiration	NOUN	NN	Number=Sing	6	nsubj	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	modify	modify	VERB	VB	VerbForm=Inf	8	acl	_	_
11	Parigot	Parigot	PROPN	NNP	Number=Sing	15	poss	_	SpaceAfter=No
12	's	's	PART	POS	_	11	case	_	_
13	natural	natural	ADJ	JJ	Degree=Pos	14	amod	_	_
14	deduction	deduction	NOUN	NN	Number=Sing	15	compound	_	_
15	systems	system	NOUN	NNS	Number=Plur	10	dobj	_	_
16	for	for	ADP	IN	_	15	prep	_	_
17	classical	classical	ADJ	JJ	Degree=Pos	18	amod	_	_
18	logic	logic	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
20	to	to	PART	TO	_	21	aux	_	_
21	produce	produce	VERB	VB	VerbForm=Inf	6	advcl	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
23	natural	natural	ADJ	JJ	Degree=Pos	24	amod	_	_
24	deduction	deduction	NOUN	NN	Number=Sing	25	compound	_	_
25	formulation	formulation	NOUN	NN	Number=Sing	21	dobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
28	term	term	NOUN	NN	Number=Sing	30	compound	_	_
29	assignment	assignment	NOUN	NN	Number=Sing	30	compound	_	_
30	system	system	NOUN	NN	Number=Sing	25	conj	_	_
31	for	for	ADP	IN	_	30	prep	_	_
32	FILL	FILL	PROPN	NNP	Number=Sing	31	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 262
# sent_id = 1
# text = We show that any free $ * $ - autonomous category is equivalent (in a strict sense) to a free $ * $ - autonomous category in which the double - involution $ ( - )^{ } $ is the identity functor and the canonical isomorphism $ Asimeq A^{ } $ is an identity arrow for all $ A $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	10	mark	_	_
4	any	any	DET	DT	_	9	det	_	_
5	free	free	ADJ	JJ	Degree=Pos	9	amod	_	_
6	$ * $	$ * $	SYM	$	_	8	advmod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	autonomous	autonomous	ADJ	JJ	Degree=Pos	9	amod	_	_
9	category	category	NOUN	NN	Number=Sing	10	nsubj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
11	equivalent	equivalent	ADJ	JJ	Degree=Pos	10	acomp	_	_
12	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	11	punct	_	SpaceAfter=No
13	in	in	ADP	IN	_	11	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	strict	strict	ADJ	JJ	Degree=Pos	16	amod	_	_
16	sense	sense	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
17	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	13	punct	_	_
18	to	to	ADP	IN	_	11	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
20	free	free	ADJ	JJ	Degree=Pos	24	amod	_	_
21	$ * $	$ * $	SYM	$	_	23	advmod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	autonomous	autonomous	ADJ	JJ	Degree=Pos	24	amod	_	_
24	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
25	in	in	ADP	IN	_	32	prep	_	_
26	which	which	PRON	WDT	_	25	pobj	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
28	double	double	ADJ	JJ	Degree=Pos	30	amod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	involution	involution	NOUN	NN	Number=Sing	31	compound	_	_
31	$ ( - )^{ } $	$ ( - )^{ } $	SYM	$	_	32	nsubj	_	_
32	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	relcl	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
34	identity	identity	NOUN	NN	Number=Sing	35	compound	_	_
35	functor	functor	NOUN	NN	Number=Sing	32	attr	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
38	canonical	canonical	ADJ	JJ	Degree=Pos	39	amod	_	_
39	isomorphism	isomorphism	NOUN	NN	Number=Sing	35	conj	_	_
40	$ Asimeq A^{ } $	$ asimeq a^{ } $	SYM	$	_	41	nsubj	_	_
41	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
42	an	an	DET	DT	Definite=Ind|PronType=Art	44	det	_	_
43	identity	identity	NOUN	NN	Number=Sing	44	compound	_	_
44	arrow	arrow	NOUN	NN	Number=Sing	41	attr	_	_
45	for	for	ADP	IN	_	44	prep	_	_
46	all	all	DET	DT	_	47	det	_	_
47	$ A $	$ a $	SYM	$	_	45	pobj	_	_
48	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 263
# sent_id = 1
# text = This paper describes the historical background and motivation involved in the discovery (or invention) of Chu categories.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	describes	describe	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	historical	historical	ADJ	JJ	Degree=Pos	6	amod	_	_
6	background	background	NOUN	NN	Number=Sing	3	dobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	motivation	motivation	NOUN	NN	Number=Sing	6	conj	_	_
9	involved	involve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	discovery	discovery	NOUN	NN	Number=Sing	10	pobj	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
14	or	or	CCONJ	CC	ConjType=Cmp	12	cc	_	_
15	invention	invention	NOUN	NN	Number=Sing	12	conj	_	SpaceAfter=No
16	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	15	punct	_	_
17	of	of	ADP	IN	_	15	prep	_	_
18	Chu	Chu	PROPN	NNP	Number=Sing	19	compound	_	_
19	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 264
# sent_id = 1
# text = We define and study familial 2 - functors primarily with a view to the development of the 2 - categorical approach to operads of Weber.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	study	study	VERB	VB	VerbForm=Inf	2	conj	_	_
5	familial	familial	ADJ	JJ	Degree=Pos	8	amod	_	_
6	2	2	NUM	CD	NumType=Card	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	functors	functor	NOUN	NNS	Number=Plur	4	dobj	_	_
9	primarily	primarily	ADV	RB	_	10	advmod	_	_
10	with	with	ADP	IN	_	4	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	view	view	NOUN	NN	Number=Sing	10	pobj	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	development	development	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
18	2	2	NUM	CD	NumType=Card	20	nummod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	categorical	categorical	ADJ	JJ	Degree=Pos	21	amod	_	_
21	approach	approach	NOUN	NN	Number=Sing	16	pobj	_	_
22	to	to	ADP	IN	_	21	prep	_	_
23	operads	operad	NOUN	NNS	Number=Plur	22	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	Weber	Weber	PROPN	NNP	Number=Sing	24	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Also included in this paper is a result in which the well - known characterisation of a category as a simplicial set via the Segal condition, is generalised to a result about nice monads on cocomplete categories.
1	Also	also	ADV	RB	_	2	advmod	_	_
2	included	include	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	advcl	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	paper	paper	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	auxpass	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	result	result	NOUN	NN	Number=Sing	6	attr	_	_
9	in	in	ADP	IN	_	15	prep	_	_
10	which	which	PRON	WDT	_	9	pobj	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
12	well	well	ADV	RB	Degree=Pos	14	advmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
15	characterisation	characterisation	NOUN	NN	Number=Sing	8	relcl	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	category	category	NOUN	NN	Number=Sing	16	pobj	_	_
19	as	as	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	simplicial	simplicial	NOUN	NN	Number=Sing	19	pobj	_	_
22	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	acl	_	_
23	via	via	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	Segal	Segal	PROPN	NNP	Number=Sing	26	compound	_	_
26	condition	condition	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	auxpass	_	_
29	generalised	generalise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
30	to	to	ADP	IN	_	29	prep	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
32	result	result	NOUN	NN	Number=Sing	30	pobj	_	_
33	about	about	ADP	IN	_	32	prep	_	_
34	nice	nice	ADJ	JJ	Degree=Pos	35	amod	_	_
35	monads	monad	NOUN	NNS	Number=Plur	33	pobj	_	_
36	on	on	ADP	IN	_	35	prep	_	_
37	cocomplete	cocomplete	ADJ	JJ	Degree=Pos	38	amod	_	_
38	categories	category	NOUN	NNS	Number=Plur	36	pobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	29	punct	_	SpaceAfter=No

# sent_id = 3
# text = Instances of this general result can be found in Leinster, Berger and Moerdijk - Weiss.
1	Instances	instance	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
4	general	general	ADJ	JJ	Degree=Pos	5	amod	_	_
5	result	result	NOUN	NN	Number=Sing	2	pobj	_	_
6	can	can	AUX	MD	VerbForm=Fin	8	aux	_	_
7	be	be	AUX	VB	VerbForm=Inf	8	auxpass	_	_
8	found	find	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	Leinster	Leinster	PROPN	NNP	Number=Sing	9	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	Berger	Berger	PROPN	NNP	Number=Sing	10	conj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	Moerdijk	Moerdijk	PROPN	NNP	Number=Sing	16	compound	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	Weiss	Weiss	PROPN	NNP	Number=Sing	12	conj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 4
# text = Aspects of this general theory are then used to show that the composite 2 - monads of Weber that describe symmetric and braided analogues of the $ omega $ - operads of Batanin, are cartesian 2 - monads and their underlying endo - 2 - functor is familial.
1	Aspects	aspect	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
4	general	general	ADJ	JJ	Degree=Pos	5	amod	_	_
5	theory	theory	NOUN	NN	Number=Sing	2	pobj	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
7	then	then	ADV	RB	PronType=Dem	8	advmod	_	_
8	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	show	show	VERB	VB	VerbForm=Inf	8	xcomp	_	_
11	that	that	SCONJ	IN	_	33	mark	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
13	composite	composite	ADJ	JJ	Degree=Pos	16	amod	_	_
14	2	2	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	monads	monad	NOUN	NNS	Number=Plur	33	nsubj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	Weber	Weber	PROPN	NNP	Number=Sing	17	pobj	_	_
19	that	that	PRON	WDT	PronType=Rel	20	nsubj	_	_
20	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	16	relcl	_	_
21	symmetric	symmetric	ADJ	JJ	Degree=Pos	24	amod	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	braided	braid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	conj	_	_
24	analogues	analogue	NOUN	NNS	Number=Plur	20	dobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
27	$ omega $	$ omega $	SYM	$	_	29	compound	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	operads	operad	NOUN	NNS	Number=Plur	25	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	Batanin	Batanin	PROPN	NNP	Number=Sing	30	pobj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
33	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	10	ccomp	_	_
34	cartesian	cartesian	ADJ	JJ	Degree=Pos	37	amod	_	_
35	2	2	NUM	CD	NumType=Card	37	nummod	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	monads	monad	NOUN	NNS	Number=Plur	46	nsubj	_	_
38	and	and	CCONJ	CC	ConjType=Cmp	37	cc	_	_
39	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	45	poss	_	_
40	underlying	underlie	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	45	amod	_	_
41	endo	endo	X	FW	Foreign=Yes	45	compound	_	_
42	-	-	PUNCT	HYPH	PunctType=Dash	43	punct	_	_
43	2	2	NUM	CD	NumType=Card	45	nummod	_	_
44	-	-	PUNCT	HYPH	PunctType=Dash	45	punct	_	_
45	functor	functor	NOUN	NN	Number=Sing	46	nsubj	_	_
46	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	conj	_	_
47	familial	familial	ADJ	JJ	Degree=Pos	46	acomp	_	SpaceAfter=No
48	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 5
# text = Intricately linked to the notion of familial 2 - functor is the theory of fibrations in a finitely complete 2 - category, and those aspects of that theory that we require, that weren't discussed in Weber's work, are reviewed here.
1	Intricately	intricately	ADV	RB	_	2	advmod	_	_
2	linked	link	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	notion	notion	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	familial	familial	ADJ	JJ	Degree=Pos	10	amod	_	_
8	2	2	NUM	CD	NumType=Card	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	functor	functor	NOUN	NN	Number=Sing	6	pobj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	auxpass	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	theory	theory	NOUN	NN	Number=Sing	11	attr	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	fibrations	fibration	NOUN	NNS	Number=Plur	14	pobj	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
18	finitely	finitely	ADV	RB	_	19	advmod	_	_
19	complete	complete	ADJ	JJ	Degree=Pos	22	amod	_	_
20	2	2	NUM	CD	NumType=Card	22	nummod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	category	category	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
25	those	those	DET	DT	Number=Plur|PronType=Dem	26	det	_	_
26	aspects	aspect	NOUN	NNS	Number=Plur	44	nsubjpass	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	that	that	DET	DT	Number=Sing|PronType=Dem	29	det	_	_
29	theory	theory	NOUN	NN	Number=Sing	27	pobj	_	_
30	that	that	SCONJ	IN	_	32	dobj	_	_
31	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	32	nsubj	_	_
32	require	require	VERB	VBP	Tense=Pres|VerbForm=Fin	26	relcl	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
34	that	that	PRON	WDT	PronType=Rel	37	nsubjpass	_	_
35	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	37	auxpass	_	SpaceAfter=No
36	n't	not	PART	RB	Polarity=Neg	37	neg	_	_
37	discussed	discuss	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	relcl	_	_
38	in	in	ADP	IN	_	37	prep	_	_
39	Weber	Weber	PROPN	NNP	Number=Sing	41	poss	_	SpaceAfter=No
40	's	's	PART	POS	_	39	case	_	_
41	work	work	NOUN	NN	Number=Sing	38	pobj	_	SpaceAfter=No
42	,	,	PUNCT	,	PunctType=Comm	44	punct	_	_
43	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	44	auxpass	_	_
44	reviewed	review	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	conj	_	_
45	here	here	ADV	RB	PronType=Dem	44	advmod	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 265
# sent_id = 1
# text = We classify the "quotients" of a tannakian category in which the objects of a tannakian subcategory become trivial, and we examine the properties of such quotient categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	classify	classify	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	5	punct	_	SpaceAfter=No
5	quotients	quotient	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
6	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	5	punct	_	_
7	of	of	ADP	IN	_	5	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	tannakian	tannakian	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
11	in	in	ADP	IN	_	19	prep	_	_
12	which	which	PRON	WDT	_	11	pobj	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	objects	object	NOUN	NNS	Number=Plur	19	nsubj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	tannakian	tannakian	ADJ	JJ	Degree=Pos	18	amod	_	_
18	subcategory	subcategory	NOUN	NN	Number=Sing	15	pobj	_	_
19	become	become	VERB	VBP	Tense=Pres|VerbForm=Fin	10	relcl	_	_
20	trivial	trivial	ADJ	JJ	Degree=Pos	19	acomp	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
23	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	24	nsubj	_	_
24	examine	examine	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	properties	property	NOUN	NNS	Number=Plur	24	dobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	such	such	ADJ	JJ	Degree=Pos	30	amod	_	_
29	quotient	quotient	ADJ	JJ	Degree=Pos	30	amod	_	_
30	categories	category	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# doc_id = 266
# sent_id = 1
# text = We prove that the monoidal 2 - category of cospans of ordinals and surjections is the universal monoidal category with an object $ X $ with a semigroup and a cosemigroup structures, where the two structures satisfy a certain 2 - dimensional separable algebra condition.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	15	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
5	monoidal	monoidal	ADJ	JJ	Degree=Pos	8	amod	_	_
6	2	2	NUM	CD	NumType=Card	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	category	category	NOUN	NN	Number=Sing	15	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	cospans	cospan	NOUN	NNS	Number=Plur	9	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	ordinals	ordinal	NOUN	NNS	Number=Plur	11	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	surjections	surjection	NOUN	NNS	Number=Plur	12	conj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
17	universal	universal	ADJ	JJ	Degree=Pos	19	amod	_	_
18	monoidal	monoidal	ADJ	JJ	Degree=Pos	19	amod	_	_
19	category	category	NOUN	NN	Number=Sing	15	attr	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	object	object	NOUN	NN	Number=Sing	20	pobj	_	_
23	$ X $	$ x $	SYM	$	_	22	appos	_	_
24	with	with	ADP	IN	_	22	prep	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
26	semigroup	semigroup	NOUN	NN	Number=Sing	24	pobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
29	cosemigroup	cosemigroup	ADJ	JJ	Degree=Pos	30	amod	_	_
30	structures	structure	NOUN	NNS	Number=Plur	26	conj	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
32	where	where	SCONJ	WRB	_	36	advmod	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
34	two	two	NUM	CD	NumType=Card	35	nummod	_	_
35	structures	structure	NOUN	NNS	Number=Plur	36	nsubj	_	_
36	satisfy	satisfy	VERB	VBP	Tense=Pres|VerbForm=Fin	30	relcl	_	_
37	a	a	DET	DT	Definite=Ind|PronType=Art	44	det	_	_
38	certain	certain	ADJ	JJ	Degree=Pos	44	amod	_	_
39	2	2	NUM	CD	NumType=Card	41	advmod	_	_
40	-	-	PUNCT	HYPH	PunctType=Dash	41	punct	_	_
41	dimensional	dimensional	ADJ	JJ	Degree=Pos	44	amod	_	_
42	separable	separable	ADJ	JJ	Degree=Pos	44	amod	_	_
43	algebra	algebra	NOUN	NN	Number=Sing	44	compound	_	_
44	condition	condition	NOUN	NN	Number=Sing	36	dobj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 267
# sent_id = 1
# text = Topological cospans and their concatenation, by pushout, appear in the theories of tangles, ribbons, cobordisms, et cetera.
1	Topological	topological	ADJ	JJ	Degree=Pos	2	amod	_	_
2	cospans	cospan	NOUN	NNS	Number=Plur	10	nsubj	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	5	poss	_	_
5	concatenation	concatenation	NOUN	NN	Number=Sing	2	conj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
7	by	by	ADP	IN	_	10	prep	_	_
8	pushout	pushout	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
10	appear	appear	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	theories	theory	NOUN	NNS	Number=Plur	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	tangles	tangle	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	ribbons	ribbon	NOUN	NNS	Number=Plur	15	conj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	cobordisms	cobordism	NOUN	NNS	Number=Plur	17	conj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	et	et	NOUN	NN	Number=Sing	22	compound	_	_
22	cetera	cetera	NOUN	NN	Number=Sing	19	conj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = Various algebraic invariants have been introduced for their study, which it would be interesting to link with the standard tools of Algebraic Topology, (co)homotopy and (co)homology functors.
1	Various	various	ADJ	JJ	Degree=Pos	3	amod	_	_
2	algebraic	algebraic	ADJ	JJ	Degree=Pos	3	amod	_	_
3	invariants	invariant	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
4	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	aux	_	_
5	been	be	AUX	VBN	Tense=Past|VerbForm=Part	6	auxpass	_	_
6	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	9	poss	_	_
9	study	study	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	which	which	PRON	WDT	_	17	dobj	_	_
12	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	14	nsubj	_	_
13	would	would	AUX	MD	VerbForm=Fin	14	aux	_	_
14	be	be	AUX	VB	VerbForm=Inf	9	relcl	_	_
15	interesting	interesting	ADJ	JJ	Degree=Pos	14	acomp	_	_
16	to	to	PART	TO	_	17	aux	_	_
17	link	link	VERB	VB	VerbForm=Inf	14	xcomp	_	_
18	with	with	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	standard	standard	ADJ	JJ	Degree=Pos	21	amod	_	_
21	tools	tool	NOUN	NNS	Number=Plur	18	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	Algebraic	Algebraic	PROPN	NNP	Number=Sing	24	compound	_	_
24	Topology	Topology	PROPN	NNP	Number=Sing	22	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
26	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	9	punct	_	SpaceAfter=No
27	co)homotopy	co)homotopy	NOUN	NN	Number=Sing	9	appos	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
29	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	27	punct	_	SpaceAfter=No
30	co)homology	co)homology	NOUN	NN	Number=Sing	31	compound	_	_
31	functors	functor	NOUN	NNS	Number=Plur	27	conj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = Here we introduce collarable (and collared) cospans between topological spaces.
1	Here	here	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	collarable	collarable	ADJ	JJ	Degree=Pos	9	amod	_	_
5	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	4	punct	_	SpaceAfter=No
6	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
7	collared	collared	ADJ	JJ	Degree=Pos	4	conj	_	SpaceAfter=No
8	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	7	punct	_	_
9	cospans	cospan	NOUN	NNS	Number=Plur	3	dobj	_	_
10	between	between	ADP	IN	_	9	prep	_	_
11	topological	topological	ADJ	JJ	Degree=Pos	12	amod	_	_
12	spaces	space	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = They generalise the cospans which appear in the previous theories, as a consequence of a classical theorem on manifolds with boundary.
1	They	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	2	nsubj	_	_
2	generalise	generalise	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	cospans	cospan	NOUN	NNS	Number=Plur	2	dobj	_	_
5	which	which	PRON	WDT	_	6	nsubj	_	_
6	appear	appear	VERB	VBP	Tense=Pres|VerbForm=Fin	4	relcl	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	previous	previous	ADJ	JJ	Degree=Pos	10	amod	_	_
10	theories	theory	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
12	as	as	ADP	IN	_	2	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	consequence	consequence	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	classical	classical	ADJ	JJ	Degree=Pos	18	amod	_	_
18	theorem	theorem	NOUN	NN	Number=Sing	15	pobj	_	_
19	on	on	ADP	IN	_	18	prep	_	_
20	manifolds	manifold	NOUN	NNS	Number=Plur	19	pobj	_	_
21	with	with	ADP	IN	_	18	prep	_	_
22	boundary	boundary	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = Their interest lies in the fact that their concatenation is realised by means of homotopy pushouts.
1	Their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	2	poss	_	_
2	interest	interest	NOUN	NN	Number=Sing	3	nsubj	_	_
3	lies	lie	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	in	in	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	fact	fact	NOUN	NN	Number=Sing	4	pobj	_	_
7	that	that	SCONJ	IN	_	11	mark	_	_
8	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	9	poss	_	_
9	concatenation	concatenation	NOUN	NN	Number=Sing	11	nsubjpass	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	realised	realise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
12	by	by	ADP	IN	_	11	agent	_	_
13	means	mean	NOUN	NNS	Number=Plur	12	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	homotopy	homotopy	NOUN	NN	Number=Sing	16	compound	_	_
16	pushouts	pushout	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = Therefore, cohomotopy functors induce `functors' from collarable cospans to spans of sets, providing—by linearisation—topological quantum field theories on manifolds and their cobordisms.
1	Therefore	therefore	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	cohomotopy	cohomotopy	NOUN	NN	Number=Sing	4	compound	_	_
4	functors	functor	NOUN	NNS	Number=Plur	5	nsubj	_	_
5	induce	induce	VERB	VB	VerbForm=Inf	0	ROOT	_	_
6	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	7	punct	_	SpaceAfter=No
7	functors	functor	NOUN	NNS	Number=Plur	5	dobj	_	SpaceAfter=No
8	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	7	case	_	_
9	from	from	ADP	IN	_	7	prep	_	_
10	collarable	collarable	ADJ	JJ	Degree=Pos	11	amod	_	_
11	cospans	cospan	NOUN	NNS	Number=Plur	9	pobj	_	_
12	to	to	ADP	IN	_	5	dative	_	_
13	spans	span	NOUN	NNS	Number=Plur	12	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	sets	set	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
17	providing	provide	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	advcl	_	SpaceAfter=No
18	—	—	PUNCT	:	_	17	punct	_	SpaceAfter=No
19	by	by	ADP	IN	_	17	prep	_	_
20	linearisation	linearisation	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
21	—	—	PUNCT	:	_	20	punct	_	SpaceAfter=No
22	topological	topological	ADJ	JJ	Degree=Pos	25	amod	_	_
23	quantum	quantum	NOUN	NN	Number=Sing	24	compound	_	_
24	field	field	NOUN	NN	Number=Sing	25	compound	_	_
25	theories	theory	NOUN	NNS	Number=Plur	17	dobj	_	_
26	on	on	ADP	IN	_	25	prep	_	_
27	manifolds	manifold	NOUN	NNS	Number=Plur	26	pobj	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
29	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	30	poss	_	_
30	cobordisms	cobordism	NOUN	NNS	Number=Plur	27	conj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 7
# text = Similarly, (co)homology and homotopy functors take collarable cospans to relations of abelian groups or (co)spans of groups, yielding other `algebraic' invariants.
1	Similarly	similarly	ADV	RB	_	8	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
3	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	8	punct	_	SpaceAfter=No
4	co)homology	co)homology	NOUN	NN	Number=Sing	7	nmod	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	homotopy	homotopy	NOUN	NN	Number=Sing	4	conj	_	_
7	functors	functor	NOUN	NNS	Number=Plur	8	nsubj	_	_
8	take	take	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	collarable	collarable	ADJ	JJ	Degree=Pos	10	amod	_	_
10	cospans	cospan	NOUN	NNS	Number=Plur	8	dobj	_	_
11	to	to	ADP	IN	_	8	prep	_	_
12	relations	relation	NOUN	NNS	Number=Plur	11	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	abelian	abelian	ADJ	JJ	Degree=Pos	15	compound	_	_
15	groups	group	NOUN	NNS	Number=Plur	13	pobj	_	_
16	or	or	CCONJ	CC	ConjType=Cmp	8	cc	_	_
17	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	18	punct	_	SpaceAfter=No
18	co)spans	co)span	NOUN	NNS	Number=Plur	8	conj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	groups	group	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
22	yielding	yield	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	advcl	_	_
23	other	other	ADJ	JJ	Degree=Pos	27	amod	_	_
24	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	27	punct	_	SpaceAfter=No
25	algebraic	algebraic	ADJ	JJ	Degree=Pos	27	amod	_	SpaceAfter=No
26	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	27	punct	_	_
27	invariants	invariant	NOUN	NNS	Number=Plur	22	dobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 8
# text = This is the second paper in a series devoted to the study of cospans in Algebraic Topology.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	second	second	ADJ	JJ	Degree=Pos	5	amod	_	_
5	paper	paper	NOUN	NN	Number=Sing	2	attr	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	series	series	NOUN	NN	Number=Sing	6	pobj	_	_
9	devoted	devote	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	study	study	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	cospans	cospan	NOUN	NNS	Number=Plur	13	pobj	_	_
15	in	in	ADP	IN	_	12	prep	_	_
16	Algebraic	Algebraic	PROPN	NNP	Number=Sing	17	compound	_	_
17	Topology	Topology	PROPN	NNP	Number=Sing	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 9
# text = It is practically independent from the first, which deals with higher cubical cospans in abstract categories.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	practically	practically	ADV	RB	_	4	advmod	_	_
4	independent	independent	ADJ	JJ	Degree=Pos	2	acomp	_	_
5	from	from	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	first	first	ADJ	JJ	Degree=Pos	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	which	which	PRON	WDT	_	10	nsubj	_	_
10	deals	deal	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	relcl	_	_
11	with	with	ADP	IN	_	10	prep	_	_
12	higher	high	ADJ	JJR	Degree=Cmp	14	amod	_	_
13	cubical	cubical	ADJ	JJ	Degree=Pos	14	amod	_	_
14	cospans	cospan	NOUN	NNS	Number=Plur	11	pobj	_	_
15	in	in	ADP	IN	_	10	prep	_	_
16	abstract	abstract	ADJ	JJ	Degree=Pos	17	amod	_	_
17	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 10
# text = The third article will proceed from both, studying cubical topological cospans and their collared version.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	third	third	ADJ	JJ	Degree=Pos	3	amod	_	_
3	article	article	NOUN	NN	Number=Sing	5	nsubj	_	_
4	will	will	AUX	MD	VerbForm=Fin	5	aux	_	_
5	proceed	proceed	VERB	VB	VerbForm=Inf	0	ROOT	_	_
6	from	from	ADP	IN	_	5	prep	_	_
7	both	both	PRON	DT	_	6	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
9	studying	study	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	advcl	_	_
10	cubical	cubical	ADJ	JJ	Degree=Pos	12	amod	_	_
11	topological	topological	ADJ	JJ	Degree=Pos	12	amod	_	_
12	cospans	cospan	NOUN	NNS	Number=Plur	9	dobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	16	poss	_	_
15	collared	collared	ADJ	JJ	Degree=Pos	16	amod	_	_
16	version	version	NOUN	NN	Number=Sing	12	conj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 268
# sent_id = 1
# text = Following the analogy between algebras (monoids) and monoidal categories the construction of nucleus for non - associative algebras is simulated on the categorical level.
1	Following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	analogy	analogy	NOUN	NN	Number=Sing	1	pobj	_	_
4	between	between	ADP	IN	_	3	prep	_	_
5	algebras	algebra	NOUN	NNS	Number=Plur	4	pobj	_	_
6	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	5	punct	_	SpaceAfter=No
7	monoids	monoid	NOUN	NNS	Number=Plur	5	appos	_	SpaceAfter=No
8	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	5	punct	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
10	monoidal	monoidal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	categories	category	NOUN	NNS	Number=Plur	5	conj	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	construction	construction	NOUN	NN	Number=Sing	22	nsubjpass	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	nucleus	nucleus	NOUN	NN	Number=Sing	14	pobj	_	_
16	for	for	ADP	IN	_	13	prep	_	_
17	non	non	ADJ	JJ	Degree=Pos	19	amod	_	_
18	-	-	ADJ	JJ	Degree=Pos	19	punct	_	_
19	associative	associative	ADJ	JJ	Degree=Pos	20	amod	_	_
20	algebras	algebra	NOUN	NNS	Number=Plur	16	pobj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	auxpass	_	_
22	simulated	simulate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
23	on	on	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	categorical	categorical	ADJ	JJ	Degree=Pos	26	amod	_	_
26	level	level	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# sent_id = 2
# text = Nuclei of categories of modules are considered as an example.
1	Nuclei	Nuclei	PROPN	NNP	Number=Sing	7	nsubjpass	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	categories	category	NOUN	NNS	Number=Plur	2	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	modules	module	NOUN	NNS	Number=Plur	4	pobj	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	as	as	ADP	IN	_	7	prep	_	_
9	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	example	example	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 269
# sent_id = 1
# text = We define the notion of an additive model category and prove that any stable, additive, combinatorial model category $ cal M $ has a model enrichment over $ Sp^Sigma(sAb) $ (symmetric spectra based on simplicial abelian groups).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	additive	additive	ADJ	JJ	Degree=Pos	9	amod	_	_
8	model	model	NOUN	NN	Number=Sing	9	compound	_	_
9	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
11	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
12	that	that	SCONJ	IN	_	22	mark	_	_
13	any	any	DET	DT	_	20	det	_	_
14	stable	stable	ADJ	JJ	Degree=Pos	20	amod	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
16	additive	additive	ADJ	JJ	Degree=Pos	20	amod	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
18	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	19	amod	_	_
19	model	model	NOUN	NN	Number=Sing	20	compound	_	_
20	category	category	NOUN	NN	Number=Sing	22	nsubj	_	_
21	$ cal M $	$ cal m $	SYM	$	_	20	appos	_	_
22	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	ccomp	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	model	model	NOUN	NN	Number=Sing	25	compound	_	_
25	enrichment	enrichment	NOUN	NN	Number=Sing	22	dobj	_	_
26	over	over	ADP	IN	_	25	prep	_	_
27	$ Sp^Sigma(sAb) $	$ sp^sigma(sab) $	SYM	$	_	26	pobj	_	_
28	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	30	punct	_	SpaceAfter=No
29	symmetric	symmetric	ADJ	JJ	Degree=Pos	30	amod	_	_
30	spectra	spectra	NOUN	NN	Number=Sing	27	appos	_	_
31	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	30	acl	_	_
32	on	on	ADP	IN	_	31	prep	_	_
33	simplicial	simplicial	ADJ	JJ	Degree=Pos	35	amod	_	_
34	abelian	abelian	ADJ	JJ	Degree=Pos	35	compound	_	_
35	groups	group	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
36	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	30	punct	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = So to any object $ X $ in $ cal M $ one can attach an endomorphism ring object, denoted $ hEnd_ad(X) $ , in the category $ Sp^Sigma(sAb) $ .
1	So	so	ADV	RB	_	10	advmod	_	_
2	to	to	ADP	IN	_	10	prep	_	_
3	any	any	DET	DT	_	4	det	_	_
4	object	object	NOUN	NN	Number=Sing	2	pobj	_	_
5	$ X $	$ x $	SYM	$	_	4	appos	_	_
6	in	in	ADP	IN	_	4	prep	_	_
7	$ cal M $	$ cal m $	SYM	$	_	8	nmod	_	_
8	one	one	PRON	PRP	PronType=Prs	6	pobj	_	_
9	can	can	AUX	MD	VerbForm=Fin	10	aux	_	_
10	attach	attach	VERB	VB	VerbForm=Inf	0	ROOT	_	_
11	an	an	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
12	endomorphism	endomorphism	NOUN	NN	Number=Sing	14	compound	_	_
13	ring	ring	NOUN	NN	Number=Sing	14	compound	_	_
14	object	object	NOUN	NN	Number=Sing	10	dobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
16	denoted	denote	VERB	VBD	Tense=Past|VerbForm=Fin	10	conj	_	_
17	$ hEnd_ad(X) $	$ hend_ad(x) $	SYM	$	_	16	dobj	_	_
18	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
19	in	in	ADP	IN	_	16	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	category	category	NOUN	NN	Number=Sing	19	pobj	_	_
22	$ Sp^Sigma(sAb) $	$ sp^sigma(sab) $	SYM	$	_	16	conj	_	_
23	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 3
# text = We establish some useful properties of these endomorphism rings.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	establish	establish	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	some	some	DET	DT	_	5	det	_	_
4	useful	useful	ADJ	JJ	Degree=Pos	5	amod	_	_
5	properties	property	NOUN	NNS	Number=Plur	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	these	these	DET	DT	Number=Plur|PronType=Dem	9	det	_	_
8	endomorphism	endomorphism	NOUN	NN	Number=Sing	9	compound	_	_
9	rings	ring	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We also develop a new notion in enriched category theory which we call `adjoint modules'.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	new	new	ADJ	JJ	Degree=Pos	6	amod	_	_
6	notion	notion	NOUN	NN	Number=Sing	3	dobj	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
9	category	category	NOUN	NN	Number=Sing	10	compound	_	_
10	theory	theory	NOUN	NN	Number=Sing	7	pobj	_	_
11	which	which	PRON	WDT	_	13	dobj	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	6	relcl	_	_
14	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	16	punct	_	SpaceAfter=No
15	adjoint	adjoint	NOUN	NN	Number=Sing	16	compound	_	_
16	modules	module	NOUN	NNS	Number=Plur	13	oprd	_	SpaceAfter=No
17	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	3	punct	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = This is used to compare enrichments over one symmetric monoidal model category with enrichments over a Quillen equivalent one.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	compare	compare	VERB	VB	VerbForm=Inf	3	xcomp	_	_
6	enrichments	enrichment	NOUN	NNS	Number=Plur	5	dobj	_	_
7	over	over	ADP	IN	_	5	prep	_	_
8	one	one	NUM	CD	NumType=Card	12	nummod	_	_
9	symmetric	symmetric	ADJ	JJ	Degree=Pos	12	amod	_	_
10	monoidal	monoidal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	model	model	NOUN	NN	Number=Sing	12	compound	_	_
12	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
13	with	with	ADP	IN	_	5	prep	_	_
14	enrichments	enrichment	NOUN	NNS	Number=Plur	13	pobj	_	_
15	over	over	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
17	Quillen	quillen	ADJ	JJ	Degree=Pos	19	amod	_	_
18	equivalent	equivalent	ADJ	JJ	Degree=Pos	19	amod	_	_
19	one	one	NUM	CD	NumType=Card	15	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = In particular, it is used here to compare enrichments over $ Sp^Sigma(sAb) $ and chain complexes.
1	In	in	ADP	IN	_	6	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
4	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	6	nsubjpass	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	here	here	ADV	RB	PronType=Dem	6	advmod	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	compare	compare	VERB	VB	VerbForm=Inf	6	xcomp	_	_
10	enrichments	enrichment	NOUN	NNS	Number=Plur	9	dobj	_	_
11	over	over	ADP	IN	_	9	prep	_	_
12	$ Sp^Sigma(sAb) $	$ sp^sigma(sab) $	SYM	$	_	11	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	chain	chain	NOUN	NN	Number=Sing	15	compound	_	_
15	complexes	complex	NOUN	NNS	Number=Plur	12	conj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 270
# sent_id = 1
# text = Given an arbitrary locally finitely presentable category $ K $ and finitary monads $ T $ and $ S $ on $ K $ , we characterize monad morphisms $ alpha: Sto T $ with the property that the induced functor $ alpha_*: K^T to K^ S $ between the categories of Eilenberg - Moore algebras is fully faithful.
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
3	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	7	amod	_	_
4	locally	locally	ADV	RB	_	5	advmod	_	_
5	finitely	finitely	ADV	RB	_	6	advmod	_	_
6	presentable	presentable	ADJ	JJ	Degree=Pos	7	amod	_	_
7	category	category	NOUN	NN	Number=Sing	1	pobj	_	_
8	$ K $	$ k $	SYM	$	_	7	appos	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
10	finitary	finitary	ADJ	JJ	Degree=Pos	11	amod	_	_
11	monads	monad	NOUN	NNS	Number=Plur	7	conj	_	_
12	$ T $	$ t $	SYM	$	_	11	dobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
14	$ S $	$ s $	SYM	$	_	1	dep	_	_
15	on	on	ADP	IN	_	1	prep	_	_
16	$ K $	$ k $	SYM	$	_	15	pobj	_	_
17	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	monad	monad	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	dobj	_	_
21	morphisms	morphism	NOUN	NNS	Number=Plur	20	dobj	_	_
22	$ alpha: Sto T $	$ alpha: sto t $	SYM	$	_	20	dep	_	_
23	with	with	ADP	IN	_	20	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	property	property	NOUN	NN	Number=Sing	23	pobj	_	_
26	that	that	PRON	WDT	PronType=Rel	39	nsubj	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	amod	_	_
29	functor	functor	NOUN	NN	Number=Sing	39	nsubj	_	_
30	$ alpha_*: K^T to K^ S $	$ alpha_*: k^t to k^ s $	SYM	$	_	29	dep	_	_
31	between	between	ADP	IN	_	29	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
33	categories	category	NOUN	NNS	Number=Plur	31	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	37	compound	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	Moore	Moore	PROPN	NNP	Number=Sing	38	compound	_	_
38	algebras	algebra	NOUN	NNS	Number=Plur	34	pobj	_	_
39	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	relcl	_	_
40	fully	fully	ADV	RB	_	41	advmod	_	_
41	faithful	faithful	ADJ	JJ	Degree=Pos	39	acomp	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 2
# text = We call such monad morphisms dense and give a characterization of them in the spirit of Beth's definability theorem: $ alpha $ is a dense monad morphism if and only if every $ T $ - operation is explicitly defined using $ S $ - operations.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	such	such	ADJ	JJ	Degree=Pos	4	amod	_	_
4	monad	monad	NOUN	NNS	Number=Plur	2	dobj	_	_
5	morphisms	morphism	NOUN	NNS	Number=Plur	6	nsubj	_	_
6	dense	dense	ADJ	JJ	Degree=Pos	2	oprd	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
8	give	give	VERB	VB	VerbForm=Inf	2	conj	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	characterization	characterization	NOUN	NN	Number=Sing	8	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	11	pobj	_	_
13	in	in	ADP	IN	_	8	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	spirit	spirit	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	Beth	Beth	PROPN	NNP	Number=Sing	19	poss	_	SpaceAfter=No
18	's	's	PART	POS	_	17	case	_	_
19	definability	definability	NOUN	NN	Number=Sing	16	pobj	_	_
20	theorem	theorem	ADJ	JJ	Degree=Pos	2	conj	_	SpaceAfter=No
21	:	:	PUNCT	:	_	20	punct	_	_
22	$ alpha $	$ alpha $	SYM	$	_	23	nsubj	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
25	dense	dense	ADJ	JJ	Degree=Pos	27	amod	_	_
26	monad	monad	NOUN	NNS	Number=Plur	27	compound	_	_
27	morphism	morphism	NOUN	NN	Number=Sing	23	attr	_	_
28	if	if	SCONJ	IN	_	2	prep	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	only	only	ADV	RB	_	38	advmod	_	_
31	if	if	SCONJ	IN	_	38	mark	_	_
32	every	every	DET	DT	_	35	det	_	_
33	$ T $	$ t $	SYM	$	_	35	compound	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	operation	operation	NOUN	NN	Number=Sing	38	nsubjpass	_	_
36	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	38	auxpass	_	_
37	explicitly	explicitly	ADV	RB	_	38	advmod	_	_
38	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	advcl	_	_
39	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	38	xcomp	_	_
40	$ S $	$ s $	SYM	$	_	42	compound	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	operations	operation	NOUN	NNS	Number=Plur	39	dobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also give a characterization in terms of epimorphic property of $ alpha $ and clarify the connection between various notions of epimorphisms between monads.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	characterization	characterization	NOUN	NN	Number=Sing	3	dobj	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	terms	term	NOUN	NNS	Number=Plur	6	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	epimorphic	epimorphic	ADJ	JJ	Degree=Pos	10	amod	_	_
10	property	property	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	$ alpha $	$ alpha $	SYM	$	_	11	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
14	clarify	clarify	VERB	VB	VerbForm=Inf	3	conj	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	connection	connection	NOUN	NN	Number=Sing	14	dobj	_	_
17	between	between	ADP	IN	_	16	prep	_	_
18	various	various	ADJ	JJ	Degree=Pos	19	amod	_	_
19	notions	notion	NOUN	NNS	Number=Plur	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	20	pobj	_	_
22	between	between	ADP	IN	_	21	prep	_	_
23	monads	monad	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 271
# sent_id = 1
# text = Loday introduced the concept of coherent unit actions on a regular operad and showed that such actions give Hopf algebra structures on the free algebras.
1	Loday	Loday	PROPN	NNP	Number=Sing	2	nsubj	_	_
2	introduced	introduce	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	concept	concept	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	coherent	coherent	ADJ	JJ	Degree=Pos	8	amod	_	_
7	unit	unit	NOUN	NN	Number=Sing	8	compound	_	_
8	actions	action	NOUN	NNS	Number=Plur	5	pobj	_	_
9	on	on	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	regular	regular	ADJ	JJ	Degree=Pos	12	amod	_	_
12	operad	operad	NOUN	NN	Number=Sing	9	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
14	showed	show	VERB	VBD	Tense=Past|VerbForm=Fin	2	conj	_	_
15	that	that	SCONJ	IN	_	18	mark	_	_
16	such	such	ADJ	JJ	Degree=Pos	17	amod	_	_
17	actions	action	NOUN	NNS	Number=Plur	18	nsubj	_	_
18	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	14	ccomp	_	_
19	Hopf	Hopf	PROPN	NNP	Number=Sing	21	compound	_	_
20	algebra	algebra	NOUN	NN	Number=Sing	21	compound	_	_
21	structures	structure	NOUN	NNS	Number=Plur	18	dobj	_	_
22	on	on	ADP	IN	_	18	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	free	free	ADJ	JJ	Degree=Pos	25	amod	_	_
25	algebras	algebra	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Hopf algebras obtained this way include the Hopf algebras of shuffles, quasi - shuffles and planar rooted trees.
1	Hopf	hopf	NOUN	NN	Number=Sing	2	compound	_	_
2	algebras	algebra	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	obtained	obtain	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	way	way	NOUN	NN	Number=Sing	3	npadvmod	_	_
6	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	3	dep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	Hopf	Hopf	PROPN	NNP	Number=Sing	9	compound	_	_
9	algebras	algebra	NOUN	NNS	Number=Plur	6	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	shuffles	shuffle	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	quasi	quasi	ADJ	JJ	Degree=Pos	9	conj	_	_
14	-	-	NOUN	NNS	Number=Plur	9	punct	_	_
15	shuffles	shuffle	NOUN	NNS	Number=Plur	9	conj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
17	planar	planar	VERB	VB	VerbForm=Inf	6	conj	_	_
18	rooted	rooted	ADJ	JJ	Degree=Pos	19	amod	_	_
19	trees	tree	NOUN	NNS	Number=Plur	17	dobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = We characterize coherent unit actions on binary quadratic regular operads in terms of linear equations of the generators of the operads.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	coherent	coherent	ADJ	JJ	Degree=Pos	5	amod	_	_
4	unit	unit	NOUN	NN	Number=Sing	5	compound	_	_
5	actions	action	NOUN	NNS	Number=Plur	2	dobj	_	_
6	on	on	ADP	IN	_	5	prep	_	_
7	binary	binary	ADJ	JJ	Degree=Pos	10	amod	_	_
8	quadratic	quadratic	ADJ	JJ	Degree=Pos	10	amod	_	_
9	regular	regular	ADJ	JJ	Degree=Pos	10	amod	_	_
10	operads	operad	NOUN	NNS	Number=Plur	6	pobj	_	_
11	in	in	ADP	IN	_	5	prep	_	_
12	terms	term	NOUN	NNS	Number=Plur	11	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	linear	linear	ADJ	JJ	Degree=Pos	15	amod	_	_
15	equations	equation	NOUN	NNS	Number=Plur	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	generators	generator	NOUN	NNS	Number=Plur	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	operads	operad	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We then use these equations to classify operads with coherent unit actions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	these	these	DET	DT	Number=Plur|PronType=Dem	5	det	_	_
5	equations	equation	NOUN	NNS	Number=Plur	3	dobj	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	classify	classify	VERB	VB	VerbForm=Inf	3	xcomp	_	_
8	operads	operad	NOUN	NNS	Number=Plur	7	dobj	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	coherent	coherent	ADJ	JJ	Degree=Pos	12	amod	_	_
11	unit	unit	NOUN	NN	Number=Sing	12	compound	_	_
12	actions	action	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = We further show that coherent unit actions are preserved under taking products and thus yield Hopf algebras on the free object of the product operads when the factor operads have coherent unit actions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	further	far	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	9	mark	_	_
5	coherent	coherent	ADJ	JJ	Degree=Pos	7	amod	_	_
6	unit	unit	NOUN	NN	Number=Sing	7	compound	_	_
7	actions	action	NOUN	NNS	Number=Plur	9	nsubjpass	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	preserved	preserve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	ccomp	_	_
10	under	under	ADP	IN	_	9	prep	_	_
11	taking	take	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	pcomp	_	_
12	products	product	NOUN	NNS	Number=Plur	11	dobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
14	thus	thus	ADV	RB	_	15	advmod	_	_
15	yield	yield	VERB	VB	VerbForm=Inf	11	conj	_	_
16	Hopf	hopf	NOUN	NN	Number=Sing	17	compound	_	_
17	algebras	algebra	NOUN	NNS	Number=Plur	15	dobj	_	_
18	on	on	ADP	IN	_	15	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	free	free	ADJ	JJ	Degree=Pos	21	amod	_	_
21	object	object	NOUN	NN	Number=Sing	18	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	product	product	NOUN	NN	Number=Sing	25	compound	_	_
25	operads	operad	NOUN	NNS	Number=Plur	22	pobj	_	_
26	when	when	SCONJ	WRB	_	30	advmod	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	factor	factor	NOUN	NN	Number=Sing	29	compound	_	_
29	operads	operad	NOUN	NNS	Number=Plur	30	nsubj	_	_
30	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	advcl	_	_
31	coherent	coherent	ADJ	JJ	Degree=Pos	33	amod	_	_
32	unit	unit	NOUN	NN	Number=Sing	33	compound	_	_
33	actions	action	NOUN	NNS	Number=Plur	30	dobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = On the other hand, coherent unit actions are never preserved under taking the dual in the operadic sense except for the operad of associative algebras.
1	On	on	ADP	IN	_	11	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	other	other	ADJ	JJ	Degree=Pos	4	amod	_	_
4	hand	hand	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
6	coherent	coherent	ADJ	JJ	Degree=Pos	7	amod	_	_
7	unit	unit	NOUN	NN	Number=Sing	8	compound	_	_
8	actions	action	NOUN	NNS	Number=Plur	11	nsubjpass	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
10	never	never	ADV	RB	_	11	neg	_	_
11	preserved	preserve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
12	under	under	ADP	IN	_	11	prep	_	_
13	taking	take	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	pcomp	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	dual	dual	ADJ	JJ	Degree=Pos	13	dobj	_	_
16	in	in	ADP	IN	_	13	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	operadic	operadic	ADJ	JJ	Degree=Pos	19	amod	_	_
19	sense	sense	NOUN	NN	Number=Sing	16	pobj	_	_
20	except	except	SCONJ	IN	_	13	prep	_	_
21	for	for	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	operad	operad	NOUN	NN	Number=Sing	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	associative	associative	ADJ	JJ	Degree=Pos	26	amod	_	_
26	algebras	algebra	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# doc_id = 272
# sent_id = 1
# text = We define a notion of weak cubical category, abstracted from the structure of $ n $ - cubical cospans $ x : wedge^n to X $ in a category $ X $ where $ wedge $ is the `formal cospan' category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	weak	weak	ADJ	JJ	Degree=Pos	8	amod	_	_
7	cubical	cubical	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
10	abstracted	abstract	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	acl	_	_
11	from	from	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	structure	structure	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	$ n $	$ n $	SYM	$	_	17	advmod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	cubical	cubical	ADJ	JJ	Degree=Pos	18	amod	_	_
18	cospans	cospan	NOUN	NNS	Number=Plur	14	pobj	_	_
19	$ x : wedge^n to X $	$ x : wedge^n to x $	SYM	$	_	18	appos	_	_
20	in	in	ADP	IN	_	10	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	category	category	NOUN	NN	Number=Sing	20	pobj	_	_
23	$ X $	$ x $	SYM	$	_	22	nummod	_	_
24	where	where	SCONJ	WRB	_	26	advmod	_	_
25	$ wedge $	$ wedge $	SYM	$	_	26	nsubj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	relcl	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
28	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	30	punct	_	SpaceAfter=No
29	formal	formal	ADJ	JJ	Degree=Pos	30	amod	_	_
30	cospan	cospan	NOUN	NN	Number=Sing	32	poss	_	SpaceAfter=No
31	'	'	PART	POS	_	30	case	_	_
32	category	category	NOUN	NN	Number=Sing	26	attr	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = These diagrams form a cubical set with compositions $ x +_i y $ in all directions, which are computed using pushouts and behave `categorically' in a weak sense, up to suitable comparisons.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	diagrams	diagram	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	form	form	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	cubical	cubical	ADJ	JJ	Degree=Pos	6	amod	_	_
6	set	set	NOUN	NN	Number=Sing	3	dobj	_	_
7	with	with	ADP	IN	_	3	prep	_	_
8	compositions	composition	NOUN	NNS	Number=Plur	7	pobj	_	_
9	$ x +_i y $	$ x +_i y $	SYM	$	_	3	dep	_	_
10	in	in	ADP	IN	_	3	prep	_	_
11	all	all	DET	DT	_	12	det	_	_
12	directions	direction	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	which	which	PRON	WDT	_	16	nsubjpass	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	16	auxpass	_	_
16	computed	compute	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	relcl	_	_
17	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	xcomp	_	_
18	pushouts	pushout	NOUN	NNS	Number=Plur	17	dobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	behave	behave	VERB	VB	VerbForm=Inf	18	conj	_	_
21	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	22	punct	_	SpaceAfter=No
22	categorically	categorically	ADV	RB	_	16	advmod	_	SpaceAfter=No
23	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	16	punct	_	_
24	in	in	ADP	IN	_	16	prep	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
26	weak	weak	ADJ	JJ	Degree=Pos	27	amod	_	_
27	sense	sense	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
29	up	up	ADP	IN	_	3	prep	_	_
30	to	to	ADP	IN	_	29	prep	_	_
31	suitable	suitable	ADJ	JJ	Degree=Pos	32	amod	_	_
32	comparisons	comparison	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Actually, we work with a `symmetric cubical structure', which includes the transposition symmetries, because this allows for a strong simplification of the coherence conditions.
1	Actually	actually	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	work	work	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	with	with	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
7	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	10	punct	_	SpaceAfter=No
8	symmetric	symmetric	ADJ	JJ	Degree=Pos	10	amod	_	_
9	cubical	cubical	ADJ	JJ	Degree=Pos	10	amod	_	_
10	structure	structure	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
11	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	10	punct	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
13	which	which	PRON	WDT	_	14	nsubj	_	_
14	includes	include	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	relcl	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	transposition	transposition	NOUN	NN	Number=Sing	17	compound	_	_
17	symmetries	symmetry	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
19	because	because	SCONJ	IN	_	21	mark	_	_
20	this	this	PRON	DT	Number=Sing|PronType=Dem	21	nsubj	_	_
21	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	advcl	_	_
22	for	for	ADP	IN	_	21	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	strong	strong	ADJ	JJ	Degree=Pos	25	amod	_	_
25	simplification	simplification	NOUN	NN	Number=Sing	22	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	coherence	coherence	NOUN	NN	Number=Sing	29	compound	_	_
29	conditions	condition	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = These notions will be used in subsequent papers to study topological cospans and their use in Algebraic Topology, from tangles to cobordisms of manifolds.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	notions	notion	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
3	will	will	AUX	MD	VerbForm=Fin	5	aux	_	_
4	be	be	AUX	VB	VerbForm=Inf	5	auxpass	_	_
5	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	subsequent	subsequent	ADJ	JJ	Degree=Pos	8	amod	_	_
8	papers	paper	NOUN	NNS	Number=Plur	6	pobj	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	study	study	VERB	VB	VerbForm=Inf	5	xcomp	_	_
11	topological	topological	ADJ	JJ	Degree=Pos	12	amod	_	_
12	cospans	cospan	NOUN	NNS	Number=Plur	10	dobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	15	poss	_	_
15	use	use	NOUN	NN	Number=Sing	12	conj	_	_
16	in	in	ADP	IN	_	10	prep	_	_
17	Algebraic	Algebraic	PROPN	NNP	Number=Sing	18	compound	_	_
18	Topology	Topology	PROPN	NNP	Number=Sing	16	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
20	from	from	ADP	IN	_	10	prep	_	_
21	tangles	tangle	NOUN	NNS	Number=Plur	20	pobj	_	_
22	to	to	ADP	IN	_	20	prep	_	_
23	cobordisms	cobordism	NOUN	NNS	Number=Plur	22	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	manifolds	manifold	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = We also introduce the more general notion of a multiple category, where—to start with—arrows belong to different sorts, varying in a countable family, and symmetries must be dropped.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	more	more	ADV	RBR	Degree=Cmp	6	advmod	_	_
6	general	general	ADJ	JJ	Degree=Pos	7	amod	_	_
7	notion	notion	NOUN	NN	Number=Sing	3	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	multiple	multiple	ADJ	JJ	Degree=Pos	11	amod	_	_
11	category	category	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	where	where	SCONJ	WRB	_	20	advmod	_	SpaceAfter=No
14	—	—	PUNCT	:	_	13	punct	_	SpaceAfter=No
15	to	to	PART	TO	_	16	aux	_	_
16	start	start	VERB	VB	VerbForm=Inf	13	nmod	_	_
17	with	with	ADP	IN	_	16	prep	_	SpaceAfter=No
18	—	—	PUNCT	:	_	20	punct	_	SpaceAfter=No
19	arrows	arrow	NOUN	NNS	Number=Plur	20	nsubj	_	_
20	belong	belong	VERB	VBP	Tense=Pres|VerbForm=Fin	11	relcl	_	_
21	to	to	ADP	IN	_	20	prep	_	_
22	different	different	ADJ	JJ	Degree=Pos	23	amod	_	_
23	sorts	sort	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
25	varying	vary	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	advcl	_	_
26	in	in	ADP	IN	_	25	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	countable	countable	ADJ	JJ	Degree=Pos	29	amod	_	_
29	family	family	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
32	symmetries	symmetry	NOUN	NNS	Number=Plur	35	nsubjpass	_	_
33	must	must	AUX	MD	VerbForm=Fin	35	aux	_	_
34	be	be	AUX	VB	VerbForm=Inf	35	auxpass	_	_
35	dropped	drop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	conj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	35	punct	_	SpaceAfter=No

# sent_id = 6
# text = The present examples seem to show that the symmetric cubical case is better suited for topological applications.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	present	present	ADJ	JJ	Degree=Pos	3	amod	_	_
3	examples	example	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	seem	seem	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	show	show	VERB	VB	VerbForm=Inf	4	xcomp	_	_
7	that	that	SCONJ	IN	_	14	mark	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
9	symmetric	symmetric	ADJ	JJ	Degree=Pos	11	amod	_	_
10	cubical	cubical	ADJ	JJ	Degree=Pos	11	amod	_	_
11	case	case	NOUN	NN	Number=Sing	14	nsubjpass	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
13	better	well	ADV	RBR	Degree=Cmp	14	advmod	_	_
14	suited	suit	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	ccomp	_	_
15	for	for	ADP	IN	_	14	prep	_	_
16	topological	topological	ADJ	JJ	Degree=Pos	17	amod	_	_
17	applications	application	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 273
# sent_id = 1
# text = We discuss an approach to constructing a weak $ n $ - category of cobordisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	discuss	discuss	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	approach	approach	NOUN	NN	Number=Sing	2	dobj	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	constructing	construct	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	weak	weak	ADJ	JJ	Degree=Pos	11	amod	_	_
9	$ n $	$ n $	SYM	$	_	11	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	category	category	NOUN	NN	Number=Sing	6	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	cobordisms	cobordism	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = First we present a generalisation of Trimble's definition of $ n $ - category which seems most appropriate for this construction; in this definition composition is parametrised by a contractible operad.
1	First	first	ADV	RB	_	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	27	ccomp	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	generalisation	generalisation	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Trimble	Trimble	PROPN	NNP	Number=Sing	9	poss	_	SpaceAfter=No
8	's	's	PART	POS	_	7	case	_	_
9	definition	definition	NOUN	NN	Number=Sing	6	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	$ n $	$ n $	SYM	$	_	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
14	which	which	PRON	WDT	_	15	nsubj	_	_
15	seems	seem	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	relcl	_	_
16	most	most	ADV	RBS	Degree=Sup	17	advmod	_	_
17	appropriate	appropriate	ADJ	JJ	Degree=Pos	15	oprd	_	_
18	for	for	ADP	IN	_	17	prep	_	_
19	this	this	DET	DT	Number=Sing|PronType=Dem	20	det	_	_
20	construction	construction	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
21	;	;	PUNCT	:	_	27	punct	_	_
22	in	in	ADP	IN	_	27	prep	_	_
23	this	this	DET	DT	Number=Sing|PronType=Dem	25	det	_	_
24	definition	definition	NOUN	NN	Number=Sing	25	compound	_	_
25	composition	composition	NOUN	NN	Number=Sing	27	nsubjpass	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	auxpass	_	_
27	parametrised	parametrise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
28	by	by	ADP	IN	_	27	agent	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	contractible	contractible	ADJ	JJ	Degree=Pos	31	amod	_	_
31	operad	operad	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	27	punct	_	SpaceAfter=No

# sent_id = 3
# text = Then we show how to use this definition to define the $ n $ - category $ nCob $ , whose $ k $ - cells are k - cobordisms, possibly with corners.
1	Then	then	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	how	how	SCONJ	WRB	_	6	advmod	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	use	use	VERB	VB	VerbForm=Inf	3	xcomp	_	_
7	this	this	DET	DT	Number=Sing|PronType=Dem	8	det	_	_
8	definition	definition	NOUN	NN	Number=Sing	6	dobj	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	define	define	VERB	VB	VerbForm=Inf	6	xcomp	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
12	$ n $	$ n $	SYM	$	_	14	nummod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	category	category	NOUN	NN	Number=Sing	10	dobj	_	_
15	$ nCob $	$ ncob $	SYM	$	_	14	appos	_	_
16	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
17	whose	whose	DET	WP$	Poss=Yes	20	poss	_	_
18	$ k $	$ k $	SYM	$	_	20	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	cells	cell	NOUN	NNS	Number=Plur	21	nsubj	_	_
21	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
22	k	k	NOUN	NN	Number=Sing	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	cobordisms	cobordisms	NOUN	NN	Number=Sing	21	attr	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	possibly	possibly	ADV	RB	_	27	advmod	_	_
27	with	with	ADP	IN	_	21	prep	_	_
28	corners	corner	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = We follow Baez and Langford in using ``manifolds embedded in cubes'' rather than general manifolds.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	follow	follow	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	Baez	Baez	PROPN	NNP	Number=Sing	2	dobj	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	Langford	Langford	PROPN	NNP	Number=Sing	3	conj	_	_
6	in	in	ADP	IN	_	2	prep	_	_
7	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	pcomp	_	_
8	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	7	punct	_	SpaceAfter=No
9	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	7	punct	_	SpaceAfter=No
10	manifolds	manifold	NOUN	NNS	Number=Plur	7	dobj	_	_
11	embedded	embed	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acl	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	cubes	cube	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
14	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	10	punct	_	_
15	rather	rather	ADV	RB	_	16	advmod	_	_
16	than	than	ADP	IN	_	10	cc	_	_
17	general	general	ADJ	JJ	Degree=Pos	18	amod	_	_
18	manifolds	manifold	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = We make the construction for 1 - manifolds embedded in 2 - and 3 - cubes.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	make	make	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	construction	construction	NOUN	NN	Number=Sing	2	dobj	_	_
5	for	for	ADP	IN	_	2	prep	_	_
6	1	1	NUM	CD	NumType=Card	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	manifolds	manifold	NOUN	NNS	Number=Plur	5	pobj	_	_
9	embedded	embed	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	2	2	NUM	CD	NumType=Card	16	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
14	3	3	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	cubes	cube	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = For general dimensions $ k $ and $ n $ we indicate what the construction should be.
1	For	for	ADP	IN	_	8	prep	_	_
2	general	general	ADJ	JJ	Degree=Pos	3	amod	_	_
3	dimensions	dimension	NOUN	NNS	Number=Plur	1	pobj	_	_
4	$ k $	$ k $	SYM	$	_	1	pobj	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	$ n $	$ n $	SYM	$	_	4	conj	_	_
7	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	8	nsubj	_	_
8	indicate	indicate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	what	what	PRON	WP	_	13	attr	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	construction	construction	NOUN	NN	Number=Sing	13	nsubj	_	_
12	should	should	AUX	MD	VerbForm=Fin	13	aux	_	_
13	be	be	AUX	VB	VerbForm=Inf	8	ccomp	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 274
# sent_id = 1
# text = Usually bundle gerbes are considered as objects of a 2 - groupoid, whose 1 - morphisms, called stable isomorphisms, are all invertible.
1	Usually	usually	ADV	RB	_	2	advmod	_	_
2	bundle	bundle	VERB	VB	VerbForm=Inf	5	advcl	_	_
3	gerbes	gerbe	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	as	as	SCONJ	IN	_	23	mark	_	_
7	objects	object	NOUN	NNS	Number=Plur	23	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
10	2	2	NUM	CD	NumType=Card	12	nummod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	groupoid	groupoid	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	whose	whose	DET	WP$	Poss=Yes	17	poss	_	_
15	1	1	NUM	CD	NumType=Card	17	nummod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	morphisms	morphism	NOUN	NNS	Number=Plur	12	appos	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
19	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
20	stable	stable	ADJ	JJ	Degree=Pos	21	amod	_	_
21	isomorphisms	isomorphism	NOUN	NNS	Number=Plur	19	oprd	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
23	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	advcl	_	_
24	all	all	ADV	RB	_	23	advmod	_	_
25	invertible	invertible	ADJ	JJ	Degree=Pos	23	acomp	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = I introduce new 1 - morphisms which include stable isomorphisms, trivializations and bundle gerbe modules.
1	I	I	PRON	PRP	Case=Nom|Number=Sing|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	new	new	ADJ	JJ	Degree=Pos	6	amod	_	_
4	1	1	NUM	CD	NumType=Card	6	nummod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	morphisms	morphism	NOUN	NNS	Number=Plur	2	dobj	_	_
7	which	which	PRON	WDT	_	8	nsubj	_	_
8	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	6	relcl	_	_
9	stable	stable	ADJ	JJ	Degree=Pos	10	amod	_	_
10	isomorphisms	isomorphism	NOUN	NNS	Number=Plur	8	dobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	trivializations	trivialization	NOUN	NNS	Number=Plur	10	conj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	bundle	bundle	NOUN	NN	Number=Sing	16	compound	_	_
15	gerbe	gerbe	PROPN	NNP	Number=Sing	16	compound	_	_
16	modules	module	NOUN	NNS	Number=Plur	12	conj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = They fit into the structure of a 2 - category of bundle gerbes, and lead to natural definitions of surface holonomy for closed surfaces, surfaces with boundary, and unoriented closed surfaces.
1	They	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	2	nsubj	_	_
2	fit	fit	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	into	into	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	structure	structure	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	2	2	NUM	CD	NumType=Card	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	bundle	bundle	NOUN	NN	Number=Sing	13	compound	_	_
13	gerbes	gerbes	PROPN	NNP	Number=Sing	11	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
16	lead	lead	VERB	VB	VerbForm=Inf	2	conj	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	natural	natural	ADJ	JJ	Degree=Pos	19	amod	_	_
19	definitions	definition	NOUN	NNS	Number=Plur	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	surface	surface	NOUN	NN	Number=Sing	22	compound	_	_
22	holonomy	holonomy	NOUN	NN	Number=Sing	20	pobj	_	_
23	for	for	ADP	IN	_	19	prep	_	_
24	closed	closed	ADJ	JJ	Degree=Pos	25	amod	_	_
25	surfaces	surface	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
27	surfaces	surface	NOUN	NNS	Number=Plur	16	conj	_	_
28	with	with	ADP	IN	_	27	prep	_	_
29	boundary	boundary	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
32	unoriented	unoriente	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	34	amod	_	_
33	closed	closed	ADJ	JJ	Degree=Pos	34	amod	_	_
34	surfaces	surface	NOUN	NNS	Number=Plur	27	conj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 275
# sent_id = 1
# text = We have shown that complete spreads (with a locally connected domain) over a bounded topos $ E $ (relative to $ S $ ) are `comprehensive' in the sense that they are precisely the second factor of a factorization associated with an instance of the comprehension scheme involving $ S $ - valued distributions on $ E $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	aux	_	_
3	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
5	complete	complete	ADJ	JJ	Degree=Pos	6	amod	_	_
6	spreads	spread	NOUN	NNS	Number=Plur	3	dobj	_	_
7	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	6	punct	_	SpaceAfter=No
8	with	with	ADP	IN	_	6	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
10	locally	locally	ADV	RB	_	11	advmod	_	_
11	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
12	domain	domain	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
13	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	6	punct	_	_
14	over	over	ADP	IN	_	3	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	bounded	bound	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	topos	topos	NOUN	NN	Number=Sing	14	pobj	_	_
18	$ E $	$ e $	SYM	$	_	17	appos	_	_
19	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	20	punct	_	SpaceAfter=No
20	relative	relative	ADJ	JJ	Degree=Pos	3	dep	_	_
21	to	to	ADP	IN	_	20	prep	_	_
22	$ S $	$ s $	SYM	$	_	21	pobj	_	_
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	3	punct	_	_
24	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	conj	_	_
25	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	24	punct	_	SpaceAfter=No
26	comprehensive	comprehensive	ADJ	JJ	Degree=Pos	24	acomp	_	SpaceAfter=No
27	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	24	punct	_	_
28	in	in	ADP	IN	_	24	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	sense	sense	NOUN	NN	Number=Sing	28	pobj	_	_
31	that	that	SCONJ	IN	_	33	mark	_	_
32	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	33	nsubj	_	_
33	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	30	acl	_	_
34	precisely	precisely	ADV	RB	_	33	advmod	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
36	second	second	ADJ	JJ	Degree=Pos	37	amod	_	_
37	factor	factor	NOUN	NN	Number=Sing	33	attr	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	a	a	DET	DT	Definite=Ind|PronType=Art	40	det	_	_
40	factorization	factorization	NOUN	NN	Number=Sing	38	pobj	_	_
41	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	40	acl	_	_
42	with	with	ADP	IN	_	41	prep	_	_
43	an	an	DET	DT	Definite=Ind|PronType=Art	44	det	_	_
44	instance	instance	NOUN	NN	Number=Sing	42	pobj	_	_
45	of	of	ADP	IN	_	44	prep	_	_
46	the	the	DET	DT	Definite=Def|PronType=Art	48	det	_	_
47	comprehension	comprehension	NOUN	NN	Number=Sing	48	compound	_	_
48	scheme	scheme	NOUN	NN	Number=Sing	45	pobj	_	_
49	involving	involve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	48	acl	_	_
50	$ S $	$ s $	SYM	$	_	52	advmod	_	_
51	-	-	PUNCT	HYPH	PunctType=Dash	52	punct	_	_
52	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	53	amod	_	_
53	distributions	distribution	NOUN	NNS	Number=Plur	49	dobj	_	_
54	on	on	ADP	IN	_	53	prep	_	_
55	$ E $	$ e $	SYM	$	_	54	pobj	_	_
56	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = Lawvere has asked whether the `Michael coverings' (or complete spreads with a definable dominance domain) are comprehensive in a similar fashion.
1	Lawvere	Lawvere	PROPN	NNP	Number=Sing	3	nsubj	_	_
2	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	aux	_	_
3	asked	ask	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	whether	whether	SCONJ	IN	_	20	mark	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
6	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	8	punct	_	SpaceAfter=No
7	Michael	Michael	PROPN	NNP	Number=Sing	8	compound	_	_
8	coverings	covering	NOUN	NNS	Number=Plur	20	nsubj	_	SpaceAfter=No
9	'	'	PART	POS	_	8	case	_	_
10	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	8	punct	_	SpaceAfter=No
11	or	or	CCONJ	CC	ConjType=Cmp	8	cc	_	_
12	complete	complete	ADJ	JJ	Degree=Pos	13	amod	_	_
13	spreads	spread	NOUN	NNS	Number=Plur	8	conj	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
16	definable	definable	ADJ	JJ	Degree=Pos	18	amod	_	_
17	dominance	dominance	NOUN	NN	Number=Sing	18	compound	_	_
18	domain	domain	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
19	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	8	punct	_	_
20	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
21	comprehensive	comprehensive	ADJ	JJ	Degree=Pos	20	acomp	_	_
22	in	in	ADP	IN	_	20	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	similar	similar	ADJ	JJ	Degree=Pos	25	amod	_	_
25	fashion	fashion	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = We give here a positive answer to this question.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	here	here	ADV	RB	PronType=Dem	2	advmod	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	positive	positive	ADJ	JJ	Degree=Pos	6	amod	_	_
6	answer	answer	NOUN	NN	Number=Sing	2	dobj	_	_
7	to	to	ADP	IN	_	6	prep	_	_
8	this	this	DET	DT	Number=Sing|PronType=Dem	9	det	_	_
9	question	question	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = In order to deal effectively with the comprehension scheme in this context, we introduce a notion of an `extensive topos doctrine, ' where the extensive quantities (or distributions) have values in a suitable subcategory of what we call `locally discrete' locales.
1	In	in	ADP	IN	_	15	prep	_	_
2	order	order	NOUN	NN	Number=Sing	1	pobj	_	_
3	to	to	PART	TO	_	4	aux	_	_
4	deal	deal	VERB	VB	VerbForm=Inf	2	acl	_	_
5	effectively	effectively	ADV	RB	_	4	advmod	_	_
6	with	with	ADP	IN	_	4	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	comprehension	comprehension	NOUN	NN	Number=Sing	9	compound	_	_
9	scheme	scheme	NOUN	NN	Number=Sing	6	pobj	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	this	this	DET	DT	Number=Sing|PronType=Dem	12	det	_	_
12	context	context	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
14	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	15	nsubj	_	_
15	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	notion	notion	NOUN	NN	Number=Sing	15	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	an	an	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
20	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	23	punct	_	SpaceAfter=No
21	extensive	extensive	ADJ	JJ	Degree=Pos	23	amod	_	_
22	topos	topos	NOUN	NN	Number=Sing	23	compound	_	_
23	doctrine	doctrine	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
25	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	23	punct	_	_
26	where	where	SCONJ	WRB	_	34	advmod	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	extensive	extensive	ADJ	JJ	Degree=Pos	29	amod	_	_
29	quantities	quantity	NOUN	NNS	Number=Plur	34	nsubj	_	_
30	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	29	punct	_	SpaceAfter=No
31	or	or	CCONJ	CC	ConjType=Cmp	29	cc	_	_
32	distributions	distribution	NOUN	NNS	Number=Plur	29	conj	_	SpaceAfter=No
33	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	29	punct	_	_
34	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	23	relcl	_	_
35	values	value	NOUN	NNS	Number=Plur	34	dobj	_	_
36	in	in	ADP	IN	_	35	prep	_	_
37	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
38	suitable	suitable	ADJ	JJ	Degree=Pos	39	amod	_	_
39	subcategory	subcategory	NOUN	NN	Number=Sing	36	pobj	_	_
40	of	of	ADP	IN	_	39	prep	_	_
41	what	what	PRON	WP	_	43	dobj	_	_
42	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	43	nsubj	_	_
43	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	40	pcomp	_	_
44	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	46	punct	_	SpaceAfter=No
45	locally	locally	ADV	RB	_	46	advmod	_	_
46	discrete	discrete	ADJ	JJ	Degree=Pos	48	amod	_	SpaceAfter=No
47	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	48	punct	_	_
48	locales	locale	NOUN	NNS	Number=Plur	43	oprd	_	SpaceAfter=No
49	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 5
# text = In the process we define what we mean by a quasi locally connected topos, a notion that we feel may be of interest in its own right.
1	In	in	ADP	IN	_	5	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	process	process	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	what	what	PRON	WP	_	8	dobj	_	_
7	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	8	nsubj	_	_
8	mean	mean	VERB	VBP	Tense=Pres|VerbForm=Fin	5	ccomp	_	_
9	by	by	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	quasi	quasi	NOUN	NN	Number=Sing	14	nmod	_	_
12	locally	locally	ADV	RB	_	13	advmod	_	_
13	connected	connected	ADJ	JJ	Degree=Pos	14	amod	_	_
14	topos	topos	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	notion	notion	NOUN	NN	Number=Sing	5	npadvmod	_	_
18	that	that	SCONJ	IN	_	20	mark	_	_
19	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	20	nsubj	_	_
20	feel	feel	VERB	VBP	Tense=Pres|VerbForm=Fin	17	acl	_	_
21	may	may	AUX	MD	VerbForm=Fin	22	aux	_	_
22	be	be	AUX	VB	VerbForm=Inf	20	ccomp	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	interest	interest	NOUN	NN	Number=Sing	23	pobj	_	_
25	in	in	ADP	IN	_	24	prep	_	_
26	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	28	poss	_	_
27	own	own	ADJ	JJ	Degree=Pos	28	amod	_	_
28	right	right	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 276
# sent_id = 1
# text = The core of a category (first defined in ``Core algebra revisited'') has the structure of an abstract core algebra (first defined in the same place).
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	core	core	NOUN	NN	Number=Sing	17	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	3	pobj	_	_
6	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	2	punct	_	SpaceAfter=No
7	first	first	ADV	RB	_	8	advmod	_	_
8	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acl	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	9	punct	_	SpaceAfter=No
11	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	9	punct	_	SpaceAfter=No
12	Core	Core	PROPN	NNP	Number=Sing	13	compound	_	_
13	algebra	algebra	NOUN	NN	Number=Sing	9	pobj	_	_
14	revisited	revisit	VERB	VBD	Tense=Past|VerbForm=Fin	13	acl	_	SpaceAfter=No
15	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	13	punct	_	SpaceAfter=No
16	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	2	punct	_	_
17	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	structure	structure	NOUN	NN	Number=Sing	17	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
22	abstract	abstract	ADJ	JJ	Degree=Pos	24	amod	_	_
23	core	core	NOUN	NN	Number=Sing	24	compound	_	_
24	algebra	algebra	PROPN	NNP	Number=Sing	20	pobj	_	_
25	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
26	first	first	ADV	RB	_	27	advmod	_	_
27	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	acl	_	_
28	in	in	ADP	IN	_	27	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
30	same	same	ADJ	JJ	Degree=Pos	31	amod	_	_
31	place	place	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
32	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	24	punct	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 2
# text = A question was left open: is there more structure yet to be defined?
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	question	question	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	4	auxpass	_	_
4	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	ccomp	_	_
5	open	open	ADJ	JJ	Degree=Pos	4	oprd	_	SpaceAfter=No
6	:	:	PUNCT	:	_	7	punct	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	there	there	PRON	EX	_	7	expl	_	_
9	more	more	ADJ	JJR	Degree=Cmp	10	amod	_	_
10	structure	structure	NOUN	NN	Number=Sing	7	attr	_	_
11	yet	yet	ADV	RB	_	7	advmod	_	_
12	to	to	PART	TO	_	14	aux	_	_
13	be	be	AUX	VB	VerbForm=Inf	14	auxpass	_	_
14	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	xcomp	_	SpaceAfter=No
15	?	?	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = The answer is no: it is shown that any operation on an object arising from the fact that the object is the core of its category can be defined using only the constant and two binary operations that appear in the definition of abstract core algebra.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	answer	answer	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	ccomp	_	_
4	no	no	NOUN	NN	Number=Sing	3	attr	_	SpaceAfter=No
5	:	:	PUNCT	:	_	8	punct	_	_
6	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	8	nsubjpass	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	that	that	SCONJ	IN	_	30	mark	_	_
10	any	any	DET	DT	_	11	det	_	_
11	operation	operation	NOUN	NN	Number=Sing	30	nsubjpass	_	_
12	on	on	ADP	IN	_	11	prep	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	object	object	NOUN	NN	Number=Sing	12	pobj	_	_
15	arising	arise	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	acl	_	_
16	from	from	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	fact	fact	NOUN	NN	Number=Sing	16	pobj	_	_
19	that	that	SCONJ	IN	_	22	mark	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	object	object	NOUN	NN	Number=Sing	22	nsubj	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	acl	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	core	core	NOUN	NN	Number=Sing	30	nsubjpass	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	27	poss	_	_
27	category	category	NOUN	NN	Number=Sing	25	pobj	_	_
28	can	can	AUX	MD	VerbForm=Fin	30	aux	_	_
29	be	be	AUX	VB	VerbForm=Inf	30	auxpass	_	_
30	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	ccomp	_	_
31	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	30	xcomp	_	_
32	only	only	ADV	RB	_	38	advmod	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
34	constant	constant	ADJ	JJ	Degree=Pos	38	amod	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	34	cc	_	_
36	two	two	NUM	CD	NumType=Card	38	nummod	_	_
37	binary	binary	ADJ	JJ	Degree=Pos	38	amod	_	_
38	operations	operation	NOUN	NNS	Number=Plur	31	dobj	_	_
39	that	that	PRON	WDT	PronType=Rel	40	nsubj	_	_
40	appear	appear	VERB	VBP	Tense=Pres|VerbForm=Fin	38	relcl	_	_
41	in	in	ADP	IN	_	40	prep	_	_
42	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
43	definition	definition	NOUN	NN	Number=Sing	41	pobj	_	_
44	of	of	ADP	IN	_	43	prep	_	_
45	abstract	abstract	ADJ	JJ	Degree=Pos	47	amod	_	_
46	core	core	NOUN	NN	Number=Sing	47	compound	_	_
47	algebra	algebra	PROPN	NNP	Number=Sing	44	pobj	_	SpaceAfter=No
48	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 4
# text = In the process a number of facts about abstract core algebras must be developed.
1	In	in	ADP	IN	_	14	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	process	process	NOUN	NN	Number=Sing	1	pobj	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	number	number	NOUN	NN	Number=Sing	14	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	facts	fact	NOUN	NNS	Number=Plur	6	pobj	_	_
8	about	about	ADP	IN	_	7	prep	_	_
9	abstract	abstract	ADJ	JJ	Degree=Pos	11	amod	_	_
10	core	core	NOUN	NN	Number=Sing	11	compound	_	_
11	algebras	algebra	NOUN	NNS	Number=Plur	8	pobj	_	_
12	must	must	AUX	MD	VerbForm=Fin	14	aux	_	_
13	be	be	AUX	VB	VerbForm=Inf	14	auxpass	_	_
14	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# doc_id = 277
# sent_id = 1
# text = New techniques for constructing a distributive law of a monad over another are studied using submonads, quotient monads, product monads, recursively - defined distributive laws, and linear equations.
1	New	new	ADJ	JJ	Degree=Pos	2	amod	_	_
2	techniques	technique	NOUN	NNS	Number=Plur	14	nsubjpass	_	_
3	for	for	ADP	IN	_	2	prep	_	_
4	constructing	construct	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	pcomp	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	distributive	distributive	ADJ	JJ	Degree=Pos	7	amod	_	_
7	law	law	NOUN	NN	Number=Sing	4	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	monad	monad	NOUN	NNS	Number=Plur	8	pobj	_	_
11	over	over	ADP	IN	_	10	prep	_	_
12	another	another	PRON	DT	_	11	pobj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	studied	study	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
15	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	xcomp	_	_
16	submonads	submonad	NOUN	NNS	Number=Plur	15	dobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	quotient	quotient	NOUN	NN	Number=Sing	19	compound	_	_
19	monads	monad	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	product	product	NOUN	NN	Number=Sing	22	compound	_	_
22	monads	monad	NOUN	NNS	Number=Plur	19	conj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	recursively	recursively	ADV	RB	_	26	advmod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	amod	_	_
27	distributive	distributive	ADJ	JJ	Degree=Pos	28	amod	_	_
28	laws	law	NOUN	NNS	Number=Plur	22	conj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
31	linear	linear	ADJ	JJ	Degree=Pos	32	amod	_	_
32	equations	equation	NOUN	NNS	Number=Plur	28	conj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 2
# text = Sequel papers will consider distributive laws in closed categories and will construct monad approximations for compositions which fail to be a monad.
1	Sequel	sequel	NOUN	NN	Number=Sing	2	compound	_	_
2	papers	paper	NOUN	NNS	Number=Plur	4	nsubj	_	_
3	will	will	AUX	MD	VerbForm=Fin	4	aux	_	_
4	consider	consider	VERB	VB	VerbForm=Inf	0	ROOT	_	_
5	distributive	distributive	ADJ	JJ	Degree=Pos	6	amod	_	_
6	laws	law	NOUN	NNS	Number=Plur	4	dobj	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	closed	closed	ADJ	JJ	Degree=Pos	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
11	will	will	AUX	MD	VerbForm=Fin	12	aux	_	_
12	construct	construct	VERB	VB	VerbForm=Inf	4	conj	_	_
13	monad	monad	NOUN	NNS	Number=Plur	14	compound	_	_
14	approximations	approximation	NOUN	NNS	Number=Plur	12	dobj	_	_
15	for	for	ADP	IN	_	12	prep	_	_
16	compositions	composition	NOUN	NNS	Number=Plur	15	pobj	_	_
17	which	which	PRON	WDT	_	18	nsubj	_	_
18	fail	fail	VERB	VBP	Tense=Pres|VerbForm=Fin	16	relcl	_	_
19	to	to	PART	TO	_	20	aux	_	_
20	be	be	AUX	VB	VerbForm=Inf	18	xcomp	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	monad	monad	NOUN	NNS	Number=Plur	20	attr	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 278
# sent_id = 1
# text = In this paper we give a characterization of constructively completely distributive lattices in presheaves on $ C $ , for $ C $ a small category with pullbacks.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	characterization	characterization	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	constructively	constructively	ADV	RB	_	11	advmod	_	_
10	completely	completely	ADV	RB	_	11	advmod	_	_
11	distributive	distributive	ADJ	JJ	Degree=Pos	12	amod	_	_
12	lattices	lattice	NOUN	NNS	Number=Plur	8	pobj	_	_
13	in	in	ADP	IN	_	5	prep	_	_
14	presheaves	presheave	NOUN	NNS	Number=Plur	13	pobj	_	_
15	on	on	ADP	IN	_	14	prep	_	_
16	$ C $	$ c $	SYM	$	_	15	pobj	_	_
17	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
18	for	for	ADP	IN	_	5	prep	_	_
19	$ C $	$ c $	SYM	$	_	22	poss	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	small	small	ADJ	JJ	Degree=Pos	22	amod	_	_
22	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
23	with	with	ADP	IN	_	22	prep	_	_
24	pullbacks	pullback	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 279
# sent_id = 1
# text = Francisco Marmolejo pointed out a mistake in the statement of a propositoin in our paper.
1	Francisco	Francisco	PROPN	NNP	Number=Sing	2	compound	_	_
2	Marmolejo	Marmolejo	PROPN	NNP	Number=Sing	3	nsubj	_	_
3	pointed	point	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
4	out	out	ADP	RP	_	3	prt	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	mistake	mistake	NOUN	NN	Number=Sing	3	dobj	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	statement	statement	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	propositoin	propositoin	NOUN	NN	Number=Sing	10	pobj	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	15	poss	_	_
15	paper	paper	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = The mistaken version is used later in that paper.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	mistaken	mistaken	ADJ	JJ	Degree=Pos	3	amod	_	_
3	version	version	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	later	later	ADV	RB	_	5	advmod	_	_
7	in	in	ADP	IN	_	5	prep	_	_
8	that	that	DET	DT	Number=Sing|PronType=Dem	9	det	_	_
9	paper	paper	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = Our purpose here is to correct the error by providing an explicit description of the finite coproduct completion of the dual of the category of connected $ G $ - sets.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	purpose	purpose	NOUN	NN	Number=Sing	4	nsubj	_	_
3	here	here	ADV	RB	PronType=Dem	2	advmod	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	correct	correct	VERB	VB	VerbForm=Inf	4	xcomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	error	error	NOUN	NN	Number=Sing	6	dobj	_	_
9	by	by	ADP	IN	_	6	prep	_	_
10	providing	provide	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	pcomp	_	_
11	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	explicit	explicit	ADJ	JJ	Degree=Pos	13	amod	_	_
13	description	description	NOUN	NN	Number=Sing	10	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
16	finite	finite	ADJ	JJ	Degree=Pos	17	amod	_	_
17	coproduct	coproduct	NOUN	NN	Number=Sing	18	compound	_	_
18	completion	completion	NOUN	NN	Number=Sing	14	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	dual	dual	ADJ	JJ	Degree=Pos	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	category	category	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	amod	_	_
27	$ G $	$ g $	SYM	$	_	29	compound	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	sets	set	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = The description uses the distinguished morphisms of a factorization system on the category of $ G $ - sets.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	description	description	NOUN	NN	Number=Sing	3	nsubj	_	_
3	uses	use	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	distinguished	distinguished	ADJ	JJ	Degree=Pos	6	amod	_	_
6	morphisms	morphism	NOUN	NNS	Number=Plur	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	factorization	factorization	NOUN	NN	Number=Sing	10	compound	_	_
10	system	system	NOUN	NN	Number=Sing	7	pobj	_	_
11	on	on	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	$ G $	$ g $	SYM	$	_	17	compound	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	sets	set	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 280
# sent_id = 1
# text = We give an interpretation of Yetter's Invariant of manifolds $ M $ in terms of the homotopy type of the function space $ TOP(M, B(cal G)) $ , where $ cal G $ is a crossed module and $ B(cal G) $ is its classifying space.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	interpretation	interpretation	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	Yetter	Yetter	PROPN	NNP	Number=Sing	8	poss	_	SpaceAfter=No
7	's	's	PART	POS	_	6	case	_	_
8	Invariant	Invariant	PROPN	NNP	Number=Sing	5	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	manifolds	manifold	NOUN	NNS	Number=Plur	9	pobj	_	_
11	$ M $	$ m $	SYM	$	_	2	dep	_	_
12	in	in	ADP	IN	_	2	prep	_	_
13	terms	term	NOUN	NNS	Number=Plur	12	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	homotopy	homotopy	NOUN	NN	Number=Sing	17	compound	_	_
17	type	type	NOUN	NN	Number=Sing	14	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	function	function	NOUN	NN	Number=Sing	21	compound	_	_
21	space	space	NOUN	NN	Number=Sing	18	pobj	_	_
22	$ TOP(M, B(cal G)) $	$ top(m, b(cal g)) $	SYM	$	_	26	nsubj	_	_
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	where	where	SCONJ	WRB	_	25	advmod	_	_
25	$ cal G $	$ cal g $	SYM	$	_	22	relcl	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	crossed	crossed	ADJ	JJ	Degree=Pos	29	amod	_	_
29	module	module	NOUN	NN	Number=Sing	26	attr	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
31	$ B(cal G) $	$ b(cal g) $	SYM	$	_	32	nsubj	_	_
32	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	conj	_	_
33	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	35	poss	_	_
34	classifying	classify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	35	amod	_	_
35	space	space	NOUN	NN	Number=Sing	32	attr	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = From this formulation, there follows that Yetter's invariant depends only on the homotopy type of $ M $ , and the weak homotopy type of the crossed module $ cal G $ .
1	From	from	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	formulation	formulation	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	there	there	PRON	EX	_	6	expl	_	_
6	follows	follow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	11	mark	_	_
8	Yetter	Yetter	PROPN	NNP	Number=Sing	10	poss	_	SpaceAfter=No
9	's	's	PART	POS	_	8	case	_	_
10	invariant	invariant	NOUN	NN	Number=Sing	11	nsubj	_	_
11	depends	depend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
12	only	only	ADV	RB	_	13	advmod	_	_
13	on	on	ADP	IN	_	11	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	homotopy	homotopy	NOUN	NN	Number=Sing	16	compound	_	_
16	type	type	NOUN	NN	Number=Sing	13	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	$ M $	$ m $	SYM	$	_	17	pobj	_	_
19	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
22	weak	weak	ADJ	JJ	Degree=Pos	24	amod	_	_
23	homotopy	homotopy	NOUN	NN	Number=Sing	24	compound	_	_
24	type	type	NOUN	NN	Number=Sing	11	conj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	amod	_	_
28	module	module	NOUN	NN	Number=Sing	25	pobj	_	_
29	$ cal G $	$ cal g $	SYM	$	_	24	appos	_	_
30	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = We use this interpretation to define a twisting of Yetter's Invariant by cohomology classes of crossed modules, defined as cohomology classes of their classifying spaces, in the form of a state sum invariant.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	interpretation	interpretation	NOUN	NN	Number=Sing	2	dobj	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	define	define	VERB	VB	VerbForm=Inf	2	xcomp	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	twisting	twisting	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Yetter	Yetter	PROPN	NNP	Number=Sing	12	poss	_	SpaceAfter=No
11	's	's	PART	POS	_	10	case	_	_
12	Invariant	Invariant	PROPN	NNP	Number=Sing	9	pobj	_	_
13	by	by	ADP	IN	_	8	prep	_	_
14	cohomology	cohomology	NOUN	NN	Number=Sing	15	compound	_	_
15	classes	class	NOUN	NNS	Number=Plur	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	crossed	crossed	ADJ	JJ	Degree=Pos	18	amod	_	_
18	modules	module	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
20	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
21	as	as	ADP	IN	_	20	prep	_	_
22	cohomology	cohomology	NOUN	NN	Number=Sing	23	compound	_	_
23	classes	class	NOUN	NNS	Number=Plur	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	27	poss	_	_
26	classifying	classify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	27	amod	_	_
27	spaces	space	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
29	in	in	ADP	IN	_	6	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	form	form	NOUN	NN	Number=Sing	29	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
34	state	state	NOUN	NN	Number=Sing	35	compound	_	_
35	sum	sum	NOUN	NN	Number=Sing	36	compound	_	_
36	invariant	invariant	ADJ	JJ	Degree=Pos	32	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = In particular, we obtain an extension of the Dijkgraaf - Witten Invariant of manifolds to categorical groups.
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	extension	extension	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
10	Dijkgraaf	Dijkgraaf	PROPN	NNP	Number=Sing	12	compound	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	Witten	Witten	PROPN	NNP	Number=Sing	13	compound	_	_
13	Invariant	Invariant	PROPN	NNP	Number=Sing	8	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	manifolds	manifold	NOUN	NNS	Number=Plur	14	pobj	_	_
16	to	to	ADP	IN	_	7	prep	_	_
17	categorical	categorical	ADJ	JJ	Degree=Pos	18	amod	_	_
18	groups	group	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = The straightforward extension to crossed complexes is also considered.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	straightforward	straightforward	ADJ	JJ	Degree=Pos	3	amod	_	_
3	extension	extension	NOUN	NN	Number=Sing	9	nsubjpass	_	_
4	to	to	ADP	IN	_	3	prep	_	_
5	crossed	crossed	ADJ	JJ	Degree=Pos	6	amod	_	_
6	complexes	complex	NOUN	NNS	Number=Plur	4	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
8	also	also	ADV	RB	_	9	advmod	_	_
9	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 281
# sent_id = 1
# text = Bicat is the tricategory of bicategories, homomorphisms, pseudonatural transformations, and modifications. $ Gray $ is the subtricategory of 2 - categories, 2 - functors, pseudonatural transformations, and modifications.
1	Bicat	Bicat	PROPN	NNP	Number=Sing	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	tricategory	tricategory	NOUN	NN	Number=Sing	2	attr	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	bicategories	bicategorie	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	homomorphisms	homomorphism	NOUN	NNS	Number=Plur	6	conj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
10	pseudonatural	pseudonatural	ADJ	JJ	Degree=Pos	11	amod	_	_
11	transformations	transformation	NOUN	NNS	Number=Plur	8	conj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
14	modifications	modification	NOUN	NNS	Number=Plur	11	conj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	_
16	$ Gray $	$ gray $	SYM	$	_	17	nsubj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	subtricategory	subtricategory	NOUN	NN	Number=Sing	17	attr	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	2	2	NUM	CD	NumType=Card	23	nummod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	categories	category	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
25	2	2	NUM	CD	NumType=Card	27	nummod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	functors	functor	NOUN	NNS	Number=Plur	17	attr	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
29	pseudonatural	pseudonatural	ADJ	JJ	Degree=Pos	30	amod	_	_
30	transformations	transformation	NOUN	NNS	Number=Plur	27	conj	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
33	modifications	modification	NOUN	NNS	Number=Plur	30	conj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that these two tricategories are not triequivalent.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	these	these	DET	DT	Number=Plur|PronType=Dem	6	det	_	_
5	two	two	NUM	CD	NumType=Card	6	nummod	_	_
6	tricategories	tricategorie	NOUN	NNS	Number=Plur	7	nsubj	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	not	not	PART	RB	Polarity=Neg	7	neg	_	_
9	triequivalent	triequivalent	ADJ	JJ	Degree=Pos	7	acomp	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 282
# sent_id = 1
# text = The notion of cartesian bicategory, introduced by Carboni and Walters for locally ordered bicategories, is extended to general bicategories.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	notion	notion	NOUN	NN	Number=Sing	18	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	cartesian	cartesian	ADJ	JJ	Degree=Pos	5	amod	_	_
5	bicategory	bicategory	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	acl	_	_
8	by	by	ADP	IN	_	7	agent	_	_
9	Carboni	Carboni	PROPN	NNP	Number=Sing	8	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	Walters	Walters	PROPN	NNP	Number=Sing	9	conj	_	_
12	for	for	ADP	IN	_	7	prep	_	_
13	locally	locally	ADV	RB	_	14	advmod	_	_
14	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
15	bicategories	bicategorie	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	auxpass	_	_
18	extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	general	general	ADJ	JJ	Degree=Pos	21	amod	_	_
21	bicategories	bicategorie	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# sent_id = 2
# text = It is shown that a cartesian bicategory is a symmetric monoidal bicategory.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	SCONJ	IN	_	8	mark	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	cartesian	cartesian	ADJ	JJ	Degree=Pos	7	amod	_	_
7	bicategory	bicategory	NOUN	NN	Number=Sing	8	nsubj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
10	symmetric	symmetric	ADJ	JJ	Degree=Pos	12	amod	_	_
11	monoidal	monoidal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	bicategory	bicategory	NOUN	NN	Number=Sing	8	attr	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 283
# sent_id = 1
# text = Iterative algebras, defined by the property that every guarded system of recursive equations has a unique solution, are proved to have a much stronger property: every system of recursive equations has a unique strict solution.
1	Iterative	iterative	ADJ	JJ	Degree=Pos	2	amod	_	_
2	algebras	algebra	NOUN	NNS	Number=Plur	21	nsubjpass	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
4	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acl	_	_
5	by	by	ADP	IN	_	4	agent	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	property	property	NOUN	NN	Number=Sing	5	pobj	_	_
8	that	that	PRON	WDT	PronType=Rel	15	nsubj	_	_
9	every	every	DET	DT	_	11	det	_	_
10	guarded	guard	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
11	system	system	NOUN	NN	Number=Sing	15	nsubj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	recursive	recursive	ADJ	JJ	Degree=Pos	14	amod	_	_
14	equations	equation	NOUN	NNS	Number=Plur	12	pobj	_	_
15	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	relcl	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	unique	unique	ADJ	JJ	Degree=Pos	18	amod	_	_
18	solution	solution	NOUN	NN	Number=Sing	15	dobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
20	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	21	auxpass	_	_
21	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	34	ccomp	_	_
22	to	to	PART	TO	_	23	aux	_	_
23	have	have	VERB	VB	VerbForm=Inf	21	xcomp	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
25	much	much	ADV	RB	_	26	advmod	_	_
26	stronger	strong	ADJ	JJR	Degree=Cmp	27	amod	_	_
27	property	property	NOUN	NN	Number=Sing	23	dobj	_	SpaceAfter=No
28	:	:	PUNCT	:	_	34	punct	_	_
29	every	every	DET	DT	_	30	det	_	_
30	system	system	NOUN	NN	Number=Sing	34	nsubj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	recursive	recursive	ADJ	JJ	Degree=Pos	33	amod	_	_
33	equations	equation	NOUN	NNS	Number=Plur	31	pobj	_	_
34	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
35	a	a	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
36	unique	unique	ADJ	JJ	Degree=Pos	38	amod	_	_
37	strict	strict	ADJ	JJ	Degree=Pos	38	amod	_	_
38	solution	solution	NOUN	NN	Number=Sing	34	dobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	34	punct	_	SpaceAfter=No

# sent_id = 2
# text = Those systems that have a unique solution in every iterative algebra are characterized.
1	Those	those	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	systems	system	NOUN	NNS	Number=Plur	13	nsubjpass	_	_
3	that	that	PRON	WDT	PronType=Rel	4	nsubj	_	_
4	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	relcl	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	unique	unique	ADJ	JJ	Degree=Pos	7	amod	_	_
7	solution	solution	NOUN	NN	Number=Sing	4	dobj	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	every	every	DET	DT	_	11	det	_	_
10	iterative	iterative	ADJ	JJ	Degree=Pos	11	amod	_	_
11	algebra	algebra	NOUN	NNS	Number=Plur	8	pobj	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# doc_id = 284
# sent_id = 1
# text = It is the aim of this paper to compute the category of Eilenberg - Moore algebras for the monad arising from the dual unit - ball functor on the category of (semi)normed spaces.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	aim	aim	NOUN	NN	Number=Sing	2	attr	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
7	paper	paper	NOUN	NN	Number=Sing	5	pobj	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	compute	compute	VERB	VB	VerbForm=Inf	2	xcomp	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	category	category	NOUN	NN	Number=Sing	9	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	Moore	Moore	PROPN	NNP	Number=Sing	16	compound	_	_
16	algebras	algebra	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	pobj	_	_
17	for	for	ADP	IN	_	9	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	monad	monad	NOUN	NNS	Number=Plur	17	pobj	_	_
20	arising	arise	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	acl	_	_
21	from	from	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
23	dual	dual	ADJ	JJ	Degree=Pos	24	amod	_	_
24	unit	unit	NOUN	NN	Number=Sing	26	compound	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	ball	ball	NOUN	NN	Number=Sing	27	compound	_	_
27	functor	functor	NOUN	NN	Number=Sing	21	pobj	_	_
28	on	on	ADP	IN	_	20	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	category	category	NOUN	NN	Number=Sing	28	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	33	punct	_	SpaceAfter=No
33	semi)normed	semi)normed	PROPN	NNP	Number=Sing	31	pobj	_	_
34	spaces	space	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that this gives rise to a stronger algebraic structure than the totally convex one obtained from the closed unit ball functor on the category of Banach spaces.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	this	this	PRON	DT	Number=Sing|PronType=Dem	5	nsubj	_	_
5	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	rise	rise	VERB	VB	VerbForm=Inf	5	dobj	_	_
7	to	to	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	stronger	strong	ADJ	JJR	Degree=Cmp	11	amod	_	_
10	algebraic	algebraic	ADJ	JJ	Degree=Pos	11	amod	_	_
11	structure	structure	NOUN	NN	Number=Sing	7	pobj	_	_
12	than	than	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
14	totally	totally	ADV	RB	_	15	advmod	_	_
15	convex	convex	ADJ	JJ	Degree=Pos	16	amod	_	_
16	one	one	NUM	CD	NumType=Card	12	pobj	_	_
17	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	acl	_	_
18	from	from	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
20	closed	closed	ADJ	JJ	Degree=Pos	21	amod	_	_
21	unit	unit	NOUN	NN	Number=Sing	23	compound	_	_
22	ball	ball	NOUN	NN	Number=Sing	23	compound	_	_
23	functor	functor	NOUN	NN	Number=Sing	18	pobj	_	_
24	on	on	ADP	IN	_	17	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	category	category	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	Banach	Banach	PROPN	NNP	Number=Sing	29	compound	_	_
29	spaces	space	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 285
# sent_id = 1
# text = Motivated by an analysis of Abramsky - Jagadeesan games, the paper considers a categorical semantics for a polarized notion of two - player games, a semantics which has close connections with the logic of (finite cartesian) sums and products, as well as with the multiplicative structure of linear logic.
1	Motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	advcl	_	_
2	by	by	ADP	IN	_	1	agent	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	analysis	analysis	NOUN	NN	Number=Sing	2	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	Abramsky	Abramsky	PROPN	NNP	Number=Sing	8	compound	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	Jagadeesan	Jagadeesan	PROPN	NNP	Number=Sing	9	compound	_	_
9	games	games	PROPN	NNPS	Number=Plur	5	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	paper	paper	NOUN	NN	Number=Sing	13	nsubj	_	_
13	considers	consider	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	categorical	categorical	ADJ	JJ	Degree=Pos	16	amod	_	_
16	semantics	semantic	NOUN	NNS	Number=Plur	13	dobj	_	_
17	for	for	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	polarized	polarized	ADJ	JJ	Degree=Pos	20	amod	_	_
20	notion	notion	NOUN	NN	Number=Sing	17	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	two	two	NUM	CD	NumType=Card	24	nummod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	player	player	NOUN	NN	Number=Sing	25	compound	_	_
25	games	game	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	semantics	semantic	NOUN	NNS	Number=Plur	25	appos	_	_
29	which	which	PRON	WDT	_	30	nsubj	_	_
30	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	28	relcl	_	_
31	close	close	ADJ	JJ	Degree=Pos	32	amod	_	_
32	connections	connection	NOUN	NNS	Number=Plur	30	dobj	_	_
33	with	with	ADP	IN	_	32	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	logic	logic	NOUN	NN	Number=Sing	33	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	36	punct	_	SpaceAfter=No
38	finite	finite	PROPN	NNP	Number=Sing	39	nmod	_	_
39	cartesian	cartesian	PROPN	NNP	Number=Sing	41	nmod	_	SpaceAfter=No
40	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	39	punct	_	_
41	sums	sum	NOUN	NNS	Number=Plur	36	pobj	_	_
42	and	and	CCONJ	CC	ConjType=Cmp	41	cc	_	_
43	products	product	NOUN	NNS	Number=Plur	41	conj	_	SpaceAfter=No
44	,	,	PUNCT	,	PunctType=Comm	41	punct	_	_
45	as	as	ADV	RB	_	47	advmod	_	_
46	well	well	ADV	RB	Degree=Pos	47	advmod	_	_
47	as	as	ADP	IN	_	36	cc	_	_
48	with	with	ADP	IN	_	35	prep	_	_
49	the	the	DET	DT	Definite=Def|PronType=Art	51	det	_	_
50	multiplicative	multiplicative	ADJ	JJ	Degree=Pos	51	amod	_	_
51	structure	structure	NOUN	NN	Number=Sing	48	pobj	_	_
52	of	of	ADP	IN	_	51	prep	_	_
53	linear	linear	ADJ	JJ	Degree=Pos	54	amod	_	_
54	logic	logic	NOUN	NN	Number=Sing	52	pobj	_	SpaceAfter=No
55	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 2
# text = In each case, the structure is polarized, in the sense that it will be modelled by two categories, one for each of two polarities, with a module structure connecting them.
1	In	in	ADP	IN	_	8	prep	_	_
2	each	each	DET	DT	_	3	det	_	_
3	case	case	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	structure	structure	NOUN	NN	Number=Sing	8	nsubjpass	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	polarized	polarize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
10	in	in	ADP	IN	_	8	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	sense	sense	NOUN	NN	Number=Sing	10	pobj	_	_
13	that	that	SCONJ	IN	_	17	mark	_	_
14	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	17	nsubjpass	_	_
15	will	will	AUX	MD	VerbForm=Fin	17	aux	_	_
16	be	be	AUX	VB	VerbForm=Inf	17	auxpass	_	_
17	modelled	model	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
18	by	by	ADP	IN	_	17	agent	_	_
19	two	two	NUM	CD	NumType=Card	20	nummod	_	_
20	categories	category	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	one	one	NUM	CD	NumType=Card	20	appos	_	_
23	for	for	ADP	IN	_	22	prep	_	_
24	each	each	PRON	DT	_	23	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	two	two	NUM	CD	NumType=Card	27	nummod	_	_
27	polarities	polarity	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
29	with	with	ADP	IN	_	20	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
31	module	module	NOUN	NN	Number=Sing	32	compound	_	_
32	structure	structure	NOUN	NN	Number=Sing	29	pobj	_	_
33	connecting	connect	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	32	acl	_	_
34	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	33	dobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 3
# text = These are studied in considerable detail, and a comparison is made with a different notion of polarization due to Olivier Laurent: there is an adjoint connection between the two notions.
1	These	these	PRON	DT	Number=Plur|PronType=Dem	3	nsubjpass	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	studied	study	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	in	in	ADP	IN	_	3	prep	_	_
5	considerable	considerable	ADJ	JJ	Degree=Pos	6	amod	_	_
6	detail	detail	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	comparison	comparison	NOUN	NN	Number=Sing	12	nsubjpass	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	made	make	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	ccomp	_	_
13	with	with	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	different	different	ADJ	JJ	Degree=Pos	16	amod	_	_
16	notion	notion	NOUN	NN	Number=Sing	13	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	polarization	polarization	NOUN	NN	Number=Sing	17	pobj	_	_
19	due	due	ADP	IN	_	12	prep	_	_
20	to	to	ADP	IN	_	19	pcomp	_	_
21	Olivier	Olivier	PROPN	NNP	Number=Sing	22	compound	_	_
22	Laurent	Laurent	PROPN	NNP	Number=Sing	19	pobj	_	SpaceAfter=No
23	:	:	PUNCT	:	_	25	punct	_	_
24	there	there	PRON	EX	_	25	expl	_	_
25	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
26	an	an	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
27	adjoint	adjoint	NOUN	NN	Number=Sing	28	compound	_	_
28	connection	connection	NOUN	NN	Number=Sing	25	attr	_	_
29	between	between	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	two	two	NUM	CD	NumType=Card	32	nummod	_	_
32	notions	notion	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	25	punct	_	SpaceAfter=No

# doc_id = 286
# sent_id = 1
# text = It is well known that the internal suplattices in the topos of sheaves on a locale are precisely the modules on that locale.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	well	well	ADV	RB	Degree=Pos	4	advmod	_	_
4	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acomp	_	_
5	that	that	SCONJ	IN	_	17	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	internal	internal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	suplattices	suplattice	NOUN	NNS	Number=Plur	17	nsubj	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	topos	topos	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	sheaves	sheaf	NOUN	NNS	Number=Plur	12	pobj	_	_
14	on	on	ADP	IN	_	8	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	locale	locale	NOUN	NN	Number=Sing	14	pobj	_	_
17	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
18	precisely	precisely	ADV	RB	_	20	advmod	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	modules	module	NOUN	NNS	Number=Plur	17	attr	_	_
21	on	on	ADP	IN	_	20	prep	_	_
22	that	that	DET	DT	Number=Sing|PronType=Dem	23	det	_	_
23	locale	locale	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Using enriched category theory and a lemma on $ KZ $ doctrines we prove (the generalization of) this fact in the case of ordered sheaves on a small quantaloid.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	advcl	_	_
2	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	amod	_	_
3	category	category	NOUN	NN	Number=Sing	4	compound	_	_
4	theory	theory	NOUN	NN	Number=Sing	1	dobj	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	lemma	lemma	NOUN	NN	Number=Sing	4	conj	_	_
8	on	on	ADP	IN	_	7	prep	_	_
9	$ KZ $	$ kz $	SYM	$	_	10	nmod	_	_
10	doctrines	doctrine	NOUN	NNS	Number=Plur	8	pobj	_	_
11	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	12	nsubj	_	_
12	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	generalization	generalization	NOUN	NN	Number=Sing	12	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	SpaceAfter=No
17	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	15	punct	_	_
18	this	this	DET	DT	Number=Sing|PronType=Dem	19	det	_	_
19	fact	fact	NOUN	NN	Number=Sing	12	npadvmod	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	case	case	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	amod	_	_
25	sheaves	sheaf	NOUN	NNS	Number=Plur	23	pobj	_	_
26	on	on	ADP	IN	_	25	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	small	small	ADJ	JJ	Degree=Pos	29	amod	_	_
29	quantaloid	quantaloid	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 3
# text = Comparing module - equivalence with sheaf - equivalence for quantaloids and using the notion of centre of a quantaloid, we refine a result of Borceux and Vitale.
1	Comparing	compare	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	advcl	_	_
2	module	module	NOUN	NN	Number=Sing	4	compound	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	equivalence	equivalence	NOUN	NN	Number=Sing	1	dobj	_	_
5	with	with	ADP	IN	_	4	prep	_	_
6	sheaf	sheaf	NOUN	NN	Number=Sing	8	compound	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	equivalence	equivalence	NOUN	NN	Number=Sing	5	pobj	_	_
9	for	for	ADP	IN	_	1	prep	_	_
10	quantaloids	quantaloid	NOUN	NNS	Number=Plur	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	1	cc	_	_
12	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	1	conj	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	notion	notion	NOUN	NN	Number=Sing	12	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	centre	centre	NOUN	NN	Number=Sing	15	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	quantaloid	quantaloid	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
21	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	22	nsubj	_	_
22	refine	refine	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	result	result	NOUN	NN	Number=Sing	22	dobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	Borceux	Borceux	PROPN	NNP	Number=Sing	25	pobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	Vitale	Vitale	PROPN	NNP	Number=Sing	26	conj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# doc_id = 287
# sent_id = 1
# text = We illustrate the formula $ (downarrow p)x = Gamma_clik(x/p) $ , which gives the reflection $ downarrow p $ of a category $ p : P to X $ over $ X $ in discrete fibrations.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	illustrate	illustrate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	formula	formula	NOUN	NN	Number=Sing	5	compound	_	_
5	$ (downarrow p)x = Gamma_clik(x/p) $	$ (downarrow p)x = Gamma_clik(x/p) $	PUNCT	.	PunctType=Peri	2	dobj	_	_
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	which	which	PRON	WDT	_	8	nsubj	_	_
8	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	relcl	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	reflection	reflection	NOUN	NN	Number=Sing	8	dative	_	_
11	$ downarrow p $	$ downarrow p $	SYM	$	_	8	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
15	$ p : P to X $	$ p : p to x $	SYM	$	_	14	nmod	_	_
16	over	over	ADP	IN	_	14	prep	_	_
17	$ X $	$ x $	SYM	$	_	16	pobj	_	_
18	in	in	ADP	IN	_	8	prep	_	_
19	discrete	discrete	ADJ	JJ	Degree=Pos	20	amod	_	_
20	fibrations	fibration	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = One of its proofs is based on a ``complement operator" which takes a discrete fibration $ A $ to the functor $ neg A $ , right adjoint to $ Gamma_clik(Atimes - ):Cat/X to Set $ and valued in discrete opfibrations.
1	One	one	NUM	CD	NumType=Card	6	nsubjpass	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	4	poss	_	_
4	proofs	proof	NOUN	NNS	Number=Plur	2	pobj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	on	on	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
9	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	12	punct	_	SpaceAfter=No
10	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	12	punct	_	SpaceAfter=No
11	complement	complement	NOUN	NN	Number=Sing	12	compound	_	_
12	operator	operator	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
13	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	12	punct	_	_
14	which	which	PRON	WDT	_	15	nsubj	_	_
15	takes	take	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	relcl	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	discrete	discrete	ADJ	JJ	Degree=Pos	18	amod	_	_
18	fibration	fibration	NOUN	NN	Number=Sing	15	dobj	_	_
19	$ A $	$ a $	SYM	$	_	15	dobj	_	_
20	to	to	ADP	IN	_	15	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	functor	functor	NOUN	NN	Number=Sing	20	pobj	_	_
23	$ neg A $	$ neg a $	SYM	$	_	15	dobj	_	_
24	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
25	right	right	ADJ	JJ	Degree=Pos	26	amod	_	_
26	adjoint	adjoint	NOUN	NN	Number=Sing	15	dobj	_	_
27	to	to	ADP	IN	_	15	prep	_	_
28	$ Gamma_clik(Atimes - ):Cat/X to Set $	$ gamma_clik(atimes - ):cat/x to set $	SYM	$	_	27	pobj	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
30	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	conj	_	_
31	in	in	ADP	IN	_	30	prep	_	_
32	discrete	discrete	ADJ	JJ	Degree=Pos	33	amod	_	_
33	opfibrations	opfibration	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = Some consequences and applications are presented.
1	Some	some	DET	DT	_	2	det	_	_
2	consequences	consequence	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	applications	application	NOUN	NNS	Number=Plur	2	conj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
7	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 288
# sent_id = 1
# text = The nature of the spatial background for classical analysis and for modern theories of continuum physics requires more than the partial invariants of locales and cohomology rings for its description.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	nature	nature	NOUN	NN	Number=Sing	17	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	spatial	spatial	ADJ	JJ	Degree=Pos	6	amod	_	_
6	background	background	NOUN	NN	Number=Sing	3	pobj	_	_
7	for	for	ADP	IN	_	2	prep	_	_
8	classical	classical	ADJ	JJ	Degree=Pos	9	amod	_	_
9	analysis	analysis	NOUN	NN	Number=Sing	7	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
11	for	for	ADP	IN	_	7	conj	_	_
12	modern	modern	ADJ	JJ	Degree=Pos	13	amod	_	_
13	theories	theory	NOUN	NNS	Number=Plur	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	continuum	continuum	ADJ	JJ	Degree=Pos	16	amod	_	_
16	physics	physics	NOUN	NN	Number=Sing	14	pobj	_	_
17	requires	require	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
18	more	more	ADJ	JJR	Degree=Cmp	17	dobj	_	_
19	than	than	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	partial	partial	ADJ	JJ	Degree=Pos	22	amod	_	_
22	invariants	invariant	NOUN	NNS	Number=Plur	19	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	locales	locale	NOUN	NNS	Number=Plur	23	pobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	cohomology	cohomology	NOUN	NN	Number=Sing	27	compound	_	_
27	rings	ring	NOUN	NNS	Number=Plur	24	conj	_	_
28	for	for	ADP	IN	_	22	prep	_	_
29	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	30	poss	_	_
30	description	description	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 2
# text = As Maxwell emphasized, this description has various levels of precision depending on the needs of investigation.
1	As	as	SCONJ	IN	_	3	mark	_	_
2	Maxwell	Maxwell	PROPN	NNP	Number=Sing	3	nsubj	_	_
3	emphasized	emphasize	VERB	VBD	Tense=Past|VerbForm=Fin	7	advcl	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	description	description	NOUN	NN	Number=Sing	7	nsubj	_	_
7	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	various	various	ADJ	JJ	Degree=Pos	9	amod	_	_
9	levels	level	NOUN	NNS	Number=Plur	7	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	precision	precision	NOUN	NN	Number=Sing	10	pobj	_	_
12	depending	depend	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	prep	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	needs	need	NOUN	NNS	Number=Plur	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	investigation	investigation	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = These levels correspond to different categories of space, all of which have intuitively the feature of cohesion.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	levels	level	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	correspond	correspond	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	to	to	ADP	IN	_	3	prep	_	_
5	different	different	ADJ	JJ	Degree=Pos	6	amod	_	_
6	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	space	space	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
10	all	all	PRON	DT	_	13	nsubj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	which	which	PRON	WDT	_	11	pobj	_	_
13	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	advcl	_	_
14	intuitively	intuitively	ADV	RB	_	13	advmod	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	feature	feature	NOUN	NN	Number=Sing	13	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	cohesion	cohesion	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = Our aim here is to continue the axiomatic study of such categories, which involves the following aspects: (i) Categories of space as cohesive background, (ii) Cohesion versus non - cohesion; quality types, (iii) Extensive quality; intensive quality in its rarefied and condensed aspects; the canonical qualities form and substance, (iv) Non - cohesion within cohesion via constancy on infinitesimals, (v) The example of reflexive graphs and their atomic numbers, (vi) Sufficient cohesion and the Grothendieck condition VII.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	aim	aim	NOUN	NN	Number=Sing	4	nsubj	_	_
3	here	here	ADV	RB	PronType=Dem	2	advmod	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	continue	continue	VERB	VB	VerbForm=Inf	4	xcomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	axiomatic	axiomatic	ADJ	JJ	Degree=Pos	9	amod	_	_
9	study	study	NOUN	NN	Number=Sing	6	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	such	such	ADJ	JJ	Degree=Pos	12	amod	_	_
12	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	which	which	PRON	WDT	_	15	nsubj	_	_
15	involves	involve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	relcl	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	18	amod	_	_
18	aspects	aspect	NOUN	NNS	Number=Plur	15	dobj	_	SpaceAfter=No
19	:	:	PUNCT	:	_	18	punct	_	_
20	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	23	punct	_	SpaceAfter=No
21	i	i	NOUN	NN	Number=Sing	23	nmod	_	SpaceAfter=No
22	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	23	punct	_	_
23	Categories	category	NOUN	NNS	Number=Plur	18	appos	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	space	space	NOUN	NN	Number=Sing	24	pobj	_	_
26	as	as	ADP	IN	_	23	prep	_	_
27	cohesive	cohesive	NOUN	NN	Number=Sing	28	compound	_	_
28	background	background	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
30	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	33	punct	_	SpaceAfter=No
31	ii	ii	NOUN	NN	Number=Sing	33	nmod	_	SpaceAfter=No
32	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	33	punct	_	_
33	Cohesion	cohesion	NOUN	NN	Number=Sing	23	appos	_	_
34	versus	versus	ADP	IN	_	33	prep	_	_
35	non	non	ADJ	JJ	Degree=Pos	37	compound	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	cohesion	cohesion	NOUN	NN	Number=Sing	34	pobj	_	SpaceAfter=No
38	;	;	PUNCT	:	_	23	punct	_	_
39	quality	quality	NOUN	NN	Number=Sing	40	compound	_	_
40	types	type	NOUN	NNS	Number=Plur	23	conj	_	SpaceAfter=No
41	,	,	PUNCT	,	PunctType=Comm	40	punct	_	_
42	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	40	punct	_	SpaceAfter=No
43	iii	iii	NOUN	NN	Number=Sing	46	nmod	_	SpaceAfter=No
44	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	46	punct	_	_
45	Extensive	extensive	ADJ	JJ	Degree=Pos	46	amod	_	_
46	quality	quality	NOUN	NN	Number=Sing	40	appos	_	SpaceAfter=No
47	;	;	PUNCT	:	_	40	punct	_	_
48	intensive	intensive	ADJ	JJ	Degree=Pos	49	amod	_	_
49	quality	quality	NOUN	NN	Number=Sing	23	conj	_	_
50	in	in	ADP	IN	_	49	prep	_	_
51	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	55	poss	_	_
52	rarefied	rarefied	ADJ	JJ	Degree=Pos	55	amod	_	_
53	and	and	CCONJ	CC	ConjType=Cmp	52	cc	_	_
54	condensed	condensed	ADJ	JJ	Degree=Pos	52	conj	_	_
55	aspects	aspect	NOUN	NNS	Number=Plur	50	pobj	_	SpaceAfter=No
56	;	;	PUNCT	:	_	6	punct	_	_
57	the	the	DET	DT	Definite=Def|PronType=Art	60	det	_	_
58	canonical	canonical	ADJ	JJ	Degree=Pos	59	amod	_	_
59	qualities	quality	NOUN	NNS	Number=Plur	60	compound	_	_
60	form	form	NOUN	NN	Number=Sing	4	dep	_	_
61	and	and	CCONJ	CC	ConjType=Cmp	60	cc	_	_
62	substance	substance	NOUN	NN	Number=Sing	60	conj	_	SpaceAfter=No
63	,	,	PUNCT	,	PunctType=Comm	60	punct	_	_
64	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	60	punct	_	SpaceAfter=No
65	iv	iv	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	60	intj	_	SpaceAfter=No
66	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	65	punct	_	_
67	Non	non	ADJ	JJ	Degree=Pos	69	compound	_	_
68	-	-	PUNCT	HYPH	PunctType=Dash	69	punct	_	_
69	cohesion	cohesion	NOUN	NN	Number=Sing	60	conj	_	_
70	within	within	ADP	IN	_	60	prep	_	_
71	cohesion	cohesion	NOUN	NN	Number=Sing	70	pobj	_	_
72	via	via	ADP	IN	_	71	prep	_	_
73	constancy	constancy	NOUN	NN	Number=Sing	72	pobj	_	_
74	on	on	ADP	IN	_	73	prep	_	_
75	infinitesimals	infinitesimal	NOUN	NNS	Number=Plur	74	pobj	_	SpaceAfter=No
76	,	,	PUNCT	,	PunctType=Comm	60	punct	_	_
77	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	78	punct	_	SpaceAfter=No
78	v	v	X	LS	NumType=Ord	81	meta	_	SpaceAfter=No
79	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	78	punct	_	_
80	The	the	DET	DT	Definite=Def|PronType=Art	81	det	_	_
81	example	example	NOUN	NN	Number=Sing	60	conj	_	_
82	of	of	ADP	IN	_	81	prep	_	_
83	reflexive	reflexive	ADJ	JJ	Degree=Pos	84	amod	_	_
84	graphs	graph	NOUN	NNS	Number=Plur	82	pobj	_	_
85	and	and	CCONJ	CC	ConjType=Cmp	84	cc	_	_
86	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	88	poss	_	_
87	atomic	atomic	ADJ	JJ	Degree=Pos	88	amod	_	_
88	numbers	number	NOUN	NNS	Number=Plur	84	conj	_	SpaceAfter=No
89	,	,	PUNCT	,	PunctType=Comm	81	punct	_	_
90	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	94	punct	_	SpaceAfter=No
91	vi	vi	NOUN	NN	Number=Sing	94	nmod	_	SpaceAfter=No
92	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	94	punct	_	_
93	Sufficient	sufficient	ADJ	JJ	Degree=Pos	94	amod	_	_
94	cohesion	cohesion	NOUN	NN	Number=Sing	81	conj	_	_
95	and	and	CCONJ	CC	ConjType=Cmp	94	cc	_	_
96	the	the	DET	DT	Definite=Def|PronType=Art	99	det	_	_
97	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	99	compound	_	_
98	condition	condition	NOUN	NN	Number=Sing	99	compound	_	_
99	VII	VII	PROPN	NNP	Number=Sing	94	conj	_	SpaceAfter=No
100	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = Weak generation of a subtopos by a quotient topos I look forward to further work on each of these aspects, as well as development of categories of dynamical laws, constitutive relations, and other mathematical structures that naturally live in cohesive categories.
1	Weak	weak	ADJ	JJ	Degree=Pos	2	amod	_	_
2	generation	generation	NOUN	NN	Number=Sing	11	dep	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	subtopos	subtopos	NOUN	NN	Number=Sing	3	pobj	_	_
6	by	by	ADP	IN	_	2	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	quotient	quotient	ADJ	JJ	Degree=Pos	9	amod	_	_
9	topos	topos	NOUN	NN	Number=Sing	6	pobj	_	_
10	I	I	PRON	PRP	Case=Nom|Number=Sing|Person=1|PronType=Prs	11	nsubj	_	_
11	look	look	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	forward	forward	ADV	RB	_	11	advmod	_	_
13	to	to	AUX	IN	_	15	aux	_	_
14	further	far	ADV	RB	_	15	advmod	_	_
15	work	work	VERB	VB	VerbForm=Inf	11	advcl	_	_
16	on	on	ADP	IN	_	15	prep	_	_
17	each	each	PRON	DT	_	16	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	these	these	DET	DT	Number=Plur|PronType=Dem	20	det	_	_
20	aspects	aspect	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
22	as	as	ADV	RB	_	24	advmod	_	_
23	well	well	ADV	RB	Degree=Pos	24	advmod	_	_
24	as	as	ADP	IN	_	17	cc	_	_
25	development	development	NOUN	NN	Number=Sing	17	conj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	categories	category	NOUN	NNS	Number=Plur	26	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	dynamical	dynamical	ADJ	JJ	Degree=Pos	30	amod	_	_
30	laws	law	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
32	constitutive	constitutive	ADJ	JJ	Degree=Pos	33	amod	_	_
33	relations	relation	NOUN	NNS	Number=Plur	25	conj	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
36	other	other	ADJ	JJ	Degree=Pos	38	amod	_	_
37	mathematical	mathematical	ADJ	JJ	Degree=Pos	38	amod	_	_
38	structures	structure	NOUN	NNS	Number=Plur	33	conj	_	_
39	that	that	PRON	WDT	PronType=Rel	41	nsubj	_	_
40	naturally	naturally	ADV	RB	_	41	advmod	_	_
41	live	live	VERB	VBP	Tense=Pres|VerbForm=Fin	38	relcl	_	_
42	in	in	ADP	IN	_	41	prep	_	_
43	cohesive	cohesive	ADJ	JJ	Degree=Pos	44	amod	_	_
44	categories	category	NOUN	NNS	Number=Plur	42	pobj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# doc_id = 289
# sent_id = 1
# text = In some bicategories, the 1 - cells are `morphisms' between the 0 - cells, such as functors between categories, but in others they are `objects' over the 0 - cells, such as bimodules, spans, distributors, or parametrized spectra.
1	In	in	ADP	IN	_	9	prep	_	_
2	some	some	DET	DT	_	3	det	_	_
3	bicategories	bicategorie	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
6	1	1	NUM	CD	NumType=Card	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	cells	cell	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	9	punct	_	SpaceAfter=No
11	morphisms	morphism	NOUN	NNS	Number=Plur	9	attr	_	SpaceAfter=No
12	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	11	punct	_	_
13	between	between	ADP	IN	_	11	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
15	0	0	NUM	CD	NumType=Card	17	nummod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	cells	cell	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	such	such	ADJ	JJ	Degree=Pos	20	amod	_	_
20	as	as	ADP	IN	_	17	prep	_	_
21	functors	functor	NOUN	NNS	Number=Plur	20	pobj	_	_
22	between	between	ADP	IN	_	21	prep	_	_
23	categories	category	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
25	but	but	CCONJ	CC	ConjType=Cmp	9	cc	_	_
26	in	in	ADP	IN	_	29	prep	_	_
27	others	other	NOUN	NNS	Number=Plur	26	pobj	_	_
28	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	29	nsubj	_	_
29	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	conj	_	_
30	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	31	punct	_	SpaceAfter=No
31	objects	object	NOUN	NNS	Number=Plur	29	attr	_	SpaceAfter=No
32	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	31	punct	_	_
33	over	over	ADP	IN	_	31	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
35	0	0	NUM	CD	NumType=Card	37	nummod	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	cells	cell	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
38	,	,	PUNCT	,	PunctType=Comm	37	punct	_	_
39	such	such	ADJ	JJ	Degree=Pos	40	amod	_	_
40	as	as	ADP	IN	_	37	prep	_	_
41	bimodules	bimodule	NOUN	NNS	Number=Plur	40	pobj	_	SpaceAfter=No
42	,	,	PUNCT	,	PunctType=Comm	41	punct	_	_
43	spans	span	NOUN	NNS	Number=Plur	41	conj	_	SpaceAfter=No
44	,	,	PUNCT	,	PunctType=Comm	43	punct	_	_
45	distributors	distributor	NOUN	NNS	Number=Plur	43	conj	_	SpaceAfter=No
46	,	,	PUNCT	,	PunctType=Comm	45	punct	_	_
47	or	or	CCONJ	CC	ConjType=Cmp	45	cc	_	_
48	parametrized	parametrized	ADJ	JJ	Degree=Pos	49	amod	_	_
49	spectra	spectra	NOUN	NN	Number=Sing	45	conj	_	SpaceAfter=No
50	.	.	PUNCT	.	PunctType=Peri	29	punct	_	SpaceAfter=No

# sent_id = 2
# text = Many bicategorical notions do not work well in these cases, because the `morphisms between 0 - cells', such as ring homomorphisms, are missing.
1	Many	many	ADJ	JJ	Degree=Pos	3	amod	_	_
2	bicategorical	bicategorical	ADJ	JJ	Degree=Pos	3	amod	_	_
3	notions	notion	NOUN	NNS	Number=Plur	6	nsubj	_	_
4	do	do	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	aux	_	_
5	not	not	PART	RB	Polarity=Neg	6	neg	_	_
6	work	work	VERB	VB	VerbForm=Inf	0	ROOT	_	_
7	well	well	ADV	RB	Degree=Pos	6	advmod	_	_
8	in	in	ADP	IN	_	6	prep	_	_
9	these	these	DET	DT	Number=Plur|PronType=Dem	10	det	_	_
10	cases	case	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
12	because	because	SCONJ	IN	_	27	mark	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	15	punct	_	SpaceAfter=No
15	morphisms	morphism	NOUN	NNS	Number=Plur	27	nsubj	_	_
16	between	between	ADP	IN	_	15	prep	_	_
17	0	0	NUM	CD	NumType=Card	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	cells	cell	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
20	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	15	punct	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
22	such	such	ADJ	JJ	Degree=Pos	23	amod	_	_
23	as	as	ADP	IN	_	15	prep	_	_
24	ring	ring	NOUN	NN	Number=Sing	25	compound	_	_
25	homomorphisms	homomorphism	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
27	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	advcl	_	_
28	missing	miss	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	27	acomp	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = We can include them by using a pseudo double category, but usually these morphisms also induce base change functors acting on the 1 - cells.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	can	can	AUX	MD	VerbForm=Fin	3	aux	_	_
3	include	include	VERB	VB	VerbForm=Inf	0	ROOT	_	_
4	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	3	dobj	_	_
5	by	by	ADP	IN	_	3	prep	_	_
6	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	pseudo	pseudo	NOUN	NN	Number=Sing	10	nmod	_	_
9	double	double	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	6	dobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
12	but	but	CCONJ	CC	ConjType=Cmp	3	cc	_	_
13	usually	usually	ADV	RB	_	17	advmod	_	_
14	these	these	DET	DT	Number=Plur|PronType=Dem	15	det	_	_
15	morphisms	morphism	NOUN	NNS	Number=Plur	17	nsubj	_	_
16	also	also	ADV	RB	_	17	advmod	_	_
17	induce	induce	VERB	VBP	Tense=Pres|VerbForm=Fin	3	conj	_	_
18	base	base	NOUN	NN	Number=Sing	19	compound	_	_
19	change	change	NOUN	NN	Number=Sing	20	compound	_	_
20	functors	functor	NOUN	NNS	Number=Plur	17	dobj	_	_
21	acting	act	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	acl	_	_
22	on	on	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
24	1	1	NUM	CD	NumType=Card	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	cells	cell	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 4
# text = We avoid complicated coherence problems by describing base change `nonalgebraically', using categorical fibrations.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	avoid	avoid	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	complicated	complicated	ADJ	JJ	Degree=Pos	5	amod	_	_
4	coherence	coherence	NOUN	NN	Number=Sing	5	compound	_	_
5	problems	problem	NOUN	NNS	Number=Plur	2	dobj	_	_
6	by	by	ADP	IN	_	2	prep	_	_
7	describing	describe	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	pcomp	_	_
8	base	base	NOUN	NN	Number=Sing	9	compound	_	_
9	change	change	NOUN	NN	Number=Sing	7	dobj	_	_
10	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	7	punct	_	SpaceAfter=No
11	nonalgebraically	nonalgebraically	ADV	RB	_	7	advmod	_	SpaceAfter=No
12	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	2	punct	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
14	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
15	categorical	categorical	ADJ	JJ	Degree=Pos	16	amod	_	_
16	fibrations	fibration	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = The resulting `framed bicategories' assemble into 2 - categories, with attendant notions of equivalence, adjunction, and so on which are more appropriate for our examples than are the usual bicategorical ones.
1	The	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
2	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	amod	_	_
3	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	5	punct	_	SpaceAfter=No
4	framed	framed	ADJ	JJ	Degree=Pos	5	amod	_	_
5	bicategories	bicategorie	NOUN	NNS	Number=Plur	7	poss	_	SpaceAfter=No
6	'	'	PART	POS	_	5	case	_	_
7	assemble	assemble	NOUN	NN	Number=Sing	0	ROOT	_	_
8	into	into	ADP	IN	_	7	prep	_	_
9	2	2	NUM	CD	NumType=Card	11	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	with	with	ADP	IN	_	7	prep	_	_
14	attendant	attendant	ADJ	JJ	Degree=Pos	15	amod	_	_
15	notions	notion	NOUN	NNS	Number=Plur	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	equivalence	equivalence	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	adjunction	adjunction	NOUN	NN	Number=Sing	17	conj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
22	so	so	ADV	RB	_	25	advmod	_	_
23	on	on	ADP	IN	_	25	prep	_	_
24	which	which	PRON	WDT	_	23	pobj	_	_
25	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	conj	_	_
26	more	more	ADV	RBR	Degree=Cmp	27	advmod	_	_
27	appropriate	appropriate	ADJ	JJ	Degree=Pos	25	acomp	_	_
28	for	for	ADP	IN	_	27	prep	_	_
29	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	30	poss	_	_
30	examples	example	NOUN	NNS	Number=Plur	28	pobj	_	_
31	than	than	SCONJ	IN	_	32	mark	_	_
32	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	27	advcl	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
34	usual	usual	ADJ	JJ	Degree=Pos	36	amod	_	_
35	bicategorical	bicategorical	ADJ	JJ	Degree=Pos	36	amod	_	_
36	ones	one	NOUN	NNS	Number=Plur	32	attr	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 6
# text = We then describe two ways to construct framed bicategories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	two	two	NUM	CD	NumType=Card	5	nummod	_	_
5	ways	way	NOUN	NNS	Number=Plur	3	dobj	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	construct	construct	VERB	VB	VerbForm=Inf	5	relcl	_	_
8	framed	framed	ADJ	JJ	Degree=Pos	9	amod	_	_
9	bicategories	bicategorie	NOUN	NNS	Number=Plur	7	dobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = One is an analogue of rings and bimodules which starts from one framed bicategory and builds another.
1	One	one	NUM	CD	NumType=Card	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	analogue	analogue	NOUN	NN	Number=Sing	2	attr	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	rings	ring	NOUN	NNS	Number=Plur	5	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	bimodules	bimodule	NOUN	NNS	Number=Plur	6	conj	_	_
9	which	which	PRON	WDT	_	10	nsubj	_	_
10	starts	start	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	relcl	_	_
11	from	from	ADP	IN	_	10	prep	_	_
12	one	one	NUM	CD	NumType=Card	14	nummod	_	_
13	framed	framed	ADJ	JJ	Degree=Pos	14	amod	_	_
14	bicategory	bicategory	NOUN	NN	Number=Sing	11	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
16	builds	build	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	conj	_	_
17	another	another	PRON	DT	_	16	dobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 8
# text = The other starts from a `monoidal fibration', meaning a parametrized family of monoidal categories, and produces an analogue of the framed bicategory of spans.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	other	other	ADJ	JJ	Degree=Pos	3	nsubj	_	_
3	starts	start	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	from	from	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
6	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	8	punct	_	SpaceAfter=No
7	monoidal	monoidal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	fibration	fibration	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
9	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	3	punct	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
11	meaning	mean	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	advcl	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	parametrized	parametrized	ADJ	JJ	Degree=Pos	14	amod	_	_
14	family	family	NOUN	NN	Number=Sing	11	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	monoidal	monoidal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
20	produces	produce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	conj	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	analogue	analogue	NOUN	NN	Number=Sing	20	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	framed	framed	ADJ	JJ	Degree=Pos	26	amod	_	_
26	bicategory	bicategory	NOUN	NN	Number=Sing	23	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	spans	span	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 9
# text = Combining the two, we obtain a construction which includes both enriched and internal categories as special cases.
1	Combining	combine	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	advcl	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	two	two	NUM	CD	NumType=Card	1	dobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	construction	construction	NOUN	NN	Number=Sing	6	dobj	_	_
9	which	which	PRON	WDT	_	10	nsubj	_	_
10	includes	include	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	relcl	_	_
11	both	both	CCONJ	CC	ConjType=Cmp	12	preconj	_	_
12	enriched	enriched	ADJ	JJ	Degree=Pos	15	amod	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	internal	internal	ADJ	JJ	Degree=Pos	12	conj	_	_
15	categories	category	NOUN	NNS	Number=Plur	10	dobj	_	_
16	as	as	ADP	IN	_	10	prep	_	_
17	special	special	ADJ	JJ	Degree=Pos	18	amod	_	_
18	cases	case	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 290
# sent_id = 1
# text = Recently, symmetric categorical groups are used for the study of the Brauer groups of symmetric monoidal categories.
1	Recently	recently	ADV	RB	_	7	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
3	symmetric	symmetric	ADJ	JJ	Degree=Pos	5	amod	_	_
4	categorical	categorical	ADJ	JJ	Degree=Pos	5	amod	_	_
5	groups	group	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	study	study	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	Brauer	Brauer	PROPN	NNP	Number=Sing	14	compound	_	_
14	groups	group	NOUN	NNS	Number=Plur	11	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	symmetric	symmetric	ADJ	JJ	Degree=Pos	18	amod	_	_
17	monoidal	monoidal	ADJ	JJ	Degree=Pos	18	amod	_	_
18	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 2
# text = As a part of these efforts, some algebraic structures of the 2 - category of symmetric categorical groups $ SCG $ are being investigated.
1	As	as	ADP	IN	_	23	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	part	part	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	these	these	DET	DT	Number=Plur|PronType=Dem	6	det	_	_
6	efforts	effort	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
8	some	some	DET	DT	_	10	det	_	_
9	algebraic	algebraic	ADJ	JJ	Degree=Pos	10	amod	_	_
10	structures	structure	NOUN	NNS	Number=Plur	23	nsubjpass	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
13	2	2	NUM	CD	NumType=Card	15	nummod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	symmetric	symmetric	ADJ	JJ	Degree=Pos	19	amod	_	_
18	categorical	categorical	ADJ	JJ	Degree=Pos	19	amod	_	_
19	groups	group	NOUN	NNS	Number=Plur	16	pobj	_	_
20	$ SCG $	$ scg $	SYM	$	_	10	appos	_	_
21	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	23	aux	_	_
22	being	be	AUX	VBG	VerbForm=Ger	23	auxpass	_	_
23	investigated	investigate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this paper, we consider a 2 - categorical analogue of an abelian category, in such a way that it contains $ SCG $ as an example.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	2	2	NUM	CD	NumType=Card	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	categorical	categorical	ADJ	JJ	Degree=Pos	11	amod	_	_
11	analogue	analogue	NOUN	NN	Number=Sing	6	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	abelian	abelian	ADJ	JJ	Degree=Pos	15	compound	_	_
15	category	category	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
17	in	in	ADP	IN	_	6	prep	_	_
18	such	such	DET	PDT	_	20	predet	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	way	way	NOUN	NN	Number=Sing	17	pobj	_	_
21	that	that	PRON	WDT	PronType=Rel	23	advmod	_	_
22	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	23	nsubj	_	_
23	contains	contain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	relcl	_	_
24	$ SCG $	$ scg $	SYM	$	_	23	dobj	_	_
25	as	as	ADP	IN	_	23	prep	_	_
26	an	an	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	example	example	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = As a main theorem, we construct a long cohomology 2 - exact sequence from any extension of complexes in such a 2 - category.
1	As	as	ADP	IN	_	7	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	main	main	ADJ	JJ	Degree=Pos	4	amod	_	_
4	theorem	theorem	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
9	long	long	ADJ	JJ	Degree=Pos	10	amod	_	_
10	cohomology	cohomology	NOUN	NN	Number=Sing	14	nmod	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	exact	exact	ADJ	JJ	Degree=Pos	14	amod	_	_
14	sequence	sequence	NOUN	NN	Number=Sing	7	dobj	_	_
15	from	from	ADP	IN	_	14	prep	_	_
16	any	any	DET	DT	_	17	det	_	_
17	extension	extension	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	complexes	complex	NOUN	NNS	Number=Plur	18	pobj	_	_
20	in	in	ADP	IN	_	17	prep	_	_
21	such	such	DET	PDT	_	25	predet	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
23	2	2	NUM	CD	NumType=Card	25	nummod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	category	category	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 5
# text = Our axiomatic and self - dual definition will enable us to simplify the proofs, by analogy with abelian categories.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	7	poss	_	_
2	axiomatic	axiomatic	ADJ	JJ	Degree=Pos	7	amod	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	self	self	NOUN	NN	Number=Sing	6	npadvmod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	dual	dual	ADJ	JJ	Degree=Pos	2	conj	_	_
7	definition	definition	NOUN	NN	Number=Sing	9	nsubj	_	_
8	will	will	AUX	MD	VerbForm=Fin	9	aux	_	_
9	enable	enable	VERB	VB	VerbForm=Inf	0	ROOT	_	_
10	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	9	dobj	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	simplify	simplify	VERB	VB	VerbForm=Inf	9	xcomp	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	proofs	proof	NOUN	NNS	Number=Plur	12	dobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
16	by	by	ADP	IN	_	12	prep	_	_
17	analogy	analogy	NOUN	NN	Number=Sing	16	pobj	_	_
18	with	with	ADP	IN	_	17	prep	_	_
19	abelian	abelian	ADJ	JJ	Degree=Pos	20	amod	_	_
20	categories	category	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 291
# sent_id = 1
# text = We prove a general theorem relating pseudo - exponentiable objects of a bicategory $ K $ to those of the Kleisli bicategory of a pseudo - monad on $ K $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	general	general	ADJ	JJ	Degree=Pos	5	amod	_	_
5	theorem	theorem	ADJ	JJ	Degree=Pos	2	dobj	_	_
6	relating	relate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	acl	_	_
7	pseudo	pseudo	NOUN	NN	Number=Sing	9	npadvmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	exponentiable	exponentiable	ADJ	JJ	Degree=Pos	10	amod	_	_
10	objects	object	NOUN	NNS	Number=Plur	6	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	bicategory	bicategory	NOUN	NN	Number=Sing	11	pobj	_	_
14	$ K $	$ k $	SYM	$	_	5	dep	_	_
15	to	to	ADP	IN	_	2	prep	_	_
16	those	those	PRON	DT	Number=Plur|PronType=Dem	15	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	Kleisli	Kleisli	PROPN	NNP	Number=Sing	20	compound	_	_
20	bicategory	bicategory	NOUN	NN	Number=Sing	17	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
23	pseudo	pseudo	NOUN	NN	Number=Sing	25	compound	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	monad	monad	NOUN	NNS	Number=Plur	21	pobj	_	_
26	on	on	ADP	IN	_	25	prep	_	_
27	$ K $	$ k $	SYM	$	_	26	pobj	_	_
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This theorem is applied to obtain pseudo - exponentiable objects of the homotopy slices $ Top//B $ of the category of topological spaces and the pseudo - slices $ Cat//B $ of the category of small categories.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	theorem	theorem	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	applied	apply	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	obtain	obtain	VERB	VB	VerbForm=Inf	4	xcomp	_	_
7	pseudo	pseudo	NOUN	NN	Number=Sing	9	npadvmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	exponentiable	exponentiable	ADJ	JJ	Degree=Pos	10	amod	_	_
10	objects	object	NOUN	NNS	Number=Plur	6	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	homotopy	homotopy	NOUN	NN	Number=Sing	11	pobj	_	_
14	slices	slice	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	conj	_	_
15	$ Top//B $	$ top//b $	SYM	$	_	14	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	category	category	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	topological	topological	ADJ	JJ	Degree=Pos	21	amod	_	_
21	spaces	space	NOUN	NNS	Number=Plur	19	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
24	pseudo	pseudo	NOUN	NN	Number=Sing	26	compound	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	slices	slice	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	conj	_	_
27	$ Cat//B $	$ cat//b $	SYM	$	_	26	appos	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	category	category	NOUN	NN	Number=Sing	28	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	small	small	ADJ	JJ	Degree=Pos	33	amod	_	_
33	categories	category	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 292
# sent_id = 1
# text = We prove that, given any small category $ A= $ , the derivator $ HOT_A $ , corresponding to the homotopy theory of presheaves of homotopy types on $ A $ , is characterized by a natural universal property.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	29	mark	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
5	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	prep	_	_
6	any	any	DET	DT	_	8	det	_	_
7	small	small	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
9	$ A= $	$ a= $	SYM	$	_	5	pcomp	_	_
10	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	derivator	derivator	NOUN	NN	Number=Sing	29	nsubjpass	_	_
13	$ HOT_A $	$ hot_a $	SYM	$	_	12	appos	_	_
14	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
15	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	amod	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	homotopy	homotopy	NOUN	NN	Number=Sing	19	compound	_	_
19	theory	theory	NOUN	NN	Number=Sing	16	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	presheaves	presheave	NOUN	NNS	Number=Plur	20	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	homotopy	homotopy	NOUN	NN	Number=Sing	24	compound	_	_
24	types	type	NOUN	NNS	Number=Plur	22	pobj	_	_
25	on	on	ADP	IN	_	21	prep	_	_
26	$ A $	$ a $	SYM	$	_	25	pobj	_	_
27	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	auxpass	_	_
29	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
30	by	by	ADP	IN	_	29	agent	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
32	natural	natural	ADJ	JJ	Degree=Pos	34	amod	_	_
33	universal	universal	ADJ	JJ	Degree=Pos	34	amod	_	_
34	property	property	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In particular, the theory of Kan extensions extends to the setting of Grothendieck derivators.
1	In	in	ADP	IN	_	9	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	theory	theory	NOUN	NN	Number=Sing	9	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Kan	Kan	PROPN	NNP	Number=Sing	8	compound	_	_
8	extensions	extension	NOUN	NNS	Number=Plur	6	pobj	_	_
9	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	setting	setting	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	15	compound	_	_
15	derivators	derivator	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 293
# sent_id = 1
# text = We develop in some generality the dualities that often arise when one object lies in two different categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	some	some	DET	DT	_	5	det	_	_
5	generality	generality	NOUN	NN	Number=Sing	3	pobj	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	dualities	duality	NOUN	NNS	Number=Plur	2	dobj	_	_
8	that	that	PRON	WDT	PronType=Rel	10	nsubj	_	_
9	often	often	ADV	RB	_	10	advmod	_	_
10	arise	arise	VERB	VBP	Tense=Pres|VerbForm=Fin	7	relcl	_	_
11	when	when	SCONJ	WRB	_	14	advmod	_	_
12	one	one	NUM	CD	NumType=Card	13	nummod	_	_
13	object	object	NOUN	NN	Number=Sing	14	nsubj	_	_
14	lies	lie	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	advcl	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	two	two	NUM	CD	NumType=Card	18	nummod	_	_
17	different	different	ADJ	JJ	Degree=Pos	18	amod	_	_
18	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In our examples, one category is equational and the other consists of the topological objects in a (generally different) equational category.
1	In	in	ADP	IN	_	7	prep	_	_
2	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	3	poss	_	_
3	examples	example	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
5	one	one	NUM	CD	NumType=Card	6	nummod	_	_
6	category	category	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	equational	equational	ADJ	JJ	Degree=Pos	7	acomp	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	other	other	ADJ	JJ	Degree=Pos	12	nsubj	_	_
12	consists	consist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	conj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	topological	topological	ADJ	JJ	Degree=Pos	16	amod	_	_
16	objects	object	NOUN	NNS	Number=Plur	13	pobj	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
19	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
20	generally	generally	ADV	RB	_	21	advmod	_	_
21	different	different	ADJ	JJ	Degree=Pos	24	amod	_	SpaceAfter=No
22	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	24	punct	_	_
23	equational	equational	ADJ	JJ	Degree=Pos	24	amod	_	_
24	category	category	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# doc_id = 294
# sent_id = 1
# text = The role of the Frobenius operations in analyzing finite spaces, as well as the extended algebraic geometry over rigs, depend partly on varieties (Birkhoffian inclusions of algebraic categories) that have coreflections as well as reflections and whose dual category of affine spaces is extensive.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	role	role	NOUN	NN	Number=Sing	22	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	Frobenius	Frobenius	PROPN	NNP	Number=Sing	6	compound	_	_
6	operations	operation	NOUN	NNS	Number=Plur	3	pobj	_	_
7	in	in	ADP	IN	_	2	prep	_	_
8	analyzing	analyze	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	pcomp	_	_
9	finite	finite	ADJ	JJ	Degree=Pos	10	compound	_	_
10	spaces	space	NOUN	NNS	Number=Plur	8	dobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	as	as	ADV	RB	_	14	advmod	_	_
13	well	well	ADV	RB	Degree=Pos	14	advmod	_	_
14	as	as	ADP	IN	_	10	cc	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
16	extended	extended	ADJ	JJ	Degree=Pos	18	amod	_	_
17	algebraic	algebraic	ADJ	JJ	Degree=Pos	18	amod	_	_
18	geometry	geometry	NOUN	NN	Number=Sing	10	conj	_	_
19	over	over	ADP	IN	_	18	prep	_	_
20	rigs	rig	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
22	depend	depend	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
23	partly	partly	ADV	RB	_	22	advmod	_	_
24	on	on	ADP	IN	_	22	prep	_	_
25	varieties	variety	NOUN	NNS	Number=Plur	24	pobj	_	_
26	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	25	punct	_	SpaceAfter=No
27	Birkhoffian	birkhoffian	ADJ	JJ	Degree=Pos	28	amod	_	_
28	inclusions	inclusion	NOUN	NNS	Number=Plur	25	appos	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	algebraic	algebraic	ADJ	JJ	Degree=Pos	31	amod	_	_
31	categories	category	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
32	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	31	punct	_	_
33	that	that	PRON	WDT	PronType=Rel	34	nsubj	_	_
34	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	28	relcl	_	_
35	coreflections	coreflection	NOUN	NNS	Number=Plur	34	dobj	_	_
36	as	as	ADV	RB	_	38	advmod	_	_
37	well	well	ADV	RB	Degree=Pos	38	advmod	_	_
38	as	as	ADP	IN	_	35	cc	_	_
39	reflections	reflection	NOUN	NNS	Number=Plur	35	conj	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	39	cc	_	_
41	whose	whose	DET	WP$	Poss=Yes	43	poss	_	_
42	dual	dual	ADJ	JJ	Degree=Pos	43	amod	_	_
43	category	category	NOUN	NN	Number=Sing	47	nsubj	_	_
44	of	of	ADP	IN	_	43	prep	_	_
45	affine	affine	NOUN	NN	Number=Sing	46	compound	_	_
46	spaces	space	NOUN	NNS	Number=Plur	44	pobj	_	_
47	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	conj	_	_
48	extensive	extensive	ADJ	JJ	Degree=Pos	47	acomp	_	SpaceAfter=No
49	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# sent_id = 2
# text = Even within the category of those rigs where 1 + 1 = 1, not only distributive lattices but also the function algebras of tropical geometry (where $ x + 1 = 1 $ ) and the dimension rigs of separable prextensive categories (where $ x + x^2 = x^2 $ ) enjoy those features.
1	Even	even	ADV	RB	_	2	advmod	_	_
2	within	within	ADP	IN	_	43	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	category	category	NOUN	NN	Number=Sing	2	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	those	those	DET	DT	Number=Plur|PronType=Dem	7	det	_	_
7	rigs	rig	NOUN	NNS	Number=Plur	5	pobj	_	_
8	where	where	SCONJ	WRB	_	18	advmod	_	_
9	1	1	NUM	CD	NumType=Card	11	compound	_	_
10	+	+	NUM	CD	NumType=Card	9	punct	_	_
11	1	1	NUM	CD	NumType=Card	18	nummod	_	_
12	=	=	SYM	SYM	_	11	punct	_	_
13	1	1	NUM	CD	NumType=Card	12	nummod	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
15	not	not	PART	RB	Polarity=Neg	18	preconj	_	_
16	only	only	ADV	RB	_	15	advmod	_	_
17	distributive	distributive	ADJ	JJ	Degree=Pos	18	amod	_	_
18	lattices	lattice	NOUN	NNS	Number=Plur	2	pcomp	_	_
19	but	but	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	also	also	ADV	RB	_	19	advmod	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	function	function	NOUN	NN	Number=Sing	23	compound	_	_
23	algebras	algebra	NOUN	NNS	Number=Plur	18	conj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	tropical	tropical	ADJ	JJ	Degree=Pos	26	amod	_	_
26	geometry	geometry	NOUN	NN	Number=Sing	24	pobj	_	_
27	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	26	punct	_	SpaceAfter=No
28	where	where	SCONJ	WRB	_	29	advmod	_	_
29	$ x + 1 = 1 $	$ x + 1 = 1 $	SYM	$	_	23	relcl	_	_
30	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	23	punct	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
33	dimension	dimension	NOUN	NN	Number=Sing	34	compound	_	_
34	rigs	rig	NOUN	NNS	Number=Plur	23	conj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	separable	separable	ADJ	JJ	Degree=Pos	38	amod	_	_
37	prextensive	prextensive	ADJ	JJ	Degree=Pos	38	amod	_	_
38	categories	category	NOUN	NNS	Number=Plur	35	pobj	_	_
39	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	38	punct	_	SpaceAfter=No
40	where	where	SCONJ	WRB	_	41	advmod	_	_
41	$ x + x^2 = x^2 $	$ x + x^2 = x^2 $	SYM	$	_	34	relcl	_	_
42	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	34	punct	_	_
43	enjoy	enjoy	VERB	VB	VerbForm=Inf	0	ROOT	_	_
44	those	those	DET	DT	Number=Plur|PronType=Dem	45	det	_	_
45	features	feature	NOUN	NNS	Number=Plur	43	dobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	43	punct	_	SpaceAfter=No

# doc_id = 295
# sent_id = 1
# text = Assuming that $ B $ is a full $ A_infty $ - subcategory of a unital $ A_infty $ - category $ cc $ we construct the quotient unital $ A_infty $ - category $ cd= $ ` $ cc/cb $ '.
1	Assuming	assume	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	18	advcl	_	_
2	that	that	SCONJ	IN	_	4	mark	_	_
3	$ B $	$ b $	SYM	$	_	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	1	ccomp	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
6	full	full	ADJ	JJ	Degree=Pos	9	amod	_	_
7	$ A_infty $	$ a_infty $	SYM	$	_	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	subcategory	subcategory	NOUN	NN	Number=Sing	4	attr	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
12	unital	unital	ADJ	JJ	Degree=Pos	15	amod	_	_
13	$ A_infty $	$ a_infty $	SYM	$	_	15	nummod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
16	$ cc $	$ cc $	SYM	$	_	4	dep	_	_
17	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	18	nsubj	_	_
18	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	quotient	quotient	NOUN	NN	Number=Sing	18	dobj	_	_
21	unital	unital	PROPN	NNP	Number=Sing	18	dobj	_	_
22	$ A_infty $	$ a_infty $	SYM	$	_	24	nummod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	category	category	NOUN	NN	Number=Sing	21	npadvmod	_	_
25	$ cd= $	$ cd= $	SYM	$	_	24	nummod	_	_
26	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	24	punct	_	_
27	$ cc/cb $	$ cc/cb $	SYM	$	_	24	appos	_	_
28	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	18	punct	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# sent_id = 2
# text = It represents the $ A_infty^u $ - 2 - functor $ A mapsto A_infty^u(C, A)_{mod B} $ , which associates with a given unital $ A_infty $ - category $ A $ the $ A_infty $ - category of unital $ A_infty $ - functors $ C to A $ , whose restriction to $ B $ is contractible.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	represents	represent	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
4	$ A_infty^u $	$ a_infty^u $	SYM	$	_	6	quantmod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	2	2	NUM	CD	NumType=Card	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	functor	functor	NOUN	NN	Number=Sing	9	compound	_	_
9	$ A mapsto A_infty^u(C, A)_{mod B} $	$ a mapsto a_infty^u(c, a)_{mod b} $	SYM	$	_	2	dobj	_	_
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	which	which	PRON	WDT	_	12	nsubj	_	_
12	associates	associate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	relcl	_	_
13	with	with	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
16	unital	unital	NOUN	NN	Number=Sing	13	pobj	_	_
17	$ A_infty $	$ a_infty $	SYM	$	_	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
20	$ A $	$ a $	SYM	$	_	19	nmod	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
22	$ A_infty $	$ a_infty $	SYM	$	_	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	category	category	NOUN	NN	Number=Sing	12	dobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	unital	unital	PROPN	NNP	Number=Sing	30	compound	_	_
27	$ A_infty $	$ a_infty $	SYM	$	_	29	compound	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	functors	functor	NOUN	NNS	Number=Plur	30	compound	_	_
30	$ C to A $	$ c to a $	SYM	$	_	25	pobj	_	_
31	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
32	whose	whose	DET	WP$	Poss=Yes	33	poss	_	_
33	restriction	restriction	NOUN	NN	Number=Sing	36	nsubj	_	_
34	to	to	ADP	IN	_	33	prep	_	_
35	$ B $	$ b $	SYM	$	_	34	pobj	_	_
36	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	relcl	_	_
37	contractible	contractible	ADJ	JJ	Degree=Pos	36	acomp	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Namely, there is a unital $ A_infty $ - functor $ e: C to D $ such that the composition $ B hookrightarrow C to^e D $ is contractible, and for an arbitrary unital $ A_infty $ - category $ A $ the restriction $ A_infty $ - functor $ (eboxtimes 1)M : A_infty^u(D, A)to A_infty^u(C, A)_{mod B} $ is an equivalence.
1	Namely	namely	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	there	there	PRON	EX	_	4	expl	_	_
4	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
6	unital	unital	ADJ	JJ	Degree=Pos	11	amod	_	_
7	$ A_infty $	$ a_infty $	SYM	$	_	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	functor	functor	NOUN	NN	Number=Sing	11	nmod	_	_
10	$ e: C to D $	$ e: c to d $	SYM	$	_	11	det	_	_
11	such	such	ADJ	JJ	Degree=Pos	4	attr	_	_
12	that	that	SCONJ	IN	_	16	mark	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	composition	composition	NOUN	NN	Number=Sing	16	nsubj	_	_
15	$ B hookrightarrow C to^e D $	$ b hookrightarrow c to^e d $	SYM	$	_	14	appos	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
17	contractible	contractible	ADJ	JJ	Degree=Pos	16	acomp	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
20	for	for	ADP	IN	_	33	prep	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	23	amod	_	_
23	unital	unital	PROPN	NNP	Number=Sing	20	pobj	_	_
24	$ A_infty $	$ a_infty $	SYM	$	_	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	category	category	NOUN	NN	Number=Sing	23	nmod	_	_
27	$ A $	$ a $	SYM	$	_	26	nummod	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	restriction	restriction	NOUN	NN	Number=Sing	23	appos	_	_
30	$ A_infty $	$ a_infty $	SYM	$	_	32	compound	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	functor	functor	NOUN	NN	Number=Sing	33	nmod	_	_
33	$ (eboxtimes 1)M : A_infty^u(D, A)to A_infty^u(C, A)_{mod B} $	$ (eboxtimes 1)M : A_infty^u(D, A)to A_infty^u(C, A)_{mod B} $	PROPN	NNP	Number=Sing	34	nsubj	_	_
34	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	conj	_	_
35	an	an	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
36	equivalence	equivalence	NOUN	NN	Number=Sing	34	attr	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = Let $ C_k $ be the differential graded category of differential graded $ k $ - modules.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ C_k $	$ c_k $	SYM	$	_	3	nsubj	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	differential	differential	ADJ	JJ	Degree=Pos	6	advmod	_	_
6	graded	grade	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
7	category	category	NOUN	NN	Number=Sing	3	attr	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	differential	differential	NOUN	NN	Number=Sing	8	pobj	_	_
10	graded	grade	VERB	VBD	Tense=Past|VerbForm=Fin	1	ccomp	_	_
11	$ k $	$ k $	SYM	$	_	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	modules	module	NOUN	NNS	Number=Plur	10	dobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 5
# text = We prove that the Yoneda $ A_infty $ - functor $ Y: A to A_infty^u(A^{op}, C_k) $ is a full embedding for an arbitrary unital $ A_infty $ - category $ A $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	10	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
5	Yoneda	Yoneda	PROPN	NNP	Number=Sing	9	nmod	_	_
6	$ A_infty $	$ a_infty $	SYM	$	_	8	compound	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	functor	functor	NOUN	NN	Number=Sing	5	nummod	_	_
9	$ Y: A to A_infty^u(A^{op}, C_k) $	$ y: a to a_infty^u(a^{op}, c_k) $	SYM	$	_	10	nsubj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	full	full	ADJ	JJ	Degree=Pos	13	amod	_	_
13	embedding	embedding	NOUN	NN	Number=Sing	10	attr	_	_
14	for	for	ADP	IN	_	13	prep	_	_
15	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	17	amod	_	_
17	unital	unital	PROPN	NNP	Number=Sing	14	pobj	_	_
18	$ A_infty $	$ a_infty $	SYM	$	_	20	nummod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	category	category	NOUN	NN	Number=Sing	17	nmod	_	_
21	$ A $	$ a $	SYM	$	_	17	nummod	_	_
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = In particular, such $ A $ is $ A_infty $ - equivalent to a differential graded category with the same set of objects.
1	In	in	ADP	IN	_	6	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
4	such	such	ADJ	JJ	Degree=Pos	5	amod	_	_
5	$ A $	$ a $	SYM	$	_	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	$ A_infty $	$ a_infty $	SYM	$	_	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	equivalent	equivalent	ADJ	JJ	Degree=Pos	6	acomp	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
12	differential	differential	ADJ	JJ	Degree=Pos	13	advmod	_	_
13	graded	grade	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
14	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
15	with	with	ADP	IN	_	6	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	same	same	ADJ	JJ	Degree=Pos	18	amod	_	_
18	set	set	NOUN	NN	Number=Sing	15	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	objects	object	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 296
# sent_id = 1
# text = If $ C $ and $ D $ are varieties of algebras in the sense of general algebra, then by a representable functor $ C - - > D $ we understand a functor which, when composed with the forgetful functor $ D - - > Set $ , gives a representable functor in the classical sense; Freyd showed that these functors are determined by $ D $ - coalgebra objects of $ C $ .
1	If	if	SCONJ	IN	_	5	mark	_	_
2	$ C $	$ c $	SYM	$	_	5	nsubj	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	$ D $	$ d $	SYM	$	_	2	conj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	23	advcl	_	_
6	varieties	variety	NOUN	NNS	Number=Plur	5	attr	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	algebras	algebra	NOUN	NNS	Number=Plur	7	pobj	_	_
9	in	in	ADP	IN	_	6	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	sense	sense	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	general	general	ADJ	JJ	Degree=Pos	14	amod	_	_
14	algebra	algebra	PROPN	NNP	Number=Sing	12	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
16	then	then	ADV	RB	PronType=Dem	17	advmod	_	_
17	by	by	ADP	IN	_	23	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	representable	representable	ADJ	JJ	Degree=Pos	20	amod	_	_
20	functor	functor	NOUN	NN	Number=Sing	17	pobj	_	_
21	$ C - - > D $	$ c - - > d $	SYM	$	_	20	dep	_	_
22	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	23	nsubj	_	_
23	understand	understand	VERB	VBP	Tense=Pres|VerbForm=Fin	46	ccomp	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
25	functor	functor	NOUN	NN	Number=Sing	23	dobj	_	_
26	which	which	PRON	WDT	_	36	nsubj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
28	when	when	SCONJ	WRB	_	29	advmod	_	_
29	composed	compose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	36	advcl	_	_
30	with	with	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	forgetful	forgetful	ADJ	JJ	Degree=Pos	33	amod	_	_
33	functor	functor	NOUN	NN	Number=Sing	30	pobj	_	_
34	$ D - - > Set $	$ d - - > set $	SYM	$	_	33	appos	_	_
35	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
36	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	relcl	_	_
37	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
38	representable	representable	ADJ	JJ	Degree=Pos	39	amod	_	_
39	functor	functor	NOUN	NN	Number=Sing	36	dobj	_	_
40	in	in	ADP	IN	_	36	prep	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
42	classical	classical	ADJ	JJ	Degree=Pos	43	amod	_	_
43	sense	sense	NOUN	NN	Number=Sing	40	pobj	_	SpaceAfter=No
44	;	;	PUNCT	:	_	46	punct	_	_
45	Freyd	Freyd	PROPN	NNP	Number=Sing	46	nsubj	_	_
46	showed	show	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
47	that	that	SCONJ	IN	_	51	mark	_	_
48	these	these	DET	DT	Number=Plur|PronType=Dem	49	det	_	_
49	functors	functor	NOUN	NNS	Number=Plur	51	nsubjpass	_	_
50	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	51	auxpass	_	_
51	determined	determine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	46	ccomp	_	_
52	by	by	ADP	IN	_	51	agent	_	_
53	$ D $	$ d $	SYM	$	_	55	amod	_	_
54	-	-	PUNCT	HYPH	PunctType=Dash	55	punct	_	_
55	coalgebra	coalgebra	NOUN	NNS	Number=Plur	56	compound	_	_
56	objects	object	NOUN	NNS	Number=Plur	52	pobj	_	_
57	of	of	ADP	IN	_	56	prep	_	_
58	$ C $	$ c $	SYM	$	_	57	pobj	_	_
59	.	.	PUNCT	.	PunctType=Peri	46	punct	_	SpaceAfter=No

# sent_id = 2
# text = Let $ Rep(C, D) $ denote the category of all such functors, a full subcategory of $ Cat(C, D) $ , opposite to the category of $ D $ - coalgebras in $ C $ .
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ Rep(C, D) $	$ rep(c, d) $	SYM	$	_	3	nsubj	_	_
3	denote	denote	VERB	VBD	Tense=Past|VerbForm=Fin	1	ccomp	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	all	all	DET	DT	_	9	det	_	_
8	such	such	ADJ	JJ	Degree=Pos	9	amod	_	_
9	functors	functor	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	full	full	ADJ	JJ	Degree=Pos	13	amod	_	_
13	subcategory	subcategory	NOUN	NN	Number=Sing	9	appos	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	$ Cat(C, D) $	$ cat(c, d) $	SYM	$	_	14	pobj	_	_
16	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
17	opposite	opposite	ADJ	JJ	Degree=Pos	3	advmod	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	$ D $	$ d $	SYM	$	_	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	coalgebras	coalgebra	NOUN	NNS	Number=Plur	21	pobj	_	_
25	in	in	ADP	IN	_	20	prep	_	_
26	$ C $	$ c $	SYM	$	_	25	pobj	_	_
27	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 3
# text = It is proved that $ Rep(C, D) $ has small colimits, and in certain situations, explicit constructions for the representing coalgebras are obtained.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	SCONJ	IN	_	6	mark	_	_
5	$ Rep(C, D) $	$ rep(c, d) $	SYM	$	_	6	nsubj	_	_
6	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
7	small	small	ADJ	JJ	Degree=Pos	8	amod	_	_
8	colimits	colimit	NOUN	NNS	Number=Plur	6	dobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
11	in	in	ADP	IN	_	22	prep	_	_
12	certain	certain	ADJ	JJ	Degree=Pos	13	amod	_	_
13	situations	situation	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
15	explicit	explicit	ADJ	JJ	Degree=Pos	16	amod	_	_
16	constructions	construction	NOUN	NNS	Number=Plur	22	nsubjpass	_	_
17	for	for	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	representing	represent	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	amod	_	_
20	coalgebras	coalgebra	NOUN	NNS	Number=Plur	17	pobj	_	_
21	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	22	auxpass	_	_
22	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	conj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = In particular, $ Rep(C, D) $ always has an initial object.
1	In	in	ADP	IN	_	6	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
4	$ Rep(C, D) $	$ rep(c, d) $	SYM	$	_	6	nsubj	_	_
5	always	always	ADV	RB	_	6	advmod	_	_
6	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	initial	initial	ADJ	JJ	Degree=Pos	9	amod	_	_
9	object	object	NOUN	NN	Number=Sing	6	dobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = This is shown to be ``trivial'' unless $ C $ and $ D $ either both have no zeroary operations, or both have more than one derived zeroary operation.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	be	be	AUX	VB	VerbForm=Inf	3	xcomp	_	_
6	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	8	punct	_	SpaceAfter=No
7	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	8	punct	_	SpaceAfter=No
8	trivial	trivial	ADJ	JJ	Degree=Pos	5	acomp	_	SpaceAfter=No
9	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	8	punct	_	_
10	unless	unless	SCONJ	IN	_	16	mark	_	_
11	$ C $	$ c $	SYM	$	_	16	nsubj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	$ D $	$ d $	SYM	$	_	11	conj	_	_
14	either	either	CCONJ	CC	ConjType=Cmp	15	preconj	_	_
15	both	both	PRON	DT	_	11	dep	_	_
16	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	advcl	_	_
17	no	no	DET	DT	_	19	det	_	_
18	zeroary	zeroary	ADJ	JJ	Degree=Pos	19	amod	_	_
19	operations	operation	NOUN	NNS	Number=Plur	16	dobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
21	or	or	CCONJ	CC	ConjType=Cmp	16	cc	_	_
22	both	both	PRON	DT	_	23	nsubj	_	_
23	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	16	conj	_	_
24	more	more	ADJ	JJR	Degree=Cmp	26	amod	_	_
25	than	than	ADP	IN	_	26	quantmod	_	_
26	one	one	NUM	CD	NumType=Card	29	nummod	_	_
27	derived	derive	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	amod	_	_
28	zeroary	zeroary	ADJ	JJ	Degree=Pos	29	amod	_	_
29	operation	operation	NOUN	NN	Number=Sing	23	dobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = In those two cases, the functors in question may have surprisingly opulent structures.
1	In	in	ADP	IN	_	11	prep	_	_
2	those	those	DET	DT	Number=Plur|PronType=Dem	4	det	_	_
3	two	two	NUM	CD	NumType=Card	4	nummod	_	_
4	cases	case	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	functors	functor	NOUN	NNS	Number=Plur	11	nsubj	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	question	question	NOUN	NN	Number=Sing	8	pobj	_	_
10	may	may	AUX	MD	VerbForm=Fin	11	aux	_	_
11	have	have	VERB	VB	VerbForm=Inf	0	ROOT	_	_
12	surprisingly	surprisingly	ADV	RB	_	13	advmod	_	_
13	opulent	opulent	ADJ	JJ	Degree=Pos	14	amod	_	_
14	structures	structure	NOUN	NNS	Number=Plur	11	dobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 7
# text = It is also shown that every set - valued representable functor on $ C $ admits a universal morphism to a $ D $ - valued representable functor.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	4	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
3	also	also	ADV	RB	_	4	advmod	_	_
4	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	that	that	SCONJ	IN	_	14	mark	_	_
6	every	every	DET	DT	_	11	det	_	_
7	set	set	NOUN	NN	Number=Sing	9	npadvmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
10	representable	representable	ADJ	JJ	Degree=Pos	11	compound	_	_
11	functor	functor	NOUN	NN	Number=Sing	14	nsubj	_	_
12	on	on	ADP	IN	_	11	prep	_	_
13	$ C $	$ c $	SYM	$	_	14	nsubj	_	_
14	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	universal	universal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	morphism	morphism	NOUN	NN	Number=Sing	14	dobj	_	_
18	to	to	ADP	IN	_	14	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
20	$ D $	$ d $	SYM	$	_	22	advmod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
23	representable	representable	ADJ	JJ	Degree=Pos	24	compound	_	_
24	functor	functor	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 8
# text = Several examples are worked out in detail, and areas for further investigation are noted.
1	Several	several	ADJ	JJ	Degree=Pos	2	amod	_	_
2	examples	example	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	worked	work	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	out	out	ADP	RP	_	4	prt	_	_
6	in	in	ADP	IN	_	4	prep	_	_
7	detail	detail	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
10	areas	area	NOUN	NNS	Number=Plur	15	nsubjpass	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	further	further	ADJ	JJ	Degree=Pos	13	amod	_	_
13	investigation	investigation	NOUN	NN	Number=Sing	11	pobj	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	noted	note	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	conj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# doc_id = 297
# sent_id = 1
# text = We construct a star - autonomous structure on the functor category $ K^J $ , where $ J $ is small, $ K $ is small - complete, and both are star - autonomous.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
4	star	star	NOUN	NN	Number=Sing	6	npadvmod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	autonomous	autonomous	ADJ	JJ	Degree=Pos	7	amod	_	_
7	structure	structure	NOUN	NN	Number=Sing	20	nsubj	_	_
8	on	on	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	functor	functor	NOUN	NN	Number=Sing	11	compound	_	_
11	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
12	$ K^J $	$ k^j $	SYM	$	_	8	pobj	_	_
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	where	where	SCONJ	WRB	_	16	advmod	_	_
15	$ J $	$ j $	SYM	$	_	16	nsubj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	relcl	_	_
17	small	small	ADJ	JJ	Degree=Pos	16	acomp	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
19	$ K $	$ k $	SYM	$	_	16	dep	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
21	small	small	ADJ	JJ	Degree=Pos	23	amod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	complete	complete	ADJ	JJ	Degree=Pos	20	acomp	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
26	both	both	PRON	DT	_	27	nsubj	_	_
27	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	20	conj	_	_
28	star	star	NOUN	NN	Number=Sing	30	compound	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	autonomous	autonomous	PROPN	NNP	Number=Sing	27	acomp	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = A weaker result, that $ K^J $ admits a linear distributive structure, is also shown under weaker hypotheses.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	weaker	weak	ADJ	JJR	Degree=Cmp	3	amod	_	_
3	result	result	NOUN	NN	Number=Sing	7	nsubj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
5	that	that	SCONJ	IN	_	7	mark	_	_
6	$ K^J $	$ k^j $	SYM	$	_	7	nsubj	_	_
7	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	ccomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	linear	linear	ADJ	JJ	Degree=Pos	11	amod	_	_
10	distributive	distributive	ADJ	JJ	Degree=Pos	11	amod	_	_
11	structure	structure	NOUN	NN	Number=Sing	7	dobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
14	also	also	ADV	RB	_	15	advmod	_	_
15	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
16	under	under	ADP	IN	_	15	prep	_	_
17	weaker	weak	ADJ	JJR	Degree=Cmp	18	amod	_	_
18	hypotheses	hypothesis	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 3
# text = The latter leads to a deeper understanding of the notion of linear functor.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	latter	latter	ADJ	JJ	Degree=Pos	3	nsubj	_	_
3	leads	lead	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	to	to	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	deeper	deep	ADJ	JJR	Degree=Cmp	7	amod	_	_
7	understanding	understanding	NOUN	NN	Number=Sing	4	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	notion	notion	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	linear	linear	PROPN	NNP	Number=Sing	13	compound	_	_
13	functor	functor	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 298
# sent_id = 1
# text = Some aspects of basic category theory are developed in a finitely complete category $ cal C $ , endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law.
1	Some	some	DET	DT	_	2	det	_	_
2	aspects	aspect	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	basic	basic	ADJ	JJ	Degree=Pos	6	amod	_	_
5	category	category	NOUN	NN	Number=Sing	6	compound	_	_
6	theory	theory	NOUN	NN	Number=Sing	3	pobj	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	finitely	finitely	ADV	RB	_	12	advmod	_	_
12	complete	complete	ADJ	JJ	Degree=Pos	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
14	$ cal C $	$ cal c $	SYM	$	_	13	nummod	_	_
15	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
16	endowed	endow	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	advcl	_	_
17	with	with	ADP	IN	_	16	prep	_	_
18	two	two	NUM	CD	NumType=Card	20	nummod	_	_
19	factorization	factorization	NOUN	NN	Number=Sing	20	compound	_	_
20	systems	system	NOUN	NNS	Number=Plur	17	pobj	_	_
21	which	which	PRON	WDT	_	22	nsubj	_	_
22	determine	determine	VERB	VBP	Tense=Pres|VerbForm=Fin	20	relcl	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
24	same	same	ADJ	JJ	Degree=Pos	26	amod	_	_
25	discrete	discrete	ADJ	JJ	Degree=Pos	26	amod	_	_
26	objects	object	NOUN	NNS	Number=Plur	22	dobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
28	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	29	auxpass	_	_
29	linked	link	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	conj	_	_
30	by	by	ADP	IN	_	29	agent	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
32	simple	simple	ADJ	JJ	Degree=Pos	35	amod	_	_
33	reciprocal	reciprocal	ADJ	JJ	Degree=Pos	34	amod	_	_
34	stability	stability	NOUN	NN	Number=Sing	35	compound	_	_
35	law	law	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = Resting on this axiomatization of final and initial functors and discrete (op)fibrations, concepts such as components, slices and coslices, colimits and limits, left and right adjunctible maps, dense maps and arrow intervals, can be naturally defined in $ cal C $ , and several classical properties concerning them can be effectively proved.
1	Resting	rest	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	43	advcl	_	_
2	on	on	ADP	IN	_	1	prep	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	axiomatization	axiomatization	NOUN	NN	Number=Sing	2	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	final	final	ADJ	JJ	Degree=Pos	9	amod	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	initial	initial	ADJ	JJ	Degree=Pos	6	conj	_	_
9	functors	functor	NOUN	NNS	Number=Plur	5	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	discrete	discrete	ADJ	JJ	Degree=Pos	9	conj	_	_
12	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	13	punct	_	SpaceAfter=No
13	op)fibrations	op)fibration	NOUN	NNS	Number=Plur	9	conj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	concepts	concept	NOUN	NNS	Number=Plur	1	dobj	_	_
16	such	such	ADJ	JJ	Degree=Pos	17	amod	_	_
17	as	as	ADP	IN	_	15	prep	_	_
18	components	component	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	slices	slice	NOUN	NNS	Number=Plur	18	conj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	coslices	coslice	NOUN	NNS	Number=Plur	20	conj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	colimits	colimit	NOUN	NNS	Number=Plur	22	conj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	limits	limit	NOUN	NNS	Number=Plur	24	conj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
28	left	left	ADJ	JJ	Degree=Pos	32	amod	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	right	right	ADJ	JJ	Degree=Pos	28	conj	_	_
31	adjunctible	adjunctible	ADJ	JJ	Degree=Pos	32	amod	_	_
32	maps	map	NOUN	NNS	Number=Plur	18	conj	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
34	dense	dense	ADJ	JJ	Degree=Pos	35	amod	_	_
35	maps	map	NOUN	NNS	Number=Plur	32	conj	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
37	arrow	arrow	NOUN	NN	Number=Sing	38	compound	_	_
38	intervals	interval	NOUN	NNS	Number=Plur	35	conj	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	43	punct	_	_
40	can	can	AUX	MD	VerbForm=Fin	43	aux	_	_
41	be	be	AUX	VB	VerbForm=Inf	43	auxpass	_	_
42	naturally	naturally	ADV	RB	_	43	advmod	_	_
43	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
44	in	in	ADP	IN	_	43	prep	_	_
45	$ cal C $	$ cal c $	SYM	$	_	44	pobj	_	_
46	,	,	PUNCT	,	PunctType=Comm	43	punct	_	_
47	and	and	CCONJ	CC	ConjType=Cmp	43	cc	_	_
48	several	several	ADJ	JJ	Degree=Pos	50	amod	_	_
49	classical	classical	ADJ	JJ	Degree=Pos	50	amod	_	_
50	properties	property	NOUN	NNS	Number=Plur	56	nsubjpass	_	_
51	concerning	concern	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	50	acl	_	_
52	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	51	dobj	_	_
53	can	can	AUX	MD	VerbForm=Fin	56	aux	_	_
54	be	be	AUX	VB	VerbForm=Inf	56	auxpass	_	_
55	effectively	effectively	ADV	RB	_	56	advmod	_	_
56	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	43	conj	_	SpaceAfter=No
57	.	.	PUNCT	.	PunctType=Peri	56	punct	_	SpaceAfter=No

# sent_id = 3
# text = For any object $ X $ of $ cal C $ , by restricting $ cal C/X $ to the slices or to the coslices of $ X $ , two dual ``underlying categories" are obtained.
1	For	for	ADP	IN	_	29	prep	_	_
2	any	any	DET	DT	_	3	det	_	_
3	object	object	NOUN	NN	Number=Sing	1	pobj	_	_
4	$ X $	$ x $	SYM	$	_	3	prep	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	$ cal C $	$ cal c $	SYM	$	_	5	pobj	_	_
7	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
8	by	by	ADP	IN	_	29	prep	_	_
9	restricting	restrict	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	pcomp	_	_
10	$ cal C/X $	$ cal c/x $	SYM	$	_	9	dobj	_	_
11	to	to	ADP	IN	_	9	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	slices	slice	NOUN	NNS	Number=Plur	11	pobj	_	_
14	or	or	CCONJ	CC	ConjType=Cmp	11	cc	_	_
15	to	to	ADP	IN	_	11	conj	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	coslices	coslice	NOUN	NNS	Number=Plur	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	$ X $	$ x $	SYM	$	_	18	pobj	_	_
20	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
21	two	two	NUM	CD	NumType=Card	26	nummod	_	_
22	dual	dual	ADJ	JJ	Degree=Pos	26	amod	_	_
23	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	SpaceAfter=No
24	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	SpaceAfter=No
25	underlying	underlying	ADJ	JJ	Degree=Pos	26	amod	_	_
26	categories	category	NOUN	NNS	Number=Plur	29	nsubjpass	_	SpaceAfter=No
27	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	26	punct	_	_
28	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	29	auxpass	_	_
29	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	29	punct	_	SpaceAfter=No

# sent_id = 4
# text = These can be enriched over internal sets (discrete objects) of $ cal C $ : internal hom - sets are given by the components of the pullback of the corresponding slice and coslice of $ X $ .
1	These	these	PRON	DT	Number=Plur|PronType=Dem	4	nsubjpass	_	_
2	can	can	AUX	MD	VerbForm=Fin	4	aux	_	_
3	be	be	AUX	VB	VerbForm=Inf	4	auxpass	_	_
4	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	over	over	ADP	IN	_	4	prep	_	_
6	internal	internal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	sets	set	NOUN	NNS	Number=Plur	5	pobj	_	_
8	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	7	punct	_	SpaceAfter=No
9	discrete	discrete	ADJ	JJ	Degree=Pos	10	amod	_	_
10	objects	object	NOUN	NNS	Number=Plur	7	appos	_	SpaceAfter=No
11	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	10	punct	_	_
12	of	of	ADP	IN	_	10	prep	_	_
13	$ cal C $	$ cal c $	SYM	$	_	12	pobj	_	_
14	:	:	PUNCT	:	_	7	punct	_	_
15	internal	internal	ADJ	JJ	Degree=Pos	18	amod	_	_
16	hom	hom	NOUN	NN	Number=Sing	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	sets	set	NOUN	NNS	Number=Plur	20	nsubjpass	_	_
19	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	20	auxpass	_	_
20	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	conj	_	_
21	by	by	ADP	IN	_	20	agent	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	components	component	NOUN	NNS	Number=Plur	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	pullback	pullback	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
29	corresponding	corresponding	ADJ	JJ	Degree=Pos	30	amod	_	_
30	slice	slice	NOUN	NN	Number=Sing	27	pobj	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
32	coslice	coslice	NOUN	NN	Number=Sing	30	conj	_	_
33	of	of	ADP	IN	_	30	prep	_	_
34	$ X $	$ x $	SYM	$	_	33	pobj	_	_
35	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 5
# text = The construction extends to give functors $ cal C to Cat $ , which preserve (or reverse) slices and adjunctible maps and which can be enriched over internal sets too.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	construction	construction	NOUN	NN	Number=Sing	3	nsubj	_	_
3	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	give	give	VERB	VB	VerbForm=Inf	3	xcomp	_	_
6	functors	functor	NOUN	NNS	Number=Plur	5	dative	_	_
7	$ cal C to Cat $	$ cal c to cat $	SYM	$	_	5	dobj	_	_
8	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
9	which	which	PRON	WDT	_	10	nsubj	_	_
10	preserve	preserve	VERB	VBP	Tense=Pres|VerbForm=Fin	7	relcl	_	_
11	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	10	punct	_	SpaceAfter=No
12	or	or	CCONJ	CC	ConjType=Cmp	10	cc	_	_
13	reverse	reverse	VERB	VB	VerbForm=Inf	15	amod	_	SpaceAfter=No
14	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	15	punct	_	_
15	slices	slice	NOUN	NNS	Number=Plur	10	conj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	adjunctible	adjunctible	ADJ	JJ	Degree=Pos	18	amod	_	_
18	maps	map	NOUN	NNS	Number=Plur	15	conj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
20	which	which	PRON	WDT	_	23	nsubjpass	_	_
21	can	can	AUX	MD	VerbForm=Fin	23	aux	_	_
22	be	be	AUX	VB	VerbForm=Inf	23	auxpass	_	_
23	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	conj	_	_
24	over	over	ADP	IN	_	23	prep	_	_
25	internal	internal	ADJ	JJ	Degree=Pos	26	amod	_	_
26	sets	set	NOUN	NNS	Number=Plur	24	pobj	_	_
27	too	too	ADV	RB	_	23	advmod	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 299
# sent_id = 1
# text = An effort to initiate the subject of the title: the basic tool is the study of the abstract closed interval equipped with certain equational structures.
1	An	an	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	effort	effort	NOUN	NN	Number=Sing	14	dep	_	_
3	to	to	PART	TO	_	4	aux	_	_
4	initiate	initiate	VERB	VB	VerbForm=Inf	2	acl	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	subject	subject	NOUN	NN	Number=Sing	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	title	title	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
10	:	:	PUNCT	:	_	14	punct	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	basic	basic	ADJ	JJ	Degree=Pos	13	amod	_	_
13	tool	tool	NOUN	NN	Number=Sing	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	study	study	NOUN	NN	Number=Sing	14	attr	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
19	abstract	abstract	ADJ	JJ	Degree=Pos	20	advmod	_	_
20	closed	closed	ADJ	JJ	Degree=Pos	21	amod	_	_
21	interval	interval	NOUN	NN	Number=Sing	17	pobj	_	_
22	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	acl	_	_
23	with	with	ADP	IN	_	22	prep	_	_
24	certain	certain	ADJ	JJ	Degree=Pos	26	amod	_	_
25	equational	equational	ADJ	JJ	Degree=Pos	26	amod	_	_
26	structures	structure	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# doc_id = 300
# sent_id = 1
# text = This paper presents a sound and complete category - theoretic notion of models for Linear Abadi and Plotkin Logic, a logic suitable for reasoning about parametricity in combination with recursion.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	presents	present	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	sound	sound	NOUN	NN	Number=Sing	11	amod	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	complete	complete	ADJ	JJ	Degree=Pos	5	conj	_	_
8	category	category	NOUN	NN	Number=Sing	10	npadvmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	theoretic	theoretic	NOUN	NN	Number=Sing	11	amod	_	_
11	notion	notion	NOUN	NN	Number=Sing	3	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	models	model	NOUN	NNS	Number=Plur	12	pobj	_	_
14	for	for	ADP	IN	_	13	prep	_	_
15	Linear	Linear	PROPN	NNP	Number=Sing	16	compound	_	_
16	Abadi	Abadi	PROPN	NNP	Number=Sing	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	Plotkin	Plotkin	PROPN	NNP	Number=Sing	19	compound	_	_
19	Logic	Logic	PROPN	NNP	Number=Sing	16	conj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	logic	logic	NOUN	NN	Number=Sing	11	appos	_	_
23	suitable	suitable	ADJ	JJ	Degree=Pos	22	amod	_	_
24	for	for	ADP	IN	_	23	prep	_	_
25	reasoning	reason	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	24	pobj	_	_
26	about	about	ADP	IN	_	25	prep	_	_
27	parametricity	parametricity	NOUN	NN	Number=Sing	26	pobj	_	_
28	in	in	ADP	IN	_	27	prep	_	_
29	combination	combination	NOUN	NN	Number=Sing	28	pobj	_	_
30	with	with	ADP	IN	_	29	prep	_	_
31	recursion	recursion	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = A subclass of these called parametric LAPL structures can be seen as an axiomatization of domain theoretic models of parametric polymorphism, and we show how to solve general (nested) recursive domain equations in these.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	subclass	subclass	NOUN	NN	Number=Sing	11	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	these	these	DET	DT	Number=Plur|PronType=Dem	8	det	_	_
5	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
6	parametric	parametric	ADJ	JJ	Degree=Pos	8	amod	_	_
7	LAPL	lapl	ADJ	JJ	Degree=Pos	8	amod	_	_
8	structures	structure	NOUN	NNS	Number=Plur	3	pobj	_	_
9	can	can	AUX	MD	VerbForm=Fin	11	aux	_	_
10	be	be	AUX	VB	VerbForm=Inf	11	auxpass	_	_
11	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
12	as	as	ADP	IN	_	11	prep	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	axiomatization	axiomatization	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	domain	domain	NOUN	NN	Number=Sing	18	nmod	_	_
17	theoretic	theoretic	ADJ	JJ	Degree=Pos	18	amod	_	_
18	models	model	NOUN	NNS	Number=Plur	15	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	parametric	parametric	ADJ	JJ	Degree=Pos	21	amod	_	_
21	polymorphism	polymorphism	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
24	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	25	nsubj	_	_
25	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	11	conj	_	_
26	how	how	SCONJ	WRB	_	28	advmod	_	_
27	to	to	PART	TO	_	28	aux	_	_
28	solve	solve	VERB	VB	VerbForm=Inf	25	xcomp	_	_
29	general	general	ADJ	JJ	Degree=Pos	35	amod	_	_
30	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	35	punct	_	SpaceAfter=No
31	nested	nested	ADJ	JJ	Degree=Pos	35	amod	_	SpaceAfter=No
32	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	35	punct	_	_
33	recursive	recursive	ADJ	JJ	Degree=Pos	35	amod	_	_
34	domain	domain	NOUN	NN	Number=Sing	35	compound	_	_
35	equations	equation	NOUN	NNS	Number=Plur	28	dobj	_	_
36	in	in	ADP	IN	_	35	prep	_	_
37	these	these	PRON	DT	Number=Plur|PronType=Dem	36	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	25	punct	_	SpaceAfter=No

# sent_id = 3
# text = Parametric LAPL structures constitute a general notion of model of parametricity in a setting with recursion.
1	Parametric	parametric	ADJ	JJ	Degree=Pos	3	amod	_	_
2	LAPL	LAPL	PROPN	NNP	Number=Sing	3	compound	_	_
3	structures	structure	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	constitute	constitute	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	general	general	ADJ	JJ	Degree=Pos	7	amod	_	_
7	notion	notion	NOUN	NN	Number=Sing	4	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	model	model	NOUN	NN	Number=Sing	8	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	parametricity	parametricity	NOUN	NN	Number=Sing	10	pobj	_	_
12	in	in	ADP	IN	_	4	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	setting	setting	NOUN	NN	Number=Sing	12	pobj	_	_
15	with	with	ADP	IN	_	14	prep	_	_
16	recursion	recursion	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = In future papers we will demonstrate this by showing how many different models of parametricity and recursion give rise to parametric LAPL structures, including Simpson and Rosolini's set theoretic models, a syntactic model based on Lily and a model based on admissible pers over a reflexive domain.
1	In	in	ADP	IN	_	6	prep	_	_
2	future	future	ADJ	JJ	Degree=Pos	3	amod	_	_
3	papers	paper	NOUN	NNS	Number=Plur	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
5	will	will	AUX	MD	VerbForm=Fin	6	aux	_	_
6	demonstrate	demonstrate	VERB	VB	VerbForm=Inf	0	ROOT	_	_
7	this	this	PRON	DT	Number=Sing|PronType=Dem	6	dobj	_	_
8	by	by	ADP	IN	_	6	prep	_	_
9	showing	show	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	pcomp	_	_
10	how	how	SCONJ	WRB	_	11	advmod	_	_
11	many	many	ADJ	JJ	Degree=Pos	13	amod	_	_
12	different	different	ADJ	JJ	Degree=Pos	13	amod	_	_
13	models	model	NOUN	NNS	Number=Plur	18	nsubj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	parametricity	parametricity	NOUN	NN	Number=Sing	14	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	recursion	recursion	NOUN	NN	Number=Sing	15	conj	_	_
18	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	9	ccomp	_	_
19	rise	rise	NOUN	NN	Number=Sing	18	dobj	_	_
20	to	to	ADP	IN	_	18	prep	_	_
21	parametric	parametric	ADJ	JJ	Degree=Pos	23	amod	_	_
22	LAPL	LAPL	PROPN	NNP	Number=Sing	23	amod	_	_
23	structures	structure	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
25	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	23	prep	_	_
26	Simpson	Simpson	PROPN	NNP	Number=Sing	32	poss	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	Rosolini	Rosolini	PROPN	NNP	Number=Sing	26	conj	_	SpaceAfter=No
29	's	's	PART	POS	_	28	case	_	_
30	set	set	ADJ	JJ	Degree=Pos	32	amod	_	_
31	theoretic	theoretic	ADJ	JJ	Degree=Pos	32	amod	_	_
32	models	model	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
35	syntactic	syntactic	ADJ	JJ	Degree=Pos	36	amod	_	_
36	model	model	NOUN	NN	Number=Sing	32	appos	_	_
37	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	36	acl	_	_
38	on	on	ADP	IN	_	37	prep	_	_
39	Lily	Lily	PROPN	NNP	Number=Sing	38	pobj	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	39	cc	_	_
41	a	a	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
42	model	model	NOUN	NN	Number=Sing	39	conj	_	_
43	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	42	acl	_	_
44	on	on	ADP	IN	_	43	prep	_	_
45	admissible	admissible	ADJ	JJ	Degree=Pos	46	amod	_	_
46	pers	per	NOUN	NNS	Number=Plur	44	pobj	_	_
47	over	over	ADP	IN	_	43	prep	_	_
48	a	a	DET	DT	Definite=Ind|PronType=Art	50	det	_	_
49	reflexive	reflexive	ADJ	JJ	Degree=Pos	50	amod	_	_
50	domain	domain	NOUN	NN	Number=Sing	47	pobj	_	SpaceAfter=No
51	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 301
# sent_id = 1
# text = The author introduced and employed certain `fundamental pushout toposes' in the construction of the coverings fundamental groupoid of a locally connected topos.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	author	author	NOUN	NN	Number=Sing	3	nsubj	_	_
3	introduced	introduce	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	employed	employ	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	conj	_	_
6	certain	certain	ADJ	JJ	Degree=Pos	10	amod	_	_
7	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	10	punct	_	SpaceAfter=No
8	fundamental	fundamental	ADJ	JJ	Degree=Pos	10	amod	_	_
9	pushout	pushout	NOUN	NN	Number=Sing	10	compound	_	_
10	toposes	topos	NOUN	NNS	Number=Plur	19	nmod	_	SpaceAfter=No
11	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	10	case	_	_
12	in	in	ADP	IN	_	10	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	construction	construction	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	coverings	covering	NOUN	NNS	Number=Plur	15	pobj	_	_
18	fundamental	fundamental	ADJ	JJ	Degree=Pos	19	amod	_	_
19	groupoid	groupoid	NOUN	NN	Number=Sing	5	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
22	locally	locally	ADV	RB	_	23	advmod	_	_
23	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
24	topos	topos	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = Our main purpose in this paper is to generalize this construction without the local connectedness assumption.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	3	poss	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	purpose	purpose	NOUN	NN	Number=Sing	7	nsubj	_	_
4	in	in	ADP	IN	_	3	prep	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	paper	paper	NOUN	NN	Number=Sing	4	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	generalize	generalize	VERB	VB	VerbForm=Inf	7	xcomp	_	_
10	this	this	DET	DT	Number=Sing|PronType=Dem	11	det	_	_
11	construction	construction	NOUN	NN	Number=Sing	9	dobj	_	_
12	without	without	ADP	IN	_	9	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
14	local	local	ADJ	JJ	Degree=Pos	16	amod	_	_
15	connectedness	connectedness	NOUN	NN	Number=Sing	16	compound	_	_
16	assumption	assumption	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = We replace connected components by constructively complemented, or definable, monomorphisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	replace	replace	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	connected	connected	ADJ	JJ	Degree=Pos	4	amod	_	_
4	components	component	NOUN	NNS	Number=Plur	2	dobj	_	_
5	by	by	ADP	IN	_	4	prep	_	_
6	constructively	constructively	ADV	RB	_	7	advmod	_	_
7	complemented	complement	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	or	or	CCONJ	CC	ConjType=Cmp	7	cc	_	_
10	definable	definable	ADJ	JJ	Degree=Pos	7	conj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
12	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = Unlike the locally connected case, where the fundamental groupoid is localic prodiscrete and its classifying topos is a Galois topos, in the general case our version of the fundamental groupoid is a locally discrete progroupoid and there is no intrinsic Galois theory in the sense of Janelidze.
1	Unlike	unlike	ADP	IN	_	18	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
3	locally	locally	ADV	RB	_	4	advmod	_	_
4	connected	connected	ADJ	JJ	Degree=Pos	5	amod	_	_
5	case	case	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	where	where	SCONJ	WRB	_	11	advmod	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	fundamental	fundamental	ADJ	JJ	Degree=Pos	10	amod	_	_
10	groupoid	groupoid	NOUN	NN	Number=Sing	11	nsubj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	relcl	_	_
12	localic	localic	ADJ	JJ	Degree=Pos	13	amod	_	_
13	prodiscrete	prodiscrete	NOUN	NN	Number=Sing	11	attr	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	17	poss	_	_
16	classifying	classify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	amod	_	_
17	topos	topos	NOUN	NN	Number=Sing	13	conj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	33	advcl	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	Galois	Galois	PROPN	NNP	Number=Sing	21	compound	_	_
21	topos	topos	NOUN	NN	Number=Sing	18	attr	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
23	in	in	ADP	IN	_	33	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	general	general	ADJ	JJ	Degree=Pos	26	amod	_	_
26	case	case	NOUN	NN	Number=Sing	23	pobj	_	_
27	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	28	poss	_	_
28	version	version	NOUN	NN	Number=Sing	33	nsubj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	fundamental	fundamental	ADJ	JJ	Degree=Pos	32	amod	_	_
32	groupoid	groupoid	NOUN	NN	Number=Sing	29	pobj	_	_
33	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
35	locally	locally	ADV	RB	_	36	advmod	_	_
36	discrete	discrete	ADJ	JJ	Degree=Pos	37	amod	_	_
37	progroupoid	progroupoid	NOUN	NN	Number=Sing	33	attr	_	_
38	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
39	there	there	PRON	EX	_	40	expl	_	_
40	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	33	conj	_	_
41	no	no	DET	DT	_	44	det	_	_
42	intrinsic	intrinsic	ADJ	JJ	Degree=Pos	44	amod	_	_
43	Galois	Galois	PROPN	NNP	Number=Sing	44	compound	_	_
44	theory	theory	NOUN	NN	Number=Sing	40	attr	_	_
45	in	in	ADP	IN	_	44	prep	_	_
46	the	the	DET	DT	Definite=Def|PronType=Art	47	det	_	_
47	sense	sense	NOUN	NN	Number=Sing	45	pobj	_	_
48	of	of	ADP	IN	_	47	prep	_	_
49	Janelidze	Janelidze	PROPN	NNP	Number=Sing	48	pobj	_	SpaceAfter=No
50	.	.	PUNCT	.	PunctType=Peri	40	punct	_	SpaceAfter=No

# sent_id = 5
# text = We also discuss covering projections, locally trivial, and branched coverings without local connectedness by analogy with, but also necessarily departing from, the locally connected case.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	discuss	discuss	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	covering	cover	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	amod	_	_
5	projections	projection	NOUN	NNS	Number=Plur	3	dobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	locally	locally	ADV	RB	_	8	advmod	_	_
8	trivial	trivial	ADJ	JJ	Degree=Pos	5	conj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
11	branched	branched	ADJ	JJ	Degree=Pos	12	amod	_	_
12	coverings	covering	NOUN	NNS	Number=Plur	8	conj	_	_
13	without	without	ADP	IN	_	12	prep	_	_
14	local	local	ADJ	JJ	Degree=Pos	15	amod	_	_
15	connectedness	connectedness	NOUN	NN	Number=Sing	13	pobj	_	_
16	by	by	ADP	IN	_	15	prep	_	_
17	analogy	analogy	NOUN	NN	Number=Sing	16	pobj	_	_
18	with	with	ADP	IN	_	12	prep	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
20	but	but	CCONJ	CC	ConjType=Cmp	3	cc	_	_
21	also	also	ADV	RB	_	20	advmod	_	_
22	necessarily	necessarily	ADV	RB	_	23	advmod	_	_
23	departing	depart	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	conj	_	_
24	from	from	ADP	IN	_	23	prep	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
27	locally	locally	ADV	RB	_	28	advmod	_	_
28	connected	connected	ADJ	JJ	Degree=Pos	29	amod	_	_
29	case	case	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = Throughout, we work abstractly in a setting given axiomatically by a category $ V $ of locally discrete locales that has as examples the categories D of discrete locales, and $ Z $ of zero - dimensional locales.
1	Throughout	throughout	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	work	work	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	abstractly	abstractly	ADV	RB	_	4	advmod	_	_
6	in	in	ADP	IN	_	4	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	setting	setting	NOUN	NN	Number=Sing	6	pobj	_	_
9	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	axiomatically	axiomatically	ADV	RB	_	9	advmod	_	_
11	by	by	ADP	IN	_	9	agent	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
14	$ V $	$ v $	SYM	$	_	13	nmod	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	locally	locally	ADV	RB	_	17	advmod	_	_
17	discrete	discrete	ADJ	JJ	Degree=Pos	18	amod	_	_
18	locales	locale	NOUN	NNS	Number=Plur	15	pobj	_	_
19	that	that	PRON	WDT	PronType=Rel	20	nsubj	_	_
20	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	relcl	_	_
21	as	as	ADP	IN	_	4	prep	_	_
22	examples	example	NOUN	NNS	Number=Plur	21	pobj	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	categories	category	NOUN	NNS	Number=Plur	4	dobj	_	_
25	D	D	PROPN	NNP	Number=Sing	24	appos	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	discrete	discrete	ADJ	JJ	Degree=Pos	28	amod	_	_
28	locales	locale	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
31	$ Z $	$ z $	SYM	$	_	24	conj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	zero	zero	NUM	CD	NumType=Card	35	npadvmod	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	dimensional	dimensional	ADJ	JJ	Degree=Pos	36	amod	_	_
36	locales	locale	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 7
# text = In this fashion we are led to give unified and often simpler proofs of old theorems in the locally connected case, as well as new ones without that assumption.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	fashion	fashion	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubjpass	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	led	lead	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	give	give	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	unified	unified	ADJ	JJ	Degree=Pos	13	amod	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	often	often	ADV	RB	_	12	advmod	_	_
12	simpler	simple	ADJ	JJR	Degree=Cmp	9	conj	_	_
13	proofs	proof	NOUN	NNS	Number=Plur	8	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	old	old	ADJ	JJ	Degree=Pos	16	amod	_	_
16	theorems	theorem	NOUN	NNS	Number=Plur	14	pobj	_	_
17	in	in	ADP	IN	_	8	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
19	locally	locally	ADV	RB	_	20	advmod	_	_
20	connected	connected	ADJ	JJ	Degree=Pos	21	amod	_	_
21	case	case	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
23	as	as	ADV	RB	_	25	advmod	_	_
24	well	well	ADV	RB	Degree=Pos	25	advmod	_	_
25	as	as	ADP	IN	_	8	cc	_	_
26	new	new	ADJ	JJ	Degree=Pos	27	amod	_	_
27	ones	one	NOUN	NNS	Number=Plur	8	dobj	_	_
28	without	without	ADP	IN	_	8	prep	_	_
29	that	that	DET	DT	Number=Sing|PronType=Dem	30	det	_	_
30	assumption	assumption	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 302
# sent_id = 1
# text = This paper deals with Kan extensions in a weak double category.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	deals	deal	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	with	with	ADP	IN	_	3	prep	_	_
5	Kan	Kan	PROPN	NNP	Number=Sing	6	compound	_	_
6	extensions	extension	NOUN	NNS	Number=Plur	4	pobj	_	_
7	in	in	ADP	IN	_	3	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	weak	weak	ADJ	JJ	Degree=Pos	11	amod	_	_
10	double	double	ADJ	JJ	Degree=Pos	11	amod	_	_
11	category	category	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = Absolute Kan extensions are closely related to the orthogonal adjunctions introduced in a previous paper.
1	Absolute	Absolute	PROPN	NNP	Number=Sing	2	compound	_	_
2	Kan	Kan	PROPN	NNP	Number=Sing	3	compound	_	_
3	extensions	extension	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
5	closely	closely	ADV	RB	_	6	advmod	_	_
6	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	to	to	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	orthogonal	orthogonal	ADJ	JJ	Degree=Pos	10	amod	_	_
10	adjunctions	adjunction	NOUN	NNS	Number=Plur	7	pobj	_	_
11	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acl	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	previous	previous	ADJ	JJ	Degree=Pos	15	amod	_	_
15	paper	paper	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = The pointwise case is treated by introducing internal comma objects, which can be defined in an arbitrary double category.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	pointwise	pointwise	ADJ	JJ	Degree=Pos	3	amod	_	_
3	case	case	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	treated	treat	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	by	by	ADP	IN	_	5	agent	_	_
7	introducing	introduce	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	pcomp	_	_
8	internal	internal	ADJ	JJ	Degree=Pos	10	amod	_	_
9	comma	comma	ADJ	JJ	Degree=Pos	10	amod	_	_
10	objects	object	NOUN	NNS	Number=Plur	7	dobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	which	which	PRON	WDT	_	15	nsubjpass	_	_
13	can	can	AUX	MD	VerbForm=Fin	15	aux	_	_
14	be	be	AUX	VB	VerbForm=Inf	15	auxpass	_	_
15	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	relcl	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	an	an	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
18	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	20	amod	_	_
19	double	double	ADJ	JJ	Degree=Pos	20	amod	_	_
20	category	category	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 303
# sent_id = 1
# text = In this paper we show that eight coherence conditions suffice for the definition of a pseudodistributive law between pseudomonads.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	10	mark	_	_
7	eight	eight	NUM	CD	NumType=Card	9	nummod	_	_
8	coherence	coherence	NOUN	NN	Number=Sing	9	compound	_	_
9	conditions	condition	NOUN	NNS	Number=Plur	10	nsubj	_	_
10	suffice	suffice	VERB	VBP	Tense=Pres|VerbForm=Fin	5	ccomp	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	definition	definition	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	pseudodistributive	pseudodistributive	ADJ	JJ	Degree=Pos	17	amod	_	_
17	law	law	NOUN	NN	Number=Sing	14	pobj	_	_
18	between	between	ADP	IN	_	17	prep	_	_
19	pseudomonads	pseudomonad	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 304
# sent_id = 1
# text = We show that, in any Maltsev (and a fortiori protomodular) category $ E $ , not only the fibre $ Grd_X E $ of internal groupoids above the object $ X $ is a naturally Maltsev category, but moreover it shares with the category $ Ab $ of abelian groups the property following which the domain of any split epimorphism is isomorphic with the direct sum of its codomain with its kernel.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	29	mark	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
5	in	in	ADP	IN	_	15	prep	_	_
6	any	any	DET	DT	_	7	det	_	_
7	Maltsev	Maltsev	PROPN	NNP	Number=Sing	5	pobj	_	_
8	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	7	punct	_	SpaceAfter=No
9	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	fortiori	fortiori	NOUN	NN	Number=Sing	12	compound	_	_
12	protomodular	protomodular	ADJ	JJ	Degree=Pos	7	conj	_	SpaceAfter=No
13	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	14	punct	_	_
14	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
15	$ E $	$ e $	SYM	$	_	4	nmod	_	_
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	not	not	PART	RB	Polarity=Neg	20	preconj	_	_
18	only	only	ADV	RB	_	17	advmod	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	fibre	fibre	NOUN	NN	Number=Sing	29	nsubj	_	_
21	$ Grd_X E $	$ grd_x e $	SYM	$	_	20	appos	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	internal	internal	ADJ	JJ	Degree=Pos	24	amod	_	_
24	groupoids	groupoid	NOUN	NNS	Number=Plur	22	pobj	_	_
25	above	above	ADP	IN	_	20	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	object	object	NOUN	NN	Number=Sing	25	pobj	_	_
28	$ X $	$ x $	SYM	$	_	20	appos	_	_
29	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
31	naturally	naturally	ADV	RB	_	32	advmod	_	_
32	Maltsev	Maltsev	PROPN	NNP	Number=Sing	33	amod	_	_
33	category	category	NOUN	NN	Number=Sing	29	attr	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
35	but	but	CCONJ	CC	ConjType=Cmp	2	cc	_	_
36	moreover	moreover	ADV	RB	_	38	advmod	_	_
37	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	38	nsubj	_	_
38	shares	share	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
39	with	with	ADP	IN	_	38	prep	_	_
40	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
41	category	category	NOUN	NN	Number=Sing	39	pobj	_	_
42	$ Ab $	$ ab $	SYM	$	_	41	appos	_	_
43	of	of	ADP	IN	_	42	prep	_	_
44	abelian	abelian	ADJ	JJ	Degree=Pos	45	compound	_	_
45	groups	group	NOUN	NNS	Number=Plur	43	pobj	_	_
46	the	the	DET	DT	Definite=Def|PronType=Art	47	det	_	_
47	property	property	NOUN	NN	Number=Sing	41	appos	_	_
48	following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	56	dep	_	_
49	which	which	PRON	WDT	_	48	pobj	_	_
50	the	the	DET	DT	Definite=Def|PronType=Art	51	det	_	_
51	domain	domain	NOUN	NN	Number=Sing	56	nsubj	_	_
52	of	of	ADP	IN	_	51	prep	_	_
53	any	any	DET	DT	_	54	det	_	_
54	split	split	NOUN	NN	Number=Sing	52	pobj	_	_
55	epimorphism	epimorphism	NOUN	NN	Number=Sing	56	nsubj	_	_
56	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	47	relcl	_	_
57	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	56	acomp	_	_
58	with	with	ADP	IN	_	57	prep	_	_
59	the	the	DET	DT	Definite=Def|PronType=Art	61	det	_	_
60	direct	direct	ADJ	JJ	Degree=Pos	61	amod	_	_
61	sum	sum	NOUN	NN	Number=Sing	58	pobj	_	_
62	of	of	ADP	IN	_	61	prep	_	_
63	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	64	poss	_	_
64	codomain	codomain	NOUN	NN	Number=Sing	62	pobj	_	_
65	with	with	ADP	IN	_	64	prep	_	_
66	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	67	poss	_	_
67	kernel	kernel	NOUN	NN	Number=Sing	65	pobj	_	SpaceAfter=No
68	.	.	PUNCT	.	PunctType=Peri	38	punct	_	SpaceAfter=No

# sent_id = 2
# text = This allows us to point at a new class of ``non - pointed additive'' categories which is necessarily protomodular.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	point	point	VERB	VB	VerbForm=Inf	2	ccomp	_	_
6	at	at	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	new	new	ADJ	JJ	Degree=Pos	9	amod	_	_
9	class	class	NOUN	NN	Number=Sing	6	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	15	punct	_	SpaceAfter=No
12	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	15	punct	_	SpaceAfter=No
13	non	non	ADV	RB	_	15	advmod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	pointed	pointed	ADJ	JJ	Degree=Pos	18	amod	_	_
16	additive	additive	NOUN	NN	Number=Sing	18	amod	_	SpaceAfter=No
17	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	18	punct	_	_
18	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
19	which	which	PRON	WDT	_	20	nsubj	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	relcl	_	_
21	necessarily	necessarily	ADV	RB	_	20	advmod	_	_
22	protomodular	protomodular	ADJ	JJ	Degree=Pos	20	acomp	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Actually this even gives rise to a larger classification table of non - pointed additive categories which gradually take place between the class of naturally Maltsev categories and the one of essentially affine categories.
1	Actually	actually	ADV	RB	_	4	advmod	_	_
2	this	this	PRON	DT	Number=Sing|PronType=Dem	4	nsubj	_	_
3	even	even	ADV	RB	_	4	advmod	_	_
4	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	rise	rise	NOUN	NN	Number=Sing	4	dobj	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	larger	large	ADJ	JJR	Degree=Cmp	10	amod	_	_
9	classification	classification	NOUN	NN	Number=Sing	10	compound	_	_
10	table	table	NOUN	NN	Number=Sing	6	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	non	non	PROPN	NNP	Number=Sing	14	npadvmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	pointed	point	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
15	additive	additive	ADJ	JJ	Degree=Pos	16	amod	_	_
16	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
17	which	which	PRON	WDT	_	19	nsubj	_	_
18	gradually	gradually	ADV	RB	_	19	advmod	_	_
19	take	take	VERB	VBP	Tense=Pres|VerbForm=Fin	16	relcl	_	_
20	place	place	NOUN	NN	Number=Sing	19	dobj	_	_
21	between	between	ADP	IN	_	19	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	class	class	NOUN	NN	Number=Sing	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	naturally	naturally	ADV	RB	_	26	advmod	_	_
26	Maltsev	maltsev	ADJ	JJ	Degree=Pos	27	amod	_	_
27	categories	category	NOUN	NNS	Number=Plur	24	pobj	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	one	one	NUM	CD	NumType=Card	27	conj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	essentially	essentially	ADV	RB	_	33	advmod	_	_
33	affine	affine	ADJ	JJ	Degree=Pos	34	amod	_	_
34	categories	category	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = As an application, when furthermore the ground category $ E $ is efficiently regular, we get a new way to produce Baer sums in the fibres $ Grd_X E $ and, more generally, in the fibres $ n - Grd_X E $ .
1	As	as	ADP	IN	_	16	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
5	when	when	SCONJ	WRB	_	11	advmod	_	_
6	furthermore	furthermore	ADV	RB	_	11	advmod	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	ground	ground	NOUN	NN	Number=Sing	9	compound	_	_
9	category	category	NOUN	NN	Number=Sing	11	nsubj	_	_
10	$ E $	$ e $	SYM	$	_	9	appos	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	advcl	_	_
12	efficiently	efficiently	ADV	RB	_	13	advmod	_	_
13	regular	regular	ADJ	JJ	Degree=Pos	11	acomp	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
15	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	16	nsubj	_	_
16	get	get	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	new	new	ADJ	JJ	Degree=Pos	19	amod	_	_
19	way	way	NOUN	NN	Number=Sing	16	dobj	_	_
20	to	to	PART	TO	_	21	aux	_	_
21	produce	produce	VERB	VB	VerbForm=Inf	19	relcl	_	_
22	Baer	Baer	PROPN	NNP	Number=Sing	23	compound	_	_
23	sums	sum	NOUN	NNS	Number=Plur	21	dobj	_	_
24	in	in	ADP	IN	_	21	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	fibres	fibre	NOUN	NNS	Number=Plur	24	pobj	_	_
27	$ Grd_X E $	$ grd_x e $	SYM	$	_	16	dep	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
30	more	more	ADV	RBR	Degree=Cmp	31	advmod	_	_
31	generally	generally	ADV	RB	_	16	advmod	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
33	in	in	ADP	IN	_	36	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	fibres	fibre	NOUN	NNS	Number=Plur	33	pobj	_	_
36	$ n - Grd_X E $	$ n - grd_x e $	SYM	$	_	16	dep	_	_
37	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# doc_id = 305
# sent_id = 1
# text = Maps (left adjoint arrows) between Frobenius objects in a cartesian bicategory $ B $ are precisely comonoid homomorphisms and, for $ A $ Frobenius and any $ T $ in $ B $ , $ map(B)(T, A) $ is a groupoid.
1	Maps	map	NOUN	NNS	Number=Plur	3	nsubj	_	_
2	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	3	punct	_	SpaceAfter=No
3	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	adjoint	adjoint	NOUN	NN	Number=Sing	5	compound	_	_
5	arrows	arrow	NOUN	NNS	Number=Plur	3	dobj	_	SpaceAfter=No
6	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	3	punct	_	_
7	between	between	ADP	IN	_	3	prep	_	_
8	Frobenius	Frobenius	PROPN	NNP	Number=Sing	9	compound	_	_
9	objects	object	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	pobj	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	cartesian	cartesian	ADJ	JJ	Degree=Pos	13	amod	_	_
13	bicategory	bicategory	NOUN	NN	Number=Sing	10	pobj	_	_
14	$ B $	$ b $	SYM	$	_	13	appos	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	conj	_	_
16	precisely	precisely	ADV	RB	_	15	advmod	_	_
17	comonoid	comonoid	NOUN	NN	Number=Sing	18	compound	_	_
18	homomorphisms	homomorphism	NOUN	NNS	Number=Plur	15	attr	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
21	for	for	ADP	IN	_	31	prep	_	_
22	$ A $	$ a $	SYM	$	_	23	nmod	_	_
23	Frobenius	Frobenius	PROPN	NNP	Number=Sing	21	pobj	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	any	any	DET	DT	_	26	det	_	_
26	$ T $	$ t $	SYM	$	_	30	nmod	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	$ B $	$ b $	SYM	$	_	27	pobj	_	_
29	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
30	$ map(B)(T, A) $	$ map(b)(t, a) $	SYM	$	_	31	nsubj	_	_
31	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	conj	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
33	groupoid	groupoid	NOUN	NN	Number=Sing	31	attr	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 306
# sent_id = 1
# text = Using the reflection of the category $ C $ of compact 0 - dimensional topological spaces into the category of Stone spaces we introduce a concept of a fibration in $ C $ .
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	advcl	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	reflection	reflection	NOUN	NN	Number=Sing	1	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
7	$ C $	$ c $	SYM	$	_	6	appos	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	compact	compact	ADJ	JJ	Degree=Pos	12	amod	_	_
10	0	0	NUM	CD	NumType=Card	9	dep	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	dimensional	dimensional	ADJ	JJ	Degree=Pos	14	amod	_	_
13	topological	topological	ADJ	JJ	Degree=Pos	14	amod	_	_
14	spaces	space	NOUN	NNS	Number=Plur	8	pobj	_	_
15	into	into	ADP	IN	_	1	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	Stone	Stone	PROPN	NNP	Number=Sing	20	compound	_	_
20	spaces	space	NOUN	NNS	Number=Plur	18	pobj	_	_
21	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	22	nsubj	_	_
22	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	concept	concept	NOUN	NN	Number=Sing	22	dobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	fibration	fibration	NOUN	NN	Number=Sing	25	pobj	_	_
28	in	in	ADP	IN	_	27	prep	_	_
29	$ C $	$ c $	SYM	$	_	28	pobj	_	_
30	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that: (i) effective descent morphisms in $ C $ are the same as the surjective fibrations; (ii) effective descent morphisms in $ C $ with respect to the fibrations are all surjections.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	13	mark	_	SpaceAfter=No
4	:	:	PUNCT	:	_	13	punct	_	_
5	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	10	punct	_	SpaceAfter=No
6	i	i	NOUN	NN	Number=Sing	10	nmod	_	SpaceAfter=No
7	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	10	punct	_	_
8	effective	effective	ADJ	JJ	Degree=Pos	10	amod	_	_
9	descent	descent	NOUN	NN	Number=Sing	10	compound	_	_
10	morphisms	morphism	NOUN	NNS	Number=Plur	13	nsubj	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	$ C $	$ c $	SYM	$	_	11	pobj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	same	same	ADJ	JJ	Degree=Pos	13	attr	_	_
16	as	as	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	surjective	surjective	ADJ	JJ	Degree=Pos	19	amod	_	_
19	fibrations	fibration	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
20	;	;	PUNCT	:	_	13	punct	_	_
21	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	26	punct	_	SpaceAfter=No
22	ii	ii	PROPN	NNP	Number=Sing	26	dep	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	26	punct	_	_
24	effective	effective	ADJ	JJ	Degree=Pos	26	amod	_	_
25	descent	descent	NOUN	NN	Number=Sing	26	compound	_	_
26	morphisms	morphism	NOUN	NNS	Number=Plur	34	nsubj	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	$ C $	$ c $	SYM	$	_	27	pobj	_	_
29	with	with	ADP	IN	_	26	prep	_	_
30	respect	respect	NOUN	NN	Number=Sing	29	pobj	_	_
31	to	to	ADP	IN	_	30	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
33	fibrations	fibration	NOUN	NNS	Number=Plur	31	pobj	_	_
34	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	conj	_	_
35	all	all	PRON	DT	_	34	advmod	_	_
36	surjections	surjection	NOUN	NNS	Number=Plur	34	attr	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 307
# sent_id = 1
# text = Two propositions in the author's article are not correct.
1	Two	two	NUM	CD	NumType=Card	2	nummod	_	_
2	propositions	proposition	NOUN	NNS	Number=Plur	8	nsubj	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	author	author	NOUN	NN	Number=Sing	7	poss	_	SpaceAfter=No
6	's	's	PART	POS	_	5	case	_	_
7	article	article	NOUN	NN	Number=Sing	3	pobj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	not	not	PART	RB	Polarity=Neg	8	neg	_	_
10	correct	correct	ADJ	JJ	Degree=Pos	8	acomp	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that their use can be avoided and all remaining results remain correct.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	8	mark	_	_
4	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	5	poss	_	_
5	use	use	NOUN	NN	Number=Sing	8	nsubjpass	_	_
6	can	can	AUX	MD	VerbForm=Fin	8	aux	_	_
7	be	be	AUX	VB	VerbForm=Inf	8	auxpass	_	_
8	avoided	avoid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	all	all	DET	DT	_	12	det	_	_
11	remaining	remain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	amod	_	_
12	results	result	NOUN	NNS	Number=Plur	13	nsubj	_	_
13	remain	remain	VERB	VBP	Tense=Pres|VerbForm=Fin	8	conj	_	_
14	correct	correct	ADJ	JJ	Degree=Pos	13	acomp	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = See note on page 24.
1	See	see	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	note	note	NOUN	NN	Number=Sing	1	dobj	_	_
3	on	on	ADP	IN	_	1	prep	_	_
4	page	page	NOUN	NN	Number=Sing	3	pobj	_	_
5	24	24	NUM	CD	NumType=Card	4	nummod	_	SpaceAfter=No
6	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# doc_id = 308
# sent_id = 1
# text = Let $ X $ and $ A $ be sets and $ alpha:Xto A $ a map between them.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ X $	$ x $	SYM	$	_	5	nsubj	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	$ A $	$ a $	SYM	$	_	2	conj	_	_
5	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
6	sets	set	NOUN	NNS	Number=Plur	5	attr	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
8	$ alpha:Xto A $	$ alpha:xto a $	SYM	$	_	5	nmod	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	map	map	NOUN	NN	Number=Sing	5	attr	_	_
11	between	between	ADP	IN	_	10	prep	_	_
12	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	11	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = We call a map $ mu:Xtimes Xtimes Xto A $ an approximate Maltsev operation with approximation $ alpha $ , if it satisfies $ mu(x, y, y) = alpha(x) = mu(y, y, x) $ for all $ x, yin X $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	map	map	NOUN	NN	Number=Sing	2	dobj	_	_
5	$ mu:Xtimes Xtimes Xto A $	$ mu:xtimes xtimes xto a $	SYM	$	_	9	nummod	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	approximate	approximate	ADJ	JJ	Degree=Pos	9	amod	_	_
8	Maltsev	Maltsev	PROPN	NNP	Number=Sing	9	compound	_	_
9	operation	operation	NOUN	NN	Number=Sing	2	dobj	_	_
10	with	with	ADP	IN	_	2	prep	_	_
11	approximation	approximation	NOUN	NN	Number=Sing	10	pobj	_	_
12	$ alpha $	$ alpha $	SYM	$	_	2	oprd	_	_
13	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
14	if	if	SCONJ	IN	_	16	mark	_	_
15	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	16	nsubj	_	_
16	satisfies	satisfy	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	advcl	_	_
17	$ mu(x, y, y) = alpha(x) = mu(y, y, x) $	$ mu(x, y, y) = alpha(x) = mu(y, y, x) $	SYM	$	_	16	dobj	_	_
18	for	for	ADP	IN	_	17	prep	_	_
19	all	all	DET	DT	_	20	det	_	_
20	$ x, yin X $	$ x, yin x $	SYM	$	_	18	pobj	_	_
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Note that if $ A = X $ and the approximation $ alpha $ is an identity map, then $ mu $ becomes an ordinary Maltsev operation.
1	Note	note	VERB	VB	VerbForm=Inf	16	advcl	_	_
2	that	that	SCONJ	IN	_	9	mark	_	_
3	if	if	SCONJ	IN	_	4	mark	_	_
4	$ A = X $	$ a = x $	SYM	$	_	9	nsubj	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	approximation	approximation	NOUN	NN	Number=Sing	4	conj	_	_
8	$ alpha $	$ alpha $	SYM	$	_	4	dobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	1	ccomp	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	identity	identity	NOUN	NN	Number=Sing	12	compound	_	_
12	map	map	NOUN	NN	Number=Sing	9	attr	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
14	then	then	ADV	RB	PronType=Dem	16	advmod	_	_
15	$ mu $	$ mu $	SYM	$	_	16	nsubj	_	_
16	becomes	become	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
17	an	an	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
18	ordinary	ordinary	ADJ	JJ	Degree=Pos	20	amod	_	_
19	Maltsev	Maltsev	PROPN	NNP	Number=Sing	20	compound	_	_
20	operation	operation	NOUN	NN	Number=Sing	16	attr	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 4
# text = We prove the following two characterization theorems: a category $ mathbb{X} $ is a Maltsev category if and only if in the functor category $ mathbf{Set}^{mathbb{X}^mathrm{op}timesmathbb{X}} $ there exists an internal approximate Maltsev operation $ mathrm{hom}_{mathbb{X}}times mathrm{hom}_{mathbb{X}}times mathrm{hom}_{mathbb{X}}rightarrow A $ whose approximation $ alpha $ satisfies a suitable condition; a regular category $ mathbb{X} $ with finite coproducts is a Maltsev category, if and only if in the functor category $ mathbb{X}^mathbb{X} $ there exists an internal approximate Maltsev co - operation $ Arightarrow 1_mathbb{X}+1_mathbb{X}+1_mathbb{X} $ whose approximation $ alpha $ is a natural transformation with every component a regular epimorphism in $ mathbb{X} $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	48	ccomp	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
4	following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	amod	_	_
5	two	two	NUM	CD	NumType=Card	6	nummod	_	_
6	characterization	characterization	NOUN	NN	Number=Sing	7	compound	_	_
7	theorems	theorem	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
8	:	:	PUNCT	:	_	7	punct	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	category	category	NOUN	NN	Number=Sing	12	nsubj	_	_
11	$ mathbb{X} $	$ mathbb{x} $	SYM	$	_	10	appos	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	Maltsev	Maltsev	PROPN	NNP	Number=Sing	15	compound	_	_
15	category	category	NOUN	NN	Number=Sing	12	attr	_	_
16	if	if	SCONJ	IN	_	26	mark	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	only	only	ADV	RB	_	20	advmod	_	_
19	if	if	SCONJ	IN	_	20	mark	_	_
20	in	in	ADP	IN	_	26	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	functor	functor	NOUN	NN	Number=Sing	23	compound	_	_
23	category	category	NOUN	NN	Number=Sing	20	pobj	_	_
24	$ mathbf{Set}^{mathbb{X}^mathrm{op}timesmathbb{X}} $	$ mathbf{set}^{mathbb{x}^mathrm{op}timesmathbb{x}} $	SYM	$	_	20	dep	_	_
25	there	there	PRON	EX	_	26	expl	_	_
26	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	advcl	_	_
27	an	an	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
28	internal	internal	ADJ	JJ	Degree=Pos	31	amod	_	_
29	approximate	approximate	ADJ	JJ	Degree=Pos	30	amod	_	_
30	Maltsev	Maltsev	PROPN	NNP	Number=Sing	31	compound	_	_
31	operation	operation	NOUN	NN	Number=Sing	26	dobj	_	_
32	$ mathrm{hom}_{mathbb{X}}times mathrm{hom}_{mathbb{X}}times mathrm{hom}_{mathbb{X}}rightarrow A $	$ mathrm{hom}_{mathbb{x}}times mathrm{hom}_{mathbb{x}}times mathrm{hom}_{mathbb{x}}rightarrow a $	SYM	$	_	31	prep	_	_
33	whose	whose	DET	WP$	Poss=Yes	34	poss	_	_
34	approximation	approximation	NOUN	NN	Number=Sing	36	nsubj	_	_
35	$ alpha $	$ alpha $	SYM	$	_	36	nummod	_	_
36	satisfies	satisfie	NOUN	NNS	Number=Plur	32	relcl	_	_
37	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
38	suitable	suitable	ADJ	JJ	Degree=Pos	39	amod	_	_
39	condition	condition	NOUN	NN	Number=Sing	26	dobj	_	SpaceAfter=No
40	;	;	PUNCT	:	_	48	punct	_	_
41	a	a	DET	DT	Definite=Ind|PronType=Art	43	det	_	_
42	regular	regular	ADJ	JJ	Degree=Pos	43	amod	_	_
43	category	category	NOUN	NN	Number=Sing	48	nsubj	_	_
44	$ mathbb{X} $	$ mathbb{x} $	SYM	$	_	43	appos	_	_
45	with	with	ADP	IN	_	43	prep	_	_
46	finite	finite	ADJ	JJ	Degree=Pos	47	amod	_	_
47	coproducts	coproduct	NOUN	NNS	Number=Plur	45	pobj	_	_
48	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	75	ccomp	_	_
49	a	a	DET	DT	Definite=Ind|PronType=Art	51	det	_	_
50	Maltsev	Maltsev	PROPN	NNP	Number=Sing	51	compound	_	_
51	category	category	NOUN	NN	Number=Sing	48	attr	_	SpaceAfter=No
52	,	,	PUNCT	,	PunctType=Comm	48	punct	_	_
53	if	if	SCONJ	IN	_	63	mark	_	_
54	and	and	CCONJ	CC	ConjType=Cmp	53	cc	_	_
55	only	only	ADV	RB	_	63	advmod	_	_
56	if	if	SCONJ	IN	_	63	mark	_	_
57	in	in	ADP	IN	_	56	prep	_	_
58	the	the	DET	DT	Definite=Def|PronType=Art	60	det	_	_
59	functor	functor	NOUN	NN	Number=Sing	60	compound	_	_
60	category	category	NOUN	NN	Number=Sing	57	pobj	_	_
61	$ mathbb{X}^mathbb{X} $	$ mathbb{x}^mathbb{x} $	SYM	$	_	56	nmod	_	_
62	there	there	PRON	EX	_	63	expl	_	_
63	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	75	advcl	_	_
64	an	an	DET	DT	Definite=Ind|PronType=Art	68	det	_	_
65	internal	internal	ADJ	JJ	Degree=Pos	68	amod	_	_
66	approximate	approximate	ADJ	JJ	Degree=Pos	68	amod	_	_
67	Maltsev	Maltsev	PROPN	NNP	Number=Sing	68	compound	_	_
68	co	co	NOUN	NN	Number=Sing	63	dobj	_	_
69	-	-	NOUN	NN	Number=Sing	63	dobj	_	_
70	operation	operation	NOUN	NN	Number=Sing	63	dobj	_	_
71	$ Arightarrow 1_mathbb{X}+1_mathbb{X}+1_mathbb{X} $	$ arightarrow 1_mathbb{x}+1_mathbb{x}+1_mathbb{x} $	SYM	$	_	75	nsubj	_	_
72	whose	whose	DET	WP$	Poss=Yes	73	poss	_	_
73	approximation	approximation	NOUN	NN	Number=Sing	74	nsubj	_	_
74	$ alpha $	$ alpha $	SYM	$	_	75	nsubj	_	_
75	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
76	a	a	DET	DT	Definite=Ind|PronType=Art	78	det	_	_
77	natural	natural	ADJ	JJ	Degree=Pos	78	amod	_	_
78	transformation	transformation	NOUN	NN	Number=Sing	75	attr	_	_
79	with	with	ADP	IN	_	78	prep	_	_
80	every	every	DET	DT	_	81	det	_	_
81	component	component	NOUN	NN	Number=Sing	79	pobj	_	_
82	a	a	DET	DT	Definite=Ind|PronType=Art	84	det	_	_
83	regular	regular	ADJ	JJ	Degree=Pos	84	amod	_	_
84	epimorphism	epimorphism	NOUN	NN	Number=Sing	81	appos	_	_
85	in	in	ADP	IN	_	81	prep	_	_
86	$ mathbb{X} $	$ mathbb{x} $	SYM	$	_	85	pobj	_	_
87	.	.	PUNCT	.	PunctType=Peri	75	punct	_	SpaceAfter=No

# sent_id = 5
# text = Note that in both of these characterization theorems, if require further the approximation $ alpha $ to be an identity morphism, then the conditions there involving $ alpha $ become equivalent to $ mathbb{X} $ being a naturally Maltsev category.
1	Note	note	VERB	VB	VerbForm=Inf	28	advcl	_	_
2	that	that	SCONJ	IN	_	11	mark	_	_
3	in	in	ADP	IN	_	11	prep	_	_
4	both	both	PRON	DT	_	3	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	these	these	DET	DT	Number=Plur|PronType=Dem	7	det	_	_
7	characterization	characterization	NOUN	NN	Number=Sing	8	compound	_	_
8	theorems	theorem	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
10	if	if	SCONJ	IN	_	11	mark	_	_
11	require	require	VERB	VB	VerbForm=Inf	1	ccomp	_	_
12	further	far	ADV	RB	_	11	advmod	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	approximation	approximation	NOUN	NN	Number=Sing	11	dobj	_	_
15	$ alpha $	$ alpha $	SYM	$	_	14	appos	_	_
16	to	to	PART	TO	_	17	aux	_	_
17	be	be	AUX	VB	VerbForm=Inf	11	xcomp	_	_
18	an	an	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	identity	identity	NOUN	NN	Number=Sing	20	compound	_	_
20	morphism	morphism	NOUN	NN	Number=Sing	17	attr	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
22	then	then	ADV	RB	PronType=Dem	28	advmod	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	conditions	condition	NOUN	NNS	Number=Plur	28	nsubj	_	_
25	there	there	ADV	RB	PronType=Dem	24	advmod	_	_
26	involving	involve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	24	acl	_	_
27	$ alpha $	$ alpha $	SYM	$	_	26	dobj	_	_
28	become	become	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
29	equivalent	equivalent	ADJ	JJ	Degree=Pos	28	acomp	_	_
30	to	to	ADP	IN	_	29	prep	_	_
31	$ mathbb{X} $	$ mathbb{x} $	SYM	$	_	30	pobj	_	_
32	being	be	AUX	VBG	VerbForm=Ger	28	advcl	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
34	naturally	naturally	ADV	RB	_	35	advmod	_	_
35	Maltsev	Maltsev	PROPN	NNP	Number=Sing	36	amod	_	_
36	category	category	NOUN	NN	Number=Sing	32	attr	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	28	punct	_	SpaceAfter=No

# doc_id = 309
# sent_id = 1
# text = We show how to formulate the notion of locally cartesian closed category without chosen pullbacks, by the use of Makkai's theory of anafunctors.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	how	how	SCONJ	WRB	_	5	advmod	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	formulate	formulate	VERB	VB	VerbForm=Inf	2	xcomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	notion	notion	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	locally	locally	ADV	RB	_	10	advmod	_	_
10	cartesian	cartesian	ADJ	JJ	Degree=Pos	12	amod	_	_
11	closed	closed	ADJ	JJ	Degree=Pos	12	amod	_	_
12	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
13	without	without	ADP	IN	_	5	prep	_	_
14	chosen	choose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
15	pullbacks	pullback	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
17	by	by	ADP	IN	_	2	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	use	use	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	Makkai	Makkai	PROPN	NNP	Number=Sing	23	poss	_	SpaceAfter=No
22	's	's	PART	POS	_	21	case	_	_
23	theory	theory	NOUN	NN	Number=Sing	20	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	anafunctors	anafunctor	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 310
# sent_id = 1
# text = Notions and techniques of enriched category theory can be used to study topological structures, like metric spaces, topological spaces and approach spaces, in the context of topological theories.
1	Notions	notion	NOUN	NNS	Number=Plur	10	nsubjpass	_	_
2	and	and	CCONJ	CC	ConjType=Cmp	1	cc	_	_
3	techniques	technique	NOUN	NNS	Number=Plur	1	conj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
6	category	category	NOUN	NN	Number=Sing	7	compound	_	_
7	theory	theory	NOUN	NN	Number=Sing	4	pobj	_	_
8	can	can	AUX	MD	VerbForm=Fin	10	aux	_	_
9	be	be	AUX	VB	VerbForm=Inf	10	auxpass	_	_
10	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	study	study	VERB	VB	VerbForm=Inf	10	xcomp	_	_
13	topological	topological	ADJ	JJ	Degree=Pos	14	amod	_	_
14	structures	structure	NOUN	NNS	Number=Plur	12	dobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	like	like	ADP	IN	_	12	prep	_	_
17	metric	metric	ADJ	JJ	Degree=Pos	18	amod	_	_
18	spaces	space	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	topological	topological	ADJ	JJ	Degree=Pos	21	amod	_	_
21	spaces	space	NOUN	NNS	Number=Plur	18	conj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	approach	approach	NOUN	NN	Number=Sing	24	compound	_	_
24	spaces	space	NOUN	NNS	Number=Plur	21	conj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
26	in	in	ADP	IN	_	12	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	context	context	NOUN	NN	Number=Sing	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	topological	topological	ADJ	JJ	Degree=Pos	31	amod	_	_
31	theories	theory	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = Recently, the construction of a Yoneda embedding allowed to identify injectivity of spaces as cocompleteness and to show monadicity of the category of injective spaces and left adjoints over $ SET $ .
1	Recently	recently	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	construction	construction	NOUN	NN	Number=Sing	0	ROOT	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	Yoneda	Yoneda	PROPN	NNP	Number=Sing	8	compound	_	_
8	embedding	embedding	NOUN	NN	Number=Sing	5	pobj	_	_
9	allowed	allow	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	identify	identify	VERB	VB	VerbForm=Inf	9	xcomp	_	_
12	injectivity	injectivity	NOUN	NN	Number=Sing	11	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	spaces	space	NOUN	NNS	Number=Plur	13	pobj	_	_
15	as	as	ADP	IN	_	11	prep	_	_
16	cocompleteness	cocompleteness	NOUN	NN	Number=Sing	15	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
18	to	to	PART	TO	_	19	aux	_	_
19	show	show	VERB	VB	VerbForm=Inf	11	conj	_	_
20	monadicity	monadicity	NOUN	NN	Number=Sing	19	dobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	category	category	NOUN	NN	Number=Sing	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	injective	injective	ADJ	JJ	Degree=Pos	26	amod	_	_
26	spaces	space	NOUN	NNS	Number=Plur	24	pobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
28	left	leave	VERB	VBD	Tense=Past|VerbForm=Fin	19	conj	_	_
29	adjoints	adjoint	NOUN	NNS	Number=Plur	28	dobj	_	_
30	over	over	ADP	IN	_	29	prep	_	_
31	$ SET $	$ set $	SYM	$	_	30	pobj	_	_
32	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this paper we generalise these results, studying cocompleteness with respect to a given class of distributors.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	generalise	generalise	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	these	these	DET	DT	Number=Plur|PronType=Dem	7	det	_	_
7	results	result	NOUN	NNS	Number=Plur	5	dobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
9	studying	study	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	advcl	_	_
10	cocompleteness	cocompleteness	NOUN	NN	Number=Sing	9	dobj	_	_
11	with	with	ADP	IN	_	9	prep	_	_
12	respect	respect	NOUN	NN	Number=Sing	11	pobj	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
16	class	class	NOUN	NN	Number=Sing	13	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	distributors	distributor	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show in particular that the description of several semantic domains presented in another paper can be translated into the $ V $ - enriched setting.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	particular	particular	ADJ	JJ	Degree=Pos	3	amod	_	_
5	that	that	SCONJ	IN	_	18	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	description	description	NOUN	NN	Number=Sing	18	nsubjpass	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	several	several	ADJ	JJ	Degree=Pos	11	amod	_	_
10	semantic	semantic	ADJ	JJ	Degree=Pos	11	amod	_	_
11	domains	domain	NOUN	NNS	Number=Plur	8	pobj	_	_
12	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acl	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	another	another	DET	DT	_	15	det	_	_
15	paper	paper	NOUN	NN	Number=Sing	13	pobj	_	_
16	can	can	AUX	MD	VerbForm=Fin	18	aux	_	_
17	be	be	AUX	VB	VerbForm=Inf	18	auxpass	_	_
18	translated	translate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
19	into	into	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
21	$ V $	$ v $	SYM	$	_	23	advmod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
24	setting	setting	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 311
# sent_id = 1
# text = For accessible set - valued functors it is well known that weak preservation of limits is equivalent to representability, and weak preservation of connected limits to familial representability.
1	For	for	ADP	IN	_	10	prep	_	_
2	accessible	accessible	ADJ	JJ	Degree=Pos	6	amod	_	_
3	set	set	NOUN	NN	Number=Sing	5	npadvmod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	amod	_	_
6	functors	functor	NOUN	NNS	Number=Plur	1	pobj	_	_
7	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	8	nsubj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
9	well	well	ADV	RB	Degree=Pos	10	advmod	_	_
10	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	that	that	SCONJ	IN	_	16	mark	_	_
12	weak	weak	ADJ	JJ	Degree=Pos	13	amod	_	_
13	preservation	preservation	NOUN	NN	Number=Sing	16	nsubj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	limits	limit	NOUN	NNS	Number=Plur	14	pobj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	ccomp	_	_
17	equivalent	equivalent	ADJ	JJ	Degree=Pos	16	acomp	_	_
18	to	to	PART	TO	_	19	aux	_	_
19	representability	representability	VERB	VB	VerbForm=Inf	17	xcomp	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
22	weak	weak	ADJ	JJ	Degree=Pos	23	amod	_	_
23	preservation	preservation	NOUN	NN	Number=Sing	16	conj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	connected	connected	ADJ	JJ	Degree=Pos	26	amod	_	_
26	limits	limit	NOUN	NNS	Number=Plur	24	pobj	_	_
27	to	to	ADP	IN	_	23	prep	_	_
28	familial	familial	ADJ	JJ	Degree=Pos	29	amod	_	_
29	representability	representability	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = In contrast, preservation of weak wide pullbacks is equivalent to being a coproduct of quotients of $ hom $ - functors modulo groups of automorphisms.
1	In	in	ADP	IN	_	9	prep	_	_
2	contrast	contrast	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
4	preservation	preservation	NOUN	NN	Number=Sing	9	nsubj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	weak	weak	ADJ	JJ	Degree=Pos	8	amod	_	_
7	wide	wide	ADJ	JJ	Degree=Pos	8	amod	_	_
8	pullbacks	pullback	NOUN	NNS	Number=Plur	5	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	equivalent	equivalent	ADJ	JJ	Degree=Pos	9	acomp	_	_
11	to	to	ADP	IN	_	10	prep	_	_
12	being	be	AUX	VBG	VerbForm=Ger	11	pcomp	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	coproduct	coproduct	NOUN	NN	Number=Sing	12	attr	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	quotients	quotient	NOUN	NNS	Number=Plur	15	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	$ hom $	$ hom $	SYM	$	_	20	nummod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	functors	functor	NOUN	NNS	Number=Plur	22	compound	_	_
21	modulo	modulo	NOUN	NN	Number=Sing	22	compound	_	_
22	groups	group	NOUN	NNS	Number=Plur	17	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	automorphisms	automorphism	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 3
# text = For finitary functors this was proved by Joyal who called these functors analytic.
1	For	for	ADP	IN	_	6	prep	_	_
2	finitary	finitary	ADJ	JJ	Degree=Pos	3	amod	_	_
3	functors	functor	NOUN	NNS	Number=Plur	1	pobj	_	_
4	this	this	PRON	DT	Number=Sing|PronType=Dem	6	nsubjpass	_	_
5	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	6	auxpass	_	_
6	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	by	by	ADP	IN	_	6	agent	_	_
8	Joyal	Joyal	PROPN	NNP	Number=Sing	7	pobj	_	_
9	who	who	PRON	WP	_	10	nsubj	_	_
10	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	4	relcl	_	_
11	these	these	DET	DT	Number=Plur|PronType=Dem	12	det	_	_
12	functors	functor	NOUN	NNS	Number=Plur	10	dobj	_	_
13	analytic	analytic	ADJ	JJ	Degree=Pos	10	oprd	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = We introduce a generalization of Joyal's concept from endofunctors of $ Set $ to endofunctors of a symmetric monoidal category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	generalization	generalization	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	Joyal	Joyal	PROPN	NNP	Number=Sing	8	poss	_	SpaceAfter=No
7	's	's	PART	POS	_	6	case	_	_
8	concept	concept	NOUN	NN	Number=Sing	5	pobj	_	_
9	from	from	ADP	IN	_	8	prep	_	_
10	endofunctors	endofunctor	NOUN	NNS	Number=Plur	9	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	$ Set $	$ set $	SYM	$	_	11	pobj	_	_
13	to	to	ADP	IN	_	2	prep	_	_
14	endofunctors	endofunctor	NOUN	NNS	Number=Plur	13	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
17	symmetric	symmetric	ADJ	JJ	Degree=Pos	19	amod	_	_
18	monoidal	monoidal	ADJ	JJ	Degree=Pos	19	amod	_	_
19	category	category	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 312
# sent_id = 1
# text = We present sufficient conditions under which effective descent morphisms in a quasivariety of universal algebras are the same as regular epimorphisms and examples for which they are the same as regular epimorphisms satisfying projectivity.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	sufficient	sufficient	ADJ	JJ	Degree=Pos	4	amod	_	_
4	conditions	condition	NOUN	NNS	Number=Plur	2	dobj	_	_
5	under	under	ADP	IN	_	9	prep	_	_
6	which	which	PRON	WDT	_	5	pobj	_	_
7	effective	effective	ADJ	JJ	Degree=Pos	9	amod	_	_
8	descent	descent	NOUN	NN	Number=Sing	9	compound	_	_
9	morphisms	morphism	NOUN	NNS	Number=Plur	4	relcl	_	_
10	in	in	ADP	IN	_	2	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	quasivariety	quasivariety	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	universal	universal	ADJ	JJ	Degree=Pos	15	amod	_	_
15	algebras	algebra	NOUN	NNS	Number=Plur	13	pobj	_	_
16	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	conj	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	same	same	ADJ	JJ	Degree=Pos	16	attr	_	_
19	as	as	ADP	IN	_	18	prep	_	_
20	regular	regular	ADJ	JJ	Degree=Pos	21	amod	_	_
21	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	19	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	examples	example	NOUN	NNS	Number=Plur	21	conj	_	_
24	for	for	ADP	IN	_	27	prep	_	_
25	which	which	PRON	WDT	_	24	pobj	_	_
26	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	27	nsubj	_	_
27	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	21	relcl	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	same	same	ADJ	JJ	Degree=Pos	27	attr	_	_
30	as	as	ADP	IN	_	29	prep	_	_
31	regular	regular	ADJ	JJ	Degree=Pos	32	amod	_	_
32	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	33	nsubj	_	_
33	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	30	pcomp	_	_
34	projectivity	projectivity	NOUN	NN	Number=Sing	33	dobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 313
# sent_id = 1
# text = Recent investigations of lax algebras—in generalization of Barr's relational algebras—make an essential use of lax extensions of monad functors on $ Set $ to the category $ Rel(V) $ of sets and $ V $ - relations (where $ V $ is a unital quantale).
1	Recent	recent	ADJ	JJ	Degree=Pos	2	amod	_	_
2	investigations	investigation	NOUN	NNS	Number=Plur	15	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	lax	lax	PROPN	NNP	Number=Sing	5	amod	_	_
5	algebras	algebra	NOUN	NNS	Number=Plur	3	pobj	_	SpaceAfter=No
6	—	—	PUNCT	:	_	2	punct	_	SpaceAfter=No
7	in	in	ADP	IN	_	2	prep	_	_
8	generalization	generalization	NOUN	NN	Number=Sing	7	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Barr	Barr	PROPN	NNP	Number=Sing	13	poss	_	SpaceAfter=No
11	's	's	PART	POS	_	10	case	_	_
12	relational	relational	ADJ	JJ	Degree=Pos	13	amod	_	_
13	algebras	algebra	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
14	—	—	PUNCT	:	_	2	punct	_	SpaceAfter=No
15	make	make	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	an	an	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	essential	essential	ADJ	JJ	Degree=Pos	18	amod	_	_
18	use	use	NOUN	NN	Number=Sing	15	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	lax	lax	ADJ	JJ	Degree=Pos	21	amod	_	_
21	extensions	extension	NOUN	NNS	Number=Plur	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	monad	monad	NOUN	NNS	Number=Plur	24	compound	_	_
24	functors	functor	NOUN	NNS	Number=Plur	22	pobj	_	_
25	on	on	ADP	IN	_	24	prep	_	_
26	$ Set $	$ set $	SYM	$	_	25	pobj	_	_
27	to	to	ADP	IN	_	15	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	category	category	NOUN	NN	Number=Sing	27	pobj	_	_
30	$ Rel(V) $	$ rel(v) $	SYM	$	_	29	appos	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	sets	set	NOUN	NNS	Number=Plur	31	pobj	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
34	$ V $	$ v $	SYM	$	_	36	compound	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	36	punct	_	_
36	relations	relation	NOUN	NNS	Number=Plur	30	conj	_	_
37	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	40	punct	_	SpaceAfter=No
38	where	where	SCONJ	WRB	_	39	advmod	_	_
39	$ V $	$ v $	SYM	$	_	40	nsubj	_	_
40	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	ccomp	_	_
41	a	a	DET	DT	Definite=Ind|PronType=Art	43	det	_	_
42	unital	unital	ADJ	JJ	Degree=Pos	43	amod	_	_
43	quantale	quantale	NOUN	NN	Number=Sing	40	attr	_	SpaceAfter=No
44	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	40	punct	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 2
# text = For a given monad there may be many such lax extensions, and different constructions appear in the literature.
1	For	for	ADP	IN	_	7	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	amod	_	_
4	monad	monad	NOUN	NNS	Number=Plur	1	pobj	_	_
5	there	there	PRON	EX	_	7	expl	_	_
6	may	may	AUX	MD	VerbForm=Fin	7	aux	_	_
7	be	be	AUX	VB	VerbForm=Inf	0	ROOT	_	_
8	many	many	ADJ	JJ	Degree=Pos	11	amod	_	_
9	such	such	ADJ	JJ	Degree=Pos	11	amod	_	_
10	lax	lax	ADJ	JJ	Degree=Pos	11	amod	_	_
11	extensions	extension	NOUN	NNS	Number=Plur	7	attr	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
14	different	different	ADJ	JJ	Degree=Pos	15	amod	_	_
15	constructions	construction	NOUN	NNS	Number=Plur	16	nsubj	_	_
16	appear	appear	VERB	VBP	Tense=Pres|VerbForm=Fin	7	conj	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	literature	literature	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 3
# text = The aim of this article is to shed a unifying light on these lax extensions, and present a symptomatic situation in which distinct monads yield isomorphic categories of lax algebras.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	aim	aim	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	article	article	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	shed	shed	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	unifying	unifying	ADJ	JJ	Degree=Pos	11	amod	_	_
11	light	light	NOUN	NN	Number=Sing	8	dobj	_	_
12	on	on	ADP	IN	_	8	prep	_	_
13	these	these	DET	DT	Number=Plur|PronType=Dem	15	det	_	_
14	lax	lax	ADJ	JJ	Degree=Pos	15	amod	_	_
15	extensions	extension	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
18	present	present	VERB	VB	VerbForm=Inf	8	conj	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	symptomatic	symptomatic	ADJ	JJ	Degree=Pos	21	amod	_	_
21	situation	situation	NOUN	NN	Number=Sing	18	dobj	_	_
22	in	in	ADP	IN	_	26	prep	_	_
23	which	which	PRON	WDT	_	22	pobj	_	_
24	distinct	distinct	ADJ	JJ	Degree=Pos	25	amod	_	_
25	monads	monad	NOUN	NNS	Number=Plur	26	nsubj	_	_
26	yield	yield	VERB	VBP	Tense=Pres|VerbForm=Fin	21	relcl	_	_
27	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	28	amod	_	_
28	categories	category	NOUN	NNS	Number=Plur	26	dobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	lax	lax	ADJ	JJ	Degree=Pos	31	amod	_	_
31	algebras	algebra	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 314
# sent_id = 1
# text = We propose a convenient category for directed homotopy consisting of "directed'' topological spaces generated by "directed'' cubes.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	propose	propose	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	convenient	convenient	ADJ	JJ	Degree=Pos	5	amod	_	_
5	category	category	NOUN	NN	Number=Sing	2	dobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
8	homotopy	homotopy	NOUN	NN	Number=Sing	6	pobj	_	_
9	consisting	consist	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	acl	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	15	punct	_	SpaceAfter=No
12	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	SpaceAfter=No
13	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	15	punct	_	_
14	topological	topological	ADJ	JJ	Degree=Pos	15	amod	_	_
15	spaces	space	NOUN	NNS	Number=Plur	10	pobj	_	_
16	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
17	by	by	ADP	IN	_	16	agent	_	_
18	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	21	punct	_	SpaceAfter=No
19	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	amod	_	SpaceAfter=No
20	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	21	punct	_	_
21	cubes	cube	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Its main advantage is that, like the category of topological spaces generated by simplices suggested by Smith, it is locally presentable.
1	Its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	3	poss	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	advantage	advantage	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	21	mark	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
7	like	like	ADP	IN	_	21	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	topological	topological	ADJ	JJ	Degree=Pos	12	amod	_	_
12	spaces	space	NOUN	NNS	Number=Plur	10	pobj	_	_
13	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
14	by	by	ADP	IN	_	13	agent	_	_
15	simplices	simplice	NOUN	NNS	Number=Plur	14	pobj	_	_
16	suggested	suggest	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
17	by	by	ADP	IN	_	16	agent	_	_
18	Smith	Smith	PROPN	NNP	Number=Sing	17	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
20	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	21	nsubj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
22	locally	locally	ADV	RB	_	23	advmod	_	_
23	presentable	presentable	ADJ	JJ	Degree=Pos	21	acomp	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 315
# sent_id = 1
# text = We introduce a notion of weakly Maltsev category, and show that: (i) every internal reflexive graph in a weakly Maltsev category admits at most one multiplicative graph structure in the sense of Janelidze, and such a structure always makes it an internal category; (ii) (unlike the special case of Maltsev categories) there are weakly Maltsev categories in which not every internal category is an internal groupoid.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	weakly	weakly	ADJ	JJ	Degree=Pos	8	amod	_	_
7	Maltsev	Maltsev	PROPN	NNP	Number=Sing	8	compound	_	_
8	category	category	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
11	show	show	VERB	VB	VerbForm=Inf	2	conj	_	_
12	that	that	SCONJ	IN	_	26	mark	_	SpaceAfter=No
13	:	:	PUNCT	:	_	26	punct	_	_
14	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	15	punct	_	SpaceAfter=No
15	i	i	NOUN	NN	Number=Sing	26	dep	_	SpaceAfter=No
16	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	15	punct	_	_
17	every	every	DET	DT	_	20	det	_	_
18	internal	internal	ADJ	JJ	Degree=Pos	20	amod	_	_
19	reflexive	reflexive	ADJ	JJ	Degree=Pos	20	amod	_	_
20	graph	graph	NOUN	NN	Number=Sing	26	nsubj	_	_
21	in	in	ADP	IN	_	20	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
23	weakly	weakly	ADJ	JJ	Degree=Pos	25	amod	_	_
24	Maltsev	Maltsev	PROPN	NNP	Number=Sing	25	compound	_	_
25	category	category	NOUN	NN	Number=Sing	21	pobj	_	_
26	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	ccomp	_	_
27	at	at	ADP	IN	_	26	prep	_	_
28	most	most	ADV	RBS	Degree=Sup	29	advmod	_	_
29	one	one	NUM	CD	NumType=Card	32	nummod	_	_
30	multiplicative	multiplicative	ADJ	JJ	Degree=Pos	32	amod	_	_
31	graph	graph	NOUN	NN	Number=Sing	32	compound	_	_
32	structure	structure	NOUN	NN	Number=Sing	27	pobj	_	_
33	in	in	ADP	IN	_	26	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	sense	sense	NOUN	NN	Number=Sing	33	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	Janelidze	Janelidze	PROPN	NNP	Number=Sing	36	pobj	_	SpaceAfter=No
38	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
39	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
40	such	such	DET	PDT	_	42	predet	_	_
41	a	a	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
42	structure	structure	NOUN	NN	Number=Sing	44	nsubj	_	_
43	always	always	ADV	RB	_	44	advmod	_	_
44	makes	make	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	conj	_	_
45	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	48	nsubj	_	_
46	an	an	DET	DT	Definite=Ind|PronType=Art	48	det	_	_
47	internal	internal	ADJ	JJ	Degree=Pos	48	amod	_	_
48	category	category	NOUN	NN	Number=Sing	44	ccomp	_	SpaceAfter=No
49	;	;	PUNCT	:	_	26	punct	_	_
50	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	51	punct	_	SpaceAfter=No
51	ii	ii	PROPN	NNP	Number=Sing	20	appos	_	SpaceAfter=No
52	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	51	punct	_	_
53	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	63	punct	_	SpaceAfter=No
54	unlike	unlike	ADP	IN	_	63	prep	_	_
55	the	the	DET	DT	Definite=Def|PronType=Art	57	det	_	_
56	special	special	ADJ	JJ	Degree=Pos	57	amod	_	_
57	case	case	NOUN	NN	Number=Sing	54	pobj	_	_
58	of	of	ADP	IN	_	57	prep	_	_
59	Maltsev	Maltsev	PROPN	NNP	Number=Sing	60	amod	_	_
60	categories	category	NOUN	NNS	Number=Plur	58	pobj	_	SpaceAfter=No
61	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	63	punct	_	_
62	there	there	PRON	EX	_	63	expl	_	_
63	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	11	ccomp	_	_
64	weakly	weakly	ADJ	JJ	Degree=Pos	66	amod	_	_
65	Maltsev	maltsev	ADJ	JJ	Degree=Pos	66	amod	_	_
66	categories	category	NOUN	NNS	Number=Plur	63	attr	_	_
67	in	in	ADP	IN	_	73	prep	_	_
68	which	which	PRON	WDT	_	67	pobj	_	_
69	not	not	PART	RB	Polarity=Neg	70	neg	_	_
70	every	every	DET	DT	_	72	det	_	_
71	internal	internal	ADJ	JJ	Degree=Pos	72	amod	_	_
72	category	category	NOUN	NN	Number=Sing	73	nsubj	_	_
73	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	66	relcl	_	_
74	an	an	DET	DT	Definite=Ind|PronType=Art	76	det	_	_
75	internal	internal	ADJ	JJ	Degree=Pos	76	amod	_	_
76	groupoid	groupoid	NOUN	NN	Number=Sing	73	attr	_	SpaceAfter=No
77	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We also give a simplified characterization of internal groupoids among internal categories in this context.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	simplified	simplified	ADJ	JJ	Degree=Pos	6	amod	_	_
6	characterization	characterization	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	internal	internal	ADJ	JJ	Degree=Pos	9	amod	_	_
9	groupoids	groupoid	NOUN	NNS	Number=Plur	7	pobj	_	_
10	among	among	ADP	IN	_	6	prep	_	_
11	internal	internal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
13	in	in	ADP	IN	_	6	prep	_	_
14	this	this	DET	DT	Number=Sing|PronType=Dem	15	det	_	_
15	context	context	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 316
# sent_id = 1
# text = The theory of completion of $ T_0 $ objects in categories of affine objects over a given complete category developed by the second author is extended to the case of $ T_0 $ objects in categories of 2affine objects.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	theory	theory	NOUN	NN	Number=Sing	24	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	completion	completion	NOUN	NN	Number=Sing	3	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	$ T_0 $	$ t_0 $	SYM	$	_	7	nummod	_	_
7	objects	object	NOUN	NNS	Number=Plur	5	pobj	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	affine	affine	NOUN	NN	Number=Sing	12	compound	_	_
12	objects	object	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	pobj	_	_
13	over	over	ADP	IN	_	2	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
16	complete	complete	ADJ	JJ	Degree=Pos	17	amod	_	_
17	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
18	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
19	by	by	ADP	IN	_	18	agent	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	second	second	ADJ	JJ	Degree=Pos	22	amod	_	_
22	author	author	NOUN	NN	Number=Sing	19	pobj	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	auxpass	_	_
24	extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
25	to	to	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	case	case	NOUN	NN	Number=Sing	25	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	$ T_0 $	$ t_0 $	SYM	$	_	30	nummod	_	_
30	objects	object	NOUN	NNS	Number=Plur	28	pobj	_	_
31	in	in	ADP	IN	_	30	prep	_	_
32	categories	category	NOUN	NNS	Number=Plur	31	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	2affine	2affine	NUM	CD	NumType=Card	35	nummod	_	_
35	objects	object	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# sent_id = 2
# text = In the paper the case of the category $ Set $ and target object the two - point set is studied in detail and an internal characterization of 2affine sets is provided.
1	In	in	ADP	IN	_	12	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	case	case	NOUN	NN	Number=Sing	12	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
9	$ Set $	$ set $	SYM	$	_	8	nummod	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
11	target	target	VERB	VB	VerbForm=Inf	12	nsubj	_	_
12	object	object	VERB	VB	VerbForm=Inf	0	ROOT	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
14	two	two	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	point	point	NOUN	NN	Number=Sing	17	compound	_	_
17	set	set	NOUN	NN	Number=Sing	19	nsubjpass	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	auxpass	_	_
19	studied	study	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	ccomp	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	detail	detail	NOUN	NN	Number=Sing	20	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
23	an	an	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	internal	internal	ADJ	JJ	Degree=Pos	25	amod	_	_
25	characterization	characterization	NOUN	NN	Number=Sing	30	nsubjpass	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	2affine	2affine	NUM	CD	NumType=Card	28	nummod	_	_
28	sets	set	NOUN	NNS	Number=Plur	26	pobj	_	_
29	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	auxpass	_	_
30	provided	provide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	conj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# doc_id = 317
# sent_id = 1
# text = In a recent paper, Daisuke Tambara defined two - sided actions on an endomodule (that is, endodistributor) of a monoidal $ V $ - category $ A $ .
1	In	in	ADP	IN	_	8	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	recent	recent	ADJ	JJ	Degree=Pos	4	amod	_	_
4	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
6	Daisuke	Daisuke	PROPN	NNP	Number=Sing	7	compound	_	_
7	Tambara	Tambara	PROPN	NNP	Number=Sing	8	nsubj	_	_
8	defined	define	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
9	two	two	NUM	CD	NumType=Card	12	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	sided	sided	ADJ	JJ	Degree=Pos	12	amod	_	_
12	actions	action	NOUN	NNS	Number=Plur	8	dobj	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	endomodule	endomodule	NOUN	NN	Number=Sing	13	pobj	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	20	punct	_	SpaceAfter=No
17	that	that	ADV	RB	_	18	nsubj	_	_
18	is	is	ADV	RB	_	20	advmod	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
20	endodistributor	endodistributor	NOUN	NN	Number=Sing	15	appos	_	SpaceAfter=No
21	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	20	punct	_	_
22	of	of	ADP	IN	_	20	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
24	monoidal	monoidal	ADJ	JJ	Degree=Pos	27	amod	_	_
25	$ V $	$ v $	SYM	$	_	27	nummod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	category	category	NOUN	NN	Number=Sing	28	compound	_	_
28	$ A $	$ a $	SYM	$	_	22	pobj	_	_
29	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = When $ A $ is autonomous (that is, rigid, or compact), he showed that the $ V $ - category (that we call $ Tamb(A) $ ) of so - equipped endomodules (that we call Tambara modules) is equivalent to the monoidal centre $ Z[A, V] $ of the convolution monoidal $ V $ - category $ [A, V] $ .
1	When	when	SCONJ	WRB	_	3	advmod	_	_
2	$ A $	$ a $	SYM	$	_	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	advcl	_	_
4	autonomous	autonomous	ADJ	JJ	Degree=Pos	3	acomp	_	_
5	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	7	punct	_	SpaceAfter=No
6	that	that	ADV	RB	_	7	nsubj	_	_
7	is	is	ADV	RB	_	4	parataxis	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	rigid	rigid	ADJ	JJ	Degree=Pos	7	acomp	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	or	or	CCONJ	CC	ConjType=Cmp	9	cc	_	_
12	compact	compact	ADJ	JJ	Degree=Pos	9	conj	_	SpaceAfter=No
13	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	3	punct	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
15	he	he	PRON	PRP	Case=Nom|Gender=Masc|Number=Sing|Person=3|PronType=Prs	16	nsubj	_	_
16	showed	show	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
17	that	that	SCONJ	IN	_	40	mark	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
19	$ V $	$ v $	SYM	$	_	21	nmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	category	category	NOUN	NN	Number=Sing	40	nsubj	_	_
22	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	25	punct	_	SpaceAfter=No
23	that	that	SCONJ	IN	_	25	mark	_	_
24	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	25	nsubj	_	_
25	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	21	parataxis	_	_
26	$ Tamb(A) $	$ tamb(a) $	SYM	$	_	25	oprd	_	_
27	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	26	punct	_	_
28	of	of	ADP	IN	_	26	prep	_	_
29	so	so	ADV	RB	_	31	advmod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	amod	_	_
32	endomodules	endomodule	NOUN	NNS	Number=Plur	28	pobj	_	_
33	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	36	punct	_	SpaceAfter=No
34	that	that	SCONJ	IN	_	36	mark	_	_
35	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	36	nsubj	_	_
36	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	21	parataxis	_	_
37	Tambara	Tambara	PROPN	NNP	Number=Sing	38	compound	_	_
38	modules	module	NOUN	NNS	Number=Plur	36	dobj	_	SpaceAfter=No
39	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	21	punct	_	_
40	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	ccomp	_	_
41	equivalent	equivalent	ADJ	JJ	Degree=Pos	40	acomp	_	_
42	to	to	ADP	IN	_	41	prep	_	_
43	the	the	DET	DT	Definite=Def|PronType=Art	45	det	_	_
44	monoidal	monoidal	ADJ	JJ	Degree=Pos	45	amod	_	_
45	centre	centre	NOUN	NN	Number=Sing	42	pobj	_	_
46	$ Z[A, V] $	$ z[a, v] $	SYM	$	_	45	appos	_	_
47	of	of	ADP	IN	_	46	prep	_	_
48	the	the	DET	DT	Definite=Def|PronType=Art	49	det	_	_
49	convolution	convolution	NOUN	NN	Number=Sing	47	pobj	_	_
50	monoidal	monoidal	NOUN	NN	Number=Sing	40	acomp	_	_
51	$ V $	$ v $	SYM	$	_	53	nummod	_	_
52	-	-	PUNCT	HYPH	PunctType=Dash	53	punct	_	_
53	category	category	NOUN	NN	Number=Sing	50	npadvmod	_	_
54	$ [A, V] $	$ [a, v] $	SYM	$	_	40	npadvmod	_	_
55	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 3
# text = Our paper extends these ideas somewhat.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	these	these	DET	DT	Number=Plur|PronType=Dem	5	det	_	_
5	ideas	idea	NOUN	NNS	Number=Plur	3	dobj	_	_
6	somewhat	somewhat	ADV	RB	_	3	advmod	_	SpaceAfter=No
7	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = For general $ A $ , we construct a promonoidal $ V $ - category $ DA $ (which we suggest should be called the double of $ A $ ) with an equivalence of $ [DA, V] $ with $ Tamb(A) $ .
1	For	for	ADP	IN	_	6	prep	_	_
2	general	general	ADJ	JJ	Degree=Pos	3	amod	_	_
3	$ A $	$ a $	SYM	$	_	1	pobj	_	_
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
8	promonoidal	promonoidal	ADJ	JJ	Degree=Pos	12	amod	_	_
9	$ V $	$ v $	SYM	$	_	11	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	category	category	NOUN	NN	Number=Sing	12	compound	_	_
12	$ DA $	$ da $	SYM	$	_	6	dobj	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
14	which	which	PRON	WDT	_	19	nsubj	_	_
15	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	16	nsubj	_	_
16	suggest	suggest	VERB	VBP	Tense=Pres|VerbForm=Fin	12	relcl	_	_
17	should	should	AUX	MD	VerbForm=Fin	19	aux	_	_
18	be	be	AUX	VB	VerbForm=Inf	19	auxpass	_	_
19	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	ccomp	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	double	double	ADJ	JJ	Degree=Pos	19	oprd	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	$ A $	$ a $	SYM	$	_	22	pobj	_	_
24	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	19	punct	_	_
25	with	with	ADP	IN	_	19	prep	_	_
26	an	an	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	equivalence	equivalence	NOUN	NN	Number=Sing	25	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	$ [DA, V] $	$ [da, v] $	SYM	$	_	28	pobj	_	_
30	with	with	ADP	IN	_	27	prep	_	_
31	$ Tamb(A) $	$ tamb(a) $	SYM	$	_	30	pobj	_	_
32	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = When $ A $ is closed, we define strong (respectively, left strong)
1	When	when	SCONJ	WRB	_	3	advmod	_	_
2	$ A $	$ a $	SYM	$	_	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	advcl	_	_
4	closed	closed	ADJ	JJ	Degree=Pos	3	acomp	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	strong	strong	ADJ	JJ	Degree=Pos	7	advmod	_	_
9	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
10	respectively	respectively	ADV	RB	_	12	advmod	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
12	left	leave	VERB	VBD	Tense=Past|VerbForm=Fin	7	ccomp	_	_
13	strong	strong	ADJ	JJ	Degree=Pos	12	oprd	_	SpaceAfter=No
14	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	12	punct	_	SpaceAfter=No

# sent_id = 6
# text = Tambara modules and show that these constitute a $ V $ - category $ Tamb_s(A) $ (respectively, $ Tamb_{ls}(A) $ ) which is equivalent to the centre (respectively, lax centre) of $ [A, V] $ .
1	Tambara	Tambara	PROPN	NNP	Number=Sing	2	compound	_	_
2	modules	module	NOUN	NNS	Number=Plur	0	ROOT	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
5	that	that	SCONJ	IN	_	7	mark	_	_
6	these	these	PRON	DT	Number=Plur|PronType=Dem	7	nsubj	_	_
7	constitute	constitute	VERB	VBP	Tense=Pres|VerbForm=Fin	4	ccomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
9	$ V $	$ v $	SYM	$	_	11	nmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	category	category	NOUN	NN	Number=Sing	8	nmod	_	_
12	$ Tamb_s(A) $	$ tamb_s(a) $	SYM	$	_	7	dobj	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
14	respectively	respectively	ADV	RB	_	12	advmod	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	$ Tamb_{ls}(A) $	$ tamb_{ls}(a) $	SYM	$	_	12	appos	_	_
17	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	12	punct	_	_
18	which	which	PRON	WDT	_	19	nsubj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	relcl	_	_
20	equivalent	equivalent	ADJ	JJ	Degree=Pos	19	acomp	_	_
21	to	to	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	centre	centre	NOUN	NN	Number=Sing	21	pobj	_	_
24	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	23	punct	_	SpaceAfter=No
25	respectively	respectively	ADV	RB	_	28	advmod	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
27	lax	lax	ADJ	JJ	Degree=Pos	28	amod	_	_
28	centre	centre	NOUN	NN	Number=Sing	23	appos	_	SpaceAfter=No
29	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	23	punct	_	_
30	of	of	ADP	IN	_	23	prep	_	_
31	$ [A, V] $	$ [a, v] $	SYM	$	_	30	pobj	_	_
32	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = We construct localizations $ D_sA $ and $ D_{ls}A $ of $ DA $ such that there are equivalences of $ Tamb_s(A) $ with $ [D_sA, V] $ and of $ Tamb_{ls}(A) $ with $ [D_{ls}A, V] $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	localizations	localization	NOUN	NNS	Number=Plur	2	dobj	_	_
4	$ D_sA $	$ d_sa $	SYM	$	_	2	npadvmod	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	$ D_{ls}A $	$ d_{ls}a $	SYM	$	_	9	nmod	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	$ DA $	$ da $	SYM	$	_	7	pobj	_	_
9	such	such	ADJ	JJ	Degree=Pos	4	conj	_	_
10	that	that	SCONJ	IN	_	12	mark	_	_
11	there	there	PRON	EX	_	12	expl	_	_
12	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
13	equivalences	equivalence	NOUN	NNS	Number=Plur	12	attr	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	$ Tamb_s(A) $	$ tamb_s(a) $	SYM	$	_	14	pobj	_	_
16	with	with	ADP	IN	_	13	prep	_	_
17	$ [D_sA, V] $	$ [d_sa, v] $	SYM	$	_	16	pobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	of	of	ADP	IN	_	17	conj	_	_
20	$ Tamb_{ls}(A) $	$ tamb_{ls}(a) $	SYM	$	_	19	pobj	_	_
21	with	with	ADP	IN	_	13	prep	_	_
22	$ [D_{ls}A, V] $	$ [d_{ls}a, v] $	SYM	$	_	21	pobj	_	_
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 8
# text = When $ A $ is autonomous, every Tambara module is strong; this implies an equivalence of $ Z[A, V] $ with $ [DA, V] $ .
1	When	when	SCONJ	WRB	_	3	advmod	_	_
2	$ A $	$ a $	SYM	$	_	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	advcl	_	_
4	autonomous	autonomous	ADJ	JJ	Degree=Pos	3	acomp	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
6	every	every	DET	DT	_	8	det	_	_
7	Tambara	Tambara	PROPN	NNP	Number=Sing	8	compound	_	_
8	module	module	NOUN	NN	Number=Sing	9	nsubj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
10	strong	strong	ADJ	JJ	Degree=Pos	9	acomp	_	SpaceAfter=No
11	;	;	PUNCT	:	_	13	punct	_	_
12	this	this	PRON	DT	Number=Sing|PronType=Dem	13	nsubj	_	_
13	implies	imply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	equivalence	equivalence	NOUN	NN	Number=Sing	13	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	$ Z[A, V] $	$ z[a, v] $	SYM	$	_	16	pobj	_	_
18	with	with	ADP	IN	_	15	prep	_	_
19	$ [DA, V] $	$ [da, v] $	SYM	$	_	18	pobj	_	_
20	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# doc_id = 318
# sent_id = 1
# text = We prove that every small strongly connected category $ k $ has a full embedding preserving all limits existing in $ k $ into a category of unary universal algebras.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	10	mark	_	_
4	every	every	DET	DT	_	8	det	_	_
5	small	small	ADJ	JJ	Degree=Pos	8	amod	_	_
6	strongly	strongly	ADV	RB	_	7	advmod	_	_
7	connected	connected	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	10	nsubj	_	_
9	$ k $	$ k $	SYM	$	_	8	appos	_	_
10	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	full	full	ADJ	JJ	Degree=Pos	13	amod	_	_
13	embedding	embedding	NOUN	NN	Number=Sing	10	dobj	_	_
14	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	acl	_	_
15	all	all	DET	DT	_	16	det	_	_
16	limits	limit	NOUN	NNS	Number=Plur	14	dobj	_	_
17	existing	exist	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	acl	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	$ k $	$ k $	SYM	$	_	18	pobj	_	_
20	into	into	ADP	IN	_	17	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	category	category	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	unary	unary	ADJ	JJ	Degree=Pos	26	amod	_	_
25	universal	universal	ADJ	JJ	Degree=Pos	26	amod	_	_
26	algebras	algebras	PROPN	NNP	Number=Sing	23	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The number of unary operations can be restricted to $ |mor k| $ in case when $ k $ has a terminal object and only preservation of limits over finitely many objects is desired.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	number	number	NOUN	NN	Number=Sing	8	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	unary	unary	ADJ	JJ	Degree=Pos	5	amod	_	_
5	operations	operation	NOUN	NNS	Number=Plur	3	pobj	_	_
6	can	can	AUX	MD	VerbForm=Fin	8	aux	_	_
7	be	be	AUX	VB	VerbForm=Inf	8	auxpass	_	_
8	restricted	restrict	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	$ |mor k| $	$ |mor k| $	SYM	$	_	9	pobj	_	_
11	in	in	ADP	IN	_	8	prep	_	_
12	case	case	NOUN	NN	Number=Sing	11	pobj	_	_
13	when	when	SCONJ	WRB	_	15	advmod	_	_
14	$ k $	$ k $	SYM	$	_	15	nsubj	_	_
15	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	advcl	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	terminal	terminal	ADJ	JJ	Degree=Pos	18	amod	_	_
18	object	object	NOUN	NN	Number=Sing	15	dobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	only	only	ADV	RB	_	21	advmod	_	_
21	preservation	preservation	NOUN	NN	Number=Sing	29	nsubjpass	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	limits	limit	NOUN	NNS	Number=Plur	22	pobj	_	_
24	over	over	ADP	IN	_	23	prep	_	_
25	finitely	finitely	ADV	RB	_	26	advmod	_	_
26	many	many	ADJ	JJ	Degree=Pos	27	amod	_	_
27	objects	object	NOUN	NNS	Number=Plur	24	pobj	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	auxpass	_	_
29	desired	desire	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	conj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 3
# text = And all limits existing in such a category k are preserved by a full embedding of $ k $ into the category of all algebraic systems with $ |mor k| $ unary operation and one unary relation.
1	And	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
2	all	all	DET	DT	_	3	det	_	_
3	limits	limit	NOUN	NNS	Number=Plur	11	nsubjpass	_	_
4	existing	exist	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	acl	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	such	such	DET	PDT	_	8	predet	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
9	k	k	NOUN	NN	Number=Sing	3	punct	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	preserved	preserve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
12	by	by	ADP	IN	_	11	agent	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	full	full	ADJ	JJ	Degree=Pos	15	amod	_	_
15	embedding	embedding	NOUN	NN	Number=Sing	12	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	$ k $	$ k $	SYM	$	_	16	pobj	_	_
18	into	into	ADP	IN	_	15	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	all	all	DET	DT	_	24	det	_	_
23	algebraic	algebraic	ADJ	JJ	Degree=Pos	24	amod	_	_
24	systems	system	NOUN	NNS	Number=Plur	21	pobj	_	_
25	with	with	ADP	IN	_	24	prep	_	_
26	$ |mor k| $	$ |mor k| $	SYM	$	_	27	nmod	_	_
27	unary	unary	ADJ	JJ	Degree=Pos	28	amod	_	_
28	operation	operation	NOUN	NN	Number=Sing	25	pobj	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	one	one	NUM	CD	NumType=Card	32	nummod	_	_
31	unary	unary	ADJ	JJ	Degree=Pos	32	amod	_	_
32	relation	relation	NOUN	NN	Number=Sing	28	conj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# doc_id = 319
# sent_id = 1
# text = A protolocalisation of a regular category is a full reflective regular subcategory, whose reflection preserves pullbacks of regular epimorphisms along arbitrary morphisms.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	protolocalisation	protolocalisation	NOUN	NN	Number=Sing	7	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	regular	regular	ADJ	JJ	Degree=Pos	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	3	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
9	full	full	ADJ	JJ	Degree=Pos	12	amod	_	_
10	reflective	reflective	ADJ	JJ	Degree=Pos	12	amod	_	_
11	regular	regular	ADJ	JJ	Degree=Pos	12	amod	_	_
12	subcategory	subcategory	NOUN	NN	Number=Sing	7	attr	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	whose	whose	DET	WP$	Poss=Yes	15	poss	_	_
15	reflection	reflection	NOUN	NN	Number=Sing	16	nsubj	_	_
16	preserves	preserve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	relcl	_	_
17	pullbacks	pullback	NOUN	NNS	Number=Plur	16	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	regular	regular	ADJ	JJ	Degree=Pos	20	amod	_	_
20	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	18	pobj	_	_
21	along	along	ADP	IN	_	20	prep	_	_
22	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	23	amod	_	_
23	morphisms	morphism	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 2
# text = We devote special attention to the epireflective protolocalisations of an exact Maltsev category; we characterise them in terms of a corresponding closure operator on equivalence relations.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	devote	devote	VERB	VBP	Tense=Pres|VerbForm=Fin	16	ccomp	_	_
3	special	special	ADJ	JJ	Degree=Pos	4	amod	_	_
4	attention	attention	NOUN	NN	Number=Sing	2	dobj	_	_
5	to	to	ADP	IN	_	2	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	epireflective	epireflective	ADJ	JJ	Degree=Pos	8	amod	_	_
8	protolocalisations	protolocalisation	NOUN	NNS	Number=Plur	5	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	exact	exact	ADJ	JJ	Degree=Pos	13	amod	_	_
12	Maltsev	Maltsev	PROPN	NNP	Number=Sing	13	compound	_	_
13	category	category	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
14	;	;	PUNCT	:	_	16	punct	_	_
15	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	16	nsubj	_	_
16	characterise	characterise	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
17	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	16	dobj	_	_
18	in	in	ADP	IN	_	16	prep	_	_
19	terms	term	NOUN	NNS	Number=Plur	18	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
22	corresponding	corresponding	ADJ	JJ	Degree=Pos	24	amod	_	_
23	closure	closure	NOUN	NN	Number=Sing	24	compound	_	_
24	operator	operator	NOUN	NN	Number=Sing	20	pobj	_	_
25	on	on	ADP	IN	_	24	prep	_	_
26	equivalence	equivalence	NOUN	NN	Number=Sing	27	compound	_	_
27	relations	relation	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 3
# text = We give some examples in algebra and in topos theory.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	some	some	DET	DT	_	4	det	_	_
4	examples	example	NOUN	NNS	Number=Plur	2	dobj	_	_
5	in	in	ADP	IN	_	2	prep	_	_
6	algebra	algebra	NOUN	NN	Number=Sing	5	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
8	in	in	ADP	IN	_	5	conj	_	_
9	topos	topos	NOUN	NN	Number=Sing	10	compound	_	_
10	theory	theory	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 320
# sent_id = 1
# text = This paper revisits the authors' notion of a differential category from a different perspective.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	revisits	revisit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	authors	author	NOUN	NNS	Number=Plur	7	poss	_	SpaceAfter=No
6	'	'	PART	POS	_	5	case	_	_
7	notion	notion	NOUN	NN	Number=Sing	3	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	differential	differential	ADJ	JJ	Degree=Pos	11	amod	_	_
11	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
12	from	from	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	different	different	ADJ	JJ	Degree=Pos	15	amod	_	_
15	perspective	perspective	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = A differential category is an additive symmetric monoidal category with a comonad (a "coalgebra modality") and a differential combinator.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	differential	differential	ADJ	JJ	Degree=Pos	3	amod	_	_
3	category	category	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
6	additive	additive	ADJ	JJ	Degree=Pos	9	amod	_	_
7	symmetric	symmetric	ADJ	JJ	Degree=Pos	9	amod	_	_
8	monoidal	monoidal	ADJ	JJ	Degree=Pos	9	amod	_	_
9	category	category	NOUN	NN	Number=Sing	4	attr	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	comonad	comonad	NOUN	NNS	Number=Plur	10	pobj	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	17	punct	_	SpaceAfter=No
14	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	17	punct	_	SpaceAfter=No
16	coalgebra	coalgebra	NOUN	NNS	Number=Plur	17	compound	_	_
17	modality	modality	NOUN	NN	Number=Sing	12	appos	_	SpaceAfter=No
18	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	17	punct	_	SpaceAfter=No
19	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	17	punct	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	differential	differential	ADJ	JJ	Degree=Pos	23	amod	_	_
23	combinator	combinator	NOUN	NN	Number=Sing	12	conj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = The morphisms of a differential category should be thought of as the linear maps; the differentiable or smooth maps would then be morphisms of the coKleisli category.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	morphisms	morphism	NOUN	NNS	Number=Plur	9	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	differential	differential	ADJ	JJ	Degree=Pos	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	3	pobj	_	_
7	should	should	AUX	MD	VerbForm=Fin	9	aux	_	_
8	be	be	AUX	VB	VerbForm=Inf	9	auxpass	_	_
9	thought	think	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	ccomp	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	as	as	ADP	IN	_	9	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	linear	linear	PROPN	NNP	Number=Sing	14	compound	_	_
14	maps	map	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
15	;	;	PUNCT	:	_	23	punct	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
17	differentiable	differentiable	ADJ	JJ	Degree=Pos	20	amod	_	_
18	or	or	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	smooth	smooth	ADJ	JJ	Degree=Pos	17	conj	_	_
20	maps	map	NOUN	NNS	Number=Plur	23	nsubj	_	_
21	would	would	AUX	MD	VerbForm=Fin	23	aux	_	_
22	then	then	ADV	RB	PronType=Dem	23	advmod	_	_
23	be	be	AUX	VB	VerbForm=Inf	0	ROOT	_	_
24	morphisms	morphism	NOUN	NNS	Number=Plur	23	attr	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	coKleisli	cokleisli	ADJ	JJ	Degree=Pos	28	amod	_	_
28	category	category	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# sent_id = 4
# text = The purpose of the present paper is to directly axiomatize differentiable maps and thus to move the emphasis from the linear notion to structures resembling the coKleisli category.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	purpose	purpose	NOUN	NN	Number=Sing	7	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	present	present	ADJ	JJ	Degree=Pos	6	amod	_	_
6	paper	paper	NOUN	NN	Number=Sing	3	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	to	to	PART	TO	_	10	aux	_	_
9	directly	directly	ADV	RB	_	10	advmod	_	_
10	axiomatize	axiomatize	VERB	VB	VerbForm=Inf	7	xcomp	_	_
11	differentiable	differentiable	ADJ	JJ	Degree=Pos	12	amod	_	_
12	maps	map	NOUN	NNS	Number=Plur	10	dobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
14	thus	thus	ADV	RB	_	16	advmod	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	move	move	VERB	VB	VerbForm=Inf	10	conj	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	emphasis	emphasis	NOUN	NN	Number=Sing	16	dobj	_	_
19	from	from	ADP	IN	_	16	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	linear	linear	ADJ	JJ	Degree=Pos	22	compound	_	_
22	notion	notion	NOUN	NN	Number=Sing	19	pobj	_	_
23	to	to	ADP	IN	_	16	prep	_	_
24	structures	structure	NOUN	NNS	Number=Plur	23	pobj	_	_
25	resembling	resemble	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	24	acl	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	coKleisli	cokleisli	ADJ	JJ	Degree=Pos	28	amod	_	_
28	category	category	NOUN	NN	Number=Sing	25	dobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 5
# text = The result is a setting with a more evident and intuitive relationship to the familiar notion of calculus on smooth maps.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	result	result	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	setting	setting	NOUN	NN	Number=Sing	3	attr	_	_
6	with	with	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
8	more	more	ADV	RBR	Degree=Cmp	9	advmod	_	_
9	evident	evident	ADJ	JJ	Degree=Pos	12	amod	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	intuitive	intuitive	ADJ	JJ	Degree=Pos	9	conj	_	_
12	relationship	relationship	NOUN	NN	Number=Sing	6	pobj	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	familiar	familiar	ADJ	JJ	Degree=Pos	16	amod	_	_
16	notion	notion	NOUN	NN	Number=Sing	13	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	calculus	calculus	NOUN	NN	Number=Sing	17	pobj	_	_
19	on	on	ADP	IN	_	18	prep	_	_
20	smooth	smooth	ADJ	JJ	Degree=Pos	21	amod	_	_
21	maps	map	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = Indeed a primary example is the category whose objects are Euclidean spaces and whose morphisms are smooth maps.
1	Indeed	indeed	ADV	RB	_	5	advmod	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	primary	primary	ADJ	JJ	Degree=Pos	4	amod	_	_
4	example	example	NOUN	NN	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	category	category	NOUN	NN	Number=Sing	5	attr	_	_
8	whose	whose	DET	WP$	Poss=Yes	9	poss	_	_
9	objects	object	NOUN	NNS	Number=Plur	10	nsubj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	relcl	_	_
11	Euclidean	euclidean	ADJ	JJ	Degree=Pos	12	amod	_	_
12	spaces	space	NOUN	NNS	Number=Plur	10	attr	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	whose	whose	DET	WP$	Poss=Yes	15	poss	_	_
15	morphisms	morphism	NOUN	NNS	Number=Plur	16	nsubj	_	_
16	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	10	conj	_	_
17	smooth	smooth	ADJ	JJ	Degree=Pos	18	amod	_	_
18	maps	map	NOUN	NNS	Number=Plur	16	attr	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 7
# text = A Cartesian differential category is a Cartesian left additive category which possesses a Cartesian differential operator.
1	A	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
2	Cartesian	cartesian	ADJ	JJ	Degree=Pos	4	amod	_	_
3	differential	differential	ADJ	JJ	Degree=Pos	4	amod	_	_
4	category	category	NOUN	NN	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	Cartesian	Cartesian	PROPN	NNP	Number=Sing	8	nsubj	_	_
8	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	ccomp	_	_
9	additive	additive	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	8	dobj	_	_
11	which	which	PRON	WDT	_	12	nsubj	_	_
12	possesses	possess	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	relcl	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
14	Cartesian	cartesian	ADJ	JJ	Degree=Pos	16	amod	_	_
15	differential	differential	ADJ	JJ	Degree=Pos	16	amod	_	_
16	operator	operator	NOUN	NN	Number=Sing	12	dobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 8
# text = The differential operator itself must satisfy a number of equations, which guarantee, in particular, that the differential of any map is `"linear" in a suitable sense.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	differential	differential	ADJ	JJ	Degree=Pos	3	amod	_	_
3	operator	operator	NOUN	NN	Number=Sing	6	nsubj	_	_
4	itself	itself	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs|Reflex=Yes	3	appos	_	_
5	must	must	AUX	MD	VerbForm=Fin	6	aux	_	_
6	satisfy	satisfy	VERB	VB	VerbForm=Inf	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	number	number	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	equations	equation	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	which	which	PRON	WDT	_	13	nsubj	_	_
13	guarantee	guarantee	VERB	VBP	Tense=Pres|VerbForm=Fin	10	relcl	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	in	in	ADP	IN	_	13	prep	_	_
16	particular	particular	ADJ	JJ	Degree=Pos	15	amod	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
18	that	that	SCONJ	IN	_	24	mark	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	differential	differential	NOUN	NN	Number=Sing	24	nsubj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	any	any	DET	DT	_	23	det	_	_
23	map	map	NOUN	NN	Number=Sing	21	pobj	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	advcl	_	_
25	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	27	punct	_	SpaceAfter=No
26	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	27	punct	_	SpaceAfter=No
27	linear	linear	NOUN	NN	Number=Sing	24	attr	_	SpaceAfter=No
28	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	27	punct	_	_
29	in	in	ADP	IN	_	27	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
31	suitable	suitable	ADJ	JJ	Degree=Pos	32	amod	_	_
32	sense	sense	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 9
# text = We present an analysis of the basic properties of Cartesian differential categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	analysis	analysis	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	basic	basic	ADJ	JJ	Degree=Pos	8	amod	_	_
8	properties	property	NOUN	NNS	Number=Plur	5	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Cartesian	cartesian	ADJ	JJ	Degree=Pos	12	amod	_	_
11	differential	differential	ADJ	JJ	Degree=Pos	12	amod	_	_
12	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 10
# text = We show that under modest and natural assumptions, the coKleisli category of a differential category is Cartesian differential.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	17	mark	_	_
4	under	under	ADP	IN	_	17	prep	_	_
5	modest	modest	ADJ	JJ	Degree=Pos	8	amod	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	natural	natural	ADJ	JJ	Degree=Pos	5	conj	_	_
8	assumptions	assumption	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	coKleisli	cokleisli	ADJ	JJ	Degree=Pos	12	amod	_	_
12	category	category	NOUN	NN	Number=Sing	17	nsubj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	differential	differential	ADJ	JJ	Degree=Pos	16	amod	_	_
16	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
18	Cartesian	cartesian	ADJ	JJ	Degree=Pos	19	amod	_	_
19	differential	differential	NOUN	NN	Number=Sing	17	attr	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 11
# text = Finally we present a (sound and complete) term calculus for these categories which allows their structure to be analysed using essentially the same language one might use for traditional multi - variable calculus.
1	Finally	finally	ADV	RB	_	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
5	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	6	punct	_	SpaceAfter=No
6	sound	sound	NOUN	NN	Number=Sing	11	amod	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	complete	complete	ADJ	JJ	Degree=Pos	6	conj	_	SpaceAfter=No
9	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	11	punct	_	_
10	term	term	NOUN	NN	Number=Sing	11	compound	_	_
11	calculus	calculus	NOUN	NN	Number=Sing	3	dobj	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	these	these	DET	DT	Number=Plur|PronType=Dem	14	det	_	_
14	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	_
15	which	which	PRON	WDT	_	16	nsubj	_	_
16	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
17	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	18	poss	_	_
18	structure	structure	NOUN	NN	Number=Sing	21	nsubjpass	_	_
19	to	to	PART	TO	_	21	aux	_	_
20	be	be	AUX	VB	VerbForm=Inf	21	auxpass	_	_
21	analysed	analyse	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	ccomp	_	_
22	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	21	xcomp	_	_
23	essentially	essentially	ADV	RB	_	22	advmod	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	same	same	ADJ	JJ	Degree=Pos	26	amod	_	_
26	language	language	NOUN	NN	Number=Sing	22	dobj	_	_
27	one	one	PRON	PRP	PronType=Prs	29	nsubj	_	_
28	might	might	AUX	MD	VerbForm=Fin	29	aux	_	_
29	use	use	VERB	VB	VerbForm=Inf	26	relcl	_	_
30	for	for	ADP	IN	_	29	prep	_	_
31	traditional	traditional	ADJ	JJ	Degree=Pos	35	amod	_	_
32	multi	multi	ADJ	JJ	Degree=Pos	34	amod	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	variable	variable	ADJ	JJ	Degree=Pos	35	amod	_	_
35	calculus	calculus	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 321
# sent_id = 1
# text = Let $ M = (M, m, u) $ be a monad and let $ (MX, m) $ be the free $ M $ - algebra on the object $ X $ .
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ M = (M, m, u) $	$ m = (m, m, u) $	SYM	$	_	3	nsubj	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	monad	monad	NOUN	NNS	Number=Plur	3	attr	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
7	let	let	VERB	VB	VerbForm=Inf	3	conj	_	_
8	$ (MX, m) $	$ (mx, m) $	SYM	$	_	9	nsubj	_	_
9	be	be	AUX	VB	VerbForm=Inf	7	ccomp	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
11	free	free	ADJ	JJ	Degree=Pos	14	amod	_	_
12	$ M $	$ m $	SYM	$	_	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	algebra	algebra	NOUN	NN	Number=Sing	9	attr	_	_
15	on	on	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	object	object	NOUN	NN	Number=Sing	15	pobj	_	_
18	$ X $	$ x $	SYM	$	_	14	appos	_	_
19	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = Consider an $ M $ - algebra $ (A, a) $ , a retraction $ r : (MX, m) - - > (A, a) $ and a section $ t : (A, a) - - > (MX, m) $ of $ r $ .
1	Consider	consider	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
3	$ M $	$ m $	SYM	$	_	5	nmod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	algebra	algebra	NOUN	NN	Number=Sing	6	compound	_	_
6	$ (A, a) $	$ (a, a) $	NOUN	NN	Number=Sing	1	dobj	_	_
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	retraction	retraction	NOUN	NN	Number=Sing	6	appos	_	_
10	$ r : (MX, m) - - > (A, a) $	$ r : (mx, m) - - > (a, a) $	SYM	$	_	9	appos	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	section	section	NOUN	NN	Number=Sing	9	conj	_	_
14	$ t : (A, a) - - > (MX, m) $	$ t : (a, a) - - > (mx, m) $	SYM	$	_	13	appos	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	$ r $	$ r $	SYM	$	_	15	pobj	_	_
17	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 3
# text = The retract $ (A, a) $ is not free in general.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	retract	retract	NOUN	NN	Number=Sing	4	nsubj	_	_
3	$ (A, a) $	$ (a, a) $	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	not	not	PART	RB	Polarity=Neg	4	neg	_	_
6	free	free	ADJ	JJ	Degree=Pos	4	acomp	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	general	general	ADJ	JJ	Degree=Pos	7	amod	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = We observe that for many monads with a `combinatorial flavor' such a retract is not only a free algebra $ (MA_0, m) $ , but it is also the case that the object $ A_0 $ of generators is determined in a canonical way by the section $ t $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	observe	observe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	16	mark	_	_
4	for	for	ADP	IN	_	16	prep	_	_
5	many	many	ADJ	JJ	Degree=Pos	6	amod	_	_
6	monads	monad	NOUN	NNS	Number=Plur	4	pobj	_	_
7	with	with	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	11	punct	_	SpaceAfter=No
10	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	11	amod	_	_
11	flavor	flavor	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
12	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	11	punct	_	_
13	such	such	DET	PDT	_	15	predet	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	retract	retract	NOUN	NN	Number=Sing	11	appos	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
17	not	not	PART	RB	Polarity=Neg	16	neg	_	_
18	only	only	ADV	RB	_	17	advmod	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	free	free	ADJ	JJ	Degree=Pos	21	amod	_	_
21	algebra	algebra	NOUN	NN	Number=Sing	22	compound	_	_
22	$ (MA_0, m) $	$ (MA_0, m) $	PROPN	NNP	Number=Sing	16	attr	_	_
23	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
24	but	but	CCONJ	CC	ConjType=Cmp	16	cc	_	_
25	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	26	nsubj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	conj	_	_
27	also	also	ADV	RB	_	26	advmod	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	case	case	NOUN	NN	Number=Sing	26	attr	_	_
30	that	that	SCONJ	IN	_	37	mark	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	object	object	NOUN	NN	Number=Sing	37	nsubjpass	_	_
33	$ A_0 $	$ a_0 $	PRON	PRP$	Poss=Yes|PronType=Prs	32	appos	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	generators	generator	NOUN	NNS	Number=Plur	34	pobj	_	_
36	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	37	auxpass	_	_
37	determined	determine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	acl	_	_
38	in	in	ADP	IN	_	37	prep	_	_
39	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
40	canonical	canonical	ADJ	JJ	Degree=Pos	41	amod	_	_
41	way	way	NOUN	NN	Number=Sing	38	pobj	_	_
42	by	by	ADP	IN	_	37	agent	_	_
43	the	the	DET	DT	Definite=Def|PronType=Art	44	det	_	_
44	section	section	NOUN	NN	Number=Sing	42	pobj	_	_
45	$ t $	$ t $	SYM	$	_	44	appos	_	_
46	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = We give a precise form of this property, prove a characterization, and discuss examples from combinatorics, universal algebra, convexity and topos theory.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	precise	precise	ADJ	JJ	Degree=Pos	5	amod	_	_
5	form	form	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	this	this	DET	DT	Number=Sing|PronType=Dem	8	det	_	_
8	property	property	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
10	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	characterization	characterization	NOUN	NN	Number=Sing	10	dobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
15	discuss	discuss	VERB	VB	VerbForm=Inf	10	conj	_	_
16	examples	example	NOUN	NNS	Number=Plur	15	dobj	_	_
17	from	from	ADP	IN	_	15	prep	_	_
18	combinatorics	combinatoric	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	universal	universal	ADJ	JJ	Degree=Pos	21	amod	_	_
21	algebra	algebra	PROPN	NNP	Number=Sing	18	conj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	convexity	convexity	NOUN	NN	Number=Sing	21	conj	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	topos	topos	NOUN	NN	Number=Sing	26	compound	_	_
26	theory	theory	NOUN	NN	Number=Sing	23	conj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 322
# sent_id = 1
# text = Globular complexes were introduced by Goubault and the author to model higher dimensional automata.
1	Globular	globular	ADJ	JJ	Degree=Pos	2	amod	_	_
2	complexes	complex	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	4	auxpass	_	_
4	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	by	by	ADP	IN	_	4	agent	_	_
6	Goubault	Goubault	PROPN	NNP	Number=Sing	5	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	author	author	NOUN	NN	Number=Sing	6	conj	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	model	model	NOUN	NN	Number=Sing	4	advcl	_	_
12	higher	high	ADJ	JJR	Degree=Cmp	14	amod	_	_
13	dimensional	dimensional	ADJ	JJ	Degree=Pos	14	amod	_	_
14	automata	automata	NOUN	NN	Number=Sing	11	dobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = Globular complexes are topological spaces equipped with a globular decomposition which is the directed analogue of the cellular decomposition of a CW - complex.
1	Globular	globular	ADJ	JJ	Degree=Pos	2	amod	_	_
2	complexes	complex	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	topological	topological	ADJ	JJ	Degree=Pos	5	amod	_	_
5	spaces	space	NOUN	NNS	Number=Plur	3	attr	_	_
6	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	acl	_	_
7	with	with	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	globular	globular	ADJ	JJ	Degree=Pos	10	amod	_	_
10	decomposition	decomposition	NOUN	NN	Number=Sing	7	pobj	_	_
11	which	which	PRON	WDT	_	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	relcl	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
15	analogue	analogue	NOUN	NN	Number=Sing	12	attr	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	cellular	cellular	ADJ	JJ	Degree=Pos	19	amod	_	_
19	decomposition	decomposition	NOUN	NN	Number=Sing	16	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
22	CW	cw	NOUN	NN	Number=Sing	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	complex	complex	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = We prove that there exists a combinatorial model category such that the cellular objects are exactly the globular complexes and such that the homotopy category is equivalent to the homotopy category of flows.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	there	there	PRON	EX	_	5	expl	_	_
5	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	8	amod	_	_
8	model	model	NOUN	NN	Number=Sing	9	compound	_	_
9	category	category	NOUN	NN	Number=Sing	5	dobj	_	_
10	such	such	ADJ	JJ	Degree=Pos	15	mark	_	_
11	that	that	SCONJ	IN	_	15	mark	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	cellular	cellular	ADJ	JJ	Degree=Pos	14	amod	_	_
14	objects	object	NOUN	NNS	Number=Plur	15	nsubj	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	advcl	_	_
16	exactly	exactly	ADV	RB	_	19	advmod	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	globular	globular	ADJ	JJ	Degree=Pos	19	amod	_	_
19	complexes	complex	NOUN	NNS	Number=Plur	15	attr	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	such	such	ADJ	JJ	Degree=Pos	19	conj	_	_
22	that	that	SCONJ	IN	_	26	mark	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	homotopy	homotopy	NOUN	NN	Number=Sing	25	compound	_	_
25	category	category	NOUN	NN	Number=Sing	26	nsubj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
27	equivalent	equivalent	ADJ	JJ	Degree=Pos	26	acomp	_	_
28	to	to	ADP	IN	_	27	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
30	homotopy	homotopy	NOUN	NN	Number=Sing	31	compound	_	_
31	category	category	NOUN	NN	Number=Sing	28	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	flows	flow	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = The underlying category of this model category is a variant of Grandis' notion of $ d $ - space over a topological space colimit generated by simplices.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	underlying	underlie	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	amod	_	_
3	category	category	NOUN	NN	Number=Sing	8	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
6	model	model	NOUN	NN	Number=Sing	7	compound	_	_
7	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	variant	variant	NOUN	NN	Number=Sing	8	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	Grandis	Grandis	PROPN	NNP	Number=Sing	14	poss	_	SpaceAfter=No
13	'	'	PART	POS	_	12	case	_	_
14	notion	notion	NOUN	NN	Number=Sing	11	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	$ d $	$ d $	SYM	$	_	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	space	space	NOUN	NN	Number=Sing	15	pobj	_	_
19	over	over	ADP	IN	_	10	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
21	topological	topological	ADJ	JJ	Degree=Pos	23	amod	_	_
22	space	space	NOUN	NN	Number=Sing	23	compound	_	_
23	colimit	colimit	NOUN	NN	Number=Sing	19	pobj	_	_
24	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	acl	_	_
25	by	by	ADP	IN	_	24	agent	_	_
26	simplices	simplice	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 5
# text = This result enables us to understand the relationship between the framework of flows and other works in directed algebraic topology using $ d $ - spaces.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	result	result	NOUN	NN	Number=Sing	3	nsubj	_	_
3	enables	enable	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	understand	understand	VERB	VB	VerbForm=Inf	3	ccomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	relationship	relationship	NOUN	NN	Number=Sing	6	dobj	_	_
9	between	between	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	framework	framework	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	flows	flow	NOUN	NNS	Number=Plur	12	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	other	other	ADJ	JJ	Degree=Pos	16	amod	_	_
16	works	work	NOUN	NNS	Number=Plur	13	conj	_	_
17	in	in	ADP	IN	_	11	prep	_	_
18	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	amod	_	_
19	algebraic	algebraic	ADJ	JJ	Degree=Pos	20	amod	_	_
20	topology	topology	NOUN	NN	Number=Sing	17	pobj	_	_
21	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	acl	_	_
22	$ d $	$ d $	SYM	$	_	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	spaces	space	NOUN	NNS	Number=Plur	21	dobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = It also enables us to prove that the underlying homotopy type functor of flows can be interpreted up to equivalences of categories as the total left derived functor of a left Quillen adjoint.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	enables	enable	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	3	dobj	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	prove	prove	VERB	VB	VerbForm=Inf	3	xcomp	_	_
7	that	that	SCONJ	IN	_	17	mark	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
9	underlying	underlie	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	amod	_	_
10	homotopy	homotopy	NOUN	NN	Number=Sing	11	compound	_	_
11	type	type	NOUN	NN	Number=Sing	12	compound	_	_
12	functor	functor	NOUN	NN	Number=Sing	17	nsubjpass	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	flows	flow	NOUN	NNS	Number=Plur	13	pobj	_	_
15	can	can	AUX	MD	VerbForm=Fin	17	aux	_	_
16	be	be	AUX	VB	VerbForm=Inf	17	auxpass	_	_
17	interpreted	interpret	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	ccomp	_	_
18	up	up	ADP	RP	_	17	prt	_	_
19	to	to	ADP	IN	_	17	prep	_	_
20	equivalences	equivalence	NOUN	NNS	Number=Plur	19	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	categories	category	NOUN	NNS	Number=Plur	21	pobj	_	_
23	as	as	SCONJ	IN	_	27	mark	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	total	total	ADJ	JJ	Degree=Pos	26	amod	_	_
26	left	left	ADV	RB	_	27	nsubj	_	_
27	derived	derive	VERB	VBD	Tense=Past|VerbForm=Fin	17	advcl	_	_
28	functor	functor	NOUN	NN	Number=Sing	27	dobj	_	_
29	of	of	ADP	IN	_	27	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
31	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	amod	_	_
32	Quillen	quillen	ADJ	JJ	Degree=Pos	33	amod	_	_
33	adjoint	adjoint	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 323
# sent_id = 1
# text = This article contains a review of categorifications of semisimple representations of various rings via abelian categories and exact endofunctors on them.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	article	article	NOUN	NN	Number=Sing	3	nsubj	_	_
3	contains	contain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	review	review	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	categorifications	categorification	NOUN	NNS	Number=Plur	6	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	semisimple	semisimple	ADJ	JJ	Degree=Pos	10	amod	_	_
10	representations	representation	NOUN	NNS	Number=Plur	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	various	various	ADJ	JJ	Degree=Pos	13	amod	_	_
13	rings	ring	NOUN	NNS	Number=Plur	11	pobj	_	_
14	via	via	ADP	IN	_	13	prep	_	_
15	abelian	abelian	ADJ	JJ	Degree=Pos	16	amod	_	_
16	categories	category	NOUN	NNS	Number=Plur	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	exact	exact	ADJ	JJ	Degree=Pos	19	amod	_	_
19	endofunctors	endofunctor	NOUN	NNS	Number=Plur	16	conj	_	_
20	on	on	ADP	IN	_	19	prep	_	_
21	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	20	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = A simple definition of an abelian categorification is presented and illustrated with several examples, including categorifications of various representations of the symmetric group and its Hecke algebra via highest weight categories of modules over the Lie algebra $ sl_n $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	simple	simple	ADJ	JJ	Degree=Pos	3	amod	_	_
3	definition	definition	NOUN	NN	Number=Sing	9	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	abelian	abelian	PROPN	NNP	Number=Sing	7	compound	_	_
7	categorification	categorification	NOUN	NN	Number=Sing	4	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	illustrated	illustrate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	conj	_	_
12	with	with	ADP	IN	_	11	prep	_	_
13	several	several	ADJ	JJ	Degree=Pos	14	amod	_	_
14	examples	example	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	prep	_	_
17	categorifications	categorification	NOUN	NNS	Number=Plur	16	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	various	various	ADJ	JJ	Degree=Pos	20	amod	_	_
20	representations	representation	NOUN	NNS	Number=Plur	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	symmetric	symmetric	ADJ	JJ	Degree=Pos	24	amod	_	_
24	group	group	NOUN	NN	Number=Sing	21	pobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	28	poss	_	_
27	Hecke	Hecke	PROPN	NNP	Number=Sing	28	compound	_	_
28	algebra	algebra	NOUN	NN	Number=Sing	24	conj	_	_
29	via	via	ADP	IN	_	20	prep	_	_
30	highest	high	ADJ	JJS	Degree=Sup	32	amod	_	_
31	weight	weight	NOUN	NN	Number=Sing	32	compound	_	_
32	categories	category	NOUN	NNS	Number=Plur	29	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	modules	module	NOUN	NNS	Number=Plur	33	pobj	_	_
35	over	over	ADP	IN	_	34	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	Lie	Lie	PROPN	NNP	Number=Sing	38	compound	_	_
38	algebra	algebra	PROPN	NNP	Number=Sing	35	pobj	_	_
39	$ sl_n $	$ sl_n $	SYM	$	_	14	appos	_	_
40	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 3
# text = The review is intended to give non - experts in representation theory who are familiar with the topological aspects of categorification (lifting quantum link invariants to homology theories) an idea for the sort of categories that appear when link homology is extended to tangles.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	review	review	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	intended	intend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	give	give	VERB	VB	VerbForm=Inf	4	xcomp	_	_
7	non	non	ADJ	JJ	Degree=Pos	9	compound	_	_
8	-	-	NOUN	NNS	Number=Plur	9	punct	_	_
9	experts	expert	NOUN	NNS	Number=Plur	6	dobj	_	_
10	in	in	ADP	IN	_	6	prep	_	_
11	representation	representation	NOUN	NN	Number=Sing	12	compound	_	_
12	theory	theory	NOUN	NN	Number=Sing	10	pobj	_	_
13	who	who	PRON	WP	_	14	nsubj	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	relcl	_	_
15	familiar	familiar	ADJ	JJ	Degree=Pos	14	acomp	_	_
16	with	with	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	topological	topological	ADJ	JJ	Degree=Pos	19	amod	_	_
19	aspects	aspect	NOUN	NNS	Number=Plur	16	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	categorification	categorification	NOUN	NN	Number=Sing	20	pobj	_	_
22	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
23	lifting	lift	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	advcl	_	_
24	quantum	quantum	NOUN	NN	Number=Sing	25	compound	_	_
25	link	link	NOUN	NN	Number=Sing	26	compound	_	_
26	invariants	invariant	NOUN	NNS	Number=Plur	23	dobj	_	_
27	to	to	ADP	IN	_	23	prep	_	_
28	homology	homology	NOUN	NN	Number=Sing	29	compound	_	_
29	theories	theory	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	4	punct	_	_
31	an	an	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
32	idea	idea	NOUN	NN	Number=Sing	4	dobj	_	_
33	for	for	ADP	IN	_	32	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	sort	sort	NOUN	NN	Number=Sing	33	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	categories	category	NOUN	NNS	Number=Plur	36	pobj	_	_
38	that	that	PRON	WDT	PronType=Rel	39	nsubj	_	_
39	appear	appear	VERB	VBP	Tense=Pres|VerbForm=Fin	35	relcl	_	_
40	when	when	SCONJ	WRB	_	44	advmod	_	_
41	link	link	PROPN	NNP	Number=Sing	42	compound	_	_
42	homology	homology	NOUN	NN	Number=Sing	44	nsubjpass	_	_
43	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	44	auxpass	_	_
44	extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	39	advcl	_	_
45	to	to	ADP	IN	_	44	prep	_	_
46	tangles	tangle	NOUN	NNS	Number=Plur	45	pobj	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 324
# sent_id = 1
# text = We study convergent (terminating and confluent) presentations of $ n $ - categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	convergent	convergent	NOUN	NN	Number=Sing	2	dobj	_	_
4	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	3	punct	_	SpaceAfter=No
5	terminating	terminate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	conj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	confluent	confluent	ADJ	JJ	Degree=Pos	5	conj	_	SpaceAfter=No
8	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	3	punct	_	_
9	presentations	presentation	NOUN	NNS	Number=Plur	2	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	$ n $	$ n $	SYM	$	_	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Using the notion of polygraph (or computad), we introduce the homotopical property of finite derivation type for $ n $ - categories, generalising the one introduced by Squier for word rewriting systems.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	advcl	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	notion	notion	NOUN	NN	Number=Sing	1	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	polygraph	polygraph	NOUN	NN	Number=Sing	4	pobj	_	_
6	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	5	punct	_	SpaceAfter=No
7	or	or	CCONJ	CC	ConjType=Cmp	5	cc	_	_
8	computad	computad	NOUN	NN	Number=Sing	5	conj	_	SpaceAfter=No
9	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	5	punct	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
11	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	12	nsubj	_	_
12	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	homotopical	homotopical	ADJ	JJ	Degree=Pos	15	amod	_	_
15	property	property	NOUN	NN	Number=Sing	12	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	finite	finite	ADJ	JJ	Degree=Pos	19	amod	_	_
18	derivation	derivation	NOUN	NN	Number=Sing	19	compound	_	_
19	type	type	NOUN	NN	Number=Sing	16	pobj	_	_
20	for	for	ADP	IN	_	15	prep	_	_
21	$ n $	$ n $	SYM	$	_	23	nummod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	categories	category	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
25	generalising	generalise	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	advcl	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	one	one	NOUN	NN	Number=Sing	25	dobj	_	_
28	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	acl	_	_
29	by	by	ADP	IN	_	28	agent	_	_
30	Squier	Squier	PROPN	NNP	Number=Sing	29	pobj	_	_
31	for	for	ADP	IN	_	28	prep	_	_
32	word	word	NOUN	NN	Number=Sing	31	pobj	_	_
33	rewriting	rewrite	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	32	acl	_	_
34	systems	system	NOUN	NNS	Number=Plur	33	dobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 3
# text = We characterise this property by using the notion of critical branching.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	characterise	characterise	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	property	property	NOUN	NN	Number=Sing	2	dobj	_	_
5	by	by	ADP	IN	_	2	prep	_	_
6	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	notion	notion	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	critical	critical	ADJ	JJ	Degree=Pos	11	amod	_	_
11	branching	branching	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = In particular, we define sufficient conditions for an $ n $ - category to have finite derivation type.
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	sufficient	sufficient	ADJ	JJ	Degree=Pos	7	amod	_	_
7	conditions	condition	NOUN	NNS	Number=Plur	5	dobj	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
10	$ n $	$ n $	SYM	$	_	12	quantmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	have	have	AUX	VB	VerbForm=Inf	12	acl	_	_
15	finite	finite	ADJ	JJ	Degree=Pos	17	compound	_	_
16	derivation	derivation	NOUN	NN	Number=Sing	17	compound	_	_
17	type	type	NOUN	NN	Number=Sing	14	dobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = Through examples, we present several techniques based on derivations of 2 - categories to study convergent presentations by 3 - polygraphs.
1	Through	through	ADP	IN	_	5	prep	_	_
2	examples	example	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	several	several	ADJ	JJ	Degree=Pos	7	amod	_	_
7	techniques	technique	NOUN	NNS	Number=Plur	5	dobj	_	_
8	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	acl	_	_
9	on	on	ADP	IN	_	8	prep	_	_
10	derivations	derivation	NOUN	NNS	Number=Plur	9	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	2	2	NUM	CD	NumType=Card	14	nummod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	study	study	VERB	VB	VerbForm=Inf	7	relcl	_	_
17	convergent	convergent	NOUN	NN	Number=Sing	18	compound	_	_
18	presentations	presentation	NOUN	NNS	Number=Plur	16	dobj	_	_
19	by	by	ADP	IN	_	16	prep	_	_
20	3	3	NUM	CD	NumType=Card	22	nummod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	polygraphs	polygraph	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 325
# sent_id = 1
# text = This paper introduces the notions of vector field and flow on a general differentiable stack.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	introduces	introduce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	notions	notion	NOUN	NNS	Number=Plur	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	vector	vector	NOUN	NN	Number=Sing	8	compound	_	_
8	field	field	NOUN	NN	Number=Sing	6	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
10	flow	flow	VERB	VB	VerbForm=Inf	3	conj	_	_
11	on	on	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	general	general	ADJ	JJ	Degree=Pos	15	amod	_	_
14	differentiable	differentiable	ADJ	JJ	Degree=Pos	15	amod	_	_
15	stack	stack	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = Our main theorem states that the flow of a vector field on a compact proper differentiable stack exists and is unique up to a uniquely determined 2 - cell.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	4	poss	_	_
2	main	main	ADJ	JJ	Degree=Pos	4	amod	_	_
3	theorem	theorem	ADJ	JJ	Degree=Pos	4	amod	_	_
4	states	state	NOUN	NNS	Number=Plur	0	ROOT	_	_
5	that	that	SCONJ	IN	_	20	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	flow	flow	NOUN	NN	Number=Sing	20	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	vector	vector	NOUN	NN	Number=Sing	11	compound	_	_
11	field	field	NOUN	NN	Number=Sing	8	pobj	_	_
12	on	on	ADP	IN	_	7	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
14	compact	compact	ADJ	JJ	Degree=Pos	18	amod	_	_
15	proper	proper	ADJ	JJ	Degree=Pos	18	amod	_	_
16	differentiable	differentiable	ADJ	JJ	Degree=Pos	17	amod	_	_
17	stack	stack	NOUN	NN	Number=Sing	18	compound	_	_
18	exists	exist	NOUN	NNS	Number=Plur	12	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	acl	_	_
21	unique	unique	ADJ	JJ	Degree=Pos	20	acomp	_	_
22	up	up	ADP	IN	_	21	prep	_	_
23	to	to	ADP	IN	_	22	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
25	uniquely	uniquely	ADV	RB	_	26	advmod	_	_
26	determined	determined	ADJ	JJ	Degree=Pos	29	amod	_	_
27	2	2	NUM	CD	NumType=Card	29	nummod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	cell	cell	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = This extends the usual result on the existence and uniqueness of flows on a manifold as well as the author's existing results for orbifolds.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	usual	usual	ADJ	JJ	Degree=Pos	5	amod	_	_
5	result	result	NOUN	NN	Number=Sing	2	dobj	_	_
6	on	on	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	existence	existence	NOUN	NN	Number=Sing	6	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	uniqueness	uniqueness	NOUN	NN	Number=Sing	8	conj	_	_
11	of	of	ADP	IN	_	8	prep	_	_
12	flows	flow	NOUN	NNS	Number=Plur	11	pobj	_	_
13	on	on	ADP	IN	_	2	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	manifold	manifold	ADJ	JJ	Degree=Pos	13	pobj	_	_
16	as	as	ADV	RB	_	18	advmod	_	_
17	well	well	ADV	RB	Degree=Pos	18	advmod	_	_
18	as	as	ADP	IN	_	2	cc	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	author	author	NOUN	NN	Number=Sing	23	poss	_	SpaceAfter=No
21	's	's	PART	POS	_	20	case	_	_
22	existing	exist	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	23	amod	_	_
23	results	result	NOUN	NNS	Number=Plur	2	dobj	_	_
24	for	for	ADP	IN	_	23	prep	_	_
25	orbifolds	orbifold	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = It sets the scene for a discussion of Morse Theory on a general proper stack and also paves the way for the categorification of other key aspects of differential geometry such as the tangent bundle and the Lie algebra of vector fields.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	sets	set	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	scene	scene	NOUN	NN	Number=Sing	2	dobj	_	_
5	for	for	ADP	IN	_	2	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	discussion	discussion	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	Morse	Morse	PROPN	NNP	Number=Sing	10	compound	_	_
10	Theory	Theory	PROPN	NNP	Number=Sing	8	pobj	_	_
11	on	on	ADP	IN	_	7	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	general	general	ADJ	JJ	Degree=Pos	15	amod	_	_
14	proper	proper	ADJ	JJ	Degree=Pos	15	amod	_	_
15	stack	stack	NOUN	NN	Number=Sing	11	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
17	also	also	ADV	RB	_	18	advmod	_	_
18	paves	pave	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	way	way	NOUN	NN	Number=Sing	18	dobj	_	_
21	for	for	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	categorification	categorification	NOUN	NN	Number=Sing	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	other	other	ADJ	JJ	Degree=Pos	27	amod	_	_
26	key	key	ADJ	JJ	Degree=Pos	27	amod	_	_
27	aspects	aspect	NOUN	NNS	Number=Plur	24	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	differential	differential	ADJ	JJ	Degree=Pos	30	amod	_	_
30	geometry	geometry	NOUN	NN	Number=Sing	28	pobj	_	_
31	such	such	ADJ	JJ	Degree=Pos	32	amod	_	_
32	as	as	ADP	IN	_	30	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
34	tangent	tangent	NOUN	NN	Number=Sing	35	compound	_	_
35	bundle	bundle	NOUN	NN	Number=Sing	32	pobj	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
38	Lie	lie	NOUN	NN	Number=Sing	39	compound	_	_
39	algebra	algebra	NOUN	NN	Number=Sing	35	conj	_	_
40	of	of	ADP	IN	_	39	prep	_	_
41	vector	vector	NOUN	NN	Number=Sing	42	compound	_	_
42	fields	field	NOUN	NNS	Number=Plur	40	pobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 326
# sent_id = 1
# text = With the representable $ T $ - categories, we form a connection between two concepts, both owed to Burroni: on the one hand, the one of $ T $ - category, and, on the other hand, the one of $ T $ - lax algebra.
1	With	with	ADP	IN	_	9	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
3	representable	representable	ADJ	JJ	Degree=Pos	6	amod	_	_
4	$ T $	$ t $	SYM	$	_	6	nummod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	categories	category	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	form	form	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	connection	connection	NOUN	NN	Number=Sing	9	dobj	_	_
12	between	between	ADP	IN	_	11	prep	_	_
13	two	two	NUM	CD	NumType=Card	14	nummod	_	_
14	concepts	concept	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	both	both	PRON	DT	_	14	appos	_	_
17	owed	owe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	acl	_	_
18	to	to	ADP	IN	_	17	dative	_	_
19	Burroni	Burroni	PROPN	NNP	Number=Sing	18	pobj	_	SpaceAfter=No
20	:	:	PUNCT	:	_	9	punct	_	_
21	on	on	ADP	IN	_	9	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	one	one	NUM	CD	NumType=Card	24	nummod	_	_
24	hand	hand	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	one	one	NUM	CD	NumType=Card	21	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	$ T $	$ t $	SYM	$	_	31	nmod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	category	category	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	41	punct	_	_
35	on	on	ADP	IN	_	41	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
37	other	other	ADJ	JJ	Degree=Pos	38	amod	_	_
38	hand	hand	NOUN	NN	Number=Sing	35	pobj	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	41	punct	_	_
40	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
41	one	one	NUM	CD	NumType=Card	21	pobj	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	$ T $	$ t $	SYM	$	_	45	quantmod	_	_
44	-	-	PUNCT	HYPH	PunctType=Dash	45	punct	_	_
45	lax	lax	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	46	amod	_	_
46	algebra	algebra	NOUN	NN	Number=Sing	42	pobj	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 2
# text = Both of them generalise the concept of algebra on a monad $ T $ .
1	Both	both	PRON	DT	_	4	nsubj	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	2	pobj	_	_
4	generalise	generalise	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	concept	concept	NOUN	NN	Number=Sing	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	algebra	algebra	NOUN	NN	Number=Sing	7	pobj	_	_
9	on	on	ADP	IN	_	4	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	monad	monad	NOUN	NNS	Number=Plur	9	pobj	_	_
12	$ T $	$ t $	SYM	$	_	11	appos	_	_
13	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 327
# sent_id = 1
# text = Let $ G $ be a non - finite profinite group and let $ G - Sets_{df} $ be the canonical site of finite discrete $ G $ - sets.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ G $	$ g $	SYM	$	_	1	dobj	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
5	non	non	ADJ	JJ	Degree=Pos	9	amod	_	_
6	-	-	ADJ	JJ	Degree=Pos	9	punct	_	_
7	finite	finite	ADJ	JJ	Degree=Pos	9	amod	_	_
8	profinite	profinite	NOUN	NN	Number=Sing	9	compound	_	_
9	group	group	NOUN	NN	Number=Sing	3	attr	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
11	let	let	VERB	VB	VerbForm=Inf	3	conj	_	_
12	$ G - Sets_{df} $	$ g - sets_{df} $	SYM	$	_	13	nsubj	_	_
13	be	be	AUX	VB	VerbForm=Inf	11	ccomp	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	canonical	canonical	ADJ	JJ	Degree=Pos	16	amod	_	_
16	site	site	NOUN	NN	Number=Sing	13	attr	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	finite	finite	PROPN	NNP	Number=Sing	19	compound	_	_
19	discrete	discrete	NOUN	NN	Number=Sing	17	pobj	_	_
20	$ G $	$ g $	SYM	$	_	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	sets	set	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = Then the category $ R^+_G $ , defined by Devinatz and Hopkins, is the category obtained by considering $ G - Sets_{df} $ together with the profinite $ G $ - space $ G $ itself, with morphisms being continuous $ G $ - equivariant maps.
1	Then	then	ADV	RB	PronType=Dem	12	advmod	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	category	category	NOUN	NN	Number=Sing	12	nsubj	_	_
4	$ R^+_G $	$ r^+_g $	SYM	$	_	3	nummod	_	_
5	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
6	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	acl	_	_
7	by	by	ADP	IN	_	6	agent	_	_
8	Devinatz	Devinatz	PROPN	NNP	Number=Sing	7	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	Hopkins	Hopkins	PROPN	NNP	Number=Sing	8	conj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	category	category	NOUN	NN	Number=Sing	12	attr	_	_
15	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	acl	_	_
16	by	by	ADP	IN	_	15	prep	_	_
17	considering	consider	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	pcomp	_	_
18	$ G - Sets_{df} $	$ g - sets_{df} $	SYM	$	_	17	dobj	_	_
19	together	together	ADV	RB	_	20	advmod	_	_
20	with	with	ADP	IN	_	17	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	profinite	profinite	NOUN	NN	Number=Sing	20	pobj	_	_
23	$ G $	$ g $	SYM	$	_	25	compound	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	space	space	NOUN	NN	Number=Sing	20	pobj	_	_
26	$ G $	$ g $	SYM	$	_	27	nmod	_	_
27	itself	itself	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs|Reflex=Yes	25	appos	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
29	with	with	ADP	IN	_	14	prep	_	_
30	morphisms	morphism	NOUN	NNS	Number=Plur	31	nsubj	_	_
31	being	be	AUX	VBG	VerbForm=Ger	29	pcomp	_	_
32	continuous	continuous	ADJ	JJ	Degree=Pos	36	amod	_	_
33	$ G $	$ g $	SYM	$	_	35	advmod	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	equivariant	equivariant	ADJ	JJ	Degree=Pos	36	amod	_	_
36	maps	map	NOUN	NNS	Number=Plur	31	attr	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that $ R^+_G $ is a site when equipped with the pretopology of epimorphic covers.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	$ R^+_G $	$ r^+_g $	SYM	$	_	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	site	site	NOUN	NN	Number=Sing	5	attr	_	_
8	when	when	SCONJ	WRB	_	9	advmod	_	_
9	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	advcl	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	pretopology	pretopology	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	epimorphic	epimorphic	ADJ	JJ	Degree=Pos	15	amod	_	_
15	covers	cover	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We point out that presheaves of spectra on $ R^+_G $ are an efficient way of organizing the data that is obtained by taking the homotopy fixed points of a continuous $ G $ - spectrum with respect to the open subgroups of $ G $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	point	point	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	out	out	ADP	RP	_	2	prt	_	_
4	that	that	SCONJ	IN	_	10	mark	_	_
5	presheaves	presheave	NOUN	NNS	Number=Plur	10	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	spectra	spectra	PROPN	NNP	Number=Sing	6	pobj	_	_
8	on	on	ADP	IN	_	5	prep	_	_
9	$ R^+_G $	$ r^+_g $	SYM	$	_	8	pobj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
11	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	efficient	efficient	ADJ	JJ	Degree=Pos	13	amod	_	_
13	way	way	NOUN	NN	Number=Sing	10	attr	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	organizing	organize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	pcomp	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	data	datum	NOUN	NNS	Number=Plur	15	dobj	_	_
18	that	that	PRON	WDT	PronType=Rel	20	nsubjpass	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	auxpass	_	_
20	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	relcl	_	_
21	by	by	ADP	IN	_	20	agent	_	_
22	taking	take	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	21	pcomp	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	homotopy	homotopy	NOUN	NN	Number=Sing	22	dobj	_	_
25	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
26	points	point	NOUN	NNS	Number=Plur	22	dobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
29	continuous	continuous	ADJ	JJ	Degree=Pos	32	amod	_	_
30	$ G $	$ g $	SYM	$	_	32	dep	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	spectrum	spectrum	NOUN	NN	Number=Sing	27	pobj	_	_
33	with	with	ADP	IN	_	32	prep	_	_
34	respect	respect	NOUN	NN	Number=Sing	33	pobj	_	_
35	to	to	ADP	IN	_	34	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
37	open	open	ADJ	JJ	Degree=Pos	38	amod	_	_
38	subgroups	subgroup	NOUN	NNS	Number=Plur	35	pobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	$ G $	$ g $	SYM	$	_	39	pobj	_	_
41	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = Additionally, utilizing the result that $ R^+_G $ is a site, we describe various model category structures on the category of presheaves of spectra on $ R^+_G $ and make some observations about them.
1	Additionally	additionally	ADV	RB	_	13	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
3	utilizing	utilize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	advcl	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	result	result	NOUN	NN	Number=Sing	3	dobj	_	_
6	that	that	SCONJ	IN	_	8	mark	_	_
7	$ R^+_G $	$ r^+_g $	SYM	$	_	8	nsubj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	acl	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	site	site	NOUN	NN	Number=Sing	8	attr	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	various	various	ADJ	JJ	Degree=Pos	17	amod	_	_
15	model	model	NOUN	NN	Number=Sing	17	compound	_	_
16	category	category	NOUN	NN	Number=Sing	17	compound	_	_
17	structures	structure	NOUN	NNS	Number=Plur	13	dobj	_	_
18	on	on	ADP	IN	_	13	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	presheaves	presheave	NOUN	NNS	Number=Plur	21	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	spectra	spectra	PROPN	NNP	Number=Sing	23	pobj	_	_
25	on	on	ADP	IN	_	13	prep	_	_
26	$ R^+_G $	$ r^+_g $	SYM	$	_	25	pobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
28	make	make	VERB	VB	VerbForm=Inf	13	conj	_	_
29	some	some	DET	DT	_	30	det	_	_
30	observations	observation	NOUN	NNS	Number=Plur	28	dobj	_	_
31	about	about	ADP	IN	_	30	prep	_	_
32	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	31	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# doc_id = 328
# sent_id = 1
# text = The purpose of this paper is to extend the results of another from the case of abelian groups (or $ Z $ - modules) to that of modules over a large class of not necessarily commutative rings.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	purpose	purpose	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	paper	paper	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	extend	extend	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	results	result	NOUN	NNS	Number=Plur	8	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	another	another	PRON	DT	_	11	pobj	_	_
13	from	from	ADP	IN	_	8	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	case	case	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	abelian	abelian	ADJ	JJ	Degree=Pos	18	compound	_	_
18	groups	group	NOUN	NNS	Number=Plur	16	pobj	_	_
19	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	18	punct	_	SpaceAfter=No
20	or	or	CCONJ	CC	ConjType=Cmp	18	cc	_	_
21	$ Z $	$ z $	SYM	$	_	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	modules	module	NOUN	NNS	Number=Plur	18	conj	_	SpaceAfter=No
24	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	18	punct	_	_
25	to	to	ADP	IN	_	8	prep	_	_
26	that	that	PRON	DT	Number=Sing|PronType=Dem	25	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	modules	module	NOUN	NNS	Number=Plur	27	pobj	_	_
29	over	over	ADP	IN	_	28	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
31	large	large	ADJ	JJ	Degree=Pos	32	amod	_	_
32	class	class	NOUN	NN	Number=Sing	29	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	not	not	PART	RB	Polarity=Neg	33	neg	_	_
35	necessarily	necessarily	ADV	RB	_	36	advmod	_	_
36	commutative	commutative	ADJ	JJ	Degree=Pos	37	amod	_	_
37	rings	ring	NOUN	NNS	Number=Plur	8	dobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 329
# sent_id = 1
# text = This paper continues the work of our previous papers.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	continues	continue	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	work	work	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	9	poss	_	_
8	previous	previous	ADJ	JJ	Degree=Pos	9	amod	_	_
9	papers	paper	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = We define eventually cyclic Boolean flows and the eventually cyclic spectrum of a Boolean flow.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	eventually	eventually	ADV	RB	_	4	advmod	_	_
4	cyclic	cyclic	ADJ	JJ	Degree=Pos	6	amod	_	_
5	Boolean	boolean	ADJ	JJ	Degree=Pos	6	amod	_	_
6	flows	flow	NOUN	NNS	Number=Plur	2	dobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
9	eventually	eventually	ADV	RB	_	10	advmod	_	_
10	cyclic	cyclic	ADJ	JJ	Degree=Pos	11	amod	_	_
11	spectrum	spectrum	NOUN	NN	Number=Sing	6	conj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	Boolean	boolean	ADJ	JJ	Degree=Pos	15	amod	_	_
15	flow	flow	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that this spectrum, as well as the spectra defined in our earlier papers, extend to parametrized flows on Stone spaces and on compact Hausdorff space when symbolic dynamics is used.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	18	mark	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	spectrum	spectrum	NOUN	NN	Number=Sing	18	nsubj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	as	as	ADV	RB	_	9	advmod	_	_
8	well	well	ADV	RB	Degree=Pos	9	advmod	_	_
9	as	as	ADP	IN	_	5	cc	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	spectra	spectra	NOUN	NN	Number=Sing	5	conj	_	_
12	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acl	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	16	poss	_	_
15	earlier	early	ADJ	JJR	Degree=Cmp	16	amod	_	_
16	papers	paper	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
18	extend	extend	VERB	VB	VerbForm=Inf	2	ccomp	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	parametrized	parametrized	ADJ	JJ	Degree=Pos	21	amod	_	_
21	flows	flow	NOUN	NNS	Number=Plur	19	pobj	_	_
22	on	on	ADP	IN	_	21	prep	_	_
23	Stone	Stone	PROPN	NNP	Number=Sing	24	compound	_	_
24	spaces	space	NOUN	NNS	Number=Plur	22	pobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
26	on	on	ADP	IN	_	19	conj	_	_
27	compact	compact	ADJ	JJ	Degree=Pos	29	amod	_	_
28	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	29	compound	_	_
29	space	space	NOUN	NN	Number=Sing	26	pobj	_	_
30	when	when	SCONJ	WRB	_	34	advmod	_	_
31	symbolic	symbolic	ADJ	JJ	Degree=Pos	32	amod	_	_
32	dynamics	dynamic	NOUN	NNS	Number=Plur	34	nsubjpass	_	_
33	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	34	auxpass	_	_
34	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	advcl	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = An example shows that the cyclic spectrum for a parameterized flow is sometimes over a non - spatial locale.
1	An	an	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	example	example	NOUN	NN	Number=Sing	3	nsubj	_	_
3	shows	show	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	7	mark	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	cyclic	cyclic	NOUN	NN	Number=Sing	7	nsubj	_	_
7	spectrum	spectrum	NOUN	NN	Number=Sing	3	ccomp	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	parameterized	parameterized	ADJ	JJ	Degree=Pos	11	amod	_	_
11	flow	flow	NOUN	NN	Number=Sing	8	pobj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
13	sometimes	sometimes	ADV	RB	_	12	advmod	_	_
14	over	over	ADP	IN	_	12	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
16	non	non	ADJ	JJ	Degree=Pos	19	amod	_	_
17	-	-	ADJ	JJ	Degree=Pos	19	amod	_	_
18	spatial	spatial	ADJ	JJ	Degree=Pos	19	amod	_	_
19	locale	locale	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 330
# sent_id = 1
# text = We axiomatically define (pre - )Hilbert categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	axiomatically	axiomatically	ADV	RB	_	3	advmod	_	_
3	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	9	punct	_	SpaceAfter=No
5	pre	pre	X	FW	Foreign=Yes	9	nmod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
7	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	9	punct	_	SpaceAfter=No
8	Hilbert	Hilbert	PROPN	NNP	Number=Sing	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	3	dobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = The axioms resemble those for monoidal Abelian categories with the addition of an involutive functor.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	axioms	axiom	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	resemble	resemble	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	those	those	PRON	DT	Number=Plur|PronType=Dem	3	dobj	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	monoidal	monoidal	ADJ	JJ	Degree=Pos	8	amod	_	_
7	Abelian	abelian	ADJ	JJ	Degree=Pos	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
9	with	with	ADP	IN	_	3	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	addition	addition	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	involutive	involutive	ADJ	JJ	Degree=Pos	15	amod	_	_
15	functor	functor	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = We then prove embedding theorems: any locally small pre - Hilbert category whose monoidal unit is a simple generator embeds (weakly) monoidally into the category of pre - Hilbert spaces and adjointable maps, preserving adjoint morphisms and all finite (co)limits.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	embedding	embed	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	xcomp	_	_
5	theorems	theorem	NOUN	NNS	Number=Plur	4	dobj	_	SpaceAfter=No
6	:	:	PUNCT	:	_	3	punct	_	_
7	any	any	DET	DT	_	13	det	_	_
8	locally	locally	ADV	RB	_	9	advmod	_	_
9	small	small	ADJ	JJ	Degree=Pos	13	amod	_	_
10	pre	pre	ADJ	AFX	Hyph=Yes	13	amod	_	_
11	-	-	ADJ	JJ	Degree=Pos	13	amod	_	_
12	Hilbert	hilbert	ADJ	JJ	Degree=Pos	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	3	dobj	_	_
14	whose	whose	DET	WP$	Poss=Yes	16	poss	_	_
15	monoidal	monoidal	ADJ	JJ	Degree=Pos	16	amod	_	_
16	unit	unit	NOUN	NN	Number=Sing	17	nsubj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	relcl	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
19	simple	simple	ADJ	JJ	Degree=Pos	20	amod	_	_
20	generator	generator	NOUN	NN	Number=Sing	21	compound	_	_
21	embeds	embed	NOUN	NNS	Number=Plur	17	attr	_	_
22	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	21	punct	_	SpaceAfter=No
23	weakly	weakly	ADJ	JJ	Degree=Pos	21	advmod	_	SpaceAfter=No
24	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	21	punct	_	_
25	monoidally	monoidally	ADV	RB	_	21	advmod	_	_
26	into	into	ADP	IN	_	21	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	category	category	NOUN	NN	Number=Sing	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	pre	pre	ADJ	JJ	Degree=Pos	33	amod	_	_
31	-	-	ADJ	JJ	Degree=Pos	33	amod	_	_
32	Hilbert	hilbert	ADJ	JJ	Degree=Pos	33	amod	_	_
33	spaces	space	NOUN	NNS	Number=Plur	29	pobj	_	_
34	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
35	adjointable	adjointable	ADJ	JJ	Degree=Pos	36	amod	_	_
36	maps	map	NOUN	NNS	Number=Plur	33	conj	_	SpaceAfter=No
37	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
38	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	advcl	_	_
39	adjoint	adjoint	NOUN	NN	Number=Sing	40	compound	_	_
40	morphisms	morphism	NOUN	NNS	Number=Plur	38	dobj	_	_
41	and	and	CCONJ	CC	ConjType=Cmp	40	cc	_	_
42	all	all	DET	DT	_	43	det	_	_
43	finite	finite	PROPN	NNP	Number=Sing	40	conj	_	_
44	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	45	punct	_	SpaceAfter=No
45	co)limits	co)limit	NOUN	NNS	Number=Plur	43	appos	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = An intermediate result that is important in its own right is that the scalars in such a category necessarily form an involutive field.
1	An	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	intermediate	intermediate	ADJ	JJ	Degree=Pos	3	amod	_	_
3	result	result	NOUN	NN	Number=Sing	11	nsubj	_	_
4	that	that	PRON	WDT	PronType=Rel	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	relcl	_	_
6	important	important	ADJ	JJ	Degree=Pos	5	acomp	_	_
7	in	in	ADP	IN	_	5	prep	_	_
8	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	10	poss	_	_
9	own	own	ADJ	JJ	Degree=Pos	10	amod	_	_
10	right	right	NOUN	NN	Number=Sing	7	pobj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	that	that	SCONJ	IN	_	20	mark	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	scalars	scalar	NOUN	NNS	Number=Plur	20	nsubj	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	such	such	DET	PDT	_	18	predet	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
19	necessarily	necessarily	ADV	RB	_	20	advmod	_	_
20	form	form	VERB	VBP	Tense=Pres|VerbForm=Fin	11	ccomp	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	involutive	involutive	ADJ	JJ	Degree=Pos	23	amod	_	_
23	field	field	NOUN	NN	Number=Sing	20	dobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 5
# text = In case of a Hilbert category, the embedding extends to the category of Hilbert spaces and continuous linear maps.
1	In	in	ADP	IN	_	10	prep	_	_
2	case	case	NOUN	NN	Number=Sing	1	pobj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	Hilbert	Hilbert	PROPN	NNP	Number=Sing	6	compound	_	_
6	category	category	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	embedding	embed	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	amod	_	_
10	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	to	to	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	Hilbert	Hilbert	PROPN	NNP	Number=Sing	16	compound	_	_
16	spaces	space	NOUN	NNS	Number=Plur	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	continuous	continuous	ADJ	JJ	Degree=Pos	20	amod	_	_
19	linear	linear	ADJ	JJ	Degree=Pos	20	compound	_	_
20	maps	map	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 6
# text = The axioms for (pre - )Hilbert categories are weaker than the axioms found in other approaches to axiomatizing 2 - Hilbert spaces.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	axioms	axiom	NOUN	NNS	Number=Plur	10	nsubj	_	_
3	for	for	ADP	IN	_	2	prep	_	_
4	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	3	punct	_	SpaceAfter=No
5	pre	pre	X	FW	Foreign=Yes	3	intj	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	3	punct	_	_
7	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	3	punct	_	SpaceAfter=No
8	Hilbert	Hilbert	PROPN	NNP	Number=Sing	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	3	pobj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	weaker	weak	ADJ	JJR	Degree=Cmp	10	acomp	_	_
12	than	than	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	axioms	axiom	NOUN	NNS	Number=Plur	12	pobj	_	_
15	found	find	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	acl	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	other	other	ADJ	JJ	Degree=Pos	18	amod	_	_
18	approaches	approach	NOUN	NNS	Number=Plur	16	pobj	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	axiomatizing	axiomatize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	pcomp	_	_
21	2	2	NUM	CD	NumType=Card	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	Hilbert	Hilbert	PROPN	NNP	Number=Sing	24	compound	_	_
24	spaces	space	NOUN	NNS	Number=Plur	20	dobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 7
# text = Neither enrichment nor a complex base field is presupposed.
1	Neither	neither	PRON	DT	_	2	preconj	_	_
2	enrichment	enrichment	NOUN	NN	Number=Sing	9	nsubjpass	_	_
3	nor	nor	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	complex	complex	ADJ	JJ	Degree=Pos	7	amod	_	_
6	base	base	NOUN	NN	Number=Sing	7	compound	_	_
7	field	field	NOUN	NN	Number=Sing	2	conj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	presupposed	presuppose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 8
# text = A comparison to other approaches will be made in the introduction.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	comparison	comparison	NOUN	NN	Number=Sing	8	nsubjpass	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	other	other	ADJ	JJ	Degree=Pos	5	amod	_	_
5	approaches	approach	NOUN	NNS	Number=Plur	3	pobj	_	_
6	will	will	AUX	MD	VerbForm=Fin	8	aux	_	_
7	be	be	AUX	VB	VerbForm=Inf	8	auxpass	_	_
8	made	make	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	introduction	introduction	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 331
# sent_id = 1
# text = Distributive laws between monads (triples) were defined by Jon Beck in the 1960s.
1	Distributive	distributive	ADJ	JJ	Degree=Pos	9	advcl	_	_
2	laws	law	NOUN	NNS	Number=Plur	1	dobj	_	_
3	between	between	ADP	IN	_	2	prep	_	_
4	monads	monad	NOUN	NNS	Number=Plur	3	pobj	_	_
5	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	4	punct	_	SpaceAfter=No
6	triples	triple	NOUN	NNS	Number=Plur	4	appos	_	SpaceAfter=No
7	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	4	punct	_	_
8	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	9	auxpass	_	_
9	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	by	by	ADP	IN	_	9	agent	_	_
11	Jon	Jon	PROPN	NNP	Number=Sing	12	compound	_	_
12	Beck	Beck	PROPN	NNP	Number=Sing	10	pobj	_	_
13	in	in	ADP	IN	_	9	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	1960s	1960	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 2
# text = They were generalized to monads in 2 - categories and noticed to be monads in a 2 - category of monads.
1	They	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	3	nsubjpass	_	_
2	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	3	auxpass	_	_
3	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	to	to	ADP	IN	_	3	prep	_	_
5	monads	monad	NOUN	NNS	Number=Plur	4	pobj	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	2	2	NUM	CD	NumType=Card	9	nummod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
11	noticed	notice	VERB	VBD	Tense=Past|VerbForm=Fin	3	conj	_	_
12	to	to	PART	TO	_	13	aux	_	_
13	be	be	AUX	VB	VerbForm=Inf	11	xcomp	_	_
14	monads	monad	NOUN	NNS	Number=Plur	13	attr	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
17	2	2	NUM	CD	NumType=Card	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	monads	monad	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Mixed distributive laws are comonads in the 2 - category of monads; if the comonad has a right adjoint monad, the mate of a mixed distributive law is an ordinary distributive law.
1	Mixed	mixed	ADJ	JJ	Degree=Pos	3	amod	_	_
2	distributive	distributive	ADJ	JJ	Degree=Pos	3	amod	_	_
3	laws	law	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	30	ccomp	_	_
5	comonads	comonad	NOUN	NNS	Number=Plur	4	attr	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	2	2	NUM	CD	NumType=Card	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	monads	monad	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
13	;	;	PUNCT	:	_	30	punct	_	_
14	if	if	SCONJ	IN	_	17	mark	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	comonad	comonad	NOUN	NNS	Number=Plur	17	nsubj	_	_
17	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	advcl	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
19	right	right	ADJ	JJ	Degree=Pos	21	amod	_	_
20	adjoint	adjoint	NOUN	NN	Number=Sing	21	compound	_	_
21	monad	monad	NOUN	NNS	Number=Plur	17	dobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	mate	mate	NOUN	NN	Number=Sing	30	nsubj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
27	mixed	mixed	ADJ	JJ	Degree=Pos	28	amod	_	_
28	distributive	distributive	ADJ	JJ	Degree=Pos	29	amod	_	_
29	law	law	NOUN	NN	Number=Sing	25	pobj	_	_
30	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
31	an	an	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
32	ordinary	ordinary	ADJ	JJ	Degree=Pos	34	amod	_	_
33	distributive	distributive	ADJ	JJ	Degree=Pos	34	amod	_	_
34	law	law	NOUN	NN	Number=Sing	30	attr	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	30	punct	_	SpaceAfter=No

# sent_id = 4
# text = Particular cases are the entwining operators between algebras and coalgebras.
1	Particular	particular	ADJ	JJ	Degree=Pos	2	amod	_	_
2	cases	case	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	entwining	entwine	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	amod	_	_
6	operators	operator	NOUN	NNS	Number=Plur	3	attr	_	_
7	between	between	ADP	IN	_	6	prep	_	_
8	algebras	algebra	NOUN	NNS	Number=Plur	7	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	coalgebras	coalgebras	PROPN	NNP	Number=Sing	8	conj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = Motivated by work on weak entwining operators, we define and study a weak notion of distributive law for monads.
1	Motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	advcl	_	_
2	by	by	ADP	IN	_	1	agent	_	_
3	work	work	NOUN	NN	Number=Sing	2	pobj	_	_
4	on	on	ADP	IN	_	3	prep	_	_
5	weak	weak	ADJ	JJ	Degree=Pos	7	amod	_	_
6	entwining	entwining	NOUN	NN	Number=Sing	7	amod	_	_
7	operators	operator	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
9	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
10	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	study	study	VERB	VB	VerbForm=Inf	10	conj	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	weak	weak	ADJ	JJ	Degree=Pos	15	amod	_	_
15	notion	notion	NOUN	NN	Number=Sing	12	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	distributive	distributive	ADJ	JJ	Degree=Pos	18	amod	_	_
18	law	law	NOUN	NN	Number=Sing	16	pobj	_	_
19	for	for	ADP	IN	_	18	prep	_	_
20	monads	monad	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 6
# text = In particular, each weak distributive law determines a wreath product monad (in the terminology of Lack and Street); this gives an advantage over the mixed case.
1	In	in	ADP	IN	_	8	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
4	each	each	DET	DT	_	7	det	_	_
5	weak	weak	ADJ	JJ	Degree=Pos	7	amod	_	_
6	distributive	distributive	ADJ	JJ	Degree=Pos	7	amod	_	_
7	law	law	NOUN	NN	Number=Sing	8	nsubj	_	_
8	determines	determine	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	ccomp	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
10	wreath	wreath	NOUN	NN	Number=Sing	11	compound	_	_
11	product	product	NOUN	NN	Number=Sing	12	compound	_	_
12	monad	monad	NOUN	NNS	Number=Plur	8	dobj	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
14	in	in	ADP	IN	_	12	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	terminology	terminology	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	Lack	Lack	PROPN	NNP	Number=Sing	17	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	Street	Street	PROPN	NNP	Number=Sing	18	conj	_	SpaceAfter=No
21	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	12	punct	_	SpaceAfter=No
22	;	;	PUNCT	:	_	24	punct	_	_
23	this	this	PRON	DT	Number=Sing|PronType=Dem	24	nsubj	_	_
24	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
25	an	an	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
26	advantage	advantage	NOUN	NN	Number=Sing	24	dobj	_	_
27	over	over	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
29	mixed	mixed	ADJ	JJ	Degree=Pos	30	amod	_	_
30	case	case	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# doc_id = 332
# sent_id = 1
# text = We introduce the notion of elementary Seely category as a notion of categorical model of Elementary Linear Logic inspired from Seely's definition of models of Linear Logic.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	elementary	elementary	ADJ	JJ	Degree=Pos	8	amod	_	_
7	Seely	Seely	PROPN	NNP	Number=Sing	8	compound	_	_
8	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
9	as	as	ADP	IN	_	2	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	notion	notion	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	categorical	categorical	ADJ	JJ	Degree=Pos	14	amod	_	_
14	model	model	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	Elementary	Elementary	PROPN	NNP	Number=Sing	18	compound	_	_
17	Linear	Linear	PROPN	NNP	Number=Sing	18	compound	_	_
18	Logic	Logic	PROPN	NNP	Number=Sing	15	pobj	_	_
19	inspired	inspire	VERB	VBD	Tense=Past|VerbForm=Fin	11	acl	_	_
20	from	from	ADP	IN	_	19	prep	_	_
21	Seely	Seely	PROPN	NNP	Number=Sing	23	poss	_	SpaceAfter=No
22	's	's	PART	POS	_	21	case	_	_
23	definition	definition	NOUN	NN	Number=Sing	20	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	models	model	NOUN	NNS	Number=Plur	24	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	Linear	Linear	PROPN	NNP	Number=Sing	28	compound	_	_
28	Logic	Logic	PROPN	NNP	Number=Sing	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In order to deal with additive connectives in Elementary Linear Logic, we use the approach of Danos and Joinet.
1	In	in	ADP	IN	_	14	prep	_	_
2	order	order	NOUN	NN	Number=Sing	1	pobj	_	_
3	to	to	PART	TO	_	4	aux	_	_
4	deal	deal	VERB	VB	VerbForm=Inf	2	acl	_	_
5	with	with	ADP	IN	_	4	prep	_	_
6	additive	additive	ADJ	JJ	Degree=Pos	7	amod	_	_
7	connectives	connective	NOUN	NNS	Number=Plur	5	pobj	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	Elementary	Elementary	PROPN	NNP	Number=Sing	11	compound	_	_
10	Linear	Linear	PROPN	NNP	Number=Sing	11	compound	_	_
11	Logic	Logic	PROPN	NNP	Number=Sing	8	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	approach	approach	NOUN	NN	Number=Sing	14	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	Danos	Danos	PROPN	NNP	Number=Sing	17	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	Joinet	Joinet	PROPN	NNP	Number=Sing	18	conj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 3
# text = From the categorical point of view, this requires us to go outside the usual interpretation of connectives by functors.
1	From	from	ADP	IN	_	9	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	categorical	categorical	ADJ	JJ	Degree=Pos	4	amod	_	_
4	point	point	NOUN	NN	Number=Sing	1	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	view	view	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
8	this	this	PRON	DT	Number=Sing|PronType=Dem	9	nsubj	_	_
9	requires	require	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	9	dobj	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	go	go	VERB	VB	VerbForm=Inf	9	xcomp	_	_
13	outside	outside	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	usual	usual	ADJ	JJ	Degree=Pos	16	amod	_	_
16	interpretation	interpretation	NOUN	NN	Number=Sing	13	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	connectives	connective	NOUN	NNS	Number=Plur	17	pobj	_	_
19	by	by	ADP	IN	_	12	prep	_	_
20	functors	functor	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 4
# text = The $ clik $ connective is decomposed into a pre - connective $ sharp $ which is interpreted by a whole family of functors (generated by $ id $ , $ tens $ and $ with $ ).
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	$ clik $	$ clik $	SYM	$	_	3	nmod	_	_
3	connective	connective	ADJ	JJ	Degree=Pos	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	decomposed	decompose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	into	into	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	pre	pre	ADJ	JJ	Degree=Pos	11	amod	_	_
9	-	-	ADJ	JJ	Degree=Pos	11	punct	_	_
10	connective	connective	ADJ	JJ	Degree=Pos	11	amod	_	_
11	$ sharp $	$ sharp $	SYM	$	_	6	pobj	_	_
12	which	which	PRON	WDT	_	14	nsubjpass	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	interpreted	interpret	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	relcl	_	_
15	by	by	ADP	IN	_	14	agent	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	whole	whole	ADJ	JJ	Degree=Pos	18	amod	_	_
18	family	family	NOUN	NN	Number=Sing	15	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	functors	functor	NOUN	NNS	Number=Plur	19	pobj	_	_
21	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	22	punct	_	SpaceAfter=No
22	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	advcl	_	_
23	by	by	ADP	IN	_	22	prep	_	_
24	$ id $	$ id $	SYM	$	_	23	pobj	_	_
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	$ tens $	$ tens $	SYM	$	_	22	dobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	$ with $	$ with $	SYM	$	_	26	conj	_	_
29	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	22	punct	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = As an application, we prove the stratified coherent model and the obsessional coherent model to be elementary Seely categories and thus models of Elementary Linear Logic.
1	As	as	ADP	IN	_	6	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	stratified	stratified	ADJ	JJ	Degree=Pos	10	amod	_	_
9	coherent	coherent	ADJ	JJ	Degree=Pos	10	amod	_	_
10	model	model	NOUN	NN	Number=Sing	6	dobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
13	obsessional	obsessional	ADJ	JJ	Degree=Pos	15	amod	_	_
14	coherent	coherent	ADJ	JJ	Degree=Pos	15	amod	_	_
15	model	model	NOUN	NN	Number=Sing	10	conj	_	_
16	to	to	PART	TO	_	17	aux	_	_
17	be	be	AUX	VB	VerbForm=Inf	6	xcomp	_	_
18	elementary	elementary	ADJ	JJ	Degree=Pos	20	amod	_	_
19	Seely	Seely	PROPN	NNP	Number=Sing	20	amod	_	_
20	categories	category	NOUN	NNS	Number=Plur	17	attr	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	thus	thus	ADV	RB	_	23	advmod	_	_
23	models	model	NOUN	NNS	Number=Plur	20	conj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	Elementary	Elementary	PROPN	NNP	Number=Sing	27	compound	_	_
26	Linear	Linear	PROPN	NNP	Number=Sing	27	compound	_	_
27	Logic	Logic	PROPN	NNP	Number=Sing	24	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 333
# sent_id = 1
# text = In this paper, we consider an enriched orthogonality for classes of spaces, with respect to groupoids, simplicial sets and spaces themselves.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	enriched	enriched	ADJ	JJ	Degree=Pos	9	amod	_	_
9	orthogonality	orthogonality	NOUN	NN	Number=Sing	6	dobj	_	_
10	for	for	ADP	IN	_	9	prep	_	_
11	classes	class	NOUN	NNS	Number=Plur	10	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	spaces	space	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
15	with	with	ADP	IN	_	6	prep	_	_
16	respect	respect	NOUN	NN	Number=Sing	15	pobj	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	groupoids	groupoid	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	simplicial	simplicial	ADJ	JJ	Degree=Pos	21	amod	_	_
21	sets	set	NOUN	NNS	Number=Plur	18	conj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	spaces	space	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	21	conj	_	_
24	themselves	themselves	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs|Reflex=Yes	23	dobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = This point of view allows one to characterize homotopy equivalences, shape and strong shape equivalences.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	point	point	NOUN	NN	Number=Sing	5	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	view	view	NOUN	NN	Number=Sing	3	pobj	_	_
5	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	one	one	PRON	PRP	PronType=Prs	8	nsubj	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	characterize	characterize	VERB	VB	VerbForm=Inf	5	ccomp	_	_
9	homotopy	homotopy	NOUN	NN	Number=Sing	10	compound	_	_
10	equivalences	equivalence	NOUN	NNS	Number=Plur	8	dobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	shape	shape	NOUN	NN	Number=Sing	10	conj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	strong	strong	ADJ	JJ	Degree=Pos	16	amod	_	_
15	shape	shape	NOUN	NN	Number=Sing	16	compound	_	_
16	equivalences	equivalence	NOUN	NNS	Number=Plur	12	conj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that there exists a class of spaces, properly containing ANR - spaces, for which shape and strong shape equivalences coincide.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	there	there	PRON	EX	_	5	expl	_	_
5	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	class	class	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	spaces	space	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
11	properly	properly	ADV	RB	_	12	advmod	_	_
12	containing	contain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	advcl	_	_
13	ANR	ANR	PROPN	NNP	Number=Sing	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	spaces	space	NOUN	NNS	Number=Plur	12	dobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	for	for	ADP	IN	_	24	prep	_	_
18	which	which	PRON	WDT	_	17	pobj	_	_
19	shape	shape	NOUN	NN	Number=Sing	17	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	strong	strong	ADJ	JJ	Degree=Pos	23	amod	_	_
22	shape	shape	NOUN	NN	Number=Sing	23	compound	_	_
23	equivalences	equivalence	NOUN	NNS	Number=Plur	19	conj	_	_
24	coincide	coincide	NOUN	NN	Number=Sing	15	relcl	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = For such a class of spaces homotopy orthogonality implies enriched orthogonality.
1	For	for	ADP	IN	_	9	prep	_	_
2	such	such	DET	PDT	_	4	predet	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	class	class	NOUN	NN	Number=Sing	8	nmod	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	spaces	space	NOUN	NNS	Number=Plur	5	pobj	_	_
7	homotopy	homotopy	PROPN	NNP	Number=Sing	8	compound	_	_
8	orthogonality	orthogonality	NOUN	NN	Number=Sing	9	nsubj	_	_
9	implies	imply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	enriched	enriched	ADJ	JJ	Degree=Pos	11	amod	_	_
11	orthogonality	orthogonality	NOUN	NN	Number=Sing	9	dobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 334
# sent_id = 1
# text = Higher Homotopy van Kampen Theorems allow some colimit calculations of certain homotopical invariants of glued spaces.
1	Higher	high	ADJ	JJR	Degree=Cmp	3	compound	_	_
2	Homotopy	Homotopy	PROPN	NNP	Number=Sing	3	compound	_	_
3	van	van	PROPN	NNP	Number=Sing	5	compound	_	_
4	Kampen	Kampen	PROPN	NNP	Number=Sing	5	compound	_	_
5	Theorems	Theorems	PROPN	NNP	Number=Sing	6	nsubj	_	_
6	allow	allow	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	some	some	DET	DT	_	9	det	_	_
8	colimit	colimit	NOUN	NN	Number=Sing	9	compound	_	_
9	calculations	calculation	NOUN	NNS	Number=Plur	6	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	certain	certain	ADJ	JJ	Degree=Pos	13	amod	_	_
12	homotopical	homotopical	ADJ	JJ	Degree=Pos	13	amod	_	_
13	invariants	invariant	NOUN	NNS	Number=Plur	10	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	glued	glued	ADJ	JJ	Degree=Pos	16	amod	_	_
16	spaces	space	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = One corollary is to describe homotopical excision in critical dimensions in terms of induced modules and crossed modules over groupoids.
1	One	one	NUM	CD	NumType=Card	2	nummod	_	_
2	corollary	corollary	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	describe	describe	VERB	VB	VerbForm=Inf	3	xcomp	_	_
6	homotopical	homotopical	ADJ	JJ	Degree=Pos	7	amod	_	_
7	excision	excision	NOUN	NN	Number=Sing	5	dobj	_	_
8	in	in	ADP	IN	_	5	prep	_	_
9	critical	critical	ADJ	JJ	Degree=Pos	10	amod	_	_
10	dimensions	dimension	NOUN	NNS	Number=Plur	8	pobj	_	_
11	in	in	ADP	IN	_	5	prep	_	_
12	terms	term	NOUN	NNS	Number=Plur	11	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	induced	induced	ADJ	JJ	Degree=Pos	15	amod	_	_
15	modules	module	NOUN	NNS	Number=Plur	13	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
17	crossed	cross	VERB	VBD	Tense=Past|VerbForm=Fin	5	conj	_	_
18	modules	module	NOUN	NNS	Number=Plur	17	dobj	_	_
19	over	over	ADP	IN	_	18	prep	_	_
20	groupoids	groupoid	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = This paper shows how fibred and cofibred categories give an overall context for discussing and computing such constructions, allowing one result to cover many cases.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	shows	show	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	how	how	SCONJ	WRB	_	5	advmod	_	_
5	fibred	fibre	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	cofibred	cofibre	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	conj	_	_
8	categories	category	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	3	ccomp	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	overall	overall	ADJ	JJ	Degree=Pos	12	amod	_	_
12	context	context	NOUN	NN	Number=Sing	9	dobj	_	_
13	for	for	ADP	IN	_	12	prep	_	_
14	discussing	discuss	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	pcomp	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	computing	compute	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	conj	_	_
17	such	such	ADJ	JJ	Degree=Pos	18	amod	_	_
18	constructions	construction	NOUN	NNS	Number=Plur	16	dobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
20	allowing	allow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	advcl	_	_
21	one	one	NUM	CD	NumType=Card	22	nummod	_	_
22	result	result	NOUN	NN	Number=Sing	20	dobj	_	_
23	to	to	PART	TO	_	24	aux	_	_
24	cover	cover	VERB	VB	VerbForm=Inf	20	advcl	_	_
25	many	many	ADJ	JJ	Degree=Pos	26	amod	_	_
26	cases	case	NOUN	NNS	Number=Plur	24	dobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = A useful general result is that the inclusion of a fibre of a fibred category preserves connected colimits.
1	A	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
2	useful	useful	ADJ	JJ	Degree=Pos	4	amod	_	_
3	general	general	ADJ	JJ	Degree=Pos	4	amod	_	_
4	result	result	NOUN	NN	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	16	mark	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	inclusion	inclusion	NOUN	NN	Number=Sing	16	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	fibre	fibre	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	fibred	fibred	ADJ	JJ	Degree=Pos	15	amod	_	_
15	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
16	preserves	preserve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
17	connected	connected	ADJ	JJ	Degree=Pos	18	amod	_	_
18	colimits	colimit	NOUN	NNS	Number=Plur	16	dobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = The main homotopical applications are to pairs of spaces with several base points; we also describe briefly applications to triads.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	4	amod	_	_
3	homotopical	homotopical	ADJ	JJ	Degree=Pos	4	amod	_	_
4	applications	application	NOUN	NNS	Number=Plur	5	nsubj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	17	ccomp	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	pairs	pair	NOUN	NNS	Number=Plur	6	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	spaces	space	NOUN	NNS	Number=Plur	8	pobj	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	several	several	ADJ	JJ	Degree=Pos	13	amod	_	_
12	base	base	NOUN	NN	Number=Sing	13	compound	_	_
13	points	point	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
14	;	;	PUNCT	:	_	17	punct	_	_
15	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	17	nsubj	_	_
16	also	also	ADV	RB	_	17	advmod	_	_
17	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
18	briefly	briefly	NOUN	NN	Number=Sing	19	compound	_	_
19	applications	application	NOUN	NNS	Number=Plur	17	dobj	_	_
20	to	to	ADP	IN	_	19	prep	_	_
21	triads	triad	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# doc_id = 335
# sent_id = 1
# text = The state space of a machine admits the structure of time.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	state	state	NOUN	NN	Number=Sing	3	compound	_	_
3	space	space	NOUN	NN	Number=Sing	7	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	machine	machine	NOUN	NN	Number=Sing	4	pobj	_	_
7	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	structure	structure	NOUN	NN	Number=Sing	7	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	time	time	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 2
# text = For example, the geometric realization of a precubical set, a generalization of an unlabeled asynchronous transition system, admits a ``local preorder'' encoding control flow.
1	For	for	ADP	IN	_	21	prep	_	_
2	example	example	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	geometric	geometric	ADJ	JJ	Degree=Pos	6	amod	_	_
6	realization	realization	NOUN	NN	Number=Sing	21	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	precubical	precubical	ADJ	JJ	Degree=Pos	10	amod	_	_
10	set	set	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	generalization	generalization	NOUN	NN	Number=Sing	10	appos	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	an	an	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
16	unlabeled	unlabeled	ADJ	JJ	Degree=Pos	19	amod	_	_
17	asynchronous	asynchronous	ADJ	JJ	Degree=Pos	19	amod	_	_
18	transition	transition	NOUN	NN	Number=Sing	19	compound	_	_
19	system	system	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
21	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
23	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	SpaceAfter=No
24	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	SpaceAfter=No
25	local	local	ADJ	JJ	Degree=Pos	26	amod	_	_
26	preorder	preorder	NOUN	NN	Number=Sing	21	dobj	_	SpaceAfter=No
27	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	26	punct	_	_
28	encoding	encode	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	26	acl	_	_
29	control	control	NOUN	NN	Number=Sing	30	compound	_	_
30	flow	flow	NOUN	NN	Number=Sing	28	dobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# sent_id = 3
# text = In the case where time does not loop, the ``locally preordered'' state space splits into causally distinct components.
1	In	in	ADP	IN	_	18	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	case	case	NOUN	NN	Number=Sing	1	pobj	_	_
4	where	where	SCONJ	WRB	_	8	advmod	_	_
5	time	time	NOUN	NN	Number=Sing	8	nsubj	_	_
6	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	aux	_	_
7	not	not	PART	RB	Polarity=Neg	8	neg	_	_
8	loop	loop	VERB	VB	VerbForm=Inf	3	relcl	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
11	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	18	punct	_	SpaceAfter=No
12	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	18	punct	_	SpaceAfter=No
13	locally	locally	ADV	RB	_	14	advmod	_	_
14	preordered	preordere	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	SpaceAfter=No
15	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	18	punct	_	_
16	state	state	NOUN	NN	Number=Sing	17	compound	_	_
17	space	space	NOUN	NN	Number=Sing	18	compound	_	_
18	splits	split	NOUN	NNS	Number=Plur	0	ROOT	_	_
19	into	into	ADP	IN	_	18	prep	_	_
20	causally	causally	ADV	RB	_	21	advmod	_	_
21	distinct	distinct	ADJ	JJ	Degree=Pos	22	amod	_	_
22	components	component	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# sent_id = 4
# text = The set of such components often gives a computable invariant of machine behavior.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	set	set	NOUN	NN	Number=Sing	7	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	such	such	ADJ	JJ	Degree=Pos	5	amod	_	_
5	components	component	NOUN	NNS	Number=Plur	3	pobj	_	_
6	often	often	ADV	RB	_	7	advmod	_	_
7	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	computable	computable	ADJ	JJ	Degree=Pos	10	amod	_	_
10	invariant	invariant	NOUN	NN	Number=Sing	7	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	machine	machine	NOUN	NN	Number=Sing	13	compound	_	_
13	behavior	behavior	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 5
# text = In the general case, no such meaningful partition could exist.
1	In	in	ADP	IN	_	11	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	general	general	ADJ	JJ	Degree=Pos	4	amod	_	_
4	case	case	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
6	no	no	DET	DT	_	9	det	_	_
7	such	such	ADJ	JJ	Degree=Pos	9	amod	_	_
8	meaningful	meaningful	ADJ	JJ	Degree=Pos	9	amod	_	_
9	partition	partition	NOUN	NN	Number=Sing	11	nsubj	_	_
10	could	could	AUX	MD	VerbForm=Fin	11	aux	_	_
11	exist	exist	VERB	VB	VerbForm=Inf	0	ROOT	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 6
# text = However, as we show in this note, the locally preordered geometric realization of a precubical set admits a ``locally monotone'' covering from a state space in which time does not loop.
1	However	however	ADV	RB	_	19	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
3	as	as	SCONJ	IN	_	5	mark	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	19	advcl	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	this	this	DET	DT	Number=Sing|PronType=Dem	8	det	_	_
8	note	note	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
11	locally	locally	ADV	RB	_	12	advmod	_	_
12	preordered	preordere	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
13	geometric	geometric	ADJ	JJ	Degree=Pos	14	amod	_	_
14	realization	realization	NOUN	NN	Number=Sing	19	nsubj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	precubical	precubical	ADJ	JJ	Degree=Pos	18	amod	_	_
18	set	set	NOUN	NN	Number=Sing	15	pobj	_	_
19	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
21	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	24	punct	_	SpaceAfter=No
22	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	24	punct	_	SpaceAfter=No
23	locally	locally	ADV	RB	_	24	advmod	_	_
24	monotone	monotone	ADJ	JJ	Degree=Pos	19	dobj	_	SpaceAfter=No
25	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	24	punct	_	_
26	covering	cover	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	24	acl	_	_
27	from	from	ADP	IN	_	26	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
29	state	state	NOUN	NN	Number=Sing	30	compound	_	_
30	space	space	NOUN	NN	Number=Sing	27	pobj	_	_
31	in	in	ADP	IN	_	36	prep	_	_
32	which	which	DET	WDT	_	33	det	_	_
33	time	time	NOUN	NN	Number=Sing	36	nsubj	_	_
34	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	36	aux	_	_
35	not	not	PART	RB	Polarity=Neg	36	neg	_	_
36	loop	loop	VERB	VB	VerbForm=Inf	30	relcl	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 7
# text = Thus we hope to extend geometric techniques in static program analysis to looping processes.
1	Thus	thus	ADV	RB	_	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	hope	hope	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	extend	extend	VERB	VB	VerbForm=Inf	3	xcomp	_	_
6	geometric	geometric	ADJ	JJ	Degree=Pos	7	amod	_	_
7	techniques	technique	NOUN	NNS	Number=Plur	5	dobj	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	static	static	ADJ	JJ	Degree=Pos	10	amod	_	_
10	program	program	NOUN	NN	Number=Sing	11	compound	_	_
11	analysis	analysis	NOUN	NN	Number=Sing	8	pobj	_	_
12	to	to	ADP	IN	_	5	prep	_	_
13	looping	loop	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	amod	_	_
14	processes	process	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 336
# sent_id = 1
# text = Prior work towards the subject of higher - dimensional categories gives rise to several examples of a category over $ Cat $ to which the slice - category construction can be lifted universally.
1	Prior	prior	ADJ	JJ	Degree=Pos	2	amod	_	_
2	work	work	NOUN	NN	Number=Sing	11	nsubj	_	_
3	towards	towards	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	subject	subject	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	higher	high	ADJ	JJR	Degree=Cmp	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	dimensional	dimensional	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
11	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	rise	rise	VERB	VB	VerbForm=Inf	11	dobj	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	several	several	ADJ	JJ	Degree=Pos	15	amod	_	_
15	examples	example	NOUN	NNS	Number=Plur	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	category	category	NOUN	NN	Number=Sing	16	pobj	_	_
19	over	over	ADP	IN	_	12	prep	_	_
20	$ Cat $	$ cat $	SYM	$	_	19	pobj	_	_
21	to	to	PART	TO	_	30	prep	_	_
22	which	which	PRON	WDT	_	21	pobj	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
24	slice	slice	NOUN	NN	Number=Sing	26	compound	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	category	category	NOUN	NN	Number=Sing	27	compound	_	_
27	construction	construction	NOUN	NN	Number=Sing	30	nsubjpass	_	_
28	can	can	AUX	MD	VerbForm=Fin	30	aux	_	_
29	be	be	AUX	VB	VerbForm=Inf	30	auxpass	_	_
30	lifted	lift	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	relcl	_	_
31	universally	universally	ADV	RB	_	30	advmod	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 2
# text = The present paper starts by supplying this last clause with a precise meaning.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	present	present	ADJ	JJ	Degree=Pos	3	amod	_	_
3	paper	paper	NOUN	NN	Number=Sing	4	nsubj	_	_
4	starts	start	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	by	by	ADP	IN	_	4	prep	_	_
6	supplying	supply	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	this	this	DET	DT	Number=Sing|PronType=Dem	9	det	_	_
8	last	last	ADJ	JJ	Degree=Pos	9	amod	_	_
9	clause	clause	NOUN	NN	Number=Sing	6	dobj	_	_
10	with	with	ADP	IN	_	6	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	precise	precise	ADJ	JJ	Degree=Pos	13	amod	_	_
13	meaning	meaning	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = It goes on to establish for any such category a certain embedding in a presheaf category, to describe the image, and hence to derive conditions collectively sufficient for that functor to be an equivalence.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	goes	go	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	on	on	ADP	RP	_	2	prt	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	establish	establish	VERB	VB	VerbForm=Inf	2	xcomp	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	any	any	DET	DT	_	9	det	_	_
8	such	such	ADJ	JJ	Degree=Pos	9	amod	_	_
9	category	category	NOUN	NN	Number=Sing	12	nsubj	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	certain	certain	ADJ	JJ	Degree=Pos	12	amod	_	_
12	embedding	embed	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	pcomp	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	presheaf	presheaf	ADJ	JJ	Degree=Pos	16	amod	_	_
16	category	category	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
18	to	to	PART	TO	_	19	aux	_	_
19	describe	describe	VERB	VB	VerbForm=Inf	2	advcl	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	image	image	NOUN	NN	Number=Sing	19	dobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
24	hence	hence	ADV	RB	_	26	advmod	_	_
25	to	to	PART	TO	_	26	aux	_	_
26	derive	derive	VERB	VB	VerbForm=Inf	19	conj	_	_
27	conditions	condition	NOUN	NNS	Number=Plur	26	dobj	_	_
28	collectively	collectively	ADV	RB	_	29	advmod	_	_
29	sufficient	sufficient	ADJ	JJ	Degree=Pos	27	amod	_	_
30	for	for	SCONJ	IN	_	34	mark	_	_
31	that	that	DET	DT	Number=Sing|PronType=Dem	32	det	_	_
32	functor	functor	NOUN	NN	Number=Sing	34	nsubj	_	_
33	to	to	PART	TO	_	34	aux	_	_
34	be	be	AUX	VB	VerbForm=Inf	26	advcl	_	_
35	an	an	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
36	equivalence	equivalence	NOUN	NN	Number=Sing	34	attr	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = These conditions are met in the foremost of the examples: the category of dendrotopic sets.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	conditions	condition	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	met	meet	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	foremost	foremost	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	examples	example	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
11	:	:	PUNCT	:	_	4	punct	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	category	category	NOUN	NN	Number=Sing	2	appos	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	dendrotopic	dendrotopic	ADJ	JJ	Degree=Pos	16	amod	_	_
16	sets	set	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 337
# sent_id = 1
# text = We continue our examination of absolute CR - epic spaces, or spaces with the property that any embedding induces an epimorphism, in the category of commutative rings, between their rings of continuous functions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	continue	continue	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	4	poss	_	_
4	examination	examination	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	absolute	absolute	ADJ	JJ	Degree=Pos	10	amod	_	_
7	CR	cr	NOUN	NN	Number=Sing	9	npadvmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	epic	epic	ADJ	JJ	Degree=Pos	10	amod	_	_
10	spaces	space	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
12	or	or	CCONJ	CC	ConjType=Cmp	4	cc	_	_
13	spaces	space	NOUN	NNS	Number=Plur	4	conj	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	property	property	NOUN	NN	Number=Sing	14	pobj	_	_
17	that	that	PRON	WDT	PronType=Rel	20	nsubj	_	_
18	any	any	DET	DT	_	20	det	_	_
19	embedding	embed	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	amod	_	_
20	induces	induce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	relcl	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	epimorphism	epimorphism	NOUN	NN	Number=Sing	20	dobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
24	in	in	ADP	IN	_	20	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	category	category	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	commutative	commutative	ADJ	JJ	Degree=Pos	29	amod	_	_
29	rings	ring	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
31	between	between	ADP	IN	_	20	prep	_	_
32	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	33	poss	_	_
33	rings	ring	NOUN	NNS	Number=Plur	31	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	continuous	continuous	ADJ	JJ	Degree=Pos	36	amod	_	_
36	functions	function	NOUN	NNS	Number=Plur	34	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We examine more closely the deleted plank construction, which generalizes the Dieudonne construction, and yields absolute CR - epic spaces which are not Lindelof.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	examine	examine	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	more	more	ADV	RBR	Degree=Cmp	4	advmod	_	_
4	closely	closely	ADV	RB	_	2	advmod	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
6	deleted	delete	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
7	plank	plank	NOUN	NN	Number=Sing	8	compound	_	_
8	construction	construction	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
10	which	which	PRON	WDT	_	11	nsubj	_	_
11	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	relcl	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	Dieudonne	Dieudonne	PROPN	NNP	Number=Sing	14	compound	_	_
14	construction	construction	NOUN	NN	Number=Sing	11	dobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
17	yields	yield	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
18	absolute	absolute	ADJ	JJ	Degree=Pos	22	amod	_	_
19	CR	cr	ADJ	JJ	Degree=Pos	21	npadvmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	epic	epic	ADJ	JJ	Degree=Pos	22	amod	_	_
22	spaces	space	NOUN	NNS	Number=Plur	17	dobj	_	_
23	which	which	PRON	WDT	_	24	nsubj	_	_
24	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	22	relcl	_	_
25	not	not	PART	RB	Polarity=Neg	24	neg	_	_
26	Lindelof	Lindelof	PROPN	NNP	Number=Sing	24	attr	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = For the Lindelof case, an earlier paper has shown the usefulness of the countable neighbourhood property, CNP, and the Alster condition (where CNP means that the space is a P - space in any compactification and the Alster condition says that any cover of the space by $ G_delta $ sets has a countable subcover, provided each compact subset can be covered by a finite subset.)
1	For	for	ADP	IN	_	10	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	Lindelof	Lindelof	PROPN	NNP	Number=Sing	4	compound	_	_
4	case	case	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	earlier	early	ADJ	JJR	Degree=Cmp	8	amod	_	_
8	paper	paper	NOUN	NN	Number=Sing	10	nsubj	_	_
9	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	aux	_	_
10	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	usefulness	usefulness	NOUN	NN	Number=Sing	10	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
15	countable	countable	ADJ	JJ	Degree=Pos	17	amod	_	_
16	neighbourhood	neighbourhood	NOUN	NN	Number=Sing	17	compound	_	_
17	property	property	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	CNP	CNP	PROPN	NNP	Number=Sing	17	conj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	Alster	Alster	PROPN	NNP	Number=Sing	24	compound	_	_
24	condition	condition	NOUN	NN	Number=Sing	19	conj	_	_
25	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
26	where	where	SCONJ	WRB	_	28	advmod	_	_
27	CNP	CNP	PROPN	NNP	Number=Sing	28	nsubj	_	_
28	means	mean	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	relcl	_	_
29	that	that	SCONJ	IN	_	32	mark	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	space	space	NOUN	NN	Number=Sing	32	nsubj	_	_
32	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	28	ccomp	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
34	P	p	NOUN	NN	Number=Sing	36	compound	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	36	punct	_	_
36	space	space	NOUN	NN	Number=Sing	32	attr	_	_
37	in	in	ADP	IN	_	36	prep	_	_
38	any	any	DET	DT	_	39	det	_	_
39	compactification	compactification	NOUN	NN	Number=Sing	37	pobj	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
42	Alster	Alster	PROPN	NNP	Number=Sing	43	compound	_	_
43	condition	condition	NOUN	NN	Number=Sing	44	nsubj	_	_
44	says	say	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	ccomp	_	_
45	that	that	SCONJ	IN	_	54	mark	_	_
46	any	any	DET	DT	_	47	det	_	_
47	cover	cover	NOUN	NN	Number=Sing	54	nsubj	_	_
48	of	of	ADP	IN	_	47	prep	_	_
49	the	the	DET	DT	Definite=Def|PronType=Art	50	det	_	_
50	space	space	NOUN	NN	Number=Sing	48	pobj	_	_
51	by	by	ADP	IN	_	47	prep	_	_
52	$ G_delta $	$ g_delta $	SYM	$	_	53	poss	_	_
53	sets	set	NOUN	NNS	Number=Plur	51	pobj	_	_
54	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	44	ccomp	_	_
55	a	a	DET	DT	Definite=Ind|PronType=Art	57	det	_	_
56	countable	countable	ADJ	JJ	Degree=Pos	57	amod	_	_
57	subcover	subcover	NOUN	NN	Number=Sing	54	dobj	_	SpaceAfter=No
58	,	,	PUNCT	,	PunctType=Comm	54	punct	_	_
59	provided	provide	VERB	VBD	Tense=Past|VerbForm=Fin	44	prep	_	_
60	each	each	DET	DT	_	62	det	_	_
61	compact	compact	ADJ	JJ	Degree=Pos	62	amod	_	_
62	subset	subset	NOUN	NN	Number=Sing	65	nsubjpass	_	_
63	can	can	AUX	MD	VerbForm=Fin	65	aux	_	_
64	be	be	AUX	VB	VerbForm=Inf	65	auxpass	_	_
65	covered	cover	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	59	ccomp	_	_
66	by	by	ADP	IN	_	65	agent	_	_
67	a	a	DET	DT	Definite=Ind|PronType=Art	69	det	_	_
68	finite	finite	ADJ	JJ	Degree=Pos	69	amod	_	_
69	subset	subset	NOUN	NN	Number=Sing	66	pobj	_	SpaceAfter=No
70	.	.	PUNCT	.	PunctType=Peri	44	punct	_	SpaceAfter=No
71	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	44	punct	_	SpaceAfter=No

# sent_id = 4
# text = In this paper, we find further properties of Lindelof CNP spaces and of Alster spaces, including constructions that preserve these properties and conditions equivalent to these properties.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	find	find	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	further	further	ADJ	JJ	Degree=Pos	8	amod	_	_
8	properties	property	NOUN	NNS	Number=Plur	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Lindelof	Lindelof	PROPN	NNP	Number=Sing	11	compound	_	_
11	CNP	CNP	PROPN	NNP	Number=Sing	12	compound	_	_
12	spaces	space	NOUN	NNS	Number=Plur	9	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
14	of	of	ADP	IN	_	9	conj	_	_
15	Alster	Alster	PROPN	NNP	Number=Sing	16	compound	_	_
16	spaces	space	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	prep	_	_
19	constructions	construction	NOUN	NNS	Number=Plur	18	pobj	_	_
20	that	that	PRON	WDT	PronType=Rel	21	nsubj	_	_
21	preserve	preserve	VERB	VBP	Tense=Pres|VerbForm=Fin	19	relcl	_	_
22	these	these	DET	DT	Number=Plur|PronType=Dem	23	det	_	_
23	properties	property	NOUN	NNS	Number=Plur	21	dobj	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	conditions	condition	NOUN	NNS	Number=Plur	23	conj	_	_
26	equivalent	equivalent	ADJ	JJ	Degree=Pos	23	amod	_	_
27	to	to	ADP	IN	_	26	prep	_	_
28	these	these	DET	DT	Number=Plur|PronType=Dem	29	det	_	_
29	properties	property	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = We explore the outgrowths of such spaces and find several examples that answer open questions in our previous work.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	explore	explore	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	outgrowths	outgrowth	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	such	such	ADJ	JJ	Degree=Pos	7	amod	_	_
7	spaces	space	NOUN	NNS	Number=Plur	5	pobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
9	find	find	VERB	VB	VerbForm=Inf	2	conj	_	_
10	several	several	ADJ	JJ	Degree=Pos	11	amod	_	_
11	examples	example	NOUN	NNS	Number=Plur	9	dobj	_	_
12	that	that	PRON	WDT	PronType=Rel	13	nsubj	_	_
13	answer	answer	VERB	VBP	Tense=Pres|VerbForm=Fin	11	relcl	_	_
14	open	open	ADJ	JJ	Degree=Pos	15	amod	_	_
15	questions	question	NOUN	NNS	Number=Plur	13	dobj	_	_
16	in	in	ADP	IN	_	13	prep	_	_
17	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	19	poss	_	_
18	previous	previous	ADJ	JJ	Degree=Pos	19	amod	_	_
19	work	work	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 338
# sent_id = 1
# text = In a triangulated closed symmetric monoidal category, there are natural dualities induced by the internal Hom.
1	In	in	ADP	IN	_	10	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
3	triangulated	triangulate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
4	closed	closed	ADJ	JJ	Degree=Pos	7	amod	_	_
5	symmetric	symmetric	ADJ	JJ	Degree=Pos	7	amod	_	_
6	monoidal	monoidal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	category	category	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
9	there	there	PRON	EX	_	10	expl	_	_
10	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	natural	natural	ADJ	JJ	Degree=Pos	12	amod	_	_
12	dualities	duality	NOUN	NNS	Number=Plur	10	attr	_	_
13	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
14	by	by	ADP	IN	_	13	agent	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	internal	internal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	Hom	Hom	PROPN	NNP	Number=Sing	14	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = Given a monoidal exact functor $ f^* $ between two such categories and adjoint couples $ (f^*, f_*) $ , $ (f_*, f^clik) $ , we establish the commutative diagrams necessary for $ f^* $ and $ f_* $ to respect certain dualities, for a projection formula to hold between them (as duality preserving exact functors) and for classical base change and composition formulas to hold when such duality preserving functors are composed.
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
3	monoidal	monoidal	ADJ	JJ	Degree=Pos	5	amod	_	_
4	exact	exact	NOUN	NN	Number=Sing	5	amod	_	_
5	functor	functor	NOUN	NN	Number=Sing	1	pobj	_	_
6	$ f^* $	$ f^* $	SYM	$	_	16	nmod	_	_
7	between	between	ADP	IN	_	6	prep	_	_
8	two	two	NUM	CD	NumType=Card	10	nummod	_	_
9	such	such	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	adjoint	adjoint	NOUN	NN	Number=Sing	13	compound	_	_
13	couples	couple	NOUN	NNS	Number=Plur	10	conj	_	_
14	$ (f^*, f_*) $	$ (f^*, f_*) $	SYM	$	_	16	nmod	_	_
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	$ (f_*, f^clik) $	$ (f_*, f^clik) $	SYM	$	_	5	relcl	_	_
17	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	establish	establish	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	commutative	commutative	ADJ	JJ	Degree=Pos	22	amod	_	_
22	diagrams	diagram	NOUN	NNS	Number=Plur	19	dobj	_	_
23	necessary	necessary	ADJ	JJ	Degree=Pos	19	advcl	_	_
24	for	for	ADP	IN	_	23	prep	_	_
25	$ f^* $	$ f^* $	SYM	$	_	24	pobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	$ f_* $	$ f_* $	SYM	$	_	25	conj	_	_
28	to	to	PART	TO	_	29	aux	_	_
29	respect	respect	VERB	VB	VerbForm=Inf	19	xcomp	_	_
30	certain	certain	ADJ	JJ	Degree=Pos	31	amod	_	_
31	dualities	duality	NOUN	NNS	Number=Plur	29	dobj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
33	for	for	ADP	IN	_	29	prep	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
35	projection	projection	NOUN	NN	Number=Sing	36	compound	_	_
36	formula	formula	NOUN	NN	Number=Sing	33	pobj	_	_
37	to	to	PART	TO	_	38	aux	_	_
38	hold	hold	VERB	VB	VerbForm=Inf	36	relcl	_	_
39	between	between	ADP	IN	_	38	prep	_	_
40	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	39	pobj	_	_
41	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	33	punct	_	SpaceAfter=No
42	as	as	ADP	IN	_	29	prep	_	_
43	duality	duality	NOUN	NN	Number=Sing	44	nsubj	_	_
44	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	42	pcomp	_	_
45	exact	exact	ADJ	JJ	Degree=Pos	46	amod	_	_
46	functors	functor	NOUN	NNS	Number=Plur	44	dobj	_	SpaceAfter=No
47	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	44	punct	_	_
48	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
49	for	for	ADP	IN	_	19	prep	_	_
50	classical	classical	ADJ	JJ	Degree=Pos	52	amod	_	_
51	base	base	NOUN	NN	Number=Sing	52	compound	_	_
52	change	change	NOUN	NN	Number=Sing	49	pobj	_	_
53	and	and	CCONJ	CC	ConjType=Cmp	52	cc	_	_
54	composition	composition	NOUN	NN	Number=Sing	55	compound	_	_
55	formulas	formula	NOUN	NNS	Number=Plur	52	conj	_	_
56	to	to	PART	TO	_	57	aux	_	_
57	hold	hold	VERB	VB	VerbForm=Inf	52	relcl	_	_
58	when	when	SCONJ	WRB	_	64	advmod	_	_
59	such	such	ADJ	JJ	Degree=Pos	62	amod	_	_
60	duality	duality	NOUN	NN	Number=Sing	61	compound	_	_
61	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	62	amod	_	_
62	functors	functor	NOUN	NNS	Number=Plur	64	nsubjpass	_	_
63	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	64	auxpass	_	_
64	composed	compose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	57	advcl	_	SpaceAfter=No
65	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 3
# text = This framework allows us to define push - forwards for Witt groups, for example.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	framework	framework	NOUN	NN	Number=Sing	3	nsubj	_	_
3	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	define	define	VERB	VB	VerbForm=Inf	3	ccomp	_	_
7	push	push	NOUN	NN	Number=Sing	9	compound	_	_
8	-	-	PUNCT	:	_	9	punct	_	_
9	forwards	forward	NOUN	NNS	Number=Plur	6	dobj	_	_
10	for	for	ADP	IN	_	6	prep	_	_
11	Witt	Witt	PROPN	NNP	Number=Sing	12	compound	_	_
12	groups	group	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
14	for	for	ADP	IN	_	6	prep	_	_
15	example	example	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 339
# sent_id = 1
# text = We show that the (co)endomorphism algebra of a sufficiently separable ``fibre'' functor into $ Vect_k $ , for $ k $ a field of characteristic 0, has the structure of what we call a ``unital'' von Neumann core in $ Vect_k $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	28	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	7	punct	_	SpaceAfter=No
6	co)endomorphism	co)endomorphism	NOUN	NN	Number=Sing	7	compound	_	_
7	algebra	algebra	NOUN	NN	Number=Sing	28	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
10	sufficiently	sufficiently	ADV	RB	_	11	advmod	_	_
11	separable	separable	ADJ	JJ	Degree=Pos	16	amod	_	_
12	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	16	punct	_	SpaceAfter=No
13	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	16	punct	_	SpaceAfter=No
14	fibre	fibre	PROPN	NNP	Number=Sing	16	nmod	_	SpaceAfter=No
15	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	16	punct	_	_
16	functor	functor	NOUN	NN	Number=Sing	8	pobj	_	_
17	into	into	ADP	IN	_	7	prep	_	_
18	$ Vect_k $	$ vect_k $	SYM	$	_	17	pobj	_	_
19	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
20	for	for	ADP	IN	_	7	prep	_	_
21	$ k $	$ k $	SYM	$	_	23	quantmod	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
23	field	field	NOUN	NN	Number=Sing	20	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	characteristic	characteristic	ADJ	JJ	Degree=Pos	24	pobj	_	_
26	0	0	NUM	CD	NumType=Card	24	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
28	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	structure	structure	NOUN	NN	Number=Sing	28	dobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	what	what	PRON	WP	_	34	dobj	_	_
33	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	34	nsubj	_	_
34	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	31	pcomp	_	_
35	a	a	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
36	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	42	punct	_	SpaceAfter=No
37	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	42	punct	_	SpaceAfter=No
38	unital	unital	PROPN	NNP	Number=Sing	42	nmod	_	SpaceAfter=No
39	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	42	punct	_	_
40	von	von	PROPN	NNP	Number=Sing	41	compound	_	_
41	Neumann	Neumann	PROPN	NNP	Number=Sing	42	compound	_	_
42	core	core	NOUN	NN	Number=Sing	34	oprd	_	_
43	in	in	ADP	IN	_	42	prep	_	_
44	$ Vect_k $	$ vect_k $	SYM	$	_	43	pobj	_	_
45	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = For $ Vect_k $ , this particular notion of algebra is weaker than that of a Hopf algebra, although the corresponding concept in $ Set $ is again that of a group.
1	For	for	ADP	IN	_	9	prep	_	_
2	$ Vect_k $	$ vect_k $	SYM	$	_	1	pobj	_	_
3	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
5	particular	particular	ADJ	JJ	Degree=Pos	6	amod	_	_
6	notion	notion	NOUN	NN	Number=Sing	9	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	algebra	algebra	PROPN	NNP	Number=Sing	7	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	weaker	weak	ADJ	JJR	Degree=Cmp	9	acomp	_	_
11	than	than	ADP	IN	_	10	prep	_	_
12	that	that	PRON	DT	Number=Sing|PronType=Dem	11	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	Hopf	Hopf	PROPN	NNP	Number=Sing	16	compound	_	_
16	algebra	algebra	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
18	although	although	SCONJ	IN	_	24	mark	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	21	amod	_	_
21	concept	concept	NOUN	NN	Number=Sing	24	nsubj	_	_
22	in	in	ADP	IN	_	21	prep	_	_
23	$ Set $	$ set $	SYM	$	_	22	pobj	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	advcl	_	_
25	again	again	ADV	RB	_	24	advmod	_	_
26	that	that	PRON	DT	Number=Sing|PronType=Dem	24	attr	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
29	group	group	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 340
# sent_id = 1
# text = We adapt the work of Power to describe general, not - necessarily composable, not - necessarily commutative 2 - categorical pasting diagrams and their composable and commutative parts.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	adapt	adapt	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	work	work	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	Power	Power	PROPN	NNP	Number=Sing	5	pobj	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	describe	describe	VERB	VB	VerbForm=Inf	2	xcomp	_	_
9	general	general	ADJ	JJ	Degree=Pos	8	dobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	not	not	PART	RB	Polarity=Neg	13	neg	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	necessarily	necessarily	ADV	RB	_	14	advmod	_	_
14	composable	composable	ADJ	JJ	Degree=Pos	19	amod	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
16	not	not	PART	RB	Polarity=Neg	19	neg	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
18	necessarily	necessarily	ADV	RB	_	19	advmod	_	_
19	commutative	commutative	ADJ	JJ	Degree=Pos	2	conj	_	_
20	2	2	NUM	CD	NumType=Card	22	nummod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	categorical	categorical	ADJ	JJ	Degree=Pos	24	amod	_	_
23	pasting	pasting	NOUN	NN	Number=Sing	24	compound	_	_
24	diagrams	diagram	NOUN	NNS	Number=Plur	19	dobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	30	poss	_	_
27	composable	composable	ADJ	JJ	Degree=Pos	30	amod	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
29	commutative	commutative	ADJ	JJ	Degree=Pos	27	conj	_	_
30	parts	part	NOUN	NNS	Number=Plur	24	conj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We provide a deformation theory for pasting diagrams valued in the 2 - category of $ k $ - linear categories, paralleling that provided for diagrams of algebras by Gerstenhaber and Schack, proving the standard results.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	deformation	deformation	NOUN	NN	Number=Sing	5	compound	_	_
5	theory	theory	NOUN	NN	Number=Sing	2	dobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	pasting	paste	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	compound	_	_
8	diagrams	diagram	NOUN	NNS	Number=Plur	6	pobj	_	_
9	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
12	2	2	NUM	CD	NumType=Card	14	nummod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	$ k $	$ k $	SYM	$	_	18	quantmod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	linear	linear	ADJ	JJ	Degree=Pos	19	amod	_	_
19	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
21	paralleling	parallel	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
22	that	that	SCONJ	IN	_	23	nsubj	_	_
23	provided	provide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	ccomp	_	_
24	for	for	ADP	IN	_	23	prep	_	_
25	diagrams	diagram	NOUN	NNS	Number=Plur	24	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	algebras	algebra	NOUN	NNS	Number=Plur	26	pobj	_	_
28	by	by	ADP	IN	_	25	prep	_	_
29	Gerstenhaber	Gerstenhaber	PROPN	NNP	Number=Sing	28	pobj	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
31	Schack	Schack	PROPN	NNP	Number=Sing	29	conj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
33	proving	prove	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
35	standard	standard	ADJ	JJ	Degree=Pos	36	amod	_	_
36	results	result	NOUN	NNS	Number=Plur	33	dobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Along the way, the construction gives rise to a bicategorical analog of the homotopy $ G $ - algebras of Gerstenhaber and Voronov.
1	Along	along	ADP	IN	_	7	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	way	way	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	construction	construction	NOUN	NN	Number=Sing	7	nsubj	_	_
7	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	rise	rise	VERB	VB	VerbForm=Inf	7	dobj	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	bicategorical	bicategorical	ADJ	JJ	Degree=Pos	12	amod	_	_
12	analog	analog	NOUN	NN	Number=Sing	9	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	homotopy	homotopy	NOUN	NN	Number=Sing	13	pobj	_	_
16	$ G $	$ g $	SYM	$	_	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	algebras	algebra	NOUN	NNS	Number=Plur	7	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	Gerstenhaber	Gerstenhaber	PROPN	NNP	Number=Sing	19	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	Voronov	Voronov	PROPN	NNP	Number=Sing	20	conj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 341
# sent_id = 1
# text = Sifted colimits, important for algebraic theories, are "almost" just the combination of filtered colimits and reflexive coequalizers.
1	Sifted	sifted	ADJ	JJ	Degree=Pos	2	amod	_	_
2	colimits	colimit	NOUN	NNS	Number=Plur	9	nsubj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
4	important	important	ADJ	JJ	Degree=Pos	2	amod	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	algebraic	algebraic	ADJ	JJ	Degree=Pos	7	amod	_	_
7	theories	theory	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	9	punct	_	SpaceAfter=No
11	almost	almost	ADV	RB	_	15	advmod	_	SpaceAfter=No
12	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	15	punct	_	_
13	just	just	ADV	RB	_	15	advmod	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	combination	combination	NOUN	NN	Number=Sing	9	attr	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	filtered	filter	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
18	colimits	colimit	NOUN	NNS	Number=Plur	16	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
20	reflexive	reflexive	VERB	VB	VerbForm=Inf	15	conj	_	_
21	coequalizers	coequalizer	NOUN	NNS	Number=Plur	20	dobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 2
# text = For example, given a finitely cocomplete category $ cal A $ , then a functor with domain $ cal A $ preserves sifted colimits if and only if it preserves filtered colimits and reflexive coequalizers.
1	For	for	ADP	IN	_	17	prep	_	_
2	example	example	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
4	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
6	finitely	finitely	ADV	RB	_	7	advmod	_	_
7	cocomplete	cocomplete	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
9	$ cal A $	$ cal a $	SYM	$	_	8	appos	_	_
10	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
11	then	then	ADV	RB	PronType=Dem	13	advmod	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	functor	functor	NOUN	NN	Number=Sing	8	appos	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	domain	domain	NOUN	NN	Number=Sing	14	pobj	_	_
16	$ cal A $	$ cal a $	SYM	$	_	4	pcomp	_	_
17	preserves	preserve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
18	sifted	sift	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
19	colimits	colimit	NOUN	NNS	Number=Plur	17	dobj	_	_
20	if	if	SCONJ	IN	_	17	dep	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	only	only	ADV	RB	_	25	advmod	_	_
23	if	if	SCONJ	IN	_	25	mark	_	_
24	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	25	nsubj	_	_
25	preserves	preserves	AUX	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	aux	_	_
26	filtered	filter	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	conj	_	_
27	colimits	colimit	NOUN	NNS	Number=Plur	26	dobj	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
29	reflexive	reflexive	VERB	VB	VerbForm=Inf	26	conj	_	_
30	coequalizers	coequalizer	NOUN	NNS	Number=Plur	29	dobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	26	punct	_	SpaceAfter=No

# sent_id = 3
# text = But for general categories $ cal A $ that statement is not true: we provide a counter - example.
1	But	but	CCONJ	CC	ConjType=Cmp	8	cc	_	_
2	for	for	ADP	IN	_	8	prep	_	_
3	general	general	ADJ	JJ	Degree=Pos	4	amod	_	_
4	categories	category	NOUN	NNS	Number=Plur	2	pobj	_	_
5	$ cal A $	$ cal a $	SYM	$	_	2	pobj	_	_
6	that	that	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
7	statement	statement	NOUN	NN	Number=Sing	8	nsubj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
9	not	not	PART	RB	Polarity=Neg	8	neg	_	_
10	true	true	ADJ	JJ	Degree=Pos	8	acomp	_	SpaceAfter=No
11	:	:	PUNCT	:	_	13	punct	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	counter	counter	NOUN	NN	Number=Sing	17	compound	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	example	example	NOUN	NN	Number=Sing	13	dobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# doc_id = 342
# sent_id = 1
# text = The notion of a subtractive category recently introduced by the author, is a pointed categorical counterpart of the notion of a subtractive variety of universal algebras in the sense of Ursini (recall that a variety is subtractive if its theory contains a constant 0 and a binary term $ s $ satisfying $ s(x, x)=0 $ and $ s(x, 0)=x $ ).
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	notion	notion	NOUN	NN	Number=Sing	13	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	subtractive	subtractive	ADJ	JJ	Degree=Pos	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	3	pobj	_	_
7	recently	recently	ADV	RB	_	8	advmod	_	_
8	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
9	by	by	ADP	IN	_	8	agent	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	author	author	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	pointed	pointed	ADJ	JJ	Degree=Pos	17	amod	_	_
16	categorical	categorical	ADJ	JJ	Degree=Pos	17	amod	_	_
17	counterpart	counterpart	NOUN	NN	Number=Sing	13	attr	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	notion	notion	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
23	subtractive	subtractive	ADJ	JJ	Degree=Pos	24	amod	_	_
24	variety	variety	NOUN	NN	Number=Sing	21	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	universal	universal	ADJ	JJ	Degree=Pos	27	amod	_	_
27	algebras	algebra	NOUN	NNS	Number=Plur	25	pobj	_	_
28	in	in	ADP	IN	_	13	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	sense	sense	NOUN	NN	Number=Sing	28	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	Ursini	Ursini	PROPN	NNP	Number=Sing	31	pobj	_	_
33	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	34	punct	_	SpaceAfter=No
34	recall	recall	NOUN	NN	Number=Sing	13	dep	_	_
35	that	that	SCONJ	IN	_	38	mark	_	_
36	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
37	variety	variety	NOUN	NN	Number=Sing	38	nsubj	_	_
38	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	34	ccomp	_	_
39	subtractive	subtractive	ADJ	JJ	Degree=Pos	38	acomp	_	_
40	if	if	SCONJ	IN	_	43	mark	_	_
41	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	42	poss	_	_
42	theory	theory	NOUN	NN	Number=Sing	43	nsubj	_	_
43	contains	contain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	38	advcl	_	_
44	a	a	DET	DT	Definite=Ind|PronType=Art	46	det	_	_
45	constant	constant	ADJ	JJ	Degree=Pos	46	amod	_	_
46	0	0	NUM	CD	NumType=Card	43	dobj	_	_
47	and	and	CCONJ	CC	ConjType=Cmp	46	cc	_	_
48	a	a	DET	DT	Definite=Ind|PronType=Art	50	det	_	_
49	binary	binary	ADJ	JJ	Degree=Pos	50	amod	_	_
50	term	term	NOUN	NN	Number=Sing	46	conj	_	_
51	$ s $	$ s $	SYM	$	_	50	appos	_	_
52	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	43	advcl	_	_
53	$ s(x, x)=0 $	$ s(x, x)=0 $	SYM	$	_	52	dobj	_	_
54	and	and	CCONJ	CC	ConjType=Cmp	53	cc	_	_
55	$ s(x, 0)=x $	$ s(x, 0)=x $	SYM	$	_	52	npadvmod	_	_
56	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	52	punct	_	SpaceAfter=No
57	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 2
# text = Let us call a pointed regular category $ mathbb{C} $ normal if every regular epimorphism in $ mathbb{C} $ is a normal epimorphism.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	call	call	VERB	VB	VerbForm=Inf	1	ccomp	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	pointed	point	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
6	regular	regular	ADJ	JJ	Degree=Pos	7	amod	_	_
7	category	category	NOUN	NN	Number=Sing	3	dobj	_	_

1	$ mathbb{C} $	$ mathbb{c} $	SYM	$	_	9	dep	_	_
2	normal	normal	ADJ	JJ	Degree=Pos	1	amod	_	_
3	if	if	SCONJ	IN	_	6	mark	_	_
4	every	every	DET	DT	_	6	det	_	_
5	regular	regular	ADJ	JJ	Degree=Pos	6	amod	_	_
6	epimorphism	epimorphism	NOUN	NN	Number=Sing	9	nsubj	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	$ mathbb{C} $	$ mathbb{c} $	SYM	$	_	7	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	normal	normal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	epimorphism	epimorphism	NOUN	NN	Number=Sing	9	attr	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 3
# text = It is well known that any homological category in the sense of Borceux and Bourn is both normal and subtractive.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	well	well	ADV	RB	Degree=Pos	4	advmod	_	_
4	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acomp	_	_
5	that	that	SCONJ	IN	_	16	mark	_	_
6	any	any	DET	DT	_	8	det	_	_
7	homological	homological	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	16	nsubj	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	sense	sense	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	Borceux	Borceux	PROPN	NNP	Number=Sing	12	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	Bourn	Bourn	PROPN	NNP	Number=Sing	13	conj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
17	both	both	PRON	DT	_	18	preconj	_	_
18	normal	normal	ADJ	JJ	Degree=Pos	16	acomp	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	subtractive	subtractive	ADJ	JJ	Degree=Pos	18	conj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We prove that in any subtractive normal category, the upper and lower $ 3times 3 $ lemmas hold true, which generalizes a similar result for homological categories due to Bourn (note that the middle $ 3times 3 $ lemma holds true if and only if the category is homological).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	16	mark	_	_
4	in	in	ADP	IN	_	16	prep	_	_
5	any	any	DET	DT	_	8	det	_	_
6	subtractive	subtractive	ADJ	JJ	Degree=Pos	8	amod	_	_
7	normal	normal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
11	upper	upper	ADJ	JJ	Degree=Pos	15	amod	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	lower	low	ADJ	JJR	Degree=Cmp	11	conj	_	_
14	$ 3times 3 $	$ 3times 3 $	SYM	$	_	15	neg	_	_
15	lemmas	lemmas	X	FW	Foreign=Yes	16	nsubj	_	_
16	hold	hold	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
17	true	true	ADJ	JJ	Degree=Pos	16	prt	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
19	which	which	PRON	WDT	_	20	nsubj	_	_
20	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	advcl	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	similar	similar	ADJ	JJ	Degree=Pos	23	amod	_	_
23	result	result	NOUN	NN	Number=Sing	20	dobj	_	_
24	for	for	ADP	IN	_	23	prep	_	_
25	homological	homological	ADJ	JJ	Degree=Pos	26	amod	_	_
26	categories	category	NOUN	NNS	Number=Plur	24	pobj	_	_
27	due	due	ADJ	JJ	Degree=Pos	26	amod	_	_
28	to	to	ADP	IN	_	27	prep	_	_
29	Bourn	Bourn	PROPN	NNP	Number=Sing	27	pobj	_	_
30	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	31	punct	_	SpaceAfter=No
31	note	note	VERB	VBP	Tense=Pres|VerbForm=Fin	20	parataxis	_	_
32	that	that	SCONJ	IN	_	37	mark	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
34	middle	middle	ADJ	JJ	Degree=Pos	36	amod	_	_
35	$ 3times 3 $	$ 3times 3 $	SYM	$	_	36	nummod	_	_
36	lemma	lemma	NOUN	NN	Number=Sing	37	nsubj	_	_
37	holds	hold	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	31	ccomp	_	_
38	true	true	ADJ	JJ	Degree=Pos	37	oprd	_	_
39	if	if	SCONJ	IN	_	45	mark	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	45	cc	_	_
41	only	only	ADV	RB	_	45	advmod	_	_
42	if	if	SCONJ	IN	_	45	mark	_	_
43	the	the	DET	DT	Definite=Def|PronType=Art	44	det	_	_
44	category	category	NOUN	NN	Number=Sing	45	nsubj	_	_
45	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	37	advcl	_	_
46	homological	homological	ADJ	JJ	Degree=Pos	45	acomp	_	SpaceAfter=No
47	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	31	punct	_	SpaceAfter=No
48	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = The technique of proof is new: the pointed subobject functor $ mathcal{S}=mathrm{Sub}( - ):mathbb{C}rightarrowmathbf{Set}_* $ turns out to have suitable preservation/reflection properties which allow us to reduce the proofs of these two diagram lemmas to the standard diagram - chasing arguments in $ mathbf{Set}_* $ (alternatively, we could use the more advanced embedding theorem for regular categories due to M.~Barr).
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	technique	technique	NOUN	NN	Number=Sing	5	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	proof	proof	NOUN	NN	Number=Sing	3	pobj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
6	new	new	ADJ	JJ	Degree=Pos	5	acomp	_	SpaceAfter=No
7	:	:	PUNCT	:	_	5	punct	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
9	pointed	pointed	ADJ	JJ	Degree=Pos	10	amod	_	_
10	subobject	subobject	NOUN	NN	Number=Sing	11	compound	_	_
11	functor	functor	PROPN	NNP	Number=Sing	13	nsubj	_	_
12	$ mathcal{S}=mathrm{Sub}( - ):mathbb{C}rightarrowmathbf{Set}_* $	$ mathcal{s}=mathrm{sub}( - ):mathbb{c}rightarrowmathbf{set}_* $	SYM	$	_	13	nsubj	_	_
13	turns	turn	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	48	ccomp	_	_
14	out	out	ADP	RP	_	13	prt	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	have	have	VERB	VB	VerbForm=Inf	13	xcomp	_	_
17	suitable	suitable	ADJ	JJ	Degree=Pos	21	amod	_	_
18	preservation	preservation	NOUN	NN	Number=Sing	20	nmod	_	SpaceAfter=No
19	/	/	SYM	SYM	_	20	punct	_	SpaceAfter=No
20	reflection	reflection	NOUN	NN	Number=Sing	21	compound	_	_
21	properties	property	NOUN	NNS	Number=Plur	16	dobj	_	_
22	which	which	PRON	WDT	_	23	nsubj	_	_
23	allow	allow	VERB	VBP	Tense=Pres|VerbForm=Fin	21	relcl	_	_
24	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	26	nsubj	_	_
25	to	to	PART	TO	_	26	aux	_	_
26	reduce	reduce	VERB	VB	VerbForm=Inf	23	ccomp	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	proofs	proof	NOUN	NNS	Number=Plur	26	dobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	these	these	DET	DT	Number=Plur|PronType=Dem	33	det	_	_
31	two	two	NUM	CD	NumType=Card	32	nummod	_	_
32	diagram	diagram	NOUN	NN	Number=Sing	33	compound	_	_
33	lemmas	lemma	NOUN	NNS	Number=Plur	29	pobj	_	_
34	to	to	ADP	IN	_	28	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
36	standard	standard	ADJ	JJ	Degree=Pos	40	amod	_	_
37	diagram	diagram	NOUN	NN	Number=Sing	39	npadvmod	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	chasing	chase	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	40	amod	_	_
40	arguments	argument	NOUN	NNS	Number=Plur	34	pobj	_	_
41	in	in	ADP	IN	_	40	prep	_	_
42	$ mathbf{Set}_* $	$ mathbf{set}_* $	SYM	$	_	41	pobj	_	_
43	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	48	punct	_	SpaceAfter=No
44	alternatively	alternatively	ADV	RB	_	48	advmod	_	SpaceAfter=No
45	,	,	PUNCT	,	PunctType=Comm	48	punct	_	_
46	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	48	nsubj	_	_
47	could	could	AUX	MD	VerbForm=Fin	48	aux	_	_
48	use	use	VERB	VB	VerbForm=Inf	0	ROOT	_	_
49	the	the	PRON	DT	Definite=Def|PronType=Art	51	advmod	_	_
50	more	more	ADV	RBR	Degree=Cmp	51	advmod	_	_
51	advanced	advanced	ADJ	JJ	Degree=Pos	52	amod	_	_
52	embedding	embed	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	53	amod	_	_
53	theorem	theorem	NOUN	NN	Number=Sing	48	dobj	_	_
54	for	for	ADP	IN	_	53	prep	_	_
55	regular	regular	ADJ	JJ	Degree=Pos	56	amod	_	_
56	categories	category	NOUN	NNS	Number=Plur	54	pobj	_	_
57	due	due	ADJ	JJ	Degree=Pos	48	prep	_	_
58	to	to	ADP	IN	_	57	pcomp	_	_
59	M.~Barr	M.~Barr	PROPN	NNP	Number=Sing	57	pobj	_	SpaceAfter=No
60	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	48	punct	_	SpaceAfter=No
61	.	.	PUNCT	.	PunctType=Peri	48	punct	_	SpaceAfter=No

# sent_id = 6
# text = The key property of $ mathcal{S} $ , which allows to obtain these diagram lemmas, is the preservation of subtractive spans.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	key	key	ADJ	JJ	Degree=Pos	3	amod	_	_
3	property	property	NOUN	NN	Number=Sing	15	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	$ mathcal{S} $	$ mathcal{s} $	SYM	$	_	4	pobj	_	_
6	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
7	which	which	PRON	WDT	_	8	nsubj	_	_
8	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	relcl	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	obtain	obtain	VERB	VB	VerbForm=Inf	8	xcomp	_	_
11	these	these	DET	DT	Number=Plur|PronType=Dem	13	det	_	_
12	diagram	diagram	NOUN	NN	Number=Sing	13	compound	_	_
13	lemmas	lemma	NOUN	NNS	Number=Plur	10	dobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	preservation	preservation	NOUN	NN	Number=Sing	15	attr	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	subtractive	subtractive	ADJ	JJ	Degree=Pos	20	amod	_	_
20	spans	span	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 7
# text = Subtractivity of a span provides a weaker version of the rule of subtraction—one of the elementary rules for chasing diagrams in abelian categories, in the sense of Mac Lane.
1	Subtractivity	subtractivity	NOUN	NN	Number=Sing	5	nsubj	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	span	span	NOUN	NN	Number=Sing	2	pobj	_	_
5	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	weaker	weak	ADJ	JJR	Degree=Cmp	8	amod	_	_
8	version	version	NOUN	NN	Number=Sing	5	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	rule	rule	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	subtraction	subtraction	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
14	—	—	PUNCT	:	_	8	punct	_	SpaceAfter=No
15	one	one	NUM	CD	NumType=Card	8	appos	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	elementary	elementary	ADJ	JJ	Degree=Pos	19	amod	_	_
19	rules	rule	NOUN	NNS	Number=Plur	16	pobj	_	_
20	for	for	ADP	IN	_	19	prep	_	_
21	chasing	chase	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	pcomp	_	_
22	diagrams	diagram	NOUN	NNS	Number=Plur	21	dobj	_	_
23	in	in	ADP	IN	_	22	prep	_	_
24	abelian	abelian	ADJ	JJ	Degree=Pos	25	amod	_	_
25	categories	category	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
27	in	in	ADP	IN	_	5	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	sense	sense	NOUN	NN	Number=Sing	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	Mac	Mac	PROPN	NNP	Number=Sing	32	compound	_	_
32	Lane	Lane	PROPN	NNP	Number=Sing	30	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 8
# text = A pointed regular category is subtractive if and only if every span in it is subtractive, and moreover, the functor $ mathcal{S} $ not only preserves but also reflects subtractive spans.
1	A	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
2	pointed	pointed	ADJ	JJ	Degree=Pos	4	amod	_	_
3	regular	regular	ADJ	JJ	Degree=Pos	4	amod	_	_
4	category	category	NOUN	NN	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	subtractive	subtractive	ADJ	JJ	Degree=Pos	5	acomp	_	_
7	if	if	SCONJ	IN	_	6	prep	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	only	only	ADV	RB	_	15	advmod	_	_
10	if	if	SCONJ	IN	_	15	mark	_	_
11	every	every	DET	DT	_	12	det	_	_
12	span	span	NOUN	NN	Number=Sing	15	nsubj	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	13	pobj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	advcl	_	_
16	subtractive	subtractive	ADJ	JJ	Degree=Pos	15	acomp	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
19	moreover	moreover	ADV	RB	_	26	advmod	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	functor	functor	NOUN	NN	Number=Sing	26	nsubj	_	_
23	$ mathcal{S} $	$ mathcal{s} $	SYM	$	_	26	quantmod	_	_
24	not	not	PART	RB	Polarity=Neg	26	preconj	_	_
25	only	only	ADV	RB	_	24	advmod	_	_
26	preserves	preserve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	conj	_	_
27	but	but	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	also	also	ADV	RB	_	29	advmod	_	_
29	reflects	reflect	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	conj	_	_
30	subtractive	subtractive	ADJ	JJ	Degree=Pos	31	amod	_	_
31	spans	span	NOUN	NNS	Number=Plur	29	dobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	26	punct	_	SpaceAfter=No

# sent_id = 9
# text = Thus, subtractivity seems to be exactly what we need in order to prove the upper/lower $ 3times 3 $ lemmas in a normal category.
1	Thus	thus	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	subtractivity	subtractivity	NOUN	NN	Number=Sing	4	nsubj	_	_
4	seems	seem	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	be	be	AUX	VB	VerbForm=Inf	4	xcomp	_	_
7	exactly	exactly	ADV	RB	_	8	advmod	_	_
8	what	what	PRON	WP	_	10	dobj	_	_
9	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
10	need	need	VERB	VBP	Tense=Pres|VerbForm=Fin	6	ccomp	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	order	order	NOUN	NN	Number=Sing	11	pobj	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	prove	prove	VERB	VB	VerbForm=Inf	12	acl	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
16	upper	upper	ADJ	JJ	Degree=Pos	18	advmod	_	SpaceAfter=No
17	/	/	SYM	SYM	_	18	punct	_	SpaceAfter=No
18	lower	low	ADJ	JJR	Degree=Cmp	20	amod	_	_
19	$ 3times 3 $	$ 3times 3 $	SYM	$	_	20	nummod	_	_
20	lemmas	lemma	NOUN	NNS	Number=Plur	14	dobj	_	_
21	in	in	ADP	IN	_	14	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
23	normal	normal	ADJ	JJ	Degree=Pos	24	amod	_	_
24	category	category	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 10
# text = Indeed, we show that a normal category is subtractive if and only if these $ 3times 3 $ lemmas hold true in it.
1	Indeed	indeed	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	9	mark	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	normal	normal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	9	nsubj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
10	subtractive	subtractive	ADJ	JJ	Degree=Pos	9	acomp	_	_
11	if	if	SCONJ	IN	_	9	prep	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	only	only	ADV	RB	_	18	advmod	_	_
14	if	if	SCONJ	IN	_	18	mark	_	_
15	these	these	DET	DT	Number=Plur|PronType=Dem	17	det	_	_
16	$ 3times 3 $	$ 3times 3 $	SYM	$	_	17	nummod	_	_
17	lemmas	lemmas	X	FW	Foreign=Yes	18	nsubj	_	_
18	hold	hold	VERB	VBP	Tense=Pres|VerbForm=Fin	9	advcl	_	_
19	true	true	ADJ	JJ	Degree=Pos	18	oprd	_	_
20	in	in	ADP	IN	_	18	prep	_	_
21	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	20	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 11
# text = Moreover, we show that for any pointed regular category $ mathbb{C} $ (not necessarily a normal one), we have: $ mathbb{C} $ is subtractive if and only if the lower $ 3times 3 $ lemma holds true in $ mathbb{C} $ .
1	Moreover	moreover	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	21	mark	_	_
6	for	for	ADP	IN	_	21	prep	_	_
7	any	any	DET	DT	_	10	det	_	_
8	pointed	point	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
9	regular	regular	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	11	nmod	_	_
11	$ mathbb{C} $	$ mathbb{c} $	SYM	$	_	6	pobj	_	_
12	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	11	punct	_	SpaceAfter=No
13	not	not	PART	RB	Polarity=Neg	14	neg	_	_
14	necessarily	necessarily	ADV	RB	_	17	advmod	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	normal	normal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	one	one	NUM	CD	NumType=Card	11	appos	_	SpaceAfter=No
18	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	11	punct	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
20	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	21	nsubj	_	_
21	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	ccomp	_	SpaceAfter=No
22	:	:	PUNCT	:	_	21	punct	_	_
23	$ mathbb{C} $	$ mathbb{c} $	SYM	$	_	24	nsubj	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
25	subtractive	subtractive	ADJ	JJ	Degree=Pos	24	acomp	_	_
26	if	if	SCONJ	IN	_	24	dep	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	only	only	ADV	RB	_	34	advmod	_	_
29	if	if	SCONJ	IN	_	34	mark	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
31	lower	low	ADJ	JJR	Degree=Cmp	32	amod	_	_
32	$ 3times 3 $	$ 3times 3 $	SYM	$	_	33	nummod	_	_
33	lemma	lemma	NOUN	NN	Number=Sing	34	nsubj	_	_
34	holds	hold	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	advcl	_	_
35	true	true	ADJ	JJ	Degree=Pos	34	oprd	_	_
36	in	in	ADP	IN	_	34	prep	_	_
37	$ mathbb{C} $	$ mathbb{c} $	SYM	$	_	36	pobj	_	_
38	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 343
# sent_id = 1
# text = The metric jets, introduced here, generalize the jets (at order one) of Charles Ehresmann.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	metric	metric	ADJ	JJ	Degree=Pos	3	amod	_	_
3	jets	jet	NOUN	NNS	Number=Plur	8	nsubj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	acl	_	_
6	here	here	ADV	RB	PronType=Dem	5	advmod	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
8	generalize	generalize	VERB	VB	VerbForm=Inf	0	ROOT	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	jets	jet	NOUN	NNS	Number=Plur	8	dobj	_	_
11	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	8	punct	_	SpaceAfter=No
12	at	at	ADP	IN	_	8	prep	_	_
13	order	order	NOUN	NN	Number=Sing	12	pobj	_	_
14	one	one	NUM	CD	NumType=Card	13	nummod	_	SpaceAfter=No
15	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	13	punct	_	_
16	of	of	ADP	IN	_	13	prep	_	_
17	Charles	Charles	PROPN	NNP	Number=Sing	18	compound	_	_
18	Ehresmann	Ehresmann	PROPN	NNP	Number=Sing	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = In short, for a ``good'' map $ f $ (said to be ``tangentiable'' at $ a $ ) between metric spaces, we define its metric jet tangent at a (composed of all the maps which are locally lipschitzian at $ a $ and tangent to $ f $ at $ a $ ) called the ``tangential'' of $ f $ at $ a $ , and denoted $ Tf_a $ .
1	In	in	ADP	IN	_	13	prep	_	_
2	short	short	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
4	for	for	ADP	IN	_	13	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
6	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	10	punct	_	SpaceAfter=No
7	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	10	punct	_	SpaceAfter=No
8	good	good	ADJ	JJ	Degree=Pos	10	amod	_	SpaceAfter=No
9	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	10	punct	_	_
10	map	map	NOUN	NN	Number=Sing	4	pobj	_	_
11	$ f $	$ f $	SYM	$	_	10	nummod	_	_
12	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	13	punct	_	SpaceAfter=No
13	said	say	VERB	VBD	Tense=Past|VerbForm=Fin	28	advcl	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	be	be	AUX	VB	VerbForm=Inf	13	xcomp	_	_
16	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	18	punct	_	SpaceAfter=No
17	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	18	punct	_	SpaceAfter=No
18	tangentiable	tangentiable	NOUN	NN	Number=Sing	15	attr	_	SpaceAfter=No
19	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	18	punct	_	_
20	at	at	ADP	IN	_	18	prep	_	_
21	$ a $	$ a $	SYM	$	_	20	pobj	_	_
22	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	18	punct	_	_
23	between	between	ADP	IN	_	18	prep	_	_
24	metric	metric	ADJ	JJ	Degree=Pos	25	amod	_	_
25	spaces	space	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
27	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	28	nsubj	_	_
28	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
29	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	32	poss	_	_
30	metric	metric	ADJ	JJ	Degree=Pos	32	amod	_	_
31	jet	jet	NOUN	NN	Number=Sing	32	compound	_	_
32	tangent	tangent	NOUN	NN	Number=Sing	28	dobj	_	_
33	at	at	ADP	IN	_	28	prep	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
35	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	36	punct	_	SpaceAfter=No
36	composed	compose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	all	all	DET	PDT	_	40	predet	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
40	maps	map	NOUN	NNS	Number=Plur	37	pobj	_	_
41	which	which	PRON	WDT	_	42	nsubj	_	_
42	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	40	relcl	_	_
43	locally	locally	ADV	RB	_	44	advmod	_	_
44	lipschitzian	lipschitzian	ADJ	JJ	Degree=Pos	42	acomp	_	_
45	at	at	ADP	IN	_	44	prep	_	_
46	$ a $	$ a $	SYM	$	_	45	pobj	_	_
47	and	and	CCONJ	CC	ConjType=Cmp	46	cc	_	_
48	tangent	tangent	NOUN	NN	Number=Sing	46	conj	_	_
49	to	to	ADP	IN	_	42	prep	_	_
50	$ f $	$ f $	SYM	$	_	49	pobj	_	_
51	at	at	ADP	IN	_	42	prep	_	_
52	$ a $	$ a $	SYM	$	_	51	pobj	_	_
53	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	36	punct	_	_
54	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	conj	_	_
55	the	the	DET	DT	Definite=Def|PronType=Art	58	det	_	_
56	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	58	punct	_	SpaceAfter=No
57	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	58	punct	_	SpaceAfter=No
58	tangential	tangential	NOUN	NN	Number=Sing	54	oprd	_	SpaceAfter=No
59	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	58	punct	_	_
60	of	of	ADP	IN	_	58	prep	_	_
61	$ f $	$ f $	SYM	$	_	60	pobj	_	_
62	at	at	ADP	IN	_	54	prep	_	_
63	$ a $	$ a $	SYM	$	_	62	pobj	_	_
64	,	,	PUNCT	,	PunctType=Comm	54	punct	_	_
65	and	and	CCONJ	CC	ConjType=Cmp	54	cc	_	_
66	denoted	denote	VERB	VBD	Tense=Past|VerbForm=Fin	54	conj	_	_
67	$ Tf_a $	$ tf_a $	SYM	$	_	66	dobj	_	_
68	.	.	PUNCT	.	PunctType=Peri	28	punct	_	SpaceAfter=No

# sent_id = 3
# text = So, in this metric context, we define a ``new differentiability'' (called ``tangentiability'') which extends the classical differentiability (while preserving most of its properties) to new maps, traditionally pathologic.
1	So	so	ADV	RB	_	9	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
3	in	in	ADP	IN	_	9	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
5	metric	metric	ADJ	JJ	Degree=Pos	6	amod	_	_
6	context	context	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
11	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	14	punct	_	SpaceAfter=No
12	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	14	punct	_	SpaceAfter=No
13	new	new	ADJ	JJ	Degree=Pos	14	amod	_	_
14	differentiability	differentiability	NOUN	NN	Number=Sing	9	dobj	_	SpaceAfter=No
15	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	14	punct	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
17	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	acl	_	_
18	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	17	punct	_	SpaceAfter=No
19	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	17	punct	_	SpaceAfter=No
20	tangentiability	tangentiability	NOUN	NN	Number=Sing	17	oprd	_	SpaceAfter=No
21	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	20	punct	_	SpaceAfter=No
22	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	14	punct	_	_
23	which	which	PRON	WDT	_	24	nsubj	_	_
24	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	classical	classical	ADJ	JJ	Degree=Pos	27	amod	_	_
27	differentiability	differentiability	NOUN	NN	Number=Sing	24	dobj	_	_
28	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
29	while	while	SCONJ	IN	_	30	mark	_	_
30	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	24	advcl	_	_
31	most	most	ADJ	JJS	Degree=Sup	30	dobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	34	poss	_	_
34	properties	property	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
35	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	30	punct	_	_
36	to	to	ADP	IN	_	30	prep	_	_
37	new	new	ADJ	JJ	Degree=Pos	38	amod	_	_
38	maps	map	NOUN	NNS	Number=Plur	36	pobj	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	38	punct	_	_
40	traditionally	traditionally	ADV	RB	_	41	advmod	_	_
41	pathologic	pathologic	ADJ	JJ	Degree=Pos	38	appos	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 344
# sent_id = 1
# text = Protomodularity, in the pointed case, is equivalent to the Split Short Five Lemma.
1	Protomodularity	protomodularity	NOUN	NN	Number=Sing	8	nsubj	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
3	in	in	ADP	IN	_	8	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	pointed	pointed	ADJ	JJ	Degree=Pos	6	amod	_	_
6	case	case	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	equivalent	equivalent	ADJ	JJ	Degree=Pos	8	acomp	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
12	Split	Split	PROPN	NNP	Number=Sing	15	compound	_	_
13	Short	Short	PROPN	NNP	Number=Sing	14	compound	_	_
14	Five	Five	PROPN	NNP	Number=Sing	15	compound	_	_
15	Lemma	Lemma	PROPN	NNP	Number=Sing	10	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = It is also well known that this condition implies that every internal category is in fact an internal groupoid.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	also	also	ADV	RB	_	2	advmod	_	_
4	well	well	ADV	RB	Degree=Pos	5	advmod	_	_
5	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acomp	_	_
6	that	that	SCONJ	IN	_	9	mark	_	_
7	this	this	DET	DT	Number=Sing|PronType=Dem	8	det	_	_
8	condition	condition	NOUN	NN	Number=Sing	9	nsubj	_	_
9	implies	imply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
10	that	that	SCONJ	IN	_	14	mark	_	_
11	every	every	DET	DT	_	13	det	_	_
12	internal	internal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	ccomp	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	fact	fact	NOUN	NN	Number=Sing	15	pobj	_	_
17	an	an	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	internal	internal	ADJ	JJ	Degree=Pos	19	amod	_	_
19	groupoid	groupoid	NOUN	NN	Number=Sing	14	attr	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this work, this is condition (ii) and we introduce two other conditions denoted (i) and (iii).
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	work	work	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	this	this	PRON	DT	Number=Sing|PronType=Dem	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	condition	condition	NOUN	NN	Number=Sing	6	attr	_	_
8	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	9	punct	_	SpaceAfter=No
9	ii	ii	PROPN	NNP	Number=Sing	7	appos	_	SpaceAfter=No
10	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	7	punct	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	6	conj	_	_
14	two	two	NUM	CD	NumType=Card	16	nummod	_	_
15	other	other	ADJ	JJ	Degree=Pos	16	amod	_	_
16	conditions	condition	NOUN	NNS	Number=Plur	13	dobj	_	_
17	denoted	denote	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	acl	_	_
18	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	17	punct	_	SpaceAfter=No
19	i	i	NOUN	NN	Number=Sing	17	npadvmod	_	SpaceAfter=No
20	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	19	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
22	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	23	punct	_	SpaceAfter=No
23	iii	iii	PROPN	NNP	Number=Sing	17	conj	_	SpaceAfter=No
24	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	17	punct	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 4
# text = Under condition (i), every multiplicative graph is an internal category.
1	Under	under	ADP	IN	_	10	prep	_	_
2	condition	condition	NOUN	NN	Number=Sing	1	pobj	_	_
3	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	2	punct	_	SpaceAfter=No
4	i	i	NOUN	NN	Number=Sing	2	appos	_	SpaceAfter=No
5	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	2	punct	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
7	every	every	DET	DT	_	9	det	_	_
8	multiplicative	multiplicative	ADJ	JJ	Degree=Pos	9	amod	_	_
9	graph	graph	NOUN	NN	Number=Sing	10	nsubj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	internal	internal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	10	attr	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 5
# text = Under condition (iii), every star - multiplicative graph can be extended (uniquely) to a multiplicative graph, a problem raised by Janelidze in the semiabelian context.
1	Under	under	ADP	IN	_	14	prep	_	_
2	condition	condition	NOUN	NN	Number=Sing	1	pobj	_	_
3	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	2	punct	_	SpaceAfter=No
4	iii	iii	PROPN	NNP	Number=Sing	2	appos	_	SpaceAfter=No
5	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	2	punct	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
7	every	every	DET	DT	_	11	det	_	_
8	star	star	NOUN	NN	Number=Sing	10	npadvmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	multiplicative	multiplicative	PROPN	NNP	Number=Sing	11	amod	_	_
11	graph	graph	NOUN	NN	Number=Sing	14	nsubjpass	_	_
12	can	can	AUX	MD	VerbForm=Fin	14	aux	_	_
13	be	be	AUX	VB	VerbForm=Inf	14	auxpass	_	_
14	extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
15	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
16	uniquely	uniquely	ADV	RB	_	14	advmod	_	SpaceAfter=No
17	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	14	punct	_	_
18	to	to	ADP	IN	_	14	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	multiplicative	multiplicative	ADJ	JJ	Degree=Pos	21	amod	_	_
21	graph	graph	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	problem	problem	NOUN	NN	Number=Sing	11	appos	_	_
25	raised	raise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	acl	_	_
26	by	by	ADP	IN	_	25	agent	_	_
27	Janelidze	Janelidze	PROPN	NNP	Number=Sing	26	pobj	_	_
28	in	in	ADP	IN	_	25	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
30	semiabelian	semiabelian	ADJ	JJ	Degree=Pos	31	amod	_	_
31	context	context	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 6
# text = When the three conditions hold, internal groupoids have a simple description, that, in the semiabelian context, correspond to the notion of internal crossed module, in the sense of Janelidze.
1	When	when	SCONJ	WRB	_	5	advmod	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	three	three	NUM	CD	NumType=Card	4	nummod	_	_
4	conditions	condition	NOUN	NNS	Number=Plur	5	nsubj	_	_
5	hold	hold	VERB	VBP	Tense=Pres|VerbForm=Fin	9	advcl	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
7	internal	internal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	groupoids	groupoid	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	simple	simple	ADJ	JJ	Degree=Pos	12	amod	_	_
12	description	description	NOUN	NN	Number=Sing	9	dobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	that	that	SCONJ	IN	_	21	mark	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
16	in	in	ADP	IN	_	21	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	semiabelian	semiabelian	ADJ	JJ	Degree=Pos	19	amod	_	_
19	context	context	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
21	correspond	correspond	VERB	VBP	Tense=Pres|VerbForm=Fin	12	relcl	_	_
22	to	to	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	notion	notion	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	internal	internal	ADJ	JJ	Degree=Pos	28	amod	_	_
27	crossed	crossed	ADJ	JJ	Degree=Pos	28	amod	_	_
28	module	module	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
30	in	in	ADP	IN	_	21	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	sense	sense	NOUN	NN	Number=Sing	30	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	Janelidze	Janelidze	PROPN	NNP	Number=Sing	33	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 345
# sent_id = 1
# text = We characterise the double central extensions in a semi - abelian category in terms of commutator conditions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	characterise	characterise	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
4	double	double	ADJ	JJ	Degree=Pos	6	amod	_	_
5	central	central	ADJ	JJ	Degree=Pos	6	amod	_	_
6	extensions	extension	NOUN	NNS	Number=Plur	2	dobj	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
9	semi	semi	ADJ	JJ	Degree=Pos	12	amod	_	_
10	-	-	ADJ	JJ	Degree=Pos	12	amod	_	_
11	abelian	abelian	ADJ	JJ	Degree=Pos	12	amod	_	_
12	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
13	in	in	ADP	IN	_	6	prep	_	_
14	terms	term	NOUN	NNS	Number=Plur	13	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	commutator	commutator	NOUN	NN	Number=Sing	17	compound	_	_
17	conditions	condition	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We prove that the third cohomology group $ H^3(Z, A) $ of an object $ Z $ with coefficients in an abelian object $ A $ classifies the double central extensions of $ Z $ by $ A $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	20	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	third	third	ADJ	JJ	Degree=Pos	6	compound	_	_
6	cohomology	cohomology	NOUN	NN	Number=Sing	7	compound	_	_
7	group	group	NOUN	NN	Number=Sing	20	nsubj	_	_
8	$ H^3(Z, A) $	$ h^3(z, a) $	SYM	$	_	7	appos	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	object	object	NOUN	NN	Number=Sing	9	pobj	_	_
12	$ Z $	$ z $	SYM	$	_	7	appos	_	_
13	with	with	ADP	IN	_	7	prep	_	_
14	coefficients	coefficient	NOUN	NNS	Number=Plur	13	pobj	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	an	an	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	abelian	abelian	ADJ	JJ	Degree=Pos	18	compound	_	_
18	object	object	NOUN	NN	Number=Sing	15	pobj	_	_
19	$ A $	$ a $	SYM	$	_	20	nummod	_	_
20	classifies	classifie	NOUN	NNS	Number=Plur	2	ccomp	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
22	double	double	ADJ	JJ	Degree=Pos	24	amod	_	_
23	central	central	ADJ	JJ	Degree=Pos	24	amod	_	_
24	extensions	extension	NOUN	NNS	Number=Plur	20	dobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	$ Z $	$ z $	SYM	$	_	25	pobj	_	_
27	by	by	ADP	IN	_	20	prep	_	_
28	$ A $	$ a $	SYM	$	_	27	pobj	_	_
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 346
# sent_id = 1
# text = We clarify the relationship between separable and covering morphisms in general categories by introducing and studying an intermediate class of morphisms that we call strongly separable.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	clarify	clarify	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	relationship	relationship	NOUN	NN	Number=Sing	2	dobj	_	_
5	between	between	ADP	IN	_	4	prep	_	_
6	separable	separable	ADJ	JJ	Degree=Pos	5	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	covering	cover	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	conj	_	_
9	morphisms	morphism	NOUN	NNS	Number=Plur	8	dobj	_	_
10	in	in	ADP	IN	_	4	prep	_	_
11	general	general	ADJ	JJ	Degree=Pos	12	amod	_	_
12	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
13	by	by	ADP	IN	_	2	prep	_	_
14	introducing	introduce	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	pcomp	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	studying	study	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	conj	_	_
17	an	an	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	intermediate	intermediate	ADJ	JJ	Degree=Pos	19	amod	_	_
19	class	class	NOUN	NN	Number=Sing	16	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	morphisms	morphism	NOUN	NNS	Number=Plur	20	pobj	_	_
22	that	that	PRON	WDT	PronType=Rel	24	dobj	_	_
23	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	24	nsubj	_	_
24	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	19	relcl	_	_
25	strongly	strongly	ADV	RB	_	26	advmod	_	_
26	separable	separable	ADJ	JJ	Degree=Pos	24	oprd	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 347
# sent_id = 1
# text = The purpose of this paper is to prove a new, incomplete - relative, version of Non - abelian Snake Lemma, where "relative" refers to a distinguished class of normal epimorphisms in the ground category, and "incomplete" refers to omitting all completeness/cocompleteness assumptions not involving that class.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	purpose	purpose	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	paper	paper	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	prove	prove	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
10	new	new	ADJ	JJ	Degree=Pos	14	amod	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
12	incomplete	incomplete	ADJ	JJ	Degree=Pos	14	amod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	relative	relative	ADJ	JJ	Degree=Pos	16	amod	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
16	version	version	NOUN	NN	Number=Sing	8	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	Non	Non	PROPN	NNP	Number=Sing	20	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	abelian	abelian	PROPN	NNP	Number=Sing	22	compound	_	_
21	Snake	Snake	PROPN	NNP	Number=Sing	22	compound	_	_
22	Lemma	Lemma	PROPN	NNP	Number=Sing	17	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	where	where	SCONJ	WRB	_	28	advmod	_	_
25	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	28	punct	_	SpaceAfter=No
26	relative	relative	ADJ	JJ	Degree=Pos	28	amod	_	SpaceAfter=No
27	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	28	punct	_	_
28	refers	refer	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	relcl	_	_
29	to	to	ADP	IN	_	28	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
31	distinguished	distinguished	ADJ	JJ	Degree=Pos	32	amod	_	_
32	class	class	NOUN	NN	Number=Sing	29	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	normal	normal	ADJ	JJ	Degree=Pos	35	amod	_	_
35	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	33	pobj	_	_
36	in	in	ADP	IN	_	32	prep	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
38	ground	ground	NOUN	NN	Number=Sing	39	compound	_	_
39	category	category	NOUN	NN	Number=Sing	36	pobj	_	SpaceAfter=No
40	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
41	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
42	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	45	punct	_	SpaceAfter=No
43	incomplete	incomplete	ADJ	JJ	Degree=Pos	45	amod	_	SpaceAfter=No
44	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	45	punct	_	_
45	refers	refer	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	28	conj	_	_
46	to	to	ADP	IN	_	45	prep	_	_
47	omitting	omit	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	46	pcomp	_	_
48	all	all	DET	DT	_	52	det	_	_
49	completeness	completeness	NOUN	NN	Number=Sing	51	compound	_	SpaceAfter=No
50	/	/	SYM	SYM	_	51	punct	_	SpaceAfter=No
51	cocompleteness	cocompleteness	NOUN	NN	Number=Sing	52	compound	_	_
52	assumptions	assumption	NOUN	NNS	Number=Plur	47	dobj	_	_
53	not	not	PART	RB	Polarity=Neg	54	neg	_	_
54	involving	involve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	52	acl	_	_
55	that	that	DET	DT	Number=Sing|PronType=Dem	56	det	_	_
56	class	class	NOUN	NN	Number=Sing	54	dobj	_	SpaceAfter=No
57	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 348
# sent_id = 1
# text = In this paper we show that in a homological category in the sense of Borceux and Bourn, the notion of an internal precrossed module corresponding to a star - multiplicative graph, in the sense of Janelidze, can be obtained by directly internalizing the usual axioms of a crossed module, via equivariance.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	42	mark	_	_
7	in	in	ADP	IN	_	42	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	homological	homological	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	sense	sense	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	Borceux	Borceux	PROPN	NNP	Number=Sing	14	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	Bourn	Bourn	PROPN	NNP	Number=Sing	15	conj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	42	punct	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	notion	notion	NOUN	NN	Number=Sing	42	nsubjpass	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	an	an	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
23	internal	internal	ADJ	JJ	Degree=Pos	26	amod	_	_
24	precrossed	precrosse	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
25	module	module	NOUN	NN	Number=Sing	26	compound	_	_
26	corresponding	corresponding	NOUN	NN	Number=Sing	21	pobj	_	_
27	to	to	ADP	IN	_	26	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
29	star	star	NOUN	NN	Number=Sing	31	compound	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	multiplicative	multiplicative	NOUN	NN	Number=Sing	32	amod	_	_
32	graph	graph	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
34	in	in	ADP	IN	_	42	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	sense	sense	NOUN	NN	Number=Sing	34	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	Janelidze	Janelidze	PROPN	NNP	Number=Sing	37	pobj	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	42	punct	_	_
40	can	can	AUX	MD	VerbForm=Fin	42	aux	_	_
41	be	be	AUX	VB	VerbForm=Inf	42	auxpass	_	_
42	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	ccomp	_	_
43	by	by	ADP	IN	_	42	prep	_	_
44	directly	directly	ADV	RB	_	45	advmod	_	_
45	internalizing	internalize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	43	pcomp	_	_
46	the	the	DET	DT	Definite=Def|PronType=Art	48	det	_	_
47	usual	usual	ADJ	JJ	Degree=Pos	48	amod	_	_
48	axioms	axiom	NOUN	NNS	Number=Plur	45	dobj	_	_
49	of	of	ADP	IN	_	48	prep	_	_
50	a	a	DET	DT	Definite=Ind|PronType=Art	52	det	_	_
51	crossed	crossed	ADJ	JJ	Degree=Pos	52	amod	_	_
52	module	module	NOUN	NN	Number=Sing	49	pobj	_	SpaceAfter=No
53	,	,	PUNCT	,	PunctType=Comm	42	punct	_	_
54	via	via	ADP	IN	_	42	prep	_	_
55	equivariance	equivariance	NOUN	NN	Number=Sing	54	pobj	_	SpaceAfter=No
56	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = We then exhibit some sufficient conditions on a homological category under which this notion coincides with the notion of an internal crossed module due to Janelidze.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	exhibit	exhibit	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	some	some	DET	DT	_	6	det	_	_
5	sufficient	sufficient	ADJ	JJ	Degree=Pos	6	amod	_	_
6	conditions	condition	NOUN	NNS	Number=Plur	3	dobj	_	_
7	on	on	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	homological	homological	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
11	under	under	ADP	IN	_	15	prep	_	_
12	which	which	PRON	WDT	_	11	pobj	_	_
13	this	this	DET	DT	Number=Sing|PronType=Dem	14	det	_	_
14	notion	notion	NOUN	NN	Number=Sing	15	nsubj	_	_
15	coincides	coincide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	relcl	_	_
16	with	with	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	notion	notion	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	an	an	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
21	internal	internal	ADJ	JJ	Degree=Pos	23	amod	_	_
22	crossed	crossed	ADJ	JJ	Degree=Pos	23	amod	_	_
23	module	module	NOUN	NN	Number=Sing	19	pobj	_	_
24	due	due	ADP	IN	_	23	prep	_	_
25	to	to	ADP	IN	_	24	pcomp	_	_
26	Janelidze	Janelidze	PROPN	NNP	Number=Sing	24	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that this is the case for any category of distributive $ Omega_2 $ - groups, in particular for the categories of groups with operations in the sense of Orzech.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	this	this	PRON	DT	Number=Sing|PronType=Dem	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	case	case	NOUN	NN	Number=Sing	5	attr	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	any	any	DET	DT	_	10	det	_	_
10	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	distributive	distributive	ADJ	JJ	Degree=Pos	15	amod	_	_
13	$ Omega_2 $	$ omega_2 $	SYM	$	_	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	groups	group	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
17	in	in	ADP	IN	_	19	prep	_	_
18	particular	particular	ADJ	JJ	Degree=Pos	17	amod	_	_
19	for	for	ADP	IN	_	5	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	categories	category	NOUN	NNS	Number=Plur	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	groups	group	NOUN	NNS	Number=Plur	22	pobj	_	_
24	with	with	ADP	IN	_	23	prep	_	_
25	operations	operation	NOUN	NNS	Number=Plur	24	pobj	_	_
26	in	in	ADP	IN	_	19	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	sense	sense	NOUN	NN	Number=Sing	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	Orzech	Orzech	PROPN	NNP	Number=Sing	29	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 349
# sent_id = 1
# text = We describe a simplified categorical approach to Galois descent theory.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
4	simplified	simplified	ADJ	JJ	Degree=Pos	6	amod	_	_
5	categorical	categorical	ADJ	JJ	Degree=Pos	6	amod	_	_
6	approach	approach	NOUN	NN	Number=Sing	2	dobj	_	_
7	to	to	ADP	IN	_	6	prep	_	_
8	Galois	Galois	PROPN	NNP	Number=Sing	10	compound	_	_
9	descent	descent	NOUN	NN	Number=Sing	10	compound	_	_
10	theory	theory	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = It is well known that Galois descent is a special case of Grothendieck descent, and that under mild additional conditions the category of Grothendieck descent data coincides with the Eilenberg - Moore category of algebras over a suitable monad.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	well	well	ADV	RB	Degree=Pos	4	advmod	_	_
4	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acomp	_	_
5	that	that	SCONJ	IN	_	8	mark	_	_
6	Galois	Galois	PROPN	NNP	Number=Sing	7	compound	_	_
7	descent	descent	NOUN	NN	Number=Sing	8	nsubj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	special	special	ADJ	JJ	Degree=Pos	11	amod	_	_
11	case	case	NOUN	NN	Number=Sing	8	attr	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	14	compound	_	_
14	descent	descent	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
17	that	that	SCONJ	IN	_	18	mark	_	_
18	under	under	ADP	IN	_	8	conj	_	_
19	mild	mild	ADJ	JJ	Degree=Pos	21	amod	_	_
20	additional	additional	ADJ	JJ	Degree=Pos	21	amod	_	_
21	conditions	condition	NOUN	NNS	Number=Plur	18	pobj	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	category	category	NOUN	NN	Number=Sing	18	npadvmod	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	27	compound	_	_
26	descent	descent	NOUN	NN	Number=Sing	27	compound	_	_
27	data	data	NOUN	NN	Number=Sing	28	compound	_	_
28	coincides	coincide	NOUN	NNS	Number=Plur	24	pobj	_	_
29	with	with	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
31	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	33	compound	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	Moore	Moore	PROPN	NNP	Number=Sing	34	compound	_	_
34	category	category	NOUN	NN	Number=Sing	29	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	algebras	algebra	NOUN	NNS	Number=Plur	35	pobj	_	_
37	over	over	ADP	IN	_	23	prep	_	_
38	a	a	DET	DT	Definite=Ind|PronType=Art	40	det	_	_
39	suitable	suitable	ADJ	JJ	Degree=Pos	40	amod	_	_
40	monad	monad	NOUN	NNS	Number=Plur	37	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = This also suggests using monads directly, and our monadic approach to Galois descent makes no reference to Grothendieck descent theory at all.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	suggests	suggest	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	xcomp	_	_
5	monads	monad	NOUN	NNS	Number=Plur	4	dobj	_	_
6	directly	directly	ADV	RB	_	4	advmod	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
9	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	11	poss	_	_
10	monadic	monadic	ADJ	JJ	Degree=Pos	11	amod	_	_
11	approach	approach	NOUN	NN	Number=Sing	15	nsubj	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	Galois	Galois	PROPN	NNP	Number=Sing	14	compound	_	_
14	descent	descent	NOUN	NN	Number=Sing	12	pobj	_	_
15	makes	make	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
16	no	no	DET	DT	_	17	det	_	_
17	reference	reference	NOUN	NN	Number=Sing	15	dobj	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	21	compound	_	_
20	descent	descent	NOUN	NN	Number=Sing	21	compound	_	_
21	theory	theory	NOUN	NN	Number=Sing	18	pobj	_	_
22	at	at	ADV	RB	_	23	advmod	_	_
23	all	all	ADV	RB	_	15	advmod	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = In order to make Galois descent constructions perfectly clear, we also describe their connections with some other related constructions of categorical algebra, and make various explicit calculations, especially with 1 - cocycles and 1 - dimensional non - abelian cohomology, usually omitted in the literature.
1	In	in	ADP	IN	_	13	prep	_	_
2	order	order	NOUN	NN	Number=Sing	1	pobj	_	_
3	to	to	PART	TO	_	4	aux	_	_
4	make	make	VERB	VB	VerbForm=Inf	2	acl	_	_
5	Galois	Galois	PROPN	NNP	Number=Sing	6	nsubj	_	_
6	descent	descent	NOUN	NN	Number=Sing	7	compound	_	_
7	constructions	construction	NOUN	NNS	Number=Plur	9	nsubj	_	_
8	perfectly	perfectly	ADV	RB	_	9	advmod	_	_
9	clear	clear	ADJ	JJ	Degree=Pos	4	ccomp	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
11	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
12	also	also	ADV	RB	_	13	advmod	_	_
13	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	15	poss	_	_
15	connections	connection	NOUN	NNS	Number=Plur	13	dobj	_	_
16	with	with	ADP	IN	_	15	prep	_	_
17	some	some	DET	DT	_	20	det	_	_
18	other	other	ADJ	JJ	Degree=Pos	20	amod	_	_
19	related	related	ADJ	JJ	Degree=Pos	20	amod	_	_
20	constructions	construction	NOUN	NNS	Number=Plur	16	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	categorical	categorical	ADJ	JJ	Degree=Pos	23	amod	_	_
23	algebra	algebra	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
26	make	make	VERB	VB	VerbForm=Inf	13	conj	_	_
27	various	various	ADJ	JJ	Degree=Pos	29	amod	_	_
28	explicit	explicit	ADJ	JJ	Degree=Pos	29	amod	_	_
29	calculations	calculation	NOUN	NNS	Number=Plur	26	dobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
31	especially	especially	ADV	RB	_	32	advmod	_	_
32	with	with	ADP	IN	_	26	prep	_	_
33	1	1	NUM	CD	NumType=Card	35	nummod	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	cocycles	cocycle	NOUN	NNS	Number=Plur	32	pobj	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
37	1	1	NUM	CD	NumType=Card	39	npadvmod	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	dimensional	dimensional	ADJ	JJ	Degree=Pos	43	amod	_	_
40	non	non	ADJ	JJ	Degree=Pos	42	amod	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	abelian	abelian	PROPN	NNP	Number=Sing	43	compound	_	_
43	cohomology	cohomology	NOUN	NN	Number=Sing	35	conj	_	SpaceAfter=No
44	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
45	usually	usually	ADV	RB	_	46	advmod	_	_
46	omitted	omit	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	advcl	_	_
47	in	in	ADP	IN	_	46	prep	_	_
48	the	the	DET	DT	Definite=Def|PronType=Art	49	det	_	_
49	literature	literature	NOUN	NN	Number=Sing	47	pobj	_	SpaceAfter=No
50	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# doc_id = 350
# sent_id = 1
# text = This is an expanded, revised and corrected version of the first author's 1981 preprint.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
4	expanded	expand	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	amod	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
6	revised	revise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	conj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	corrected	correct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	conj	_	_
9	version	version	NOUN	NN	Number=Sing	2	attr	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	first	first	ADJ	JJ	Degree=Pos	13	amod	_	_
13	author	author	NOUN	NN	Number=Sing	16	poss	_	SpaceAfter=No
14	's	's	PART	POS	_	13	case	_	_
15	1981	1981	NUM	CD	NumType=Card	16	nummod	_	_
16	preprint	preprint	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The discussion of one - dimensional cohomology $ H^{1} $ in a fairly general category $ E $ involves passing to the 2 - category $ Cat(E) $ of categories $ E $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	discussion	discussion	NOUN	NN	Number=Sing	15	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	one	one	NUM	CD	NumType=Card	6	npadvmod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	dimensional	dimensional	ADJ	JJ	Degree=Pos	7	amod	_	_
7	cohomology	cohomology	NOUN	NN	Number=Sing	3	pobj	_	_
8	$ H^{1} $	$ h^{1} $	SYM	$	_	7	appos	_	_
9	in	in	ADP	IN	_	2	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	fairly	fairly	ADV	RB	_	12	advmod	_	_
12	general	general	ADJ	JJ	Degree=Pos	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
14	$ E $	$ e $	SYM	$	_	15	nsubj	_	_
15	involves	involve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	passing	pass	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	xcomp	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
19	2	2	NUM	CD	NumType=Card	21	nummod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	category	category	NOUN	NN	Number=Sing	22	compound	_	_
22	$ Cat(E) $	$ cat(e) $	SYM	$	_	17	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	categories	category	NOUN	NNS	Number=Plur	23	pobj	_	_
25	$ E $	$ e $	SYM	$	_	22	appos	_	_
26	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 3
# text = In particular, the coefficient object is a category $ B $ in $ E $ and the torsors that $ H^{1} $ classifies are particular functors in $ E $ .
1	In	in	ADP	IN	_	7	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	coefficient	coefficient	ADJ	JJ	Degree=Pos	6	amod	_	_
6	object	object	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	category	category	NOUN	NN	Number=Sing	10	nmod	_	_
10	$ B $	$ b $	SYM	$	_	7	attr	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	$ E $	$ e $	SYM	$	_	11	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	torsors	torsor	NOUN	NNS	Number=Plur	10	conj	_	_
16	that	that	PRON	WDT	PronType=Rel	22	pobj	_	_
17	$ H^{1} $	$ h^{1} $	SYM	$	_	18	poss	_	_
18	classifies	classifie	NOUN	NNS	Number=Plur	19	nsubj	_	_
19	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	relcl	_	_
20	particular	particular	ADJ	JJ	Degree=Pos	21	amod	_	_
21	functors	functor	NOUN	NNS	Number=Plur	19	attr	_	_
22	in	in	ADP	IN	_	21	prep	_	_
23	$ E $	$ e $	SYM	$	_	22	pobj	_	_
24	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = We only impose conditions on $ E $ that are satisfied also by $ Cat(E) $ and argue that $ H^{1} $ for $ Cat(E) $ is a kind of $ H^{2} $ for $ E $ , and so on recursively.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	only	only	ADV	RB	_	3	advmod	_	_
3	impose	impose	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	conditions	condition	NOUN	NNS	Number=Plur	3	dobj	_	_
5	on	on	ADP	IN	_	4	prep	_	_
6	$ E $	$ e $	SYM	$	_	5	pobj	_	_
7	that	that	PRON	WDT	PronType=Rel	8	nsubj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	relcl	_	_
9	satisfied	satisfied	ADJ	JJ	Degree=Pos	8	acomp	_	_
10	also	also	ADV	RB	_	9	advmod	_	_
11	by	by	ADP	IN	_	9	prep	_	_
12	$ Cat(E) $	$ cat(e) $	SYM	$	_	11	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
14	argue	argue	VERB	VBP	Tense=Pres|VerbForm=Fin	3	conj	_	_
15	that	that	SCONJ	IN	_	19	mark	_	_
16	$ H^{1} $	$ h^{1} $	SYM	$	_	19	nsubj	_	_
17	for	for	ADP	IN	_	16	prep	_	_
18	$ Cat(E) $	$ cat(e) $	SYM	$	_	19	nsubj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	ccomp	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	kind	kind	NOUN	NN	Number=Sing	19	attr	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	$ H^{2} $	$ h^{2} $	SYM	$	_	22	pobj	_	_
24	for	for	ADP	IN	_	21	prep	_	_
25	$ E $	$ e $	SYM	$	_	24	pobj	_	_
26	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
28	so	so	ADV	RB	_	29	advmod	_	_
29	on	on	ADP	IN	_	30	advmod	_	_
30	recursively	recursively	ADV	RB	_	19	advmod	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = For us, it is too much to ask $ E $ to be a topos (or even internally complete) since, even if $ E $ is, $ Cat(E) $ is not.
1	For	for	ADP	IN	_	5	prep	_	_
2	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	ccomp	_	_
6	too	too	ADV	RB	_	7	advmod	_	_
7	much	much	ADJ	JJ	Degree=Pos	5	acomp	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	ask	ask	VERB	VB	VerbForm=Inf	5	xcomp	_	_
10	$ E $	$ e $	SYM	$	_	9	dobj	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	be	be	AUX	VB	VerbForm=Inf	9	xcomp	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	topos	topos	NOUN	NN	Number=Sing	12	attr	_	_
15	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
16	or	or	CCONJ	CC	ConjType=Cmp	14	cc	_	_
17	even	even	ADV	RB	_	19	advmod	_	_
18	internally	internally	ADV	RB	_	19	advmod	_	_
19	complete	complete	ADJ	JJ	Degree=Pos	14	conj	_	SpaceAfter=No
20	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	14	punct	_	_
21	since	since	SCONJ	IN	_	5	prep	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
23	even	even	ADV	RB	_	26	advmod	_	_
24	if	if	SCONJ	IN	_	26	mark	_	_
25	$ E $	$ e $	SYM	$	_	26	nsubj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	advcl	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
28	$ Cat(E) $	$ cat(e) $	SYM	$	_	29	nsubj	_	_
29	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
30	not	not	PART	RB	Polarity=Neg	29	neg	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	29	punct	_	SpaceAfter=No

# sent_id = 6
# text = With this motivation, we are led to examine morphisms in $ E $ which act as internal families and to internalize the comprehensive factorization of functors into a final functor followed by a discrete fibration.
1	With	with	ADP	IN	_	7	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	motivation	motivation	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubjpass	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	led	lead	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	examine	examine	VERB	VB	VerbForm=Inf	7	xcomp	_	_
10	morphisms	morphism	NOUN	NNS	Number=Plur	9	dobj	_	_
11	in	in	ADP	IN	_	9	prep	_	_
12	$ E $	$ e $	SYM	$	_	11	pobj	_	_
13	which	which	PRON	WDT	_	14	nsubj	_	_
14	act	act	VERB	VBP	Tense=Pres|VerbForm=Fin	12	relcl	_	_
15	as	as	ADP	IN	_	14	prep	_	_
16	internal	internal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	families	family	NOUN	NNS	Number=Plur	15	pobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
19	to	to	PART	TO	_	20	aux	_	_
20	internalize	internalize	VERB	VB	VerbForm=Inf	14	conj	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	comprehensive	comprehensive	ADJ	JJ	Degree=Pos	23	amod	_	_
23	factorization	factorization	NOUN	NN	Number=Sing	20	dobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	functors	functor	NOUN	NNS	Number=Plur	24	pobj	_	_
26	into	into	ADP	IN	_	20	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	final	final	ADJ	JJ	Degree=Pos	29	amod	_	_
29	functor	functor	NOUN	NN	Number=Sing	26	pobj	_	_
30	followed	follow	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	acl	_	_
31	by	by	ADP	IN	_	30	agent	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
33	discrete	discrete	ADJ	JJ	Degree=Pos	34	amod	_	_
34	fibration	fibration	NOUN	NN	Number=Sing	31	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 7
# text = We define $ B $ - torsors for a category $ B $ in $ E $ and prove clutching and classification theorems.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	$ B $	$ b $	SYM	$	_	5	compound	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	torsors	torsor	NOUN	NNS	Number=Plur	2	dobj	_	_
6	for	for	ADP	IN	_	2	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	category	category	NOUN	NN	Number=Sing	9	nmod	_	_
9	$ B $	$ b $	SYM	$	_	6	pobj	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	$ E $	$ e $	SYM	$	_	10	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
13	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
14	clutching	clutch	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	amod	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	classification	classification	NOUN	NN	Number=Sing	14	conj	_	_
17	theorems	theorem	NOUN	NNS	Number=Plur	13	dobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 8
# text = The former theorem clutches Cech cocycles to construct torsors while the latter constructs a coefficient category to classify structures locally isomorphic to members of a given internal family of structures.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	former	former	ADJ	JJ	Degree=Pos	3	amod	_	_
3	theorem	theorem	ADJ	JJ	Degree=Pos	4	nsubj	_	_
4	clutches	clutch	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	Cech	Cech	PROPN	NNP	Number=Sing	6	compound	_	_
6	cocycles	cocycle	NOUN	NNS	Number=Plur	4	dobj	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	construct	construct	VERB	VB	VerbForm=Inf	4	xcomp	_	_
9	torsors	torsor	NOUN	NNS	Number=Plur	8	dobj	_	_
10	while	while	SCONJ	IN	_	13	mark	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	latter	latter	ADJ	JJ	Degree=Pos	13	nsubj	_	_
13	constructs	construct	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	advcl	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	coefficient	coefficient	ADJ	JJ	Degree=Pos	16	amod	_	_
16	category	category	NOUN	NN	Number=Sing	13	dobj	_	_
17	to	to	PART	TO	_	18	aux	_	_
18	classify	classify	VERB	VB	VerbForm=Inf	16	acl	_	_
19	structures	structure	NOUN	NNS	Number=Plur	18	dobj	_	_
20	locally	locally	ADV	RB	_	21	advmod	_	_
21	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	18	acomp	_	_
22	to	to	ADP	IN	_	18	prep	_	_
23	members	member	NOUN	NNS	Number=Plur	22	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
26	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	amod	_	_
27	internal	internal	ADJ	JJ	Degree=Pos	28	amod	_	_
28	family	family	NOUN	NN	Number=Sing	24	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	structures	structure	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 9
# text = We conclude with applications to examples.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	conclude	conclude	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	with	with	ADP	IN	_	2	prep	_	_
4	applications	application	NOUN	NNS	Number=Plur	3	pobj	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	examples	example	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
7	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 351
# sent_id = 1
# text = Any semi - abelian category $ A $ appears, via the discrete functor, as a full replete reflective subcategory of the semi - abelian category of internal groupoids in $ A $ .
1	Any	any	DET	DT	_	5	det	_	_
2	semi	semi	ADJ	JJ	Degree=Pos	5	amod	_	_
3	-	-	ADJ	JJ	Degree=Pos	5	amod	_	_
4	abelian	abelian	ADJ	JJ	Degree=Pos	5	amod	_	_
5	category	category	NOUN	NN	Number=Sing	7	nsubj	_	_
6	$ A $	$ a $	SYM	$	_	5	appos	_	_
7	appears	appear	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	via	via	ADP	IN	_	7	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	discrete	discrete	ADJ	JJ	Degree=Pos	12	amod	_	_
12	functor	functor	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
14	as	as	ADP	IN	_	7	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
16	full	full	ADJ	JJ	Degree=Pos	19	amod	_	_
17	replete	replete	ADJ	JJ	Degree=Pos	19	amod	_	_
18	reflective	reflective	ADJ	JJ	Degree=Pos	19	amod	_	_
19	subcategory	subcategory	NOUN	NN	Number=Sing	14	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
22	semi	semi	ADJ	JJ	Degree=Pos	25	amod	_	_
23	-	-	ADJ	JJ	Degree=Pos	25	amod	_	_
24	abelian	abelian	ADJ	JJ	Degree=Pos	25	amod	_	_
25	category	category	NOUN	NN	Number=Sing	20	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	internal	internal	ADJ	JJ	Degree=Pos	28	amod	_	_
28	groupoids	groupoid	NOUN	NNS	Number=Plur	26	pobj	_	_
29	in	in	ADP	IN	_	25	prep	_	_
30	$ A $	$ a $	SYM	$	_	29	pobj	_	_
31	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 2
# text = This allows one to study the homology of $ n $ - fold internal groupoids with coefficients in a semi - abelian category $ A $ , and to compute explicit higher Hopf formulae.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	one	one	PRON	PRP	PronType=Prs	5	nsubj	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	study	study	VERB	VB	VerbForm=Inf	2	ccomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	homology	homology	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	$ n $	$ n $	SYM	$	_	10	nmod	_	_
10	-	-	ADJ	JJ	Degree=Pos	13	amod	_	_
11	fold	fold	ADJ	JJ	Degree=Pos	13	amod	_	_
12	internal	internal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	groupoids	groupoid	NOUN	NNS	Number=Plur	8	pobj	_	_
14	with	with	ADP	IN	_	5	prep	_	_
15	coefficients	coefficient	NOUN	NNS	Number=Plur	14	pobj	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
18	semi	semi	ADJ	JJ	Degree=Pos	21	amod	_	_
19	-	-	ADJ	JJ	Degree=Pos	21	amod	_	_
20	abelian	abelian	ADJ	JJ	Degree=Pos	21	amod	_	_
21	category	category	NOUN	NN	Number=Sing	16	pobj	_	_
22	$ A $	$ a $	SYM	$	_	21	nummod	_	_
23	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
25	to	to	PART	TO	_	26	aux	_	_
26	compute	compute	VERB	VB	VerbForm=Inf	5	conj	_	_
27	explicit	explicit	ADJ	JJ	Degree=Pos	30	amod	_	_
28	higher	high	ADJ	JJR	Degree=Cmp	30	amod	_	_
29	Hopf	Hopf	PROPN	NNP	Number=Sing	30	compound	_	_
30	formulae	formulae	NOUN	NN	Number=Sing	26	dobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The crucial concept making such computations possible is the notion of protoadditive functor, which can be seen as a natural generalisation of the notion of additive functor.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	crucial	crucial	ADJ	JJ	Degree=Pos	3	amod	_	_
3	concept	concept	NOUN	NN	Number=Sing	8	nsubj	_	_
4	making	make	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	acl	_	_
5	such	such	ADJ	JJ	Degree=Pos	6	amod	_	_
6	computations	computation	NOUN	NNS	Number=Plur	4	dobj	_	_
7	possible	possible	ADJ	JJ	Degree=Pos	6	amod	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	notion	notion	NOUN	NN	Number=Sing	8	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	protoadditive	protoadditive	NOUN	NN	Number=Sing	13	compound	_	_
13	functor	functor	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	which	which	PRON	WDT	_	18	nsubjpass	_	_
16	can	can	AUX	MD	VerbForm=Fin	18	aux	_	_
17	be	be	AUX	VB	VerbForm=Inf	18	auxpass	_	_
18	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	relcl	_	_
19	as	as	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	natural	natural	ADJ	JJ	Degree=Pos	22	amod	_	_
22	generalisation	generalisation	NOUN	NN	Number=Sing	19	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	notion	notion	NOUN	NN	Number=Sing	23	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	additive	additive	ADJ	JJ	Degree=Pos	28	amod	_	_
28	functor	functor	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 352
# sent_id = 1
# text = We present a general treatment of measures and integrals in certain (monoidal closed) categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	general	general	ADJ	JJ	Degree=Pos	5	amod	_	_
5	treatment	treatment	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	measures	measure	NOUN	NNS	Number=Plur	6	pobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	integrals	integral	NOUN	NNS	Number=Plur	7	conj	_	_
10	in	in	ADP	IN	_	7	prep	_	_
11	certain	certain	ADJ	JJ	Degree=Pos	16	amod	_	_
12	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	16	punct	_	SpaceAfter=No
13	monoidal	monoidal	NOUN	NN	Number=Sing	16	amod	_	_
14	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	nmod	_	SpaceAfter=No
15	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	16	punct	_	_
16	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Under appropriate conditions the integral can be defined by a universal property, and the universal measure is at the same time a universal multiplicative measure.
1	Under	under	ADP	IN	_	8	prep	_	_
2	appropriate	appropriate	ADJ	JJ	Degree=Pos	3	amod	_	_
3	conditions	condition	NOUN	NNS	Number=Plur	1	pobj	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	integral	integral	NOUN	NN	Number=Sing	8	nsubjpass	_	_
6	can	can	AUX	MD	VerbForm=Fin	8	aux	_	_
7	be	be	AUX	VB	VerbForm=Inf	8	auxpass	_	_
8	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	by	by	ADP	IN	_	8	agent	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	universal	universal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	property	property	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	universal	universal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	measure	measure	NOUN	NN	Number=Sing	18	nsubj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	conj	_	_
19	at	at	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	same	same	ADJ	JJ	Degree=Pos	22	amod	_	_
22	time	time	NOUN	NN	Number=Sing	19	pobj	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
24	universal	universal	ADJ	JJ	Degree=Pos	26	amod	_	_
25	multiplicative	multiplicative	ADJ	JJ	Degree=Pos	26	amod	_	_
26	measure	measure	NOUN	NN	Number=Sing	18	attr	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# sent_id = 3
# text = In the multiplicative case this assignment is right adjoint to the formation of the Boolean algebra of idempotents.
1	In	in	ADP	IN	_	7	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	multiplicative	multiplicative	ADJ	JJ	Degree=Pos	4	amod	_	_
4	case	case	NOUN	NN	Number=Sing	1	pobj	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	assignment	assignment	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	right	right	ADJ	JJ	Degree=Pos	9	amod	_	_
9	adjoint	adjoint	NOUN	NN	Number=Sing	7	attr	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	formation	formation	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	Boolean	boolean	ADJ	JJ	Degree=Pos	16	amod	_	_
16	algebra	algebra	NOUN	NN	Number=Sing	13	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	idempotents	idempotent	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = Now coproduct preservation yields an approach to product measures.
1	Now	now	ADV	RB	_	2	advmod	_	_
2	coproduct	coproduct	VERB	VB	VerbForm=Inf	0	ROOT	_	_
3	preservation	preservation	NOUN	NN	Number=Sing	4	compound	_	_
4	yields	yield	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	dobj	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	approach	approach	NOUN	NN	Number=Sing	4	dobj	_	_
7	to	to	ADP	IN	_	6	prep	_	_
8	product	product	NOUN	NN	Number=Sing	9	compound	_	_
9	measures	measure	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 353
# sent_id = 1
# text = The 2 - category of constructively completely distributive lattices is shown to be bidual to a 2 - category of generalized orders that admits a monadic schizophrenic object biadjunction over the 2 - category of ordered sets.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	2	2	NUM	CD	NumType=Card	4	nummod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	category	category	NOUN	NN	Number=Sing	11	nsubjpass	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	constructively	constructively	ADV	RB	_	8	advmod	_	_
7	completely	completely	ADV	RB	_	8	advmod	_	_
8	distributive	distributive	ADJ	JJ	Degree=Pos	9	amod	_	_
9	lattices	lattice	NOUN	NNS	Number=Plur	5	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
12	to	to	PART	TO	_	13	aux	_	_
13	be	be	AUX	VB	VerbForm=Inf	11	xcomp	_	_
14	bidual	bidual	ADJ	JJ	Degree=Pos	13	acomp	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
17	2	2	NUM	CD	NumType=Card	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	amod	_	_
22	orders	order	NOUN	NNS	Number=Plur	20	pobj	_	_
23	that	that	PRON	WDT	PronType=Rel	24	nsubj	_	_
24	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	relcl	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
26	monadic	monadic	ADJ	JJ	Degree=Pos	29	amod	_	_
27	schizophrenic	schizophrenic	ADJ	JJ	Degree=Pos	29	amod	_	_
28	object	object	NOUN	NN	Number=Sing	29	compound	_	_
29	biadjunction	biadjunction	NOUN	NN	Number=Sing	24	dobj	_	_
30	over	over	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
32	2	2	NUM	CD	NumType=Card	34	nummod	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	category	category	NOUN	NN	Number=Sing	30	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	37	amod	_	_
37	sets	set	NOUN	NNS	Number=Plur	35	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# doc_id = 354
# sent_id = 1
# text = We show that categories weakly enriched over symmetric monoidal categories can be strictified to categories enriched in permutative categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	6	mark	_	_
4	categories	category	NOUN	NNS	Number=Plur	6	nsubj	_	_
5	weakly	weakly	ADV	RB	_	6	advmod	_	_
6	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
7	over	over	ADP	IN	_	6	prep	_	_
8	symmetric	symmetric	ADJ	JJ	Degree=Pos	10	amod	_	_
9	monoidal	monoidal	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
11	can	can	AUX	MD	VerbForm=Fin	13	aux	_	_
12	be	be	AUX	VB	VerbForm=Inf	13	auxpass	_	_
13	strictified	strictifie	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	categories	category	NOUN	NNS	Number=Plur	14	pobj	_	_
16	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	permutative	permutative	ADJ	JJ	Degree=Pos	19	amod	_	_
19	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This is a "many 0 - cells" version of the strictification of bimonoidal categories to strict ones.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
4	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	8	punct	_	SpaceAfter=No
5	many	many	ADJ	JJ	Degree=Pos	8	amod	_	_
6	0	0	NUM	CD	NumType=Card	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	cells	cell	NOUN	NNS	Number=Plur	10	nmod	_	SpaceAfter=No
9	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	8	punct	_	_
10	version	version	NOUN	NN	Number=Sing	2	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	strictification	strictification	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	bimonoidal	bimonoidal	NOUN	NN	Number=Sing	16	compound	_	_
16	categories	category	NOUN	NNS	Number=Plur	14	pobj	_	_
17	to	to	ADP	IN	_	10	prep	_	_
18	strict	strict	ADJ	JJ	Degree=Pos	19	amod	_	_
19	ones	one	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 355
# sent_id = 1
# text = We prove that every category of interest (in the sense of Orzech) is action accessible in the sense of Bourn and Janelidze.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	15	mark	_	_
4	every	every	DET	DT	_	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	15	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	interest	interest	NOUN	NN	Number=Sing	6	pobj	_	_
8	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	5	punct	_	SpaceAfter=No
9	in	in	ADP	IN	_	8	nmod	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	sense	sense	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	Orzech	Orzech	PROPN	NNP	Number=Sing	12	pobj	_	SpaceAfter=No
14	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	5	punct	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
16	action	action	NOUN	NN	Number=Sing	15	attr	_	_
17	accessible	accessible	ADJ	JJ	Degree=Pos	16	amod	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	sense	sense	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	Bourn	Bourn	PROPN	NNP	Number=Sing	21	pobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	Janelidze	Janelidze	PROPN	NNP	Number=Sing	22	conj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This fact allows us to give an intrinsic description of centers and centralizers in this class of categories.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	fact	fact	NOUN	NN	Number=Sing	3	nsubj	_	_
3	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	give	give	VERB	VB	VerbForm=Inf	3	ccomp	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	intrinsic	intrinsic	ADJ	JJ	Degree=Pos	9	amod	_	_
9	description	description	NOUN	NN	Number=Sing	6	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	centers	center	NOUN	NNS	Number=Plur	10	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	centralizers	centralizer	NOUN	NNS	Number=Plur	11	conj	_	_
14	in	in	ADP	IN	_	6	prep	_	_
15	this	this	DET	DT	Number=Sing|PronType=Dem	16	det	_	_
16	class	class	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = We give also some new examples of categories of interest, mainly arising from Loday's papers.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	also	also	ADV	RB	_	2	advmod	_	_
4	some	some	DET	DT	_	6	det	_	_
5	new	new	ADJ	JJ	Degree=Pos	6	amod	_	_
6	examples	example	NOUN	NNS	Number=Plur	2	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	interest	interest	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
12	mainly	mainly	ADV	RB	_	13	advmod	_	_
13	arising	arise	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
14	from	from	ADP	IN	_	13	prep	_	_
15	Loday	Loday	PROPN	NNP	Number=Sing	17	poss	_	SpaceAfter=No
16	's	's	PART	POS	_	15	case	_	_
17	papers	paper	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 356
# sent_id = 1
# text = Notions of generalized multicategory have been defined in numerous contexts throughout the literature, and include such diverse examples as symmetric multicategories, globular operads, Lawvere theories, and topological spaces.
1	Notions	notion	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	generalized	generalized	ADJ	JJ	Degree=Pos	4	amod	_	_
4	multicategory	multicategory	NOUN	NN	Number=Sing	2	pobj	_	_
5	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	aux	_	_
6	been	be	AUX	VBN	Tense=Past|VerbForm=Part	7	auxpass	_	_
7	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	numerous	numerous	ADJ	JJ	Degree=Pos	10	amod	_	_
10	contexts	context	NOUN	NNS	Number=Plur	8	pobj	_	_
11	throughout	throughout	ADP	IN	_	7	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	literature	literature	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
16	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	7	conj	_	_
17	such	such	ADJ	JJ	Degree=Pos	19	amod	_	_
18	diverse	diverse	ADJ	JJ	Degree=Pos	19	amod	_	_
19	examples	example	NOUN	NNS	Number=Plur	16	dobj	_	_
20	as	as	ADP	IN	_	19	prep	_	_
21	symmetric	symmetric	ADJ	JJ	Degree=Pos	22	amod	_	_
22	multicategories	multicategorie	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	globular	globular	ADJ	JJ	Degree=Pos	25	amod	_	_
25	operads	operad	NOUN	NNS	Number=Plur	22	conj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
27	Lawvere	Lawvere	PROPN	NNP	Number=Sing	28	compound	_	_
28	theories	theory	NOUN	NNS	Number=Plur	25	conj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
31	topological	topological	ADJ	JJ	Degree=Pos	32	amod	_	_
32	spaces	space	NOUN	NNS	Number=Plur	28	conj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 2
# text = In each case, generalized multicategories are defined as the ``lax algebras'' or ``Kleisli monoids'' relative to a ``monad'' on a bicategory.
1	In	in	ADP	IN	_	8	prep	_	_
2	each	each	DET	DT	_	3	det	_	_
3	case	case	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
5	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	amod	_	_
6	multicategories	multicategorie	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	as	as	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
11	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	14	punct	_	SpaceAfter=No
12	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	14	punct	_	SpaceAfter=No
13	lax	lax	ADJ	JJ	Degree=Pos	14	amod	_	_
14	algebras	algebra	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
15	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	14	punct	_	_
16	or	or	CCONJ	CC	ConjType=Cmp	8	cc	_	_
17	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	19	punct	_	SpaceAfter=No
18	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	19	punct	_	SpaceAfter=No
19	Kleisli	Kleisli	PROPN	NNP	Number=Sing	20	nmod	_	_
20	monoids	monoid	NOUN	NNS	Number=Plur	8	conj	_	SpaceAfter=No
21	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	20	punct	_	_
22	relative	relative	ADJ	JJ	Degree=Pos	20	amod	_	_
23	to	to	ADP	IN	_	22	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
25	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	27	punct	_	SpaceAfter=No
26	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	27	punct	_	SpaceAfter=No
27	monad	monad	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
28	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	27	punct	_	_
29	on	on	ADP	IN	_	20	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
31	bicategory	bicategory	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 3
# text = However, the meanings of these words differ from author to author, as do the specific bicategories considered.
1	However	however	ADV	RB	_	8	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	meanings	meaning	NOUN	NNS	Number=Plur	8	nsubj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	these	these	DET	DT	Number=Plur|PronType=Dem	7	det	_	_
7	words	word	NOUN	NNS	Number=Plur	5	pobj	_	_
8	differ	differ	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	from	from	ADP	IN	_	8	prep	_	_
10	author	author	NOUN	NN	Number=Sing	9	pobj	_	_
11	to	to	ADP	IN	_	9	prep	_	_
12	author	author	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
14	as	as	SCONJ	IN	_	15	mark	_	_
15	do	do	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	advcl	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	specific	specific	ADJ	JJ	Degree=Pos	18	amod	_	_
18	bicategories	bicategorie	NOUN	NNS	Number=Plur	15	nsubj	_	_
19	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	acl	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 4
# text = We propose a unified framework: by working with monads on double categories and related structures (rather than bicategories), one can define generalized multicategories in a way that unifies all previous examples, while at the same time simplifying and clarifying much of the theory.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	propose	propose	VERB	VBP	Tense=Pres|VerbForm=Fin	25	ccomp	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	unified	unified	ADJ	JJ	Degree=Pos	5	amod	_	_
5	framework	framework	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
6	:	:	PUNCT	:	_	2	punct	_	_
7	by	by	ADP	IN	_	2	prep	_	_
8	working	work	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	pcomp	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	monads	monad	NOUN	NNS	Number=Plur	9	pobj	_	_
11	on	on	ADP	IN	_	10	prep	_	_
12	double	double	ADJ	JJ	Degree=Pos	13	amod	_	_
13	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	related	related	ADJ	JJ	Degree=Pos	16	amod	_	_
16	structures	structure	NOUN	NNS	Number=Plur	13	conj	_	_
17	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	13	punct	_	SpaceAfter=No
18	rather	rather	ADV	RB	_	19	advmod	_	_
19	than	than	ADP	IN	_	13	prep	_	_
20	bicategories	bicategorie	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
21	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	2	punct	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
23	one	one	PRON	PRP	PronType=Prs	25	nsubj	_	_
24	can	can	AUX	MD	VerbForm=Fin	25	aux	_	_
25	define	define	VERB	VB	VerbForm=Inf	0	ROOT	_	_
26	generalized	generalized	ADJ	JJ	Degree=Pos	27	amod	_	_
27	multicategories	multicategorie	NOUN	NNS	Number=Plur	25	dobj	_	_
28	in	in	ADP	IN	_	25	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
30	way	way	NOUN	NN	Number=Sing	28	pobj	_	_
31	that	that	PRON	WDT	PronType=Rel	32	nsubj	_	_
32	unifies	unify	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	relcl	_	_
33	all	all	DET	DT	_	35	det	_	_
34	previous	previous	ADJ	JJ	Degree=Pos	35	amod	_	_
35	examples	example	NOUN	NNS	Number=Plur	32	dobj	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
37	while	while	SCONJ	IN	_	38	mark	_	_
38	at	at	ADP	IN	_	25	prep	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
40	same	same	ADJ	JJ	Degree=Pos	41	amod	_	_
41	time	time	NOUN	NN	Number=Sing	38	pobj	_	_
42	simplifying	simplify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	38	pcomp	_	_
43	and	and	CCONJ	CC	ConjType=Cmp	42	cc	_	_
44	clarifying	clarify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	42	conj	_	_
45	much	much	ADJ	JJ	Degree=Pos	44	dobj	_	_
46	of	of	ADP	IN	_	45	prep	_	_
47	the	the	DET	DT	Definite=Def|PronType=Art	48	det	_	_
48	theory	theory	NOUN	NN	Number=Sing	46	pobj	_	SpaceAfter=No
49	.	.	PUNCT	.	PunctType=Peri	25	punct	_	SpaceAfter=No

# doc_id = 357
# sent_id = 1
# text = Groupoidification is a form of categorification in which vector spaces are replaced by groupoids and linear operators are replaced by spans of groupoids.
1	Groupoidification	Groupoidification	PROPN	NNP	Number=Sing	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	form	form	NOUN	NN	Number=Sing	19	nsubjpass	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	categorification	categorification	NOUN	NN	Number=Sing	5	pobj	_	_
7	in	in	ADP	IN	_	12	prep	_	_
8	which	which	PRON	WDT	_	7	pobj	_	_
9	vector	vector	NOUN	NN	Number=Sing	10	compound	_	_
10	spaces	space	NOUN	NNS	Number=Plur	12	nsubjpass	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	replaced	replace	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	relcl	_	_
13	by	by	ADP	IN	_	12	agent	_	_
14	groupoids	groupoid	NOUN	NNS	Number=Plur	13	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	linear	linear	ADJ	JJ	Degree=Pos	17	amod	_	_
17	operators	operator	NOUN	NNS	Number=Plur	14	conj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	19	auxpass	_	_
19	replaced	replace	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
20	by	by	ADP	IN	_	19	agent	_	_
21	spans	span	NOUN	NNS	Number=Plur	20	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	groupoids	groupoid	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 2
# text = We introduce this idea with a detailed exposition of `degroupoidification': a systematic process that turns groupoids and spans into vector spaces and linear operators.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	idea	idea	NOUN	NN	Number=Sing	2	dobj	_	_
5	with	with	ADP	IN	_	2	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	detailed	detailed	ADJ	JJ	Degree=Pos	8	amod	_	_
8	exposition	exposition	NOUN	NN	Number=Sing	5	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	9	punct	_	SpaceAfter=No
11	degroupoidification	degroupoidification	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	2	punct	_	SpaceAfter=No
13	:	:	PUNCT	:	_	2	punct	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	systematic	systematic	ADJ	JJ	Degree=Pos	16	amod	_	_
16	process	process	NOUN	NN	Number=Sing	2	dobj	_	_
17	that	that	PRON	WDT	PronType=Rel	18	nsubj	_	_
18	turns	turn	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	relcl	_	_
19	groupoids	groupoid	NOUN	NNS	Number=Plur	18	dobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	spans	span	NOUN	NNS	Number=Plur	19	conj	_	_
22	into	into	ADP	IN	_	18	prep	_	_
23	vector	vector	NOUN	NN	Number=Sing	24	compound	_	_
24	spaces	space	NOUN	NNS	Number=Plur	22	pobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	linear	linear	ADJ	JJ	Degree=Pos	27	amod	_	_
27	operators	operator	NOUN	NNS	Number=Plur	24	conj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Then we present three applications of groupoidification.
1	Then	then	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	three	three	NUM	CD	NumType=Card	5	nummod	_	_
5	applications	application	NOUN	NNS	Number=Plur	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	groupoidification	groupoidification	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = The first is to Feynman diagrams.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	first	first	ADJ	JJ	Degree=Pos	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	to	to	ADP	IN	_	3	prep	_	_
5	Feynman	Feynman	PROPN	NNP	Number=Sing	6	compound	_	_
6	diagrams	diagram	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
7	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = The Hilbert space for the quantum harmonic oscillator arises naturally from degroupoidifying the groupoid of finite sets and bijections.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	Hilbert	Hilbert	PROPN	NNP	Number=Sing	3	compound	_	_
3	space	space	NOUN	NN	Number=Sing	9	nsubj	_	_
4	for	for	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
6	quantum	quantum	PROPN	NNP	Number=Sing	8	amod	_	_
7	harmonic	harmonic	ADJ	JJ	Degree=Pos	8	amod	_	_
8	oscillator	oscillator	NOUN	NN	Number=Sing	4	pobj	_	_
9	arises	arise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	naturally	naturally	ADV	RB	_	9	advmod	_	_
11	from	from	ADP	IN	_	9	prep	_	_
12	degroupoidifying	degroupoidifye	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	pcomp	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	groupoid	groupoid	NOUN	NN	Number=Sing	12	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	finite	finite	ADJ	JJ	Degree=Pos	17	compound	_	_
17	sets	set	NOUN	NNS	Number=Plur	15	pobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	bijections	bijection	NOUN	NNS	Number=Plur	17	conj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 6
# text = This allows for a purely combinatorial interpretation of creation and annihilation operators, their commutation relations, field operators, their normal - ordered powers, and finally Feynman diagrams.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	ccomp	_	_
3	for	for	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	purely	purely	ADV	RB	_	6	advmod	_	_
6	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	7	amod	_	_
7	interpretation	interpretation	NOUN	NN	Number=Sing	3	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	creation	creation	NOUN	NN	Number=Sing	12	nmod	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	annihilation	annihilation	NOUN	NN	Number=Sing	9	conj	_	_
12	operators	operator	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
14	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	16	poss	_	_
15	commutation	commutation	NOUN	NN	Number=Sing	16	compound	_	_
16	relations	relation	NOUN	NNS	Number=Plur	0	ROOT	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	field	field	NOUN	NN	Number=Sing	19	compound	_	_
19	operators	operator	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
21	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	25	poss	_	_
22	normal	normal	ADJ	JJ	Degree=Pos	24	advmod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	amod	_	_
25	powers	power	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
28	finally	finally	ADV	RB	_	30	advmod	_	_
29	Feynman	Feynman	PROPN	NNP	Number=Sing	30	compound	_	_
30	diagrams	diagram	NOUN	NNS	Number=Plur	25	conj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 7
# text = The second application is to Hecke algebras.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	second	second	ADJ	JJ	Degree=Pos	3	amod	_	_
3	application	application	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	Hecke	Hecke	PROPN	NNP	Number=Sing	7	compound	_	_
7	algebras	algebra	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 8
# text = We explain how to groupoidify the Hecke algebra associated to a Dynkin diagram whenever the deformation parameter $ q $ is a prime power.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	explain	explain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	how	how	SCONJ	WRB	_	5	advmod	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	groupoidify	groupoidify	VERB	VB	VerbForm=Inf	2	xcomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	Hecke	Hecke	PROPN	NNP	Number=Sing	8	compound	_	_
8	algebra	algebra	NOUN	NN	Number=Sing	5	dobj	_	_
9	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	Dynkin	Dynkin	PROPN	NNP	Number=Sing	13	compound	_	_
13	diagram	diagram	NOUN	NN	Number=Sing	10	pobj	_	_
14	whenever	whenever	SCONJ	WRB	_	19	advmod	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	deformation	deformation	NOUN	NN	Number=Sing	17	compound	_	_
17	parameter	parameter	NOUN	NN	Number=Sing	19	nsubj	_	_
18	$ q $	$ q $	SYM	$	_	17	appos	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	advcl	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	prime	prime	ADJ	JJ	Degree=Pos	22	amod	_	_
22	power	power	NOUN	NN	Number=Sing	19	attr	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 9
# text = We illustrate this with the simplest nontrivial example, coming from the $ A_2 $ Dynkin diagram.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	illustrate	illustrate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	this	this	PRON	DT	Number=Sing|PronType=Dem	2	dobj	_	_
4	with	with	ADP	IN	_	2	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
6	simplest	simple	ADJ	JJS	Degree=Sup	8	amod	_	_
7	nontrivial	nontrivial	ADJ	JJ	Degree=Pos	8	amod	_	_
8	example	example	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
10	coming	come	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
11	from	from	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
13	$ A_2 $	$ a_2 $	SYM	$	_	15	nmod	_	_
14	Dynkin	Dynkin	PROPN	NNP	Number=Sing	15	compound	_	_
15	diagram	diagram	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 10
# text = In this example we show that the solution of the Yang - Baxter equation built into the $ A_2 $ Hecke algebra arises naturally from the axioms of projective geometry applied to the projective plane over the finite field $ mathbb{F}_q $ .
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	example	example	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	21	mark	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	solution	solution	NOUN	NN	Number=Sing	21	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
11	Yang	Yang	PROPN	NNP	Number=Sing	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	Baxter	Baxter	PROPN	NNP	Number=Sing	14	compound	_	_
14	equation	equation	NOUN	NN	Number=Sing	9	pobj	_	_
15	built	build	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	acl	_	_
16	into	into	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
18	$ A_2 $	$ a_2 $	SYM	$	_	20	nmod	_	_
19	Hecke	Hecke	PROPN	NNP	Number=Sing	20	compound	_	_
20	algebra	algebra	NOUN	NN	Number=Sing	16	pobj	_	_
21	arises	arise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
22	naturally	naturally	ADV	RB	_	21	advmod	_	_
23	from	from	ADP	IN	_	21	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	axioms	axiom	NOUN	NNS	Number=Plur	23	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	projective	projective	ADJ	JJ	Degree=Pos	28	amod	_	_
28	geometry	geometry	NOUN	NN	Number=Sing	26	pobj	_	_
29	applied	apply	VERB	VBD	Tense=Past|VerbForm=Fin	25	acl	_	_
30	to	to	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	projective	projective	ADJ	JJ	Degree=Pos	33	amod	_	_
33	plane	plane	NOUN	NN	Number=Sing	30	pobj	_	_
34	over	over	ADP	IN	_	29	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
36	finite	finite	ADJ	JJ	Degree=Pos	37	compound	_	_
37	field	field	NOUN	NN	Number=Sing	34	pobj	_	_
38	$ mathbb{F}_q $	$ mathbb{f}_q $	SYM	$	_	37	appos	_	_
39	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 11
# text = The third application is to Hall algebras.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	third	third	ADJ	JJ	Degree=Pos	3	amod	_	_
3	application	application	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	Hall	Hall	PROPN	NNP	Number=Sing	7	compound	_	_
7	algebras	algebra	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 12
# text = We explain how the standard construction of the Hall algebra from the category of $ mathbb{F}_q $ representations of a simply - laced quiver can be seen as an example of degroupoidification.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	explain	explain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	how	how	SCONJ	WRB	_	25	advmod	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	standard	standard	ADJ	JJ	Degree=Pos	6	amod	_	_
6	construction	construction	NOUN	NN	Number=Sing	25	nsubjpass	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	Hall	Hall	PROPN	NNP	Number=Sing	10	compound	_	_
10	algebra	algebra	NOUN	NN	Number=Sing	7	pobj	_	_
11	from	from	ADP	IN	_	6	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	$ mathbb{F}_q $	$ mathbb{f}_q $	SYM	$	_	16	poss	_	_
16	representations	representation	NOUN	NNS	Number=Plur	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
19	simply	simply	ADV	RB	_	21	advmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	laced	laced	ADJ	JJ	Degree=Pos	22	amod	_	_
22	quiver	quiver	NOUN	NN	Number=Sing	25	nsubjpass	_	_
23	can	can	AUX	MD	VerbForm=Fin	25	aux	_	_
24	be	be	AUX	VB	VerbForm=Inf	25	auxpass	_	_
25	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
26	as	as	ADP	IN	_	25	prep	_	_
27	an	an	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	example	example	NOUN	NN	Number=Sing	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	degroupoidification	degroupoidification	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 13
# text = This in turn provides a new way to categorify—or more precisely, groupoidify—the positive part of the quantum group associated to the quiver.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	4	nsubj	_	_
2	in	in	ADP	IN	_	4	prep	_	_
3	turn	turn	NOUN	NN	Number=Sing	2	pobj	_	_
4	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	new	new	ADJ	JJ	Degree=Pos	7	amod	_	_
7	way	way	NOUN	NN	Number=Sing	4	dobj	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	categorify	categorify	VERB	VB	VerbForm=Inf	7	relcl	_	SpaceAfter=No
10	—	—	PUNCT	:	_	7	punct	_	SpaceAfter=No
11	or	or	CCONJ	CC	ConjType=Cmp	7	cc	_	_
12	more	more	ADV	RBR	Degree=Cmp	13	advmod	_	_
13	precisely	precisely	ADV	RB	_	15	advmod	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
15	groupoidify	groupoidify	VERB	VB	VerbForm=Inf	4	conj	_	SpaceAfter=No
16	—	—	PUNCT	:	_	15	punct	_	SpaceAfter=No
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	positive	positive	ADJ	JJ	Degree=Pos	19	amod	_	_
19	part	part	NOUN	NN	Number=Sing	15	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	quantum	quantum	NOUN	NN	Number=Sing	23	compound	_	_
23	group	group	NOUN	NN	Number=Sing	20	pobj	_	_
24	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	acl	_	_
25	to	to	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	quiver	quiver	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 358
# sent_id = 1
# text = We clarify the relationship between internal profunctors and connectors on pairs $ (R, S) $ of equivalence relations which originally appeared in our new profunctorial approach of the Schreier - Mac Lane extension theorem.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	clarify	clarify	VERB	VBP	Tense=Pres|VerbForm=Fin	31	ccomp	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	relationship	relationship	NOUN	NN	Number=Sing	2	dobj	_	_
5	between	between	ADP	IN	_	4	prep	_	_
6	internal	internal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	profunctors	profunctor	NOUN	NNS	Number=Plur	5	pobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	connectors	connector	NOUN	NNS	Number=Plur	7	conj	_	_
10	on	on	ADP	IN	_	2	prep	_	_
11	pairs	pair	NOUN	NNS	Number=Plur	10	pobj	_	_
12	$ (R, S) $	$ (r, s) $	SYM	$	_	31	nsubj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	equivalence	equivalence	NOUN	NN	Number=Sing	15	compound	_	_
15	relations	relation	NOUN	NNS	Number=Plur	13	pobj	_	_
16	which	which	PRON	WDT	_	18	nsubj	_	_
17	originally	originally	ADV	RB	_	18	advmod	_	_
18	appeared	appear	VERB	VBD	Tense=Past|VerbForm=Fin	15	relcl	_	_
19	in	in	ADP	IN	_	18	prep	_	_
20	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	23	poss	_	_
21	new	new	ADJ	JJ	Degree=Pos	23	amod	_	_
22	profunctorial	profunctorial	ADJ	JJ	Degree=Pos	23	amod	_	_
23	approach	approach	NOUN	NN	Number=Sing	19	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
26	Schreier	Schreier	PROPN	NNP	Number=Sing	28	compound	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	Mac	Mac	PROPN	NNP	Number=Sing	29	compound	_	_
29	Lane	Lane	PROPN	NNP	Number=Sing	30	compound	_	_
30	extension	extension	NOUN	NN	Number=Sing	24	pobj	_	_
31	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	31	punct	_	SpaceAfter=No

# sent_id = 2
# text = This clarification allows us to extend this Schreier - Mac Lane theorem to any exact Maltsev category with centralizers.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	clarification	clarification	NOUN	NN	Number=Sing	3	nsubj	_	_
3	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	extend	extend	VERB	VB	VerbForm=Inf	3	ccomp	_	_
7	this	this	DET	DT	Number=Sing|PronType=Dem	11	det	_	_
8	Schreier	Schreier	PROPN	NNP	Number=Sing	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	Mac	Mac	PROPN	NNP	Number=Sing	11	compound	_	_
11	Lane	Lane	PROPN	NNP	Number=Sing	12	nsubj	_	_
12	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	3	ccomp	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	any	any	DET	DT	_	17	det	_	_
15	exact	exact	ADJ	JJ	Degree=Pos	17	amod	_	_
16	Maltsev	Maltsev	PROPN	NNP	Number=Sing	17	compound	_	_
17	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
18	with	with	ADP	IN	_	17	prep	_	_
19	centralizers	centralizer	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = On the other hand, still in the Maltsev context and in respect to the categorical Galois theory associated with a reflection $ I $ , it allows us to produce the faithful action of a certain abelian group on the set of classes (up to isomorphism) of $ I $ - normal extensions having a given Galois groupoid.
1	On	on	ADP	IN	_	26	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	other	other	ADJ	JJ	Degree=Pos	4	amod	_	_
4	hand	hand	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
6	still	still	ADV	RB	_	7	advmod	_	_
7	in	in	ADP	IN	_	26	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	Maltsev	maltsev	ADJ	JJ	Degree=Pos	10	amod	_	_
10	context	context	NOUN	NN	Number=Sing	7	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
12	in	in	ADP	IN	_	26	prep	_	_
13	respect	respect	NOUN	NN	Number=Sing	12	pobj	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
16	categorical	categorical	ADJ	JJ	Degree=Pos	18	amod	_	_
17	Galois	Galois	PROPN	NNP	Number=Sing	18	compound	_	_
18	theory	theory	NOUN	NN	Number=Sing	14	pobj	_	_
19	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	acl	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	reflection	reflection	NOUN	NN	Number=Sing	20	pobj	_	_
23	$ I $	$ i $	SYM	$	_	22	appos	_	_
24	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
25	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	26	nsubj	_	_
26	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
27	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	29	nsubj	_	_
28	to	to	PART	TO	_	29	aux	_	_
29	produce	produce	VERB	VB	VerbForm=Inf	26	ccomp	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	faithful	faithful	ADJ	JJ	Degree=Pos	32	amod	_	_
32	action	action	NOUN	NN	Number=Sing	29	dobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
35	certain	certain	ADJ	JJ	Degree=Pos	37	amod	_	_
36	abelian	abelian	ADJ	JJ	Degree=Pos	37	compound	_	_
37	group	group	NOUN	NN	Number=Sing	33	pobj	_	_
38	on	on	ADP	IN	_	29	prep	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
40	set	set	NOUN	NN	Number=Sing	38	pobj	_	_
41	of	of	ADP	IN	_	40	prep	_	_
42	classes	class	NOUN	NNS	Number=Plur	41	pobj	_	_
43	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	42	punct	_	SpaceAfter=No
44	up	up	ADP	IN	_	29	prep	_	_
45	to	to	ADP	IN	_	44	prep	_	_
46	isomorphism	isomorphism	NOUN	NN	Number=Sing	45	pobj	_	SpaceAfter=No
47	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	29	punct	_	_
48	of	of	ADP	IN	_	29	prep	_	_
49	$ I $	$ i $	SYM	$	_	51	advmod	_	_
50	-	-	PUNCT	HYPH	PunctType=Dash	51	punct	_	_
51	normal	normal	ADJ	JJ	Degree=Pos	52	amod	_	_
52	extensions	extension	NOUN	NNS	Number=Plur	48	pobj	_	_
53	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	52	acl	_	_
54	a	a	DET	DT	Definite=Ind|PronType=Art	57	det	_	_
55	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	57	amod	_	_
56	Galois	Galois	PROPN	NNP	Number=Sing	57	compound	_	_
57	groupoid	groupoid	NOUN	NN	Number=Sing	53	dobj	_	SpaceAfter=No
58	.	.	PUNCT	.	PunctType=Peri	26	punct	_	SpaceAfter=No

# doc_id = 359
# sent_id = 1
# text = A combinatorial category Disk was introduced by André Joyal to play a role in his definition of weak $ omega $ - category.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	3	amod	_	_
3	category	category	NOUN	NN	Number=Sing	6	nsubjpass	_	_
4	Disk	Disk	PROPN	NNP	Number=Sing	3	appos	_	_
5	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	6	auxpass	_	_
6	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	by	by	ADP	IN	_	6	agent	_	_
8	André	André	PROPN	NNP	Number=Sing	9	compound	_	_
9	Joyal	Joyal	PROPN	NNP	Number=Sing	7	pobj	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	play	play	VERB	VB	VerbForm=Inf	6	xcomp	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	role	role	NOUN	NN	Number=Sing	11	dobj	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	his	his	PRON	PRP$	Gender=Masc|Number=Sing|Person=3|Poss=Yes|PronType=Prs	16	poss	_	_
16	definition	definition	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	weak	weak	ADJ	JJ	Degree=Pos	21	amod	_	_
19	$ omega $	$ omega $	SYM	$	_	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	category	category	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = He defined the category $ Theta $ to be dual to Disk.
1	He	he	PRON	PRP	Case=Nom|Gender=Masc|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	defined	define	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	category	category	NOUN	NN	Number=Sing	2	dobj	_	_
5	$ Theta $	$ theta $	SYM	$	_	4	appos	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	be	be	AUX	VB	VerbForm=Inf	2	xcomp	_	_
8	dual	dual	ADJ	JJ	Degree=Pos	7	acomp	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	Disk	Disk	PROPN	NNP	Number=Sing	9	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = In the ensuing literature, a more concrete description of $ Theta $ was provided.
1	In	in	ADP	IN	_	13	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	ensuing	ensue	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	amod	_	_
4	literature	literature	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	more	more	ADV	RBR	Degree=Cmp	8	advmod	_	_
8	concrete	concrete	ADJ	JJ	Degree=Pos	9	amod	_	_
9	description	description	NOUN	NN	Number=Sing	13	nsubjpass	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	$ Theta $	$ theta $	SYM	$	_	10	pobj	_	_
12	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	13	auxpass	_	_
13	provided	provide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 4
# text = In this paper we provide another proof of the dual equivalence and introduce various categories equivalent to Disk or $ Theta $ , each providing a helpful viewpoint.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	another	another	DET	DT	_	7	det	_	_
7	proof	proof	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	dual	dual	ADJ	JJ	Degree=Pos	11	amod	_	_
11	equivalence	equivalence	NOUN	NN	Number=Sing	8	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
13	introduce	introduce	VERB	VB	VerbForm=Inf	5	conj	_	_
14	various	various	ADJ	JJ	Degree=Pos	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	13	dobj	_	_
16	equivalent	equivalent	ADJ	JJ	Degree=Pos	15	amod	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	Disk	Disk	PROPN	NNP	Number=Sing	17	pobj	_	_
19	or	or	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	$ Theta $	$ theta $	SYM	$	_	18	conj	_	_
21	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
22	each	each	PRON	DT	_	13	dep	_	_
23	providing	provide	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	acl	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
25	helpful	helpful	ADJ	JJ	Degree=Pos	26	amod	_	_
26	viewpoint	viewpoint	NOUN	NN	Number=Sing	23	dobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 360
# sent_id = 1
# text = We present two generalizations of the Span construction.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	two	two	NUM	CD	NumType=Card	4	nummod	_	_
4	generalizations	generalization	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	Span	Span	PROPN	NNP	Number=Sing	8	compound	_	_
8	construction	construction	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The first generalization gives Span of a category with all pullbacks as a (weak) double category.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	first	first	ADJ	JJ	Degree=Pos	3	amod	_	_
3	generalization	generalization	NOUN	NN	Number=Sing	4	nsubj	_	_
4	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	Span	Span	PROPN	NNP	Number=Sing	4	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	all	all	DET	DT	_	11	det	_	_
11	pullbacks	pullback	NOUN	NNS	Number=Plur	9	pobj	_	_
12	as	as	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
14	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	18	punct	_	SpaceAfter=No
15	weak	weak	ADJ	JJ	Degree=Pos	18	amod	_	SpaceAfter=No
16	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	18	punct	_	_
17	double	double	ADJ	JJ	Degree=Pos	18	amod	_	_
18	category	category	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = This double category $ Span A $ can be viewed as the free double category on the vertical category $ A $ where every vertical arrow has both a companion and a conjoint (and these companions and conjoints are adjoint to each other).
1	This	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
2	double	double	ADJ	JJ	Degree=Pos	3	amod	_	_
3	category	category	NOUN	NN	Number=Sing	7	nsubjpass	_	_
4	$ Span A $	$ span a $	SYM	$	_	3	appos	_	_
5	can	can	AUX	MD	VerbForm=Fin	7	aux	_	_
6	be	be	AUX	VB	VerbForm=Inf	7	auxpass	_	_
7	viewed	view	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	as	as	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
10	free	free	ADJ	JJ	Degree=Pos	12	amod	_	_
11	double	double	ADJ	JJ	Degree=Pos	12	amod	_	_
12	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	vertical	vertical	ADJ	JJ	Degree=Pos	16	amod	_	_
16	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
17	$ A $	$ a $	SYM	$	_	16	appos	_	_
18	where	where	SCONJ	WRB	_	22	advmod	_	_
19	every	every	DET	DT	_	21	det	_	_
20	vertical	vertical	ADJ	JJ	Degree=Pos	21	amod	_	_
21	arrow	arrow	NOUN	NN	Number=Sing	22	nsubj	_	_
22	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	relcl	_	_
23	both	both	CCONJ	CC	ConjType=Cmp	25	preconj	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
25	companion	companion	NOUN	NN	Number=Sing	22	dobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	conjoint	conjoint	NOUN	NN	Number=Sing	25	conj	_	_
29	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	28	punct	_	SpaceAfter=No
30	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
31	these	these	DET	DT	Number=Plur|PronType=Dem	32	det	_	_
32	companions	companion	NOUN	NNS	Number=Plur	35	nsubj	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
34	conjoints	conjoint	NOUN	NNS	Number=Plur	32	conj	_	_
35	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	conj	_	_
36	adjoint	adjoint	ADJ	JJ	Degree=Pos	35	acomp	_	_
37	to	to	ADP	IN	_	36	prep	_	_
38	each	each	DET	DT	_	39	det	_	_
39	other	other	ADJ	JJ	Degree=Pos	37	pobj	_	SpaceAfter=No
40	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	35	punct	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	35	punct	_	SpaceAfter=No

# sent_id = 4
# text = Thus defined, $ Span : Cat - - > Doub $ becomes a 2 - functor, which is a partial left bi - adjoint to the forgetful functor $ Vrt : Doub - - > Cat $ , which sends a double category to its category of vertical arrows.
1	Thus	thus	ADV	RB	_	2	advmod	_	_
2	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	advcl	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	$ Span : Cat - - > Doub $	$ span : cat - - > doub $	SYM	$	_	5	nsubj	_	_
5	becomes	become	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	2	2	NUM	CD	NumType=Card	9	nummod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	functor	functor	NOUN	NN	Number=Sing	5	attr	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	which	which	PRON	WDT	_	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	relcl	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
14	partial	partial	ADJ	JJ	Degree=Pos	16	amod	_	_
15	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
16	bi	bi	NOUN	NN	Number=Sing	12	attr	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	adjoint	adjoint	NOUN	NN	Number=Sing	12	attr	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	forgetful	forgetful	ADJ	JJ	Degree=Pos	22	amod	_	_
22	functor	functor	NOUN	NN	Number=Sing	19	pobj	_	_
23	$ Vrt : Doub - - > Cat $	$ vrt : doub - - > cat $	SYM	$	_	22	appos	_	_
24	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
25	which	which	PRON	WDT	_	26	nsubj	_	_
26	sends	send	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	relcl	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	double	double	ADJ	JJ	Degree=Pos	29	amod	_	_
29	category	category	NOUN	NN	Number=Sing	26	dobj	_	_
30	to	to	ADP	IN	_	26	prep	_	_
31	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	32	poss	_	_
32	category	category	NOUN	NN	Number=Sing	30	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	vertical	vertical	ADJ	JJ	Degree=Pos	35	amod	_	_
35	arrows	arrow	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = The second generalization gives Span of an arbitrary category as an oplax normal double category.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	second	second	ADJ	JJ	Degree=Pos	3	amod	_	_
3	generalization	generalization	NOUN	NN	Number=Sing	4	nsubj	_	_
4	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	Span	Span	PROPN	NNP	Number=Sing	4	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	9	amod	_	_
9	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
10	as	as	ADP	IN	_	9	prep	_	_
11	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
12	oplax	oplax	ADJ	JJ	Degree=Pos	15	nmod	_	_
13	normal	normal	ADJ	JJ	Degree=Pos	15	amod	_	_
14	double	double	ADJ	JJ	Degree=Pos	15	amod	_	_
15	category	category	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 6
# text = The universal property can again be given in terms of companions and conjoints and the presence of their composites.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	universal	universal	ADJ	JJ	Degree=Pos	3	amod	_	_
3	property	property	NOUN	NN	Number=Sing	7	nsubjpass	_	_
4	can	can	AUX	MD	VerbForm=Fin	7	aux	_	_
5	again	again	ADV	RB	_	7	advmod	_	_
6	be	be	AUX	VB	VerbForm=Inf	7	auxpass	_	_
7	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	terms	term	NOUN	NNS	Number=Plur	8	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	companions	companion	NOUN	NNS	Number=Plur	10	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	conjoints	conjoint	NOUN	NNS	Number=Plur	11	conj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	presence	presence	NOUN	NN	Number=Sing	9	conj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	19	poss	_	_
19	composites	composite	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 7
# text = Moreover, $ Span A $ is universal with this property in the sense that $ Span : Cat - - > OplaxNDoub $ is left bi - adjoint to the forgetful functor which sends an oplax double category to its vertical arrow category.
1	Moreover	moreover	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	$ Span A $	$ span a $	SYM	$	_	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	universal	universal	ADJ	JJ	Degree=Pos	4	acomp	_	_
6	with	with	ADP	IN	_	5	prep	_	_
7	this	this	DET	DT	Number=Sing|PronType=Dem	8	det	_	_
8	property	property	NOUN	NN	Number=Sing	6	pobj	_	_
9	in	in	ADP	IN	_	4	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	sense	sense	NOUN	NN	Number=Sing	9	pobj	_	_
12	that	that	SCONJ	IN	_	15	mark	_	_
13	$ Span : Cat - - > OplaxNDoub $	$ span : cat - - > oplaxndoub $	SYM	$	_	15	nsubjpass	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acl	_	_
16	bi	bi	PROPN	NNP	Number=Sing	15	oprd	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	adjoint	adjoint	NOUN	NN	Number=Sing	15	oprd	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	forgetful	forgetful	ADJ	JJ	Degree=Pos	22	amod	_	_
22	functor	functor	NOUN	NN	Number=Sing	19	pobj	_	_
23	which	which	PRON	WDT	_	24	nsubj	_	_
24	sends	send	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	relcl	_	_
25	an	an	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
26	oplax	oplax	NOUN	NN	Number=Sing	28	nmod	_	_
27	double	double	ADJ	JJ	Degree=Pos	28	amod	_	_
28	category	category	NOUN	NN	Number=Sing	24	dobj	_	_
29	to	to	ADP	IN	_	24	prep	_	_
30	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	33	poss	_	_
31	vertical	vertical	ADJ	JJ	Degree=Pos	33	amod	_	_
32	arrow	arrow	NOUN	NN	Number=Sing	33	compound	_	_
33	category	category	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 361
# sent_id = 1
# text = We present a doctrinal approach to category theory, obtained by abstracting from the indexed inclusion (via discrete fibrations and opfibrations) of left and of right actions of $ X $ in $ Cat $ in categories over $ X $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	doctrinal	doctrinal	ADJ	JJ	Degree=Pos	5	amod	_	_
5	approach	approach	NOUN	NN	Number=Sing	2	dobj	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	category	category	NOUN	NN	Number=Sing	8	compound	_	_
8	theory	theory	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
10	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	acl	_	_
11	by	by	ADP	IN	_	10	agent	_	_
12	abstracting	abstract	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	pcomp	_	_
13	from	from	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	indexed	indexed	ADJ	JJ	Degree=Pos	16	amod	_	_
16	inclusion	inclusion	NOUN	NN	Number=Sing	13	pobj	_	_
17	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
18	via	via	ADP	IN	_	12	prep	_	_
19	discrete	discrete	ADJ	JJ	Degree=Pos	20	amod	_	_
20	fibrations	fibration	NOUN	NNS	Number=Plur	18	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	opfibrations	opfibration	NOUN	NNS	Number=Plur	20	conj	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	12	punct	_	_
24	of	of	ADP	IN	_	12	prep	_	_
25	left	left	ADJ	JJ	Degree=Pos	24	pobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	of	of	ADP	IN	_	24	conj	_	_
28	right	right	ADJ	JJ	Degree=Pos	29	amod	_	_
29	actions	action	NOUN	NNS	Number=Plur	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	$ X $	$ x $	SYM	$	_	30	pobj	_	_
32	in	in	ADP	IN	_	29	prep	_	_
33	$ Cat $	$ cat $	SYM	$	_	32	pobj	_	_
34	in	in	ADP	IN	_	29	prep	_	_
35	categories	category	NOUN	NNS	Number=Plur	34	pobj	_	_
36	over	over	ADP	IN	_	35	prep	_	_
37	$ X $	$ x $	SYM	$	_	36	pobj	_	_
38	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Namely, a ``weak temporal doctrine'' consists essentially of two indexed functors with the same codomain such that the induced functors have both left and right adjoints satisfying some exactness conditions, in the spirit of categorical logic.
1	Namely	namely	ADV	RB	_	10	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
4	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	8	punct	_	SpaceAfter=No
5	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	8	punct	_	SpaceAfter=No
6	weak	weak	ADJ	JJ	Degree=Pos	8	amod	_	_
7	temporal	temporal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	doctrine	doctrine	NOUN	NN	Number=Sing	10	nsubj	_	SpaceAfter=No
9	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	8	punct	_	_
10	consists	consist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	essentially	essentially	ADV	RB	_	10	advmod	_	_
12	of	of	ADP	IN	_	10	prep	_	_
13	two	two	NUM	CD	NumType=Card	15	nummod	_	_
14	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
15	functors	functor	NOUN	NNS	Number=Plur	12	pobj	_	_
16	with	with	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	same	same	ADJ	JJ	Degree=Pos	19	amod	_	_
19	codomain	codomain	NOUN	NN	Number=Sing	16	pobj	_	_
20	such	such	ADJ	JJ	Degree=Pos	27	amod	_	_
21	that	that	SCONJ	IN	_	27	mark	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
24	functors	functor	NOUN	NNS	Number=Plur	27	nsubj	_	_
25	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	27	aux	_	_
26	both	both	PRON	DT	_	27	preconj	_	_
27	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	advcl	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
29	right	right	ADJ	JJ	Degree=Pos	30	amod	_	_
30	adjoints	adjoint	NOUN	NNS	Number=Plur	27	conj	_	_
31	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	30	acl	_	_
32	some	some	DET	DT	_	34	det	_	_
33	exactness	exactness	ADJ	JJ	Degree=Pos	34	amod	_	_
34	conditions	condition	NOUN	NNS	Number=Plur	31	dobj	_	SpaceAfter=No
35	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
36	in	in	ADP	IN	_	27	prep	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	spirit	spirit	NOUN	NN	Number=Sing	36	pobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	categorical	categorical	ADJ	JJ	Degree=Pos	41	amod	_	_
41	logic	logic	NOUN	NN	Number=Sing	39	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 3
# text = The derived logical rules include some adjunction - like laws involving the truth - values - enriched hom and tensor functors, which condense several basic categorical properties and display a nice symmetry.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	derived	derive	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	amod	_	_
3	logical	logical	ADJ	JJ	Degree=Pos	4	amod	_	_
4	rules	rule	NOUN	NNS	Number=Plur	5	nsubj	_	_
5	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	some	some	DET	DT	_	10	det	_	_
7	adjunction	adjunction	NOUN	NN	Number=Sing	9	npadvmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	like	like	ADJ	JJ	Degree=Pos	10	amod	_	_
10	laws	law	NOUN	NNS	Number=Plur	5	dobj	_	_
11	involving	involve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	acl	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
13	truth	truth	NOUN	NN	Number=Sing	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	values	value	NOUN	NNS	Number=Plur	17	npadvmod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	amod	_	_
18	hom	hom	NOUN	NN	Number=Sing	17	nmod	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	tensor	tensor	NOUN	NN	Number=Sing	18	conj	_	_
21	functors	functor	NOUN	NNS	Number=Plur	11	dobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	which	which	PRON	WDT	_	24	nsubj	_	_
24	condense	condense	VERB	VBP	Tense=Pres|VerbForm=Fin	21	relcl	_	_
25	several	several	ADJ	JJ	Degree=Pos	28	amod	_	_
26	basic	basic	ADJ	JJ	Degree=Pos	28	amod	_	_
27	categorical	categorical	ADJ	JJ	Degree=Pos	28	amod	_	_
28	properties	property	NOUN	NNS	Number=Plur	24	dobj	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
30	display	display	VERB	VB	VerbForm=Inf	24	conj	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
32	nice	nice	ADJ	JJ	Degree=Pos	33	amod	_	_
33	symmetry	symmetry	NOUN	NN	Number=Sing	30	dobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = The symmetry becomes more apparent in the slightly stronger context of ``temporal doctrines'', which we initially treat and which include as an instance the inclusion of lower and upper sets in the parts of a poset, as well as the inclusion of left and right actions of a graph in the graphs over it.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	symmetry	symmetry	NOUN	NN	Number=Sing	3	nsubj	_	_
3	becomes	become	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	more	more	ADV	RBR	Degree=Cmp	5	advmod	_	_
5	apparent	apparent	ADJ	JJ	Degree=Pos	3	acomp	_	_
6	in	in	ADP	IN	_	3	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	slightly	slightly	ADV	RB	_	9	advmod	_	_
9	stronger	strong	ADJ	JJR	Degree=Cmp	10	amod	_	_
10	context	context	NOUN	NN	Number=Sing	6	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	11	punct	_	SpaceAfter=No
13	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	15	punct	_	SpaceAfter=No
14	temporal	temporal	ADJ	JJ	Degree=Pos	15	amod	_	_
15	doctrines	doctrine	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
16	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	15	punct	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
18	which	which	PRON	WDT	_	21	dobj	_	_
19	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	21	nsubj	_	_
20	initially	initially	ADV	RB	_	21	advmod	_	_
21	treat	treat	VERB	VBP	Tense=Pres|VerbForm=Fin	15	relcl	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	which	which	PRON	WDT	_	24	nsubj	_	_
24	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	21	conj	_	_
25	as	as	ADP	IN	_	24	prep	_	_
26	an	an	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	instance	instance	NOUN	NN	Number=Sing	25	pobj	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	inclusion	inclusion	NOUN	NN	Number=Sing	24	dobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	lower	low	ADJ	JJR	Degree=Cmp	34	amod	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	upper	upper	ADJ	JJ	Degree=Pos	31	conj	_	_
34	sets	set	NOUN	NNS	Number=Plur	30	pobj	_	_
35	in	in	ADP	IN	_	34	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	parts	part	NOUN	NNS	Number=Plur	35	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	a	a	DET	DT	Definite=Ind|PronType=Art	40	det	_	_
40	poset	poset	NOUN	NN	Number=Sing	38	pobj	_	SpaceAfter=No
41	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
42	as	as	ADV	RB	_	44	advmod	_	_
43	well	well	ADV	RB	Degree=Pos	44	advmod	_	_
44	as	as	ADP	IN	_	29	cc	_	_
45	the	the	DET	DT	Definite=Def|PronType=Art	46	det	_	_
46	inclusion	inclusion	NOUN	NN	Number=Sing	29	conj	_	_
47	of	of	ADP	IN	_	46	prep	_	_
48	left	left	ADJ	JJ	Degree=Pos	51	amod	_	_
49	and	and	CCONJ	CC	ConjType=Cmp	48	cc	_	_
50	right	right	ADJ	JJ	Degree=Pos	48	conj	_	_
51	actions	action	NOUN	NNS	Number=Plur	47	pobj	_	_
52	of	of	ADP	IN	_	51	prep	_	_
53	a	a	DET	DT	Definite=Ind|PronType=Art	54	det	_	_
54	graph	graph	NOUN	NN	Number=Sing	52	pobj	_	_
55	in	in	ADP	IN	_	54	prep	_	_
56	the	the	DET	DT	Definite=Def|PronType=Art	57	det	_	_
57	graphs	graph	NOUN	NNS	Number=Plur	55	pobj	_	_
58	over	over	ADP	IN	_	57	prep	_	_
59	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	58	pobj	_	SpaceAfter=No
60	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 362
# sent_id = 1
# text = Let $ R $ be a commutative ring whose complete ring of quotients is $ R $ - injective.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ R $	$ r $	SYM	$	_	1	ccomp	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	commutative	commutative	ADJ	JJ	Degree=Pos	6	amod	_	_
6	ring	ring	NOUN	NN	Number=Sing	3	attr	_	_
7	whose	whose	DET	WP$	Poss=Yes	9	poss	_	_
8	complete	complete	ADJ	JJ	Degree=Pos	9	amod	_	_
9	ring	ring	NOUN	NN	Number=Sing	12	nsubj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	quotients	quotient	NOUN	NNS	Number=Plur	10	pobj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	relcl	_	_
13	$ R $	$ r $	SYM	$	_	15	advmod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	injective	injective	ADJ	JJ	Degree=Pos	12	acomp	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that the category of topological $ R $ - modules contains a full subcategory that is $ * $ - autonomous using $ R $ itself as dualizing object.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	11	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	11	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	topological	topological	ADJ	JJ	Degree=Pos	10	amod	_	_
8	$ R $	$ r $	SYM	$	_	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	modules	module	NOUN	NNS	Number=Plur	6	pobj	_	_
11	contains	contain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	full	full	ADJ	JJ	Degree=Pos	14	amod	_	_
14	subcategory	subcategory	NOUN	NN	Number=Sing	11	dobj	_	_
15	that	that	PRON	WDT	PronType=Rel	16	nsubj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
17	$ * $	$ * $	SYM	$	_	19	advmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	autonomous	autonomous	ADJ	JJ	Degree=Pos	16	acomp	_	_
20	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	advcl	_	_
21	$ R $	$ r $	SYM	$	_	22	nmod	_	_
22	itself	itself	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs|Reflex=Yes	20	dobj	_	_
23	as	as	ADP	IN	_	20	prep	_	_
24	dualizing	dualize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	23	pcomp	_	_
25	object	object	NOUN	NN	Number=Sing	24	dobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = In order to do this, we develop a new variation on the category $ chu(D, R) $ , where $ D $ is the category of discrete $ R $ - modules: the high wide subcategory, which we show equivalent to the category of reflexive topological modules.
1	In	in	ADP	IN	_	8	prep	_	_
2	order	order	NOUN	NN	Number=Sing	1	pobj	_	_
3	to	to	PART	TO	_	4	aux	_	_
4	do	do	AUX	VB	VerbForm=Inf	2	acl	_	_
5	this	this	PRON	DT	Number=Sing|PronType=Dem	4	dobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
7	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	8	nsubj	_	_
8	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	new	new	ADJ	JJ	Degree=Pos	11	amod	_	_
11	variation	variation	NOUN	NN	Number=Sing	8	dobj	_	_
12	on	on	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
15	$ chu(D, R) $	$ chu(d, r) $	X	FW	Foreign=Yes	14	appos	_	_
16	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
17	where	where	SCONJ	WRB	_	19	advmod	_	_
18	$ D $	$ d $	SYM	$	_	19	nsubj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	category	category	NOUN	NN	Number=Sing	19	attr	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	discrete	discrete	ADJ	JJ	Degree=Pos	26	amod	_	_
24	$ R $	$ r $	SYM	$	_	26	compound	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	modules	module	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
27	:	:	PUNCT	:	_	8	punct	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
29	high	high	ADJ	JJ	Degree=Pos	30	amod	_	_
30	wide	wide	ADJ	JJ	Degree=Pos	31	amod	_	_
31	subcategory	subcategory	NOUN	NN	Number=Sing	8	dobj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
33	which	which	PRON	WDT	_	35	dobj	_	_
34	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	35	nsubj	_	_
35	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	31	relcl	_	_
36	equivalent	equivalent	ADJ	JJ	Degree=Pos	35	acomp	_	_
37	to	to	ADP	IN	_	36	prep	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
39	category	category	NOUN	NN	Number=Sing	37	pobj	_	_
40	of	of	ADP	IN	_	39	prep	_	_
41	reflexive	reflexive	ADJ	JJ	Degree=Pos	43	amod	_	_
42	topological	topological	ADJ	JJ	Degree=Pos	43	amod	_	_
43	modules	module	NOUN	NNS	Number=Plur	40	pobj	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 363
# sent_id = 1
# text = Deterministic automata are algebras of the monad $ T_M $ associated to a free monoid $ M $ .
1	Deterministic	deterministic	ADJ	JJ	Degree=Pos	2	amod	_	_
2	automata	automata	NOUN	NN	Number=Sing	3	nsubj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	algebras	algebra	NOUN	NNS	Number=Plur	3	attr	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	monad	monad	NOUN	NNS	Number=Plur	5	pobj	_	_
8	$ T_M $	$ t_m $	SYM	$	_	7	appos	_	_
9	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	free	free	ADJ	JJ	Degree=Pos	13	amod	_	_
13	monoid	monoid	NOUN	NN	Number=Sing	10	pobj	_	_
14	$ M $	$ m $	SYM	$	_	3	dep	_	_
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = To extend to nondeterministic and stochastic automata such a monadic formalism, it is suitable to resort to a notion richer than the one of monad, but equally basic: the notion of distributive law between two monads.
1	To	to	PART	TO	_	2	aux	_	_
2	extend	extend	VERB	VB	VerbForm=Inf	14	advcl	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	nondeterministic	nondeterministic	ADJ	JJ	Degree=Pos	7	amod	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	stochastic	stochastic	ADJ	JJ	Degree=Pos	4	conj	_	_
7	automata	automata	NOUN	NN	Number=Sing	3	pobj	_	_
8	such	such	DET	PDT	_	11	predet	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	monadic	monadic	ADJ	JJ	Degree=Pos	11	amod	_	_
11	formalism	formalism	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
13	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	suitable	suitable	ADJ	JJ	Degree=Pos	14	acomp	_	_
16	to	to	PART	TO	_	17	aux	_	_
17	resort	resort	VERB	VB	VerbForm=Inf	15	xcomp	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	notion	notion	NOUN	NN	Number=Sing	18	pobj	_	_
21	richer	rich	ADJ	JJR	Degree=Cmp	20	amod	_	_
22	than	than	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	one	one	NUM	CD	NumType=Card	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	monad	monad	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
28	but	but	CCONJ	CC	ConjType=Cmp	14	cc	_	_
29	equally	equally	ADV	RB	_	30	advmod	_	_
30	basic	basic	ADJ	JJ	Degree=Pos	14	conj	_	SpaceAfter=No
31	:	:	PUNCT	:	_	14	punct	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
33	notion	notion	NOUN	NN	Number=Sing	13	appos	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	distributive	distributive	ADJ	JJ	Degree=Pos	36	amod	_	_
36	law	law	NOUN	NN	Number=Sing	34	pobj	_	_
37	between	between	ADP	IN	_	36	prep	_	_
38	two	two	NUM	CD	NumType=Card	39	nummod	_	_
39	monads	monad	NOUN	NNS	Number=Plur	37	pobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 3
# text = The notion of algebra on a monad is then generalized by the one of algebra for a distributive law.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	notion	notion	NOUN	NN	Number=Sing	10	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	algebra	algebra	NOUN	NN	Number=Sing	3	pobj	_	_
5	on	on	ADP	IN	_	2	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	monad	monad	NOUN	NNS	Number=Plur	5	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
9	then	then	ADV	RB	PronType=Dem	10	advmod	_	_
10	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	by	by	ADP	IN	_	10	agent	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	one	one	NUM	CD	NumType=Card	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	algebra	algebra	NOUN	NN	Number=Sing	14	pobj	_	_
16	for	for	ADP	IN	_	13	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	distributive	distributive	ADJ	JJ	Degree=Pos	19	amod	_	_
19	law	law	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 4
# text = The nondeterministic and stochastic automata are precisely algebras for distributive laws whose first monad is $ T_M $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
2	nondeterministic	nondeterministic	ADJ	JJ	Degree=Pos	5	amod	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	stochastic	stochastic	ADJ	JJ	Degree=Pos	2	conj	_	_
5	automata	automata	NOUN	NN	Number=Sing	6	nsubj	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	precisely	precisely	ADV	RB	_	8	advmod	_	_
8	algebras	algebra	NOUN	NNS	Number=Plur	6	attr	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	distributive	distributive	ADJ	JJ	Degree=Pos	11	amod	_	_
11	laws	law	NOUN	NNS	Number=Plur	9	pobj	_	_
12	whose	whose	DET	WP$	Poss=Yes	14	poss	_	_
13	first	first	ADJ	JJ	Degree=Pos	14	amod	_	_
14	monad	monad	NOUN	NNS	Number=Plur	15	nsubj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	conj	_	_
16	$ T_M $	$ t_m $	SYM	$	_	15	attr	_	_
17	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 5
# text = If the nondeterministic case involves a distributive law between $ T_M $ and the well - known power set monad, the stochastic case involves a distributive law between $ T_M $ (where, here, $ M $ is a measurable monoid) and the probability monad.
1	If	if	SCONJ	IN	_	5	mark	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	nondeterministic	nondeterministic	ADJ	JJ	Degree=Pos	4	amod	_	_
4	case	case	NOUN	NN	Number=Sing	5	nsubj	_	_
5	involves	involve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	advcl	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	distributive	distributive	ADJ	JJ	Degree=Pos	8	amod	_	_
8	law	law	NOUN	NN	Number=Sing	5	dobj	_	_
9	between	between	ADP	IN	_	8	prep	_	_
10	$ T_M $	$ t_m $	SYM	$	_	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
13	well	well	ADV	RB	Degree=Pos	15	advmod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
16	power	power	NOUN	NN	Number=Sing	17	compound	_	_
17	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	compound	_	_
18	monad	monad	NOUN	NNS	Number=Plur	10	conj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	stochastic	stochastic	ADJ	JJ	Degree=Pos	22	amod	_	_
22	case	case	NOUN	NN	Number=Sing	23	nsubj	_	_
23	involves	involve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
25	distributive	distributive	ADJ	JJ	Degree=Pos	26	amod	_	_
26	law	law	NOUN	NN	Number=Sing	23	dobj	_	_
27	between	between	ADP	IN	_	26	prep	_	_
28	$ T_M $	$ t_m $	SYM	$	_	27	pobj	_	_
29	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	28	punct	_	SpaceAfter=No
30	where	where	SCONJ	WRB	_	35	advmod	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
32	here	here	ADV	RB	PronType=Dem	35	advmod	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
34	$ M $	$ m $	SYM	$	_	35	nsubj	_	_
35	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	ccomp	_	_
36	a	a	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
37	measurable	measurable	ADJ	JJ	Degree=Pos	38	amod	_	_
38	monoid	monoid	NOUN	NN	Number=Sing	35	attr	_	SpaceAfter=No
39	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	35	punct	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
42	probability	probability	NOUN	NN	Number=Sing	43	compound	_	_
43	monad	monad	NOUN	NNS	Number=Plur	35	conj	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# sent_id = 6
# text = This allows presentation of the stochastic automata as algebras for this distributive law.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	presentation	presentation	NOUN	NN	Number=Sing	2	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	stochastic	stochastic	ADJ	JJ	Degree=Pos	7	amod	_	_
7	automata	automata	NOUN	NN	Number=Sing	4	pobj	_	_
8	as	as	ADP	IN	_	3	prep	_	_
9	algebras	algebra	NOUN	NNS	Number=Plur	8	pobj	_	_
10	for	for	ADP	IN	_	3	prep	_	_
11	this	this	DET	DT	Number=Sing|PronType=Dem	13	det	_	_
12	distributive	distributive	ADJ	JJ	Degree=Pos	13	amod	_	_
13	law	law	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = This paper taking place at the confluence of category, automata and probability theories, we have, for the convenience of the reader not aware of each area, made useful reviews about these subjects (in several appendices).
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	taking	take	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	advcl	_	_
4	place	place	NOUN	NN	Number=Sing	3	dobj	_	_
5	at	at	ADP	IN	_	3	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	confluence	confluence	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	category	category	NOUN	NN	Number=Sing	14	nmod	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	automata	automata	NOUN	NN	Number=Sing	14	nmod	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	probability	probability	NOUN	NN	Number=Sing	11	conj	_	_
14	theories	theory	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
16	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	17	nsubj	_	_
17	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	31	aux	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	for	for	ADP	IN	_	17	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	convenience	convenience	NOUN	NN	Number=Sing	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	reader	reader	NOUN	NN	Number=Sing	22	pobj	_	_
25	not	not	PART	RB	Polarity=Neg	26	neg	_	_
26	aware	aware	ADJ	JJ	Degree=Pos	17	xcomp	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	each	each	DET	DT	_	29	det	_	_
29	area	area	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
31	made	make	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
32	useful	useful	ADJ	JJ	Degree=Pos	33	amod	_	_
33	reviews	review	NOUN	NNS	Number=Plur	31	dobj	_	_
34	about	about	ADP	IN	_	33	prep	_	_
35	these	these	DET	DT	Number=Plur|PronType=Dem	36	det	_	_
36	subjects	subject	NOUN	NNS	Number=Plur	34	pobj	_	_
37	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	31	punct	_	SpaceAfter=No
38	in	in	ADP	IN	_	31	prep	_	_
39	several	several	ADJ	JJ	Degree=Pos	40	amod	_	_
40	appendices	appendix	NOUN	NNS	Number=Plur	38	pobj	_	SpaceAfter=No
41	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	31	punct	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	31	punct	_	SpaceAfter=No

# sent_id = 8
# text = We also recall the detailed construction of the probability monad; and we construct precisely the distributive law which links it to the monad $ T_M $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	recall	recall	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	detailed	detailed	ADJ	JJ	Degree=Pos	6	amod	_	_
6	construction	construction	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	probability	probability	NOUN	NN	Number=Sing	10	compound	_	_
10	monad	monad	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
11	;	;	PUNCT	:	_	3	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	3	conj	_	_
15	precisely	precisely	ADV	RB	_	18	advmod	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	distributive	distributive	ADJ	JJ	Degree=Pos	18	amod	_	_
18	law	law	NOUN	NN	Number=Sing	14	dobj	_	_
19	which	which	PRON	WDT	_	20	nsubj	_	_
20	links	link	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	relcl	_	_
21	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	20	dobj	_	_
22	to	to	ADP	IN	_	20	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	monad	monad	NOUN	NNS	Number=Plur	22	pobj	_	_
25	$ T_M $	$ t_m $	SYM	$	_	24	appos	_	_
26	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# doc_id = 364
# sent_id = 1
# text = An alternative description of the tensor product of sup - lattices is given with yet another description provided for the tensor product in the special case of CCD sup - lattices.
1	An	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	alternative	alternative	ADJ	JJ	Degree=Pos	3	amod	_	_
3	description	description	NOUN	NN	Number=Sing	13	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	tensor	tensor	NOUN	NN	Number=Sing	7	compound	_	_
7	product	product	NOUN	NN	Number=Sing	4	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	sup	sup	NOUN	NN	Number=Sing	11	compound	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	lattices	lattice	NOUN	NNS	Number=Plur	8	pobj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	yet	yet	ADV	RB	_	16	advmod	_	_
16	another	another	DET	DT	_	17	det	_	_
17	description	description	NOUN	NN	Number=Sing	14	pobj	_	_
18	provided	provide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
19	for	for	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	tensor	tensor	NOUN	NN	Number=Sing	22	compound	_	_
22	product	product	NOUN	NN	Number=Sing	19	pobj	_	_
23	in	in	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	special	special	ADJ	JJ	Degree=Pos	26	amod	_	_
26	case	case	NOUN	NN	Number=Sing	23	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	CCD	CCD	PROPN	NNP	Number=Sing	31	compound	_	_
29	sup	sup	NOUN	NN	Number=Sing	31	compound	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	lattices	lattice	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 2
# text = In the course of developing the latter, properties of sup - preserving functions and the totally below relation are generalized to not - necessarily - complete ordered sets.
1	In	in	ADP	IN	_	21	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	course	course	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	developing	develop	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	pcomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	latter	latter	ADJ	JJ	Degree=Pos	5	dobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
9	properties	property	NOUN	NNS	Number=Plur	21	nsubjpass	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	sup	sup	NOUN	NN	Number=Sing	13	npadvmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	amod	_	_
14	functions	function	NOUN	NNS	Number=Plur	10	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	totally	totally	ADV	RB	_	18	advmod	_	_
18	below	below	ADP	IN	_	9	prep	_	_
19	relation	relation	NOUN	NN	Number=Sing	18	pobj	_	_
20	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	21	auxpass	_	_
21	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
22	to	to	PART	TO	_	21	prep	_	_
23	not	not	PART	RB	Polarity=Neg	25	neg	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	necessarily	necessarily	ADV	RB	_	27	advmod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	complete	complete	ADJ	JJ	Degree=Pos	29	amod	_	_
28	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	amod	_	_
29	sets	set	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# doc_id = 365
# sent_id = 1
# text = An unpublished result by the first author states that there exists a Hopf algebra $ H $ such that for any Möbius category $ cal C $ (in the sense of Leroux) there exists a canonical algebra morphism from the dual $ H^* $ of $ H $ to the incidence algebra of $ cal C $ .
1	An	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	unpublished	unpublished	ADJ	JJ	Degree=Pos	3	amod	_	_
3	result	result	NOUN	NN	Number=Sing	8	nsubj	_	_
4	by	by	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	first	first	ADJ	JJ	Degree=Pos	7	amod	_	_
7	author	author	NOUN	NN	Number=Sing	4	pobj	_	_
8	states	state	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	that	that	SCONJ	IN	_	11	mark	_	_
10	there	there	PRON	EX	_	11	expl	_	_
11	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	ccomp	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	Hopf	Hopf	PROPN	NNP	Number=Sing	14	compound	_	_
14	algebra	algebra	NOUN	NN	Number=Sing	11	dobj	_	_
15	$ H $	$ h $	SYM	$	_	17	predet	_	_
16	such	such	ADJ	JJ	Degree=Pos	17	amod	_	_
17	that	that	SCONJ	IN	_	11	dobj	_	_
18	for	for	ADP	IN	_	31	prep	_	_
19	any	any	DET	DT	_	21	det	_	_
20	Möbius	Möbius	PROPN	NNP	Number=Sing	21	compound	_	_
21	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
22	$ cal C $	$ cal c $	SYM	$	_	21	nummod	_	_
23	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	31	punct	_	SpaceAfter=No
24	in	in	ADP	IN	_	31	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	sense	sense	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	Leroux	Leroux	PROPN	NNP	Number=Sing	27	pobj	_	SpaceAfter=No
29	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	31	punct	_	_
30	there	there	PRON	EX	_	31	expl	_	_
31	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	advcl	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
33	canonical	canonical	ADJ	JJ	Degree=Pos	34	amod	_	_
34	algebra	algebra	NOUN	NN	Number=Sing	35	compound	_	_
35	morphism	morphism	NOUN	NN	Number=Sing	31	dobj	_	_
36	from	from	ADP	IN	_	31	prep	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
38	dual	dual	ADJ	JJ	Degree=Pos	39	amod	_	_
39	$ H^* $	$ h^* $	SYM	$	_	36	pobj	_	_
40	of	of	ADP	IN	_	39	prep	_	_
41	$ H $	$ h $	SYM	$	_	40	pobj	_	_
42	to	to	ADP	IN	_	36	prep	_	_
43	the	the	DET	DT	Definite=Def|PronType=Art	45	det	_	_
44	incidence	incidence	NOUN	NN	Number=Sing	45	compound	_	_
45	algebra	algebra	NOUN	NN	Number=Sing	42	pobj	_	_
46	of	of	ADP	IN	_	45	prep	_	_
47	$ cal C $	$ cal c $	SYM	$	_	46	pobj	_	_
48	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = Moreover, the Möbius inversion principle in incidence algebras follows from a `master' inversion result in $ H^* $ .
1	Moreover	moreover	ADV	RB	_	10	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
4	Möbius	Möbius	PROPN	NNP	Number=Sing	6	compound	_	_
5	inversion	inversion	NOUN	NN	Number=Sing	6	compound	_	_
6	principle	principle	NOUN	NN	Number=Sing	10	nsubj	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	incidence	incidence	NOUN	NN	Number=Sing	9	compound	_	_
9	algebras	algebra	NOUN	NNS	Number=Plur	7	pobj	_	_
10	follows	follow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	from	from	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
13	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	17	punct	_	SpaceAfter=No
14	master	master	NOUN	NN	Number=Sing	17	poss	_	SpaceAfter=No
15	'	'	PART	POS	_	14	case	_	_
16	inversion	inversion	NOUN	NN	Number=Sing	17	compound	_	_
17	result	result	NOUN	NN	Number=Sing	11	pobj	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	$ H^* $	$ h^* $	SYM	$	_	18	pobj	_	_
20	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 3
# text = The underlying module of $ H $ was originally defined as the free module on the set of isomorphism classes of Möbius intervals, that is Möbius categories with initial and terminal objects.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	underlying	underlie	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	amod	_	_
3	module	module	NOUN	NN	Number=Sing	8	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	$ H $	$ h $	SYM	$	_	4	pobj	_	_
6	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	8	auxpass	_	_
7	originally	originally	ADV	RB	_	8	advmod	_	_
8	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	ccomp	_	_
9	as	as	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	free	free	ADJ	JJ	Degree=Pos	12	amod	_	_
12	module	module	NOUN	NN	Number=Sing	9	pobj	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	set	set	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	isomorphism	isomorphism	NOUN	NN	Number=Sing	18	compound	_	_
18	classes	class	NOUN	NNS	Number=Plur	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	Möbius	Möbius	PROPN	NNP	Number=Sing	21	compound	_	_
21	intervals	interval	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
23	that	that	PRON	WDT	PronType=Rel	24	nsubj	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
25	Möbius	Möbius	PROPN	NNP	Number=Sing	26	compound	_	_
26	categories	category	NOUN	NNS	Number=Plur	24	attr	_	_
27	with	with	ADP	IN	_	26	prep	_	_
28	initial	initial	ADJ	JJ	Degree=Pos	31	amod	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	terminal	terminal	ADJ	JJ	Degree=Pos	28	conj	_	_
31	objects	object	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# sent_id = 4
# text = Here we consider a category of Möbius intervals and construct the Hopf algebra via the objective approach applied to a monoidal extensive category of combinatorial objects, with the values in appropriate rings being abstracted from combinatorial functors on the objects.
1	Here	here	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Möbius	Möbius	PROPN	NNP	Number=Sing	8	compound	_	_
8	intervals	interval	NOUN	NNS	Number=Plur	6	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
10	construct	construct	VERB	VB	VerbForm=Inf	3	conj	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	Hopf	Hopf	PROPN	NNP	Number=Sing	13	compound	_	_
13	algebra	algebra	NOUN	NN	Number=Sing	10	dobj	_	_
14	via	via	ADP	IN	_	10	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	objective	objective	ADJ	JJ	Degree=Pos	17	amod	_	_
17	approach	approach	NOUN	NN	Number=Sing	14	pobj	_	_
18	applied	apply	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
21	monoidal	monoidal	ADJ	JJ	Degree=Pos	23	amod	_	_
22	extensive	extensive	ADJ	JJ	Degree=Pos	23	amod	_	_
23	category	category	NOUN	NN	Number=Sing	19	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	26	amod	_	_
26	objects	object	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
28	with	with	ADP	IN	_	10	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	values	value	NOUN	NNS	Number=Plur	28	pobj	_	_
31	in	in	ADP	IN	_	30	prep	_	_
32	appropriate	appropriate	ADJ	JJ	Degree=Pos	33	amod	_	_
33	rings	ring	NOUN	NNS	Number=Plur	31	pobj	_	_
34	being	be	AUX	VBG	VerbForm=Ger	35	auxpass	_	_
35	abstracted	abstract	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	acl	_	_
36	from	from	ADP	IN	_	35	prep	_	_
37	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	38	amod	_	_
38	functors	functor	NOUN	NNS	Number=Plur	36	pobj	_	_
39	on	on	ADP	IN	_	38	prep	_	_
40	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
41	objects	object	NOUN	NNS	Number=Plur	39	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = The explicit consideration of a category of Möbius intervals leads also to two new characterizations of Möbius categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	explicit	explicit	ADJ	JJ	Degree=Pos	3	amod	_	_
3	consideration	consideration	NOUN	NN	Number=Sing	10	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	Möbius	Möbius	PROPN	NNP	Number=Sing	9	compound	_	_
9	intervals	interval	NOUN	NNS	Number=Plur	7	pobj	_	_
10	leads	lead	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	also	also	ADV	RB	_	10	advmod	_	_
12	to	to	ADP	IN	_	10	prep	_	_
13	two	two	NUM	CD	NumType=Card	15	nummod	_	_
14	new	new	ADJ	JJ	Degree=Pos	15	amod	_	_
15	characterizations	characterization	NOUN	NNS	Number=Plur	12	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	Möbius	Möbius	PROPN	NNP	Number=Sing	18	compound	_	_
18	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# doc_id = 366
# sent_id = 1
# text = Let $ cal K $ be a locally finitely presentable category.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ cal K $	$ cal k $	SYM	$	_	1	ccomp	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	conj	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
5	locally	locally	ADV	RB	_	6	advmod	_	_
6	finitely	finitely	ADV	RB	_	7	advmod	_	_
7	presentable	presentable	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	3	attr	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = If $ cal K $ is abelian and the sequence $ 0 to K to^k X to^c C to 0 $ is short exact, we show that (i) $ K $ is finitely generated if and only if $ c $ is finitely presentable; (ii) $ k $ is finitely presentable if and only if $ C $ is finitely presentable.
1	If	if	SCONJ	IN	_	3	mark	_	_
2	$ cal K $	$ cal k $	SYM	$	_	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	advcl	_	_
4	abelian	abelian	ADJ	JJ	Degree=Pos	3	attr	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	sequence	sequence	NOUN	NN	Number=Sing	4	conj	_	_
8	$ 0 to K to^k X to^c C to 0 $	$ 0 to k to^k x to^c c to 0 $	SYM	$	_	9	nsubj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	ccomp	_	_
10	short	short	ADJ	JJ	Degree=Pos	11	amod	_	_
11	exact	exact	ADV	RB	_	9	acomp	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	that	that	SCONJ	IN	_	22	mark	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	17	punct	_	SpaceAfter=No
17	i	i	NOUN	NN	Number=Sing	22	nsubjpass	_	SpaceAfter=No
18	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	17	punct	_	_
19	$ K $	$ k $	SYM	$	_	17	appos	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	auxpass	_	_
21	finitely	finitely	ADV	RB	_	22	advmod	_	_
22	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	ccomp	_	_
23	if	if	SCONJ	IN	_	22	prep	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	only	only	ADV	RB	_	28	advmod	_	_
26	if	if	SCONJ	IN	_	28	mark	_	_
27	$ c $	$ c $	SYM	$	_	28	nsubj	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	36	advcl	_	_
29	finitely	finitely	ADV	RB	_	30	advmod	_	_
30	presentable	presentable	ADJ	JJ	Degree=Pos	28	acomp	_	SpaceAfter=No
31	;	;	PUNCT	:	_	36	punct	_	_
32	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	33	punct	_	SpaceAfter=No
33	ii	ii	PROPN	NNP	Number=Sing	36	nsubj	_	SpaceAfter=No
34	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	33	punct	_	_
35	$ k $	$ k $	SYM	$	_	33	nmod	_	_
36	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	ccomp	_	_
37	finitely	finitely	ADV	RB	_	38	advmod	_	_
38	presentable	presentable	ADJ	JJ	Degree=Pos	36	acomp	_	_
39	if	if	SCONJ	IN	_	36	dep	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	39	cc	_	_
41	only	only	ADV	RB	_	44	advmod	_	_
42	if	if	SCONJ	IN	_	44	mark	_	_
43	$ C $	$ c $	SYM	$	_	44	nsubj	_	_
44	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	36	advcl	_	_
45	finitely	finitely	ADV	RB	_	46	advmod	_	_
46	presentable	presentable	ADJ	JJ	Degree=Pos	44	acomp	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 3
# text = The ``if" directions fail for semi - abelian varieties.
1	The	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
2	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	7	punct	_	SpaceAfter=No
3	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	7	punct	_	SpaceAfter=No
4	if	if	SCONJ	IN	_	7	mark	_	SpaceAfter=No
5	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	7	punct	_	_
6	directions	direction	NOUN	NNS	Number=Plur	7	nsubj	_	_
7	fail	fail	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	semi	semi	ADJ	JJ	Degree=Pos	12	amod	_	_
10	-	-	ADJ	JJ	Degree=Pos	12	punct	_	_
11	abelian	abelian	ADJ	JJ	Degree=Pos	12	amod	_	_
12	varieties	variety	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show that all but (possibly) (ii) in the if direction follow from analogous properties which hold in all locally finitely presentable categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	12	mark	_	_
4	all	all	PRON	DT	_	12	nsubj	_	_
5	but	but	SCONJ	IN	_	4	cc	_	_
6	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	7	punct	_	SpaceAfter=No
7	possibly	possibly	ADV	RB	_	4	conj	_	SpaceAfter=No
8	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	4	punct	_	_
9	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	10	punct	_	SpaceAfter=No
10	ii	ii	PROPN	NNP	Number=Sing	4	appos	_	SpaceAfter=No
11	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	4	punct	_	_
12	in	in	ADP	IN	_	2	ccomp	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
14	if	if	SCONJ	IN	_	16	mark	_	_
15	direction	direction	NOUN	NN	Number=Sing	16	compound	_	_
16	follow	follow	VERB	VBP	Tense=Pres|VerbForm=Fin	12	pobj	_	_
17	from	from	ADP	IN	_	16	prep	_	_
18	analogous	analogous	ADJ	JJ	Degree=Pos	19	amod	_	_
19	properties	property	NOUN	NNS	Number=Plur	17	pobj	_	_
20	which	which	PRON	WDT	_	21	nsubj	_	_
21	hold	hold	VERB	VBP	Tense=Pres|VerbForm=Fin	19	relcl	_	_
22	in	in	ADP	RP	_	21	prt	_	_
23	all	all	DET	DT	_	27	det	_	_
24	locally	locally	ADV	RB	_	25	advmod	_	_
25	finitely	finitely	ADV	RB	_	27	amod	_	_
26	presentable	presentable	ADJ	JJ	Degree=Pos	27	amod	_	_
27	categories	category	NOUN	NNS	Number=Plur	21	dobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = As for (ii) in the if direction, it holds as soon as $ cal K $ is also co - homological, and all its strong epimorphisms are regular.
1	As	as	ADP	IN	_	12	prep	_	_
2	for	for	ADP	IN	_	1	prep	_	_
3	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	2	punct	_	SpaceAfter=No
4	ii	ii	PROPN	NNP	Number=Sing	2	pobj	_	SpaceAfter=No
5	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	2	punct	_	_
6	in	in	ADP	IN	_	1	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	if	if	SCONJ	IN	_	9	det	_	_
9	direction	direction	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
11	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	12	nsubj	_	_
12	holds	hold	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	as	as	ADV	RB	_	14	advmod	_	_
14	soon	soon	ADV	RB	_	12	advmod	_	_
15	as	as	SCONJ	IN	_	16	mark	_	_
16	$ cal K $	$ cal k $	SYM	$	_	14	advcl	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	ccomp	_	_
18	also	also	ADV	RB	_	17	advmod	_	_
19	co	co	NOUN	NN	Number=Sing	17	attr	_	_
20	-	-	ADJ	JJ	Degree=Pos	17	acomp	_	_
21	homological	homological	ADJ	JJ	Degree=Pos	17	acomp	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
24	all	all	DET	DT	_	27	det	_	_
25	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	27	poss	_	_
26	strong	strong	ADJ	JJ	Degree=Pos	27	amod	_	_
27	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	28	nsubj	_	_
28	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	17	conj	_	_
29	regular	regular	ADJ	JJ	Degree=Pos	28	acomp	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 6
# text = Finally, locally finitely coherent (respectively, noetherian) abelian categories are characterized as those for which all finitely presentable morphisms have finitely generated (respectively, presentable) kernel objects.
1	Finally	finally	ADV	RB	_	14	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
3	locally	locally	ADV	RB	_	5	advmod	_	_
4	finitely	finitely	ADV	RB	_	5	advmod	_	_
5	coherent	coherent	ADJ	JJ	Degree=Pos	14	amod	_	_
6	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
7	respectively	respectively	ADV	RB	_	14	advmod	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
9	noetherian	noetherian	ADJ	JJ	Degree=Pos	12	amod	_	SpaceAfter=No
10	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	12	punct	_	_
11	abelian	abelian	PROPN	NNP	Number=Sing	12	compound	_	_
12	categories	category	NOUN	NNS	Number=Plur	14	nsubjpass	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
15	as	as	ADP	IN	_	14	prep	_	_
16	those	those	PRON	DT	Number=Plur|PronType=Dem	15	pobj	_	_
17	for	for	ADP	IN	_	25	prep	_	_
18	which	which	PRON	WDT	_	17	pobj	_	_
19	all	all	DET	DT	_	22	det	_	_
20	finitely	finitely	ADV	RB	_	21	advmod	_	_
21	presentable	presentable	ADJ	JJ	Degree=Pos	22	amod	_	_
22	morphisms	morphism	NOUN	NNS	Number=Plur	25	nsubj	_	_
23	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	25	aux	_	_
24	finitely	finitely	ADV	RB	_	25	advmod	_	_
25	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	relcl	_	_
26	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	32	punct	_	SpaceAfter=No
27	respectively	respectively	ADV	RB	_	32	advmod	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
29	presentable	presentable	ADJ	JJ	Degree=Pos	31	amod	_	SpaceAfter=No
30	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	31	punct	_	_
31	kernel	kernel	NOUN	NN	Number=Sing	32	compound	_	_
32	objects	object	NOUN	NNS	Number=Plur	25	dobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# doc_id = 367
# sent_id = 1
# text = Variations on the notions of Reedy model structures and projective model structures on categories of diagrams in a model category are introduced.
1	Variations	variation	NOUN	NNS	Number=Plur	22	nsubjpass	_	_
2	on	on	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	notions	notion	NOUN	NNS	Number=Plur	2	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	Reedy	reedy	ADJ	JJ	Degree=Pos	8	amod	_	_
7	model	model	NOUN	NN	Number=Sing	8	compound	_	_
8	structures	structure	NOUN	NNS	Number=Plur	5	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	projective	projective	ADJ	JJ	Degree=Pos	12	amod	_	_
11	model	model	NOUN	NN	Number=Sing	12	compound	_	_
12	structures	structure	NOUN	NNS	Number=Plur	8	conj	_	_
13	on	on	ADP	IN	_	8	prep	_	_
14	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	diagrams	diagram	NOUN	NNS	Number=Plur	15	pobj	_	_
17	in	in	ADP	IN	_	1	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	model	model	NOUN	NN	Number=Sing	20	compound	_	_
20	category	category	NOUN	NN	Number=Sing	17	pobj	_	_
21	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	22	auxpass	_	_
22	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# sent_id = 2
# text = These allow one to choose only a subset of the entries when defining weak equivalences, or to use different model categories at different entries of the diagrams.
1	These	these	PRON	DT	Number=Plur|PronType=Dem	2	nsubj	_	_
2	allow	allow	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	one	one	NUM	CD	NumType=Card	5	nsubj	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	choose	choose	VERB	VB	VerbForm=Inf	2	ccomp	_	_
6	only	only	ADV	RB	_	8	advmod	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	subset	subset	NOUN	NN	Number=Sing	5	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	entries	entry	NOUN	NNS	Number=Plur	9	pobj	_	_
12	when	when	SCONJ	WRB	_	13	advmod	_	_
13	defining	define	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	advcl	_	_
14	weak	weak	ADJ	JJ	Degree=Pos	15	amod	_	_
15	equivalences	equivalence	NOUN	NNS	Number=Plur	13	dobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
17	or	or	CCONJ	CC	ConjType=Cmp	5	cc	_	_
18	to	to	PART	TO	_	19	aux	_	_
19	use	use	VERB	VB	VerbForm=Inf	5	conj	_	_
20	different	different	ADJ	JJ	Degree=Pos	22	amod	_	_
21	model	model	NOUN	NN	Number=Sing	22	compound	_	_
22	categories	category	NOUN	NNS	Number=Plur	19	dobj	_	_
23	at	at	ADP	IN	_	19	prep	_	_
24	different	different	ADJ	JJ	Degree=Pos	25	amod	_	_
25	entries	entry	NOUN	NNS	Number=Plur	23	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	diagrams	diagram	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = As a result, a bisimplicial model category that can be used to recover the algebraic K - theory for any Waldhausen subcategory of a model category is produced.
1	As	as	ADP	IN	_	29	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	result	result	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
6	bisimplicial	bisimplicial	ADJ	JJ	Degree=Pos	8	amod	_	_
7	model	model	NOUN	NN	Number=Sing	8	compound	_	_
8	category	category	NOUN	NN	Number=Sing	29	nsubjpass	_	_
9	that	that	PRON	WDT	PronType=Rel	12	nsubjpass	_	_
10	can	can	AUX	MD	VerbForm=Fin	12	aux	_	_
11	be	be	AUX	VB	VerbForm=Inf	12	auxpass	_	_
12	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	relcl	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	recover	recover	VERB	VB	VerbForm=Inf	12	xcomp	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
16	algebraic	algebraic	ADJ	JJ	Degree=Pos	19	amod	_	_
17	K	K	PROPN	NNP	Number=Sing	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	theory	theory	PROPN	NNP	Number=Sing	14	dobj	_	_
20	for	for	ADP	IN	_	19	prep	_	_
21	any	any	DET	DT	_	23	det	_	_
22	Waldhausen	Waldhausen	PROPN	NNP	Number=Sing	23	compound	_	_
23	subcategory	subcategory	NOUN	NN	Number=Sing	20	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
26	model	model	NOUN	NN	Number=Sing	27	compound	_	_
27	category	category	NOUN	NN	Number=Sing	24	pobj	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	auxpass	_	_
29	produced	produce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	29	punct	_	SpaceAfter=No

# doc_id = 368
# sent_id = 1
# text = Implementing an idea due to John Baez and James Dolan we define new invariants of Whitney stratified manifolds by considering the homotopy theory of smooth transversal maps.
1	Implementing	implement	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	advcl	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	idea	idea	NOUN	NN	Number=Sing	1	dobj	_	_
4	due	due	ADP	IN	_	1	prep	_	_
5	to	to	ADP	IN	_	4	pcomp	_	_
6	John	John	PROPN	NNP	Number=Sing	7	compound	_	_
7	Baez	Baez	PROPN	NNP	Number=Sing	4	pobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	James	James	PROPN	NNP	Number=Sing	10	compound	_	_
10	Dolan	Dolan	PROPN	NNP	Number=Sing	7	conj	_	_
11	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	12	nsubj	_	_
12	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	new	new	ADJ	JJ	Degree=Pos	14	amod	_	_
14	invariants	invariant	NOUN	NNS	Number=Plur	12	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	Whitney	Whitney	PROPN	NNP	Number=Sing	15	pobj	_	_
17	stratified	stratify	VERB	VBD	Tense=Past|VerbForm=Fin	12	conj	_	_
18	manifolds	manifold	NOUN	NNS	Number=Plur	17	dobj	_	_
19	by	by	ADP	IN	_	17	prep	_	_
20	considering	consider	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	pcomp	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	homotopy	homotopy	NOUN	NN	Number=Sing	23	compound	_	_
23	theory	theory	NOUN	NN	Number=Sing	20	dobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	smooth	smooth	ADJ	JJ	Degree=Pos	27	amod	_	_
26	transversal	transversal	ADJ	JJ	Degree=Pos	27	amod	_	_
27	maps	map	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 2
# text = To each stratified manifold we assign transversal homotopy monoids, one for each natural number.
1	To	to	ADP	IN	_	6	prep	_	_
2	each	each	DET	DT	_	4	det	_	_
3	stratified	stratified	ADJ	JJ	Degree=Pos	4	amod	_	_
4	manifold	manifold	NOUN	NN	Number=Sing	1	pobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	assign	assign	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	transversal	transversal	ADJ	JJ	Degree=Pos	9	amod	_	_
8	homotopy	homotopy	NOUN	NN	Number=Sing	9	compound	_	_
9	monoids	monoid	NOUN	NNS	Number=Plur	6	dobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	one	one	NUM	CD	NumType=Card	9	appos	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	each	each	DET	DT	_	15	det	_	_
14	natural	natural	ADJ	JJ	Degree=Pos	15	amod	_	_
15	number	number	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = The assignment is functorial for a natural class of maps which we call stratified normal submersions.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	assignment	assignment	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	functorial	functorial	ADJ	JJ	Degree=Pos	3	acomp	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	natural	natural	ADJ	JJ	Degree=Pos	8	amod	_	_
8	class	class	NOUN	NN	Number=Sing	5	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	maps	map	NOUN	NNS	Number=Plur	9	pobj	_	_
11	which	which	PRON	WDT	_	13	nsubj	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	8	relcl	_	_
14	stratified	stratify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
15	normal	normal	ADJ	JJ	Degree=Pos	16	amod	_	_
16	submersions	submersion	NOUN	NNS	Number=Plur	13	oprd	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = When the stratification is trivial the transversal homotopy monoids are isomorphic to the usual homotopy groups.
1	When	when	SCONJ	WRB	_	4	advmod	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	stratification	stratification	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	advcl	_	_
5	trivial	trivial	ADJ	JJ	Degree=Pos	4	acomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
7	transversal	transversal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	homotopy	homotopy	NOUN	NN	Number=Sing	9	compound	_	_
9	monoids	monoid	NOUN	NNS	Number=Plur	10	nsubj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	10	acomp	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
14	usual	usual	ADJ	JJ	Degree=Pos	16	amod	_	_
15	homotopy	homotopy	NOUN	NN	Number=Sing	16	compound	_	_
16	groups	group	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 5
# text = We compute some simple examples and explore the elementary properties of these invariants.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	compute	compute	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	some	some	DET	DT	_	5	det	_	_
4	simple	simple	ADJ	JJ	Degree=Pos	5	amod	_	_
5	examples	example	NOUN	NNS	Number=Plur	2	dobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
7	explore	explore	VERB	VB	VerbForm=Inf	2	conj	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	elementary	elementary	ADJ	JJ	Degree=Pos	10	amod	_	_
10	properties	property	NOUN	NNS	Number=Plur	7	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	these	these	DET	DT	Number=Plur|PronType=Dem	13	det	_	_
13	invariants	invariant	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = We also assign `higher invariants', the transversal homotopy categories, to each stratified manifold.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	assign	assign	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	6	punct	_	SpaceAfter=No
5	higher	high	ADJ	JJR	Degree=Cmp	6	amod	_	_
6	invariants	invariant	NOUN	NNS	Number=Plur	3	dobj	_	SpaceAfter=No
7	'	'	PART	POS	_	6	punct	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
10	transversal	transversal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	homotopy	homotopy	NOUN	NN	Number=Sing	12	compound	_	_
12	categories	category	NOUN	NNS	Number=Plur	6	appos	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
14	to	to	ADP	IN	_	6	prep	_	_
15	each	each	DET	DT	_	17	det	_	_
16	stratified	stratified	ADJ	JJ	Degree=Pos	17	amod	_	_
17	manifold	manifold	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = These have a rich structure; they are rigid monoidal categories for $ n > 1 $ and ribbon categories for $ n > 2 $ .
1	These	these	PRON	DT	Number=Plur|PronType=Dem	2	nsubj	_	_
2	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	ccomp	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	rich	rich	ADJ	JJ	Degree=Pos	5	amod	_	_
5	structure	structure	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
6	;	;	PUNCT	:	_	8	punct	_	_
7	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	8	nsubj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	rigid	rigid	ADJ	JJ	Degree=Pos	11	amod	_	_
10	monoidal	monoidal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	categories	category	NOUN	NNS	Number=Plur	8	attr	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	$ n > 1 $	$ n > 1 $	SYM	$	_	16	nmod	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	ribbon	ribbon	NOUN	NN	Number=Sing	13	conj	_	_
16	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	_
17	for	for	ADP	IN	_	16	prep	_	_
18	$ n > 2 $	$ n > 2 $	SYM	$	_	17	pobj	_	_
19	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 8
# text = As an example we show that the transversal homotopy categories of a sphere, stratified by a point and its complement, are equivalent to categories of framed tangles.
1	As	as	ADP	IN	_	5	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	example	example	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	23	mark	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	transversal	transversal	ADJ	JJ	Degree=Pos	9	amod	_	_
9	homotopy	homotopy	NOUN	NN	Number=Sing	10	compound	_	_
10	categories	category	NOUN	NNS	Number=Plur	23	nsubj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	sphere	sphere	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	stratified	stratify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	acl	_	_
16	by	by	ADP	IN	_	15	agent	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	point	point	NOUN	NN	Number=Sing	16	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
20	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	21	poss	_	_
21	complement	complement	NOUN	NN	Number=Sing	10	conj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
23	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
24	equivalent	equivalent	ADJ	JJ	Degree=Pos	23	acomp	_	_
25	to	to	ADP	IN	_	24	prep	_	_
26	categories	category	NOUN	NNS	Number=Plur	25	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	framed	framed	ADJ	JJ	Degree=Pos	29	amod	_	_
29	tangles	tangle	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 369
# sent_id = 1
# text = We define the notion of a torsor for an inverse semigroup, which is based on semigroup actions, and prove that this is precisely the structure classified by the topos associated with an inverse semigroup.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	torsor	torsor	NOUN	NN	Number=Sing	5	pobj	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	inverse	inverse	ADJ	JJ	Degree=Pos	11	amod	_	_
11	semigroup	semigroup	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	which	which	PRON	WDT	_	15	nsubjpass	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	relcl	_	_
16	on	on	ADP	IN	_	15	prep	_	_
17	semigroup	semigroup	NOUN	NN	Number=Sing	18	compound	_	_
18	actions	action	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
21	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
22	that	that	SCONJ	IN	_	24	mark	_	_
23	this	this	PRON	DT	Number=Sing|PronType=Dem	24	nsubj	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	21	ccomp	_	_
25	precisely	precisely	ADV	RB	_	24	advmod	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	structure	structure	NOUN	NN	Number=Sing	24	attr	_	_
28	classified	classify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	acl	_	_
29	by	by	ADP	IN	_	28	agent	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	topos	topos	NOUN	NN	Number=Sing	29	pobj	_	_
32	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	acl	_	_
33	with	with	ADP	IN	_	32	prep	_	_
34	an	an	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
35	inverse	inverse	ADJ	JJ	Degree=Pos	36	amod	_	_
36	semigroup	semigroup	NOUN	NN	Number=Sing	33	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Unlike in the group case, not all set - theoretic torsors are isomorphic: we shall give a complete description of the category of torsors.
1	Unlike	unlike	ADP	IN	_	13	prep	_	_
2	in	in	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	group	group	NOUN	NN	Number=Sing	5	compound	_	_
5	case	case	NOUN	NN	Number=Sing	2	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	not	not	PART	RB	Polarity=Neg	12	neg	_	_
8	all	all	DET	DT	_	12	det	_	_
9	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	theoretic	theoretic	NOUN	NN	Number=Sing	12	amod	_	_
12	torsors	torsor	NOUN	NNS	Number=Plur	13	nsubj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	18	ccomp	_	_
14	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	13	acomp	_	SpaceAfter=No
15	:	:	PUNCT	:	_	18	punct	_	_
16	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	18	nsubj	_	_
17	shall	shall	AUX	MD	VerbType=Mod	18	aux	_	_
18	give	give	VERB	VB	VerbForm=Inf	0	ROOT	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	complete	complete	ADJ	JJ	Degree=Pos	21	amod	_	_
21	description	description	NOUN	NN	Number=Sing	18	dobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	category	category	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	torsors	torsor	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# sent_id = 3
# text = We explain how a semigroup prehomomorphism gives rise to an adjunction between a restrictions - of - scalars functor and a tensor product functor, which we relate to the theory of covering spaces and $ E $ - unitary semigroups.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	explain	explain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	how	how	SCONJ	WRB	_	7	advmod	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	semigroup	semigroup	NOUN	NN	Number=Sing	6	compound	_	_
6	prehomomorphism	prehomomorphism	NOUN	NN	Number=Sing	7	nsubj	_	_
7	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	rise	rise	VERB	VB	VerbForm=Inf	7	dobj	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	adjunction	adjunction	NOUN	NN	Number=Sing	9	pobj	_	_
12	between	between	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	restrictions	restriction	NOUN	NNS	Number=Plur	12	pobj	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
16	of	of	ADP	IN	_	14	prep	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
18	scalars	scalar	NOUN	NNS	Number=Plur	16	pobj	_	_
19	functor	functor	NOUN	NN	Number=Sing	14	conj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
22	tensor	tensor	NOUN	NN	Number=Sing	23	compound	_	_
23	product	product	NOUN	NN	Number=Sing	24	compound	_	_
24	functor	functor	NOUN	NN	Number=Sing	19	conj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	which	which	PRON	WDT	_	28	dobj	_	_
27	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	28	nsubj	_	_
28	relate	relate	VERB	VBP	Tense=Pres|VerbForm=Fin	24	relcl	_	_
29	to	to	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	theory	theory	NOUN	NN	Number=Sing	29	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	covering	cover	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	32	pcomp	_	_
34	spaces	space	NOUN	NNS	Number=Plur	33	dobj	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	34	cc	_	_
36	$ E $	$ e $	SYM	$	_	38	advmod	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	38	punct	_	_
38	unitary	unitary	ADJ	JJ	Degree=Pos	39	amod	_	_
39	semigroups	semigroup	NOUN	NNS	Number=Plur	34	conj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We also interpret for semigroups the Lawvere - product of a sheaf and distribution and finally, we indicate how the theory might be extended to general semigroups, by defining a notion of torsor and a classifying topos for those.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	interpret	interpret	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	for	for	ADP	IN	_	3	prep	_	_
5	semigroups	semigroup	NOUN	NNS	Number=Plur	4	pobj	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
7	Lawvere	Lawvere	PROPN	NNP	Number=Sing	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	product	product	NOUN	NN	Number=Sing	5	appos	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	sheaf	sheaf	NOUN	NN	Number=Sing	10	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	distribution	distribution	NOUN	NN	Number=Sing	12	conj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
16	finally	finally	ADV	RB	_	19	advmod	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	indicate	indicate	VERB	VBP	Tense=Pres|VerbForm=Fin	3	conj	_	_
20	how	how	SCONJ	WRB	_	25	advmod	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	theory	theory	NOUN	NN	Number=Sing	25	nsubjpass	_	_
23	might	might	AUX	MD	VerbForm=Fin	25	aux	_	_
24	be	be	AUX	VB	VerbForm=Inf	25	auxpass	_	_
25	extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	ccomp	_	_
26	to	to	ADP	IN	_	25	prep	_	_
27	general	general	ADJ	JJ	Degree=Pos	28	amod	_	_
28	semigroups	semigroup	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
30	by	by	ADP	IN	_	25	prep	_	_
31	defining	define	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	30	pcomp	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
33	notion	notion	NOUN	NN	Number=Sing	31	dobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	torsor	torsor	NOUN	NN	Number=Sing	34	pobj	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
37	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
38	classifying	classify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	39	amod	_	_
39	topos	topos	NOUN	NN	Number=Sing	33	conj	_	_
40	for	for	ADP	IN	_	39	prep	_	_
41	those	those	PRON	DT	Number=Plur|PronType=Dem	40	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# doc_id = 370
# sent_id = 1
# text = We show that the class of weak equivalences of a combinatorial model category can be detected by an accessible functor into simplicial sets.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	16	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	class	class	NOUN	NN	Number=Sing	16	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	weak	weak	ADJ	JJ	Degree=Pos	8	amod	_	_
8	equivalences	equivalence	NOUN	NNS	Number=Plur	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	12	amod	_	_
12	model	model	NOUN	NN	Number=Sing	13	compound	_	_
13	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
14	can	can	AUX	MD	VerbForm=Fin	16	aux	_	_
15	be	be	AUX	VB	VerbForm=Inf	16	auxpass	_	_
16	detected	detect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
17	by	by	ADP	IN	_	16	agent	_	_
18	an	an	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	accessible	accessible	ADJ	JJ	Degree=Pos	20	amod	_	_
20	functor	functor	NOUN	NN	Number=Sing	17	pobj	_	_
21	into	into	ADP	IN	_	16	prep	_	_
22	simplicial	simplicial	ADJ	JJ	Degree=Pos	23	amod	_	_
23	sets	set	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 371
# sent_id = 1
# text = We introduce a description of the algebras for a monad in terms of extension systems, similar to the one for monads given by Manes.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	description	description	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	algebras	algebra	NOUN	NNS	Number=Plur	5	pobj	_	_
8	for	for	ADP	IN	_	2	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	monad	monad	NOUN	NNS	Number=Plur	8	pobj	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	terms	term	NOUN	NNS	Number=Plur	11	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	extension	extension	NOUN	NN	Number=Sing	15	compound	_	_
15	systems	system	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	similar	similar	ADJ	JJ	Degree=Pos	15	amod	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	one	one	NUM	CD	NumType=Card	18	pobj	_	_
21	for	for	ADP	IN	_	20	prep	_	_
22	monads	monad	NOUN	NNS	Number=Plur	21	pobj	_	_
23	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	acl	_	_
24	by	by	ADP	IN	_	23	agent	_	_
25	Manes	Manes	PROPN	NNPS	Number=Plur	24	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We rewrite distributive laws for monads and wreaths in terms of this description, avoiding the iteration of the functors involved.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	rewrite	rewrite	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	distributive	distributive	ADJ	JJ	Degree=Pos	4	amod	_	_
4	laws	law	NOUN	NNS	Number=Plur	2	dobj	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	monads	monad	NOUN	NNS	Number=Plur	5	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	wreaths	wreath	NOUN	NNS	Number=Plur	6	conj	_	_
9	in	in	ADP	IN	_	6	prep	_	_
10	terms	term	NOUN	NNS	Number=Plur	9	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	this	this	DET	DT	Number=Sing|PronType=Dem	13	det	_	_
13	description	description	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
15	avoiding	avoid	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	iteration	iteration	NOUN	NN	Number=Sing	15	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	functors	functor	NOUN	NNS	Number=Plur	18	pobj	_	_
21	involved	involve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	acl	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We give a profunctorial explanation of why Manes' description of monads in terms of extension systems works.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	profunctorial	profunctorial	ADJ	JJ	Degree=Pos	5	amod	_	_
5	explanation	explanation	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	why	why	SCONJ	WRB	_	10	advmod	_	_
8	Manes	Manes	PROPN	NNPS	Number=Plur	10	poss	_	SpaceAfter=No
9	'	'	PART	POS	_	8	case	_	_
10	description	description	NOUN	NN	Number=Sing	6	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	monads	monad	NOUN	NNS	Number=Plur	11	pobj	_	_
13	in	in	ADP	IN	_	10	prep	_	_
14	terms	term	NOUN	NNS	Number=Plur	13	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	extension	extension	NOUN	NN	Number=Sing	17	compound	_	_
17	systems	system	NOUN	NNS	Number=Plur	18	compound	_	_
18	works	work	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 372
# sent_id = 1
# text = We generalize to the context internal to an autonomous monoidal bicategory the work of Bruguieres, Virelizier, and the second - named author on lifting closed structure on a monoidal category to the category of Eilenberg - Moore algebras for an opmonoidal monad.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	context	context	NOUN	NN	Number=Sing	3	pobj	_	_
6	internal	internal	ADJ	JJ	Degree=Pos	5	amod	_	_
7	to	to	ADP	IN	_	6	prep	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	autonomous	autonomous	ADJ	JJ	Degree=Pos	11	amod	_	_
10	monoidal	monoidal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	bicategory	bicategory	NOUN	NN	Number=Sing	7	pobj	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	work	work	NOUN	NN	Number=Sing	2	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	Bruguieres	Bruguieres	PROPN	NNPS	Number=Plur	14	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	Virelizier	Virelizier	PROPN	NNP	Number=Sing	15	conj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
21	second	second	ADV	RB	_	23	advmod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	named	name	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
24	author	author	NOUN	NN	Number=Sing	13	conj	_	_
25	on	on	ADP	IN	_	24	prep	_	_
26	lifting	lift	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	25	pcomp	_	_
27	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	amod	_	_
28	structure	structure	NOUN	NN	Number=Sing	26	dobj	_	_
29	on	on	ADP	IN	_	28	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
31	monoidal	monoidal	ADJ	JJ	Degree=Pos	32	amod	_	_
32	category	category	NOUN	NN	Number=Sing	29	pobj	_	_
33	to	to	ADP	IN	_	24	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	category	category	NOUN	NN	Number=Sing	33	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	39	compound	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	Moore	Moore	PROPN	NNP	Number=Sing	40	compound	_	_
40	algebras	algebra	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	36	pobj	_	_
41	for	for	ADP	IN	_	40	prep	_	_
42	an	an	DET	DT	Definite=Ind|PronType=Art	44	det	_	_
43	opmonoidal	opmonoidal	ADJ	JJ	Degree=Pos	44	amod	_	_
44	monad	monad	NOUN	NNS	Number=Plur	41	pobj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The result then applies to quantum categories and bialgebroids.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	result	result	NOUN	NN	Number=Sing	4	nsubj	_	_
3	then	then	ADV	RB	PronType=Dem	4	advmod	_	_
4	applies	apply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	quantum	quantum	ADJ	JJ	Degree=Pos	7	amod	_	_
7	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	bialgebroids	bialgebroid	NOUN	NNS	Number=Plur	7	conj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 373
# sent_id = 1
# text = The notion of Frobenius algebra originally arose in ring theory, but it is a fairly easy observation that this notion can be extended to arbitrary monoidal categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	notion	notion	NOUN	NN	Number=Sing	7	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	Frobenius	Frobenius	PROPN	NNP	Number=Sing	5	compound	_	_
5	algebra	algebra	NOUN	NNS	Number=Plur	3	pobj	_	_
6	originally	originally	ADV	RB	_	7	advmod	_	_
7	arose	arise	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	ring	ring	NOUN	NN	Number=Sing	10	compound	_	_
10	theory	theory	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
12	but	but	CCONJ	CC	ConjType=Cmp	7	cc	_	_
13	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	conj	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
16	fairly	fairly	ADV	RB	_	17	advmod	_	_
17	easy	easy	ADJ	JJ	Degree=Pos	18	amod	_	_
18	observation	observation	NOUN	NN	Number=Sing	14	attr	_	_
19	that	that	SCONJ	IN	_	24	mark	_	_
20	this	this	DET	DT	Number=Sing|PronType=Dem	21	det	_	_
21	notion	notion	NOUN	NN	Number=Sing	24	nsubjpass	_	_
22	can	can	AUX	MD	VerbForm=Fin	24	aux	_	_
23	be	be	AUX	VB	VerbForm=Inf	24	auxpass	_	_
24	extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	acl	_	_
25	to	to	ADP	IN	_	24	prep	_	_
26	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	28	amod	_	_
27	monoidal	monoidal	ADJ	JJ	Degree=Pos	28	amod	_	_
28	categories	category	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 2
# text = But, is this really the correct level of generalisation?
1	But	but	CCONJ	CC	ConjType=Cmp	3	cc	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	this	this	PRON	DT	Number=Sing|PronType=Dem	3	nsubj	_	_
5	really	really	ADV	RB	_	3	advmod	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	correct	correct	ADJ	JJ	Degree=Pos	8	amod	_	_
8	level	level	NOUN	NN	Number=Sing	3	attr	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	generalisation	generalisation	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
11	?	?	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = For example, when studying Frobenius algebras in the $ * $ - autonomous category $ Sup $ , the standard concept using only the usual tensor product is less interesting than a similar one in which both the usual tensor product and its de Morgan dual are used.
1	For	for	ADP	IN	_	25	prep	_	_
2	example	example	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
4	when	when	SCONJ	WRB	_	5	advmod	_	_
5	studying	study	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	25	advcl	_	_
6	Frobenius	Frobenius	PROPN	NNP	Number=Sing	7	compound	_	_
7	algebras	algebra	NOUN	NNS	Number=Plur	5	dobj	_	_
8	in	in	ADP	IN	_	5	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
10	$ * $	$ * $	SYM	$	_	12	advmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	autonomous	autonomous	ADJ	JJ	Degree=Pos	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
14	$ Sup $	$ sup $	SYM	$	_	13	appos	_	_
15	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	standard	standard	ADJ	JJ	Degree=Pos	18	amod	_	_
18	concept	concept	NOUN	NN	Number=Sing	25	nsubj	_	_
19	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	18	acl	_	_
20	only	only	ADV	RB	_	24	advmod	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
22	usual	usual	ADJ	JJ	Degree=Pos	24	amod	_	_
23	tensor	tensor	NOUN	NN	Number=Sing	24	compound	_	_
24	product	product	NOUN	NN	Number=Sing	19	dobj	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
26	less	less	ADV	RBR	Degree=Cmp	27	advmod	_	_
27	interesting	interesting	ADJ	JJ	Degree=Pos	25	acomp	_	_
28	than	than	ADP	IN	_	27	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	similar	similar	ADJ	JJ	Degree=Pos	31	amod	_	_
31	one	one	NUM	CD	NumType=Card	28	pobj	_	_
32	in	in	ADP	IN	_	45	prep	_	_
33	which	which	PRON	WDT	_	32	pobj	_	_
34	both	both	CCONJ	CC	ConjType=Cmp	38	preconj	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
36	usual	usual	ADJ	JJ	Degree=Pos	38	amod	_	_
37	tensor	tensor	NOUN	NN	Number=Sing	38	compound	_	_
38	product	product	NOUN	NN	Number=Sing	45	nsubjpass	_	_
39	and	and	CCONJ	CC	ConjType=Cmp	38	cc	_	_
40	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	42	poss	_	_
41	de	de	PROPN	NNP	Number=Sing	42	nmod	_	_
42	Morgan	Morgan	PROPN	NNP	Number=Sing	38	conj	_	_
43	dual	dual	ADV	RB	_	38	advmod	_	_
44	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	45	auxpass	_	_
45	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	relcl	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	25	punct	_	SpaceAfter=No

# sent_id = 4
# text = Thus we maintain that the notion of linear - distributive category (which has both a tensor and a par, but is nevertheless more general than the notion of monoidal category) provides the correct framework in which to interpret the concept of Frobenius algebra.
1	Thus	thus	ADV	RB	_	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	maintain	maintain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	23	mark	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	notion	notion	NOUN	NN	Number=Sing	23	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	linear	linear	ADJ	JJ	Degree=Pos	10	amod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	distributive	distributive	ADJ	JJ	Degree=Pos	11	amod	_	_
11	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
12	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	11	punct	_	SpaceAfter=No
13	which	which	PRON	WDT	_	14	nsubj	_	_
14	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	relcl	_	_
15	both	both	CCONJ	CC	ConjType=Cmp	17	preconj	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	tensor	tensor	NOUN	NN	Number=Sing	14	dobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	par	par	NOUN	NN	Number=Sing	17	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
22	but	but	CCONJ	CC	ConjType=Cmp	6	cc	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
24	nevertheless	nevertheless	ADV	RB	_	23	advmod	_	_
25	more	more	ADV	RBR	Degree=Cmp	26	advmod	_	_
26	general	general	ADJ	JJ	Degree=Pos	23	acomp	_	_
27	than	than	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	notion	notion	NOUN	NN	Number=Sing	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	monoidal	monoidal	ADJ	JJ	Degree=Pos	32	amod	_	_
32	category	category	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
33	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	23	punct	_	_
34	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
36	correct	correct	ADJ	JJ	Degree=Pos	37	amod	_	_
37	framework	framework	NOUN	NN	Number=Sing	34	dobj	_	_
38	in	in	ADP	IN	_	41	prep	_	_
39	which	which	PRON	WDT	_	38	pobj	_	_
40	to	to	PART	TO	_	41	aux	_	_
41	interpret	interpret	VERB	VB	VerbForm=Inf	37	relcl	_	_
42	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
43	concept	concept	NOUN	NN	Number=Sing	41	dobj	_	_
44	of	of	ADP	IN	_	43	prep	_	_
45	Frobenius	Frobenius	PROPN	NNP	Number=Sing	46	compound	_	_
46	algebra	algebra	PROPN	NNP	Number=Sing	44	pobj	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 374
# sent_id = 1
# text = We explain in detail why the notion of list - arithmetic pretopos should be taken as the general categorical definition for the construction of arithmetic universes introduced by André Joyal to give a categorical proof of Gödel's incompleteness results.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	explain	explain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	detail	detail	NOUN	NN	Number=Sing	3	pobj	_	_
5	why	why	SCONJ	WRB	_	15	advmod	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	notion	notion	NOUN	NN	Number=Sing	15	nsubjpass	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	list	list	NOUN	NN	Number=Sing	11	npadvmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	arithmetic	arithmetic	ADJ	JJ	Degree=Pos	12	amod	_	_
12	pretopos	pretopos	NOUN	NN	Number=Sing	8	pobj	_	_
13	should	should	AUX	MD	VerbForm=Fin	15	aux	_	_
14	be	be	AUX	VB	VerbForm=Inf	15	auxpass	_	_
15	taken	take	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
16	as	as	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
18	general	general	ADJ	JJ	Degree=Pos	20	amod	_	_
19	categorical	categorical	ADJ	JJ	Degree=Pos	20	amod	_	_
20	definition	definition	NOUN	NN	Number=Sing	16	pobj	_	_
21	for	for	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	construction	construction	NOUN	NN	Number=Sing	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	arithmetic	arithmetic	ADJ	JJ	Degree=Pos	26	amod	_	_
26	universes	universe	NOUN	NNS	Number=Plur	24	pobj	_	_
27	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	acl	_	_
28	by	by	ADP	IN	_	27	agent	_	_
29	André	André	PROPN	NNP	Number=Sing	30	compound	_	_
30	Joyal	Joyal	PROPN	NNP	Number=Sing	28	pobj	_	_
31	to	to	PART	TO	_	32	aux	_	_
32	give	give	VERB	VB	VerbForm=Inf	15	advcl	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
34	categorical	categorical	ADJ	JJ	Degree=Pos	35	amod	_	_
35	proof	proof	NOUN	NN	Number=Sing	32	dobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	Gödel	Gödel	PROPN	NNP	Number=Sing	40	poss	_	SpaceAfter=No
38	's	's	PART	POS	_	37	case	_	_
39	incompleteness	incompleteness	NOUN	NN	Number=Sing	40	compound	_	_
40	results	result	NOUN	NNS	Number=Plur	36	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 375
# sent_id = 1
# text = Bicategories of spans are characterized as cartesian bicategories in which every comonad has an Eilenberg - Moore object and every left adjoint arrow is comonadic.
1	Bicategories	bicategorie	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	spans	span	NOUN	NNS	Number=Plur	2	pobj	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	as	as	SCONJ	IN	_	24	mark	_	_
7	cartesian	cartesian	ADJ	JJ	Degree=Pos	8	amod	_	_
8	bicategories	bicategorie	NOUN	NNS	Number=Plur	24	nsubj	_	_
9	in	in	ADP	IN	_	13	prep	_	_
10	which	which	PRON	WDT	_	9	pobj	_	_
11	every	every	DET	DT	_	12	det	_	_
12	comonad	comonad	NOUN	NNS	Number=Plur	13	nsubj	_	_
13	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	relcl	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
15	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	17	compound	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	Moore	Moore	PROPN	NNP	Number=Sing	18	compound	_	_
18	object	object	NOUN	NN	Number=Sing	13	dobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	every	every	DET	DT	_	23	det	_	_
21	left	left	ADJ	JJ	Degree=Pos	22	amod	_	_
22	adjoint	adjoint	NOUN	NN	Number=Sing	23	compound	_	_
23	arrow	arrow	NOUN	NN	Number=Sing	18	conj	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	advcl	_	_
25	comonadic	comonadic	ADJ	JJ	Degree=Pos	24	acomp	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 376
# sent_id = 1
# text = Symbolic dynamics is partly the study of walks in a directed graph.
1	Symbolic	symbolic	ADJ	JJ	Degree=Pos	2	amod	_	_
2	dynamics	dynamic	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	partly	partly	ADV	RB	_	3	advmod	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	study	study	NOUN	NN	Number=Sing	3	attr	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	walks	walk	NOUN	NNS	Number=Plur	7	pobj	_	_
9	in	in	ADP	IN	_	6	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
12	graph	graph	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = By a walk, here we mean a morphism to the graph from the Cayley graph of the monoid of non - negative integers.
1	By	by	ADP	IN	_	7	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	walk	walk	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
5	here	here	ADV	RB	PronType=Dem	7	advmod	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	mean	mean	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	morphism	morphism	NOUN	NN	Number=Sing	7	dobj	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	graph	graph	NOUN	NN	Number=Sing	10	pobj	_	_
13	from	from	ADP	IN	_	9	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	Cayley	Cayley	PROPN	NNP	Number=Sing	16	compound	_	_
16	graph	graph	NOUN	NN	Number=Sing	13	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	monoid	monoid	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	non	non	ADJ	JJ	Degree=Pos	23	amod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	negative	negative	ADJ	JJ	Degree=Pos	24	amod	_	_
24	integers	integer	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = Sets of these walks are also important in other areas, such as stochastic processes, automata, combinatorial group theory, $ C^* $ - algebras, et cetera.
1	Sets	set	NOUN	NNS	Number=Plur	5	nsubj	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	these	these	DET	DT	Number=Plur|PronType=Dem	4	det	_	_
4	walks	walk	NOUN	NNS	Number=Plur	2	pobj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	also	also	ADV	RB	_	5	advmod	_	_
7	important	important	ADJ	JJ	Degree=Pos	5	acomp	_	_
8	in	in	ADP	IN	_	5	prep	_	_
9	other	other	ADJ	JJ	Degree=Pos	10	amod	_	_
10	areas	area	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	such	such	ADJ	JJ	Degree=Pos	13	amod	_	_
13	as	as	ADP	IN	_	10	prep	_	_
14	stochastic	stochastic	ADJ	JJ	Degree=Pos	15	amod	_	_
15	processes	process	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	automata	automata	PROPN	NNP	Number=Sing	15	conj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	20	compound	_	_
20	group	group	NOUN	NN	Number=Sing	21	compound	_	_
21	theory	theory	NOUN	NN	Number=Sing	17	conj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
23	$ C^* $	$ c^* $	SYM	$	_	25	compound	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	algebras	algebra	NOUN	NNS	Number=Plur	17	conj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
27	et	et	NOUN	NN	Number=Sing	28	compound	_	_
28	cetera	cetera	NOUN	NN	Number=Sing	15	appos	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = We put a Quillen model structure on the category of directed graphs, for which the weak equivalences are those graph morphisms which induce bijections on the set of walks.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	put	put	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
4	Quillen	quillen	ADJ	JJ	Degree=Pos	6	amod	_	_
5	model	model	NOUN	NN	Number=Sing	6	compound	_	_
6	structure	structure	NOUN	NN	Number=Sing	2	dobj	_	_
7	on	on	ADP	IN	_	2	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
12	graphs	graph	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	for	for	ADP	IN	_	19	prep	_	_
15	which	which	PRON	WDT	_	14	pobj	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	weak	weak	ADJ	JJ	Degree=Pos	18	amod	_	_
18	equivalences	equivalence	NOUN	NNS	Number=Plur	19	nsubj	_	_
19	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	relcl	_	_
20	those	those	DET	DT	Number=Plur|PronType=Dem	22	det	_	_
21	graph	graph	NOUN	NN	Number=Sing	22	compound	_	_
22	morphisms	morphism	NOUN	NNS	Number=Plur	19	attr	_	_
23	which	which	PRON	WDT	_	24	nsubj	_	_
24	induce	induce	VERB	VBP	Tense=Pres|VerbForm=Fin	22	relcl	_	_
25	bijections	bijection	NOUN	NNS	Number=Plur	24	dobj	_	_
26	on	on	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	set	set	NOUN	NN	Number=Sing	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	walks	walk	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = We determine the resulting homotopy category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	determine	determine	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
4	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	amod	_	_
5	homotopy	homotopy	NOUN	NN	Number=Sing	6	compound	_	_
6	category	category	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
7	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = We also introduce a "finite - level" homotopy category which respects the natural topology on the set of walks.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
5	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	11	punct	_	SpaceAfter=No
6	finite	finite	ADJ	JJ	Degree=Pos	8	amod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	level	level	NOUN	NN	Number=Sing	11	nmod	_	SpaceAfter=No
9	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	11	punct	_	_
10	homotopy	homotopy	NOUN	NN	Number=Sing	11	compound	_	_
11	category	category	NOUN	NN	Number=Sing	3	dobj	_	_
12	which	which	PRON	WDT	_	13	nsubj	_	_
13	respects	respect	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	relcl	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	natural	natural	ADJ	JJ	Degree=Pos	16	amod	_	_
16	topology	topology	NOUN	NN	Number=Sing	13	dobj	_	_
17	on	on	ADP	IN	_	13	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	set	set	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	walks	walk	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = To each graph we associate a basal graph, well defined up to isomorphism.
1	To	to	ADP	IN	_	5	prep	_	_
2	each	each	DET	DT	_	3	det	_	_
3	graph	graph	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	associate	associate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	basal	basal	NOUN	NN	Number=Sing	8	compound	_	_
8	graph	graph	NOUN	NN	Number=Sing	5	dobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
10	well	well	ADV	RB	Degree=Pos	11	advmod	_	_
11	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	conj	_	_
12	up	up	ADP	RP	_	11	prt	_	_
13	to	to	ADP	IN	_	11	prep	_	_
14	isomorphism	isomorphism	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 8
# text = We show that the basal graph is a homotopy invariant for our model structure, and that it is a finer invariant than the zeta series of a finite graph.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	basal	basal	NOUN	NN	Number=Sing	6	compound	_	_
6	graph	graph	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	homotopy	homotopy	NOUN	NN	Number=Sing	10	compound	_	_
10	invariant	invariant	ADJ	JJ	Degree=Pos	7	attr	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	14	poss	_	_
13	model	model	NOUN	NN	Number=Sing	14	compound	_	_
14	structure	structure	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
17	that	that	SCONJ	IN	_	19	mark	_	_
18	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	19	nsubj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	conj	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	finer	finer	ADJ	JJ	Degree=Pos	22	amod	_	_
22	invariant	invariant	NOUN	NN	Number=Sing	19	attr	_	_
23	than	than	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	zeta	zeta	NOUN	NN	Number=Sing	26	compound	_	_
26	series	series	NOUN	NN	Number=Sing	23	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
29	finite	finite	ADJ	JJ	Degree=Pos	30	amod	_	_
30	graph	graph	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 9
# text = We also show that, for finite walkable graphs, if $ B $ is basal and separated then the walk spaces for $ X $ and $ B $ are topologically conjugate if and only if $ X $ and $ B $ are homotopically equivalent for our model structure.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	13	mark	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
6	for	for	ADP	IN	_	13	prep	_	_
7	finite	finite	ADJ	JJ	Degree=Pos	9	amod	_	_
8	walkable	walkable	ADJ	JJ	Degree=Pos	9	amod	_	_
9	graphs	graph	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
11	if	if	SCONJ	IN	_	13	mark	_	_
12	$ B $	$ b $	SYM	$	_	13	nsubj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
14	basal	basal	NOUN	NN	Number=Sing	13	attr	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
16	separated	separate	VERB	VBD	Tense=Past|VerbForm=Fin	13	conj	_	_
17	then	then	ADV	RB	PronType=Dem	16	advmod	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	walk	walk	NOUN	NN	Number=Sing	20	compound	_	_
20	spaces	space	NOUN	NNS	Number=Plur	25	nsubj	_	_
21	for	for	ADP	IN	_	20	prep	_	_
22	$ X $	$ x $	SYM	$	_	21	pobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	$ B $	$ b $	SYM	$	_	22	conj	_	_
25	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	conj	_	_
26	topologically	topologically	ADV	RB	_	27	advmod	_	_
27	conjugate	conjugate	ADJ	JJ	Degree=Pos	25	acomp	_	_
28	if	if	SCONJ	IN	_	35	mark	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
30	only	only	ADV	RB	_	35	advmod	_	_
31	if	if	SCONJ	IN	_	35	mark	_	_
32	$ X $	$ x $	SYM	$	_	35	nsubj	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
34	$ B $	$ b $	SYM	$	_	32	conj	_	_
35	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	25	advcl	_	_
36	homotopically	homotopically	ADV	RB	_	37	advmod	_	_
37	equivalent	equivalent	ADJ	JJ	Degree=Pos	35	acomp	_	_
38	for	for	ADP	IN	_	37	prep	_	_
39	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	41	poss	_	_
40	model	model	NOUN	NN	Number=Sing	41	compound	_	_
41	structure	structure	NOUN	NN	Number=Sing	38	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 377
# sent_id = 1
# text = We combine two recent ideas: cartesian differential categories, and restriction categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	combine	combine	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	two	two	NUM	CD	NumType=Card	5	nummod	_	_
4	recent	recent	ADJ	JJ	Degree=Pos	5	amod	_	_
5	ideas	idea	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
6	:	:	PUNCT	:	_	5	punct	_	_
7	cartesian	cartesian	ADJ	JJ	Degree=Pos	9	amod	_	_
8	differential	differential	ADJ	JJ	Degree=Pos	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	5	appos	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
12	restriction	restriction	NOUN	NN	Number=Sing	13	compound	_	_
13	categories	category	NOUN	NNS	Number=Plur	9	conj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The result is a new structure which axiomatizes the category of smooth maps defined on open subsets of $ R^n $ in a way that is completely algebraic.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	result	result	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	new	new	ADJ	JJ	Degree=Pos	6	amod	_	_
6	structure	structure	NOUN	NN	Number=Sing	3	attr	_	_
7	which	which	PRON	WDT	_	8	nsubj	_	_
8	axiomatizes	axiomatize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	relcl	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	category	category	NOUN	NN	Number=Sing	8	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	smooth	smooth	ADJ	JJ	Degree=Pos	13	amod	_	_
13	maps	map	NOUN	NNS	Number=Plur	11	pobj	_	_
14	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	acl	_	_
15	on	on	ADP	IN	_	14	prep	_	_
16	open	open	ADJ	JJ	Degree=Pos	17	amod	_	_
17	subsets	subset	NOUN	NNS	Number=Plur	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	$ R^n $	$ r^n $	SYM	$	_	18	pobj	_	_
20	in	in	ADP	IN	_	14	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	way	way	NOUN	NN	Number=Sing	20	pobj	_	_
23	that	that	PRON	WDT	PronType=Rel	24	nsubj	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	relcl	_	_
25	completely	completely	ADV	RB	_	26	advmod	_	_
26	algebraic	algebraic	ADJ	JJ	Degree=Pos	24	acomp	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also give other models for the resulting structure, discuss what it means for a partial map to be additive or linear, and show that differential restriction structure can be lifted through various completion operations.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	other	other	ADJ	JJ	Degree=Pos	5	amod	_	_
5	models	model	NOUN	NNS	Number=Plur	3	dobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	amod	_	_
9	structure	structure	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
11	discuss	discuss	VERB	VB	VerbForm=Inf	3	advcl	_	_
12	what	what	PRON	WP	_	14	dobj	_	_
13	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	14	nsubj	_	_
14	means	mean	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	ccomp	_	_
15	for	for	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	partial	partial	ADJ	JJ	Degree=Pos	18	amod	_	_
18	map	map	NOUN	NN	Number=Sing	15	pobj	_	_
19	to	to	PART	TO	_	20	aux	_	_
20	be	be	AUX	VB	VerbForm=Inf	18	acl	_	_
21	additive	additive	ADJ	JJ	Degree=Pos	20	acomp	_	_
22	or	or	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	linear	linear	ADJ	JJ	Degree=Pos	21	conj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
26	show	show	VERB	VB	VerbForm=Inf	11	conj	_	_
27	that	that	SCONJ	IN	_	33	mark	_	_
28	differential	differential	ADJ	JJ	Degree=Pos	29	amod	_	_
29	restriction	restriction	NOUN	NN	Number=Sing	30	compound	_	_
30	structure	structure	NOUN	NN	Number=Sing	33	nsubjpass	_	_
31	can	can	AUX	MD	VerbForm=Fin	33	aux	_	_
32	be	be	AUX	VB	VerbForm=Inf	33	auxpass	_	_
33	lifted	lift	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	ccomp	_	_
34	through	through	ADP	IN	_	33	prep	_	_
35	various	various	ADJ	JJ	Degree=Pos	37	amod	_	_
36	completion	completion	NOUN	NN	Number=Sing	37	compound	_	_
37	operations	operation	NOUN	NNS	Number=Plur	34	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 378
# sent_id = 1
# text = This paper reviews the basic properties of coherent spaces, characterizes them, and proves a theorem about countable meets of open sets.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	reviews	review	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	basic	basic	ADJ	JJ	Degree=Pos	6	amod	_	_
6	properties	property	NOUN	NNS	Number=Plur	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	coherent	coherent	ADJ	JJ	Degree=Pos	9	amod	_	_
9	spaces	space	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
11	characterizes	characterize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
12	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	11	dobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
15	proves	prove	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	conj	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	theorem	theorem	ADJ	JJ	Degree=Pos	15	dobj	_	_
18	about	about	ADP	IN	_	17	prep	_	_
19	countable	countable	ADJ	JJ	Degree=Pos	20	amod	_	_
20	meets	meet	NOUN	NNS	Number=Plur	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	open	open	ADJ	JJ	Degree=Pos	23	amod	_	_
23	sets	set	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = A number of examples of coherent spaces are given, including the set of all congruences (equipped with the Zariski topology) of a model of a theory based on a set of partial operations.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	number	number	NOUN	NN	Number=Sing	9	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	examples	example	NOUN	NNS	Number=Plur	3	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	coherent	coherent	ADJ	JJ	Degree=Pos	7	amod	_	_
7	spaces	space	NOUN	NNS	Number=Plur	5	pobj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	set	set	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	all	all	DET	DT	_	16	det	_	_
16	congruences	congruence	NOUN	NNS	Number=Plur	14	pobj	_	_
17	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	16	punct	_	SpaceAfter=No
18	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	acl	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	Zariski	Zariski	PROPN	NNP	Number=Sing	22	compound	_	_
22	topology	topology	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	13	punct	_	_
24	of	of	ADP	IN	_	13	prep	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
26	model	model	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
29	theory	theory	NOUN	NN	Number=Sing	27	pobj	_	_
30	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	acl	_	_
31	on	on	ADP	IN	_	30	prep	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
33	set	set	NOUN	NN	Number=Sing	31	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	partial	partial	ADJ	JJ	Degree=Pos	36	amod	_	_
36	operations	operation	NOUN	NNS	Number=Plur	34	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also give two alternate proofs of the main theorem, one using a theorem of Isbell's and a second using an unpublished theorem of Makkai's.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	two	two	NUM	CD	NumType=Card	6	nummod	_	_
5	alternate	alternate	ADJ	JJ	Degree=Pos	6	amod	_	_
6	proofs	proof	NOUN	NNS	Number=Plur	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	main	main	ADJ	JJ	Degree=Pos	10	amod	_	_
10	theorem	theorem	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	one	one	NUM	CD	NumType=Card	10	appos	_	_
13	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	acl	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	theorem	theorem	NOUN	NN	Number=Sing	13	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	Isbell	Isbell	PROPN	NNP	Number=Sing	16	pobj	_	SpaceAfter=No
18	's	's	PART	POS	_	17	case	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	second	second	NOUN	NN	Number=Sing	17	conj	_	_
22	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	acl	_	_
23	an	an	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	unpublished	unpublished	ADJ	JJ	Degree=Pos	25	amod	_	_
25	theorem	theorem	NOUN	NN	Number=Sing	22	dobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	Makkai	Makkai	PROPN	NNP	Number=Sing	26	pobj	_	SpaceAfter=No
28	's	's	PART	POS	_	27	case	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = Finally, we apply these results to the Boolean cyclic spectrum and give some relevant examples.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	apply	apply	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	these	these	DET	DT	Number=Plur|PronType=Dem	6	det	_	_
6	results	result	NOUN	NNS	Number=Plur	4	dobj	_	_
7	to	to	ADP	IN	_	4	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
9	Boolean	Boolean	PROPN	NNP	Number=Sing	11	amod	_	_
10	cyclic	cyclic	NOUN	NN	Number=Sing	11	compound	_	_
11	spectrum	spectrum	NOUN	NN	Number=Sing	7	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
13	give	give	VERB	VB	VerbForm=Inf	4	conj	_	_
14	some	some	DET	DT	_	16	det	_	_
15	relevant	relevant	ADJ	JJ	Degree=Pos	16	amod	_	_
16	examples	example	NOUN	NNS	Number=Plur	13	dobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 379
# sent_id = 1
# text = We show that a reflective/coreflective pair of full subcategories satisfies a ``maximal - normal'' - type equivalence if and only if it is an associated pair in the sense of Kelly and Lawvere.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	12	mark	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
5	reflective	reflective	ADJ	JJ	Degree=Pos	8	amod	_	SpaceAfter=No
6	/	/	SYM	SYM	_	7	punct	_	SpaceAfter=No
7	coreflective	coreflective	ADJ	JJ	Degree=Pos	8	amod	_	_
8	pair	pair	NOUN	NN	Number=Sing	12	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	full	full	ADJ	JJ	Degree=Pos	11	amod	_	_
11	subcategories	subcategorie	NOUN	NNS	Number=Plur	9	pobj	_	_
12	satisfies	satisfie	NOUN	NNS	Number=Plur	2	ccomp	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
14	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	22	punct	_	SpaceAfter=No
15	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	22	punct	_	SpaceAfter=No
16	maximal	maximal	ADJ	JJ	Degree=Pos	18	amod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	normal	normal	ADJ	JJ	Degree=Pos	22	amod	_	SpaceAfter=No
19	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	21	punct	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	type	type	NOUN	NN	Number=Sing	22	compound	_	_
22	equivalence	equivalence	NOUN	NN	Number=Sing	12	dobj	_	_
23	if	if	SCONJ	IN	_	2	dep	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	only	only	ADV	RB	_	28	advmod	_	_
26	if	if	SCONJ	IN	_	28	mark	_	_
27	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	28	nsubj	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	conj	_	_
29	an	an	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	associated	associated	ADJ	JJ	Degree=Pos	31	amod	_	_
31	pair	pair	NOUN	NN	Number=Sing	28	attr	_	_
32	in	in	ADP	IN	_	31	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
34	sense	sense	NOUN	NN	Number=Sing	32	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	Kelly	Kelly	PROPN	NNP	Number=Sing	35	pobj	_	_
37	and	and	CCONJ	CC	ConjType=Cmp	36	cc	_	_
38	Lawvere	Lawvere	PROPN	NNP	Number=Sing	36	conj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 380
# sent_id = 1
# text = The category of $ Set $ - valued presheaves on a small category $ B $ is a topos.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	13	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	$ Set $	$ set $	SYM	$	_	6	advmod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
7	presheaves	presheave	NOUN	NNS	Number=Plur	3	pobj	_	_
8	on	on	ADP	IN	_	2	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	small	small	ADJ	JJ	Degree=Pos	11	amod	_	_
11	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
12	$ B $	$ b $	SYM	$	_	11	appos	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	topos	topos	NOUN	NN	Number=Sing	13	attr	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 2
# text = Replacing $ Set $ by a bicategory $ S $ whose objects are sets and morphisms are spans, relations, or partial maps, we consider a category $ Lax(B, S) $ of $ S $ - valued lax functors on $ B $ .
1	Replacing	replace	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	23	advcl	_	_
2	$ Set $	$ set $	SYM	$	_	1	dobj	_	_
3	by	by	ADP	IN	_	1	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	bicategory	bicategory	NOUN	NN	Number=Sing	3	pobj	_	_
6	$ S $	$ s $	SYM	$	_	5	nmod	_	_
7	whose	whose	DET	WP$	Poss=Yes	8	poss	_	_
8	objects	object	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	relcl	_	_
10	sets	set	NOUN	NNS	Number=Plur	9	attr	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
12	morphisms	morphism	NOUN	NNS	Number=Plur	13	nsubj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	conj	_	_
14	spans	span	NOUN	NNS	Number=Plur	13	attr	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	relations	relation	NOUN	NNS	Number=Plur	14	conj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	or	or	CCONJ	CC	ConjType=Cmp	16	cc	_	_
19	partial	partial	ADJ	JJ	Degree=Pos	20	amod	_	_
20	maps	map	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
22	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	23	nsubj	_	_
23	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
25	category	category	NOUN	NN	Number=Sing	23	dobj	_	_
26	$ Lax(B, S) $	$ lax(b, s) $	SYM	$	_	25	appos	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	$ S $	$ s $	SYM	$	_	30	dep	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	amod	_	_
31	lax	lax	ADJ	JJ	Degree=Pos	32	amod	_	_
32	functors	functor	NOUN	NNS	Number=Plur	27	pobj	_	_
33	on	on	ADP	IN	_	32	prep	_	_
34	$ B $	$ b $	SYM	$	_	33	pobj	_	_
35	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# sent_id = 3
# text = When $ S = Span $ , the resulting category is equivalent to $ Cat/B $ , and hence, is rarely even cartesian closed.
1	When	when	SCONJ	WRB	_	2	advmod	_	_
2	$ S = Span $	$ s = span $	SYM	$	_	7	advcl	_	_
3	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	equivalent	equivalent	ADJ	JJ	Degree=Pos	7	acomp	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	$ Cat/B $	$ cat/b $	SYM	$	_	9	pobj	_	_
11	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
13	hence	hence	ADV	RB	_	15	advmod	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	conj	_	_
16	rarely	rarely	ADV	RB	_	15	advmod	_	_
17	even	even	ADV	RB	_	18	advmod	_	_
18	cartesian	cartesian	ADJ	JJ	Degree=Pos	19	nsubj	_	_
19	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	15	acomp	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 4
# text = Restricting this equivalence gives rise to exponentiability characterizations for $ Lax(B, Rel) $ by Niefield and for $ Lax(B, Par) $ in this paper.
1	Restricting	restrict	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	csubj	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	equivalence	equivalence	NOUN	NN	Number=Sing	1	dobj	_	_
4	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	rise	rise	NOUN	NN	Number=Sing	4	dobj	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	exponentiability	exponentiability	NOUN	NN	Number=Sing	8	compound	_	_
8	characterizations	characterization	NOUN	NNS	Number=Plur	6	pobj	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	$ Lax(B, Rel) $	$ lax(b, rel) $	SYM	$	_	9	pobj	_	_
11	by	by	ADP	IN	_	10	agent	_	_
12	Niefield	Niefield	PROPN	NNP	Number=Sing	11	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
14	for	for	ADP	IN	_	11	conj	_	_
15	$ Lax(B, Par) $	$ lax(b, par) $	SYM	$	_	14	pobj	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	this	this	DET	DT	Number=Sing|PronType=Dem	18	det	_	_
18	paper	paper	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = Along the way, we obtain a characterization of those $ B $ for which the category $ UFL/B $ is a coreflective subcategory of $ Cat/B $ , and hence, a topos.
1	Along	along	ADP	IN	_	6	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	way	way	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	characterization	characterization	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	those	those	DET	DT	Number=Plur|PronType=Dem	11	det	_	_
11	$ B $	$ b $	SYM	$	_	9	pobj	_	_
12	for	for	ADP	IN	_	17	prep	_	_
13	which	which	PRON	WDT	_	12	pobj	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	category	category	NOUN	NN	Number=Sing	17	nsubj	_	_
16	$ UFL/B $	$ ufl/b $	X	ADD	_	15	appos	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	relcl	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	coreflective	coreflective	ADJ	JJ	Degree=Pos	20	amod	_	_
20	subcategory	subcategory	NOUN	NN	Number=Sing	17	attr	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	$ Cat/B $	$ cat/b $	SYM	$	_	21	pobj	_	_
23	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
25	hence	hence	ADV	RB	_	11	advmod	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	topos	topos	NOUN	NN	Number=Sing	11	appos	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 381
# sent_id = 1
# text = A flow on a compact Hausdorff space is an automorphism.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	flow	flow	NOUN	NN	Number=Sing	8	nsubj	_	_
3	on	on	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	compact	compact	ADJ	JJ	Degree=Pos	7	amod	_	_
6	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	7	compound	_	_
7	space	space	NOUN	NN	Number=Sing	3	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	automorphism	automorphism	NOUN	NN	Number=Sing	8	attr	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = Using the closed structure on the category of uniform spaces, a flow gives rise, by iteration, to an action of the integers on the topological group of automorphisms of the object.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	advcl	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	closed	closed	ADJ	JJ	Degree=Pos	4	amod	_	_
4	structure	structure	NOUN	NN	Number=Sing	1	dobj	_	_
5	on	on	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	uniform	uniform	PROPN	NNP	Number=Sing	10	compound	_	_
10	spaces	space	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	flow	flow	NOUN	NN	Number=Sing	14	nsubj	_	_
14	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	rise	rise	NOUN	NN	Number=Sing	14	dobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
17	by	by	ADP	IN	_	14	prep	_	_
18	iteration	iteration	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
20	to	to	ADP	IN	_	14	prep	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	action	action	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	integers	integer	NOUN	NNS	Number=Plur	23	pobj	_	_
26	on	on	ADP	IN	_	22	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	topological	topological	ADJ	JJ	Degree=Pos	29	amod	_	_
29	group	group	NOUN	NN	Number=Sing	26	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	automorphisms	automorphism	NOUN	NNS	Number=Plur	30	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
34	object	object	NOUN	NN	Number=Sing	32	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 3
# text = We study special classes of flows: periodic, cocyclic, and almost cocyclic, mainly in term of the possibility of extending this action continuously to various compactifications of the integers.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	special	special	ADJ	JJ	Degree=Pos	4	amod	_	_
4	classes	class	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	flows	flow	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
7	:	:	PUNCT	:	_	6	punct	_	_
8	periodic	periodic	ADJ	JJ	Degree=Pos	2	dobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
10	cocyclic	cocyclic	NOUN	NN	Number=Sing	8	conj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
13	almost	almost	ADV	RB	_	14	advmod	_	_
14	cocyclic	cocyclic	ADJ	JJ	Degree=Pos	10	conj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
16	mainly	mainly	ADV	RB	_	17	advmod	_	_
17	in	in	ADP	IN	_	2	prep	_	_
18	term	term	NOUN	NN	Number=Sing	17	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	possibility	possibility	NOUN	NN	Number=Sing	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	extending	extend	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	pcomp	_	_
24	this	this	DET	DT	Number=Sing|PronType=Dem	25	det	_	_
25	action	action	NOUN	NN	Number=Sing	23	dobj	_	_
26	continuously	continuously	ADV	RB	_	23	advmod	_	_
27	to	to	ADP	IN	_	23	prep	_	_
28	various	various	ADJ	JJ	Degree=Pos	29	amod	_	_
29	compactifications	compactification	NOUN	NNS	Number=Plur	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	integers	integer	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 382
# sent_id = 1
# text = We present a new explicit construction of categorical semidirect products in an arbitrary variety $ V $ of right $ Omega $ - loops and use it to obtain simplified descriptions of internal precrossed and crossed modules in $ V $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
4	new	new	ADJ	JJ	Degree=Pos	6	amod	_	_
5	explicit	explicit	ADJ	JJ	Degree=Pos	6	amod	_	_
6	construction	construction	NOUN	NN	Number=Sing	2	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	categorical	categorical	ADJ	JJ	Degree=Pos	10	amod	_	_
9	semidirect	semidirect	NOUN	NN	Number=Sing	10	compound	_	_
10	products	product	NOUN	NNS	Number=Plur	7	pobj	_	_
11	in	in	ADP	IN	_	2	prep	_	_
12	an	an	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	14	amod	_	_
14	variety	variety	NOUN	NN	Number=Sing	11	pobj	_	_
15	$ V $	$ v $	SYM	$	_	2	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	right	right	ADJ	JJ	Degree=Pos	20	amod	_	_
18	$ Omega $	$ omega $	SYM	$	_	20	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	loops	loop	NOUN	NNS	Number=Plur	16	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
22	use	use	VERB	VB	VerbForm=Inf	2	conj	_	_
23	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	22	dobj	_	_
24	to	to	PART	TO	_	25	aux	_	_
25	obtain	obtain	VERB	VB	VerbForm=Inf	22	xcomp	_	_
26	simplified	simplified	ADJ	JJ	Degree=Pos	27	amod	_	_
27	descriptions	description	NOUN	NNS	Number=Plur	25	dobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	internal	internal	ADJ	JJ	Degree=Pos	30	amod	_	_
30	precrossed	precrosse	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	pobj	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
32	crossed	cross	VERB	VBD	Tense=Past|VerbForm=Fin	30	conj	_	_
33	modules	module	NOUN	NNS	Number=Plur	32	dobj	_	_
34	in	in	ADP	IN	_	33	prep	_	_
35	$ V $	$ v $	SYM	$	_	34	pobj	_	_
36	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 383
# sent_id = 1
# text = Representables for double categories are defined to be lax morphisms into a certain double category of sets.
1	Representables	representable	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
2	for	for	ADP	IN	_	1	prep	_	_
3	double	double	ADJ	JJ	Degree=Pos	4	amod	_	_
4	categories	category	NOUN	NNS	Number=Plur	2	pobj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	be	be	AUX	VB	VerbForm=Inf	6	xcomp	_	_
9	lax	lax	ADJ	JJ	Degree=Pos	10	amod	_	_
10	morphisms	morphism	NOUN	NNS	Number=Plur	8	attr	_	_
11	into	into	ADP	IN	_	8	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	certain	certain	ADJ	JJ	Degree=Pos	15	amod	_	_
14	double	double	ADJ	JJ	Degree=Pos	15	amod	_	_
15	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	sets	set	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that horizontal transformations from representables into lax morphisms correspond to elements of that lax morphism.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	11	mark	_	_
4	horizontal	horizontal	ADJ	JJ	Degree=Pos	5	amod	_	_
5	transformations	transformation	NOUN	NNS	Number=Plur	11	nsubj	_	_
6	from	from	ADP	IN	_	5	prep	_	_
7	representables	representable	NOUN	NNS	Number=Plur	6	pobj	_	_
8	into	into	ADP	IN	_	7	prep	_	_
9	lax	lax	ADJ	JJ	Degree=Pos	10	amod	_	_
10	morphisms	morphism	NOUN	NNS	Number=Plur	8	pobj	_	_
11	correspond	correspond	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	elements	element	NOUN	NNS	Number=Plur	12	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	that	that	DET	DT	Number=Sing|PronType=Dem	17	det	_	_
16	lax	lax	ADJ	JJ	Degree=Pos	17	amod	_	_
17	morphism	morphism	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Vertical arrows give rise to modules between representables.
1	Vertical	vertical	ADJ	JJ	Degree=Pos	2	amod	_	_
2	arrows	arrow	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	rise	rise	NOUN	NN	Number=Sing	3	dobj	_	_
5	to	to	ADP	IN	_	3	prep	_	_
6	modules	module	NOUN	NNS	Number=Plur	5	pobj	_	_
7	between	between	ADP	IN	_	6	prep	_	_
8	representables	representable	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = We establish that the Yoneda embedding is a strong morphism of lax double categories which is horizontally full and faithful and dense.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	establish	establish	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	Yoneda	Yoneda	PROPN	NNP	Number=Sing	6	nsubj	_	_
6	embedding	embed	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	csubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	strong	strong	ADJ	JJ	Degree=Pos	10	amod	_	_
10	morphism	morphism	NOUN	NN	Number=Sing	7	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	lax	lax	ADJ	JJ	Degree=Pos	14	amod	_	_
13	double	double	ADJ	JJ	Degree=Pos	14	amod	_	_
14	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
15	which	which	PRON	WDT	_	16	nsubj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
17	horizontally	horizontally	ADV	RB	_	16	advmod	_	_
18	full	full	ADJ	JJ	Degree=Pos	16	acomp	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	faithful	faithful	ADJ	JJ	Degree=Pos	18	conj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	dense	dense	ADJ	JJ	Degree=Pos	20	conj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 384
# sent_id = 1
# text = In the context of Cartesian differential categories, the structure of the first - order chain rule gives rise to a fibration, the ``bundle category''.
1	In	in	ADP	IN	_	18	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	context	context	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	Cartesian	cartesian	ADJ	JJ	Degree=Pos	7	amod	_	_
6	differential	differential	ADJ	JJ	Degree=Pos	7	amod	_	_
7	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	structure	structure	NOUN	NN	Number=Sing	18	nsubj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
13	first	first	ADJ	JJ	Degree=Pos	15	amod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	order	order	NOUN	NN	Number=Sing	17	compound	_	_
16	chain	chain	NOUN	NN	Number=Sing	17	compound	_	_
17	rule	rule	NOUN	NN	Number=Sing	11	pobj	_	_
18	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
19	rise	rise	VERB	VB	VerbForm=Inf	18	dobj	_	_
20	to	to	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	fibration	fibration	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
25	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	28	punct	_	SpaceAfter=No
26	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	28	punct	_	SpaceAfter=No
27	bundle	bundle	NOUN	NN	Number=Sing	28	compound	_	_
28	category	category	NOUN	NN	Number=Sing	18	dobj	_	SpaceAfter=No
29	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	28	punct	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# sent_id = 2
# text = In the present paper we generalise this to the higher - order chain rule (originally developed in the traditional setting by Faà di Bruno in the nineteenth century); given any Cartesian differential category $ X $ , there is a ``higher - order chain rule fibration'' $ Faa(X) - - > X $ over it.
1	In	in	ADP	IN	_	6	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	present	present	ADJ	JJ	Degree=Pos	4	amod	_	_
4	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	generalise	generalise	VERB	VBP	Tense=Pres|VerbForm=Fin	40	ccomp	_	_
7	this	this	PRON	DT	Number=Sing|PronType=Dem	6	dobj	_	_
8	to	to	ADP	IN	_	6	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
10	higher	high	ADJ	JJR	Degree=Cmp	12	amod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	order	order	NOUN	NN	Number=Sing	14	compound	_	_
13	chain	chain	NOUN	NN	Number=Sing	14	compound	_	_
14	rule	rule	NOUN	NN	Number=Sing	8	pobj	_	_
15	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
16	originally	originally	ADV	RB	_	17	advmod	_	_
17	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	acl	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	traditional	traditional	ADJ	JJ	Degree=Pos	21	amod	_	_
21	setting	setting	NOUN	NN	Number=Sing	18	pobj	_	_
22	by	by	ADP	IN	_	21	prep	_	_
23	Faà	Faà	PROPN	NNP	Number=Sing	25	compound	_	_
24	di	di	PROPN	NNP	Number=Sing	25	compound	_	_
25	Bruno	Bruno	PROPN	NNP	Number=Sing	22	pobj	_	_
26	in	in	ADP	IN	_	17	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	nineteenth	nineteenth	ADJ	JJ	Degree=Pos	29	amod	_	_
29	century	century	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
30	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	14	punct	_	SpaceAfter=No
31	;	;	PUNCT	:	_	40	punct	_	_
32	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	40	prep	_	_
33	any	any	DET	DT	_	36	det	_	_
34	Cartesian	cartesian	ADJ	JJ	Degree=Pos	36	amod	_	_
35	differential	differential	ADJ	JJ	Degree=Pos	36	amod	_	_
36	category	category	NOUN	NN	Number=Sing	32	pobj	_	_
37	$ X $	$ x $	SYM	$	_	36	appos	_	_
38	,	,	PUNCT	,	PunctType=Comm	40	punct	_	_
39	there	there	PRON	EX	_	40	expl	_	_
40	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
41	a	a	DET	DT	Definite=Ind|PronType=Art	49	det	_	_
42	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	49	punct	_	SpaceAfter=No
43	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	49	punct	_	SpaceAfter=No
44	higher	high	ADJ	JJR	Degree=Cmp	46	amod	_	_
45	-	-	PUNCT	HYPH	PunctType=Dash	46	punct	_	_
46	order	order	NOUN	NN	Number=Sing	47	compound	_	_
47	chain	chain	NOUN	NN	Number=Sing	48	compound	_	_
48	rule	rule	NOUN	NN	Number=Sing	49	compound	_	_
49	fibration	fibration	NOUN	NN	Number=Sing	40	attr	_	SpaceAfter=No
50	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	49	punct	_	_
51	$ Faa(X) - - > X $	$ faa(x) - - > x $	SYM	$	_	40	dep	_	_
52	over	over	ADP	IN	_	51	prep	_	_
53	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	52	pobj	_	SpaceAfter=No
54	.	.	PUNCT	.	PunctType=Peri	40	punct	_	SpaceAfter=No

# sent_id = 3
# text = In fact, $ Faa $ is a comonad (over the category of Cartesian left (semi - )additive categories).
1	In	in	ADP	IN	_	5	prep	_	_
2	fact	fact	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	$ Faa $	$ faa $	SYM	$	_	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	comonad	comonad	NOUN	NNS	Number=Plur	5	attr	_	_
8	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	7	punct	_	SpaceAfter=No
9	over	over	ADP	IN	_	7	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	Cartesian	Cartesian	PROPN	NNP	Number=Sing	12	pobj	_	_
14	left	leave	VERB	VBD	Tense=Past|VerbForm=Fin	7	acl	_	_
15	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
16	semi	semi	ADV	RB	_	20	amod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
18	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	20	punct	_	SpaceAfter=No
19	additive	additive	ADJ	JJ	Degree=Pos	20	amod	_	_
20	categories	category	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
21	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	14	punct	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = Our main theorem is that the coalgebras for this comonad are precisely the Cartesian differential categories.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	3	poss	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	theorem	theorem	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	11	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	coalgebras	coalgebra	NOUN	NNS	Number=Plur	11	nsubj	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	this	this	DET	DT	Number=Sing|PronType=Dem	10	det	_	_
10	comonad	comonad	NOUN	NNS	Number=Plur	8	pobj	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
12	precisely	precisely	ADV	RB	_	11	advmod	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
14	Cartesian	cartesian	ADJ	JJ	Degree=Pos	16	amod	_	_
15	differential	differential	ADJ	JJ	Degree=Pos	16	amod	_	_
16	categories	category	NOUN	NNS	Number=Plur	11	attr	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = In a sense, this result affirms the ``correctness'' of the notion of Cartesian differential categories.
1	In	in	ADP	IN	_	7	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	sense	sense	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	result	result	NOUN	NN	Number=Sing	7	nsubj	_	_
7	affirms	affirm	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
9	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	11	punct	_	SpaceAfter=No
10	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	11	punct	_	SpaceAfter=No
11	correctness	correctness	NOUN	NN	Number=Sing	7	dobj	_	SpaceAfter=No
12	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	11	punct	_	_
13	of	of	ADP	IN	_	11	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	notion	notion	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	Cartesian	cartesian	ADJ	JJ	Degree=Pos	19	amod	_	_
18	differential	differential	ADJ	JJ	Degree=Pos	19	amod	_	_
19	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 385
# sent_id = 1
# text = In this paper, we consider a non - posetal analogue of the notion of involutive quantale; specifically, a (planar) monoidal category equipped with a covariant involution that reverses the order of tensoring.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	non	non	ADJ	JJ	Degree=Pos	10	amod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	posetal	posetal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	analogue	analogue	NOUN	NN	Number=Sing	6	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	notion	notion	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	involutive	involutive	ADJ	JJ	Degree=Pos	17	amod	_	_
17	quantale	quantale	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
18	;	;	PUNCT	:	_	6	punct	_	_
19	specifically	specifically	ADV	RB	_	26	advmod	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
22	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	26	punct	_	SpaceAfter=No
23	planar	planar	ADJ	JJ	Degree=Pos	26	amod	_	SpaceAfter=No
24	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	26	punct	_	_
25	monoidal	monoidal	ADJ	JJ	Degree=Pos	26	amod	_	_
26	category	category	NOUN	NN	Number=Sing	11	appos	_	_
27	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	acl	_	_
28	with	with	ADP	IN	_	27	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	covariant	covariant	ADJ	JJ	Degree=Pos	31	amod	_	_
31	involution	involution	NOUN	NN	Number=Sing	28	pobj	_	_
32	that	that	PRON	WDT	PronType=Rel	33	nsubj	_	_
33	reverses	reverse	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	31	relcl	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	order	order	NOUN	NN	Number=Sing	33	dobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	tensoring	tensoring	NOUN	NN	Number=Sing	36	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = We study the coherence issues that inevitably result when passing from posets to categories; we also link our subject with other notions already in the literature, such as balanced monoidal categories and dagger pivotal categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	18	ccomp	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	coherence	coherence	NOUN	NN	Number=Sing	5	compound	_	_
5	issues	issue	NOUN	NNS	Number=Plur	2	dobj	_	_
6	that	that	PRON	WDT	PronType=Rel	8	nsubj	_	_
7	inevitably	inevitably	ADV	RB	_	8	advmod	_	_
8	result	result	VERB	VBP	Tense=Pres|VerbForm=Fin	5	relcl	_	_
9	when	when	SCONJ	WRB	_	10	advmod	_	_
10	passing	pass	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	advcl	_	_
11	from	from	ADP	IN	_	10	prep	_	_
12	posets	poset	NOUN	NNS	Number=Plur	11	pobj	_	_
13	to	to	ADP	IN	_	10	prep	_	_
14	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
15	;	;	PUNCT	:	_	18	punct	_	_
16	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	18	nsubj	_	_
17	also	also	ADV	RB	_	18	advmod	_	_
18	link	link	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
19	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	20	poss	_	_
20	subject	subject	NOUN	NN	Number=Sing	18	dobj	_	_
21	with	with	ADP	IN	_	20	prep	_	_
22	other	other	ADJ	JJ	Degree=Pos	23	amod	_	_
23	notions	notion	NOUN	NNS	Number=Plur	21	pobj	_	_
24	already	already	ADV	RB	_	25	advmod	_	_
25	in	in	ADP	IN	_	18	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	literature	literature	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
29	such	such	ADJ	JJ	Degree=Pos	30	amod	_	_
30	as	as	ADP	IN	_	27	prep	_	_
31	balanced	balanced	ADJ	JJ	Degree=Pos	33	amod	_	_
32	monoidal	monoidal	ADJ	JJ	Degree=Pos	33	amod	_	_
33	categories	category	NOUN	NNS	Number=Plur	30	pobj	_	_
34	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
35	dagger	dagger	NOUN	NN	Number=Sing	37	nmod	_	_
36	pivotal	pivotal	ADJ	JJ	Degree=Pos	37	amod	_	_
37	categories	category	NOUN	NNS	Number=Plur	33	conj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# doc_id = 386
# sent_id = 1
# text = For small involutive and integral quantaloids $ {cal Q} $ it is shown that covariant presheaves on symmetric $ {cal Q} $ - categories are equivalent to certain subalgebras of a specific monad on the category of symmetric $ {cal Q} $ - categories.
1	For	for	ADP	IN	_	10	prep	_	_
2	small	small	ADJ	JJ	Degree=Pos	3	amod	_	_
3	involutive	involutive	NOUN	NN	Number=Sing	6	amod	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	integral	integral	ADJ	JJ	Degree=Pos	3	conj	_	_
6	quantaloids	quantaloid	NOUN	NNS	Number=Plur	1	pobj	_	_
7	$ {cal Q} $	$ {cal q} $	SYM	$	_	1	nmod	_	_
8	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	10	nsubjpass	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	that	that	SCONJ	IN	_	13	det	_	_
12	covariant	covariant	ADJ	JJ	Degree=Pos	13	amod	_	_
13	presheaves	presheave	NOUN	NNS	Number=Plur	19	nsubj	_	_
14	on	on	ADP	IN	_	13	prep	_	_
15	symmetric	symmetric	ADJ	JJ	Degree=Pos	18	amod	_	_
16	$ {cal Q} $	$ {cal Q} $	PROPN	NNP	Number=Sing	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	categories	category	NOUN	NNS	Number=Plur	14	pobj	_	_
19	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	10	ccomp	_	_
20	equivalent	equivalent	ADJ	JJ	Degree=Pos	19	acomp	_	_
21	to	to	ADP	IN	_	20	prep	_	_
22	certain	certain	ADJ	JJ	Degree=Pos	23	amod	_	_
23	subalgebras	subalgebra	NOUN	NNS	Number=Plur	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
26	specific	specific	ADJ	JJ	Degree=Pos	27	amod	_	_
27	monad	monad	NOUN	NNS	Number=Plur	24	pobj	_	_
28	on	on	ADP	IN	_	27	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	category	category	NOUN	NN	Number=Sing	28	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	symmetric	symmetric	ADJ	JJ	Degree=Pos	35	amod	_	_
33	$ {cal Q} $	$ {cal Q} $	PROPN	NNP	Number=Sing	35	compound	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	categories	category	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = This construction is related to a weakening of the subobject classifier axiom which does not require the classification of all subalgebras, but only guarantees that classifiable subalgebras are uniquely classifiable.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	construction	construction	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	weakening	weakening	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	subobject	subobject	NOUN	NN	Number=Sing	11	compound	_	_
11	classifier	classifier	PROPN	NNP	Number=Sing	12	compound	_	_
12	axiom	axiom	NOUN	NN	Number=Sing	8	pobj	_	_
13	which	which	PRON	WDT	_	16	nsubj	_	_
14	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	aux	_	_
15	not	not	PART	RB	Polarity=Neg	16	neg	_	_
16	require	require	VERB	VB	VerbForm=Inf	7	relcl	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	classification	classification	NOUN	NN	Number=Sing	16	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	all	all	DET	DT	_	21	det	_	_
21	subalgebras	subalgebras	PROPN	NNP	Number=Sing	19	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
23	but	but	CCONJ	CC	ConjType=Cmp	4	cc	_	_
24	only	only	ADV	RB	_	25	advmod	_	_
25	guarantees	guarantee	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	conj	_	_
26	that	that	SCONJ	IN	_	29	mark	_	_
27	classifiable	classifiable	ADJ	JJ	Degree=Pos	28	amod	_	_
28	subalgebras	subalgebras	PROPN	NNP	Number=Sing	29	nsubj	_	_
29	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	25	ccomp	_	_
30	uniquely	uniquely	ADV	RB	_	31	advmod	_	_
31	classifiable	classifiable	ADJ	JJ	Degree=Pos	29	acomp	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	25	punct	_	SpaceAfter=No

# sent_id = 3
# text = As an application the identification of closed left ideals of non - commutative $ C^* $ - algebras with certain "open", subalgebras of freely generated algebras is given.
1	As	as	ADP	IN	_	29	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	identification	identification	NOUN	NN	Number=Sing	1	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	closed	closed	ADJ	JJ	Degree=Pos	9	amod	_	_
8	left	left	ADJ	JJ	Degree=Pos	9	amod	_	_
9	ideals	ideal	NOUN	NNS	Number=Plur	6	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	non	non	PROPN	NNP	Number=Sing	13	amod	_	_
12	-	-	PROPN	NNP	Number=Sing	13	punct	_	_
13	commutative	commutative	ADJ	JJ	Degree=Pos	16	amod	_	_
14	$ C^* $	$ c^* $	SYM	$	_	16	compound	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	algebras	algebra	NOUN	NNS	Number=Plur	10	pobj	_	_
17	with	with	ADP	IN	_	5	prep	_	_
18	certain	certain	ADJ	JJ	Degree=Pos	20	amod	_	_
19	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	20	punct	_	SpaceAfter=No
20	open	open	ADJ	JJ	Degree=Pos	17	pobj	_	SpaceAfter=No
21	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	20	punct	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
23	subalgebras	subalgebras	PROPN	NNP	Number=Sing	29	nsubjpass	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	freely	freely	ADV	RB	_	26	advmod	_	_
26	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	amod	_	_
27	algebras	algebra	NOUN	NNS	Number=Plur	24	pobj	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	auxpass	_	_
29	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	29	punct	_	SpaceAfter=No

# doc_id = 387
# sent_id = 1
# text = We proved in a previous work that Cattani - Sassone's higher dimensional transition systems can be interpreted as a small - orthogonality class of a topological locally finitely presentable category of weak higher dimensional transition systems.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	proved	prove	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	previous	previous	ADJ	JJ	Degree=Pos	6	amod	_	_
6	work	work	NOUN	NN	Number=Sing	3	pobj	_	_
7	that	that	PRON	WDT	PronType=Rel	18	mark	_	_
8	Cattani	Cattani	PROPN	NNP	Number=Sing	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	Sassone	Sassone	PROPN	NNP	Number=Sing	15	poss	_	SpaceAfter=No
11	's	's	PART	POS	_	10	case	_	_
12	higher	high	ADJ	JJR	Degree=Cmp	15	amod	_	_
13	dimensional	dimensional	ADJ	JJ	Degree=Pos	15	amod	_	_
14	transition	transition	NOUN	NN	Number=Sing	15	compound	_	_
15	systems	system	NOUN	NNS	Number=Plur	18	nsubjpass	_	_
16	can	can	AUX	MD	VerbForm=Fin	18	aux	_	_
17	be	be	AUX	VB	VerbForm=Inf	18	auxpass	_	_
18	interpreted	interpret	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	relcl	_	_
19	as	as	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
21	small	small	ADJ	JJ	Degree=Pos	23	amod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	orthogonality	orthogonality	NOUN	NN	Number=Sing	24	compound	_	_
24	class	class	NOUN	NN	Number=Sing	19	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
27	topological	topological	ADJ	JJ	Degree=Pos	31	amod	_	_
28	locally	locally	ADV	RB	_	29	advmod	_	_
29	finitely	finitely	ADV	RB	_	30	advmod	_	_
30	presentable	presentable	ADJ	JJ	Degree=Pos	31	amod	_	_
31	category	category	NOUN	NN	Number=Sing	25	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	weak	weak	ADJ	JJ	Degree=Pos	37	amod	_	_
34	higher	high	ADJ	JJR	Degree=Cmp	37	amod	_	_
35	dimensional	dimensional	ADJ	JJ	Degree=Pos	37	amod	_	_
36	transition	transition	NOUN	NN	Number=Sing	37	compound	_	_
37	systems	system	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper, we turn our attention to the full subcategory of weak higher dimensional transition systems which are unions of cubes.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	turn	turn	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	8	poss	_	_
8	attention	attention	NOUN	NN	Number=Sing	6	dobj	_	_
9	to	to	ADP	IN	_	6	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	full	full	ADJ	JJ	Degree=Pos	12	amod	_	_
12	subcategory	subcategory	NOUN	NN	Number=Sing	9	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	weak	weak	ADJ	JJ	Degree=Pos	18	amod	_	_
15	higher	high	ADJ	JJR	Degree=Cmp	18	amod	_	_
16	dimensional	dimensional	ADJ	JJ	Degree=Pos	18	amod	_	_
17	transition	transition	NOUN	NN	Number=Sing	18	compound	_	_
18	systems	system	NOUN	NNS	Number=Plur	13	pobj	_	_
19	which	which	PRON	WDT	_	20	nsubj	_	_
20	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	18	relcl	_	_
21	unions	union	NOUN	NNS	Number=Plur	20	attr	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	cubes	cube	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = It is proved that there exists a left proper combinatorial model structure such that two objects are weakly equivalent if and only if they have the same cubes after simplification of the labelling.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	SCONJ	IN	_	6	mark	_	_
5	there	there	PRON	EX	_	6	expl	_	_
6	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
8	left	left	ADJ	JJ	Degree=Pos	12	amod	_	_
9	proper	proper	ADJ	JJ	Degree=Pos	12	amod	_	_
10	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	11	amod	_	_
11	model	model	NOUN	NN	Number=Sing	12	compound	_	_
12	structure	structure	NOUN	NN	Number=Sing	6	dobj	_	_
13	such	such	ADJ	JJ	Degree=Pos	17	amod	_	_
14	that	that	SCONJ	IN	_	17	mark	_	_
15	two	two	NUM	CD	NumType=Card	16	nummod	_	_
16	objects	object	NOUN	NNS	Number=Plur	17	nsubj	_	_
17	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	advcl	_	_
18	weakly	weakly	ADV	RB	_	19	advmod	_	_
19	equivalent	equivalent	ADJ	JJ	Degree=Pos	17	acomp	_	_
20	if	if	SCONJ	IN	_	17	prep	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	only	only	ADV	RB	_	25	advmod	_	_
23	if	if	SCONJ	IN	_	25	mark	_	_
24	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	25	nsubj	_	_
25	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	20	conj	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	same	same	ADJ	JJ	Degree=Pos	28	amod	_	_
28	cubes	cube	NOUN	NNS	Number=Plur	25	dobj	_	_
29	after	after	ADP	IN	_	28	prep	_	_
30	simplification	simplification	NOUN	NN	Number=Sing	29	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
33	labelling	labelling	NOUN	NN	Number=Sing	31	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = This model structure is obtained by Bousfield localizing a model structure which is left determined with respect to a class of maps which is not the class of monomorphisms.
1	This	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
2	model	model	NOUN	NN	Number=Sing	3	compound	_	_
3	structure	structure	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	by	by	ADP	IN	_	5	agent	_	_
7	Bousfield	Bousfield	PROPN	NNP	Number=Sing	6	pobj	_	_
8	localizing	localize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	advcl	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	model	model	NOUN	NN	Number=Sing	11	compound	_	_
11	structure	structure	NOUN	NN	Number=Sing	8	dobj	_	_
12	which	which	PRON	WDT	_	14	nsubjpass	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	relcl	_	_
15	determined	determined	ADJ	JJ	Degree=Pos	14	oprd	_	_
16	with	with	ADP	IN	_	15	prep	_	_
17	respect	respect	NOUN	NN	Number=Sing	16	pobj	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	class	class	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	maps	map	NOUN	NNS	Number=Plur	21	pobj	_	_
23	which	which	PRON	WDT	_	24	nsubj	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	relcl	_	_
25	not	not	PART	RB	Polarity=Neg	24	neg	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	class	class	NOUN	NN	Number=Sing	24	attr	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = We prove that the higher dimensional transition systems corresponding to two process algebras are weakly equivalent if and only if they are isomorphic.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	14	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
5	higher	high	ADJ	JJR	Degree=Cmp	8	amod	_	_
6	dimensional	dimensional	ADJ	JJ	Degree=Pos	8	amod	_	_
7	transition	transition	NOUN	NN	Number=Sing	8	compound	_	_
8	systems	system	NOUN	NNS	Number=Plur	14	nsubj	_	_
9	corresponding	corresponding	ADJ	JJ	Degree=Pos	8	amod	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	two	two	NUM	CD	NumType=Card	12	nummod	_	_
12	process	process	NOUN	NN	Number=Sing	13	compound	_	_
13	algebras	algebra	NOUN	NNS	Number=Plur	10	pobj	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
15	weakly	weakly	ADV	RB	_	16	advmod	_	_
16	equivalent	equivalent	ADJ	JJ	Degree=Pos	14	acomp	_	_
17	if	if	SCONJ	IN	_	14	prep	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	only	only	ADV	RB	_	22	advmod	_	_
20	if	if	SCONJ	IN	_	22	mark	_	_
21	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	22	nsubj	_	_
22	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	advcl	_	_
23	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	22	acomp	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = We also construct a second Bousfield localization in which two bisimilar cubical transition systems are weakly equivalent.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	second	second	ADJ	JJ	Degree=Pos	7	amod	_	_
6	Bousfield	Bousfield	PROPN	NNP	Number=Sing	7	compound	_	_
7	localization	localization	NOUN	NN	Number=Sing	3	dobj	_	_
8	in	in	ADP	IN	_	15	prep	_	_
9	which	which	PRON	WDT	_	8	pobj	_	_
10	two	two	NUM	CD	NumType=Card	14	nummod	_	_
11	bisimilar	bisimilar	ADJ	JJ	Degree=Pos	14	amod	_	_
12	cubical	cubical	ADJ	JJ	Degree=Pos	13	amod	_	_
13	transition	transition	NOUN	NN	Number=Sing	14	compound	_	_
14	systems	system	NOUN	NNS	Number=Plur	15	nsubj	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	relcl	_	_
16	weakly	weakly	ADJ	JJ	Degree=Pos	17	advmod	_	_
17	equivalent	equivalent	ADJ	JJ	Degree=Pos	15	acomp	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = The appendix contains a technical lemma about smallness of weak factorization systems in coreflective subcategories which can be of independent interest.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	appendix	appendix	NOUN	NN	Number=Sing	3	nsubj	_	_
3	contains	contain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	technical	technical	ADJ	JJ	Degree=Pos	6	amod	_	_
6	lemma	lemma	NOUN	NN	Number=Sing	3	dobj	_	_
7	about	about	ADP	IN	_	6	prep	_	_
8	smallness	smallness	NOUN	NN	Number=Sing	7	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	weak	weak	ADJ	JJ	Degree=Pos	12	amod	_	_
11	factorization	factorization	NOUN	NN	Number=Sing	12	compound	_	_
12	systems	system	NOUN	NNS	Number=Plur	9	pobj	_	_
13	in	in	ADP	IN	_	8	prep	_	_
14	coreflective	coreflective	ADJ	JJ	Degree=Pos	15	amod	_	_
15	subcategories	subcategorie	NOUN	NNS	Number=Plur	13	pobj	_	_
16	which	which	PRON	WDT	_	18	nsubj	_	_
17	can	can	AUX	MD	VerbForm=Fin	18	aux	_	_
18	be	be	AUX	VB	VerbForm=Inf	15	relcl	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	independent	independent	ADJ	JJ	Degree=Pos	21	amod	_	_
21	interest	interest	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 8
# text = This paper is a first step towards a homotopical interpretation of bisimulation for higher dimensional transition systems.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	first	first	ADJ	JJ	Degree=Pos	6	amod	_	_
6	step	step	NOUN	NN	Number=Sing	3	attr	_	_
7	towards	towards	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	homotopical	homotopical	ADJ	JJ	Degree=Pos	10	amod	_	_
10	interpretation	interpretation	NOUN	NN	Number=Sing	7	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	bisimulation	bisimulation	NOUN	NN	Number=Sing	11	pobj	_	_
13	for	for	ADP	IN	_	10	prep	_	_
14	higher	high	ADJ	JJR	Degree=Cmp	17	amod	_	_
15	dimensional	dimensional	ADJ	JJ	Degree=Pos	17	amod	_	_
16	transition	transition	NOUN	NN	Number=Sing	17	compound	_	_
17	systems	system	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 388
# sent_id = 1
# text = We formulate an elementary condition on an involutive quantaloid $ Q $ under which there is a distributive law from the Cauchy completion monad over the symmetrisation comonad on the category of $ Q $ - enriched categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	formulate	formulate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	elementary	elementary	ADJ	JJ	Degree=Pos	5	amod	_	_
5	condition	condition	NOUN	NN	Number=Sing	2	dobj	_	_
6	on	on	ADP	IN	_	2	prep	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	involutive	involutive	ADJ	JJ	Degree=Pos	9	amod	_	_
9	quantaloid	quantaloid	NOUN	NN	Number=Sing	6	pobj	_	_
10	$ Q $	$ q $	SYM	$	_	9	nmod	_	_
11	under	under	ADP	IN	_	14	prep	_	_
12	which	which	PRON	WDT	_	11	pobj	_	_
13	there	there	PRON	EX	_	14	expl	_	_
14	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	relcl	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	distributive	distributive	ADJ	JJ	Degree=Pos	17	amod	_	_
17	law	law	NOUN	NN	Number=Sing	14	attr	_	_
18	from	from	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	Cauchy	Cauchy	PROPN	NNP	Number=Sing	21	compound	_	_
21	completion	completion	NOUN	NN	Number=Sing	22	compound	_	_
22	monad	monad	NOUN	NNS	Number=Plur	18	pobj	_	_
23	over	over	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	symmetrisation	symmetrisation	NOUN	NN	Number=Sing	26	compound	_	_
26	comonad	comonad	NOUN	NNS	Number=Plur	23	pobj	_	_
27	on	on	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	category	category	NOUN	NN	Number=Sing	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	$ Q $	$ q $	SYM	$	_	33	advmod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	34	amod	_	_
34	categories	category	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = For such quantaloids, which we call Cauchy - bilateral quantaloids, it follows that the Cauchy completion of any symmetric $ Q $ - enriched category is again symmetric.
1	For	for	ADP	IN	_	14	prep	_	_
2	such	such	ADJ	JJ	Degree=Pos	3	amod	_	_
3	quantaloids	quantaloid	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	which	which	PRON	WDT	_	7	dobj	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	3	relcl	_	_
8	Cauchy	Cauchy	PROPN	NNP	Number=Sing	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	bilateral	bilateral	ADJ	JJ	Degree=Pos	11	amod	_	_
11	quantaloids	quantaloid	NOUN	NNS	Number=Plur	7	oprd	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
13	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	14	nsubj	_	_
14	follows	follow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	that	that	SCONJ	IN	_	26	mark	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	Cauchy	Cauchy	PROPN	NNP	Number=Sing	18	compound	_	_
18	completion	completion	NOUN	NN	Number=Sing	26	nsubj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	any	any	DET	DT	_	25	det	_	_
21	symmetric	symmetric	ADJ	JJ	Degree=Pos	25	amod	_	_
22	$ Q $	$ q $	SYM	$	_	24	advmod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	amod	_	_
25	category	category	NOUN	NN	Number=Sing	19	pobj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	ccomp	_	_
27	again	again	ADV	RB	_	28	advmod	_	_
28	symmetric	symmetric	ADJ	JJ	Degree=Pos	26	acomp	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 3
# text = Examples include Lawvere's quantale of non - negative real numbers and Walters' small quantaloids of closed cribles.
1	Examples	example	NOUN	NNS	Number=Plur	2	nsubj	_	_
2	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	Lawvere	Lawvere	PROPN	NNP	Number=Sing	5	poss	_	SpaceAfter=No
4	's	's	PART	POS	_	3	case	_	_
5	quantale	quantale	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	non	non	ADJ	JJ	Degree=Pos	9	amod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	negative	negative	ADJ	JJ	Degree=Pos	11	amod	_	_
10	real	real	ADJ	JJ	Degree=Pos	11	amod	_	_
11	numbers	number	NOUN	NNS	Number=Plur	6	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	Walters	Walters	PROPN	NNP	Number=Sing	16	poss	_	SpaceAfter=No
14	'	'	PART	POS	_	13	case	_	_
15	small	small	ADJ	JJ	Degree=Pos	16	amod	_	_
16	quantaloids	quantaloid	NOUN	NNS	Number=Plur	5	conj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	closed	closed	ADJ	JJ	Degree=Pos	19	amod	_	_
19	cribles	crible	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 389
# sent_id = 1
# text = Various concerns suggest looking for internal co - categories in categories with strong logical structure.
1	Various	various	ADJ	JJ	Degree=Pos	2	amod	_	_
2	concerns	concern	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	suggest	suggest	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	looking	look	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	xcomp	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	internal	internal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	co	co	NOUN	NNS	Number=Plur	5	pobj	_	_
8	-	-	NOUN	NNS	Number=Plur	5	pobj	_	_
9	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
12	with	with	ADP	IN	_	11	prep	_	_
13	strong	strong	ADJ	JJ	Degree=Pos	15	amod	_	_
14	logical	logical	ADJ	JJ	Degree=Pos	15	amod	_	_
15	structure	structure	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = It turns out that in any coherent category $ E $ , all co - categories are co - equivalence relations.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	turns	turn	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	out	out	ADP	RP	_	2	prt	_	_
4	that	that	SCONJ	IN	_	15	mark	_	_
5	in	in	ADP	IN	_	15	prep	_	_
6	any	any	DET	DT	_	8	det	_	_
7	coherent	coherent	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
9	$ E $	$ e $	SYM	$	_	8	nummod	_	_
10	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
11	all	all	DET	DT	_	12	det	_	_
12	co	co	NOUN	NN	Number=Sing	15	nsubj	_	_
13	-	-	NOUN	NNS	Number=Plur	15	punct	_	_
14	categories	category	NOUN	NNS	Number=Plur	15	nsubj	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
16	co	co	ADJ	JJ	Degree=Pos	19	amod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	19	amod	_	_
18	equivalence	equivalence	NOUN	NN	Number=Sing	19	compound	_	_
19	relations	relation	NOUN	NNS	Number=Plur	15	attr	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 390
# sent_id = 1
# text = This paper constructs model structures on the categories of coalgebras and pointed irreducible coalgebras over an operad whose components are projective, finitely generated in each dimension, and satisfy a condition that allows one to take tensor products with a unit interval.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	constructs	construct	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	model	model	NOUN	NN	Number=Sing	5	compound	_	_
5	structures	structure	NOUN	NNS	Number=Plur	3	dobj	_	_
6	on	on	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	coalgebras	coalgebra	NOUN	NNS	Number=Plur	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
12	pointed	point	VERB	VBD	Tense=Past|VerbForm=Fin	3	conj	_	_
13	irreducible	irreducible	ADJ	JJ	Degree=Pos	14	amod	_	_
14	coalgebras	coalgebra	NOUN	NNS	Number=Plur	12	dobj	_	_
15	over	over	ADP	IN	_	12	prep	_	_
16	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	operad	operad	NOUN	NN	Number=Sing	15	pobj	_	_
18	whose	whose	DET	WP$	Poss=Yes	19	poss	_	_
19	components	component	NOUN	NNS	Number=Plur	20	nsubj	_	_
20	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	17	relcl	_	_
21	projective	projective	ADJ	JJ	Degree=Pos	20	acomp	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
23	finitely	finitely	ADV	RB	_	24	advmod	_	_
24	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
25	in	in	ADP	IN	_	24	prep	_	_
26	each	each	DET	DT	_	27	det	_	_
27	dimension	dimension	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
30	satisfy	satisfy	VERB	VB	VerbForm=Inf	24	conj	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
32	condition	condition	NOUN	NN	Number=Sing	30	dobj	_	_
33	that	that	PRON	WDT	PronType=Rel	34	nsubj	_	_
34	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	32	relcl	_	_
35	one	one	PRON	PRP	PronType=Prs	37	nsubj	_	_
36	to	to	PART	TO	_	37	aux	_	_
37	take	take	VERB	VB	VerbForm=Inf	34	ccomp	_	_
38	tensor	tensor	NOUN	NN	Number=Sing	39	compound	_	_
39	products	product	NOUN	NNS	Number=Plur	37	dobj	_	_
40	with	with	ADP	IN	_	37	prep	_	_
41	a	a	DET	DT	Definite=Ind|PronType=Art	43	det	_	_
42	unit	unit	NOUN	NN	Number=Sing	43	compound	_	_
43	interval	interval	NOUN	NN	Number=Sing	40	pobj	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = The underlying chain - complex is assumed to be unbounded and the results for bounded coalgebras over an operad are derived from the unbounded case.
1	The	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
2	underlying	underlie	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	amod	_	_
3	chain	chain	NOUN	NN	Number=Sing	5	compound	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	complex	complex	ADJ	JJ	Degree=Pos	7	nsubjpass	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	assumed	assume	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	be	be	AUX	VB	VerbForm=Inf	7	xcomp	_	_
10	unbounded	unbounded	ADJ	JJ	Degree=Pos	9	acomp	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	results	result	NOUN	NNS	Number=Plur	21	nsubjpass	_	_
14	for	for	ADP	IN	_	13	prep	_	_
15	bounded	bound	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
16	coalgebras	coalgebra	NOUN	NNS	Number=Plur	14	pobj	_	_
17	over	over	ADP	IN	_	13	prep	_	_
18	an	an	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	operad	operad	NOUN	NN	Number=Sing	17	pobj	_	_
20	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	21	auxpass	_	_
21	derived	derive	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	conj	_	_
22	from	from	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	unbounded	unbounded	ADJ	JJ	Degree=Pos	25	amod	_	_
25	case	case	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# doc_id = 391
# sent_id = 1
# text = We define Lie 3 - algebras and prove that these are in one - to - one correspondence with the 3 - term Lie infinity algebras whose bilinear and trilinear maps vanish in degree $ (1, 1) $ and in total degree 1, respectively.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	Lie	lie	NOUN	NN	Number=Sing	2	dobj	_	_
4	3	3	NUM	CD	NumType=Card	6	nummod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	algebras	algebra	NOUN	NNS	Number=Plur	2	dobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
8	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
9	that	that	SCONJ	IN	_	11	mark	_	_
10	these	these	PRON	DT	Number=Plur|PronType=Dem	11	nsubj	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	ccomp	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	one	one	NUM	CD	NumType=Card	18	nummod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
15	to	to	ADP	IN	_	13	prep	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
17	one	one	NUM	CD	NumType=Card	15	pobj	_	_
18	correspondence	correspondence	NOUN	NN	Number=Sing	12	pobj	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
21	3	3	NUM	CD	NumType=Card	23	nummod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	term	term	NOUN	NN	Number=Sing	25	compound	_	_
24	Lie	lie	NOUN	NN	Number=Sing	25	compound	_	_
25	infinity	infinity	NOUN	NN	Number=Sing	26	compound	_	_
26	algebras	algebra	NOUN	NNS	Number=Plur	19	pobj	_	_
27	whose	whose	DET	WP$	Poss=Yes	31	poss	_	_
28	bilinear	bilinear	NOUN	NN	Number=Sing	31	nmod	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	trilinear	trilinear	NOUN	NN	Number=Sing	28	conj	_	_
31	maps	map	NOUN	NNS	Number=Plur	32	nsubj	_	_
32	vanish	vanish	VERB	VBP	Tense=Pres|VerbForm=Fin	8	ccomp	_	_
33	in	in	ADP	IN	_	32	prep	_	_
34	degree	degree	NOUN	NN	Number=Sing	33	pobj	_	_
35	$ (1, 1) $	$ (1, 1) $	NUM	CD	NumType=Card	32	dobj	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
37	in	in	ADP	IN	_	35	conj	_	_
38	total	total	ADJ	JJ	Degree=Pos	39	amod	_	_
39	degree	degree	NOUN	NN	Number=Sing	37	pobj	_	_
40	1	1	NUM	CD	NumType=Card	39	nummod	_	SpaceAfter=No
41	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
42	respectively	respectively	ADV	RB	_	32	advmod	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Further, we give an answer to a question of Roytenberg pertaining to the use of the nerve and normalization functors in the study of the relationship between categorified algebras and truncated $ sh $ algebras.
1	Further	far	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	answer	answer	NOUN	NN	Number=Sing	4	dobj	_	_
7	to	to	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	question	question	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	Roytenberg	Roytenberg	PROPN	NNP	Number=Sing	10	pobj	_	_
12	pertaining	pertain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	acl	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	use	use	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
18	nerve	nerve	NOUN	NN	Number=Sing	21	nmod	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	normalization	normalization	NOUN	NN	Number=Sing	18	conj	_	_
21	functors	functor	NOUN	NNS	Number=Plur	16	pobj	_	_
22	in	in	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	study	study	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	relationship	relationship	NOUN	NN	Number=Sing	25	pobj	_	_
28	between	between	ADP	IN	_	27	prep	_	_
29	categorified	categorified	ADJ	JJ	Degree=Pos	30	amod	_	_
30	algebras	algebra	NOUN	NNS	Number=Plur	28	pobj	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
32	truncated	truncate	VERB	VBD	Tense=Past|VerbForm=Fin	4	conj	_	_
33	$ sh $	$ sh $	SYM	$	_	34	nmod	_	_
34	algebras	algebra	NOUN	NNS	Number=Plur	32	dobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 392
# sent_id = 1
# text = Adhesive categories are categories which have pushouts with one leg a monomorphism, all pullbacks, and certain exactness conditions relating these pushouts and pullbacks.
1	Adhesive	adhesive	ADJ	JJ	Degree=Pos	2	amod	_	_
2	categories	category	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	categories	category	NOUN	NNS	Number=Plur	3	attr	_	_
5	which	which	PRON	WDT	_	6	nsubj	_	_
6	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	relcl	_	_
7	pushouts	pushout	NOUN	NNS	Number=Plur	6	dobj	_	_
8	with	with	ADP	IN	_	7	prep	_	_
9	one	one	NUM	CD	NumType=Card	10	nummod	_	_
10	leg	leg	NOUN	NN	Number=Sing	8	pobj	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	monomorphism	monomorphism	NOUN	NN	Number=Sing	6	dobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
14	all	all	DET	DT	_	15	det	_	_
15	pullbacks	pullback	NOUN	NNS	Number=Plur	4	conj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
18	certain	certain	ADJ	JJ	Degree=Pos	20	amod	_	_
19	exactness	exactness	ADJ	JJ	Degree=Pos	20	amod	_	_
20	conditions	condition	NOUN	NNS	Number=Plur	15	conj	_	_
21	relating	relate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	acl	_	_
22	these	these	DET	DT	Number=Plur|PronType=Dem	23	det	_	_
23	pushouts	pushout	NOUN	NNS	Number=Plur	21	dobj	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	pullbacks	pullback	NOUN	NNS	Number=Plur	23	conj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = We give a new proof of the fact that every topos is adhesive.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	new	new	ADJ	JJ	Degree=Pos	5	amod	_	_
5	proof	proof	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	fact	fact	NOUN	NN	Number=Sing	6	pobj	_	_
9	that	that	SCONJ	IN	_	13	mark	_	_
10	every	every	DET	DT	_	11	det	_	_
11	topos	topos	NOUN	NN	Number=Sing	13	nsubjpass	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	adhesive	adhesive	ADJ	JJ	Degree=Pos	8	acl	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also prove a converse: every small adhesive category has a fully faithful functor in a topos, with the functor preserving the all the structure.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	11	ccomp	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	converse	converse	NOUN	NN	Number=Sing	3	dobj	_	SpaceAfter=No
6	:	:	PUNCT	:	_	11	punct	_	_
7	every	every	DET	DT	_	10	det	_	_
8	small	small	ADJ	JJ	Degree=Pos	10	amod	_	_
9	adhesive	adhesive	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	11	nsubj	_	_
11	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	fully	fully	ADV	RB	_	14	advmod	_	_
14	faithful	faithful	ADJ	JJ	Degree=Pos	15	amod	_	_
15	functor	functor	NOUN	NN	Number=Sing	11	dobj	_	_
16	in	in	ADP	IN	_	11	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	topos	topos	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
20	with	with	ADP	IN	_	11	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	functor	functor	NOUN	NN	Number=Sing	23	nsubj	_	_
23	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	pcomp	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
25	all	all	DET	PDT	_	27	predet	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	structure	structure	NOUN	NN	Number=Sing	23	dobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 4
# text = Combining these two results, we see that the exactness conditions in the definition of adhesive category are exactly the relationship between pushouts along monomorphisms and pullbacks which hold in any topos.
1	Combining	combine	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	advcl	_	_
2	these	these	DET	DT	Number=Plur|PronType=Dem	4	det	_	_
3	two	two	NUM	CD	NumType=Card	4	nummod	_	_
4	results	result	NOUN	NNS	Number=Plur	1	dobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	see	see	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	that	that	SCONJ	IN	_	18	mark	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	exactness	exactness	ADJ	JJ	Degree=Pos	11	amod	_	_
11	conditions	condition	NOUN	NNS	Number=Plur	18	nsubj	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	definition	definition	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	adhesive	adhesive	ADJ	JJ	Degree=Pos	17	amod	_	_
17	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	ccomp	_	_
19	exactly	exactly	ADV	RB	_	18	advmod	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	relationship	relationship	NOUN	NN	Number=Sing	18	attr	_	_
22	between	between	ADP	IN	_	21	prep	_	_
23	pushouts	pushout	NOUN	NNS	Number=Plur	22	pobj	_	_
24	along	along	ADP	IN	_	23	prep	_	_
25	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	24	pobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	pullbacks	pullback	NOUN	NNS	Number=Plur	25	conj	_	_
28	which	which	PRON	WDT	_	29	nsubj	_	_
29	hold	hold	VERB	VBP	Tense=Pres|VerbForm=Fin	25	relcl	_	_
30	in	in	ADP	IN	_	29	prep	_	_
31	any	any	DET	DT	_	32	det	_	_
32	topos	topos	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 393
# sent_id = 1
# text = We explore a curious type of equivalence between certain pairs of reflective and coreflective subcategories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	explore	explore	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	curious	curious	ADJ	JJ	Degree=Pos	5	amod	_	_
5	type	type	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	equivalence	equivalence	NOUN	NN	Number=Sing	6	pobj	_	_
8	between	between	ADP	IN	_	5	prep	_	_
9	certain	certain	ADJ	JJ	Degree=Pos	10	amod	_	_
10	pairs	pair	NOUN	NNS	Number=Plur	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	reflective	reflective	ADJ	JJ	Degree=Pos	15	amod	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	coreflective	coreflective	ADJ	JJ	Degree=Pos	12	conj	_	_
15	subcategories	subcategorie	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We illustrate with examples involving noncommutative duality for $ C^* $ - dynamical systems and compact quantum groups, as well as examples where the subcategories are actually isomorphic.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	illustrate	illustrate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	with	with	ADP	IN	_	2	prep	_	_
4	examples	example	NOUN	NNS	Number=Plur	3	pobj	_	_
5	involving	involve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	acl	_	_
6	noncommutative	noncommutative	ADJ	JJ	Degree=Pos	7	amod	_	_
7	duality	duality	NOUN	NN	Number=Sing	5	dobj	_	_
8	for	for	ADP	IN	_	5	prep	_	_
9	$ C^* $	$ c^* $	SYM	$	_	11	advmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	dynamical	dynamical	ADJ	JJ	Degree=Pos	12	amod	_	_
12	systems	system	NOUN	NNS	Number=Plur	8	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	compact	compact	ADJ	JJ	Degree=Pos	15	amod	_	_
15	quantum	quantum	NOUN	NN	Number=Sing	16	compound	_	_
16	groups	group	NOUN	NNS	Number=Plur	12	conj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	as	as	ADV	RB	_	20	advmod	_	_
19	well	well	ADV	RB	Degree=Pos	20	advmod	_	_
20	as	as	ADP	IN	_	16	cc	_	_
21	examples	example	NOUN	NNS	Number=Plur	16	conj	_	_
22	where	where	SCONJ	WRB	_	25	advmod	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	subcategories	subcategorie	NOUN	NNS	Number=Plur	25	nsubj	_	_
25	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	21	relcl	_	_
26	actually	actually	ADV	RB	_	25	advmod	_	_
27	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	25	acomp	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 394
# sent_id = 1
# text = This article represents a preliminary attempt to link Kan extensions, and some of their further developments, to Fourier theory and quantum algebra through $ * $ - autonomous monoidal categories and related structures.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	article	article	NOUN	NN	Number=Sing	3	nsubj	_	_
3	represents	represent	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	preliminary	preliminary	ADJ	JJ	Degree=Pos	6	amod	_	_
6	attempt	attempt	NOUN	NN	Number=Sing	3	dobj	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	link	link	VERB	VB	VerbForm=Inf	6	acl	_	_
9	Kan	Kan	PROPN	NNP	Number=Sing	10	compound	_	_
10	extensions	extension	NOUN	NNS	Number=Plur	8	dobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
13	some	some	PRON	DT	_	3	conj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	17	poss	_	_
16	further	further	ADJ	JJ	Degree=Pos	17	amod	_	_
17	developments	development	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
19	to	to	ADP	IN	_	13	prep	_	_
20	Fourier	fourier	ADJ	JJ	Degree=Pos	21	amod	_	_
21	theory	theory	NOUN	NN	Number=Sing	19	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	quantum	quantum	ADJ	JJ	Degree=Pos	24	compound	_	_
24	algebra	algebra	NOUN	NN	Number=Sing	21	conj	_	_
25	through	through	ADP	IN	_	21	prep	_	_
26	$ * $	$ * $	SYM	$	_	28	advmod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	autonomous	autonomous	ADJ	JJ	Degree=Pos	30	amod	_	_
29	monoidal	monoidal	ADJ	JJ	Degree=Pos	30	amod	_	_
30	categories	category	NOUN	NNS	Number=Plur	25	pobj	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
32	related	related	ADJ	JJ	Degree=Pos	33	amod	_	_
33	structures	structure	NOUN	NNS	Number=Plur	30	conj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = There is a close resemblance to convolution products and the Wiener algebra (of transforms) in functional analysis.
1	There	there	PRON	EX	_	2	expl	_	_
2	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	close	close	ADJ	JJ	Degree=Pos	5	amod	_	_
5	resemblance	resemblance	NOUN	NN	Number=Sing	2	attr	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	convolution	convolution	NOUN	NN	Number=Sing	8	compound	_	_
8	products	product	NOUN	NNS	Number=Plur	6	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	Wiener	Wiener	PROPN	NNP	Number=Sing	12	compound	_	_
12	algebra	algebra	NOUN	NN	Number=Sing	8	conj	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
14	of	of	ADP	IN	_	12	prep	_	_
15	transforms	transform	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
16	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	12	punct	_	_
17	in	in	ADP	IN	_	5	prep	_	_
18	functional	functional	ADJ	JJ	Degree=Pos	19	amod	_	_
19	analysis	analysis	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The analysis term ``kernel'' (of a distribution) has also been adapted below in connection with certain special types of ``distributors'' (in the terminology of Benabou) or ``modules'' (in the terminology of Street) in category theory.
1	The	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
2	analysis	analysis	NOUN	NN	Number=Sing	3	compound	_	_
3	term	term	NOUN	NN	Number=Sing	6	nmod	_	_
4	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	6	punct	_	SpaceAfter=No
5	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	6	punct	_	SpaceAfter=No
6	kernel	kernel	PROPN	NNP	Number=Sing	16	nsubjpass	_	SpaceAfter=No
7	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	6	punct	_	_
8	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	6	punct	_	SpaceAfter=No
9	of	of	ADP	IN	_	6	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	distribution	distribution	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	6	punct	_	_
13	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	aux	_	_
14	also	also	ADV	RB	_	16	advmod	_	_
15	been	be	AUX	VBN	Tense=Past|VerbForm=Part	16	auxpass	_	_
16	adapted	adapt	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
17	below	below	ADV	RB	_	16	advmod	_	_
18	in	in	ADP	IN	_	16	prep	_	_
19	connection	connection	NOUN	NN	Number=Sing	18	pobj	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	certain	certain	ADJ	JJ	Degree=Pos	23	amod	_	_
22	special	special	ADJ	JJ	Degree=Pos	23	amod	_	_
23	types	type	NOUN	NNS	Number=Plur	20	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	27	punct	_	SpaceAfter=No
26	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	27	punct	_	SpaceAfter=No
27	distributors	distributor	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
28	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	27	punct	_	_
29	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
30	in	in	ADP	IN	_	19	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	terminology	terminology	NOUN	NN	Number=Sing	30	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	Benabou	Benabou	PROPN	NNP	Number=Sing	33	pobj	_	SpaceAfter=No
35	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	30	punct	_	_
36	or	or	CCONJ	CC	ConjType=Cmp	19	cc	_	_
37	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	39	punct	_	SpaceAfter=No
38	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	39	punct	_	SpaceAfter=No
39	modules	module	NOUN	NNS	Number=Plur	19	conj	_	SpaceAfter=No
40	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	39	punct	_	_
41	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	39	punct	_	SpaceAfter=No
42	in	in	ADP	IN	_	39	prep	_	_
43	the	the	DET	DT	Definite=Def|PronType=Art	44	det	_	_
44	terminology	terminology	NOUN	NN	Number=Sing	42	pobj	_	_
45	of	of	ADP	IN	_	44	prep	_	_
46	Street	Street	PROPN	NNP	Number=Sing	45	pobj	_	SpaceAfter=No
47	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	39	punct	_	_
48	in	in	ADP	IN	_	39	prep	_	_
49	category	category	NOUN	NN	Number=Sing	50	compound	_	_
50	theory	theory	NOUN	NN	Number=Sing	48	pobj	_	SpaceAfter=No
51	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 4
# text = In using the term ``graphic'', in a very broad sense, we are clearly distinguishing the categorical methods employed in this article from standard Fourier and wavelet mathematics.
1	In	in	ADP	IN	_	19	prep	_	_
2	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	1	pcomp	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	term	term	NOUN	NN	Number=Sing	7	nmod	_	_
5	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	7	punct	_	SpaceAfter=No
6	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	7	punct	_	SpaceAfter=No
7	graphic	graphic	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
8	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	7	punct	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
10	in	in	ADP	IN	_	19	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
12	very	very	ADV	RB	_	13	advmod	_	_
13	broad	broad	ADJ	JJ	Degree=Pos	14	amod	_	_
14	sense	sense	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
16	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
17	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	19	aux	_	_
18	clearly	clearly	ADV	RB	_	19	advmod	_	_
19	distinguishing	distinguish	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	0	ROOT	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	categorical	categorical	ADJ	JJ	Degree=Pos	22	amod	_	_
22	methods	method	NOUN	NNS	Number=Plur	19	dobj	_	_
23	employed	employ	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	acl	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	this	this	DET	DT	Number=Sing|PronType=Dem	26	det	_	_
26	article	article	NOUN	NN	Number=Sing	24	pobj	_	_
27	from	from	ADP	IN	_	23	prep	_	_
28	standard	standard	ADJ	JJ	Degree=Pos	32	amod	_	_
29	Fourier	Fourier	PROPN	NNP	Number=Sing	32	nmod	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
31	wavelet	wavelet	ADJ	JJ	Degree=Pos	29	conj	_	_
32	mathematics	mathematic	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 5
# text = The term ``graphic'' also applies to promultiplicative graphs, and related concepts, which can feature prominently in the theory.
1	The	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
2	term	term	NOUN	NN	Number=Sing	5	nmod	_	_
3	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	5	punct	_	SpaceAfter=No
4	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	5	punct	_	SpaceAfter=No
5	graphic	graphic	NOUN	NN	Number=Sing	8	nsubj	_	SpaceAfter=No
6	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	5	punct	_	_
7	also	also	ADV	RB	_	8	advmod	_	_
8	applies	apply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	promultiplicative	promultiplicative	ADJ	JJ	Degree=Pos	11	amod	_	_
11	graphs	graph	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
14	related	related	ADJ	JJ	Degree=Pos	15	amod	_	_
15	concepts	concept	NOUN	NNS	Number=Plur	11	conj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	which	which	PRON	WDT	_	19	nsubj	_	_
18	can	can	AUX	MD	VerbForm=Fin	19	aux	_	_
19	feature	feature	VERB	VB	VerbForm=Inf	15	relcl	_	_
20	prominently	prominently	ADV	RB	_	19	advmod	_	_
21	in	in	ADP	IN	_	19	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	theory	theory	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 395
# sent_id = 1
# text = We compare various different definitions of "the category of smooth objects".
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	compare	compare	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	various	various	ADJ	JJ	Degree=Pos	5	amod	_	_
4	different	different	ADJ	JJ	Degree=Pos	5	amod	_	_
5	definitions	definition	NOUN	NNS	Number=Plur	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	6	punct	_	SpaceAfter=No
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	smooth	smooth	ADJ	JJ	Degree=Pos	12	amod	_	_
12	objects	object	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	2	punct	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The definitions compared are due to Chen, Frolicher, Sikorski, Smith, and Souriau.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	definitions	definition	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	compared	compare	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	pobj	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	due	due	ADJ	JJ	Degree=Pos	4	acomp	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	Chen	Chen	PROPN	NNP	Number=Sing	6	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	Frolicher	Frolicher	PROPN	NNP	Number=Sing	7	conj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	Sikorski	Sikorski	PROPN	NNP	Number=Sing	9	conj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	Smith	Smith	PROPN	NNP	Number=Sing	11	conj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
16	Souriau	Souriau	PROPN	NNP	Number=Sing	13	conj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = The method of comparison is to construct functors between the categories that enable us to see how the categories relate to each other.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	method	method	NOUN	NN	Number=Sing	5	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	comparison	comparison	NOUN	NN	Number=Sing	3	pobj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	construct	construct	VERB	VB	VerbForm=Inf	5	xcomp	_	_
8	functors	functor	NOUN	NNS	Number=Plur	7	dobj	_	_
9	between	between	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	_
12	that	that	PRON	WDT	PronType=Rel	13	nsubj	_	_
13	enable	enable	VERB	VBP	Tense=Pres|VerbForm=Fin	11	relcl	_	_
14	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	13	dobj	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	see	see	VERB	VB	VerbForm=Inf	13	xcomp	_	_
17	how	how	SCONJ	WRB	_	20	advmod	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	categories	category	NOUN	NNS	Number=Plur	20	nsubj	_	_
20	relate	relate	VERB	VBP	Tense=Pres|VerbForm=Fin	16	ccomp	_	_
21	to	to	ADP	IN	_	20	prep	_	_
22	each	each	DET	DT	_	23	det	_	_
23	other	other	ADJ	JJ	Degree=Pos	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = Our method of study involves finding a general context into which these categories can be placed.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	method	method	NOUN	NN	Number=Sing	5	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	study	study	NOUN	NN	Number=Sing	3	pobj	_	_
5	involves	involve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	finding	find	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	xcomp	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	general	general	ADJ	JJ	Degree=Pos	9	amod	_	_
9	context	context	NOUN	NN	Number=Sing	6	dobj	_	_
10	into	into	ADP	IN	_	16	prep	_	_
11	which	which	PRON	WDT	_	10	pobj	_	_
12	these	these	DET	DT	Number=Plur|PronType=Dem	13	det	_	_
13	categories	category	NOUN	NNS	Number=Plur	16	nsubjpass	_	_
14	can	can	AUX	MD	VerbForm=Fin	16	aux	_	_
15	be	be	AUX	VB	VerbForm=Inf	16	auxpass	_	_
16	placed	place	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	relcl	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = This involves considering categories wherein objects are considered in relation to a certain collection of standard test objects.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	involves	involve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	considering	consider	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	xcomp	_	_
4	categories	category	NOUN	NNS	Number=Plur	3	dobj	_	_
5	wherein	wherein	SCONJ	WRB	_	6	amod	_	_
6	objects	object	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	relcl	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	relation	relation	NOUN	NN	Number=Sing	9	pobj	_	_
11	to	to	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	certain	certain	ADJ	JJ	Degree=Pos	14	amod	_	_
14	collection	collection	NOUN	NN	Number=Sing	11	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	standard	standard	ADJ	JJ	Degree=Pos	18	amod	_	_
17	test	test	NOUN	NN	Number=Sing	18	compound	_	_
18	objects	object	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = This therefore applies beyond the question of categories of smooth spaces.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	3	nsubj	_	_
2	therefore	therefore	ADV	RB	_	3	advmod	_	_
3	applies	apply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	beyond	beyond	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	question	question	NOUN	NN	Number=Sing	4	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	smooth	smooth	ADJ	JJ	Degree=Pos	11	amod	_	_
11	spaces	space	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 396
# sent_id = 1
# text = We study the condition, on a connected and locally connected geometric morphism $ p : cal E to cal S $ , that the canonical natural transformation $ p_*to p_clik $ should be (pointwise) epimorphic—a condition which Lawvere called the `Nullstellensatz', but which we prefer to call `punctual local connectedness'.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	condition	condition	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
6	on	on	ADP	IN	_	2	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
8	connected	connected	ADJ	JJ	Degree=Pos	13	amod	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	locally	locally	ADV	RB	_	11	advmod	_	_
11	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	conj	_	_
12	geometric	geometric	ADJ	JJ	Degree=Pos	13	amod	_	_
13	morphism	morphism	NOUN	NN	Number=Sing	6	pobj	_	_
14	$ p : cal E to cal S $	$ p : cal e to cal s $	SYM	$	_	13	appos	_	_
15	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
16	that	that	SCONJ	IN	_	23	mark	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
18	canonical	canonical	ADJ	JJ	Degree=Pos	20	amod	_	_
19	natural	natural	ADJ	JJ	Degree=Pos	20	amod	_	_
20	transformation	transformation	NOUN	NN	Number=Sing	23	nsubj	_	_
21	$ p_*to p_clik $	$ p_*to p_clik $	SYM	$	_	20	appos	_	_
22	should	should	AUX	MD	VerbForm=Fin	23	aux	_	_
23	be	be	AUX	VB	VerbForm=Inf	2	ccomp	_	_
24	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	27	punct	_	SpaceAfter=No
25	pointwise	pointwise	NOUN	NN	Number=Sing	27	nmod	_	SpaceAfter=No
26	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	27	punct	_	_
27	epimorphic	epimorphic	NOUN	NN	Number=Sing	23	attr	_	SpaceAfter=No
28	—	—	PUNCT	:	_	27	punct	_	SpaceAfter=No
29	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
30	condition	condition	NOUN	NN	Number=Sing	27	appos	_	_
31	which	which	PRON	WDT	_	33	nsubjpass	_	_
32	Lawvere	lawvere	AUX	NNP	Number=Sing	33	auxpass	_	_
33	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	30	relcl	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
35	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	36	punct	_	SpaceAfter=No
36	Nullstellensatz	Nullstellensatz	PROPN	NNP	Number=Sing	33	oprd	_	SpaceAfter=No
37	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	33	oprd	_	SpaceAfter=No
38	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
39	but	but	CCONJ	CC	ConjType=Cmp	23	cc	_	_
40	which	which	PRON	WDT	_	44	dobj	_	_
41	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	42	nsubj	_	_
42	prefer	prefer	VERB	VBP	Tense=Pres|VerbForm=Fin	23	conj	_	_
43	to	to	PART	TO	_	44	aux	_	_
44	call	call	VERB	VB	VerbForm=Inf	42	xcomp	_	_
45	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	48	punct	_	SpaceAfter=No
46	punctual	punctual	ADJ	JJ	Degree=Pos	48	amod	_	_
47	local	local	ADJ	JJ	Degree=Pos	48	amod	_	_
48	connectedness	connectedness	NOUN	NN	Number=Sing	44	oprd	_	SpaceAfter=No
49	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	2	punct	_	SpaceAfter=No
50	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that this condition implies that $ p_clik $ preserves finite products, and that, for bounded morphisms between toposes with natural number objects, it is equivalent to being both local and hyperconnected.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	6	mark	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	condition	condition	NOUN	NN	Number=Sing	6	nsubj	_	_
6	implies	imply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
7	that	that	SCONJ	IN	_	9	mark	_	_
8	$ p_clik $	$ p_clik $	X	ADD	_	9	nsubj	_	_
9	preserves	preserve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
10	finite	finite	ADJ	JJ	Degree=Pos	11	compound	_	_
11	products	product	NOUN	NNS	Number=Plur	9	dobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
14	that	that	SCONJ	IN	_	27	mark	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
16	for	for	ADP	IN	_	27	prep	_	_
17	bounded	bound	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
18	morphisms	morphism	NOUN	NNS	Number=Plur	16	pobj	_	_
19	between	between	ADP	IN	_	18	prep	_	_
20	toposes	topos	NOUN	NNS	Number=Plur	19	pobj	_	_
21	with	with	ADP	IN	_	20	prep	_	_
22	natural	natural	ADJ	JJ	Degree=Pos	23	amod	_	_
23	number	number	NOUN	NN	Number=Sing	24	compound	_	_
24	objects	object	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
26	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	27	nsubj	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	conj	_	_
28	equivalent	equivalent	ADJ	JJ	Degree=Pos	27	acomp	_	_
29	to	to	ADP	IN	_	28	prep	_	_
30	being	be	AUX	VBG	VerbForm=Ger	29	pcomp	_	_
31	both	both	CCONJ	CC	ConjType=Cmp	32	preconj	_	_
32	local	local	ADJ	JJ	Degree=Pos	30	acomp	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
34	hyperconnected	hyperconnecte	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	conj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 397
# sent_id = 1
# text = We consider commutative Frobenius algebras in braided strict monoidal categories in the study of the circuits and communicating systems which occur in Computer Science, including circuits in which the wires are tangled.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	commutative	commutative	ADJ	JJ	Degree=Pos	2	ccomp	_	_
4	Frobenius	Frobenius	PROPN	NNP	Number=Sing	5	compound	_	_
5	algebras	algebra	NOUN	NNS	Number=Plur	3	dobj	_	_
6	in	in	ADP	IN	_	3	prep	_	_
7	braided	braid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
8	strict	strict	ADJ	JJ	Degree=Pos	10	amod	_	_
9	monoidal	monoidal	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	study	study	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	circuits	circuit	NOUN	NNS	Number=Plur	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	communicating	communicating	NOUN	NN	Number=Sing	19	compound	_	_
19	systems	system	NOUN	NNS	Number=Plur	16	conj	_	_
20	which	which	PRON	WDT	_	21	nsubj	_	_
21	occur	occur	VERB	VBP	Tense=Pres|VerbForm=Fin	16	relcl	_	_
22	in	in	ADP	IN	_	21	prep	_	_
23	Computer	Computer	PROPN	NNP	Number=Sing	24	compound	_	_
24	Science	Science	PROPN	NNP	Number=Sing	22	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	24	prep	_	_
27	circuits	circuit	NOUN	NNS	Number=Plur	26	pobj	_	_
28	in	in	ADP	IN	_	33	prep	_	_
29	which	which	PRON	WDT	_	28	pobj	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	wires	wire	NOUN	NNS	Number=Plur	33	nsubjpass	_	_
32	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	33	auxpass	_	_
33	tangled	tangle	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	relcl	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We indicate also some possible novel geometric interest in such algebras.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	indicate	indicate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	also	also	ADV	RB	_	2	advmod	_	_
4	some	some	DET	DT	_	8	det	_	_
5	possible	possible	ADJ	JJ	Degree=Pos	8	amod	_	_
6	novel	novel	ADJ	JJ	Degree=Pos	8	amod	_	_
7	geometric	geometric	ADJ	JJ	Degree=Pos	8	amod	_	_
8	interest	interest	NOUN	NN	Number=Sing	2	dobj	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	such	such	ADJ	JJ	Degree=Pos	11	amod	_	_
11	algebras	algebra	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = For example, we show how Armstrong's description of knot colourings and knot groups fit into this context.
1	For	for	ADP	IN	_	5	prep	_	_
2	example	example	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	how	how	SCONJ	WRB	_	9	advmod	_	_
7	Armstrong	Armstrong	PROPN	NNP	Number=Sing	9	poss	_	SpaceAfter=No
8	's	's	PART	POS	_	7	case	_	_
9	description	description	NOUN	NN	Number=Sing	5	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	knot	knot	NOUN	NN	Number=Sing	12	compound	_	_
12	colourings	colouring	NOUN	NNS	Number=Plur	10	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
14	knot	knot	VERB	VB	VerbForm=Inf	5	conj	_	_
15	groups	group	NOUN	NNS	Number=Plur	14	dobj	_	_
16	fit	fit	VERB	VBP	Tense=Pres|VerbForm=Fin	14	oprd	_	_
17	into	into	ADP	IN	_	16	prep	_	_
18	this	this	DET	DT	Number=Sing|PronType=Dem	19	det	_	_
19	context	context	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 398
# sent_id = 1
# text = In this article we review the theory of anafunctors introduced by Makkai and Bartels, and show that given a subcanonical site $ S $ , one can form a bicategorical localisation of various 2 - categories of internal categories or groupoids at weak equivalences using anafunctors as 1 - arrows.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	article	article	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	review	review	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	theory	theory	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	anafunctors	anafunctor	NOUN	NNS	Number=Plur	8	pobj	_	_
10	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	acl	_	_
11	by	by	ADP	IN	_	10	agent	_	_
12	Makkai	Makkai	PROPN	NNP	Number=Sing	11	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	Bartels	Bartels	PROPN	NNP	Number=Sing	12	conj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
17	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	5	conj	_	_
18	that	that	SCONJ	IN	_	27	mark	_	_
19	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	subcanonical	subcanonical	ADJ	JJ	Degree=Pos	22	amod	_	_
22	site	site	NOUN	NN	Number=Sing	19	pobj	_	_
23	$ S $	$ s $	SYM	$	_	22	appos	_	_
24	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
25	one	one	PRON	PRP	PronType=Prs	27	nsubj	_	_
26	can	can	AUX	MD	VerbForm=Fin	27	aux	_	_
27	form	form	VERB	VB	VerbForm=Inf	17	ccomp	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
29	bicategorical	bicategorical	ADJ	JJ	Degree=Pos	30	amod	_	_
30	localisation	localisation	NOUN	NN	Number=Sing	27	dobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	various	various	ADJ	JJ	Degree=Pos	35	amod	_	_
33	2	2	NUM	CD	NumType=Card	35	nummod	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	categories	category	NOUN	NNS	Number=Plur	31	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	internal	internal	ADJ	JJ	Degree=Pos	38	amod	_	_
38	categories	category	NOUN	NNS	Number=Plur	36	pobj	_	_
39	or	or	CCONJ	CC	ConjType=Cmp	38	cc	_	_
40	groupoids	groupoid	NOUN	NNS	Number=Plur	38	conj	_	_
41	at	at	ADP	IN	_	27	prep	_	_
42	weak	weak	ADJ	JJ	Degree=Pos	43	amod	_	_
43	equivalences	equivalence	NOUN	NNS	Number=Plur	41	pobj	_	_
44	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	43	acl	_	_
45	anafunctors	anafunctor	NOUN	NNS	Number=Plur	44	dobj	_	_
46	as	as	ADP	IN	_	44	prep	_	_
47	1	1	NUM	CD	NumType=Card	49	nummod	_	_
48	-	-	PUNCT	HYPH	PunctType=Dash	49	punct	_	_
49	arrows	arrow	NOUN	NNS	Number=Plur	46	pobj	_	SpaceAfter=No
50	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = This unifies a number of proofs throughout the literature, using the fewest assumptions possible on $ S $ .
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	unifies	unify	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	number	number	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	proofs	proof	NOUN	NNS	Number=Plur	5	pobj	_	_
7	throughout	throughout	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	literature	literature	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
11	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	fewest	few	ADJ	JJS	Degree=Sup	14	amod	_	_
14	assumptions	assumption	NOUN	NNS	Number=Plur	11	dobj	_	_
15	possible	possible	ADJ	JJ	Degree=Pos	14	amod	_	_
16	on	on	ADP	IN	_	11	prep	_	_
17	$ S $	$ s $	SYM	$	_	16	pobj	_	_
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 399
# sent_id = 1
# text = We analyze the algebraic structure of the Connes fusion tensor product in the case of bi - finite Hilbert modules over a von Neumann algebra $ M $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	analyze	analyze	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	algebraic	algebraic	ADJ	JJ	Degree=Pos	5	amod	_	_
5	structure	structure	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
8	Connes	Connes	PROPN	NNPS	Number=Plur	9	compound	_	_
9	fusion	fusion	NOUN	NN	Number=Sing	11	compound	_	_
10	tensor	tensor	NOUN	NN	Number=Sing	11	compound	_	_
11	product	product	NOUN	NN	Number=Sing	6	pobj	_	_
12	in	in	ADP	IN	_	2	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	case	case	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	bi	bi	PROPN	NNP	Number=Sing	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	finite	finite	PROPN	NNP	Number=Sing	20	amod	_	_
19	Hilbert	Hilbert	PROPN	NNP	Number=Sing	20	compound	_	_
20	modules	module	NOUN	NNS	Number=Plur	15	pobj	_	_
21	over	over	ADP	IN	_	2	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
23	von	von	PROPN	NNP	Number=Sing	24	compound	_	_
24	Neumann	Neumann	PROPN	NNP	Number=Sing	25	compound	_	_
25	algebra	algebra	PROPN	NNP	Number=Sing	21	pobj	_	_
26	$ M $	$ m $	SYM	$	_	2	dep	_	_
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = It turns out that all complications in its definition disappear if one uses the closely related bi - modules of bounded vectors.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	turns	turn	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	out	out	ADP	RP	_	2	prt	_	_
4	that	that	SCONJ	IN	_	10	mark	_	_
5	all	all	DET	DT	_	6	det	_	_
6	complications	complication	NOUN	NNS	Number=Plur	10	nsubj	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	9	poss	_	_
9	definition	definition	NOUN	NN	Number=Sing	7	pobj	_	_
10	disappear	disappear	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
11	if	if	SCONJ	IN	_	13	mark	_	_
12	one	one	PRON	PRP	PronType=Prs	13	nsubj	_	_
13	uses	use	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	advcl	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
15	closely	closely	ADV	RB	_	16	advmod	_	_
16	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
17	bi	bi	NOUN	NN	Number=Sing	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	modules	module	NOUN	NNS	Number=Plur	13	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	bounded	bound	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	amod	_	_
22	vectors	vector	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We construct an equivalence of monoidal categories with duality between a category of Hilbert bi - modules over $ M $ with Connes fusion tensor product and some natural category of bi - modules over $ M $ with the usual relative algebraic tensor product.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	equivalence	equivalence	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	monoidal	monoidal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
8	with	with	ADP	IN	_	4	prep	_	_
9	duality	duality	NOUN	NN	Number=Sing	8	pobj	_	_
10	between	between	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	Hilbert	Hilbert	PROPN	NNP	Number=Sing	17	compound	_	_
15	bi	bi	PROPN	NNP	Number=Sing	17	compound	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	modules	module	NOUN	NNS	Number=Plur	13	pobj	_	_
18	over	over	ADP	IN	_	17	prep	_	_
19	$ M $	$ m $	SYM	$	_	18	pobj	_	_
20	with	with	ADP	IN	_	17	prep	_	_
21	Connes	Connes	PROPN	NNP	Number=Sing	22	compound	_	_
22	fusion	fusion	NOUN	NN	Number=Sing	24	compound	_	_
23	tensor	tensor	NOUN	NN	Number=Sing	24	compound	_	_
24	product	product	NOUN	NN	Number=Sing	20	pobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	some	some	DET	DT	_	28	det	_	_
27	natural	natural	ADJ	JJ	Degree=Pos	28	amod	_	_
28	category	category	NOUN	NN	Number=Sing	12	conj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	bi	bi	PROPN	NNP	Number=Sing	32	compound	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	modules	module	NOUN	NNS	Number=Plur	29	pobj	_	_
33	over	over	ADP	IN	_	32	prep	_	_
34	$ M $	$ m $	SYM	$	_	33	pobj	_	_
35	with	with	ADP	IN	_	4	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
37	usual	usual	ADJ	JJ	Degree=Pos	41	amod	_	_
38	relative	relative	ADJ	JJ	Degree=Pos	41	amod	_	_
39	algebraic	algebraic	ADJ	JJ	Degree=Pos	41	amod	_	_
40	tensor	tensor	NOUN	NN	Number=Sing	41	compound	_	_
41	product	product	NOUN	NN	Number=Sing	35	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 400
# sent_id = 1
# text = Given a bisimplicial set, there are two ways to extract from it a simplicial set: the diagonal simplicial set and the less well known total simplicial set of Artin and Mazur.
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	bisimplicial	bisimplicial	ADJ	JJ	Degree=Pos	4	amod	_	_
4	set	set	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	there	there	PRON	EX	_	7	expl	_	_
7	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	two	two	NUM	CD	NumType=Card	9	nummod	_	_
9	ways	way	NOUN	NNS	Number=Plur	7	attr	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	extract	extract	VERB	VB	VerbForm=Inf	9	relcl	_	_
12	from	from	ADP	IN	_	11	prep	_	_
13	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	12	pobj	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	simplicial	simplicial	ADJ	JJ	Degree=Pos	16	amod	_	_
16	set	set	NOUN	NN	Number=Sing	11	dobj	_	SpaceAfter=No
17	:	:	PUNCT	:	_	9	punct	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	diagonal	diagonal	ADJ	JJ	Degree=Pos	20	amod	_	_
20	simplicial	simplicial	NOUN	NN	Number=Sing	21	nsubj	_	_
21	set	set	NOUN	NN	Number=Sing	9	appos	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
24	less	less	ADV	RBR	Degree=Cmp	25	advmod	_	_
25	well	well	ADV	RB	Degree=Pos	26	advmod	_	_
26	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	amod	_	_
27	total	total	ADJ	JJ	Degree=Pos	28	amod	_	_
28	simplicial	simplicial	ADJ	JJ	Degree=Pos	29	amod	_	_
29	set	set	NOUN	NN	Number=Sing	21	conj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	Artin	Artin	PROPN	NNP	Number=Sing	30	pobj	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	Mazur	Mazur	PROPN	NNP	Number=Sing	31	conj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 2
# text = There is a natural comparison map between these simplicial sets, and it is a theorem due to Cegarra and Remedios and independently Joyal and Tierney, that this comparison map is a weak homotopy equivalence for any bisimplicial set.
1	There	there	PRON	EX	_	2	expl	_	_
2	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
4	natural	natural	ADJ	JJ	Degree=Pos	6	amod	_	_
5	comparison	comparison	NOUN	NN	Number=Sing	6	compound	_	_
6	map	map	NOUN	NN	Number=Sing	2	attr	_	_
7	between	between	ADP	IN	_	6	prep	_	_
8	these	these	DET	DT	Number=Plur|PronType=Dem	10	det	_	_
9	simplicial	simplicial	ADJ	JJ	Degree=Pos	10	amod	_	_
10	sets	set	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
13	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	theorem	theorem	ADJ	JJ	Degree=Pos	14	attr	_	_
17	due	due	ADP	IN	_	14	prep	_	_
18	to	to	ADP	IN	_	17	pcomp	_	_
19	Cegarra	Cegarra	PROPN	NNP	Number=Sing	17	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	Remedios	Remedios	PROPN	NNP	Number=Sing	19	conj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	independently	independently	ADV	RB	_	24	advmod	_	_
24	Joyal	Joyal	PROPN	NNP	Number=Sing	21	conj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	Tierney	Tierney	PROPN	NNP	Number=Sing	24	conj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
28	that	that	SCONJ	IN	_	32	mark	_	_
29	this	this	DET	DT	Number=Sing|PronType=Dem	31	det	_	_
30	comparison	comparison	NOUN	NN	Number=Sing	31	compound	_	_
31	map	map	NOUN	NN	Number=Sing	32	nsubj	_	_
32	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	ccomp	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
34	weak	weak	ADJ	JJ	Degree=Pos	36	amod	_	_
35	homotopy	homotopy	NOUN	NN	Number=Sing	36	compound	_	_
36	equivalence	equivalence	NOUN	NN	Number=Sing	32	attr	_	_
37	for	for	ADP	IN	_	36	prep	_	_
38	any	any	DET	DT	_	40	det	_	_
39	bisimplicial	bisimplicial	ADJ	JJ	Degree=Pos	40	amod	_	_
40	set	set	NOUN	NN	Number=Sing	37	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this paper we will give a new, elementary proof of this result.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
5	will	will	AUX	MD	VerbForm=Fin	6	aux	_	_
6	give	give	VERB	VB	VerbForm=Inf	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	new	new	ADJ	JJ	Degree=Pos	11	amod	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
10	elementary	elementary	ADJ	JJ	Degree=Pos	11	amod	_	_
11	proof	proof	NOUN	NN	Number=Sing	6	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	this	this	DET	DT	Number=Sing|PronType=Dem	14	det	_	_
14	result	result	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = As an application, we will revisit Kan's simplicial loop group functor $ G $ .
1	As	as	ADP	IN	_	7	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
6	will	will	AUX	MD	VerbForm=Fin	7	aux	_	_
7	revisit	revisit	VERB	VB	VerbForm=Inf	0	ROOT	_	_
8	Kan	Kan	PROPN	NNP	Number=Sing	12	poss	_	SpaceAfter=No
9	's	's	PART	POS	_	8	case	_	_
10	simplicial	simplicial	ADJ	JJ	Degree=Pos	11	amod	_	_
11	loop	loop	NOUN	NN	Number=Sing	12	compound	_	_
12	group	group	NOUN	NN	Number=Sing	7	dobj	_	_
13	functor	functor	NOUN	NN	Number=Sing	7	dobj	_	_
14	$ G $	$ g $	SYM	$	_	7	npadvmod	_	_
15	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 5
# text = We will give a simple formula for this functor, which is based on a factorization, due to Duskin, of Eilenberg and Mac Lane's classifying complex functor $ overline{W} $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	will	will	AUX	MD	VerbForm=Fin	3	aux	_	_
3	give	give	VERB	VB	VerbForm=Inf	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	simple	simple	ADJ	JJ	Degree=Pos	6	amod	_	_
6	formula	formula	NOUN	NN	Number=Sing	3	dobj	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	this	this	DET	DT	Number=Sing|PronType=Dem	9	det	_	_
9	functor	functor	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	which	which	PRON	WDT	_	13	nsubjpass	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	relcl	_	_
14	on	on	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	factorization	factorization	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
18	due	due	ADP	IN	_	3	prep	_	_
19	to	to	ADP	IN	_	18	pcomp	_	_
20	Duskin	Duskin	PROPN	NNP	Number=Sing	18	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	of	of	ADP	IN	_	20	prep	_	_
23	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	30	poss	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	Mac	Mac	PROPN	NNP	Number=Sing	26	compound	_	_
26	Lane	Lane	PROPN	NNP	Number=Sing	23	conj	_	SpaceAfter=No
27	's	's	PART	POS	_	26	case	_	_
28	classifying	classify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	30	amod	_	_
29	complex	complex	ADJ	JJ	Degree=Pos	30	amod	_	_
30	functor	functor	NOUN	NN	Number=Sing	22	pobj	_	_
31	$ overline{W} $	$ overline{w} $	SYM	$	_	3	dobj	_	_
32	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = We will give a new, short, proof of Kan's result that the unit map for the adjunction $ Gdashv overline{W} $ is a weak homotopy equivalence for reduced simplicial sets.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	will	will	AUX	MD	VerbForm=Fin	3	aux	_	_
3	give	give	VERB	VB	VerbForm=Inf	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
5	new	new	ADJ	JJ	Degree=Pos	9	amod	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
7	short	short	ADJ	JJ	Degree=Pos	9	amod	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
9	proof	proof	NOUN	NN	Number=Sing	3	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	Kan	Kan	PROPN	NNP	Number=Sing	13	poss	_	SpaceAfter=No
12	's	's	PART	POS	_	11	case	_	_
13	result	result	NOUN	NN	Number=Sing	10	pobj	_	_
14	that	that	SCONJ	IN	_	22	mark	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	unit	unit	NOUN	NN	Number=Sing	17	compound	_	_
17	map	map	NOUN	NN	Number=Sing	22	nsubj	_	_
18	for	for	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	adjunction	adjunction	NOUN	NN	Number=Sing	18	pobj	_	_
21	$ Gdashv overline{W} $	$ gdashv overline{w} $	SYM	$	_	17	npadvmod	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	acl	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
24	weak	weak	ADJ	JJ	Degree=Pos	26	amod	_	_
25	homotopy	homotopy	NOUN	NN	Number=Sing	26	compound	_	_
26	equivalence	equivalence	NOUN	NN	Number=Sing	22	attr	_	_
27	for	for	ADP	IN	_	26	prep	_	_
28	reduced	reduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	30	amod	_	_
29	simplicial	simplicial	ADJ	JJ	Degree=Pos	30	amod	_	_
30	sets	set	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 401
# sent_id = 1
# text = Quantum categories were introduced by Day and Street as generalizations of both bi(co)algebroids and small categories.
1	Quantum	Quantum	PROPN	NNP	Number=Sing	2	compound	_	_
2	categories	category	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	4	auxpass	_	_
4	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	by	by	ADP	IN	_	4	agent	_	_
6	Day	Day	PROPN	NNP	Number=Sing	5	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	Street	Street	PROPN	NNP	Number=Sing	6	conj	_	_
9	as	as	ADP	IN	_	4	prep	_	_
10	generalizations	generalization	NOUN	NNS	Number=Plur	9	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	both	both	CCONJ	CC	ConjType=Cmp	13	preconj	_	_
13	bi(co)algebroids	bi(co)algebroid	NOUN	NNS	Number=Plur	11	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	small	small	ADJ	JJ	Degree=Pos	16	amod	_	_
16	categories	category	NOUN	NNS	Number=Plur	13	conj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = We clarify details of that work.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	clarify	clarify	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	details	detail	NOUN	NNS	Number=Plur	2	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	that	that	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	work	work	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
7	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = In particular, we show explicitly how the monadic definition of a quantum category unpacks to a set of axioms close to the definitions of a bialgebroid in the Hopf algebraic literature.
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	explicitly	explicitly	ADV	RB	_	5	advmod	_	_
7	how	how	SCONJ	WRB	_	10	advmod	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	monadic	monadic	ADJ	JJ	Degree=Pos	10	amod	_	_
10	definition	definition	NOUN	NN	Number=Sing	5	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	quantum	quantum	ADJ	JJ	Degree=Pos	15	amod	_	_
14	category	category	NOUN	NN	Number=Sing	15	compound	_	_
15	unpacks	unpack	NOUN	NNS	Number=Plur	11	pobj	_	_
16	to	to	ADP	IN	_	10	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	set	set	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	axioms	axiom	NOUN	NNS	Number=Plur	19	pobj	_	_
21	close	close	ADV	RB	_	10	advmod	_	_
22	to	to	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	definitions	definition	NOUN	NNS	Number=Plur	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	bialgebroid	bialgebroid	NOUN	NN	Number=Sing	25	pobj	_	_
28	in	in	ADP	IN	_	27	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
30	Hopf	Hopf	PROPN	NNP	Number=Sing	32	nmod	_	_
31	algebraic	algebraic	ADJ	JJ	Degree=Pos	32	amod	_	_
32	literature	literature	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = We introduce notions of functor and natural transformation for quantum categories and consider various constructions on quantum structures.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	notions	notion	NOUN	NNS	Number=Plur	2	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	functor	functor	NOUN	NN	Number=Sing	4	pobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	natural	natural	ADJ	JJ	Degree=Pos	8	amod	_	_
8	transformation	transformation	NOUN	NN	Number=Sing	5	conj	_	_
9	for	for	ADP	IN	_	3	prep	_	_
10	quantum	quantum	ADJ	JJ	Degree=Pos	11	amod	_	_
11	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
13	consider	consider	VERB	VB	VerbForm=Inf	2	conj	_	_
14	various	various	ADJ	JJ	Degree=Pos	15	amod	_	_
15	constructions	construction	NOUN	NNS	Number=Plur	13	dobj	_	_
16	on	on	ADP	IN	_	15	prep	_	_
17	quantum	quantum	ADJ	JJ	Degree=Pos	18	compound	_	_
18	structures	structure	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 402
# sent_id = 1
# text = We discuss the problem of characterizing the property of a Grothendieck topos to satisfy a given `geometric' invariant as a property of its sites of definition, and indicate a set of general techniques for establishing such criteria.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	discuss	discuss	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	problem	problem	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	characterizing	characterize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	property	property	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	12	compound	_	_
12	topos	topos	NOUN	NN	Number=Sing	9	pobj	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	satisfy	satisfy	VERB	VB	VerbForm=Inf	6	advcl	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
16	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	amod	_	_
17	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	20	punct	_	SpaceAfter=No
18	geometric	geometric	ADJ	JJ	Degree=Pos	20	amod	_	SpaceAfter=No
19	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	20	punct	_	_
20	invariant	invariant	ADJ	JJ	Degree=Pos	14	dobj	_	_
21	as	as	ADP	IN	_	14	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
23	property	property	NOUN	NN	Number=Sing	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	26	poss	_	_
26	sites	site	NOUN	NNS	Number=Plur	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	definition	definition	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
31	indicate	indicate	VERB	VB	VerbForm=Inf	2	conj	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
33	set	set	NOUN	NN	Number=Sing	31	dobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	general	general	ADJ	JJ	Degree=Pos	36	amod	_	_
36	techniques	technique	NOUN	NNS	Number=Plur	34	pobj	_	_
37	for	for	ADP	IN	_	33	prep	_	_
38	establishing	establish	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	37	pcomp	_	_
39	such	such	ADJ	JJ	Degree=Pos	40	amod	_	_
40	criteria	criterion	NOUN	NNS	Number=Plur	38	dobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We then apply our methodologies to specific invariants, notably including the property of a Grothendieck topos to be localic (respectively, atomic, locally connected, equivalent to a presheaf topos), obtaining explicit site characterizations for them.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	apply	apply	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	5	poss	_	_
5	methodologies	methodology	NOUN	NNS	Number=Plur	3	dobj	_	_
6	to	to	ADP	IN	_	3	prep	_	_
7	specific	specific	ADJ	JJ	Degree=Pos	8	amod	_	_
8	invariants	invariant	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
10	notably	notably	ADV	RB	_	11	advmod	_	_
11	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	property	property	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	17	compound	_	_
17	topos	topos	NOUN	NN	Number=Sing	14	pobj	_	_
18	to	to	PART	TO	_	19	aux	_	_
19	be	be	AUX	VB	VerbForm=Inf	3	advcl	_	_
20	localic	localic	ADJ	JJ	Degree=Pos	19	acomp	_	_
21	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	27	punct	_	SpaceAfter=No
22	respectively	respectively	ADV	RB	_	27	advmod	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
24	atomic	atomic	ADJ	JJ	Degree=Pos	27	amod	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
26	locally	locally	ADV	RB	_	27	advmod	_	_
27	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	advcl	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
29	equivalent	equivalent	ADJ	JJ	Degree=Pos	27	conj	_	_
30	to	to	ADP	IN	_	29	prep	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
32	presheaf	presheaf	ADJ	JJ	Degree=Pos	33	amod	_	_
33	topos	topos	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
34	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	27	punct	_	SpaceAfter=No
35	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
36	obtaining	obtain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	27	advcl	_	_
37	explicit	explicit	ADJ	JJ	Degree=Pos	39	amod	_	_
38	site	site	NOUN	NN	Number=Sing	39	compound	_	_
39	characterizations	characterization	NOUN	NNS	Number=Plur	36	dobj	_	_
40	for	for	ADP	IN	_	36	prep	_	_
41	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	40	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 403
# sent_id = 1
# text = Given a double category $ mathbb D $ such that $ mathbb D_0 $ has pushouts, we characterize oplax/lax adjunctions between $ mathbb D $ and $ Cospan(mathbb D_0) $ for which the right adjoint is normal and restricts to the identity on $ mathbb D_0 $ , where $ Cospan(mathbb D_0) $ is the double category on $ mathbb D_0 $ whose vertical morphisms are cospans.
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	double	double	ADJ	JJ	Degree=Pos	4	amod	_	_
4	category	category	NOUN	NN	Number=Sing	1	pobj	_	_
5	$ mathbb D $	$ mathbb d $	SYM	$	_	6	nummod	_	_
6	such	such	ADJ	JJ	Degree=Pos	4	appos	_	_
7	that	that	SCONJ	IN	_	9	nsubj	_	_
8	$ mathbb D_0 $	$ mathbb d_0 $	SYM	$	_	7	pobj	_	_
9	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	relcl	_	_
10	pushouts	pushout	NOUN	NNS	Number=Plur	9	dobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	oplax	oplax	PROPN	NNP	Number=Sing	16	npadvmod	_	SpaceAfter=No
15	/	/	SYM	SYM	_	16	punct	_	SpaceAfter=No
16	lax	lax	PROPN	NNP	Number=Sing	17	compound	_	_
17	adjunctions	adjunction	NOUN	NNS	Number=Plur	13	dobj	_	_
18	between	between	ADP	IN	_	17	prep	_	_
19	$ mathbb D $	$ mathbb d $	SYM	$	_	18	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
21	$ Cospan(mathbb D_0) $	$ cospan(mathbb d_0) $	SYM	$	_	17	conj	_	_
22	for	for	ADP	IN	_	27	prep	_	_
23	which	which	PRON	WDT	_	22	pobj	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	right	right	ADJ	JJ	Degree=Pos	26	amod	_	_
26	adjoint	adjoint	NOUN	NN	Number=Sing	27	nsubj	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	21	relcl	_	_
28	normal	normal	ADJ	JJ	Degree=Pos	27	acomp	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
30	restricts	restrict	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	conj	_	_
31	to	to	ADP	IN	_	30	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
33	identity	identity	NOUN	NN	Number=Sing	31	pobj	_	_
34	on	on	ADP	IN	_	33	prep	_	_
35	$ mathbb D_0 $	$ mathbb d_0 $	SYM	$	_	34	pobj	_	_
36	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
37	where	where	SCONJ	WRB	_	39	advmod	_	_
38	$ Cospan(mathbb D_0) $	$ cospan(mathbb d_0) $	SYM	$	_	39	nsubj	_	_
39	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	35	relcl	_	_
40	the	the	DET	DT	Definite=Def|PronType=Art	42	det	_	_
41	double	double	ADJ	JJ	Degree=Pos	42	amod	_	_
42	category	category	NOUN	NN	Number=Sing	39	attr	_	_
43	on	on	ADP	IN	_	42	prep	_	_
44	$ mathbb D_0 $	$ mathbb d_0 $	SYM	$	_	43	pobj	_	_
45	whose	whose	DET	WP$	Poss=Yes	47	poss	_	_
46	vertical	vertical	ADJ	JJ	Degree=Pos	47	amod	_	_
47	morphisms	morphism	NOUN	NNS	Number=Plur	48	nsubj	_	_
48	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	39	ccomp	_	_
49	cospans	cospan	NOUN	NNS	Number=Plur	48	attr	_	SpaceAfter=No
50	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that such a pair exists if and only if $ mathbb D $ has companions, conjoints, and 1 - cotabulators.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	such	such	DET	PDT	_	6	predet	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	pair	pair	NOUN	NN	Number=Sing	7	nsubj	_	_
7	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	if	if	SCONJ	IN	_	13	mark	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	only	only	ADV	RB	_	13	advmod	_	_
11	if	if	SCONJ	IN	_	13	mark	_	_
12	$ mathbb D $	$ mathbb d $	SYM	$	_	13	nsubj	_	_
13	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	advcl	_	_
14	companions	companion	NOUN	NNS	Number=Plur	13	dobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	conjoints	conjoint	NOUN	NNS	Number=Plur	14	conj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
19	1	1	NUM	CD	NumType=Card	21	nummod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	cotabulators	cotabulator	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The right adjoints are induced by the companions and conjoints, and the left adjoints by the 1 - cotabulators.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	right	right	ADJ	JJ	Degree=Pos	3	amod	_	_
3	adjoints	adjoint	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	by	by	ADP	IN	_	5	agent	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	companions	companion	NOUN	NNS	Number=Plur	6	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	conjoints	conjoint	NOUN	NNS	Number=Plur	8	conj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	left	left	ADJ	JJ	Degree=Pos	15	amod	_	_
15	adjoints	adjoint	NOUN	NNS	Number=Plur	5	conj	_	_
16	by	by	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
18	1	1	NUM	CD	NumType=Card	20	nummod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	cotabulators	cotabulator	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = The notion of a 1 - cotabulator is a common generalization of the symmetric algebra of a module and Artin - Wraith glueing of toposes, locales, and topological spaces.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	notion	notion	NOUN	NN	Number=Sing	8	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	1	1	NUM	CD	NumType=Card	7	nummod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	cotabulator	cotabulator	NOUN	NN	Number=Sing	3	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	common	common	ADJ	JJ	Degree=Pos	11	amod	_	_
11	generalization	generalization	NOUN	NN	Number=Sing	8	attr	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	symmetric	symmetric	ADJ	JJ	Degree=Pos	15	amod	_	_
15	algebra	algebra	PROPN	NNP	Number=Sing	12	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	module	module	NOUN	NN	Number=Sing	23	nmod	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	Artin	Artin	PROPN	NNP	Number=Sing	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	Wraith	Wraith	PROPN	NNP	Number=Sing	23	compound	_	_
23	glueing	glueing	NOUN	NN	Number=Sing	16	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	toposes	topos	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
27	locales	locale	NOUN	NNS	Number=Plur	25	conj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
30	topological	topological	ADJ	JJ	Degree=Pos	31	amod	_	_
31	spaces	space	NOUN	NNS	Number=Plur	27	conj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 404
# sent_id = 1
# text = Motivated by constructions in the theory of inverse semigroups and etale groupoids, we define and investigate the concept of isotropy from a topos - theoretic perspective.
1	Motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	advcl	_	_
2	by	by	ADP	IN	_	1	agent	_	_
3	constructions	construction	NOUN	NNS	Number=Plur	2	pobj	_	_
4	in	in	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	theory	theory	NOUN	NN	Number=Sing	4	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	inverse	inverse	ADJ	JJ	Degree=Pos	9	amod	_	_
9	semigroups	semigroup	NOUN	NNS	Number=Plur	7	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	etale	etale	NOUN	NN	Number=Sing	12	compound	_	_
12	groupoids	groupoid	NOUN	NNS	Number=Plur	9	conj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
14	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	15	nsubj	_	_
15	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	investigate	investigate	VERB	VB	VerbForm=Inf	15	conj	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	concept	concept	NOUN	NN	Number=Sing	17	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	isotropy	isotropy	NOUN	NN	Number=Sing	20	pobj	_	_
22	from	from	ADP	IN	_	19	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
24	topos	topos	NOUN	NN	Number=Sing	26	npadvmod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	theoretic	theoretic	ADJ	JJ	Degree=Pos	27	amod	_	_
27	perspective	perspective	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 2
# text = Our main conceptual tool is a monad on the category of grouped toposes.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	4	poss	_	_
2	main	main	ADJ	JJ	Degree=Pos	4	amod	_	_
3	conceptual	conceptual	ADJ	JJ	Degree=Pos	4	amod	_	_
4	tool	tool	NOUN	NN	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	monad	monad	NOUN	NNS	Number=Plur	5	attr	_	_
8	on	on	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	grouped	grouped	ADJ	JJ	Degree=Pos	13	amod	_	_
13	toposes	topos	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = Its algebras correspond to a generalized notion of crossed module, which we call a crossed topos.
1	Its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	2	poss	_	_
2	algebras	algebra	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	correspond	correspond	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	to	to	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	generalized	generalized	ADJ	JJ	Degree=Pos	7	amod	_	_
7	notion	notion	NOUN	NN	Number=Sing	4	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	crossed	crossed	ADJ	JJ	Degree=Pos	10	amod	_	_
10	module	module	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	which	which	PRON	WDT	_	14	dobj	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	10	relcl	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	topos	topos	NOUN	NN	Number=Sing	14	oprd	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = As an application, we present a topos - theoretic characterization and generalization of the `Clifford, fundamental' sequence associated with an inverse semigroup.
1	As	as	ADP	IN	_	6	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	topos	topos	NOUN	NN	Number=Sing	10	npadvmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	theoretic	theoretic	ADJ	JJ	Degree=Pos	11	amod	_	_
11	characterization	characterization	NOUN	NN	Number=Sing	6	dobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	generalization	generalization	NOUN	NN	Number=Sing	11	conj	_	_
14	of	of	ADP	IN	_	11	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
16	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	21	punct	_	SpaceAfter=No
17	Clifford	Clifford	PROPN	NNP	Number=Sing	21	nmod	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
19	fundamental	fundamental	ADJ	JJ	Degree=Pos	21	amod	_	SpaceAfter=No
20	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	21	punct	_	_
21	sequence	sequence	NOUN	NN	Number=Sing	14	pobj	_	_
22	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	acl	_	_
23	with	with	ADP	IN	_	22	prep	_	_
24	an	an	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
25	inverse	inverse	ADJ	JJ	Degree=Pos	26	amod	_	_
26	semigroup	semigroup	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 405
# sent_id = 1
# text = By the Lefschetz fixed point theorem, if an endomorphism of a topological space is fixed - point - free, then its Lefschetz number vanishes.
1	By	by	ADP	IN	_	6	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
3	Lefschetz	Lefschetz	PROPN	NNP	Number=Sing	5	amod	_	_
4	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	amod	_	_
5	point	point	NOUN	NN	Number=Sing	1	pobj	_	_
6	theorem	theorem	ADJ	JJ	Degree=Pos	0	ROOT	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	if	if	SCONJ	IN	_	15	mark	_	_
9	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	endomorphism	endomorphism	NOUN	NN	Number=Sing	15	nsubj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	topological	topological	ADJ	JJ	Degree=Pos	14	amod	_	_
14	space	space	NOUN	NN	Number=Sing	11	pobj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	advcl	_	_
16	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	amod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
18	point	point	NOUN	NN	Number=Sing	20	npadvmod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	free	free	ADJ	JJ	Degree=Pos	26	amod	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
22	then	then	ADV	RB	PronType=Dem	26	advmod	_	_
23	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	26	poss	_	_
24	Lefschetz	lefschetz	ADJ	JJ	Degree=Pos	26	amod	_	_
25	number	number	NOUN	NN	Number=Sing	26	compound	_	_
26	vanishes	vanishe	NOUN	NNS	Number=Plur	15	attr	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = This necessary condition is not usually sufficient, however; for that we need a refinement of the Lefschetz number called the Reidemeister trace.
1	This	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
2	necessary	necessary	ADJ	JJ	Degree=Pos	3	amod	_	_
3	condition	condition	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	ccomp	_	_
5	not	not	PART	RB	Polarity=Neg	4	neg	_	_
6	usually	usually	ADV	RB	_	4	advmod	_	_
7	sufficient	sufficient	ADJ	JJ	Degree=Pos	4	acomp	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
9	however	however	ADV	RB	_	4	advmod	_	SpaceAfter=No
10	;	;	PUNCT	:	_	14	punct	_	_
11	for	for	SCONJ	IN	_	14	mark	_	_
12	that	that	SCONJ	IN	_	14	mark	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	need	need	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	refinement	refinement	NOUN	NN	Number=Sing	14	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	Lefschetz	lefschetz	ADJ	JJ	Degree=Pos	20	amod	_	_
20	number	number	NOUN	NN	Number=Sing	17	pobj	_	_
21	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	20	acl	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	Reidemeister	Reidemeister	PROPN	NNP	Number=Sing	24	compound	_	_
24	trace	trace	NOUN	NN	Number=Sing	21	oprd	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 3
# text = Abstractly, the Lefschetz number is a trace in a symmetric monoidal category, while the Reidemeister trace is a trace in a bicategory; in this paper we relate these contexts using indexed symmetric monoidal categories.
1	Abstractly	abstractly	ADV	RB	_	6	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	Lefschetz	lefschetz	ADJ	JJ	Degree=Pos	5	amod	_	_
5	number	number	NOUN	NN	Number=Sing	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	ccomp	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	trace	trace	NOUN	NN	Number=Sing	6	attr	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	symmetric	symmetric	ADJ	JJ	Degree=Pos	13	amod	_	_
12	monoidal	monoidal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
15	while	while	SCONJ	IN	_	19	mark	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	Reidemeister	Reidemeister	PROPN	NNP	Number=Sing	18	compound	_	_
18	trace	trace	NOUN	NN	Number=Sing	19	nsubj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	advcl	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	trace	trace	NOUN	NN	Number=Sing	19	attr	_	_
22	in	in	ADP	IN	_	21	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	bicategory	bicategory	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
25	;	;	PUNCT	:	_	30	punct	_	_
26	in	in	ADP	IN	_	30	prep	_	_
27	this	this	DET	DT	Number=Sing|PronType=Dem	28	det	_	_
28	paper	paper	NOUN	NN	Number=Sing	26	pobj	_	_
29	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	30	nsubj	_	_
30	relate	relate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
31	these	these	DET	DT	Number=Plur|PronType=Dem	32	det	_	_
32	contexts	context	NOUN	NNS	Number=Plur	30	dobj	_	_
33	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	30	advcl	_	_
34	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	37	amod	_	_
35	symmetric	symmetric	ADJ	JJ	Degree=Pos	37	amod	_	_
36	monoidal	monoidal	ADJ	JJ	Degree=Pos	37	amod	_	_
37	categories	category	NOUN	NNS	Number=Plur	33	dobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	30	punct	_	SpaceAfter=No

# sent_id = 4
# text = In particular, we will show that for any symmetric monoidal category with an associated indexed symmetric monoidal category, there is an associated bicategory which produces refinements of trace analogous to the Reidemeister trace.
1	In	in	ADP	IN	_	6	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
5	will	will	AUX	MD	VerbForm=Fin	6	aux	_	_
6	show	show	VERB	VB	VerbForm=Inf	0	ROOT	_	_
7	that	that	SCONJ	IN	_	22	mark	_	_
8	for	for	ADP	IN	_	22	prep	_	_
9	any	any	DET	DT	_	12	det	_	_
10	symmetric	symmetric	ADJ	JJ	Degree=Pos	12	amod	_	_
11	monoidal	monoidal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
13	with	with	ADP	IN	_	12	prep	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
15	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
16	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
17	symmetric	symmetric	ADJ	JJ	Degree=Pos	19	amod	_	_
18	monoidal	monoidal	ADJ	JJ	Degree=Pos	19	amod	_	_
19	category	category	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
21	there	there	PRON	EX	_	22	expl	_	_
22	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
23	an	an	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	associated	associated	ADJ	JJ	Degree=Pos	25	amod	_	_
25	bicategory	bicategory	NOUN	NN	Number=Sing	22	attr	_	_
26	which	which	PRON	WDT	_	27	nsubj	_	_
27	produces	produce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	relcl	_	_
28	refinements	refinement	NOUN	NNS	Number=Plur	27	dobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	trace	trace	NOUN	NN	Number=Sing	29	pobj	_	_
31	analogous	analogous	ADJ	JJ	Degree=Pos	28	amod	_	_
32	to	to	ADP	IN	_	31	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
34	Reidemeister	Reidemeister	PROPN	NNP	Number=Sing	35	compound	_	_
35	trace	trace	NOUN	NN	Number=Sing	32	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = This bicategory also produces a new notion of trace for parametrized spaces with dualizable fibers, which refines the obvious ``fiberwise'' traces by incorporating the action of the fundamental group of the base space.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	bicategory	bicategory	NOUN	NN	Number=Sing	4	nsubj	_	_
3	also	also	ADV	RB	_	4	advmod	_	_
4	produces	produce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	new	new	ADJ	JJ	Degree=Pos	7	amod	_	_
7	notion	notion	NOUN	NN	Number=Sing	4	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	trace	trace	NOUN	NN	Number=Sing	8	pobj	_	_
10	for	for	ADP	IN	_	7	prep	_	_
11	parametrized	parametrized	ADJ	JJ	Degree=Pos	12	amod	_	_
12	spaces	space	NOUN	NNS	Number=Plur	10	pobj	_	_
13	with	with	ADP	IN	_	12	prep	_	_
14	dualizable	dualizable	ADJ	JJ	Degree=Pos	15	amod	_	_
15	fibers	fiber	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	which	which	PRON	WDT	_	18	nsubj	_	_
18	refines	refine	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	relcl	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
20	obvious	obvious	ADJ	JJ	Degree=Pos	25	amod	_	_
21	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	25	punct	_	SpaceAfter=No
22	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	25	punct	_	SpaceAfter=No
23	fiberwise	fiberwise	NOUN	NN	Number=Sing	25	nmod	_	SpaceAfter=No
24	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	25	punct	_	_
25	traces	trace	NOUN	NNS	Number=Plur	18	dobj	_	_
26	by	by	ADP	IN	_	18	prep	_	_
27	incorporating	incorporate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	26	pcomp	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	action	action	NOUN	NN	Number=Sing	27	dobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	fundamental	fundamental	ADJ	JJ	Degree=Pos	33	amod	_	_
33	group	group	NOUN	NN	Number=Sing	30	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
36	base	base	NOUN	NN	Number=Sing	37	compound	_	_
37	space	space	NOUN	NN	Number=Sing	34	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 6
# text = We also advance the basic theory of indexed monoidal categories, including introducing a string diagram calculus which makes calculations much more tractable.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	advance	advance	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	basic	basic	ADJ	JJ	Degree=Pos	6	amod	_	_
6	theory	theory	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
9	monoidal	monoidal	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	prep	_	_
13	introducing	introduce	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	pcomp	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	string	string	NOUN	NN	Number=Sing	16	compound	_	_
16	diagram	diagram	NOUN	NN	Number=Sing	17	compound	_	_
17	calculus	calculus	NOUN	NN	Number=Sing	13	dobj	_	_
18	which	which	PRON	WDT	_	19	nsubj	_	_
19	makes	make	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
20	calculations	calculation	NOUN	NNS	Number=Plur	23	nsubj	_	_
21	much	much	ADV	RB	_	22	advmod	_	_
22	more	more	ADV	RBR	Degree=Cmp	23	advmod	_	_
23	tractable	tractable	ADJ	JJ	Degree=Pos	19	ccomp	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = This abstract framework lays the foundation for generalizations of these ideas to other contexts.
1	This	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
2	abstract	abstract	ADJ	JJ	Degree=Pos	3	amod	_	_
3	framework	framework	NOUN	NN	Number=Sing	4	nsubj	_	_
4	lays	lay	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	foundation	foundation	NOUN	NN	Number=Sing	4	dobj	_	_
7	for	for	ADP	IN	_	4	prep	_	_
8	generalizations	generalization	NOUN	NNS	Number=Plur	7	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	these	these	DET	DT	Number=Plur|PronType=Dem	11	det	_	_
11	ideas	idea	NOUN	NNS	Number=Plur	9	pobj	_	_
12	to	to	ADP	IN	_	8	prep	_	_
13	other	other	ADJ	JJ	Degree=Pos	14	amod	_	_
14	contexts	context	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 406
# sent_id = 1
# text = Let $ {Ldashv R:cal X rightarrowcal Y} $ be an adjunction with $ R $ monadic and $ L $ comonadic.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ {Ldashv R:cal X rightarrowcal Y} $	$ {ldashv r:cal x rightarrowcal y} $	SYM	$	_	3	nsubj	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	adjunction	adjunction	NOUN	NN	Number=Sing	3	attr	_	_
6	with	with	ADP	IN	_	5	prep	_	_
7	$ R $	$ r $	SYM	$	_	8	nmod	_	_
8	monadic	monadic	ADJ	JJ	Degree=Pos	6	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_

1	$ L $	$ l $	SYM	$	_	0	ROOT	_	_
2	comonadic	comonadic	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = Denote the induced monad on $ cal Y $ by $ M $ and the induced comonad on $ calX $ by $ C $ .
1	Denote	Denote	PROPN	NNP	Number=Sing	0	ROOT	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	amod	_	_
4	monad	monad	NOUN	NNS	Number=Plur	1	dobj	_	_
5	on	on	ADP	IN	_	4	prep	_	_
6	$ cal Y $	$ cal y $	SYM	$	_	5	pobj	_	_
7	by	by	ADP	IN	_	1	prep	_	_
8	$ M $	$ m $	SYM	$	_	7	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	1	cc	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
12	comonad	comonad	NOUN	NNS	Number=Plur	1	conj	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	$ calX $	$ calx $	SYM	$	_	13	pobj	_	_
15	by	by	ADP	IN	_	1	prep	_	_
16	$ C $	$ c $	SYM	$	_	15	pobj	_	_
17	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 3
# text = We characterize those $ C $ such that $ M $ satisfies the Explicit Basis property.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	those	those	DET	DT	Number=Plur|PronType=Dem	4	det	_	_
4	$ C $	$ c $	SYM	$	_	5	nmod	_	_
5	such	such	ADJ	JJ	Degree=Pos	8	nsubj	_	_
6	that	that	SCONJ	IN	_	8	det	_	_
7	$ M $	$ m $	SYM	$	_	8	nmod	_	_
8	satisfies	satisfie	NOUN	NNS	Number=Plur	2	ccomp	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
10	Explicit	Explicit	PROPN	NNP	Number=Sing	12	compound	_	_
11	Basis	Basis	PROPN	NNP	Number=Sing	12	compound	_	_
12	property	property	NOUN	NN	Number=Sing	8	dobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We also discuss some new examples and results motivated by this characterization.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	discuss	discuss	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	some	some	DET	DT	_	6	det	_	_
5	new	new	ADJ	JJ	Degree=Pos	6	amod	_	_
6	examples	example	NOUN	NNS	Number=Plur	3	dobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	results	result	NOUN	NNS	Number=Plur	6	conj	_	_
9	motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
10	by	by	ADP	IN	_	9	agent	_	_
11	this	this	DET	DT	Number=Sing|PronType=Dem	12	det	_	_
12	characterization	characterization	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 407
# sent_id = 1
# text = We obtain semantic characterizations, holding for any Grothendieck site $ (C, J) $ , for the models of a theory classified by a topos of the form $ Sh(C, J) $ in terms of the models of a theory classified by a topos $ [C^{op}, Set] $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	semantic	semantic	ADJ	JJ	Degree=Pos	4	amod	_	_
4	characterizations	characterization	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
6	holding	hold	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	any	any	DET	DT	_	10	det	_	_
9	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	10	compound	_	_
10	site	site	NOUN	NN	Number=Sing	11	compound	_	_
11	$ (C, J) $	$ (c, j) $	NOUN	NN	Number=Sing	7	pobj	_	_
12	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
13	for	for	ADP	IN	_	6	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	models	model	NOUN	NNS	Number=Plur	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	theory	theory	NOUN	NN	Number=Sing	16	pobj	_	_
19	classified	classify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	acl	_	_
20	by	by	ADP	IN	_	19	agent	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	topos	topos	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	form	form	NOUN	NN	Number=Sing	23	pobj	_	_
26	$ Sh(C, J) $	$ sh(c, j) $	SYM	$	_	6	dep	_	_
27	in	in	ADP	IN	_	6	prep	_	_
28	terms	term	NOUN	NNS	Number=Plur	27	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	models	model	NOUN	NNS	Number=Plur	29	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
34	theory	theory	NOUN	NN	Number=Sing	32	pobj	_	_
35	classified	classify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	34	acl	_	_
36	by	by	ADP	IN	_	35	agent	_	_
37	a	a	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
38	topos	topos	NOUN	NN	Number=Sing	36	pobj	_	_
39	$ [C^{op}, Set] $	$ [c^{op}, set] $	SYM	$	_	38	appos	_	_
40	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = These characterizations arise from an appropriate representation of flat functors into Grothendieck toposes based on an application of the Yoneda Lemma in conjunction with ideas from indexed category theory, and turn out to be relevant also in different contexts, in particular for addressing questions in classical Model Theory.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	characterizations	characterization	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	arise	arise	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	from	from	ADP	IN	_	3	prep	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	appropriate	appropriate	ADJ	JJ	Degree=Pos	7	amod	_	_
7	representation	representation	NOUN	NN	Number=Sing	4	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	flat	flat	ADJ	JJ	Degree=Pos	10	amod	_	_
10	functors	functor	NOUN	NNS	Number=Plur	8	pobj	_	_
11	into	into	ADP	IN	_	7	prep	_	_
12	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	13	compound	_	_
13	toposes	topos	NOUN	NNS	Number=Plur	11	pobj	_	_
14	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	acl	_	_
15	on	on	ADP	IN	_	14	prep	_	_
16	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	application	application	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	Yoneda	Yoneda	PROPN	NNP	Number=Sing	21	compound	_	_
21	Lemma	Lemma	PROPN	NNP	Number=Sing	18	pobj	_	_
22	in	in	ADP	IN	_	17	prep	_	_
23	conjunction	conjunction	NOUN	NN	Number=Sing	22	pobj	_	_
24	with	with	ADP	IN	_	23	prep	_	_
25	ideas	idea	NOUN	NNS	Number=Plur	24	pobj	_	_
26	from	from	ADP	IN	_	25	prep	_	_
27	indexed	indexed	ADJ	JJ	Degree=Pos	29	amod	_	_
28	category	category	NOUN	NN	Number=Sing	29	compound	_	_
29	theory	theory	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
32	turn	turn	VERB	VB	VerbForm=Inf	3	conj	_	_
33	out	out	ADP	RP	_	32	prt	_	_
34	to	to	PART	TO	_	35	aux	_	_
35	be	be	AUX	VB	VerbForm=Inf	32	xcomp	_	_
36	relevant	relevant	ADJ	JJ	Degree=Pos	35	acomp	_	_
37	also	also	ADV	RB	_	35	advmod	_	_
38	in	in	ADP	IN	_	35	prep	_	_
39	different	different	ADJ	JJ	Degree=Pos	40	amod	_	_
40	contexts	context	NOUN	NNS	Number=Plur	38	pobj	_	SpaceAfter=No
41	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
42	in	in	ADP	IN	_	35	prep	_	_
43	particular	particular	ADJ	JJ	Degree=Pos	42	amod	_	_
44	for	for	ADP	IN	_	42	prep	_	_
45	addressing	address	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	44	pcomp	_	_
46	questions	question	NOUN	NNS	Number=Plur	45	dobj	_	_
47	in	in	ADP	IN	_	46	prep	_	_
48	classical	classical	ADJ	JJ	Degree=Pos	50	amod	_	_
49	Model	Model	PROPN	NNP	Number=Sing	50	compound	_	_
50	Theory	Theory	PROPN	NNP	Number=Sing	47	pobj	_	SpaceAfter=No
51	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 408
# sent_id = 1
# text = Classification of homotopy $ n $ - types has focused on developing algebraic categories which are equivalent to categories of $ n $ - types.
1	Classification	classification	NOUN	NN	Number=Sing	8	nsubj	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	homotopy	homotopy	PROPN	NNP	Number=Sing	2	pobj	_	_
4	$ n $	$ n $	SYM	$	_	6	compound	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	types	type	NOUN	NNS	Number=Plur	1	conj	_	_
7	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	aux	_	_
8	focused	focus	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	on	on	ADP	IN	_	8	prep	_	_
10	developing	develop	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	pcomp	_	_
11	algebraic	algebraic	ADJ	JJ	Degree=Pos	12	amod	_	_
12	categories	category	NOUN	NNS	Number=Plur	10	dobj	_	_
13	which	which	PRON	WDT	_	14	nsubj	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	relcl	_	_
15	equivalent	equivalent	ADJ	JJ	Degree=Pos	14	acomp	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	$ n $	$ n $	SYM	$	_	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	types	type	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = We expand this theory by providing algebraic models of homotopy - theoretic constructions for stable one - types.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	expand	expand	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	theory	theory	NOUN	NN	Number=Sing	2	dobj	_	_
5	by	by	ADP	IN	_	2	prep	_	_
6	providing	provide	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	algebraic	algebraic	ADJ	JJ	Degree=Pos	8	amod	_	_
8	models	model	NOUN	NNS	Number=Plur	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	homotopy	homotopy	NOUN	NN	Number=Sing	12	npadvmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	theoretic	theoretic	ADJ	JJ	Degree=Pos	13	amod	_	_
13	constructions	construction	NOUN	NNS	Number=Plur	9	pobj	_	_
14	for	for	ADP	IN	_	13	prep	_	_
15	stable	stable	ADJ	JJ	Degree=Pos	18	amod	_	_
16	one	one	NUM	CD	NumType=Card	18	nummod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	types	type	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = These include a model for the Postnikov one - truncation of the sphere spectrum, and for its action on the model of a stable one - type.
1	These	these	PRON	DT	Number=Plur|PronType=Dem	2	nsubj	_	_
2	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	model	model	NOUN	NN	Number=Sing	2	dobj	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
7	Postnikov	Postnikov	PROPN	NNP	Number=Sing	6	nmod	_	_
8	one	one	NUM	CD	NumType=Card	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	truncation	truncation	NOUN	NN	Number=Sing	5	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	sphere	sphere	NOUN	NN	Number=Sing	14	compound	_	_
14	spectrum	spectrum	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
17	for	for	ADP	IN	_	2	conj	_	_
18	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	19	poss	_	_
19	action	action	NOUN	NN	Number=Sing	17	pobj	_	_
20	on	on	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	model	model	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
25	stable	stable	ADJ	JJ	Degree=Pos	28	amod	_	_
26	one	one	NUM	CD	NumType=Card	28	nummod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	type	type	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show that a bicategorical cokernel introduced by Vitale models the cofiber of a map between stable one - types, and apply this to develop an algebraic model for the Postnikov data of a stable one - type.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	6	mark	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	bicategorical	bicategorical	ADJ	JJ	Degree=Pos	6	amod	_	_
6	cokernel	cokernel	NOUN	NN	Number=Sing	2	ccomp	_	_
7	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
8	by	by	ADP	IN	_	7	agent	_	_
9	Vitale	Vitale	PROPN	NNP	Number=Sing	10	compound	_	_
10	models	model	NOUN	NNS	Number=Plur	8	pobj	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	cofiber	cofiber	NOUN	NN	Number=Sing	6	appos	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	map	map	NOUN	NN	Number=Sing	13	pobj	_	_
16	between	between	ADP	IN	_	15	prep	_	_
17	stable	stable	ADJ	JJ	Degree=Pos	20	amod	_	_
18	one	one	NUM	CD	NumType=Card	20	nummod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	types	type	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
23	apply	apply	VERB	VB	VerbForm=Inf	6	conj	_	_
24	this	this	PRON	DT	Number=Sing|PronType=Dem	23	dobj	_	_
25	to	to	PART	TO	_	26	aux	_	_
26	develop	develop	VERB	VB	VerbForm=Inf	23	advcl	_	_
27	an	an	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	algebraic	algebraic	ADJ	JJ	Degree=Pos	29	amod	_	_
29	model	model	NOUN	NN	Number=Sing	26	dobj	_	_
30	for	for	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	Postnikov	Postnikov	PROPN	NNP	Number=Sing	33	compound	_	_
33	data	datum	NOUN	NNS	Number=Plur	30	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
36	stable	stable	ADJ	JJ	Degree=Pos	39	amod	_	_
37	one	one	NUM	CD	NumType=Card	39	nummod	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	type	type	NOUN	NN	Number=Sing	34	pobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 409
# sent_id = 1
# text = We give a simple algebraic description of opetopes in terms of chain complexes, and we show how this description is related to combinatorial descriptions in terms of treelike structures.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
4	simple	simple	ADJ	JJ	Degree=Pos	6	amod	_	_
5	algebraic	algebraic	ADJ	JJ	Degree=Pos	6	amod	_	_
6	description	description	NOUN	NN	Number=Sing	2	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	opetopes	opetope	NOUN	NNS	Number=Plur	7	pobj	_	_
9	in	in	ADP	IN	_	2	prep	_	_
10	terms	term	NOUN	NNS	Number=Plur	9	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	chain	chain	NOUN	NN	Number=Sing	13	compound	_	_
13	complexes	complex	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
16	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	17	nsubj	_	_
17	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
18	how	how	SCONJ	WRB	_	22	advmod	_	_
19	this	this	DET	DT	Number=Sing|PronType=Dem	20	det	_	_
20	description	description	NOUN	NN	Number=Sing	22	nsubjpass	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	auxpass	_	_
22	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	ccomp	_	_
23	to	to	ADP	IN	_	22	prep	_	_
24	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	25	amod	_	_
25	descriptions	description	NOUN	NNS	Number=Plur	23	pobj	_	_
26	in	in	ADP	IN	_	25	prep	_	_
27	terms	term	NOUN	NNS	Number=Plur	26	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	treelike	treelike	ADJ	JJ	Degree=Pos	30	amod	_	_
30	structures	structure	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 2
# text = More generally, we show that the chain complexes associated to higher categories generate graphlike structures.
1	More	more	ADV	RBR	Degree=Cmp	2	advmod	_	_
2	generally	generally	ADV	RB	_	5	advmod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	14	mark	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	chain	chain	NOUN	NN	Number=Sing	9	compound	_	_
9	complexes	complex	NOUN	NNS	Number=Plur	14	nsubj	_	_
10	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	acl	_	_
11	to	to	ADP	IN	_	10	prep	_	_
12	higher	high	ADJ	JJR	Degree=Cmp	13	amod	_	_
13	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
14	generate	generate	VERB	VBP	Tense=Pres|VerbForm=Fin	5	ccomp	_	_
15	graphlike	graphlike	NOUN	NN	Number=Sing	16	compound	_	_
16	structures	structure	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = The algebraic description gives a relationship between the opetopic approach and other approaches to higher category theory.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	algebraic	algebraic	ADJ	JJ	Degree=Pos	3	amod	_	_
3	description	description	NOUN	NN	Number=Sing	4	nsubj	_	_
4	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	relationship	relationship	NOUN	NN	Number=Sing	4	dobj	_	_
7	between	between	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	opetopic	opetopic	ADJ	JJ	Degree=Pos	10	amod	_	_
10	approach	approach	NOUN	NN	Number=Sing	7	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	other	other	ADJ	JJ	Degree=Pos	13	amod	_	_
13	approaches	approach	NOUN	NNS	Number=Plur	10	conj	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	higher	high	ADJ	JJR	Degree=Cmp	17	amod	_	_
16	category	category	NOUN	NN	Number=Sing	17	compound	_	_
17	theory	theory	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = It also gives an easy way to calculate the sources and targets of opetopes.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	easy	easy	ADJ	JJ	Degree=Pos	6	amod	_	_
6	way	way	NOUN	NN	Number=Sing	3	dobj	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	calculate	calculate	VERB	VB	VerbForm=Inf	6	relcl	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	sources	source	NOUN	NNS	Number=Plur	8	dobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	targets	target	NOUN	NNS	Number=Plur	10	conj	_	_
13	of	of	ADP	IN	_	10	prep	_	_
14	opetopes	opetope	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 410
# sent_id = 1
# text = In this paper, which is the second part of a study of partial map categories with images, we investigate the interaction between images and various other kinds of categorical structure and properties.
1	In	in	ADP	IN	_	21	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	which	which	PRON	WDT	_	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	relcl	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	second	second	ADJ	JJ	Degree=Pos	9	amod	_	_
9	part	part	NOUN	NN	Number=Sing	6	attr	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	study	study	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	partial	partial	ADJ	JJ	Degree=Pos	16	amod	_	_
15	map	map	NOUN	NN	Number=Sing	16	compound	_	_
16	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	_
17	with	with	ADP	IN	_	12	prep	_	_
18	images	image	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
20	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	21	nsubj	_	_
21	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	interaction	interaction	NOUN	NN	Number=Sing	21	dobj	_	_
24	between	between	ADP	IN	_	23	prep	_	_
25	images	image	NOUN	NNS	Number=Plur	24	pobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	various	various	ADJ	JJ	Degree=Pos	29	amod	_	_
28	other	other	ADJ	JJ	Degree=Pos	29	amod	_	_
29	kinds	kind	NOUN	NNS	Number=Plur	25	conj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	categorical	categorical	ADJ	JJ	Degree=Pos	32	amod	_	_
32	structure	structure	NOUN	NN	Number=Sing	30	pobj	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
34	properties	property	NOUN	NNS	Number=Plur	32	conj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# sent_id = 2
# text = In particular, we consider images in the context of partial products, meets and discreteness and survey a taxonomy of structures leading towards the partial map categories of regular categories.
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	images	image	NOUN	NNS	Number=Plur	5	dobj	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	context	context	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	partial	partial	ADJ	JJ	Degree=Pos	12	amod	_	_
12	products	product	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
14	meets	meet	NOUN	NNS	Number=Plur	5	conj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	discreteness	discreteness	NOUN	NN	Number=Sing	14	conj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
18	survey	survey	VERB	VB	VerbForm=Inf	14	conj	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	taxonomy	taxonomy	NOUN	NN	Number=Sing	18	dobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	structures	structure	NOUN	NNS	Number=Plur	21	pobj	_	_
23	leading	lead	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	acl	_	_
24	towards	towards	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
26	partial	partial	ADJ	JJ	Degree=Pos	28	amod	_	_
27	map	map	NOUN	NN	Number=Sing	28	compound	_	_
28	categories	category	NOUN	NNS	Number=Plur	24	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	regular	regular	ADJ	JJ	Degree=Pos	31	amod	_	_
31	categories	category	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also present a term logic for cartesian partial map categories with images and prove a soundness and completeness theorem for this logic.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	term	term	NOUN	NN	Number=Sing	6	compound	_	_
6	logic	logic	NOUN	NN	Number=Sing	3	dobj	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	cartesian	cartesian	ADJ	JJ	Degree=Pos	11	amod	_	_
9	partial	partial	ADJ	JJ	Degree=Pos	10	amod	_	_
10	map	map	NOUN	NN	Number=Sing	11	compound	_	_
11	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
12	with	with	ADP	IN	_	3	prep	_	_
13	images	image	NOUN	NNS	Number=Plur	12	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
15	prove	prove	VERB	VB	VerbForm=Inf	3	conj	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	soundness	soundness	NOUN	NN	Number=Sing	15	dobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	completeness	completeness	NOUN	NN	Number=Sing	17	conj	_	_
20	theorem	theorem	ADJ	JJ	Degree=Pos	15	oprd	_	_
21	for	for	ADP	IN	_	20	prep	_	_
22	this	this	DET	DT	Number=Sing|PronType=Dem	23	det	_	_
23	logic	logic	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = Finally, we exhibit several free constructions relating the different classes of categories under consideration.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	exhibit	exhibit	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	several	several	ADJ	JJ	Degree=Pos	7	amod	_	_
6	free	free	ADJ	JJ	Degree=Pos	7	amod	_	_
7	constructions	construction	NOUN	NNS	Number=Plur	4	dobj	_	_
8	relating	relate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	acl	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	different	different	ADJ	JJ	Degree=Pos	11	amod	_	_
11	classes	class	NOUN	NNS	Number=Plur	8	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	_
14	under	under	ADP	IN	_	8	prep	_	_
15	consideration	consideration	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 411
# sent_id = 1
# text = In this two - part paper, we undertake a systematic study of abstract partial map categories in which every map has both a restriction (domain of definition) and a range (image).
1	In	in	ADP	IN	_	9	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
3	two	two	NUM	CD	NumType=Card	5	nummod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	part	part	NOUN	NN	Number=Sing	6	compound	_	_
6	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	undertake	undertake	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	systematic	systematic	ADJ	JJ	Degree=Pos	12	amod	_	_
12	study	study	NOUN	NN	Number=Sing	9	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	abstract	abstract	ADJ	JJ	Degree=Pos	17	amod	_	_
15	partial	partial	ADJ	JJ	Degree=Pos	17	amod	_	_
16	map	map	NOUN	NN	Number=Sing	17	compound	_	_
17	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	_
18	in	in	ADP	IN	_	22	prep	_	_
19	which	which	PRON	WDT	_	18	pobj	_	_
20	every	every	DET	DT	_	21	det	_	_
21	map	map	NOUN	NN	Number=Sing	22	nsubj	_	_
22	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
23	both	both	CCONJ	CC	ConjType=Cmp	25	preconj	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
25	restriction	restriction	NOUN	NN	Number=Sing	22	dobj	_	_
26	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	25	punct	_	SpaceAfter=No
27	domain	domain	NOUN	NN	Number=Sing	25	appos	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	definition	definition	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
30	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	27	punct	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
33	range	range	NOUN	NN	Number=Sing	25	conj	_	_
34	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	35	punct	_	SpaceAfter=No
35	image	image	NOUN	NN	Number=Sing	33	appos	_	SpaceAfter=No
36	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	33	punct	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this first part, we explore connections with related structures such as inverse categories and allegories, and establish two representational results.
1	In	in	ADP	IN	_	7	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
3	first	first	ADJ	JJ	Degree=Pos	4	amod	_	_
4	part	part	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	explore	explore	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	connections	connection	NOUN	NNS	Number=Plur	7	dobj	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
11	structures	structure	NOUN	NNS	Number=Plur	9	pobj	_	_
12	such	such	ADJ	JJ	Degree=Pos	13	amod	_	_
13	as	as	ADP	IN	_	11	prep	_	_
14	inverse	inverse	ADJ	JJ	Degree=Pos	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	allegories	allegory	NOUN	NNS	Number=Plur	15	conj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
20	establish	establish	VERB	VB	VerbForm=Inf	7	conj	_	_
21	two	two	NUM	CD	NumType=Card	23	nummod	_	_
22	representational	representational	ADJ	JJ	Degree=Pos	23	amod	_	_
23	results	result	NOUN	NNS	Number=Plur	20	dobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = The first of these explains how every range category can be fully and faithfully embedded into a category of partial maps equipped with a suitable factorization system.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	first	first	ADJ	JJ	Degree=Pos	5	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	these	these	PRON	DT	Number=Plur|PronType=Dem	3	pobj	_	_
5	explains	explain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	how	how	SCONJ	WRB	_	15	advmod	_	_
7	every	every	DET	DT	_	9	det	_	_
8	range	range	NOUN	NN	Number=Sing	9	compound	_	_
9	category	category	NOUN	NN	Number=Sing	15	nsubjpass	_	_
10	can	can	AUX	MD	VerbForm=Fin	15	aux	_	_
11	be	be	AUX	VB	VerbForm=Inf	15	auxpass	_	_
12	fully	fully	ADV	RB	_	15	advmod	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	faithfully	faithfully	ADV	RB	_	12	conj	_	_
15	embedded	embed	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	ccomp	_	_
16	into	into	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	category	category	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	partial	partial	ADJ	JJ	Degree=Pos	21	amod	_	_
21	maps	map	NOUN	NNS	Number=Plur	19	pobj	_	_
22	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	acl	_	_
23	with	with	ADP	IN	_	22	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
25	suitable	suitable	ADJ	JJ	Degree=Pos	27	amod	_	_
26	factorization	factorization	NOUN	NN	Number=Sing	27	compound	_	_
27	system	system	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = The second is a generalization of a result from semigroup theory by Boris Schein, and says that every small range category satisfying the additional condition that every map is an epimorphism onto its range can be faithfully embedded into the category of sets and partial functions with the usual notion of range.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	second	second	ADJ	JJ	Degree=Pos	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	generalization	generalization	NOUN	NN	Number=Sing	3	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	result	result	NOUN	NN	Number=Sing	6	pobj	_	_
9	from	from	ADP	IN	_	8	prep	_	_
10	semigroup	semigroup	NOUN	NN	Number=Sing	11	compound	_	_
11	theory	theory	NOUN	NN	Number=Sing	9	pobj	_	_
12	by	by	ADP	IN	_	11	prep	_	_
13	Boris	Boris	PROPN	NNP	Number=Sing	14	compound	_	_
14	Schein	Schein	PROPN	NNP	Number=Sing	12	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
17	says	say	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
18	that	that	SCONJ	IN	_	39	mark	_	_
19	every	every	DET	DT	_	22	det	_	_
20	small	small	ADJ	JJ	Degree=Pos	22	amod	_	_
21	range	range	NOUN	NN	Number=Sing	22	compound	_	_
22	category	category	NOUN	NN	Number=Sing	39	nsubjpass	_	_
23	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	acl	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	additional	additional	ADJ	JJ	Degree=Pos	26	amod	_	_
26	condition	condition	NOUN	NN	Number=Sing	23	dobj	_	_
27	that	that	SCONJ	IN	_	30	mark	_	_
28	every	every	DET	DT	_	29	det	_	_
29	map	map	NOUN	NN	Number=Sing	30	nsubj	_	_
30	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	acl	_	_
31	an	an	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
32	epimorphism	epimorphism	NOUN	NN	Number=Sing	30	attr	_	_
33	onto	onto	ADP	IN	_	30	prep	_	_
34	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	35	poss	_	_
35	range	range	NOUN	NN	Number=Sing	33	pobj	_	_
36	can	can	AUX	MD	VerbForm=Fin	39	aux	_	_
37	be	be	AUX	VB	VerbForm=Inf	39	auxpass	_	_
38	faithfully	faithfully	ADV	RB	_	39	advmod	_	_
39	embedded	embed	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	ccomp	_	_
40	into	into	ADP	IN	_	39	prep	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	42	det	_	_
42	category	category	NOUN	NN	Number=Sing	40	pobj	_	_
43	of	of	ADP	IN	_	42	prep	_	_
44	sets	set	NOUN	NNS	Number=Plur	43	pobj	_	_
45	and	and	CCONJ	CC	ConjType=Cmp	44	cc	_	_
46	partial	partial	ADJ	JJ	Degree=Pos	47	amod	_	_
47	functions	function	NOUN	NNS	Number=Plur	44	conj	_	_
48	with	with	ADP	IN	_	39	prep	_	_
49	the	the	DET	DT	Definite=Def|PronType=Art	51	det	_	_
50	usual	usual	ADJ	JJ	Degree=Pos	51	amod	_	_
51	notion	notion	NOUN	NN	Number=Sing	48	pobj	_	_
52	of	of	ADP	IN	_	51	prep	_	_
53	range	range	NOUN	NN	Number=Sing	52	pobj	_	SpaceAfter=No
54	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = Finally, we give an explicit construction of the free range category on a partial map category in terms of certain types of labeled trees.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	explicit	explicit	ADJ	JJ	Degree=Pos	7	amod	_	_
7	construction	construction	NOUN	NN	Number=Sing	4	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
10	free	free	ADJ	JJ	Degree=Pos	11	amod	_	_
11	range	range	NOUN	NN	Number=Sing	12	compound	_	_
12	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
13	on	on	ADP	IN	_	4	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	partial	partial	ADJ	JJ	Degree=Pos	17	amod	_	_
16	map	map	NOUN	NN	Number=Sing	17	compound	_	_
17	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
18	in	in	ADP	IN	_	4	prep	_	_
19	terms	term	NOUN	NNS	Number=Plur	18	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	certain	certain	ADJ	JJ	Degree=Pos	22	amod	_	_
22	types	type	NOUN	NNS	Number=Plur	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	labeled	label	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	amod	_	_
25	trees	tree	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 412
# sent_id = 1
# text = We give a generalized version of the Freyd conjecture and a way to think about a possible proof.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	amod	_	_
5	version	version	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	Freyd	Freyd	PROPN	NNP	Number=Sing	9	compound	_	_
9	conjecture	conjecture	NOUN	NN	Number=Sing	6	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	way	way	NOUN	NN	Number=Sing	5	conj	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	think	think	VERB	VB	VerbForm=Inf	12	relcl	_	_
15	about	about	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	possible	possible	ADJ	JJ	Degree=Pos	18	amod	_	_
18	proof	proof	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The essential point is to describe an elementary formal reduction of the question that holds in any triangulated category.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	essential	essential	ADJ	JJ	Degree=Pos	3	amod	_	_
3	point	point	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	describe	describe	VERB	VB	VerbForm=Inf	4	xcomp	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	elementary	elementary	ADJ	JJ	Degree=Pos	10	amod	_	_
9	formal	formal	ADJ	JJ	Degree=Pos	10	amod	_	_
10	reduction	reduction	NOUN	NN	Number=Sing	6	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	question	question	NOUN	NN	Number=Sing	11	pobj	_	_
14	that	that	PRON	WDT	PronType=Rel	15	nsubj	_	_
15	holds	hold	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	relcl	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	any	any	DET	DT	_	19	det	_	_
18	triangulated	triangulate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
19	category	category	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = There are no new results, but at least one known example drops out very easily.
1	There	there	PRON	EX	_	2	expl	_	_
2	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	no	no	DET	DT	_	5	det	_	_
4	new	new	ADJ	JJ	Degree=Pos	5	amod	_	_
5	results	result	NOUN	NNS	Number=Plur	2	attr	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
7	but	but	CCONJ	CC	ConjType=Cmp	2	cc	_	_
8	at	at	ADP	IN	_	9	advmod	_	_
9	least	least	ADV	RBS	Degree=Sup	10	advmod	_	_
10	one	one	NUM	CD	NumType=Card	12	nummod	_	_
11	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
12	example	example	NOUN	NN	Number=Sing	13	nsubj	_	_
13	drops	drop	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
14	out	out	ADP	RP	_	13	prt	_	_
15	very	very	ADV	RB	_	16	advmod	_	_
16	easily	easily	ADV	RB	_	13	advmod	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# doc_id = 413
# sent_id = 1
# text = Kornel Szlachanyi recently used the term skew - monoidal category for a particular laxified version of monoidal category.
1	Kornel	Kornel	PROPN	NNP	Number=Sing	2	compound	_	_
2	Szlachanyi	Szlachanyi	PROPN	NNP	Number=Sing	4	nsubj	_	_
3	recently	recently	ADV	RB	_	4	advmod	_	_
4	used	use	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
6	term	term	NOUN	NN	Number=Sing	10	nmod	_	_
7	skew	skew	NOUN	NN	Number=Sing	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	monoidal	monoidal	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	4	dobj	_	_
11	for	for	ADP	IN	_	4	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	particular	particular	ADJ	JJ	Degree=Pos	15	amod	_	_
14	laxified	laxified	ADJ	JJ	Degree=Pos	15	amod	_	_
15	version	version	NOUN	NN	Number=Sing	11	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	monoidal	monoidal	ADJ	JJ	Degree=Pos	18	amod	_	_
18	category	category	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = He showed that bialgebroids $ H $ with base ring $ R $ could be characterized in terms of skew - monoidal structures on the category of one - sided $ R $ - modules for which the lax unit was $ R $ itself.
1	He	he	PRON	PRP	Case=Nom|Gender=Masc|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	showed	show	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	4	nsubj	_	_
4	bialgebroids	bialgebroid	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
5	$ H $	$ h $	SYM	$	_	4	dobj	_	_
6	with	with	ADP	IN	_	4	prep	_	_
7	base	base	NOUN	NN	Number=Sing	8	compound	_	_
8	ring	ring	NOUN	NN	Number=Sing	6	pobj	_	_
9	$ R $	$ r $	SYM	$	_	12	nsubjpass	_	_
10	could	could	AUX	MD	VerbForm=Fin	12	aux	_	_
11	be	be	AUX	VB	VerbForm=Inf	12	auxpass	_	_
12	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	terms	term	NOUN	NNS	Number=Plur	13	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	skew	skew	NOUN	NN	Number=Sing	18	advmod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	monoidal	monoidal	ADJ	JJ	Degree=Pos	19	amod	_	_
19	structures	structure	NOUN	NNS	Number=Plur	15	pobj	_	_
20	on	on	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	category	category	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	one	one	NUM	CD	NumType=Card	23	pobj	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	sided	sided	ADJ	JJ	Degree=Pos	29	amod	_	_
27	$ R $	$ r $	SYM	$	_	29	compound	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	modules	module	NOUN	NNS	Number=Plur	2	dobj	_	_
30	for	for	ADP	IN	_	35	prep	_	_
31	which	which	PRON	WDT	_	30	pobj	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
33	lax	lax	ADJ	JJ	Degree=Pos	34	amod	_	_
34	unit	unit	NOUN	NN	Number=Sing	35	nsubj	_	_
35	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	29	relcl	_	_
36	$ R $	$ r $	SYM	$	_	37	nmod	_	_
37	itself	itself	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs|Reflex=Yes	35	attr	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We define skew monoidales (or skew pseudo - monoids) in any monoidal bicategory $ cal M $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	skew	skew	NOUN	NN	Number=Sing	4	compound	_	_
4	monoidales	monoidale	NOUN	NNS	Number=Plur	2	dobj	_	_
5	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	4	punct	_	SpaceAfter=No
6	or	or	CCONJ	CC	ConjType=Cmp	4	cc	_	_
7	skew	skew	VERB	VB	VerbForm=Inf	10	compound	_	_
8	pseudo	pseudo	NOUN	NN	Number=Sing	7	dobj	_	_
9	-	-	PUNCT	:	_	10	punct	_	_
10	monoids	monoid	NOUN	NNS	Number=Plur	4	conj	_	SpaceAfter=No
11	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	4	punct	_	_
12	in	in	ADP	IN	_	2	prep	_	_
13	any	any	DET	DT	_	15	det	_	_
14	monoidal	monoidal	ADJ	JJ	Degree=Pos	15	amod	_	_
15	bicategory	bicategory	NOUN	NN	Number=Sing	12	pobj	_	_
16	$ cal M $	$ cal m $	SYM	$	_	2	dep	_	_
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = These are skew - monoidal categories when $ cal M $ is $ Cat $ .
1	These	these	PRON	DT	Number=Plur|PronType=Dem	2	nsubj	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	skew	skew	NOUN	NN	Number=Sing	5	advmod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	monoidal	monoidal	ADJ	JJ	Degree=Pos	6	amod	_	_
6	categories	category	NOUN	NNS	Number=Plur	2	attr	_	_
7	when	when	SCONJ	WRB	_	9	advmod	_	_
8	$ cal M $	$ cal m $	SYM	$	_	9	nsubj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	advcl	_	_
10	$ Cat $	$ cat $	SYM	$	_	9	attr	_	_
11	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = Our main results are presented at the level of monoidal bicategories.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	3	poss	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	results	result	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	at	at	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	level	level	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	monoidal	monoidal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	bicategories	bicategorie	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 6
# text = However, a consequence is that quantum categories with base comonoid $ C $ in a suitably complete braided monoidal category $ CV $ are precisely skew monoidales in $ Comod (cal V) $ with unit coming from the counit of $ C $ .
1	However	however	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	consequence	consequence	NOUN	NN	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	DET	DT	Number=Sing|PronType=Dem	8	det	_	_
7	quantum	quantum	ADJ	JJ	Degree=Pos	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	21	nsubj	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	base	base	NOUN	NN	Number=Sing	11	compound	_	_
11	comonoid	comonoid	NOUN	NN	Number=Sing	9	pobj	_	_
12	$ C $	$ c $	SYM	$	_	8	appos	_	_
13	in	in	ADP	IN	_	8	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
15	suitably	suitably	ADV	RB	_	16	advmod	_	_
16	complete	complete	ADJ	JJ	Degree=Pos	19	amod	_	_
17	braided	braid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
18	monoidal	monoidal	ADJ	JJ	Degree=Pos	19	amod	_	_
19	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
20	$ CV $	$ cv $	SYM	$	_	8	appos	_	_
21	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
22	precisely	precisely	ADV	RB	_	23	advmod	_	_
23	skew	skew	VERB	VB	VerbForm=Inf	24	amod	_	_
24	monoidales	monoidale	NOUN	NNS	Number=Plur	21	attr	_	_
25	in	in	ADP	IN	_	24	prep	_	_
26	$ Comod (cal V) $	$ comod (cal v) $	SYM	$	_	25	pobj	_	_
27	with	with	ADP	IN	_	24	prep	_	_
28	unit	unit	NOUN	NN	Number=Sing	27	pobj	_	_
29	coming	come	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	28	acl	_	_
30	from	from	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	counit	counit	NOUN	NN	Number=Sing	30	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	$ C $	$ c $	SYM	$	_	33	pobj	_	_
35	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 7
# text = Quantum groupoids are those skew monoidales with invertible associativity constraint.
1	Quantum	quantum	NOUN	NN	Number=Sing	2	compound	_	_
2	groupoids	groupoid	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	those	those	DET	DT	Number=Plur|PronType=Dem	6	det	_	_
5	skew	skew	NOUN	NN	Number=Sing	6	compound	_	_
6	monoidales	monoidale	NOUN	NNS	Number=Plur	10	nsubj	_	_
7	with	with	ADP	IN	_	6	prep	_	_
8	invertible	invertible	ADJ	JJ	Degree=Pos	9	amod	_	_
9	associativity	associativity	NOUN	NN	Number=Sing	7	pobj	_	_
10	constraint	constraint	VERB	VBP	Tense=Pres|VerbForm=Fin	3	ccomp	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 8
# text = In fact, we provide some very general results connecting opmonoidal monads and skew monoidales.
1	In	in	ADP	IN	_	5	prep	_	_
2	fact	fact	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	some	some	DET	DT	_	9	det	_	_
7	very	very	ADV	RB	_	8	advmod	_	_
8	general	general	ADJ	JJ	Degree=Pos	9	amod	_	_
9	results	result	NOUN	NNS	Number=Plur	5	dobj	_	_
10	connecting	connect	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	acl	_	_
11	opmonoidal	opmonoidal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	monads	monad	NOUN	NNS	Number=Plur	10	dobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	skew	skew	NOUN	NN	Number=Sing	15	amod	_	_
15	monoidales	monoidale	NOUN	NNS	Number=Plur	12	conj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 9
# text = We use a lax version of the concept of warping defined by Booker and Street to modify monoidal structures.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	lax	lax	ADJ	JJ	Degree=Pos	5	amod	_	_
5	version	version	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	concept	concept	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	warping	warp	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	pcomp	_	_
11	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	xcomp	_	_
12	by	by	ADP	IN	_	11	agent	_	_
13	Booker	Booker	PROPN	NNP	Number=Sing	12	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	Street	Street	PROPN	NNP	Number=Sing	13	conj	_	_
16	to	to	PART	TO	_	17	aux	_	_
17	modify	modify	VERB	VB	VerbForm=Inf	2	xcomp	_	_
18	monoidal	monoidal	ADJ	JJ	Degree=Pos	19	amod	_	_
19	structures	structure	NOUN	NNS	Number=Plur	17	dobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 414
# sent_id = 1
# text = We show that every internal biequivalence in a tricategory $ T $ is part of a biadjoint biequivalence.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	11	mark	_	_
4	every	every	DET	DT	_	6	det	_	_
5	internal	internal	ADJ	JJ	Degree=Pos	6	amod	_	_
6	biequivalence	biequivalence	NOUN	NN	Number=Sing	11	nsubj	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	tricategory	tricategory	NOUN	NN	Number=Sing	7	pobj	_	_
10	$ T $	$ t $	SYM	$	_	11	nsubj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
12	part	part	NOUN	NN	Number=Sing	11	attr	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	biadjoint	biadjoint	NOUN	NN	Number=Sing	16	compound	_	_
16	biequivalence	biequivalence	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We give two applications of this result, one for transporting monoidal structures and one for equipping a monoidal bicategory with invertible objects with a coherent choice of those inverses.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	two	two	NUM	CD	NumType=Card	4	nummod	_	_
4	applications	application	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
7	result	result	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
9	one	one	NUM	CD	NumType=Card	4	appos	_	_
10	for	for	ADP	IN	_	9	prep	_	_
11	transporting	transport	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	pcomp	_	_
12	monoidal	monoidal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	structures	structure	NOUN	NNS	Number=Plur	11	dobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
15	one	one	NUM	CD	NumType=Card	9	conj	_	_
16	for	for	ADP	IN	_	15	prep	_	_
17	equipping	equip	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	pcomp	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	monoidal	monoidal	ADJ	JJ	Degree=Pos	20	amod	_	_
20	bicategory	bicategory	NOUN	NN	Number=Sing	17	dobj	_	_
21	with	with	ADP	IN	_	17	prep	_	_
22	invertible	invertible	ADJ	JJ	Degree=Pos	23	amod	_	_
23	objects	object	NOUN	NNS	Number=Plur	21	pobj	_	_
24	with	with	ADP	IN	_	23	prep	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
26	coherent	coherent	ADJ	JJ	Degree=Pos	27	amod	_	_
27	choice	choice	NOUN	NN	Number=Sing	24	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	those	those	DET	DT	Number=Plur|PronType=Dem	30	det	_	_
30	inverses	inverse	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 415
# sent_id = 1
# text = We find the injective hulls of partially ordered monoids in the category whose objects are po - monoids and submultiplicative order - preserving functions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	find	find	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	injective	injective	ADJ	JJ	Degree=Pos	5	amod	_	_
5	hulls	hull	NOUN	NNS	Number=Plur	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	partially	partially	ADV	RB	_	8	advmod	_	_
8	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	amod	_	_
9	monoids	monoid	NOUN	NNS	Number=Plur	6	pobj	_	_
10	in	in	ADP	IN	_	5	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
13	whose	whose	DET	WP$	Poss=Yes	14	poss	_	_
14	objects	object	NOUN	NNS	Number=Plur	15	nsubj	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	relcl	_	_
16	po	po	NOUN	NN	Number=Sing	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	monoids	monoid	NOUN	NNS	Number=Plur	15	attr	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	submultiplicative	submultiplicative	ADJ	JJ	Degree=Pos	24	amod	_	_
21	order	order	NOUN	NN	Number=Sing	23	npadvmod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	24	amod	_	_
24	functions	function	NOUN	NNS	Number=Plur	18	conj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = These injective hulls are with respect to a special class of monics called ``embeddings''.
1	These	these	DET	DT	Number=Plur|PronType=Dem	3	det	_	_
2	injective	injective	ADJ	JJ	Degree=Pos	3	amod	_	_
3	hulls	hull	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	with	with	ADP	IN	_	4	prep	_	_
6	respect	respect	NOUN	NN	Number=Sing	5	pobj	_	_
7	to	to	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	special	special	ADJ	JJ	Degree=Pos	10	amod	_	_
10	class	class	NOUN	NN	Number=Sing	7	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	monics	monic	NOUN	NNS	Number=Plur	11	pobj	_	_
13	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acl	_	_
14	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	16	punct	_	SpaceAfter=No
15	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	16	punct	_	SpaceAfter=No
16	embeddings	embedding	NOUN	NNS	Number=Plur	13	oprd	_	SpaceAfter=No
17	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	4	punct	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show as well that the injective objects with respect to these embeddings are precisely the quantales.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	as	as	ADV	RB	_	4	advmod	_	_
4	well	well	ADV	RB	Degree=Pos	2	advmod	_	_
5	that	that	SCONJ	IN	_	14	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	injective	injective	ADJ	JJ	Degree=Pos	8	amod	_	_
8	objects	object	NOUN	NNS	Number=Plur	14	nsubj	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	respect	respect	NOUN	NN	Number=Sing	9	pobj	_	_
11	to	to	ADP	IN	_	10	prep	_	_
12	these	these	DET	DT	Number=Plur|PronType=Dem	13	det	_	_
13	embeddings	embedding	NOUN	NNS	Number=Plur	11	pobj	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
15	precisely	precisely	ADV	RB	_	14	advmod	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	quantales	quantale	NOUN	NNS	Number=Plur	14	attr	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 416
# sent_id = 1
# text = Two categories are called Morita equivalent if the categories of functors from these categories to the category of sets are equivalent.
1	Two	two	NUM	CD	NumType=Card	2	nummod	_	_
2	categories	category	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	Morita	Morita	PROPN	NNP	Number=Sing	6	compound	_	_
6	equivalent	equivalent	ADJ	JJ	Degree=Pos	4	oprd	_	_
7	if	if	SCONJ	IN	_	20	mark	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	categories	category	NOUN	NNS	Number=Plur	20	nsubj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	functors	functor	NOUN	NNS	Number=Plur	10	pobj	_	_
12	from	from	ADP	IN	_	9	prep	_	_
13	these	these	DET	DT	Number=Plur|PronType=Dem	14	det	_	_
14	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	_
15	to	to	ADP	IN	_	9	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	sets	set	NOUN	NNS	Number=Plur	18	pobj	_	_
20	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	advcl	_	_
21	equivalent	equivalent	ADJ	JJ	Degree=Pos	20	acomp	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = We prove that congruence lattices of Morita equivalent small categories are isomorphic.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	11	mark	_	_
4	congruence	congruence	NOUN	NN	Number=Sing	5	compound	_	_
5	lattices	lattice	NOUN	NNS	Number=Plur	11	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Morita	Morita	PROPN	NNP	Number=Sing	10	nmod	_	_
8	equivalent	equivalent	ADJ	JJ	Degree=Pos	10	amod	_	_
9	small	small	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
12	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	11	acomp	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 417
# sent_id = 1
# text = The relative cell complexes with respect to a generating set of cofibrations are an important class of morphisms in any model structure.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	relative	relative	ADJ	JJ	Degree=Pos	3	amod	_	_
3	cell	cell	NOUN	NN	Number=Sing	4	compound	_	_
4	complexes	complexe	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	nsubj	_	_
5	with	with	ADP	IN	_	4	prep	_	_
6	respect	respect	NOUN	NN	Number=Sing	5	pobj	_	_
7	to	to	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	generating	generating	NOUN	NN	Number=Sing	10	amod	_	_
10	set	set	NOUN	NN	Number=Sing	7	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	cofibrations	cofibration	NOUN	NNS	Number=Plur	11	pobj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	important	important	ADJ	JJ	Degree=Pos	16	amod	_	_
16	class	class	NOUN	NN	Number=Sing	13	attr	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	morphisms	morphism	NOUN	NNS	Number=Plur	17	pobj	_	_
19	in	in	ADP	IN	_	16	prep	_	_
20	any	any	DET	DT	_	22	det	_	_
21	model	model	NOUN	NN	Number=Sing	22	compound	_	_
22	structure	structure	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 2
# text = In the particular case of the standard (algebraic) model structure on Top, we give a new expression of these morphisms by defining a category of relative cell complexes, which has a forgetful functor to the arrow category.
1	In	in	ADP	IN	_	17	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	particular	particular	ADJ	JJ	Degree=Pos	4	amod	_	_
4	case	case	NOUN	NN	Number=Sing	1	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
7	standard	standard	ADJ	JJ	Degree=Pos	12	amod	_	_
8	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
9	algebraic	algebraic	ADJ	JJ	Degree=Pos	11	amod	_	SpaceAfter=No
10	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	11	punct	_	_
11	model	model	NOUN	NN	Number=Sing	12	compound	_	_
12	structure	structure	NOUN	NN	Number=Sing	5	pobj	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	Top	Top	PROPN	NNP	Number=Sing	13	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
16	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	17	nsubj	_	_
17	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	new	new	ADJ	JJ	Degree=Pos	20	amod	_	_
20	expression	expression	NOUN	NN	Number=Sing	17	dobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	these	these	DET	DT	Number=Plur|PronType=Dem	23	det	_	_
23	morphisms	morphism	NOUN	NNS	Number=Plur	21	pobj	_	_
24	by	by	ADP	IN	_	17	prep	_	_
25	defining	define	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	24	pcomp	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	category	category	NOUN	NN	Number=Sing	25	dobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	relative	relative	ADJ	JJ	Degree=Pos	31	amod	_	_
30	cell	cell	NOUN	NN	Number=Sing	31	compound	_	_
31	complexes	complex	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
33	which	which	PRON	WDT	_	34	nsubj	_	_
34	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	31	relcl	_	_
35	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
36	forgetful	forgetful	ADJ	JJ	Degree=Pos	37	amod	_	_
37	functor	functor	NOUN	NN	Number=Sing	34	dobj	_	_
38	to	to	ADP	IN	_	34	prep	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
40	arrow	arrow	NOUN	NN	Number=Sing	41	compound	_	_
41	category	category	NOUN	NN	Number=Sing	38	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 3
# text = This allows us to prove a conjecture of Richard Garner: considering the algebraic weak factorisation system given in that algebraic model structure between cofibrations and trivial fibrations, we show that the category of relative cell complexes is equivalent to the category of coalgebras.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	31	ccomp	_	_
3	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	prove	prove	VERB	VB	VerbForm=Inf	2	ccomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	conjecture	conjecture	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	Richard	Richard	PROPN	NNP	Number=Sing	10	compound	_	_
10	Garner	Garner	PROPN	NNP	Number=Sing	8	pobj	_	SpaceAfter=No
11	:	:	PUNCT	:	_	2	punct	_	_
12	considering	consider	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
14	algebraic	algebraic	ADJ	JJ	Degree=Pos	17	amod	_	_
15	weak	weak	ADJ	JJ	Degree=Pos	17	amod	_	_
16	factorisation	factorisation	NOUN	NN	Number=Sing	17	compound	_	_
17	system	system	NOUN	NN	Number=Sing	12	dobj	_	_
18	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
19	in	in	ADP	IN	_	18	prep	_	_
20	that	that	DET	DT	Number=Sing|PronType=Dem	23	det	_	_
21	algebraic	algebraic	ADJ	JJ	Degree=Pos	22	amod	_	_
22	model	model	NOUN	NN	Number=Sing	23	compound	_	_
23	structure	structure	NOUN	NN	Number=Sing	19	pobj	_	_
24	between	between	ADP	IN	_	23	prep	_	_
25	cofibrations	cofibration	NOUN	NNS	Number=Plur	24	pobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	trivial	trivial	ADJ	JJ	Degree=Pos	28	amod	_	_
28	fibrations	fibration	NOUN	NNS	Number=Plur	25	conj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
30	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	31	nsubj	_	_
31	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
32	that	that	SCONJ	IN	_	39	mark	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
34	category	category	NOUN	NN	Number=Sing	39	nsubj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	relative	relative	ADJ	JJ	Degree=Pos	38	amod	_	_
37	cell	cell	NOUN	NN	Number=Sing	38	compound	_	_
38	complexes	complex	NOUN	NNS	Number=Plur	35	pobj	_	_
39	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	31	ccomp	_	_
40	equivalent	equivalent	ADJ	JJ	Degree=Pos	39	acomp	_	_
41	to	to	ADP	IN	_	40	prep	_	_
42	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
43	category	category	NOUN	NN	Number=Sing	41	pobj	_	_
44	of	of	ADP	IN	_	43	prep	_	_
45	coalgebras	coalgebras	PROPN	NNP	Number=Sing	44	pobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	31	punct	_	SpaceAfter=No

# doc_id = 418
# sent_id = 1
# text = For a generalisation of the classical theory of Hopf algebra over fields, Bruguièeres and Virelizier study opmonoidal monads on monoidal categories (which they called bimonads).
1	For	for	ADP	IN	_	0	ROOT	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	generalisation	generalisation	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	classical	classical	ADJ	JJ	Degree=Pos	7	amod	_	_
7	theory	theory	NOUN	NN	Number=Sing	4	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	Hopf	Hopf	PROPN	NNP	Number=Sing	10	compound	_	_
10	algebra	algebra	NOUN	NNS	Number=Plur	8	pobj	_	_
11	over	over	ADP	IN	_	10	prep	_	_
12	fields	field	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	Bruguièeres	Bruguièeres	PROPN	NNP	Number=Sing	17	nmod	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	Virelizier	Virelizier	PROPN	NNP	Number=Sing	14	conj	_	_
17	study	study	NOUN	NN	Number=Sing	19	nmod	_	_
18	opmonoidal	opmonoidal	ADJ	JJ	Degree=Pos	19	amod	_	_
19	monads	monad	NOUN	NNS	Number=Plur	12	conj	_	_
20	on	on	ADP	IN	_	19	prep	_	_
21	monoidal	monoidal	ADJ	JJ	Degree=Pos	22	amod	_	_
22	categories	category	NOUN	NNS	Number=Plur	20	pobj	_	_
23	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	22	punct	_	SpaceAfter=No
24	which	which	PRON	WDT	_	26	dobj	_	_
25	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	26	nsubj	_	_
26	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	22	relcl	_	_
27	bimonads	bimonad	NOUN	NNS	Number=Plur	26	dobj	_	SpaceAfter=No
28	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	1	punct	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = In a recent joint paper with Lack, the same authors define the notion of a pre - Hopf monad by requiring only a special form of the fusion operator to be invertible.
1	In	in	ADP	IN	_	12	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
3	recent	recent	ADJ	JJ	Degree=Pos	5	amod	_	_
4	joint	joint	ADJ	JJ	Degree=Pos	5	amod	_	_
5	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
6	with	with	ADP	IN	_	5	prep	_	_
7	Lack	Lack	PROPN	NNP	Number=Sing	6	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	same	same	ADJ	JJ	Degree=Pos	11	amod	_	_
11	authors	author	NOUN	NNS	Number=Plur	12	nsubj	_	_
12	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	notion	notion	NOUN	NN	Number=Sing	12	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
17	pre	pre	ADJ	JJ	Degree=Pos	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	Hopf	hopf	ADJ	JJ	Degree=Pos	20	amod	_	_
20	monad	monad	NOUN	NNS	Number=Plur	15	pobj	_	_
21	by	by	ADP	IN	_	12	prep	_	_
22	requiring	require	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	21	pcomp	_	_
23	only	only	ADV	RB	_	26	advmod	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
25	special	special	ADJ	JJ	Degree=Pos	26	amod	_	_
26	form	form	NOUN	NN	Number=Sing	22	dobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
29	fusion	fusion	NOUN	NN	Number=Sing	30	compound	_	_
30	operator	operator	NOUN	NN	Number=Sing	27	pobj	_	_
31	to	to	PART	TO	_	32	aux	_	_
32	be	be	AUX	VB	VerbForm=Inf	22	xcomp	_	_
33	invertible	invertible	ADJ	JJ	Degree=Pos	32	acomp	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 3
# text = In previous papers it was observed by the present authors that bimonads yield a special case of an entwining of a pair of functors (on arbitrary categories).
1	In	in	ADP	IN	_	6	prep	_	_
2	previous	previous	ADJ	JJ	Degree=Pos	3	amod	_	_
3	papers	paper	NOUN	NNS	Number=Plur	1	pobj	_	_
4	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	6	nsubjpass	_	_
5	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	6	auxpass	_	_
6	observed	observe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	by	by	ADP	IN	_	6	agent	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	present	present	ADJ	JJ	Degree=Pos	10	amod	_	_
10	authors	author	NOUN	NNS	Number=Plur	7	pobj	_	_
11	that	that	PRON	WDT	PronType=Rel	13	nsubj	_	_
12	bimonads	bimonad	NOUN	NNS	Number=Plur	13	nsubj	_	_
13	yield	yield	VERB	VBP	Tense=Pres|VerbForm=Fin	10	relcl	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	special	special	ADJ	JJ	Degree=Pos	16	amod	_	_
16	case	case	NOUN	NN	Number=Sing	13	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	an	an	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	entwining	entwining	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	pair	pair	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	functors	functor	NOUN	NNS	Number=Plur	23	pobj	_	_
25	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	22	punct	_	SpaceAfter=No
26	on	on	ADP	IN	_	22	prep	_	_
27	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	28	amod	_	_
28	categories	category	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
29	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	6	punct	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = The purpose of this note is to show that in this setting the pre - Hopf monads are a special case of Galois entwinings.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	purpose	purpose	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	note	note	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	show	show	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	that	that	SCONJ	IN	_	18	mark	_	_
10	in	in	ADP	IN	_	18	prep	_	_
11	this	this	PRON	DT	Number=Sing|PronType=Dem	10	pobj	_	_
12	setting	set	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	acl	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
14	pre	pre	ADJ	JJ	Degree=Pos	16	compound	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	Hopf	hopf	ADJ	JJ	Degree=Pos	17	compound	_	_
17	monads	monad	NOUN	NNS	Number=Plur	12	dobj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	ccomp	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	special	special	ADJ	JJ	Degree=Pos	21	amod	_	_
21	case	case	NOUN	NN	Number=Sing	18	attr	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	Galois	Galois	PROPN	NNP	Number=Sing	24	compound	_	_
24	entwinings	entwining	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = As a byproduct some new properties are detected which make a (general) bimonad on a Cauchy complete category to a Hopf monad.
1	As	as	ADP	IN	_	8	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	byproduct	byproduct	NOUN	NN	Number=Sing	1	pobj	_	_
4	some	some	DET	DT	_	6	det	_	_
5	new	new	ADJ	JJ	Degree=Pos	6	amod	_	_
6	properties	property	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	detected	detect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	which	which	PRON	WDT	_	10	nsubj	_	_
10	make	make	VERB	VBP	Tense=Pres|VerbForm=Fin	6	relcl	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
12	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	15	punct	_	SpaceAfter=No
13	general	general	ADJ	JJ	Degree=Pos	15	amod	_	SpaceAfter=No
14	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	15	punct	_	_
15	bimonad	bimonad	NOUN	NNS	Number=Plur	10	dobj	_	_
16	on	on	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
18	Cauchy	cauchy	ADJ	JJ	Degree=Pos	20	nmod	_	_
19	complete	complete	ADJ	JJ	Degree=Pos	20	amod	_	_
20	category	category	NOUN	NN	Number=Sing	16	pobj	_	_
21	to	to	ADP	IN	_	10	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
23	Hopf	Hopf	PROPN	NNP	Number=Sing	24	compound	_	_
24	monad	monad	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 6
# text = In the final section applications to cartesian monoidal categories are considered.
1	In	in	ADP	IN	_	11	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
3	final	final	ADJ	JJ	Degree=Pos	5	amod	_	_
4	section	section	NOUN	NN	Number=Sing	5	compound	_	_
5	applications	application	NOUN	NNS	Number=Plur	1	pobj	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	cartesian	cartesian	ADJ	JJ	Degree=Pos	9	amod	_	_
8	monoidal	monoidal	ADJ	JJ	Degree=Pos	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# doc_id = 419
# sent_id = 1
# text = Tannaka duality describes the relationship between algebraic objects in a given category and functors into that category; an important case is that of Hopf algebras and their categories of representations; these have strong monoidal forgetful ``fibre functors'' to the category of vector spaces.
1	Tannaka	Tannaka	PROPN	NNP	Number=Sing	2	compound	_	_
2	duality	duality	NOUN	NN	Number=Sing	3	nsubj	_	_
3	describes	describe	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	ccomp	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	relationship	relationship	NOUN	NN	Number=Sing	3	dobj	_	_
6	between	between	ADP	IN	_	5	prep	_	_
7	algebraic	algebraic	ADJ	JJ	Degree=Pos	8	amod	_	_
8	objects	object	NOUN	NNS	Number=Plur	6	pobj	_	_
9	in	in	ADP	IN	_	3	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
12	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	functors	functor	NOUN	NNS	Number=Plur	12	conj	_	_
15	into	into	ADP	IN	_	12	prep	_	_
16	that	that	DET	DT	Number=Sing|PronType=Dem	17	det	_	_
17	category	category	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
18	;	;	PUNCT	:	_	22	punct	_	_
19	an	an	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	important	important	ADJ	JJ	Degree=Pos	21	amod	_	_
21	case	case	NOUN	NN	Number=Sing	22	nsubj	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	34	ccomp	_	_
23	that	that	PRON	DT	Number=Sing|PronType=Dem	22	nsubj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	Hopf	Hopf	PROPN	NNP	Number=Sing	26	compound	_	_
26	algebras	algebra	NOUN	NNS	Number=Plur	24	pobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	29	poss	_	_
29	categories	category	NOUN	NNS	Number=Plur	26	conj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	representations	representation	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
32	;	;	PUNCT	:	_	34	punct	_	_
33	these	these	PRON	DT	Number=Plur|PronType=Dem	34	nsubj	_	_
34	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
35	strong	strong	ADJ	JJ	Degree=Pos	41	amod	_	_
36	monoidal	monoidal	ADJ	JJ	Degree=Pos	41	amod	_	_
37	forgetful	forgetful	ADJ	JJ	Degree=Pos	41	amod	_	_
38	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	41	punct	_	SpaceAfter=No
39	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	41	punct	_	SpaceAfter=No
40	fibre	fibre	NOUN	NN	Number=Sing	41	compound	_	_
41	functors	functor	NOUN	NNS	Number=Plur	34	dobj	_	SpaceAfter=No
42	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	41	punct	_	_
43	to	to	ADP	IN	_	34	prep	_	_
44	the	the	DET	DT	Definite=Def|PronType=Art	45	det	_	_
45	category	category	NOUN	NN	Number=Sing	43	pobj	_	_
46	of	of	ADP	IN	_	45	prep	_	_
47	vector	vector	NOUN	NN	Number=Sing	48	compound	_	_
48	spaces	space	NOUN	NNS	Number=Plur	46	pobj	_	SpaceAfter=No
49	.	.	PUNCT	.	PunctType=Peri	34	punct	_	SpaceAfter=No

# sent_id = 2
# text = We simultaneously generalize the theory of Tannaka duality in two ways: first, we replace Hopf algebras with weak Hopf algebras and strong monoidal functors with separable Frobenius monoidal functors; second, we replace the category of vector spaces with an arbitrary braided monoidal category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	simultaneously	simultaneously	ADV	RB	_	3	advmod	_	_
3	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	16	ccomp	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	theory	theory	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Tannaka	Tannaka	PROPN	NNP	Number=Sing	8	compound	_	_
8	duality	duality	NOUN	NN	Number=Sing	6	pobj	_	_
9	in	in	ADP	IN	_	3	prep	_	_
10	two	two	NUM	CD	NumType=Card	11	nummod	_	_
11	ways	way	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
12	:	:	PUNCT	:	_	16	punct	_	_
13	first	first	ADV	RB	_	16	advmod	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
15	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	16	nsubj	_	_
16	replace	replace	VERB	VBP	Tense=Pres|VerbForm=Fin	36	ccomp	_	_
17	Hopf	Hopf	PROPN	NNP	Number=Sing	18	compound	_	_
18	algebras	algebra	NOUN	NNS	Number=Plur	16	dobj	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	weak	weak	ADJ	JJ	Degree=Pos	22	amod	_	_
21	Hopf	Hopf	PROPN	NNP	Number=Sing	22	compound	_	_
22	algebras	algebra	NOUN	NNS	Number=Plur	19	pobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	strong	strong	ADJ	JJ	Degree=Pos	26	amod	_	_
25	monoidal	monoidal	ADJ	JJ	Degree=Pos	26	amod	_	_
26	functors	functor	NOUN	NNS	Number=Plur	22	conj	_	_
27	with	with	ADP	IN	_	26	prep	_	_
28	separable	separable	ADJ	JJ	Degree=Pos	31	amod	_	_
29	Frobenius	Frobenius	PROPN	NNP	Number=Sing	31	compound	_	_
30	monoidal	monoidal	NOUN	NN	Number=Sing	31	compound	_	_
31	functors	functor	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
32	;	;	PUNCT	:	_	36	punct	_	_
33	second	second	X	LS	NumType=Ord	36	advmod	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
35	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	36	nsubj	_	_
36	replace	replace	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	category	category	NOUN	NN	Number=Sing	36	dobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	vector	vector	NOUN	NN	Number=Sing	41	compound	_	_
41	spaces	space	NOUN	NNS	Number=Plur	39	pobj	_	_
42	with	with	ADP	IN	_	38	prep	_	_
43	an	an	DET	DT	Definite=Ind|PronType=Art	47	det	_	_
44	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	47	amod	_	_
45	braided	braid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	47	amod	_	_
46	monoidal	monoidal	ADJ	JJ	Degree=Pos	47	amod	_	_
47	category	category	NOUN	NN	Number=Sing	42	pobj	_	SpaceAfter=No
48	.	.	PUNCT	.	PunctType=Peri	36	punct	_	SpaceAfter=No

# sent_id = 3
# text = To accomplish this goal, we make use of a graphical notation for functors between monoidal categories, using string diagrams with coloured regions.
1	To	to	PART	TO	_	2	aux	_	_
2	accomplish	accomplish	VERB	VB	VerbForm=Inf	7	advcl	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	goal	goal	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	make	make	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	use	use	NOUN	NN	Number=Sing	7	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	graphical	graphical	ADJ	JJ	Degree=Pos	12	amod	_	_
12	notation	notation	NOUN	NN	Number=Sing	9	pobj	_	_
13	for	for	ADP	IN	_	12	prep	_	_
14	functors	functor	NOUN	NNS	Number=Plur	13	pobj	_	_
15	between	between	ADP	IN	_	14	prep	_	_
16	monoidal	monoidal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
19	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	advcl	_	_
20	string	string	NOUN	NN	Number=Sing	21	compound	_	_
21	diagrams	diagram	NOUN	NNS	Number=Plur	19	dobj	_	_
22	with	with	ADP	IN	_	21	prep	_	_
23	coloured	coloured	ADJ	JJ	Degree=Pos	24	amod	_	_
24	regions	region	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = Not only does this notation extend our capacity to give simple proofs of complicated calculations, it makes plain some of the connections between Frobenius monoidal or separable Frobenius monoidal functors and the topology of the axioms defining certain algebraic structures.
1	Not	not	PART	RB	Polarity=Neg	6	preconj	_	_
2	only	only	ADV	RB	_	1	advmod	_	_
3	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	aux	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	notation	notation	NOUN	NN	Number=Sing	6	nsubj	_	_
6	extend	extend	VERB	VB	VerbForm=Inf	18	ccomp	_	_
7	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	8	poss	_	_
8	capacity	capacity	NOUN	NN	Number=Sing	6	dobj	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	give	give	VERB	VB	VerbForm=Inf	8	acl	_	_
11	simple	simple	ADJ	JJ	Degree=Pos	12	amod	_	_
12	proofs	proof	NOUN	NNS	Number=Plur	10	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	complicated	complicated	ADJ	JJ	Degree=Pos	15	amod	_	_
15	calculations	calculation	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
17	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	18	nsubj	_	_
18	makes	make	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
19	plain	plain	ADJ	JJ	Degree=Pos	20	amod	_	_
20	some	some	PRON	DT	_	18	dobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	connections	connection	NOUN	NNS	Number=Plur	21	pobj	_	_
24	between	between	ADP	IN	_	23	prep	_	_
25	Frobenius	Frobenius	PROPN	NNP	Number=Sing	26	compound	_	_
26	monoidal	monoidal	NOUN	NN	Number=Sing	24	pobj	_	_
27	or	or	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	separable	separable	ADJ	JJ	Degree=Pos	31	amod	_	_
29	Frobenius	Frobenius	PROPN	NNP	Number=Sing	31	compound	_	_
30	monoidal	monoidal	NOUN	NN	Number=Sing	31	amod	_	_
31	functors	functor	NOUN	NNS	Number=Plur	26	conj	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
34	topology	topology	NOUN	NN	Number=Sing	31	conj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	axioms	axiom	NOUN	NNS	Number=Plur	35	pobj	_	_
38	defining	define	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	37	acl	_	_
39	certain	certain	ADJ	JJ	Degree=Pos	41	amod	_	_
40	algebraic	algebraic	ADJ	JJ	Degree=Pos	41	amod	_	_
41	structures	structure	NOUN	NNS	Number=Plur	38	dobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# sent_id = 5
# text = Finally, having generalized Tannaka duality to an arbitrary base category, we briefly discuss the functoriality of the construction as this base is varied.
1	Finally	finally	ADV	RB	_	15	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
3	having	having	AUX	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	aux	_	_
4	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	advcl	_	_
5	Tannaka	Tannaka	PROPN	NNP	Number=Sing	6	compound	_	_
6	duality	duality	NOUN	NN	Number=Sing	4	dobj	_	_
7	to	to	ADP	IN	_	4	prep	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	11	amod	_	_
10	base	base	NOUN	NN	Number=Sing	11	compound	_	_
11	category	category	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	15	nsubj	_	_
14	briefly	briefly	ADV	RB	_	15	advmod	_	_
15	discuss	discuss	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	functoriality	functoriality	NOUN	NN	Number=Sing	15	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	construction	construction	NOUN	NN	Number=Sing	18	pobj	_	_
21	as	as	SCONJ	IN	_	24	mark	_	_
22	this	this	DET	DT	Number=Sing|PronType=Dem	23	det	_	_
23	base	base	NOUN	NN	Number=Sing	24	nsubj	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	advcl	_	_
25	varied	varied	ADJ	JJ	Degree=Pos	24	acomp	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# doc_id = 420
# sent_id = 1
# text = In this note we provide a characterization, in terms of additional algebraic structure, of those strict intervals (certain cocategory objects) in a symmetric monoidal closed category $ cal E $ that are representable in the sense of inducing on $ cal E $ the structure of a finitely bicomplete 2 - category.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	note	note	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	characterization	characterization	NOUN	NN	Number=Sing	5	dobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
9	in	in	ADP	IN	_	5	prep	_	_
10	terms	term	NOUN	NNS	Number=Plur	9	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	additional	additional	ADJ	JJ	Degree=Pos	14	amod	_	_
13	algebraic	algebraic	ADJ	JJ	Degree=Pos	14	amod	_	_
14	structure	structure	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	of	of	ADP	IN	_	14	prep	_	_
17	those	those	DET	DT	Number=Plur|PronType=Dem	19	det	_	_
18	strict	strict	ADJ	JJ	Degree=Pos	19	amod	_	_
19	intervals	interval	NOUN	NNS	Number=Plur	16	pobj	_	_
20	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	19	punct	_	SpaceAfter=No
21	certain	certain	ADJ	JJ	Degree=Pos	23	amod	_	_
22	cocategory	cocategory	NOUN	NN	Number=Sing	23	compound	_	_
23	objects	object	NOUN	NNS	Number=Plur	19	appos	_	SpaceAfter=No
24	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	19	punct	_	_
25	in	in	ADP	IN	_	5	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
27	symmetric	symmetric	ADJ	JJ	Degree=Pos	28	amod	_	_
28	monoidal	monoidal	NOUN	NN	Number=Sing	25	pobj	_	_
29	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	5	conj	_	_
30	category	category	NOUN	NN	Number=Sing	29	dobj	_	_
31	$ cal E $	$ cal e $	SYM	$	_	29	dep	_	_
32	that	that	PRON	WDT	PronType=Rel	33	nsubj	_	_
33	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	31	relcl	_	_
34	representable	representable	ADJ	JJ	Degree=Pos	33	acomp	_	_
35	in	in	ADP	IN	_	34	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	sense	sense	NOUN	NN	Number=Sing	35	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	inducing	induce	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	38	pcomp	_	_
40	on	on	ADP	RP	_	39	prt	_	_
41	$ cal E $	$ cal e $	SYM	$	_	29	prep	_	_
42	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
43	structure	structure	NOUN	NN	Number=Sing	29	dobj	_	_
44	of	of	ADP	IN	_	43	prep	_	_
45	a	a	DET	DT	Definite=Ind|PronType=Art	50	det	_	_
46	finitely	finitely	ADV	RB	_	47	advmod	_	_
47	bicomplete	bicomplete	ADJ	JJ	Degree=Pos	50	amod	_	_
48	2	2	NUM	CD	NumType=Card	50	nummod	_	_
49	-	-	PUNCT	HYPH	PunctType=Dash	50	punct	_	_
50	category	category	NOUN	NN	Number=Sing	44	pobj	_	SpaceAfter=No
51	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = Several examples and connections with the homotopy theory of 2 - categories are also discussed.
1	Several	several	ADJ	JJ	Degree=Pos	2	amod	_	_
2	examples	example	NOUN	NNS	Number=Plur	15	nsubjpass	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	connections	connection	NOUN	NNS	Number=Plur	2	conj	_	_
5	with	with	ADP	IN	_	2	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	homotopy	homotopy	NOUN	NN	Number=Sing	8	compound	_	_
8	theory	theory	NOUN	NN	Number=Sing	5	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	2	2	NUM	CD	NumType=Card	12	nummod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
14	also	also	ADV	RB	_	15	advmod	_	_
15	discussed	discuss	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# doc_id = 421
# sent_id = 1
# text = We develop an alternative approach to star - autonomous comonads via linearly distributive categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	alternative	alternative	ADJ	JJ	Degree=Pos	5	amod	_	_
5	approach	approach	NOUN	NN	Number=Sing	2	dobj	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	star	star	NOUN	NN	Number=Sing	9	npadvmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	autonomous	autonomous	ADJ	JJ	Degree=Pos	10	amod	_	_
10	comonads	comonad	NOUN	NNS	Number=Plur	6	pobj	_	_
11	via	via	ADP	IN	_	5	prep	_	_
12	linearly	linearly	ADV	RB	_	13	advmod	_	_
13	distributive	distributive	ADJ	JJ	Degree=Pos	14	amod	_	_
14	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = It is shown that in the autonomous case the notions of star - autonomous comonad and Hopf comonad coincide.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	SCONJ	IN	_	10	mark	_	_
5	in	in	ADP	IN	_	10	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	autonomous	autonomous	ADJ	JJ	Degree=Pos	8	amod	_	_
8	case	case	NOUN	NN	Number=Sing	5	pobj	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	notions	notion	NOUN	NNS	Number=Plur	3	ccomp	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	star	star	NOUN	NN	Number=Sing	14	npadvmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	autonomous	autonomous	ADJ	JJ	Degree=Pos	15	amod	_	_
15	comonad	comonad	NOUN	NNS	Number=Plur	11	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	Hopf	Hopf	PROPN	NNP	Number=Sing	18	compound	_	_
18	comonad	comonad	NOUN	NNS	Number=Plur	19	compound	_	_
19	coincide	coincide	NOUN	NN	Number=Sing	15	conj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 422
# sent_id = 1
# text = We give characterizations, for various fragments of geometric logic, of the class of theories classified by a locally connected (respectively connected and locally connected, atomic, compact, presheaf) topos, and exploit the existence of multiple sites of definition for a given topos to establish various results on quotients of theories of presheaf type.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	characterizations	characterization	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
5	for	for	ADP	IN	_	2	prep	_	_
6	various	various	ADJ	JJ	Degree=Pos	7	amod	_	_
7	fragments	fragment	NOUN	NNS	Number=Plur	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	geometric	geometric	ADJ	JJ	Degree=Pos	10	amod	_	_
10	logic	logic	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
12	of	of	ADP	IN	_	7	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	class	class	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	theories	theory	NOUN	NNS	Number=Plur	15	pobj	_	_
17	classified	classify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	acl	_	_
18	by	by	ADP	IN	_	17	agent	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
20	locally	locally	ADV	RB	_	21	advmod	_	_
21	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	35	amod	_	_
22	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	35	punct	_	SpaceAfter=No
23	respectively	respectively	ADV	RB	_	24	advmod	_	_
24	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	35	amod	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	locally	locally	ADV	RB	_	27	advmod	_	_
27	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	conj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
29	atomic	atomic	ADJ	JJ	Degree=Pos	33	amod	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
31	compact	compact	ADJ	JJ	Degree=Pos	29	conj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
33	presheaf	presheaf	ADJ	JJ	Degree=Pos	35	amod	_	SpaceAfter=No
34	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	35	punct	_	_
35	topos	topos	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
37	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
38	exploit	exploit	VERB	VB	VerbForm=Inf	2	conj	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
40	existence	existence	NOUN	NN	Number=Sing	38	dobj	_	_
41	of	of	ADP	IN	_	40	prep	_	_
42	multiple	multiple	ADJ	JJ	Degree=Pos	43	amod	_	_
43	sites	site	NOUN	NNS	Number=Plur	41	pobj	_	_
44	of	of	ADP	IN	_	43	prep	_	_
45	definition	definition	NOUN	NN	Number=Sing	44	pobj	_	_
46	for	for	ADP	IN	_	38	prep	_	_
47	a	a	DET	DT	Definite=Ind|PronType=Art	49	det	_	_
48	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	49	amod	_	_
49	topos	topo	NOUN	NNS	Number=Plur	46	pobj	_	_
50	to	to	PART	TO	_	51	aux	_	_
51	establish	establish	VERB	VB	VerbForm=Inf	38	advcl	_	_
52	various	various	ADJ	JJ	Degree=Pos	53	amod	_	_
53	results	result	NOUN	NNS	Number=Plur	51	dobj	_	_
54	on	on	ADP	IN	_	51	prep	_	_
55	quotients	quotient	NOUN	NNS	Number=Plur	54	pobj	_	_
56	of	of	ADP	IN	_	55	prep	_	_
57	theories	theory	NOUN	NNS	Number=Plur	56	pobj	_	_
58	of	of	ADP	IN	_	57	prep	_	_
59	presheaf	presheaf	ADJ	JJ	Degree=Pos	60	amod	_	_
60	type	type	NOUN	NN	Number=Sing	58	pobj	_	SpaceAfter=No
61	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 423
# sent_id = 1
# text = We prove that the 2 - category of closed categories of Eilenberg and Kelly is equivalent to a suitable full 2 - subcategory of the 2 - category of closed multicategories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	15	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	2	2	NUM	CD	NumType=Card	7	nummod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	category	category	NOUN	NN	Number=Sing	15	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	closed	closed	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	11	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	Kelly	Kelly	PROPN	NNP	Number=Sing	12	conj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
16	equivalent	equivalent	ADJ	JJ	Degree=Pos	15	acomp	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
19	suitable	suitable	ADJ	JJ	Degree=Pos	23	amod	_	_
20	full	full	ADJ	JJ	Degree=Pos	23	amod	_	_
21	2	2	NUM	CD	NumType=Card	23	nummod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	subcategory	subcategory	NOUN	NN	Number=Sing	17	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
26	2	2	NUM	CD	NumType=Card	28	nummod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	category	category	NOUN	NN	Number=Sing	24	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	closed	closed	ADJ	JJ	Degree=Pos	31	amod	_	_
31	multicategories	multicategorie	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 424
# sent_id = 1
# text = It is shown how the theory of commutative monads provides an axiomatic framework for several aspects of distribution theory in a broad sense, including probability distributions, physical extensive quantities, and Schwartz distributions of compact support.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	how	how	SCONJ	WRB	_	10	advmod	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	theory	theory	NOUN	NN	Number=Sing	10	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	commutative	commutative	ADJ	JJ	Degree=Pos	9	amod	_	_
9	monads	monad	NOUN	NNS	Number=Plur	7	pobj	_	_
10	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
11	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	axiomatic	axiomatic	ADJ	JJ	Degree=Pos	13	amod	_	_
13	framework	framework	NOUN	NN	Number=Sing	10	dobj	_	_
14	for	for	ADP	IN	_	13	prep	_	_
15	several	several	ADJ	JJ	Degree=Pos	16	amod	_	_
16	aspects	aspect	NOUN	NNS	Number=Plur	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	distribution	distribution	NOUN	NN	Number=Sing	19	compound	_	_
19	theory	theory	NOUN	NN	Number=Sing	17	pobj	_	_
20	in	in	ADP	IN	_	10	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	broad	broad	ADJ	JJ	Degree=Pos	23	amod	_	_
23	sense	sense	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
25	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	prep	_	_
26	probability	probability	NOUN	NN	Number=Sing	27	compound	_	_
27	distributions	distribution	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
29	physical	physical	ADJ	JJ	Degree=Pos	31	amod	_	_
30	extensive	extensive	ADJ	JJ	Degree=Pos	31	amod	_	_
31	quantities	quantity	NOUN	NNS	Number=Plur	27	conj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
34	Schwartz	Schwartz	PROPN	NNP	Number=Sing	35	compound	_	_
35	distributions	distribution	NOUN	NNS	Number=Plur	31	conj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	compact	compact	ADJ	JJ	Degree=Pos	38	amod	_	_
38	support	support	NOUN	NN	Number=Sing	36	pobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = Among the particular aspects considered here are the notions of convolution, density, expectation, and conditional probability.
1	Among	among	ADP	IN	_	7	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	particular	particular	ADJ	JJ	Degree=Pos	4	amod	_	_
4	aspects	aspect	NOUN	NNS	Number=Plur	1	pobj	_	_
5	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	acl	_	_
6	here	here	ADV	RB	PronType=Dem	5	advmod	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	notions	notion	NOUN	NNS	Number=Plur	7	nsubj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	convolution	convolution	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	density	density	NOUN	NN	Number=Sing	11	conj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	expectation	expectation	NOUN	NN	Number=Sing	13	conj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
18	conditional	conditional	ADJ	JJ	Degree=Pos	19	amod	_	_
19	probability	probability	NOUN	NN	Number=Sing	15	conj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 425
# sent_id = 1
# text = We construct, for any double complex in an abelian category, certain ``short - distance'' maps, and an exact sequence involving these, instances of which can be pieced together to give the ``long - distance'' maps and exact sequences of results such as the Snake Lemma.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
4	for	for	ADP	IN	_	2	prep	_	_
5	any	any	DET	DT	_	7	det	_	_
6	double	double	ADJ	JJ	Degree=Pos	7	amod	_	_
7	complex	complex	NOUN	NN	Number=Sing	4	pobj	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	abelian	abelian	ADJ	JJ	Degree=Pos	11	amod	_	_
11	category	category	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
13	certain	certain	ADJ	JJ	Degree=Pos	20	amod	_	_
14	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	20	punct	_	SpaceAfter=No
15	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	20	punct	_	SpaceAfter=No
16	short	short	ADJ	JJ	Degree=Pos	18	amod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	distance	distance	NOUN	NN	Number=Sing	20	nmod	_	SpaceAfter=No
19	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	20	punct	_	_
20	maps	map	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
23	an	an	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	exact	exact	ADJ	JJ	Degree=Pos	25	amod	_	_
25	sequence	sequence	NOUN	NN	Number=Sing	20	conj	_	_
26	involving	involve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	25	acl	_	_
27	these	these	PRON	DT	Number=Plur|PronType=Dem	26	dobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	34	punct	_	_
29	instances	instance	NOUN	NNS	Number=Plur	34	nsubjpass	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	which	which	PRON	WDT	_	30	pobj	_	_
32	can	can	AUX	MD	VerbForm=Fin	34	aux	_	_
33	be	be	AUX	VB	VerbForm=Inf	34	auxpass	_	_
34	pieced	piece	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
35	together	together	ADV	RB	_	34	advmod	_	_
36	to	to	PART	TO	_	37	aux	_	_
37	give	give	VERB	VB	VerbForm=Inf	34	xcomp	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	45	det	_	_
39	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	45	punct	_	SpaceAfter=No
40	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	45	punct	_	SpaceAfter=No
41	long	long	ADJ	JJ	Degree=Pos	43	amod	_	_
42	-	-	PUNCT	HYPH	PunctType=Dash	43	punct	_	_
43	distance	distance	NOUN	NN	Number=Sing	45	nmod	_	SpaceAfter=No
44	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	45	punct	_	_
45	maps	map	NOUN	NNS	Number=Plur	37	dobj	_	_
46	and	and	CCONJ	CC	ConjType=Cmp	45	cc	_	_
47	exact	exact	ADJ	JJ	Degree=Pos	48	amod	_	_
48	sequences	sequence	NOUN	NNS	Number=Plur	45	conj	_	_
49	of	of	ADP	IN	_	45	prep	_	_
50	results	result	NOUN	NNS	Number=Plur	49	pobj	_	_
51	such	such	ADJ	JJ	Degree=Pos	52	amod	_	_
52	as	as	ADP	IN	_	50	prep	_	_
53	the	the	DET	DT	Definite=Def|PronType=Art	55	det	_	_
54	Snake	Snake	PROPN	NNP	Number=Sing	55	compound	_	_
55	Lemma	Lemma	PROPN	NNP	Number=Sing	52	pobj	_	SpaceAfter=No
56	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Further applications are given.
1	Further	further	ADJ	JJ	Degree=Pos	2	amod	_	_
2	applications	application	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
5	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also note what the building blocks of an analogous study of triple complexes would be.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	note	note	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	what	what	PRON	WP	_	16	attr	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	building	building	NOUN	NN	Number=Sing	7	compound	_	_
7	blocks	block	NOUN	NNS	Number=Plur	16	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	analogous	analogous	ADJ	JJ	Degree=Pos	11	amod	_	_
11	study	study	NOUN	NN	Number=Sing	8	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	triple	triple	ADJ	JJ	Degree=Pos	14	amod	_	_
14	complexes	complex	NOUN	NNS	Number=Plur	12	pobj	_	_
15	would	would	AUX	MD	VerbForm=Fin	16	aux	_	_
16	be	be	AUX	VB	VerbForm=Inf	3	ccomp	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 426
# sent_id = 1
# text = Based on a study of the 2 - category of weak distributive laws, we describe a method of iterating Street's weak wreath product construction.
1	Based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	prep	_	_
2	on	on	ADP	IN	_	1	prep	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	study	study	NOUN	NN	Number=Sing	2	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
7	2	2	NUM	CD	NumType=Card	9	nummod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	weak	weak	ADJ	JJ	Degree=Pos	13	amod	_	_
12	distributive	distributive	ADJ	JJ	Degree=Pos	13	amod	_	_
13	laws	law	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
15	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	16	nsubj	_	_
16	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	method	method	NOUN	NN	Number=Sing	16	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	iterating	iterate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	pcomp	_	_
21	Street	Street	PROPN	NNP	Number=Sing	26	poss	_	SpaceAfter=No
22	's	's	PART	POS	_	21	case	_	_
23	weak	weak	ADJ	JJ	Degree=Pos	26	amod	_	_
24	wreath	wreath	NOUN	NN	Number=Sing	25	compound	_	_
25	product	product	NOUN	NN	Number=Sing	26	compound	_	_
26	construction	construction	NOUN	NN	Number=Sing	20	dobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 2
# text = That is, for any 2 - category $ cal K $ and for any non - negative integer $ n $ , we introduce 2 - categories $ Wdl^{(n)}(cal K) $ , of $ (n+1) $ - tuples of monads in $ cal K $ pairwise related by weak distributive laws obeying the Yang - Baxter equation.
1	That	that	ADV	RB	_	2	advmod	_	_
2	is	is	ADV	RB	_	20	advmod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
4	for	for	ADP	IN	_	20	prep	_	_
5	any	any	DET	DT	_	8	det	_	_
6	2	2	NUM	CD	NumType=Card	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
9	$ cal K $	$ cal k $	SYM	$	_	8	nummod	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
11	for	for	ADP	IN	_	4	conj	_	_
12	any	any	DET	DT	_	16	det	_	_
13	non	non	ADJ	JJ	Degree=Pos	15	amod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	negative	negative	ADJ	JJ	Degree=Pos	16	amod	_	_
16	integer	integer	NOUN	NN	Number=Sing	11	pobj	_	_
17	$ n $	$ n $	SYM	$	_	16	appos	_	_
18	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
19	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	20	nsubj	_	_
20	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
21	2	2	NUM	CD	NumType=Card	23	nummod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	categories	category	NOUN	NNS	Number=Plur	24	compound	_	_
24	$ Wdl^{(n)}(cal K) $	$ wdl^{(n)}(cal k) $	SYM	$	_	20	dobj	_	_
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	of	of	ADP	IN	_	24	prep	_	_
27	$ (n+1) $	$ (n+1) $	SYM	$	_	29	compound	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	tuples	tuple	NOUN	NNS	Number=Plur	26	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	monads	monad	NOUN	NNS	Number=Plur	30	pobj	_	_
32	in	in	ADP	IN	_	29	prep	_	_
33	$ cal K $	$ cal k $	SYM	$	_	34	nmod	_	_
34	pairwise	pairwise	NOUN	NN	Number=Sing	32	pobj	_	_
35	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	34	acl	_	_
36	by	by	ADP	IN	_	35	agent	_	_
37	weak	weak	ADJ	JJ	Degree=Pos	39	amod	_	_
38	distributive	distributive	ADJ	JJ	Degree=Pos	39	amod	_	_
39	laws	law	NOUN	NNS	Number=Plur	36	pobj	_	_
40	obeying	obey	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	39	acl	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	45	det	_	_
42	Yang	Yang	PROPN	NNP	Number=Sing	44	compound	_	_
43	-	-	PUNCT	HYPH	PunctType=Dash	44	punct	_	_
44	Baxter	Baxter	PROPN	NNP	Number=Sing	45	compound	_	_
45	equation	equation	NOUN	NN	Number=Sing	40	dobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 3
# text = The first instance $ Wdl^{(0)}(cal K) $ coincides with $ Mnd(cal K) $ , the usual 2 - category of monads in $ cal K $ , and for other values of $ n $ , $ Wdl^{(n)}(cal K) $ contains $ Mnd^{n+1}(cK) $ as a full 2 - subcategory.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	first	first	ADJ	JJ	Degree=Pos	3	amod	_	_
3	instance	instance	NOUN	NN	Number=Sing	5	nsubj	_	_
4	$ Wdl^{(0)}(cal K) $	$ wdl^{(0)}(cal k) $	SYM	$	_	5	nsubj	_	_
5	coincides	coincide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	with	with	ADP	IN	_	5	prep	_	_
7	$ Mnd(cal K) $	$ mnd(cal k) $	SYM	$	_	6	pobj	_	_
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
10	usual	usual	ADJ	JJ	Degree=Pos	13	amod	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	category	category	NOUN	NN	Number=Sing	7	appos	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	monads	monad	NOUN	NNS	Number=Plur	14	pobj	_	_
16	in	in	ADP	IN	_	13	prep	_	_
17	$ cal K $	$ cal k $	SYM	$	_	16	pobj	_	_
18	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
20	for	for	ADP	IN	_	27	prep	_	_
21	other	other	ADJ	JJ	Degree=Pos	22	amod	_	_
22	values	value	NOUN	NNS	Number=Plur	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	$ n $	$ n $	SYM	$	_	23	pobj	_	_
25	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
26	$ Wdl^{(n)}(cal K) $	$ wdl^{(n)}(cal k) $	SYM	$	_	27	nsubj	_	_
27	contains	contain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	conj	_	_
28	$ Mnd^{n+1}(cK) $	$ mnd^{n+1}(ck) $	SYM	$	_	27	dep	_	_
29	as	as	ADP	IN	_	28	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
31	full	full	ADJ	JJ	Degree=Pos	34	amod	_	_
32	2	2	NUM	CD	NumType=Card	34	nummod	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	subcategory	subcategory	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	27	punct	_	SpaceAfter=No

# sent_id = 4
# text = For the local idempotent closure $ overline cal K $ of $ cal K $ , extending the multiplication of the 2 - monad $ Mnd $ , we equip these 2 - categories with $ n $ possible `weak wreath product' 2 - functors $ Wdl^{(n)}(ocK)to Wdl^{(n - 1)}(overline cal K) $ , such that all of their possible $ n $ - fold composites $ Wdl^{(n)}(overline cal K)to Wdl^{(0)}(overline cal K) $ are equal; that is, such that the weak wreath product is `associative'.
1	For	for	ADP	IN	_	21	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
3	local	local	ADJ	JJ	Degree=Pos	5	amod	_	_
4	idempotent	idempotent	NOUN	NN	Number=Sing	5	amod	_	_
5	closure	closure	NOUN	NN	Number=Sing	1	pobj	_	_
6	$ overline cal K $	$ overline cal k $	SYM	$	_	5	prep	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	$ cal K $	$ cal k $	SYM	$	_	7	pobj	_	_
9	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
10	extending	extend	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	21	advcl	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	multiplication	multiplication	NOUN	NN	Number=Sing	10	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
15	2	2	NUM	CD	NumType=Card	17	nummod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	monad	monad	NOUN	NNS	Number=Plur	18	compound	_	_
18	$ Mnd $	$ mnd $	SYM	$	_	13	pobj	_	_
19	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
20	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	21	nsubj	_	_
21	equip	equip	VERB	VBP	Tense=Pres|VerbForm=Fin	54	ccomp	_	_
22	these	these	DET	DT	Number=Plur|PronType=Dem	25	det	_	_
23	2	2	NUM	CD	NumType=Card	25	nummod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	categories	category	NOUN	NNS	Number=Plur	21	dobj	_	_
26	with	with	ADP	IN	_	21	prep	_	_
27	$ n $	$ n $	SYM	$	_	32	quantmod	_	_
28	possible	possible	ADJ	JJ	Degree=Pos	32	amod	_	_
29	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	32	punct	_	SpaceAfter=No
30	weak	weak	ADJ	JJ	Degree=Pos	32	amod	_	_
31	wreath	wreath	NOUN	NN	Number=Sing	32	compound	_	_
32	product	product	NOUN	NN	Number=Sing	37	poss	_	SpaceAfter=No
33	'	'	PART	POS	_	32	case	_	_
34	2	2	NUM	CD	NumType=Card	36	nummod	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	36	punct	_	_
36	functors	functor	NOUN	NNS	Number=Plur	37	compound	_	_
37	$ Wdl^{(n)}(ocK)to Wdl^{(n - 1)}(overline cal K) $	$ wdl^{(n)}(ock)to wdl^{(n - 1)}(overline cal k) $	SYM	$	_	26	pobj	_	_
38	,	,	PUNCT	,	PunctType=Comm	37	punct	_	_
39	such	such	ADJ	JJ	Degree=Pos	50	amod	_	_
40	that	that	SCONJ	IN	_	50	mark	_	_
41	all	all	PRON	DT	_	50	nsubj	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	46	poss	_	_
44	possible	possible	ADJ	JJ	Degree=Pos	43	acomp	_	_
45	$ n $	$ n $	SYM	$	_	44	nmod	_	_
46	-	-	ADJ	JJ	Degree=Pos	48	amod	_	_
47	fold	fold	ADJ	JJ	Degree=Pos	48	amod	_	_
48	composites	composite	NOUN	NNS	Number=Plur	42	pobj	_	_
49	$ Wdl^{(n)}(overline cal K)to Wdl^{(0)}(overline cal K) $	$ wdl^{(n)}(overline cal k)to wdl^{(0)}(overline cal k) $	SYM	$	_	41	appos	_	_
50	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	21	ccomp	_	_
51	equal	equal	ADJ	JJ	Degree=Pos	50	acomp	_	SpaceAfter=No
52	;	;	PUNCT	:	_	54	punct	_	_
53	that	that	PRON	DT	Number=Sing|PronType=Dem	54	nsubj	_	_
54	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
55	,	,	PUNCT	,	PunctType=Comm	54	punct	_	_
56	such	such	ADJ	JJ	Degree=Pos	54	acomp	_	_
57	that	that	SCONJ	IN	_	62	mark	_	_
58	the	the	DET	DT	Definite=Def|PronType=Art	61	det	_	_
59	weak	weak	ADJ	JJ	Degree=Pos	61	amod	_	_
60	wreath	wreath	NOUN	NN	Number=Sing	61	compound	_	_
61	product	product	NOUN	NN	Number=Sing	62	nsubj	_	_
62	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	54	ccomp	_	_
63	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	62	punct	_	SpaceAfter=No
64	associative	associative	NOUN	NN	Number=Sing	62	acomp	_	SpaceAfter=No
65	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	62	punct	_	SpaceAfter=No
66	.	.	PUNCT	.	PunctType=Peri	54	punct	_	SpaceAfter=No

# sent_id = 5
# text = Whenever idempotent 2 - cells in $ cal K $ split, this leads to pseudofunctors $ Wdl^{(n)}(cal K)to Wdl^{(n - 1)}(cal K) $ obeying the associativity property up - to isomorphism.
1	Whenever	whenever	SCONJ	WRB	_	2	advmod	_	_
2	idempotent	idempotent	ADJ	JJ	Degree=Pos	5	amod	_	_
3	2	2	NUM	CD	NumType=Card	5	nummod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	cells	cell	NOUN	NNS	Number=Plur	11	advcl	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	$ cal K $	$ cal k $	SYM	$	_	8	det	_	_
8	split	split	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
10	this	this	PRON	DT	Number=Sing|PronType=Dem	11	nsubj	_	_
11	leads	lead	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	pseudofunctors	pseudofunctor	NOUN	NNS	Number=Plur	12	pobj	_	_
14	$ Wdl^{(n)}(cal K)to Wdl^{(n - 1)}(cal K) $	$ wdl^{(n)}(cal k)to wdl^{(n - 1)}(cal k) $	SYM	$	_	11	dobj	_	_
15	obeying	obey	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	acl	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	associativity	associativity	NOUN	NN	Number=Sing	18	compound	_	_
18	property	property	NOUN	NN	Number=Sing	15	dobj	_	_
19	up	up	ADP	IN	_	22	nmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
21	to	to	ADP	IN	_	19	prep	_	_
22	isomorphism	isomorphism	NOUN	NN	Number=Sing	15	dobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 6
# text = We present a practically important occurrence of an iterated weak wreath product: the algebra of observable quantities in an Ising type quantum spin chain where the spins take their values in a dual pair of finite weak Hopf algebras.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
4	practically	practically	ADV	RB	_	5	advmod	_	_
5	important	important	ADJ	JJ	Degree=Pos	6	amod	_	_
6	occurrence	occurrence	NOUN	NN	Number=Sing	2	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
9	iterated	iterate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
10	weak	weak	ADJ	JJ	Degree=Pos	12	amod	_	_
11	wreath	wreath	NOUN	NN	Number=Sing	12	compound	_	_
12	product	product	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
13	:	:	PUNCT	:	_	6	punct	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	algebra	algebra	NOUN	NN	Number=Sing	6	appos	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	observable	observable	ADJ	JJ	Degree=Pos	18	amod	_	_
18	quantities	quantity	NOUN	NNS	Number=Plur	16	pobj	_	_
19	in	in	ADP	IN	_	15	prep	_	_
20	an	an	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
21	Ising	Ising	PROPN	NNP	Number=Sing	23	compound	_	_
22	type	type	NOUN	NN	Number=Sing	23	compound	_	_
23	quantum	quantum	NOUN	NN	Number=Sing	25	compound	_	_
24	spin	spin	NOUN	NN	Number=Sing	25	compound	_	_
25	chain	chain	NOUN	NN	Number=Sing	19	pobj	_	_
26	where	where	SCONJ	WRB	_	29	advmod	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	spins	spin	NOUN	NNS	Number=Plur	29	nsubj	_	_
29	take	take	VERB	VBP	Tense=Pres|VerbForm=Fin	25	relcl	_	_
30	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	31	poss	_	_
31	values	value	NOUN	NNS	Number=Plur	29	dobj	_	_
32	in	in	ADP	IN	_	29	prep	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
34	dual	dual	ADJ	JJ	Degree=Pos	35	amod	_	_
35	pair	pair	NOUN	NN	Number=Sing	32	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	finite	finite	ADJ	JJ	Degree=Pos	40	nmod	_	_
38	weak	weak	ADJ	JJ	Degree=Pos	40	amod	_	_
39	Hopf	Hopf	PROPN	NNP	Number=Sing	40	compound	_	_
40	algebras	algebra	NOUN	NNS	Number=Plur	36	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = We also construct a fully faithful embedding of $ Wdl^{(n)}(overline cal K) $ into the 2 - category of commutative $ n+1 $ dimensional cubes in $ Mnd(overline cal K) $ (hence into the 2 - category of commutative $ n+1 $ dimensional cubes in $ cal K $ whenever $ cal K $ has Eilenberg - Moore objects and its idempotent 2 - cells split).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	38	ccomp	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	fully	fully	ADV	RB	_	6	advmod	_	_
6	faithful	faithful	ADJ	JJ	Degree=Pos	7	amod	_	_
7	embedding	embedding	NOUN	NN	Number=Sing	3	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	$ Wdl^{(n)}(overline cal K) $	$ wdl^{(n)}(overline cal k) $	SYM	$	_	8	pobj	_	_
10	into	into	ADP	IN	_	3	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
12	2	2	NUM	CD	NumType=Card	14	nummod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	commutative	commutative	ADJ	JJ	Degree=Pos	19	amod	_	_
17	$ n+1 $	$ n+1 $	SYM	$	_	19	nmod	_	_
18	dimensional	dimensional	ADJ	JJ	Degree=Pos	19	amod	_	_
19	cubes	cube	NOUN	NNS	Number=Plur	15	pobj	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	$ Mnd(overline cal K) $	$ mnd(overline cal k) $	SYM	$	_	20	pobj	_	_
22	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	3	punct	_	SpaceAfter=No
23	hence	hence	ADV	RB	_	24	advmod	_	_
24	into	into	ADP	IN	_	38	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
26	2	2	NUM	CD	NumType=Card	28	nummod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	category	category	NOUN	NN	Number=Sing	24	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	commutative	commutative	ADJ	JJ	Degree=Pos	33	amod	_	_
31	$ n+1 $	$ n+1 $	SYM	$	_	33	nmod	_	_
32	dimensional	dimensional	ADJ	JJ	Degree=Pos	33	amod	_	_
33	cubes	cube	NOUN	NNS	Number=Plur	29	pobj	_	_
34	in	in	ADP	IN	_	28	prep	_	_
35	$ cal K $	$ cal k $	SYM	$	_	34	pobj	_	_
36	whenever	whenever	SCONJ	WRB	_	37	advmod	_	_
37	$ cal K $	$ cal k $	SYM	$	_	38	nsubj	_	_
38	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
39	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	41	compound	_	_
40	-	-	PUNCT	HYPH	PunctType=Dash	41	punct	_	_
41	Moore	Moore	PROPN	NNP	Number=Sing	42	compound	_	_
42	objects	object	NOUN	NNS	Number=Plur	38	dobj	_	_
43	and	and	CCONJ	CC	ConjType=Cmp	42	cc	_	_
44	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	48	poss	_	_
45	idempotent	idempotent	ADJ	JJ	Degree=Pos	48	amod	_	_
46	2	2	NUM	CD	NumType=Card	48	nummod	_	_
47	-	-	PUNCT	HYPH	PunctType=Dash	48	punct	_	_
48	cells	cell	NOUN	NNS	Number=Plur	49	nsubj	_	_
49	split	split	VERB	VBP	Tense=Pres|VerbForm=Fin	42	conj	_	SpaceAfter=No
50	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	42	punct	_	SpaceAfter=No
51	.	.	PUNCT	.	PunctType=Peri	38	punct	_	SpaceAfter=No

# sent_id = 8
# text = Finally we give a sufficient and necessary condition on a monad in $ overline cal K $ to be isomorphic to an $ n $ - ary weak wreath product.
1	Finally	finally	ADV	RB	_	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
5	sufficient	sufficient	ADJ	JJ	Degree=Pos	8	amod	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	necessary	necessary	ADJ	JJ	Degree=Pos	5	conj	_	_
8	condition	condition	NOUN	NN	Number=Sing	3	dobj	_	_
9	on	on	ADP	IN	_	3	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	monad	monad	NOUN	NNS	Number=Plur	9	pobj	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	$ overline cal K $	$ overline cal k $	SYM	$	_	12	pobj	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	be	be	AUX	VB	VerbForm=Inf	3	advcl	_	_
16	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	15	acomp	_	_
17	to	to	ADP	IN	_	15	prep	_	_
18	an	an	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
19	$ n $	$ n $	SYM	$	_	21	quantmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	ary	ary	PROPN	NNP	Number=Sing	24	nmod	_	_
22	weak	weak	ADJ	JJ	Degree=Pos	24	amod	_	_
23	wreath	wreath	NOUN	NN	Number=Sing	24	compound	_	_
24	product	product	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 427
# sent_id = 1
# text = We show that colax idempotent pseudomonads and their algebras can be presented in terms of right Kan extensions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	12	mark	_	_
4	colax	colax	ADJ	JJ	Degree=Pos	6	amod	_	_
5	idempotent	idempotent	ADJ	JJ	Degree=Pos	6	amod	_	_
6	pseudomonads	pseudomonad	NOUN	NNS	Number=Plur	12	nsubjpass	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	9	poss	_	_
9	algebras	algebra	NOUN	NNS	Number=Plur	6	conj	_	_
10	can	can	AUX	MD	VerbForm=Fin	12	aux	_	_
11	be	be	AUX	VB	VerbForm=Inf	12	auxpass	_	_
12	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	terms	term	NOUN	NNS	Number=Plur	13	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	right	right	ADJ	JJ	Degree=Pos	18	amod	_	_
17	Kan	Kan	PROPN	NNP	Number=Sing	18	compound	_	_
18	extensions	extension	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Dually, lax idempotent pseudomonads and their algebras can be presented in terms of left Kan extensions.
1	Dually	Dually	PROPN	NNP	Number=Sing	11	npadvmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
3	lax	lax	ADJ	JJ	Degree=Pos	5	amod	_	_
4	idempotent	idempotent	ADJ	JJ	Degree=Pos	5	amod	_	_
5	pseudomonads	pseudomonad	NOUN	NNS	Number=Plur	11	nsubjpass	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	8	poss	_	_
8	algebras	algebra	NOUN	NNS	Number=Plur	5	conj	_	_
9	can	can	AUX	MD	VerbForm=Fin	11	aux	_	_
10	be	be	AUX	VB	VerbForm=Inf	11	auxpass	_	_
11	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	terms	term	NOUN	NNS	Number=Plur	12	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
16	Kan	Kan	PROPN	NNP	Number=Sing	17	compound	_	_
17	extensions	extension	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also show that a distributive law of a colax idempotent pseudomonad over a lax idempotent pseudomonad has a presentation in terms of Kan extensions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	18	mark	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	distributive	distributive	ADJ	JJ	Degree=Pos	7	amod	_	_
7	law	law	NOUN	NN	Number=Sing	18	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
10	colax	colax	ADJ	JJ	Degree=Pos	12	amod	_	_
11	idempotent	idempotent	ADJ	JJ	Degree=Pos	12	amod	_	_
12	pseudomonad	pseudomonad	NOUN	NNS	Number=Plur	8	pobj	_	_
13	over	over	ADP	IN	_	7	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	lax	lax	ADJ	JJ	Degree=Pos	17	amod	_	_
16	idempotent	idempotent	ADJ	JJ	Degree=Pos	17	amod	_	_
17	pseudomonad	pseudomonad	NOUN	NNS	Number=Plur	13	pobj	_	_
18	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	presentation	presentation	NOUN	NN	Number=Sing	18	dobj	_	_
21	in	in	ADP	IN	_	20	prep	_	_
22	terms	term	NOUN	NNS	Number=Plur	21	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	Kan	Kan	PROPN	NNP	Number=Sing	25	compound	_	_
25	extensions	extension	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 428
# sent_id = 1
# text = The paper presents algebraic and logical developments.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	presents	present	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	algebraic	algebraic	ADJ	JJ	Degree=Pos	7	amod	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	logical	logical	ADJ	JJ	Degree=Pos	4	conj	_	_
7	developments	development	NOUN	NNS	Number=Plur	3	dobj	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = From the algebraic viewpoint, we introduce Monadic Equational Systems as an abstract enriched notion of equational presentation.
1	From	from	ADP	IN	_	7	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	algebraic	algebraic	ADJ	JJ	Degree=Pos	4	amod	_	_
4	viewpoint	viewpoint	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	Monadic	Monadic	PROPN	NNP	Number=Sing	10	compound	_	_
9	Equational	Equational	PROPN	NNP	Number=Sing	10	compound	_	_
10	Systems	Systems	PROPN	NNPS	Number=Plur	7	dobj	_	_
11	as	as	ADP	IN	_	7	prep	_	_
12	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	abstract	abstract	ADJ	JJ	Degree=Pos	15	amod	_	_
14	enriched	enriched	ADJ	JJ	Degree=Pos	15	amod	_	_
15	notion	notion	NOUN	NN	Number=Sing	11	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	equational	equational	ADJ	JJ	Degree=Pos	18	amod	_	_
18	presentation	presentation	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = From the logical viewpoint, we provide Equational Metalogic as a general formal deductive system for the derivability of equational consequences.
1	From	from	ADP	IN	_	7	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	logical	logical	ADJ	JJ	Degree=Pos	4	amod	_	_
4	viewpoint	viewpoint	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	Equational	Equational	PROPN	NNP	Number=Sing	9	compound	_	_
9	Metalogic	Metalogic	PROPN	NNP	Number=Sing	7	dobj	_	_
10	as	as	ADP	IN	_	7	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
12	general	general	ADJ	JJ	Degree=Pos	15	amod	_	_
13	formal	formal	ADJ	JJ	Degree=Pos	15	amod	_	_
14	deductive	deductive	ADJ	JJ	Degree=Pos	15	amod	_	_
15	system	system	NOUN	NN	Number=Sing	10	pobj	_	_
16	for	for	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	derivability	derivability	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	equational	equational	ADJ	JJ	Degree=Pos	21	amod	_	_
21	consequences	consequence	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = Relating the two, a canonical model theory for Monadic Equational Systems is given and for it the soundness of Equational Metalogic is established.
1	Relating	relate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	advcl	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	two	two	NUM	CD	NumType=Card	1	dobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
6	canonical	canonical	ADJ	JJ	Degree=Pos	7	amod	_	_
7	model	model	NOUN	NN	Number=Sing	8	compound	_	_
8	theory	theory	NOUN	NN	Number=Sing	14	nsubjpass	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	Monadic	Monadic	PROPN	NNP	Number=Sing	12	compound	_	_
11	Equational	Equational	PROPN	NNP	Number=Sing	12	compound	_	_
12	Systems	Systems	PROPN	NNPS	Number=Plur	9	pobj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	for	for	ADP	IN	_	24	prep	_	_
17	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	16	pobj	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	soundness	soundness	NOUN	NN	Number=Sing	24	nsubjpass	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	Equational	Equational	PROPN	NNP	Number=Sing	22	compound	_	_
22	Metalogic	Metalogic	PROPN	NNP	Number=Sing	20	pobj	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	auxpass	_	_
24	established	establish	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	conj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# sent_id = 5
# text = This development involves a study of clone and double - dualization structures.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	development	development	NOUN	NN	Number=Sing	3	nsubj	_	_
3	involves	involve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	study	study	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	clone	clone	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	nmod	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	double	double	ADJ	JJ	Degree=Pos	11	amod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	dualization	dualization	NOUN	NN	Number=Sing	7	conj	_	_
12	structures	structure	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = We also show that in the presence of free algebras %constructions the model theory of Monadic Equational Systems satisfies an internal strong - completeness property.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	5	mark	_	_
5	in	in	ADP	IN	_	3	ccomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	presence	presence	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	free	free	ADJ	JJ	Degree=Pos	10	amod	_	_
10	algebras	algebra	NOUN	NNS	Number=Plur	11	compound	_	_
11	%	%	NOUN	NN	Number=Sing	12	compound	_	SpaceAfter=No
12	constructions	construction	NOUN	NNS	Number=Plur	8	pobj	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	model	model	NOUN	NN	Number=Sing	15	compound	_	_
15	theory	theory	NOUN	NN	Number=Sing	5	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	Monadic	Monadic	PROPN	NNP	Number=Sing	19	compound	_	_
18	Equational	Equational	PROPN	NNP	Number=Sing	19	compound	_	_
19	Systems	Systems	PROPN	NNPS	Number=Plur	20	compound	_	_
20	satisfies	satisfie	NOUN	NNS	Number=Plur	16	pobj	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
22	internal	internal	ADJ	JJ	Degree=Pos	26	amod	_	_
23	strong	strong	ADJ	JJ	Degree=Pos	25	amod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	completeness	completeness	NOUN	NN	Number=Sing	26	compound	_	_
26	property	property	NOUN	NN	Number=Sing	20	dobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 429
# sent_id = 1
# text = We extend the notion of exact completion on a category with weak finite limits to Lawvere's elementary doctrines.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	extend	extend	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	exact	exact	ADJ	JJ	Degree=Pos	7	amod	_	_
7	completion	completion	NOUN	NN	Number=Sing	5	pobj	_	_
8	on	on	ADP	IN	_	4	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
11	with	with	ADP	IN	_	10	prep	_	_
12	weak	weak	ADJ	JJ	Degree=Pos	14	amod	_	_
13	finite	finite	ADJ	JJ	Degree=Pos	14	compound	_	_
14	limits	limit	NOUN	NNS	Number=Plur	11	pobj	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	Lawvere	Lawvere	PROPN	NNP	Number=Sing	19	poss	_	SpaceAfter=No
17	's	's	PART	POS	_	16	case	_	_
18	elementary	elementary	ADJ	JJ	Degree=Pos	19	amod	_	_
19	doctrines	doctrine	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show how any such doctrine admits an elementary quotient completion, which is the universal solution to adding certain quotients.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	how	how	SCONJ	WRB	_	7	advmod	_	_
4	any	any	DET	DT	_	6	det	_	_
5	such	such	ADJ	JJ	Degree=Pos	6	amod	_	_
6	doctrine	doctrine	NOUN	NN	Number=Sing	7	nsubj	_	_
7	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	elementary	elementary	ADJ	JJ	Degree=Pos	11	amod	_	_
10	quotient	quotient	NOUN	NN	Number=Sing	11	compound	_	_
11	completion	completion	NOUN	NN	Number=Sing	7	dobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	which	which	PRON	WDT	_	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	relcl	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	universal	universal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	solution	solution	NOUN	NN	Number=Sing	14	attr	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	adding	add	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	18	pcomp	_	_
20	certain	certain	ADJ	JJ	Degree=Pos	21	amod	_	_
21	quotients	quotient	NOUN	NNS	Number=Plur	19	dobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We note that the elementary quotient completion can be obtained as the composite of two other universal constructions: one adds effective quotients, the other forces extensionality of morphisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	note	note	VERB	VBP	Tense=Pres|VerbForm=Fin	21	ccomp	_	_
3	that	that	SCONJ	IN	_	10	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	elementary	elementary	ADJ	JJ	Degree=Pos	6	amod	_	_
6	quotient	quotient	NOUN	NN	Number=Sing	7	compound	_	_
7	completion	completion	NOUN	NN	Number=Sing	10	nsubjpass	_	_
8	can	can	AUX	MD	VerbForm=Fin	10	aux	_	_
9	be	be	AUX	VB	VerbForm=Inf	10	auxpass	_	_
10	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
11	as	as	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	composite	composite	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	two	two	NUM	CD	NumType=Card	18	nummod	_	_
16	other	other	ADJ	JJ	Degree=Pos	18	amod	_	_
17	universal	universal	ADJ	JJ	Degree=Pos	18	amod	_	_
18	constructions	construction	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
19	:	:	PUNCT	:	_	21	punct	_	_
20	one	one	NUM	CD	NumType=Card	21	nsubj	_	_
21	adds	add	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
22	effective	effective	ADJ	JJ	Degree=Pos	23	amod	_	_
23	quotients	quotient	NOUN	NNS	Number=Plur	21	dobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	other	other	ADJ	JJ	Degree=Pos	27	amod	_	_
27	forces	force	NOUN	NNS	Number=Plur	28	compound	_	_
28	extensionality	extensionality	NOUN	NN	Number=Sing	21	dobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	morphisms	morphism	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# sent_id = 4
# text = We also prove that each construction preserves comprehension.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	7	mark	_	_
5	each	each	DET	DT	_	6	det	_	_
6	construction	construction	NOUN	NN	Number=Sing	7	nsubj	_	_
7	preserves	preserve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
8	comprehension	comprehension	NOUN	NN	Number=Sing	7	dobj	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 430
# sent_id = 1
# text = Bruguières, Lack and Virelizier have recently obtained a vast generalization of Sweedler's Fundamental Theorem of Hopf modules, in which the role of the Hopf algebra is played by a bimonad.
1	Bruguières	bruguière	NOUN	NNS	Number=Plur	8	nsubj	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	1	punct	_	_
3	Lack	Lack	PROPN	NNP	Number=Sing	1	conj	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	Virelizier	Virelizier	PROPN	NNP	Number=Sing	3	conj	_	_
6	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	aux	_	_
7	recently	recently	ADV	RB	_	8	advmod	_	_
8	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	vast	vast	ADJ	JJ	Degree=Pos	11	amod	_	_
11	generalization	generalization	NOUN	NN	Number=Sing	8	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	Sweedler	Sweedler	PROPN	NNP	Number=Sing	16	poss	_	SpaceAfter=No
14	's	's	PART	POS	_	13	case	_	_
15	Fundamental	fundamental	ADJ	JJ	Degree=Pos	16	amod	_	_
16	Theorem	Theorem	PROPN	NNP	Number=Sing	12	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	Hopf	Hopf	PROPN	NNP	Number=Sing	19	compound	_	_
19	modules	module	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
21	in	in	ADP	IN	_	30	prep	_	_
22	which	which	PRON	WDT	_	21	pobj	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	role	role	NOUN	NN	Number=Sing	30	nsubjpass	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	Hopf	Hopf	PROPN	NNP	Number=Sing	28	compound	_	_
28	algebra	algebra	NOUN	NN	Number=Sing	25	pobj	_	_
29	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	auxpass	_	_
30	played	play	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	relcl	_	_
31	by	by	ADP	IN	_	30	agent	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
33	bimonad	bimonad	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = We present an extension of this result which involves, in addition to the bimonad, a comodule - monad and a algebra - comonoid over it.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	extension	extension	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
7	result	result	NOUN	NN	Number=Sing	5	pobj	_	_
8	which	which	PRON	WDT	_	9	nsubj	_	_
9	involves	involve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	relcl	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	in	in	ADP	IN	_	9	prep	_	_
12	addition	addition	NOUN	NN	Number=Sing	11	pobj	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	bimonad	bimonad	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
18	comodule	comodule	NOUN	NN	Number=Sing	20	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	monad	monad	NOUN	NNS	Number=Plur	4	appos	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
23	algebra	algebra	NOUN	NN	Number=Sing	25	compound	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	comonoid	comonoid	NOUN	NN	Number=Sing	20	conj	_	_
26	over	over	ADP	IN	_	25	prep	_	_
27	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	26	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = As an application we obtain a generalization of another classical theorem from the Hopf algebra literature, due to Schneider, which itself is an extension of Sweedler's result (to the setting of Hopf Galois extensions).
1	As	as	ADP	IN	_	5	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	generalization	generalization	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	another	another	DET	DT	_	11	det	_	_
10	classical	classical	ADJ	JJ	Degree=Pos	11	amod	_	_
11	theorem	theorem	NOUN	NN	Number=Sing	8	pobj	_	_
12	from	from	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
14	Hopf	Hopf	PROPN	NNP	Number=Sing	16	compound	_	_
15	algebra	algebra	NOUN	NN	Number=Sing	16	compound	_	_
16	literature	literature	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
18	due	due	ADP	IN	_	5	prep	_	_
19	to	to	ADP	IN	_	18	pcomp	_	_
20	Schneider	Schneider	PROPN	NNP	Number=Sing	18	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	which	which	PRON	WDT	_	24	nsubj	_	_
23	itself	itself	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs|Reflex=Yes	22	appos	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	relcl	_	_
25	an	an	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
26	extension	extension	NOUN	NN	Number=Sing	24	attr	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	Sweedler	Sweedler	PROPN	NNP	Number=Sing	30	poss	_	SpaceAfter=No
29	's	's	PART	POS	_	28	case	_	_
30	result	result	NOUN	NN	Number=Sing	27	pobj	_	_
31	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	20	punct	_	SpaceAfter=No
32	to	to	ADP	IN	_	5	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
34	setting	setting	NOUN	NN	Number=Sing	32	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	Hopf	Hopf	PROPN	NNP	Number=Sing	37	compound	_	_
37	Galois	Galois	PROPN	NNP	Number=Sing	38	compound	_	_
38	extensions	extension	NOUN	NNS	Number=Plur	35	pobj	_	SpaceAfter=No
39	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	5	punct	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 431
# sent_id = 1
# text = We study the composition of modules between lax functors of weak double categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	composition	composition	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	modules	module	NOUN	NNS	Number=Plur	5	pobj	_	_
7	between	between	ADP	IN	_	6	prep	_	_
8	lax	lax	ADJ	JJ	Degree=Pos	9	amod	_	_
9	functors	functor	NOUN	NNS	Number=Plur	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	weak	weak	ADJ	JJ	Degree=Pos	13	amod	_	_
12	double	double	ADJ	JJ	Degree=Pos	13	amod	_	_
13	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We adapt the bicategorical notion of local cocompleteness to weak double categories, which the codomain of our lax functors will be assumed to satisfy.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	adapt	adapt	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	bicategorical	bicategorical	ADJ	JJ	Degree=Pos	5	amod	_	_
5	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	local	local	ADJ	JJ	Degree=Pos	8	amod	_	_
8	cocompleteness	cocompleteness	NOUN	NN	Number=Sing	6	pobj	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	weak	weak	ADJ	JJ	Degree=Pos	12	amod	_	_
11	double	double	ADJ	JJ	Degree=Pos	12	amod	_	_
12	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	which	which	PRON	WDT	_	25	dobj	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	codomain	codomain	NOUN	NN	Number=Sing	23	nsubjpass	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	20	poss	_	_
19	lax	lax	ADJ	JJ	Degree=Pos	20	amod	_	_
20	functors	functor	NOUN	NNS	Number=Plur	17	pobj	_	_
21	will	will	AUX	MD	VerbForm=Fin	23	aux	_	_
22	be	be	AUX	VB	VerbForm=Inf	23	auxpass	_	_
23	assumed	assume	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	relcl	_	_
24	to	to	PART	TO	_	25	aux	_	_
25	satisfy	satisfy	VERB	VB	VerbForm=Inf	23	xcomp	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We introduce a notion of factorization of cells, which most weak double categories of interest possess, and which is sufficient to guarantee the strong representability of composites of modules between lax functors whose domain satisfies it.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	factorization	factorization	NOUN	NN	Number=Sing	5	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	cells	cell	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
10	which	which	DET	WDT	_	14	det	_	_
11	most	most	ADV	RBS	Degree=Sup	12	advmod	_	_
12	weak	weak	ADJ	JJ	Degree=Pos	14	amod	_	_
13	double	double	ADJ	JJ	Degree=Pos	14	amod	_	_
14	categories	category	NOUN	NNS	Number=Plur	4	relcl	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	interest	interest	NOUN	NN	Number=Sing	17	compound	_	_
17	possess	possess	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
20	which	which	PRON	WDT	_	21	nsubj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
22	sufficient	sufficient	ADJ	JJ	Degree=Pos	21	acomp	_	_
23	to	to	PART	TO	_	24	aux	_	_
24	guarantee	guarantee	VERB	VB	VerbForm=Inf	22	xcomp	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	strong	strong	ADJ	JJ	Degree=Pos	27	amod	_	_
27	representability	representability	NOUN	NN	Number=Sing	24	dobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	composites	composite	NOUN	NNS	Number=Plur	28	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	modules	module	NOUN	NNS	Number=Plur	30	pobj	_	_
32	between	between	ADP	IN	_	31	prep	_	_
33	lax	lax	ADJ	JJ	Degree=Pos	34	amod	_	_
34	functors	functor	NOUN	NNS	Number=Plur	32	pobj	_	_
35	whose	whose	DET	WP$	Poss=Yes	36	poss	_	_
36	domain	domain	NOUN	NN	Number=Sing	37	nsubj	_	_
37	satisfies	satisfy	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	34	relcl	_	_
38	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	37	dobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 432
# sent_id = 1
# text = Let $ G $ be an object of a finitely cocomplete homological category $ mathbb C $ .
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ G $	$ g $	SYM	$	_	1	dobj	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	object	object	NOUN	NN	Number=Sing	3	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	finitely	finitely	ADV	RB	_	9	advmod	_	_
9	cocomplete	cocomplete	ADJ	JJ	Degree=Pos	11	amod	_	_
10	homological	homological	ADJ	JJ	Degree=Pos	11	amod	_	_
11	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
12	$ mathbb C $	$ mathbb c $	SYM	$	_	11	appos	_	_
13	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = We study actions of $ G $ on objects $ A $ of $ mathbb C $ (defined by Bourn and Janelidze as being algebras over a certain monad $ mathbb T_G $ ), with two objectives: investigating to which extent actions can be described in terms of smaller data, called action cores; and to single out those abstract action cores which extend to actions corresponding to semi - direct products of $ A $ and $ G $ (in a non - exact setting, not every action does).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	actions	action	NOUN	NNS	Number=Plur	2	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	$ G $	$ g $	SYM	$	_	4	pobj	_	_
6	on	on	ADP	IN	_	2	prep	_	_
7	objects	object	NOUN	NNS	Number=Plur	6	pobj	_	_
8	$ A $	$ a $	SYM	$	_	7	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	$ mathbb C $	$ mathbb c $	SYM	$	_	9	pobj	_	_
11	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	8	punct	_	SpaceAfter=No
12	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	acl	_	_
13	by	by	ADP	IN	_	12	agent	_	_
14	Bourn	Bourn	PROPN	NNP	Number=Sing	13	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	Janelidze	Janelidze	PROPN	NNP	Number=Sing	14	conj	_	_
17	as	as	ADP	IN	_	12	prep	_	_
18	being	be	AUX	VBG	VerbForm=Ger	17	pcomp	_	_
19	algebras	algebra	NOUN	NNS	Number=Plur	18	attr	_	_
20	over	over	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	certain	certain	ADJ	JJ	Degree=Pos	23	amod	_	_
23	monad	monad	NOUN	NNS	Number=Plur	20	pobj	_	_
24	$ mathbb T_G $	$ mathbb t_g $	SYM	$	_	18	npadvmod	_	_
25	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	7	punct	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
27	with	with	ADP	IN	_	2	prep	_	_
28	two	two	NUM	CD	NumType=Card	29	nummod	_	_
29	objectives	objective	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	:	:	PUNCT	:	_	29	punct	_	_
31	investigating	investigate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	29	acl	_	_
32	to	to	PART	TO	_	38	prep	_	_
33	which	which	PRON	WDT	_	32	pobj	_	_
34	extent	extent	NOUN	NN	Number=Sing	35	compound	_	_
35	actions	action	NOUN	NNS	Number=Plur	38	nsubjpass	_	_
36	can	can	AUX	MD	VerbForm=Fin	38	aux	_	_
37	be	be	AUX	VB	VerbForm=Inf	38	auxpass	_	_
38	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	advcl	_	_
39	in	in	ADP	IN	_	38	prep	_	_
40	terms	term	NOUN	NNS	Number=Plur	39	pobj	_	_
41	of	of	ADP	IN	_	40	prep	_	_
42	smaller	small	ADJ	JJR	Degree=Cmp	43	amod	_	_
43	data	datum	NOUN	NNS	Number=Plur	41	pobj	_	SpaceAfter=No
44	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
45	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	acl	_	_
46	action	action	NOUN	NN	Number=Sing	47	compound	_	_
47	cores	core	NOUN	NNS	Number=Plur	45	oprd	_	SpaceAfter=No
48	;	;	PUNCT	:	_	27	punct	_	_
49	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
50	to	to	PART	TO	_	51	aux	_	_
51	single	single	VERB	VB	VerbForm=Inf	82	advcl	_	_
52	out	out	ADP	RP	_	51	prt	_	_
53	those	those	DET	DT	Number=Plur|PronType=Dem	56	det	_	_
54	abstract	abstract	ADJ	JJ	Degree=Pos	56	amod	_	_
55	action	action	NOUN	NN	Number=Sing	56	compound	_	_
56	cores	core	NOUN	NNS	Number=Plur	51	dobj	_	_
57	which	which	PRON	WDT	_	58	nsubj	_	_
58	extend	extend	VERB	VBP	Tense=Pres|VerbForm=Fin	56	relcl	_	_
59	to	to	ADP	IN	_	58	prep	_	_
60	actions	action	NOUN	NNS	Number=Plur	59	pobj	_	_
61	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	60	acl	_	_
62	to	to	ADP	IN	_	61	prep	_	_
63	semi	semi	ADJ	JJ	Degree=Pos	65	advmod	_	_
64	-	-	ADJ	JJ	Degree=Pos	65	punct	_	_
65	direct	direct	ADJ	JJ	Degree=Pos	66	amod	_	_
66	products	product	NOUN	NNS	Number=Plur	62	pobj	_	_
67	of	of	ADP	IN	_	66	prep	_	_
68	$ A $	$ a $	SYM	$	_	67	pobj	_	_
69	and	and	CCONJ	CC	ConjType=Cmp	68	cc	_	_
70	$ G $	$ g $	SYM	$	_	68	conj	_	_
71	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	51	punct	_	SpaceAfter=No
72	in	in	ADP	IN	_	51	prep	_	_
73	a	a	DET	DT	Definite=Ind|PronType=Art	77	det	_	_
74	non	non	ADJ	JJ	Degree=Pos	76	amod	_	_
75	-	-	PUNCT	HYPH	PunctType=Dash	76	punct	_	_
76	exact	exact	ADJ	JJ	Degree=Pos	77	amod	_	_
77	setting	setting	NOUN	NN	Number=Sing	72	pobj	_	SpaceAfter=No
78	,	,	PUNCT	,	PunctType=Comm	82	punct	_	_
79	not	not	PART	RB	Polarity=Neg	80	neg	_	_
80	every	every	DET	DT	_	81	det	_	_
81	action	action	NOUN	NN	Number=Sing	82	nsubj	_	_
82	does	do	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	SpaceAfter=No
83	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	2	punct	_	SpaceAfter=No
84	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = This amounts to exhibiting a subcategory of the category of the actions of $ G $ on objects $ A $ which is equivalent with the category of points in $ mathbb C $ over $ G $ , and to describing it in terms of action cores.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	amounts	amount	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	exhibiting	exhibit	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	pcomp	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	subcategory	subcategory	NOUN	NN	Number=Sing	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	actions	action	NOUN	NNS	Number=Plur	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	$ G $	$ g $	SYM	$	_	13	pobj	_	_
15	on	on	ADP	IN	_	2	prep	_	_
16	objects	object	NOUN	NNS	Number=Plur	15	pobj	_	_
17	$ A $	$ a $	SYM	$	_	16	dobj	_	_
18	which	which	PRON	WDT	_	19	nsubj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
20	equivalent	equivalent	ADJ	JJ	Degree=Pos	19	acomp	_	_
21	with	with	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	category	category	NOUN	NN	Number=Sing	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	points	point	NOUN	NNS	Number=Plur	24	pobj	_	_
26	in	in	ADP	IN	_	23	prep	_	_
27	$ mathbb C $	$ mathbb c $	SYM	$	_	29	nmod	_	_
28	over	over	ADP	IN	_	29	advmod	_	_
29	$ G $	$ g $	SYM	$	_	26	pobj	_	_
30	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
32	to	to	ADP	IN	_	2	conj	_	_
33	describing	describe	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	32	pcomp	_	_
34	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	33	dobj	_	_
35	in	in	ADP	IN	_	33	prep	_	_
36	terms	term	NOUN	NNS	Number=Plur	35	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	action	action	NOUN	NN	Number=Sing	39	compound	_	_
39	cores	core	NOUN	NNS	Number=Plur	37	pobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = This notion and its study are based on a preliminary investigation of co - smash products, in which cross - effects of functors in a general categorical context turn out to be a useful tool.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	notion	notion	NOUN	NN	Number=Sing	7	nsubjpass	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	5	poss	_	_
5	study	study	NOUN	NN	Number=Sing	2	conj	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	on	on	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	preliminary	preliminary	ADJ	JJ	Degree=Pos	11	amod	_	_
11	investigation	investigation	NOUN	NN	Number=Sing	8	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	co	co	NOUN	NN	Number=Sing	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	smash	smash	VERB	VB	VerbForm=Inf	16	compound	_	_
16	products	product	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
18	in	in	ADP	IN	_	22	prep	_	_
19	which	which	PRON	WDT	_	18	pobj	_	_
20	cross	cross	NOUN	NN	Number=Sing	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	effects	effect	NOUN	NNS	Number=Plur	30	nsubj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	functors	functor	NOUN	NNS	Number=Plur	23	pobj	_	_
25	in	in	ADP	IN	_	22	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
27	general	general	ADJ	JJ	Degree=Pos	29	amod	_	_
28	categorical	categorical	ADJ	JJ	Degree=Pos	29	amod	_	_
29	context	context	NOUN	NN	Number=Sing	25	pobj	_	_
30	turn	turn	VERB	VB	VerbForm=Inf	7	dep	_	_
31	out	out	ADP	RP	_	30	prt	_	_
32	to	to	PART	TO	_	33	aux	_	_
33	be	be	AUX	VB	VerbForm=Inf	30	xcomp	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
35	useful	useful	ADJ	JJ	Degree=Pos	36	amod	_	_
36	tool	tool	NOUN	NN	Number=Sing	33	attr	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 5
# text = The co - smash products also allow us to define higher categorical commutators, different from the ones of Huq, which are not generally expressible in terms of nested binary ones.
1	The	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
2	co	co	NOUN	NN	Number=Sing	4	compound	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	smash	smash	NOUN	NN	Number=Sing	5	compound	_	_
5	products	product	NOUN	NNS	Number=Plur	7	nsubj	_	_
6	also	also	ADV	RB	_	7	advmod	_	_
7	allow	allow	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	define	define	VERB	VB	VerbForm=Inf	7	ccomp	_	_
11	higher	high	ADJ	JJR	Degree=Cmp	13	amod	_	_
12	categorical	categorical	ADJ	JJ	Degree=Pos	13	amod	_	_
13	commutators	commutator	NOUN	NNS	Number=Plur	10	dobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
15	different	different	ADJ	JJ	Degree=Pos	10	advmod	_	_
16	from	from	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	ones	one	NOUN	NNS	Number=Plur	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	Huq	Huq	PROPN	NNP	Number=Sing	19	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	which	which	PRON	WDT	_	23	nsubj	_	_
23	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	20	relcl	_	_
24	not	not	PART	RB	Polarity=Neg	23	neg	_	_
25	generally	generally	ADV	RB	_	26	advmod	_	_
26	expressible	expressible	ADJ	JJ	Degree=Pos	23	acomp	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	terms	term	NOUN	NNS	Number=Plur	27	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	nested	nested	ADJ	JJ	Degree=Pos	32	amod	_	_
31	binary	binary	ADJ	JJ	Degree=Pos	32	amod	_	_
32	ones	one	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 6
# text = We use strict action cores to show that any normal subobject of an object $ E $ (that is, the equivalence class of $ 0 $ for some equivalence relation on $ E $ in $ mathbb C $ ) admits a strict conjugation action of $ E $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	strict	strict	ADJ	JJ	Degree=Pos	5	amod	_	_
4	action	action	NOUN	NN	Number=Sing	5	compound	_	_
5	cores	core	NOUN	NNS	Number=Plur	2	dobj	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	show	show	VERB	VB	VerbForm=Inf	2	xcomp	_	_
8	that	that	SCONJ	IN	_	34	mark	_	_
9	any	any	DET	DT	_	11	det	_	_
10	normal	normal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	subobject	subobject	NOUN	NN	Number=Sing	34	nsubj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	object	object	NOUN	NN	Number=Sing	12	pobj	_	_
15	$ E $	$ e $	SYM	$	_	11	appos	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	11	punct	_	SpaceAfter=No
17	that	that	ADV	RB	_	18	advmod	_	_
18	is	is	ADV	RB	_	11	parataxis	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	equivalence	equivalence	NOUN	NN	Number=Sing	22	compound	_	_
22	class	class	NOUN	NN	Number=Sing	11	appos	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	$ 0 $	$ 0 $	SYM	$	_	23	pobj	_	_
25	for	for	ADP	IN	_	22	prep	_	_
26	some	some	DET	DT	_	28	det	_	_
27	equivalence	equivalence	NOUN	NN	Number=Sing	28	compound	_	_
28	relation	relation	NOUN	NN	Number=Sing	25	pobj	_	_
29	on	on	ADP	IN	_	28	prep	_	_
30	$ E $	$ e $	SYM	$	_	29	pobj	_	_
31	in	in	ADP	IN	_	28	prep	_	_
32	$ mathbb C $	$ mathbb c $	SYM	$	_	31	pobj	_	_
33	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	11	punct	_	_
34	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	ccomp	_	_
35	a	a	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
36	strict	strict	ADJ	JJ	Degree=Pos	38	amod	_	_
37	conjugation	conjugation	NOUN	NN	Number=Sing	38	compound	_	_
38	action	action	NOUN	NN	Number=Sing	34	dobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	$ E $	$ e $	SYM	$	_	39	pobj	_	_
41	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = If $ mathbb C $ is semi - abelian, we show that for subobjects $ X $ , $ Y $ of some object $ A $ , $ X $ is proper in the supremum of $ X $ and $ Y $ if and only if $ X $ is stable under the restriction to $ Y $ of the conjugation action of $ A $ on itself.
1	If	if	SCONJ	IN	_	3	mark	_	_
2	$ mathbb C $	$ mathbb c $	SYM	$	_	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	advcl	_	_
4	semi	semi	ADJ	JJ	Degree=Pos	3	acomp	_	_
5	-	-	ADJ	JJ	Degree=Pos	3	attr	_	_
6	abelian	abelian	ADJ	JJ	Degree=Pos	3	acomp	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	that	that	SCONJ	IN	_	22	mark	_	_
11	for	for	ADP	IN	_	22	prep	_	_
12	subobjects	subobject	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	pobj	_	_
13	$ X $	$ x $	SYM	$	_	11	punct	_	_
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	$ Y $	$ y $	SYM	$	_	11	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	some	some	DET	DT	_	18	det	_	_
18	object	object	NOUN	NN	Number=Sing	16	pobj	_	_
19	$ A $	$ a $	SYM	$	_	18	nummod	_	_
20	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
21	$ X $	$ x $	SYM	$	_	11	pcomp	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	ccomp	_	_
23	proper	proper	ADJ	JJ	Degree=Pos	22	acomp	_	_
24	in	in	ADP	IN	_	22	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	supremum	supremum	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	$ X $	$ x $	SYM	$	_	27	pobj	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
30	$ Y $	$ y $	SYM	$	_	31	nmod	_	_
31	if	if	SCONJ	IN	_	22	dep	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	only	only	ADV	RB	_	36	advmod	_	_
34	if	if	SCONJ	IN	_	36	mark	_	_
35	$ X $	$ x $	SYM	$	_	36	nsubj	_	_
36	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	advcl	_	_
37	stable	stable	ADJ	JJ	Degree=Pos	36	acomp	_	_
38	under	under	ADP	IN	_	36	prep	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
40	restriction	restriction	NOUN	NN	Number=Sing	38	pobj	_	_
41	to	to	ADP	IN	_	36	prep	_	_
42	$ Y $	$ y $	SYM	$	_	41	pobj	_	_
43	of	of	ADP	IN	_	42	prep	_	_
44	the	the	DET	DT	Definite=Def|PronType=Art	46	det	_	_
45	conjugation	conjugation	NOUN	NN	Number=Sing	46	compound	_	_
46	action	action	NOUN	NN	Number=Sing	43	pobj	_	_
47	of	of	ADP	IN	_	46	prep	_	_
48	$ A $	$ a $	SYM	$	_	47	pobj	_	_
49	on	on	ADP	IN	_	36	prep	_	_
50	itself	itself	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs|Reflex=Yes	49	pobj	_	SpaceAfter=No
51	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 8
# text = This also amounts to an alternative proof of Bourn and Janelidze's category equivalence between points over $ G $ in $ mathbb C $ and actions of $ G $ in the semi - abelian context.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	amounts	amount	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	to	to	ADP	IN	_	3	prep	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	alternative	alternative	ADJ	JJ	Degree=Pos	7	amod	_	_
7	proof	proof	NOUN	NN	Number=Sing	4	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	Bourn	Bourn	PROPN	NNP	Number=Sing	8	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	Janelidze	Janelidze	PROPN	NNP	Number=Sing	14	poss	_	SpaceAfter=No
12	's	's	PART	POS	_	11	case	_	_
13	category	category	NOUN	NN	Number=Sing	14	compound	_	_
14	equivalence	equivalence	NOUN	NN	Number=Sing	9	conj	_	_
15	between	between	ADP	IN	_	7	prep	_	_
16	points	point	NOUN	NNS	Number=Plur	15	pobj	_	_
17	over	over	ADP	IN	_	16	prep	_	_
18	$ G $	$ g $	SYM	$	_	17	pobj	_	_
19	in	in	ADP	IN	_	16	prep	_	_
20	$ mathbb C $	$ mathbb c $	SYM	$	_	19	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
22	actions	action	NOUN	NNS	Number=Plur	16	conj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	$ G $	$ g $	SYM	$	_	23	pobj	_	_
25	in	in	ADP	IN	_	7	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
27	semi	semi	ADJ	JJ	Degree=Pos	30	amod	_	_
28	-	-	ADJ	JJ	Degree=Pos	30	amod	_	_
29	abelian	abelian	ADJ	JJ	Degree=Pos	30	amod	_	_
30	context	context	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 9
# text = Finally, we show that the two axioms of an algebra which characterize $ G $ - actions are equivalent with three others ones, in terms of action cores.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	17	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	two	two	NUM	CD	NumType=Card	8	nummod	_	_
8	axioms	axiom	NOUN	NNS	Number=Plur	17	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	algebra	algebra	NOUN	NN	Number=Sing	9	pobj	_	_
12	which	which	PRON	WDT	_	13	nsubj	_	_
13	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	11	relcl	_	_
14	$ G $	$ g $	SYM	$	_	16	compound	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	actions	action	NOUN	NNS	Number=Plur	17	nsubj	_	_
17	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
18	equivalent	equivalent	ADJ	JJ	Degree=Pos	17	acomp	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	three	three	NUM	CD	NumType=Card	22	nummod	_	_
21	others	other	NOUN	NNS	Number=Plur	22	compound	_	_
22	ones	one	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
24	in	in	ADP	IN	_	17	prep	_	_
25	terms	term	NOUN	NNS	Number=Plur	24	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	action	action	NOUN	NN	Number=Sing	28	compound	_	_
28	cores	core	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 10
# text = These axioms are commutative squares involving only co - smash products.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	axioms	axiom	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	commutative	commutative	ADJ	JJ	Degree=Pos	5	amod	_	_
5	squares	square	NOUN	NNS	Number=Plur	3	attr	_	_
6	involving	involve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	acl	_	_
7	only	only	ADV	RB	_	11	amod	_	_
8	co	co	NOUN	NN	Number=Sing	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	smash	smash	VERB	VB	VerbForm=Inf	11	compound	_	_
11	products	product	NOUN	NNS	Number=Plur	6	dobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 11
# text = Two of them are associativity type conditions which generalize the usual properties of an action of one group on another, while the third is kind of a higher coherence condition which is a consequence of the other two in the category of groups, but probably not in general.
1	Two	two	NUM	CD	NumType=Card	4	nsubj	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	2	pobj	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	associativity	associativity	NOUN	NN	Number=Sing	7	compound	_	_
6	type	type	NOUN	NN	Number=Sing	7	compound	_	_
7	conditions	condition	NOUN	NNS	Number=Plur	4	attr	_	_
8	which	which	PRON	WDT	_	9	nsubj	_	_
9	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	7	relcl	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	usual	usual	ADJ	JJ	Degree=Pos	12	amod	_	_
12	properties	property	NOUN	NNS	Number=Plur	9	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	action	action	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	one	one	NUM	CD	NumType=Card	18	nummod	_	_
18	group	group	NOUN	NN	Number=Sing	16	pobj	_	_
19	on	on	ADP	IN	_	15	prep	_	_
20	another	another	PRON	DT	_	19	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
22	while	while	SCONJ	IN	_	25	mark	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	third	third	ADJ	JJ	Degree=Pos	25	nsubj	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	advcl	_	_
26	kind	kind	ADV	RB	_	27	advmod	_	_
27	of	of	ADV	RB	_	31	advmod	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
29	higher	high	ADJ	JJR	Degree=Cmp	31	amod	_	_
30	coherence	coherence	NOUN	NN	Number=Sing	31	compound	_	_
31	condition	condition	NOUN	NN	Number=Sing	25	attr	_	_
32	which	which	PRON	WDT	_	33	nsubj	_	_
33	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	31	relcl	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
35	consequence	consequence	NOUN	NN	Number=Sing	33	attr	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
38	other	other	ADJ	JJ	Degree=Pos	39	amod	_	_
39	two	two	NUM	CD	NumType=Card	36	pobj	_	_
40	in	in	ADP	IN	_	39	prep	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	42	det	_	_
42	category	category	NOUN	NN	Number=Sing	40	pobj	_	_
43	of	of	ADP	IN	_	42	prep	_	_
44	groups	group	NOUN	NNS	Number=Plur	43	pobj	_	SpaceAfter=No
45	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
46	but	but	CCONJ	CC	ConjType=Cmp	33	cc	_	_
47	probably	probably	ADV	RB	_	49	advmod	_	_
48	not	not	PART	RB	Polarity=Neg	49	neg	_	_
49	in	in	ADP	IN	_	33	conj	_	_
50	general	general	ADJ	JJ	Degree=Pos	49	amod	_	SpaceAfter=No
51	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 12
# text = As an application, we characterize abelian action cores, that is, action cores corresponding to Beck modules; here also the coherence condition follows from the others.
1	As	as	ADP	IN	_	6	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	26	ccomp	_	_
7	abelian	abelian	ADJ	JJ	Degree=Pos	9	amod	_	_
8	action	action	NOUN	NN	Number=Sing	9	compound	_	_
9	cores	core	NOUN	NNS	Number=Plur	6	dobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	that	that	ADV	RB	_	12	advmod	_	_
12	is	is	ADV	RB	_	9	relcl	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
14	action	action	NOUN	NN	Number=Sing	15	compound	_	_
15	cores	core	NOUN	NNS	Number=Plur	6	dobj	_	_
16	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	amod	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	Beck	Beck	PROPN	NNP	Number=Sing	19	compound	_	_
19	modules	module	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	;	;	PUNCT	:	_	26	punct	_	_
21	here	here	ADV	RB	PronType=Dem	26	advmod	_	_
22	also	also	ADV	RB	_	26	advmod	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	coherence	coherence	NOUN	NN	Number=Sing	25	compound	_	_
25	condition	condition	NOUN	NN	Number=Sing	26	nsubj	_	_
26	follows	follow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
27	from	from	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	others	other	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	26	punct	_	SpaceAfter=No

# doc_id = 433
# sent_id = 1
# text = Lawvere's notion of completeness for quantale - enriched categories has been extended to the theory of lax algebras under the name of $ L $ - completeness.
1	Lawvere	Lawvere	PROPN	NNP	Number=Sing	3	poss	_	SpaceAfter=No
2	's	's	PART	POS	_	1	case	_	_
3	notion	notion	NOUN	NN	Number=Sing	13	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	completeness	completeness	NOUN	NN	Number=Sing	4	pobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	quantale	quantale	ADJ	JJ	Degree=Pos	9	npadvmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
11	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	aux	_	_
12	been	be	AUX	VBN	Tense=Past|VerbForm=Part	13	auxpass	_	_
13	extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	theory	theory	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	lax	lax	ADJ	JJ	Degree=Pos	19	amod	_	_
19	algebras	algebra	NOUN	NNS	Number=Plur	17	pobj	_	_
20	under	under	ADP	IN	_	13	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	name	name	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	$ L $	$ l $	SYM	$	_	26	compound	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	completeness	completeness	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper we introduce the corresponding morphism concept and examine its properties.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
7	corresponding	corresponding	ADJ	JJ	Degree=Pos	9	amod	_	_
8	morphism	morphism	NOUN	NN	Number=Sing	9	compound	_	_
9	concept	concept	NOUN	NN	Number=Sing	5	dobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
11	examine	examine	VERB	VB	VerbForm=Inf	5	conj	_	_
12	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	13	poss	_	_
13	properties	property	NOUN	NNS	Number=Plur	11	dobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = We explore some important relativized topological concepts like separatedness, denseness, compactness and compactification with respect to $ L $ - complete morphisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	explore	explore	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	some	some	DET	DT	_	7	det	_	_
4	important	important	ADJ	JJ	Degree=Pos	7	amod	_	_
5	relativized	relativize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
6	topological	topological	ADJ	JJ	Degree=Pos	7	amod	_	_
7	concepts	concept	NOUN	NNS	Number=Plur	2	dobj	_	_
8	like	like	ADP	IN	_	7	prep	_	_
9	separatedness	separatedness	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	denseness	denseness	ADJ	JJ	Degree=Pos	9	conj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	compactness	compactness	NOUN	NN	Number=Sing	11	conj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	compactification	compactification	NOUN	NN	Number=Sing	13	conj	_	_
16	with	with	ADP	IN	_	2	prep	_	_
17	respect	respect	NOUN	NN	Number=Sing	16	pobj	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	$ L $	$ l $	SYM	$	_	21	advmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	complete	complete	ADJ	JJ	Degree=Pos	22	amod	_	_
22	morphisms	morphism	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = Moreover, we show that separated $ L $ - complete morphisms belong to a factorization system.
1	Moreover	moreover	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	PRON	WDT	PronType=Rel	6	nsubj	_	_
6	separated	separate	VERB	VBD	Tense=Past|VerbForm=Fin	4	ccomp	_	_
7	$ L $	$ l $	SYM	$	_	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	complete	complete	ADJ	JJ	Degree=Pos	10	amod	_	_
10	morphisms	morphism	NOUN	NNS	Number=Plur	11	nsubj	_	_
11	belong	belong	VERB	VBP	Tense=Pres|VerbForm=Fin	6	ccomp	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	factorization	factorization	NOUN	NN	Number=Sing	15	compound	_	_
15	system	system	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 434
# sent_id = 1
# text = The characterization of stably closed maps of topological spaces as the closed maps with compact fibres and the role of the Kuratowski - Mrówka' Theorem in this characterization are being explored in the general context of lax $ (T, V) $ - algebras, for a quantale $ V $ and a $ Set $ - monad $ T $ with a lax extension to $ V $ - relations.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	characterization	characterization	NOUN	NN	Number=Sing	32	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	stably	stably	ADV	RB	_	5	advmod	_	_
5	closed	closed	ADJ	JJ	Degree=Pos	6	amod	_	_
6	maps	map	NOUN	NNS	Number=Plur	3	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	topological	topological	ADJ	JJ	Degree=Pos	9	amod	_	_
9	spaces	space	NOUN	NNS	Number=Plur	7	pobj	_	_
10	as	as	ADP	IN	_	2	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	closed	closed	ADJ	JJ	Degree=Pos	13	amod	_	_
13	maps	map	NOUN	NNS	Number=Plur	10	pobj	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	compact	compact	ADJ	JJ	Degree=Pos	16	amod	_	_
16	fibres	fibre	NOUN	NNS	Number=Plur	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	role	role	NOUN	NN	Number=Sing	32	nsubjpass	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
22	Kuratowski	Kuratowski	PROPN	NNP	Number=Sing	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	Mrówka	Mrówka	PROPN	NNP	Number=Sing	26	poss	_	SpaceAfter=No
25	'	'	PART	POS	_	24	case	_	_
26	Theorem	Theorem	PROPN	NNP	Number=Sing	20	pobj	_	_
27	in	in	ADP	IN	_	19	prep	_	_
28	this	this	DET	DT	Number=Sing|PronType=Dem	29	det	_	_
29	characterization	characterization	NOUN	NN	Number=Sing	27	pobj	_	_
30	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	32	aux	_	_
31	being	be	AUX	VBG	VerbForm=Ger	32	auxpass	_	_
32	explored	explore	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
33	in	in	ADP	IN	_	32	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
35	general	general	ADJ	JJ	Degree=Pos	36	amod	_	_
36	context	context	NOUN	NN	Number=Sing	33	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	lax	lax	ADJ	JJ	Degree=Pos	41	amod	_	_
39	$ (T, V) $	$ (t, v) $	SYM	$	_	41	compound	_	_
40	-	-	PUNCT	HYPH	PunctType=Dash	41	punct	_	_
41	algebras	algebra	NOUN	NNS	Number=Plur	37	pobj	_	SpaceAfter=No
42	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
43	for	for	ADP	IN	_	32	prep	_	_
44	a	a	DET	DT	Definite=Ind|PronType=Art	46	det	_	_
45	quantale	quantale	ADJ	JJ	Degree=Pos	46	compound	_	_
46	$ V $	$ v $	SYM	$	_	43	pobj	_	_
47	and	and	CCONJ	CC	ConjType=Cmp	46	cc	_	_
48	a	a	DET	DT	Definite=Ind|PronType=Art	51	det	_	_
49	$ Set $	$ set $	SYM	$	_	51	compound	_	_
50	-	-	PUNCT	HYPH	PunctType=Dash	51	punct	_	_
51	monad	monad	NOUN	NNS	Number=Plur	46	conj	_	_
52	$ T $	$ t $	SYM	$	_	46	appos	_	_
53	with	with	ADP	IN	_	46	prep	_	_
54	a	a	DET	DT	Definite=Ind|PronType=Art	56	det	_	_
55	lax	lax	ADJ	JJ	Degree=Pos	56	amod	_	_
56	extension	extension	NOUN	NN	Number=Sing	53	pobj	_	_
57	to	to	ADP	IN	_	56	prep	_	_
58	$ V $	$ v $	SYM	$	_	60	compound	_	_
59	-	-	PUNCT	HYPH	PunctType=Dash	60	punct	_	_
60	relations	relation	NOUN	NNS	Number=Plur	57	pobj	_	SpaceAfter=No
61	.	.	PUNCT	.	PunctType=Peri	32	punct	_	SpaceAfter=No

# sent_id = 2
# text = The general results are being applied in standard (topological and metric) and non - standard (labeled graphs) contexts.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	general	general	ADJ	JJ	Degree=Pos	3	amod	_	_
3	results	result	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	aux	_	_
5	being	be	AUX	VBG	VerbForm=Ger	6	auxpass	_	_
6	applied	apply	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	standard	standard	ADJ	JJ	Degree=Pos	22	amod	_	_
9	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	8	punct	_	SpaceAfter=No
10	topological	topological	ADJ	JJ	Degree=Pos	8	conj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	metric	metric	ADJ	JJ	Degree=Pos	10	conj	_	SpaceAfter=No
13	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	8	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
15	non	non	ADJ	JJ	Degree=Pos	20	amod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
17	standard	standard	ADJ	JJ	Degree=Pos	20	amod	_	_
18	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	20	punct	_	SpaceAfter=No
19	labeled	label	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	amod	_	_
20	graphs	graph	NOUN	NNS	Number=Plur	22	nmod	_	SpaceAfter=No
21	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	22	punct	_	_
22	contexts	context	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 435
# sent_id = 1
# text = We consider a symmetric monoidal closed category $ V = (V, otimes, I, [ - , - ]) $ together with a regular injective object $ Q $ such that the functor $ [ - , Q] : to V^{op} $ is comonadic and prove that in such a category, as in the monoidal category of abelian groups, a morphism of commutative monoids is an effective descent morphism for modules if and only if it is a pure monomorphism.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	symmetric	symmetric	ADJ	JJ	Degree=Pos	5	amod	_	_
5	monoidal	monoidal	NOUN	NN	Number=Sing	6	nsubj	_	_
6	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	2	ccomp	_	_
7	category	category	NOUN	NN	Number=Sing	6	dobj	_	_
8	$ V = (V, otimes, I, [ - , - ]) $	$ v = (v, otimes, i, [ - , - ]) $	SYM	$	_	6	dep	_	_
9	together	together	ADV	RB	_	10	advmod	_	_
10	with	with	ADP	IN	_	6	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
12	regular	regular	ADJ	JJ	Degree=Pos	14	amod	_	_
13	injective	injective	ADJ	JJ	Degree=Pos	14	amod	_	_
14	object	object	NOUN	NN	Number=Sing	10	pobj	_	_
15	$ Q $	$ q $	SYM	$	_	14	appos	_	_
16	such	such	ADJ	JJ	Degree=Pos	14	appos	_	_
17	that	that	SCONJ	IN	_	21	mark	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	functor	functor	NOUN	NN	Number=Sing	21	nsubj	_	_
20	$ [ - , Q] : to V^{op} $	$ [ - , q] : to v^{op} $	SYM	$	_	19	appos	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	advcl	_	_
22	comonadic	comonadic	ADJ	JJ	Degree=Pos	21	acomp	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
24	prove	prove	VERB	VB	VerbForm=Inf	21	conj	_	_
25	that	that	SCONJ	IN	_	45	mark	_	_
26	in	in	ADP	IN	_	45	prep	_	_
27	such	such	DET	PDT	_	29	predet	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
29	category	category	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	45	punct	_	_
31	as	as	ADP	IN	_	45	prep	_	_
32	in	in	ADP	IN	_	31	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
34	monoidal	monoidal	ADJ	JJ	Degree=Pos	35	amod	_	_
35	category	category	NOUN	NN	Number=Sing	32	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	abelian	abelian	ADJ	JJ	Degree=Pos	38	compound	_	_
38	groups	group	NOUN	NNS	Number=Plur	36	pobj	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	45	punct	_	_
40	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
41	morphism	morphism	NOUN	NN	Number=Sing	45	nsubj	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	commutative	commutative	ADJ	JJ	Degree=Pos	44	amod	_	_
44	monoids	monoid	NOUN	NNS	Number=Plur	42	pobj	_	_
45	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	ccomp	_	_
46	an	an	DET	DT	Definite=Ind|PronType=Art	49	det	_	_
47	effective	effective	ADJ	JJ	Degree=Pos	49	amod	_	_
48	descent	descent	NOUN	NN	Number=Sing	49	compound	_	_
49	morphism	morphism	NOUN	NN	Number=Sing	45	attr	_	_
50	for	for	ADP	IN	_	49	prep	_	_
51	modules	module	NOUN	NNS	Number=Plur	50	pobj	_	_
52	if	if	SCONJ	IN	_	45	dep	_	_
53	and	and	CCONJ	CC	ConjType=Cmp	52	cc	_	_
54	only	only	ADV	RB	_	57	advmod	_	_
55	if	if	SCONJ	IN	_	57	mark	_	_
56	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	57	nsubj	_	_
57	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	45	advcl	_	_
58	a	a	DET	DT	Definite=Ind|PronType=Art	60	det	_	_
59	pure	pure	ADJ	JJ	Degree=Pos	60	amod	_	_
60	monomorphism	monomorphism	NOUN	NN	Number=Sing	57	attr	_	SpaceAfter=No
61	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Examples of this kind of monoidal categories are elementary toposes considered as cartesian closed monoidal categories, the module categories over a commutative ring object in a Grothendieck topos and Barr's star - autonomous categories.
1	Examples	example	NOUN	NNS	Number=Plur	8	nsubj	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	kind	kind	NOUN	NN	Number=Sing	2	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	monoidal	monoidal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	elementary	elementary	ADJ	JJ	Degree=Pos	10	amod	_	_
10	toposes	topos	NOUN	NNS	Number=Plur	8	attr	_	_
11	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acl	_	_
12	as	as	SCONJ	IN	_	14	mark	_	_
13	cartesian	cartesian	NOUN	NN	Number=Sing	14	nsubj	_	_
14	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	11	advcl	_	_
15	monoidal	monoidal	ADJ	JJ	Degree=Pos	16	amod	_	_
16	categories	category	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	module	module	NOUN	NN	Number=Sing	20	compound	_	_
20	categories	category	NOUN	NNS	Number=Plur	8	dep	_	_
21	over	over	ADP	IN	_	20	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
23	commutative	commutative	ADJ	JJ	Degree=Pos	25	amod	_	_
24	ring	ring	NOUN	NN	Number=Sing	25	compound	_	_
25	object	object	NOUN	NN	Number=Sing	21	pobj	_	_
26	in	in	ADP	IN	_	25	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	29	compound	_	_
29	topos	topo	NOUN	NNS	Number=Plur	26	pobj	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
31	Barr	Barr	PROPN	NNP	Number=Sing	36	poss	_	SpaceAfter=No
32	's	's	PART	POS	_	31	case	_	_
33	star	star	NOUN	NN	Number=Sing	35	npadvmod	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	autonomous	autonomous	ADJ	JJ	Degree=Pos	36	amod	_	_
36	categories	category	NOUN	NNS	Number=Plur	29	conj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 436
# sent_id = 1
# text = In 2001 Barr and Kleisli described $ * $ - autonomous structures on two full subcategories of topological abelian groups.
1	In	in	ADP	IN	_	6	prep	_	_
2	2001	2001	NUM	CD	NumType=Card	1	pobj	_	_
3	Barr	Barr	PROPN	NNP	Number=Sing	6	nsubj	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	Kleisli	Kleisli	PROPN	NNP	Number=Sing	3	conj	_	_
6	described	describe	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
7	$ * $	$ * $	SYM	$	_	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	autonomous	autonomous	ADJ	JJ	Degree=Pos	10	amod	_	_
10	structures	structure	NOUN	NNS	Number=Plur	6	dobj	_	_
11	on	on	ADP	IN	_	10	prep	_	_
12	two	two	NUM	CD	NumType=Card	14	nummod	_	_
13	full	full	ADJ	JJ	Degree=Pos	14	amod	_	_
14	subcategories	subcategorie	NOUN	NNS	Number=Plur	11	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	topological	topological	ADJ	JJ	Degree=Pos	18	amod	_	_
17	abelian	abelian	ADJ	JJ	Degree=Pos	18	compound	_	_
18	groups	group	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper we do the same for sup semi - lattices except that uniform structures play the role that topology did in the earlier paper.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	do	do	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	same	same	ADJ	JJ	Degree=Pos	5	dobj	_	_
8	for	for	ADP	IN	_	5	prep	_	_
9	sup	sup	NOUN	NN	Number=Sing	8	pobj	_	_
10	semi	semi	NOUN	NNS	Number=Plur	5	advmod	_	_
11	-	-	NOUN	NNS	Number=Plur	5	punct	_	_
12	lattices	lattice	NOUN	NNS	Number=Plur	5	dobj	_	_
13	except	except	SCONJ	IN	_	12	prep	_	_
14	that	that	SCONJ	IN	_	17	mark	_	_
15	uniform	uniform	ADJ	JJ	Degree=Pos	16	amod	_	_
16	structures	structure	NOUN	NNS	Number=Plur	17	nsubj	_	_
17	play	play	VERB	VBP	Tense=Pres|VerbForm=Fin	13	pcomp	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	role	role	NOUN	NN	Number=Sing	17	dobj	_	_
20	that	that	PRON	WDT	PronType=Rel	22	dobj	_	_
21	topology	topology	NOUN	NN	Number=Sing	22	nsubj	_	_
22	did	do	VERB	VBD	Tense=Past|VerbForm=Fin	19	relcl	_	_
23	in	in	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	earlier	early	ADJ	JJR	Degree=Cmp	26	amod	_	_
26	paper	paper	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 437
# sent_id = 1
# text = We prove that all semi - abelian categories with the the Smith is Huq property satisfy the Commutator Condition: higher central extensions may be characterised in terms of binary (Huq or Smith) commutators.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	26	ccomp	_	_
3	that	that	SCONJ	IN	_	13	mark	_	_
4	all	all	DET	DT	_	8	det	_	_
5	semi	semi	ADJ	JJ	Degree=Pos	8	amod	_	_
6	-	-	ADJ	JJ	Degree=Pos	8	amod	_	_
7	abelian	abelian	ADJ	JJ	Degree=Pos	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	13	nsubj	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	Smith	Smith	PROPN	NNP	Number=Sing	9	pobj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
14	Huq	Huq	PROPN	NNP	Number=Sing	16	compound	_	_
15	property	property	NOUN	NN	Number=Sing	16	compound	_	_
16	satisfy	satisfy	NOUN	NN	Number=Sing	13	attr	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	Commutator	Commutator	PROPN	NNP	Number=Sing	19	compound	_	_
19	Condition	Condition	PROPN	NNP	Number=Sing	16	dobj	_	SpaceAfter=No
20	:	:	PUNCT	:	_	26	punct	_	_
21	higher	high	ADJ	JJR	Degree=Cmp	23	amod	_	_
22	central	central	ADJ	JJ	Degree=Pos	23	amod	_	_
23	extensions	extension	NOUN	NNS	Number=Plur	26	nsubjpass	_	_
24	may	may	AUX	MD	VerbForm=Fin	26	aux	_	_
25	be	be	AUX	VB	VerbForm=Inf	26	auxpass	_	_
26	characterised	characterise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	terms	term	NOUN	NNS	Number=Plur	27	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	binary	binary	NOUN	NN	Number=Sing	36	amod	_	_
31	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	30	punct	_	SpaceAfter=No
32	Huq	Huq	PROPN	NNP	Number=Sing	30	appos	_	_
33	or	or	CCONJ	CC	ConjType=Cmp	32	cc	_	_
34	Smith	Smith	PROPN	NNP	Number=Sing	32	conj	_	SpaceAfter=No
35	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	30	punct	_	_
36	commutators	commutator	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	26	punct	_	SpaceAfter=No

# sent_id = 2
# text = In fact, even Higgins commutators suffice.
1	In	in	ADP	IN	_	7	prep	_	_
2	fact	fact	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
4	even	even	ADV	RB	_	7	advmod	_	_
5	Higgins	Higgins	PROPN	NNP	Number=Sing	6	compound	_	_
6	commutators	commutator	NOUN	NNS	Number=Plur	7	nsubj	_	_
7	suffice	suffice	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = As a consequence, in the presence of enough projectives we obtain explicit Hopf formulae for homology with coefficients in the abelianisation functor, and an interpretation of cohomology with coefficients in an abelian object in terms of equivalence classes of higher central extensions.
1	As	as	ADP	IN	_	5	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	consequence	consequence	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
5	in	in	ADP	IN	_	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	presence	presence	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	enough	enough	ADJ	JJ	Degree=Pos	10	amod	_	_
10	projectives	projective	NOUN	NNS	Number=Plur	8	pobj	_	_
11	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	12	nsubj	_	_
12	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	10	relcl	_	_
13	explicit	explicit	ADJ	JJ	Degree=Pos	15	amod	_	_
14	Hopf	hopf	NOUN	NN	Number=Sing	15	compound	_	_
15	formulae	formulae	ADJ	JJ	Degree=Pos	12	dobj	_	_
16	for	for	ADP	IN	_	15	prep	_	_
17	homology	homology	NOUN	NN	Number=Sing	16	pobj	_	_
18	with	with	ADP	IN	_	12	prep	_	_
19	coefficients	coefficient	NOUN	NNS	Number=Plur	18	pobj	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	abelianisation	abelianisation	NOUN	NN	Number=Sing	23	compound	_	_
23	functor	functor	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
26	an	an	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	interpretation	interpretation	NOUN	NN	Number=Sing	5	conj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	cohomology	cohomology	NOUN	NN	Number=Sing	28	pobj	_	_
30	with	with	ADP	IN	_	27	prep	_	_
31	coefficients	coefficient	NOUN	NNS	Number=Plur	30	pobj	_	_
32	in	in	ADP	IN	_	31	prep	_	_
33	an	an	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
34	abelian	abelian	ADJ	JJ	Degree=Pos	35	compound	_	_
35	object	object	NOUN	NN	Number=Sing	32	pobj	_	_
36	in	in	ADP	IN	_	31	prep	_	_
37	terms	term	NOUN	NNS	Number=Plur	36	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	equivalence	equivalence	NOUN	NN	Number=Sing	40	compound	_	_
40	classes	class	NOUN	NNS	Number=Plur	38	pobj	_	_
41	of	of	ADP	IN	_	40	prep	_	_
42	higher	high	ADJ	JJR	Degree=Cmp	44	amod	_	_
43	central	central	ADJ	JJ	Degree=Pos	44	amod	_	_
44	extensions	extension	NOUN	NNS	Number=Plur	41	pobj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = We also give a counterexample against Commutator Condition in the semi - abelian category of (commutative) loops.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	counterexample	counterexample	NOUN	NN	Number=Sing	3	dobj	_	_
6	against	against	ADP	IN	_	3	prep	_	_
7	Commutator	Commutator	PROPN	NNP	Number=Sing	8	compound	_	_
8	Condition	Condition	PROPN	NNP	Number=Sing	6	pobj	_	_
9	in	in	ADP	IN	_	3	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
11	semi	semi	ADJ	JJ	Degree=Pos	14	amod	_	_
12	-	-	ADJ	JJ	Degree=Pos	14	amod	_	_
13	abelian	abelian	ADJ	JJ	Degree=Pos	14	amod	_	_
14	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	15	punct	_	SpaceAfter=No
17	commutative	commutative	PROPN	NNP	Number=Sing	15	pobj	_	SpaceAfter=No
18	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	15	punct	_	_
19	loops	loop	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 438
# sent_id = 1
# text = We introduce an intrinsic description of the Ursini commutator in any ideal determined category and we compare it with the Higgins and Huq commutators.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	intrinsic	intrinsic	ADJ	JJ	Degree=Pos	5	amod	_	_
5	description	description	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	Ursini	Ursini	PROPN	NNP	Number=Sing	9	compound	_	_
9	commutator	commutator	NOUN	NN	Number=Sing	6	pobj	_	_
10	in	in	ADP	IN	_	2	prep	_	_
11	any	any	DET	DT	_	14	det	_	_
12	ideal	ideal	ADJ	JJ	Degree=Pos	14	amod	_	_
13	determined	determined	ADJ	JJ	Degree=Pos	14	amod	_	_
14	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
16	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	17	nsubj	_	_
17	compare	compare	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
18	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	17	dobj	_	_
19	with	with	ADP	IN	_	17	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	Higgins	Higgins	PROPN	NNP	Number=Sing	19	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	Huq	Huq	PROPN	NNP	Number=Sing	21	conj	_	_
24	commutators	commutator	NOUN	NNS	Number=Plur	21	conj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 2
# text = After describing also the Smith - Pedicchio commutator by means of canonical arrows from a coproduct, we compare the two notions, showing that in any exact Maltsev normal category the Ursini commutator $ [H, K]_{U} $ of two subobjects $ H $ , $ K $ of $ A $ is the normalization of the Smith - Pedicchio commutator of the equivalence relations generated by $ H $ and $ K $ , extending the result valid for ideal determined varieties given by Ursini and Gumm.
1	After	after	ADP	IN	_	19	prep	_	_
2	describing	describe	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	1	pcomp	_	_
3	also	also	ADV	RB	_	2	advmod	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
5	Smith	Smith	PROPN	NNP	Number=Sing	7	compound	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	Pedicchio	Pedicchio	PROPN	NNP	Number=Sing	8	compound	_	_
8	commutator	commutator	NOUN	NN	Number=Sing	2	dobj	_	_
9	by	by	ADP	IN	_	2	prep	_	_
10	means	mean	NOUN	NNS	Number=Plur	9	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	canonical	canonical	ADJ	JJ	Degree=Pos	13	amod	_	_
13	arrows	arrow	NOUN	NNS	Number=Plur	11	pobj	_	_
14	from	from	ADP	IN	_	10	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	coproduct	coproduct	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	compare	compare	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	two	two	NUM	CD	NumType=Card	22	nummod	_	_
22	notions	notion	NOUN	NNS	Number=Plur	19	dobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
24	showing	show	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	44	csubj	_	_
25	that	that	SCONJ	IN	_	38	mark	_	_
26	in	in	ADP	IN	_	38	prep	_	_
27	any	any	DET	DT	_	31	det	_	_
28	exact	exact	ADJ	JJ	Degree=Pos	31	amod	_	_
29	Maltsev	Maltsev	PROPN	NNP	Number=Sing	31	nmod	_	_
30	normal	normal	ADJ	JJ	Degree=Pos	31	amod	_	_
31	category	category	NOUN	NN	Number=Sing	26	pobj	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
33	Ursini	Ursini	PROPN	NNP	Number=Sing	34	compound	_	_
34	commutator	commutator	NOUN	NN	Number=Sing	31	appos	_	_
35	$ [H, K]_{U} $	$ [h, k]_{u} $	SYM	$	_	38	nsubj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	two	two	NUM	CD	NumType=Card	36	pobj	_	_
38	subobjects	subobject	NOUN	NNS	Number=Plur	24	ccomp	_	_
39	$ H $	$ h $	SYM	$	_	38	dobj	_	_
40	,	,	PUNCT	,	PunctType=Comm	39	punct	_	_
41	$ K $	$ k $	SYM	$	_	38	dep	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	$ A $	$ a $	SYM	$	_	42	pobj	_	_
44	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	advcl	_	_
45	the	the	DET	DT	Definite=Def|PronType=Art	46	det	_	_
46	normalization	normalization	NOUN	NN	Number=Sing	44	attr	_	_
47	of	of	ADP	IN	_	46	prep	_	_
48	the	the	DET	DT	Definite=Def|PronType=Art	52	det	_	_
49	Smith	Smith	PROPN	NNP	Number=Sing	51	compound	_	_
50	-	-	PUNCT	HYPH	PunctType=Dash	51	punct	_	_
51	Pedicchio	Pedicchio	PROPN	NNP	Number=Sing	52	compound	_	_
52	commutator	commutator	NOUN	NN	Number=Sing	47	pobj	_	_
53	of	of	ADP	IN	_	52	prep	_	_
54	the	the	DET	DT	Definite=Def|PronType=Art	56	det	_	_
55	equivalence	equivalence	NOUN	NN	Number=Sing	56	compound	_	_
56	relations	relation	NOUN	NNS	Number=Plur	53	pobj	_	_
57	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	56	acl	_	_
58	by	by	ADP	IN	_	57	agent	_	_
59	$ H $	$ h $	SYM	$	_	58	pobj	_	_
60	and	and	CCONJ	CC	ConjType=Cmp	59	cc	_	_
61	$ K $	$ k $	SYM	$	_	57	advmod	_	_
62	,	,	PUNCT	,	PunctType=Comm	44	punct	_	_
63	extending	extend	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	44	advcl	_	_
64	the	the	DET	DT	Definite=Def|PronType=Art	65	det	_	_
65	result	result	NOUN	NN	Number=Sing	63	dobj	_	_
66	valid	valid	ADJ	JJ	Degree=Pos	63	oprd	_	_
67	for	for	ADP	IN	_	66	prep	_	_
68	ideal	ideal	ADJ	JJ	Degree=Pos	70	amod	_	_
69	determined	determined	ADJ	JJ	Degree=Pos	70	amod	_	_
70	varieties	variety	NOUN	NNS	Number=Plur	67	pobj	_	_
71	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	70	acl	_	_
72	by	by	ADP	IN	_	71	agent	_	_
73	Ursini	Ursini	PROPN	NNP	Number=Sing	72	pobj	_	_
74	and	and	CCONJ	CC	ConjType=Cmp	73	cc	_	_
75	Gumm	Gumm	PROPN	NNP	Number=Sing	73	conj	_	SpaceAfter=No
76	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# doc_id = 439
# sent_id = 1
# text = We prove a general theorem which includes most notions of "exact completion" as special cases.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	general	general	ADJ	JJ	Degree=Pos	5	amod	_	_
5	theorem	theorem	NOUN	NN	Number=Sing	2	dobj	_	_
6	which	which	PRON	WDT	_	7	nsubj	_	_
7	includes	include	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	relcl	_	_
8	most	most	ADJ	JJS	Degree=Sup	9	amod	_	_
9	notions	notion	NOUN	NNS	Number=Plur	7	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	13	punct	_	SpaceAfter=No
12	exact	exact	ADJ	JJ	Degree=Pos	13	amod	_	_
13	completion	completion	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
14	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	13	punct	_	_
15	as	as	ADP	IN	_	7	prep	_	_
16	special	special	ADJ	JJ	Degree=Pos	17	amod	_	_
17	cases	case	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The theorem is that " $ κ $ - ary exact categories" are a reflective sub - 2 - category of " $ κ $ - ary sites", for any regular cardinal $ κ $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	theorem	theorem	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	12	mark	_	_
5	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	12	punct	_	_
6	$ κ $	$ κ $	SYM	$	_	8	quantmod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	ary	ary	ADJ	JJ	Degree=Pos	10	nmod	_	_
9	exact	exact	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	12	nsubj	_	SpaceAfter=No
11	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	10	punct	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
14	reflective	reflective	ADJ	JJ	Degree=Pos	19	amod	_	_
15	sub	sub	NOUN	NN	Number=Sing	19	nmod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
17	2	2	NUM	CD	NumType=Card	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	category	category	NOUN	NN	Number=Sing	12	attr	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	25	punct	_	_
22	$ κ $	$ κ $	SYM	$	_	24	quantmod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	ary	ary	ADJ	JJ	Degree=Pos	25	compound	_	_
25	sites	site	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
26	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	12	punct	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
28	for	for	ADP	IN	_	32	prep	_	_
29	any	any	DET	DT	_	31	det	_	_
30	regular	regular	ADJ	JJ	Degree=Pos	31	amod	_	_
31	cardinal	cardinal	NOUN	NN	Number=Sing	28	pobj	_	_
32	$ κ $	$ κ $	SYM	$	_	12	dep	_	_
33	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = A $ κ $ - ary exact category is an exact category with disjoint and universal $ κ $ - small coproducts, and a $ κ $ - ary site is a site whose covering sieves are generated by $ κ $ - small families and which satisfies a solution - set condition for finite limits relative to $ κ $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
2	$ κ $	$ κ $	SYM	$	_	4	quantmod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	ary	ary	ADJ	JJ	Degree=Pos	6	nmod	_	_
5	exact	exact	ADJ	JJ	Degree=Pos	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	exact	exact	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	7	attr	_	_
11	with	with	ADP	IN	_	10	prep	_	_
12	disjoint	disjoint	NOUN	NN	Number=Sing	11	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	universal	universal	ADJ	JJ	Degree=Pos	12	conj	_	_
15	$ κ $	$ κ $	SYM	$	_	17	advmod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	small	small	ADJ	JJ	Degree=Pos	18	amod	_	_
18	coproducts	coproduct	NOUN	NNS	Number=Plur	12	conj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
22	$ κ $	$ κ $	SYM	$	_	24	quantmod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	ary	ary	ADJ	JJ	Degree=Pos	25	amod	_	_
25	site	site	NOUN	NN	Number=Sing	26	nsubj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	conj	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	site	site	NOUN	NN	Number=Sing	26	attr	_	_
29	whose	whose	DET	WP$	Poss=Yes	31	poss	_	_
30	covering	cover	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	31	amod	_	_
31	sieves	sieve	NOUN	NNS	Number=Plur	33	nsubjpass	_	_
32	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	33	auxpass	_	_
33	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	relcl	_	_
34	by	by	ADP	IN	_	33	agent	_	_
35	$ κ $	$ κ $	SYM	$	_	37	advmod	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	small	small	ADJ	JJ	Degree=Pos	38	amod	_	_
38	families	family	NOUN	NNS	Number=Plur	34	pobj	_	_
39	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
40	which	which	PRON	WDT	_	41	nsubj	_	_
41	satisfies	satisfy	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	33	conj	_	_
42	a	a	DET	DT	Definite=Ind|PronType=Art	46	det	_	_
43	solution	solution	NOUN	NN	Number=Sing	45	npadvmod	_	_
44	-	-	PUNCT	HYPH	PunctType=Dash	45	punct	_	_
45	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	46	amod	_	_
46	condition	condition	NOUN	NN	Number=Sing	41	dobj	_	_
47	for	for	ADP	IN	_	46	prep	_	_
48	finite	finite	ADJ	JJ	Degree=Pos	49	compound	_	_
49	limits	limit	NOUN	NNS	Number=Plur	47	pobj	_	_
50	relative	relative	ADJ	JJ	Degree=Pos	49	amod	_	_
51	to	to	ADP	IN	_	50	prep	_	_
52	$ κ $	$ κ $	SYM	$	_	51	pobj	_	_
53	.	.	PUNCT	.	PunctType=Peri	26	punct	_	SpaceAfter=No

# sent_id = 4
# text = In the unary case, this includes the exact completions of a regular category, of a category with (weak) finite limits, and of a category with a factorization system.
1	In	in	ADP	IN	_	7	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	unary	unary	ADJ	JJ	Degree=Pos	4	amod	_	_
4	case	case	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	this	this	PRON	DT	Number=Sing|PronType=Dem	7	nsubj	_	_
7	includes	include	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	exact	exact	ADJ	JJ	Degree=Pos	10	amod	_	_
10	completions	completion	NOUN	NNS	Number=Plur	7	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	regular	regular	ADJ	JJ	Degree=Pos	14	amod	_	_
14	category	category	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
16	of	of	ADP	IN	_	10	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	category	category	NOUN	NN	Number=Sing	16	pobj	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
21	weak	weak	ADJ	JJ	Degree=Pos	24	amod	_	SpaceAfter=No
22	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	24	punct	_	_
23	finite	finite	ADJ	JJ	Degree=Pos	24	compound	_	_
24	limits	limit	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
27	of	of	ADP	IN	_	16	conj	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
29	category	category	NOUN	NN	Number=Sing	27	pobj	_	_
30	with	with	ADP	IN	_	29	prep	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
32	factorization	factorization	NOUN	NN	Number=Sing	33	compound	_	_
33	system	system	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 5
# text = When κ=ω it includes the pretopos completion of a coherent category.
1	When	when	SCONJ	WRB	_	6	advmod	_	_
2	κ	κ	PROPN	NNP	Number=Sing	6	dep	_	SpaceAfter=No
3	=	=	X	XX	_	2	punct	_	SpaceAfter=No
4	ω	ω	NUM	CD	NumType=Card	2	punct	_	_
5	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	6	nsubj	_	_
6	includes	include	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	pretopos	pretopos	NOUN	NN	Number=Sing	9	compound	_	_
9	completion	completion	NOUN	NN	Number=Sing	6	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	coherent	coherent	ADJ	JJ	Degree=Pos	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 6
# text = And when $ κ=∞ $ is the size of the universe, it includes the category of sheaves on a small site, and the category of small presheaves on a locally small and finitely complete category.
1	And	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
2	when	when	SCONJ	WRB	_	4	advmod	_	_
3	$ κ=∞ $	$ κ=∞ $	SYM	$	_	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	advcl	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	size	size	NOUN	NN	Number=Sing	4	attr	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	universe	universe	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
11	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	12	nsubj	_	_
12	includes	include	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	category	category	NOUN	NN	Number=Sing	12	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	sheaves	sheaf	NOUN	NNS	Number=Plur	15	pobj	_	_
17	on	on	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	small	small	ADJ	JJ	Degree=Pos	20	amod	_	_
20	site	site	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	category	category	NOUN	NN	Number=Sing	12	conj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	small	small	ADJ	JJ	Degree=Pos	27	amod	_	_
27	presheaves	presheave	NOUN	NNS	Number=Plur	25	pobj	_	_
28	on	on	ADP	IN	_	24	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
30	locally	locally	ADV	RB	_	31	advmod	_	_
31	small	small	ADJ	JJ	Degree=Pos	35	amod	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	finitely	finitely	ADV	RB	_	34	advmod	_	_
34	complete	complete	ADJ	JJ	Degree=Pos	31	conj	_	_
35	category	category	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 7
# text = The $ ∞ $ - ary exact completion of a large nontrivial site gives a well - behaved "category of small sheaves".
1	The	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
2	$ ∞ $	$ ∞ $	SYM	$	_	4	advmod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	ary	ary	ADJ	JJ	Degree=Pos	6	nmod	_	_
5	exact	exact	ADJ	JJ	Degree=Pos	6	amod	_	_
6	completion	completion	NOUN	NN	Number=Sing	12	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	large	large	ADJ	JJ	Degree=Pos	11	amod	_	_
10	nontrivial	nontrivial	ADJ	JJ	Degree=Pos	11	amod	_	_
11	site	site	NOUN	NN	Number=Sing	7	pobj	_	_
12	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
14	well	well	ADV	RB	Degree=Pos	16	advmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	behaved	behave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
17	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	18	punct	_	SpaceAfter=No
18	category	category	NOUN	NN	Number=Sing	12	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	small	small	ADJ	JJ	Degree=Pos	21	amod	_	_
21	sheaves	sheaf	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
22	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	12	punct	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 8
# text = Along the way, we define a slightly generalized notion of "morphism of sites" and show that $ κ $ - ary sites are equivalent to a type of "enhanced allegory".
1	Along	along	ADP	IN	_	6	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	way	way	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	slightly	slightly	ADV	RB	_	9	advmod	_	_
9	generalized	generalized	ADJ	JJ	Degree=Pos	10	amod	_	_
10	notion	notion	NOUN	NN	Number=Sing	6	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	11	punct	_	SpaceAfter=No
13	morphism	morphism	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	sites	site	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
16	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	6	punct	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
18	show	show	VERB	VB	VerbForm=Inf	6	conj	_	_
19	that	that	SCONJ	IN	_	24	mark	_	_
20	$ κ $	$ κ $	SYM	$	_	22	quantmod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	ary	ary	ADJ	JJ	Degree=Pos	23	amod	_	_
23	sites	site	NOUN	NNS	Number=Plur	24	nsubj	_	_
24	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	18	ccomp	_	_
25	equivalent	equivalent	ADJ	JJ	Degree=Pos	24	acomp	_	_
26	to	to	ADP	IN	_	25	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	type	type	NOUN	NN	Number=Sing	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	32	punct	_	SpaceAfter=No
31	enhanced	enhanced	ADJ	JJ	Degree=Pos	32	amod	_	_
32	allegory	allegory	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
33	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	24	punct	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 9
# text = This enables us to construct the exact completion in two ways, which can be regarded as decategorifications of "representable profunctors" (that is, entire functional relations) and "anafunctors", respectively.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	enables	enable	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	2	dobj	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	construct	construct	VERB	VB	VerbForm=Inf	2	xcomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	exact	exact	ADJ	JJ	Degree=Pos	8	amod	_	_
8	completion	completion	NOUN	NN	Number=Sing	5	dobj	_	_
9	in	in	ADP	IN	_	5	prep	_	_
10	two	two	NUM	CD	NumType=Card	11	nummod	_	_
11	ways	way	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	which	which	PRON	WDT	_	16	nsubjpass	_	_
14	can	can	AUX	MD	VerbForm=Fin	16	aux	_	_
15	be	be	AUX	VB	VerbForm=Inf	16	auxpass	_	_
16	regarded	regard	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	relcl	_	_
17	as	as	ADP	IN	_	16	prep	_	_
18	decategorifications	decategorification	NOUN	NNS	Number=Plur	17	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	22	punct	_	SpaceAfter=No
21	representable	representable	ADJ	JJ	Degree=Pos	22	amod	_	_
22	profunctors	profunctor	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
23	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	22	punct	_	_
24	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	22	punct	_	SpaceAfter=No
25	that	that	ADV	RB	_	26	advmod	_	_
26	is	is	ADV	RB	_	30	advmod	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
28	entire	entire	ADJ	JJ	Degree=Pos	30	amod	_	_
29	functional	functional	ADJ	JJ	Degree=Pos	30	amod	_	_
30	relations	relation	NOUN	NNS	Number=Plur	22	appos	_	SpaceAfter=No
31	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	22	punct	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
33	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	34	punct	_	SpaceAfter=No
34	anafunctors	anafunctor	NOUN	NNS	Number=Plur	22	conj	_	SpaceAfter=No
35	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	34	punct	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	34	punct	_	_
37	respectively	respectively	ADV	RB	_	34	advmod	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 440
# sent_id = 1
# text = We investigate $ 3 $ - permutability, in the sense of universal algebra, in an abstract categorical setting which unifies the pointed and the non - pointed contexts in categorical algebra.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	$ 3 $	$ 3 $	SYM	$	_	5	nummod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	permutability	permutability	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
7	in	in	ADP	IN	_	2	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	sense	sense	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	universal	universal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	algebra	algebra	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
14	in	in	ADP	IN	_	7	prep	_	_
15	an	an	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
16	abstract	abstract	ADJ	JJ	Degree=Pos	18	amod	_	_
17	categorical	categorical	ADJ	JJ	Degree=Pos	18	amod	_	_
18	setting	setting	NOUN	NN	Number=Sing	14	pobj	_	_
19	which	which	PRON	WDT	_	20	nsubj	_	_
20	unifies	unify	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	relcl	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	pointed	pointed	NOUN	NN	Number=Sing	20	dobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
25	non	non	PROPN	NNP	Number=Sing	27	npadvmod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	pointed	pointed	ADJ	JJ	Degree=Pos	28	amod	_	_
28	contexts	context	NOUN	NNS	Number=Plur	22	conj	_	_
29	in	in	ADP	IN	_	22	prep	_	_
30	categorical	categorical	ADJ	JJ	Degree=Pos	31	amod	_	_
31	algebra	algebra	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This leads to a unified treatment of regular subtractive categories and of regular Goursat categories, as well as of $ E $ - subtractive varieties (where $ E $ is the set of constants in a variety) recently introduced by the fourth author.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	leads	lead	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	unified	unified	ADJ	JJ	Degree=Pos	6	amod	_	_
6	treatment	treatment	NOUN	NN	Number=Sing	3	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	regular	regular	ADJ	JJ	Degree=Pos	10	amod	_	_
9	subtractive	subtractive	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
12	of	of	ADP	IN	_	7	conj	_	_
13	regular	regular	ADJ	JJ	Degree=Pos	15	amod	_	_
14	Goursat	Goursat	PROPN	NNP	Number=Sing	15	compound	_	_
15	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
17	as	as	ADV	RB	_	19	advmod	_	_
18	well	well	ADV	RB	Degree=Pos	19	advmod	_	_
19	as	as	ADP	IN	_	6	cc	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	$ E $	$ e $	SYM	$	_	23	advmod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	subtractive	subtractive	ADJ	JJ	Degree=Pos	24	amod	_	_
24	varieties	variety	NOUN	NNS	Number=Plur	20	pobj	_	_
25	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
26	where	where	SCONJ	WRB	_	27	advmod	_	_
27	$ E $	$ e $	SYM	$	_	6	relcl	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	advcl	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	set	set	NOUN	NN	Number=Sing	28	attr	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	constants	constant	NOUN	NNS	Number=Plur	31	pobj	_	_
33	in	in	ADP	IN	_	30	prep	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
35	variety	variety	NOUN	NN	Number=Sing	33	pobj	_	SpaceAfter=No
36	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	28	punct	_	_
37	recently	recently	ADV	RB	_	38	advmod	_	_
38	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	advcl	_	_
39	by	by	ADP	IN	_	38	agent	_	_
40	the	the	DET	DT	Definite=Def|PronType=Art	42	det	_	_
41	fourth	fourth	ADJ	JJ	Degree=Pos	42	amod	_	_
42	author	author	NOUN	NN	Number=Sing	39	pobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = As an application, we show that ``ideals'' coincide with ``clots'' in any regular subtractive category, which can be considered as a pointed analogue of a known result for regular Goursat categories.
1	As	as	ADP	IN	_	6	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	12	mark	_	_
8	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	10	punct	_	SpaceAfter=No
9	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	10	punct	_	SpaceAfter=No
10	ideals	ideal	NOUN	NNS	Number=Plur	12	nsubj	_	SpaceAfter=No
11	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	10	punct	_	_
12	coincide	coincide	NOUN	NN	Number=Sing	6	ccomp	_	_
13	with	with	ADP	IN	_	12	prep	_	_
14	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	16	punct	_	SpaceAfter=No
15	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	16	punct	_	SpaceAfter=No
16	clots	clot	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
17	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	16	punct	_	_
18	in	in	ADP	IN	_	16	prep	_	_
19	any	any	DET	DT	_	22	det	_	_
20	regular	regular	ADJ	JJ	Degree=Pos	22	amod	_	_
21	subtractive	subtractive	ADJ	JJ	Degree=Pos	22	amod	_	_
22	category	category	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	which	which	PRON	WDT	_	27	nsubjpass	_	_
25	can	can	AUX	MD	VerbForm=Fin	27	aux	_	_
26	be	be	AUX	VB	VerbForm=Inf	27	auxpass	_	_
27	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	relcl	_	_
28	as	as	ADP	IN	_	27	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	pointed	pointed	ADJ	JJ	Degree=Pos	31	amod	_	_
31	analogue	analogue	NOUN	NN	Number=Sing	28	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
34	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	35	amod	_	_
35	result	result	NOUN	NN	Number=Sing	32	pobj	_	_
36	for	for	ADP	IN	_	35	prep	_	_
37	regular	regular	ADJ	JJ	Degree=Pos	39	amod	_	_
38	Goursat	Goursat	PROPN	NNP	Number=Sing	39	compound	_	_
39	categories	category	NOUN	NNS	Number=Plur	36	pobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 441
# sent_id = 1
# text = We define a strong relation in a category $ mathbb{C} $ to be a span which is ``orthogonal'' to the class of jointly epimorphic pairs of morphisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	strong	strong	ADJ	JJ	Degree=Pos	5	amod	_	_
5	relation	relation	NOUN	NN	Number=Sing	2	dobj	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	9	nmod	_	_
9	$ mathbb{C} $	$ mathbb{c} $	SYM	$	_	6	pobj	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	be	be	AUX	VB	VerbForm=Inf	5	acl	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	span	span	NOUN	NN	Number=Sing	11	attr	_	_
14	which	which	PRON	WDT	_	15	nsubj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	relcl	_	_
16	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	15	punct	_	SpaceAfter=No
17	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	18	punct	_	SpaceAfter=No
18	orthogonal	orthogonal	ADJ	JJ	Degree=Pos	15	acomp	_	SpaceAfter=No
19	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	18	punct	_	_
20	to	to	ADP	IN	_	18	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	class	class	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	jointly	jointly	ADV	RB	_	25	advmod	_	_
25	epimorphic	epimorphic	ADJ	JJ	Degree=Pos	26	amod	_	_
26	pairs	pair	NOUN	NNS	Number=Plur	23	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	morphisms	morphism	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Under the presence of finite limits, a strong relation is simply a strong monomorphism $ Rrightarrow Xtimes Y $ .
1	Under	under	ADP	IN	_	11	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	presence	presence	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	finite	finite	ADJ	JJ	Degree=Pos	6	compound	_	_
6	limits	limit	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	strong	strong	ADJ	JJ	Degree=Pos	10	amod	_	_
10	relation	relation	NOUN	NN	Number=Sing	11	nsubj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	simply	simply	ADV	RB	_	11	advmod	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	strong	strong	ADJ	JJ	Degree=Pos	15	amod	_	_
15	monomorphism	monomorphism	NOUN	NN	Number=Sing	11	attr	_	_
16	$ Rrightarrow Xtimes Y $	$ rrightarrow xtimes y $	SYM	$	_	15	prep	_	_
17	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that a category $ mathbb{C} $ with pullbacks and equalizers is a weakly Maltsev category if and only if every reflexive strong relation in $ mathbb{C} $ is an equivalence relation.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	11	mark	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	11	nsubj	_	_
6	$ mathbb{C} $	$ mathbb{c} $	SYM	$	_	5	appos	_	_
7	with	with	ADP	IN	_	5	prep	_	_
8	pullbacks	pullback	NOUN	NNS	Number=Plur	7	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	equalizers	equalizer	NOUN	NNS	Number=Plur	8	conj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	weakly	weakly	ADJ	JJ	Degree=Pos	15	amod	_	_
14	Maltsev	Maltsev	PROPN	NNP	Number=Sing	15	compound	_	_
15	category	category	NOUN	NN	Number=Sing	11	attr	_	_
16	if	if	SCONJ	IN	_	26	mark	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	only	only	ADV	RB	_	23	advmod	_	_
19	if	if	SCONJ	IN	_	23	mark	_	_
20	every	every	DET	DT	_	23	det	_	_
21	reflexive	reflexive	ADJ	JJ	Degree=Pos	23	amod	_	_
22	strong	strong	ADJ	JJ	Degree=Pos	23	amod	_	_
23	relation	relation	NOUN	NN	Number=Sing	26	nsubj	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	$ mathbb{C} $	$ mathbb{c} $	SYM	$	_	24	pobj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	advcl	_	_
27	an	an	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	equivalence	equivalence	NOUN	NN	Number=Sing	29	compound	_	_
29	relation	relation	NOUN	NN	Number=Sing	26	attr	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = In fact, we obtain a more general result which includes, as its another particular instance, a similar well - known characterization of Maltsev categories.
1	In	in	ADP	IN	_	5	prep	_	_
2	fact	fact	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	more	more	ADV	RBR	Degree=Cmp	8	advmod	_	_
8	general	general	ADJ	JJ	Degree=Pos	9	amod	_	_
9	result	result	NOUN	NN	Number=Sing	5	dobj	_	_
10	which	which	PRON	WDT	_	11	nsubj	_	_
11	includes	include	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	relcl	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	as	as	ADP	IN	_	11	prep	_	_
14	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	17	poss	_	_
15	another	another	DET	DT	_	17	det	_	_
16	particular	particular	ADJ	JJ	Degree=Pos	17	amod	_	_
17	instance	instance	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
20	similar	similar	ADJ	JJ	Degree=Pos	24	amod	_	_
21	well	well	ADV	RB	Degree=Pos	23	advmod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
24	characterization	characterization	NOUN	NN	Number=Sing	17	appos	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	Maltsev	maltsev	ADJ	JJ	Degree=Pos	27	amod	_	_
27	categories	category	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 442
# sent_id = 1
# text = A category is adhesive if it has all pullbacks, all push - outs along monomorphisms, and all exactness conditions between pullbacks and pushouts along monomorphisms which hold in a topos.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	adhesive	adhesive	ADJ	JJ	Degree=Pos	3	acomp	_	_
5	if	if	SCONJ	IN	_	7	mark	_	_
6	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	7	nsubj	_	_
7	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	advcl	_	_
8	all	all	DET	DT	_	9	det	_	_
9	pullbacks	pullback	NOUN	NNS	Number=Plur	7	dobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
11	all	all	DET	DT	_	14	det	_	_
12	push	push	NOUN	NN	Number=Sing	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	outs	out	NOUN	NNS	Number=Plur	3	attr	_	_
15	along	along	ADP	IN	_	14	prep	_	_
16	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
19	all	all	DET	DT	_	21	det	_	_
20	exactness	exactness	ADJ	JJ	Degree=Pos	21	amod	_	_
21	conditions	condition	NOUN	NNS	Number=Plur	14	conj	_	_
22	between	between	ADP	IN	_	21	prep	_	_
23	pullbacks	pullback	NOUN	NNS	Number=Plur	22	pobj	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	pushouts	pushout	NOUN	NNS	Number=Plur	23	conj	_	_
26	along	along	ADP	IN	_	23	prep	_	_
27	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	26	pobj	_	_
28	which	which	PRON	WDT	_	29	nsubj	_	_
29	hold	hold	VERB	VBP	Tense=Pres|VerbForm=Fin	27	relcl	_	_
30	in	in	ADP	IN	_	29	prep	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
32	topos	topos	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = This condition can be modified by considering only pushouts along regular monomorphisms, or by asking only for the exactness conditions which hold in a quasitopos.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	condition	condition	NOUN	NN	Number=Sing	5	nsubjpass	_	_
3	can	can	AUX	MD	VerbForm=Fin	5	aux	_	_
4	be	be	AUX	VB	VerbForm=Inf	5	auxpass	_	_
5	modified	modify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	by	by	ADP	IN	_	5	prep	_	_
7	considering	consider	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	pcomp	_	_
8	only	only	ADJ	JJ	Degree=Pos	9	advmod	_	_
9	pushouts	pushout	NOUN	NNS	Number=Plur	7	dobj	_	_
10	along	along	ADP	IN	_	9	prep	_	_
11	regular	regular	ADJ	JJ	Degree=Pos	12	amod	_	_
12	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
14	or	or	CCONJ	CC	ConjType=Cmp	6	cc	_	_
15	by	by	ADP	IN	_	6	conj	_	_
16	asking	ask	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	pcomp	_	_
17	only	only	ADV	RB	_	18	advmod	_	_
18	for	for	ADP	IN	_	16	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	exactness	exactness	ADJ	JJ	Degree=Pos	21	amod	_	_
21	conditions	condition	NOUN	NNS	Number=Plur	18	pobj	_	_
22	which	which	PRON	WDT	_	23	nsubj	_	_
23	hold	hold	VERB	VBP	Tense=Pres|VerbForm=Fin	21	relcl	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
26	quasitopos	quasitopos	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = We prove four characterization theorems dealing with adhesive categories and their variants.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	four	four	NUM	CD	NumType=Card	5	nummod	_	_
4	characterization	characterization	NOUN	NN	Number=Sing	5	compound	_	_
5	theorems	theorem	NOUN	NNS	Number=Plur	2	dobj	_	_
6	dealing	deal	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	acl	_	_
7	with	with	ADP	IN	_	6	prep	_	_
8	adhesive	adhesive	ADJ	JJ	Degree=Pos	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	12	poss	_	_
12	variants	variant	NOUN	NNS	Number=Plur	9	conj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 443
# sent_id = 1
# text = For a small category $ B $ and a double category $ mathbb D $ , let $ {rm Lax}_N(B, mathbb D) $ denote the category whose objects are vertical normal lax functors $ Btomathbb D $ and morphisms are horizontal lax transformations.
1	For	for	ADP	IN	_	12	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	small	small	ADJ	JJ	Degree=Pos	4	amod	_	_
4	category	category	NOUN	NN	Number=Sing	1	pobj	_	_
5	$ B $	$ b $	SYM	$	_	4	nummod	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	double	double	ADJ	JJ	Degree=Pos	9	amod	_	_
9	category	category	NOUN	NN	Number=Sing	4	conj	_	_
10	$ mathbb D $	$ mathbb d $	SYM	$	_	4	appos	_	_
11	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
12	let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
13	$ {rm Lax}_N(B, mathbb D) $	$ {rm lax}_n(b, mathbb d) $	SYM	$	_	14	nsubj	_	_
14	denote	denote	VERB	VBD	Tense=Past|VerbForm=Fin	12	ccomp	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	category	category	NOUN	NN	Number=Sing	14	dobj	_	_
17	whose	whose	DET	WP$	Poss=Yes	18	poss	_	_
18	objects	object	NOUN	NNS	Number=Plur	19	nsubj	_	_
19	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	16	relcl	_	_
20	vertical	vertical	ADJ	JJ	Degree=Pos	23	amod	_	_
21	normal	normal	ADJ	JJ	Degree=Pos	23	amod	_	_
22	lax	lax	PROPN	NNP	Number=Sing	23	amod	_	_
23	functors	functor	NOUN	NNS	Number=Plur	19	attr	_	_
24	$ Btomathbb D $	$ btomathbb d $	SYM	$	_	14	dep	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
26	morphisms	morphism	NOUN	NNS	Number=Plur	27	nsubj	_	_
27	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	conj	_	_
28	horizontal	horizontal	ADJ	JJ	Degree=Pos	30	amod	_	_
29	lax	lax	ADJ	JJ	Degree=Pos	30	amod	_	_
30	transformations	transformation	NOUN	NNS	Number=Plur	27	attr	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 2
# text = It is well known that $ Lax_N(B, mathbb Cat) simeq Cat/B $ , where $ mathbb Cat $ is the double category of small categories, functors, and profunctors.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	well	well	ADV	RB	Degree=Pos	4	advmod	_	_
4	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acomp	_	_
5	that	that	SCONJ	IN	_	10	mark	_	_
6	$ Lax_N(B, mathbb Cat) simeq Cat/B $	$ lax_n(b, mathbb cat) simeq cat/b $	SYM	$	_	10	nsubj	_	_
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	where	where	SCONJ	WRB	_	9	advmod	_	_
9	$ mathbb Cat $	$ mathbb cat $	SYM	$	_	6	relcl	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	double	double	ADJ	JJ	Degree=Pos	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	10	attr	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	small	small	ADJ	JJ	Degree=Pos	16	amod	_	_
16	categories	category	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	functors	functor	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
21	profunctors	profunctor	NOUN	NNS	Number=Plur	18	conj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We generalized this equivalence to certain double categories, in the case where $ B $ is a finite poset.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	generalized	generalize	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	equivalence	equivalence	NOUN	NN	Number=Sing	2	dobj	_	_
5	to	to	ADP	IN	_	2	prep	_	_
6	certain	certain	ADJ	JJ	Degree=Pos	8	amod	_	_
7	double	double	ADJ	JJ	Degree=Pos	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
10	in	in	ADP	IN	_	2	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	case	case	NOUN	NN	Number=Sing	10	pobj	_	_
13	where	where	SCONJ	WRB	_	15	advmod	_	_
14	$ B $	$ b $	SYM	$	_	15	nsubj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	relcl	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	finite	finite	ADJ	JJ	Degree=Pos	18	amod	_	_
18	poset	poset	NOUN	NN	Number=Sing	15	attr	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = Street showed that $ Yto B $ is exponentiable in $ Cat/B $ if and only if the corresponding normal lax functor $ Bto mathbb Cat $ is a pseudo - functor.
1	Street	Street	PROPN	NNP	Number=Sing	2	nsubj	_	_
2	showed	show	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	$ Yto B $	$ yto b $	SYM	$	_	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	exponentiable	exponentiable	ADJ	JJ	Degree=Pos	5	acomp	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	$ Cat/B $	$ cat/b $	SYM	$	_	7	pobj	_	_
9	if	if	SCONJ	IN	_	5	dep	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	only	only	ADV	RB	_	19	advmod	_	_
12	if	if	SCONJ	IN	_	19	mark	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
14	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	amod	_	_
15	normal	normal	ADJ	JJ	Degree=Pos	17	amod	_	_
16	lax	lax	PROPN	NNP	Number=Sing	17	compound	_	_
17	functor	functor	NOUN	NN	Number=Sing	19	nsubj	_	_
18	$ Bto mathbb Cat $	$ bto mathbb cat $	SYM	$	_	17	appos	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	advcl	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
21	pseudo	pseudo	NOUN	NN	Number=Sing	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	functor	functor	NOUN	NN	Number=Sing	19	attr	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = Using our generalized equivalence, we show that a morphism $ Yto B $ is exponentiable in $ {mathbb D}_0/B $ if and only if the corresponding normal lax functor $ Btomathbb D $ is a pseudo - functor plus an additional condition that holds for all $ Xto clikB $ in $ Cat $ .
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	advcl	_	_
2	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	4	poss	_	_
3	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	amod	_	_
4	equivalence	equivalence	NOUN	NN	Number=Sing	1	dobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	that	that	SCONJ	IN	_	12	mark	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	morphism	morphism	NOUN	NN	Number=Sing	12	nsubj	_	_
11	$ Yto B $	$ yto b $	SYM	$	_	10	appos	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	ccomp	_	_
13	exponentiable	exponentiable	ADJ	JJ	Degree=Pos	12	acomp	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	$ {mathbb D}_0/B $	$ {mathbb d}_0/b $	SYM	$	_	14	pobj	_	_
16	if	if	SCONJ	IN	_	12	dep	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	only	only	ADV	RB	_	26	advmod	_	_
19	if	if	SCONJ	IN	_	26	mark	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
21	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	24	amod	_	_
22	normal	normal	ADJ	JJ	Degree=Pos	24	amod	_	_
23	lax	lax	PROPN	NNP	Number=Sing	24	compound	_	_
24	functor	functor	NOUN	NN	Number=Sing	26	nsubj	_	_
25	$ Btomathbb D $	$ btomathbb d $	SYM	$	_	24	appos	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	advcl	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
28	pseudo	pseudo	NOUN	NN	Number=Sing	30	compound	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	functor	functor	NOUN	NN	Number=Sing	26	attr	_	_
31	plus	plus	CCONJ	CC	ConjType=Cmp	30	cc	_	_
32	an	an	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
33	additional	additional	ADJ	JJ	Degree=Pos	34	amod	_	_
34	condition	condition	NOUN	NN	Number=Sing	30	conj	_	_
35	that	that	PRON	WDT	PronType=Rel	36	nsubj	_	_
36	holds	hold	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	34	relcl	_	_
37	for	for	ADP	IN	_	36	prep	_	_
38	all	all	PRON	DT	_	40	advmod	_	_
39	$ Xto clikB $	$ xto clikb $	SYM	$	_	38	nmod	_	_
40	in	in	ADP	IN	_	36	prep	_	_
41	$ Cat $	$ cat $	SYM	$	_	40	pobj	_	_
42	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 6
# text = Thus, we obtain a single theorem which yields characterizations of certain exponentiable morphisms of small categories, topological spaces, locales, and posets.
1	Thus	thus	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	single	single	ADJ	JJ	Degree=Pos	7	amod	_	_
7	theorem	theorem	NOUN	NN	Number=Sing	4	dobj	_	_
8	which	which	PRON	WDT	_	9	nsubj	_	_
9	yields	yield	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	relcl	_	_
10	characterizations	characterization	NOUN	NNS	Number=Plur	9	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	certain	certain	ADJ	JJ	Degree=Pos	14	amod	_	_
13	exponentiable	exponentiable	ADJ	JJ	Degree=Pos	14	amod	_	_
14	morphisms	morphism	NOUN	NNS	Number=Plur	11	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	small	small	ADJ	JJ	Degree=Pos	17	amod	_	_
17	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	topological	topological	ADJ	JJ	Degree=Pos	20	amod	_	_
20	spaces	space	NOUN	NNS	Number=Plur	17	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	locales	locale	NOUN	NNS	Number=Plur	20	conj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
25	posets	poset	NOUN	NNS	Number=Plur	22	conj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 444
# sent_id = 1
# text = There is a lot of redundancy in the usual definition of adjoint functors.
1	There	there	PRON	EX	_	2	expl	_	_
2	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	lot	lot	NOUN	NN	Number=Sing	2	attr	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	redundancy	redundancy	NOUN	NN	Number=Sing	5	pobj	_	_
7	in	in	ADP	IN	_	4	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	usual	usual	ADJ	JJ	Degree=Pos	10	amod	_	_
10	definition	definition	NOUN	NN	Number=Sing	7	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	adjoint	adjoint	NOUN	NN	Number=Sing	13	compound	_	_
13	functors	functor	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We define and prove the core of what is required.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	core	core	NOUN	NN	Number=Sing	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	what	what	PRON	WP	_	10	nsubjpass	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	required	require	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	pcomp	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = First we do this in the hom - enriched context.
1	First	first	ADV	RB	_	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	do	do	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	this	this	PRON	DT	Number=Sing|PronType=Dem	3	dobj	_	_
5	in	in	ADP	IN	_	3	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
7	hom	hom	ADV	RB	_	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	context	context	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = Then we do it in the cocompletion of a bicategory with respect to Kleisli objects, which we then apply to internal categories.
1	Then	then	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	do	do	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	dobj	_	_
5	in	in	ADP	IN	_	3	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	cocompletion	cocompletion	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	bicategory	bicategory	NOUN	NN	Number=Sing	8	pobj	_	_
11	with	with	ADP	IN	_	10	prep	_	_
12	respect	respect	NOUN	NN	Number=Sing	11	pobj	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	Kleisli	Kleisli	PROPN	NNP	Number=Sing	15	compound	_	_
15	objects	object	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	which	which	PRON	WDT	_	20	dobj	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	20	nsubj	_	_
19	then	then	ADV	RB	PronType=Dem	20	advmod	_	_
20	apply	apply	VERB	VBP	Tense=Pres|VerbForm=Fin	15	relcl	_	_
21	to	to	ADP	IN	_	20	prep	_	_
22	internal	internal	ADJ	JJ	Degree=Pos	23	amod	_	_
23	categories	category	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = Finally, we describe a doctrinal setting.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	doctrinal	doctrinal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	setting	setting	NOUN	NN	Number=Sing	4	dobj	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 445
# sent_id = 1
# text = We call a finitely complete category diexact if every difunctional relation admits a pushout which is stable under pullback and itself a pullback.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
4	finitely	finitely	ADV	RB	_	5	advmod	_	_
5	complete	complete	ADJ	JJ	Degree=Pos	7	amod	_	_
6	category	category	NOUN	NN	Number=Sing	7	compound	_	_
7	diexact	diexact	NOUN	NN	Number=Sing	2	dobj	_	_
8	if	if	SCONJ	IN	_	12	mark	_	_
9	every	every	DET	DT	_	11	det	_	_
10	difunctional	difunctional	ADJ	JJ	Degree=Pos	11	amod	_	_
11	relation	relation	NOUN	NN	Number=Sing	12	nsubj	_	_
12	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	advcl	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	pushout	pushout	NOUN	NN	Number=Sing	12	dobj	_	_
15	which	which	PRON	WDT	_	16	nsubj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
17	stable	stable	ADJ	JJ	Degree=Pos	16	acomp	_	_
18	under	under	ADP	IN	_	17	prep	_	_
19	pullback	pullback	NOUN	NN	Number=Sing	18	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	itself	itself	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs|Reflex=Yes	19	conj	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
23	pullback	pullback	NOUN	NN	Number=Sing	16	attr	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We prove three results relating to diexact categories: firstly, that a category is a pretopos if and only if it is diexact with a strict initial object; secondly, that a category is diexact if and only if it is Barr - exact, and every pair of monomorphisms admits a pushout which is stable and a pullback; and thirdly, that a small category with finite limits and pushouts of difunctional relations is diexact if and only if it admits a full structure - preserving embedding into a Grothendieck topos.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	15	ccomp	_	_
3	three	three	NUM	CD	NumType=Card	4	nummod	_	_
4	results	result	NOUN	NNS	Number=Plur	2	dobj	_	_
5	relating	relate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	acl	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	diexact	diexact	VERB	VB	VerbForm=Inf	5	advcl	_	_
8	categories	category	NOUN	NNS	Number=Plur	7	dobj	_	SpaceAfter=No
9	:	:	PUNCT	:	_	2	punct	_	_
10	firstly	firstly	ADV	RB	_	15	advmod	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
12	that	that	SCONJ	IN	_	15	mark	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	category	category	NOUN	NN	Number=Sing	15	nsubj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	36	ccomp	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	pretopos	pretopos	NOUN	NN	Number=Sing	15	attr	_	_
18	if	if	SCONJ	IN	_	17	prep	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	only	only	ADV	RB	_	23	advmod	_	_
21	if	if	SCONJ	IN	_	23	mark	_	_
22	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	23	nsubj	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	advcl	_	_
24	diexact	diexact	NOUN	NN	Number=Sing	23	attr	_	_
25	with	with	ADP	IN	_	24	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
27	strict	strict	ADJ	JJ	Degree=Pos	29	amod	_	_
28	initial	initial	ADJ	JJ	Degree=Pos	29	amod	_	_
29	object	object	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
30	;	;	PUNCT	:	_	36	punct	_	_
31	secondly	secondly	ADV	RB	_	36	advmod	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
33	that	that	SCONJ	IN	_	36	mark	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
35	category	category	NOUN	NN	Number=Sing	36	nsubj	_	_
36	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
37	diexact	diexact	NOUN	NN	Number=Sing	36	attr	_	_
38	if	if	SCONJ	IN	_	43	mark	_	_
39	and	and	CCONJ	CC	ConjType=Cmp	43	cc	_	_
40	only	only	ADV	RB	_	43	advmod	_	_
41	if	if	SCONJ	IN	_	43	mark	_	_
42	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	43	nsubj	_	_
43	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	36	advcl	_	_
44	Barr	Barr	PROPN	NNP	Number=Sing	43	attr	_	_
45	-	-	PUNCT	HYPH	PunctType=Dash	46	punct	_	_
46	exact	exact	ADJ	JJ	Degree=Pos	43	acomp	_	SpaceAfter=No
47	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
48	and	and	CCONJ	CC	ConjType=Cmp	36	cc	_	_
49	every	every	DET	DT	_	50	det	_	_
50	pair	pair	NOUN	NN	Number=Sing	53	nsubj	_	_
51	of	of	ADP	IN	_	50	prep	_	_
52	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	51	pobj	_	_
53	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	36	conj	_	_
54	a	a	DET	DT	Definite=Ind|PronType=Art	55	det	_	_
55	pushout	pushout	NOUN	NN	Number=Sing	53	dobj	_	_
56	which	which	PRON	WDT	_	57	nsubj	_	_
57	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	55	relcl	_	_
58	stable	stable	ADJ	JJ	Degree=Pos	57	acomp	_	_
59	and	and	CCONJ	CC	ConjType=Cmp	58	cc	_	_
60	a	a	DET	DT	Definite=Ind|PronType=Art	61	det	_	_
61	pullback	pullback	NOUN	NN	Number=Sing	58	conj	_	SpaceAfter=No
62	;	;	PUNCT	:	_	53	punct	_	_
63	and	and	CCONJ	CC	ConjType=Cmp	53	cc	_	_
64	thirdly	thirdly	ADV	RB	_	78	advmod	_	SpaceAfter=No
65	,	,	PUNCT	,	PunctType=Comm	78	punct	_	_
66	that	that	SCONJ	IN	_	78	mark	_	_
67	a	a	DET	DT	Definite=Ind|PronType=Art	69	det	_	_
68	small	small	ADJ	JJ	Degree=Pos	69	amod	_	_
69	category	category	NOUN	NN	Number=Sing	78	nsubj	_	_
70	with	with	ADP	IN	_	69	prep	_	_
71	finite	finite	ADJ	JJ	Degree=Pos	72	compound	_	_
72	limits	limit	NOUN	NNS	Number=Plur	70	pobj	_	_
73	and	and	CCONJ	CC	ConjType=Cmp	72	cc	_	_
74	pushouts	pushout	NOUN	NNS	Number=Plur	72	conj	_	_
75	of	of	ADP	IN	_	74	prep	_	_
76	difunctional	difunctional	ADJ	JJ	Degree=Pos	77	amod	_	_
77	relations	relation	NOUN	NNS	Number=Plur	75	pobj	_	_
78	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	53	conj	_	_
79	diexact	diexact	NOUN	NN	Number=Sing	78	attr	_	_
80	if	if	SCONJ	IN	_	91	mark	_	_
81	and	and	CCONJ	CC	ConjType=Cmp	91	cc	_	_
82	only	only	ADV	RB	_	85	advmod	_	_
83	if	if	SCONJ	IN	_	85	mark	_	_
84	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	85	nsubj	_	_
85	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	91	advcl	_	_
86	a	a	DET	DT	Definite=Ind|PronType=Art	90	det	_	_
87	full	full	ADJ	JJ	Degree=Pos	90	amod	_	_
88	structure	structure	NOUN	NN	Number=Sing	90	npadvmod	_	_
89	-	-	PUNCT	HYPH	PunctType=Dash	90	punct	_	_
90	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	91	nsubj	_	_
91	embedding	embed	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	78	advcl	_	_
92	into	into	ADP	IN	_	91	prep	_	_
93	a	a	DET	DT	Definite=Ind|PronType=Art	95	det	_	_
94	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	95	compound	_	_
95	topos	topos	NOUN	NN	Number=Sing	92	pobj	_	SpaceAfter=No
96	.	.	PUNCT	.	PunctType=Peri	78	punct	_	SpaceAfter=No

# doc_id = 446
# sent_id = 1
# text = The classes of stably - vertical, normal, separable, inseparable, purely inseparable and covering morphisms, defined in categorical Galois theory, are characterized for the reflection of the variety of commutative semigroups into its subvariety of semilattices.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	classes	class	NOUN	NNS	Number=Plur	27	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	stably	stably	ADV	RB	_	6	advmod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	vertical	vertical	ADJ	JJ	Degree=Pos	10	amod	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
8	normal	normal	ADJ	JJ	Degree=Pos	10	amod	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
10	separable	separable	ADJ	JJ	Degree=Pos	18	amod	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	inseparable	inseparable	ADJ	JJ	Degree=Pos	10	conj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	purely	purely	ADV	RB	_	15	advmod	_	_
15	inseparable	inseparable	ADJ	JJ	Degree=Pos	10	conj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	covering	cover	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	conj	_	_
18	morphisms	morphism	NOUN	NNS	Number=Plur	3	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
20	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acl	_	_
21	in	in	ADP	IN	_	20	prep	_	_
22	categorical	categorical	ADJ	JJ	Degree=Pos	24	amod	_	_
23	Galois	Galois	PROPN	NNP	Number=Sing	24	compound	_	_
24	theory	theory	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
26	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	27	auxpass	_	_
27	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
28	for	for	ADP	IN	_	27	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	reflection	reflection	NOUN	NN	Number=Sing	28	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
33	variety	variety	NOUN	NN	Number=Sing	31	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	commutative	commutative	ADJ	JJ	Degree=Pos	36	amod	_	_
36	semigroups	semigroup	NOUN	NNS	Number=Plur	34	pobj	_	_
37	into	into	ADP	IN	_	30	prep	_	_
38	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	39	poss	_	_
39	subvariety	subvariety	NOUN	NN	Number=Sing	37	pobj	_	_
40	of	of	ADP	IN	_	39	prep	_	_
41	semilattices	semilattice	NOUN	NNS	Number=Plur	40	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	27	punct	_	SpaceAfter=No

# sent_id = 2
# text = It is also shown that there is an inseparable - separable factorization, but there is no monotone - light factorization.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	4	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
3	also	also	ADV	RB	_	4	advmod	_	_
4	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	that	that	SCONJ	IN	_	7	mark	_	_
6	there	there	PRON	EX	_	7	expl	_	_
7	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
9	inseparable	inseparable	ADJ	JJ	Degree=Pos	11	amod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	separable	separable	ADJ	JJ	Degree=Pos	12	amod	_	_
12	factorization	factorization	NOUN	NN	Number=Sing	7	attr	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
14	but	but	CCONJ	CC	ConjType=Cmp	4	cc	_	_
15	there	there	PRON	EX	_	16	expl	_	_
16	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	conj	_	_
17	no	no	DET	DT	_	21	det	_	_
18	monotone	monotone	ADJ	JJ	Degree=Pos	20	amod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	light	light	ADJ	JJ	Degree=Pos	21	amod	_	_
21	factorization	factorization	NOUN	NN	Number=Sing	16	attr	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# doc_id = 447
# sent_id = 1
# text = Recently Benno van den Berg introduced a new class of realizability toposes which he christened Herbrand toposes.
1	Recently	recently	ADV	RB	_	6	advmod	_	_
2	Benno	Benno	PROPN	NNP	Number=Sing	3	compound	_	_
3	van	van	PROPN	NNP	Number=Sing	4	compound	_	_
4	den	den	NOUN	NN	Number=Sing	5	compound	_	_
5	Berg	Berg	PROPN	NNP	Number=Sing	6	nsubj	_	_
6	introduced	introduce	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	new	new	ADJ	JJ	Degree=Pos	9	amod	_	_
9	class	class	NOUN	NN	Number=Sing	6	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	realizability	realizability	NOUN	NN	Number=Sing	12	compound	_	_
12	toposes	topos	NOUN	NNS	Number=Plur	10	pobj	_	_
13	which	which	PRON	WDT	_	15	dobj	_	_
14	he	he	PRON	PRP	Case=Nom|Gender=Masc|Number=Sing|Person=3|PronType=Prs	15	nsubj	_	_
15	christened	christen	VERB	VBD	Tense=Past|VerbForm=Fin	12	relcl	_	_
16	Herbrand	Herbrand	PROPN	NNP	Number=Sing	15	dobj	_	_
17	toposes	topos	NOUN	NNS	Number=Plur	15	dobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = These toposes have strikingly different properties from ordinary realizability toposes, notably the (related) properties that the `constant object' functor from the topos of sets preserves finite coproducts, and that De Morgan's law is satisfied.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	toposes	topos	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	strikingly	strikingly	ADV	RB	_	5	advmod	_	_
5	different	different	ADJ	JJ	Degree=Pos	6	amod	_	_
6	properties	property	NOUN	NNS	Number=Plur	3	dobj	_	_
7	from	from	ADP	IN	_	6	prep	_	_
8	ordinary	ordinary	ADJ	JJ	Degree=Pos	10	amod	_	_
9	realizability	realizability	NOUN	NN	Number=Sing	10	compound	_	_
10	toposes	topos	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	notably	notably	ADV	RB	_	17	advmod	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
14	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	17	punct	_	SpaceAfter=No
15	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	SpaceAfter=No
16	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	17	punct	_	_
17	properties	property	NOUN	NNS	Number=Plur	10	appos	_	_
18	that	that	SCONJ	IN	_	30	mark	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
20	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	22	punct	_	SpaceAfter=No
21	constant	constant	ADJ	JJ	Degree=Pos	22	amod	_	_
22	object	object	NOUN	NN	Number=Sing	24	nmod	_	SpaceAfter=No
23	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	24	punct	_	_
24	functor	functor	NOUN	NN	Number=Sing	30	nsubj	_	_
25	from	from	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	topos	topos	NOUN	NN	Number=Sing	25	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	sets	set	NOUN	NNS	Number=Plur	28	pobj	_	_
30	preserves	preserve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
31	finite	finite	ADJ	JJ	Degree=Pos	32	amod	_	_
32	coproducts	coproduct	NOUN	NNS	Number=Plur	30	dobj	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
34	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
35	that	that	SCONJ	IN	_	40	mark	_	_
36	De	De	PROPN	NNP	Number=Sing	37	compound	_	_
37	Morgan	Morgan	PROPN	NNP	Number=Sing	39	poss	_	SpaceAfter=No
38	's	's	PART	POS	_	37	case	_	_
39	law	law	NOUN	NN	Number=Sing	40	nsubj	_	_
40	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
41	satisfied	satisfied	ADJ	JJ	Degree=Pos	40	acomp	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this paper we show that these properties are no accident: for any Schonfinkel algebra $ Lambda $ , the Herbrand realizability topos over $ Lambda $ may be obtained as the Gleason cover (in the sense of Johnstone) of the ordinary realizability topos over $ Lambda $ .
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	9	mark	_	_
7	these	these	DET	DT	Number=Plur|PronType=Dem	8	det	_	_
8	properties	property	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
10	no	no	DET	DT	_	11	det	_	_
11	accident	accident	NOUN	NN	Number=Sing	9	attr	_	SpaceAfter=No
12	:	:	PUNCT	:	_	9	punct	_	_
13	for	for	ADP	IN	_	27	prep	_	_
14	any	any	DET	DT	_	16	det	_	_
15	Schonfinkel	Schonfinkel	PROPN	NNP	Number=Sing	16	compound	_	_
16	algebra	algebra	NOUN	NN	Number=Sing	13	pobj	_	_
17	$ Lambda $	$ lambda $	SYM	$	_	13	pobj	_	_
18	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
20	Herbrand	Herbrand	PROPN	NNP	Number=Sing	22	compound	_	_
21	realizability	realizability	NOUN	NN	Number=Sing	22	compound	_	_
22	topos	topos	NOUN	NN	Number=Sing	27	nsubjpass	_	_
23	over	over	ADP	IN	_	22	prep	_	_
24	$ Lambda $	$ lambda $	SYM	$	_	23	pobj	_	_
25	may	may	AUX	MD	VerbForm=Fin	27	aux	_	_
26	be	be	AUX	VB	VerbForm=Inf	27	auxpass	_	_
27	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	ccomp	_	_
28	as	as	ADP	IN	_	27	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
30	Gleason	Gleason	PROPN	NNP	Number=Sing	31	compound	_	_
31	cover	cover	NOUN	NN	Number=Sing	28	pobj	_	_
32	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	31	punct	_	SpaceAfter=No
33	in	in	ADP	IN	_	27	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	sense	sense	NOUN	NN	Number=Sing	33	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	Johnstone	Johnstone	PROPN	NNP	Number=Sing	36	pobj	_	SpaceAfter=No
38	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	33	punct	_	_
39	of	of	ADP	IN	_	27	prep	_	_
40	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
41	ordinary	ordinary	ADJ	JJ	Degree=Pos	42	amod	_	_
42	realizability	realizability	NOUN	NN	Number=Sing	43	compound	_	_
43	topos	topos	PROPN	NNP	Number=Sing	39	pobj	_	_
44	over	over	ADP	IN	_	27	prep	_	_
45	$ Lambda $	$ lambda $	SYM	$	_	44	pobj	_	_
46	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = As a corollary, we obtain the functoriality of the Herbrand realizability construction on the category of Schonfinkel algebras and computationally dense applicative morphisms.
1	As	as	ADP	IN	_	6	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	corollary	corollary	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	functoriality	functoriality	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
11	Herbrand	Herbrand	PROPN	NNP	Number=Sing	13	compound	_	_
12	realizability	realizability	NOUN	NN	Number=Sing	13	compound	_	_
13	construction	construction	NOUN	NN	Number=Sing	9	pobj	_	_
14	on	on	ADP	IN	_	8	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	category	category	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	Schonfinkel	Schonfinkel	PROPN	NNP	Number=Sing	19	compound	_	_
19	algebras	algebra	NOUN	NNS	Number=Plur	17	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
21	computationally	computationally	ADV	RB	_	22	advmod	_	_
22	dense	dense	ADJ	JJ	Degree=Pos	24	amod	_	_
23	applicative	applicative	ADJ	JJ	Degree=Pos	24	amod	_	_
24	morphisms	morphism	NOUN	NNS	Number=Plur	8	conj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 448
# sent_id = 1
# text = An ergodic action of a compact quantum group $ G $ on an operator algebra $ A $ can be interpreted as a quantum homogeneous space for $ G $ .
1	An	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	ergodic	ergodic	ADJ	JJ	Degree=Pos	3	amod	_	_
3	action	action	NOUN	NN	Number=Sing	17	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
6	compact	compact	ADJ	JJ	Degree=Pos	7	amod	_	_
7	quantum	quantum	NOUN	NN	Number=Sing	8	compound	_	_
8	group	group	NOUN	NN	Number=Sing	4	pobj	_	_
9	$ G $	$ g $	SYM	$	_	8	appos	_	_
10	on	on	ADP	IN	_	3	prep	_	_
11	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	operator	operator	NOUN	NN	Number=Sing	13	compound	_	_
13	algebra	algebra	NOUN	NN	Number=Sing	10	pobj	_	_
14	$ A $	$ a $	SYM	$	_	17	nsubjpass	_	_
15	can	can	AUX	MD	VerbForm=Fin	17	aux	_	_
16	be	be	AUX	VB	VerbForm=Inf	17	auxpass	_	_
17	interpreted	interpret	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
18	as	as	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
20	quantum	quantum	ADJ	JJ	Degree=Pos	22	amod	_	_
21	homogeneous	homogeneous	ADJ	JJ	Degree=Pos	22	amod	_	_
22	space	space	NOUN	NN	Number=Sing	18	pobj	_	_
23	for	for	ADP	IN	_	22	prep	_	_
24	$ G $	$ g $	SYM	$	_	23	pobj	_	_
25	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 2
# text = Such an action gives rise to the category of finite equivariant Hilbert modules over $ A $ , which has a module structure over the tensor category $ Rep(G) $ of finite - dimensional representations of $ G $ .
1	Such	such	DET	PDT	_	3	predet	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	action	action	NOUN	NN	Number=Sing	4	nsubj	_	_
4	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	rise	rise	NOUN	NN	Number=Sing	4	dobj	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	finite	finite	PROPN	NNP	Number=Sing	11	amod	_	_
11	equivariant	equivariant	ADJ	JJ	Degree=Pos	13	compound	_	_
12	Hilbert	Hilbert	PROPN	NNP	Number=Sing	13	compound	_	_
13	modules	module	NOUN	NNS	Number=Plur	9	pobj	_	_
14	over	over	ADP	IN	_	13	prep	_	_
15	$ A $	$ a $	SYM	$	_	14	pobj	_	_
16	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
17	which	which	PRON	WDT	_	18	nsubj	_	_
18	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	relcl	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	module	module	NOUN	NN	Number=Sing	21	compound	_	_
21	structure	structure	NOUN	NN	Number=Sing	18	dobj	_	_
22	over	over	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	tensor	tensor	NOUN	NN	Number=Sing	25	compound	_	_
25	category	category	NOUN	NN	Number=Sing	22	pobj	_	_
26	$ Rep(G) $	$ rep(g) $	SYM	$	_	25	appos	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	finite	finite	ADJ	JJ	Degree=Pos	30	amod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	dimensional	dimensional	ADJ	JJ	Degree=Pos	31	amod	_	_
31	representations	representation	NOUN	NNS	Number=Plur	27	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	$ G $	$ g $	SYM	$	_	32	pobj	_	_
34	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that there is a one - to - one correspondence between the quantum $ G $ - homogeneous spaces up to equivariant Morita equivalence, and indecomposable module $ C^* $ - categories over $ Rep(G) $ up to natural equivalence.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	there	there	PRON	EX	_	5	expl	_	_
5	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
7	one	one	NUM	CD	NumType=Card	12	nummod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
9	to	to	ADP	IN	_	7	prep	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
11	one	one	NUM	CD	NumType=Card	9	pobj	_	_
12	correspondence	correspondence	NOUN	NN	Number=Sing	5	attr	_	_
13	between	between	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	quantum	quantum	NOUN	NN	Number=Sing	13	pobj	_	_
16	$ G $	$ g $	SYM	$	_	18	advmod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	homogeneous	homogeneous	ADJ	JJ	Degree=Pos	19	amod	_	_
19	spaces	space	NOUN	NNS	Number=Plur	12	conj	_	_
20	up	up	ADP	RP	_	19	prep	_	_
21	to	to	ADP	IN	_	20	prep	_	_
22	equivariant	equivariant	ADJ	JJ	Degree=Pos	24	amod	_	_
23	Morita	Morita	PROPN	NNP	Number=Sing	24	compound	_	_
24	equivalence	equivalence	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
27	indecomposable	indecomposable	ADJ	JJ	Degree=Pos	28	amod	_	_
28	module	module	NOUN	NN	Number=Sing	19	conj	_	_
29	$ C^* $	$ c^* $	SYM	$	_	31	nummod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	categories	category	NOUN	NNS	Number=Plur	28	appos	_	_
32	over	over	ADP	IN	_	31	prep	_	_
33	$ Rep(G) $	$ rep(g) $	SYM	$	_	32	pobj	_	_
34	up	up	ADP	IN	_	5	prep	_	_
35	to	to	ADP	IN	_	34	prep	_	_
36	natural	natural	ADJ	JJ	Degree=Pos	37	amod	_	_
37	equivalence	equivalence	NOUN	NN	Number=Sing	35	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = This gives a global approach to the duality theory for ergodic actions as developed by Pinzari and Roberts.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	global	global	ADJ	JJ	Degree=Pos	5	amod	_	_
5	approach	approach	NOUN	NN	Number=Sing	2	dobj	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	duality	duality	NOUN	NN	Number=Sing	9	compound	_	_
9	theory	theory	NOUN	NN	Number=Sing	6	pobj	_	_
10	for	for	ADP	IN	_	9	prep	_	_
11	ergodic	ergodic	ADJ	JJ	Degree=Pos	12	amod	_	_
12	actions	action	NOUN	NNS	Number=Plur	10	pobj	_	_
13	as	as	SCONJ	IN	_	14	mark	_	_
14	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	advcl	_	_
15	by	by	ADP	IN	_	14	agent	_	_
16	Pinzari	Pinzari	PROPN	NNP	Number=Sing	15	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	Roberts	Roberts	PROPN	NNP	Number=Sing	16	conj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 449
# sent_id = 1
# text = This is the first in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero).
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	first	first	ADJ	JJ	Degree=Pos	2	attr	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	series	series	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	papers	paper	NOUN	NNS	Number=Plur	8	pobj	_	_
10	laying	lay	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	acl	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	foundations	foundation	NOUN	NNS	Number=Plur	10	dobj	_	_
13	for	for	ADP	IN	_	10	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	differential	differential	ADJ	JJ	Degree=Pos	16	advmod	_	_
16	graded	grade	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	approach	approach	NOUN	NN	Number=Sing	13	pobj	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	derived	derive	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	amod	_	_
20	differential	differential	ADJ	JJ	Degree=Pos	21	amod	_	_
21	geometry	geometry	NOUN	NN	Number=Sing	18	pobj	_	_
22	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	21	punct	_	SpaceAfter=No
23	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
24	other	other	ADJ	JJ	Degree=Pos	25	amod	_	_
25	geometries	geometry	NOUN	NNS	Number=Plur	17	conj	_	_
26	in	in	ADP	IN	_	25	prep	_	_
27	characteristic	characteristic	ADJ	JJ	Degree=Pos	28	amod	_	_
28	zero	zero	NUM	CD	NumType=Card	26	pobj	_	SpaceAfter=No
29	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	25	punct	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper, we study theories of supercommutative algebras for which infinitely differentiable functions can be evaluated on elements.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	theories	theory	NOUN	NNS	Number=Plur	6	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	supercommutative	supercommutative	ADJ	JJ	Degree=Pos	10	amod	_	_
10	algebras	algebra	NOUN	NNS	Number=Plur	8	pobj	_	_
11	for	for	ADP	IN	_	18	prep	_	_
12	which	which	PRON	WDT	_	11	pobj	_	_
13	infinitely	infinitely	ADV	RB	_	14	advmod	_	_
14	differentiable	differentiable	ADJ	JJ	Degree=Pos	15	amod	_	_
15	functions	function	NOUN	NNS	Number=Plur	18	nsubjpass	_	_
16	can	can	AUX	MD	VerbForm=Fin	18	aux	_	_
17	be	be	AUX	VB	VerbForm=Inf	18	auxpass	_	_
18	evaluated	evaluate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	relcl	_	_
19	on	on	ADP	IN	_	18	prep	_	_
20	elements	element	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = Such a theory is called a super Fermat theory.
1	Such	such	DET	PDT	_	3	predet	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	theory	theory	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	super	super	ADJ	JJ	Degree=Pos	9	amod	_	_
8	Fermat	Fermat	PROPN	NNP	Number=Sing	9	compound	_	_
9	theory	theory	NOUN	NN	Number=Sing	5	oprd	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = Any category of superspaces and smooth functions has an associated such theory.
1	Any	any	DET	DT	_	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	8	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	superspaces	superspace	NOUN	NNS	Number=Plur	3	pobj	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	smooth	smooth	ADJ	JJ	Degree=Pos	7	amod	_	_
7	functions	function	NOUN	NNS	Number=Plur	4	conj	_	_
8	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
10	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
11	such	such	ADJ	JJ	Degree=Pos	12	amod	_	_
12	theory	theory	NOUN	NN	Number=Sing	8	dobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 5
# text = This includes both real and complex supermanifolds, as well as algebraic superschemes.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	includes	include	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	both	both	CCONJ	CC	ConjType=Cmp	7	det	_	_
4	real	real	ADJ	JJ	Degree=Pos	7	amod	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	complex	complex	ADJ	JJ	Degree=Pos	4	conj	_	_
7	supermanifolds	supermanifold	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	as	as	ADV	RB	_	11	advmod	_	_
10	well	well	ADV	RB	Degree=Pos	11	advmod	_	_
11	as	as	ADP	IN	_	7	cc	_	_
12	algebraic	algebraic	ADJ	JJ	Degree=Pos	13	amod	_	_
13	superschemes	superscheme	NOUN	NNS	Number=Plur	7	conj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = In particular, there is a super Fermat theory of $ C^infty $ - superalgebras. $ C^infty $ - superalgebras are the appropriate notion of supercommutative algebras in the world of $ C^infty $ - rings, the latter being of central importance both to synthetic differential geometry and to all existing models of derived smooth manifolds.
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	there	there	PRON	EX	_	5	expl	_	_
5	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	super	super	ADJ	JJ	Degree=Pos	9	amod	_	_
8	Fermat	Fermat	PROPN	NNP	Number=Sing	9	compound	_	_
9	theory	theory	NOUN	NN	Number=Sing	5	attr	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	$ C^infty $	$ c^infty $	SYM	$	_	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	superalgebras	superalgebra	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	5	punct	_	_
15	$ C^infty $	$ c^infty $	SYM	$	_	17	nummod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	superalgebras	superalgebra	NOUN	NNS	Number=Plur	18	nsubj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	conj	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	appropriate	appropriate	ADJ	JJ	Degree=Pos	21	amod	_	_
21	notion	notion	NOUN	NN	Number=Sing	18	attr	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	supercommutative	supercommutative	ADJ	JJ	Degree=Pos	24	amod	_	_
24	algebras	algebra	NOUN	NNS	Number=Plur	22	pobj	_	_
25	in	in	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	world	world	NOUN	NN	Number=Sing	25	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	$ C^infty $	$ c^infty $	SYM	$	_	31	compound	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	rings	ring	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
34	latter	latter	ADJ	JJ	Degree=Pos	35	amod	_	_
35	being	being	NOUN	NN	Number=Sing	21	appos	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	central	central	ADJ	JJ	Degree=Pos	38	amod	_	_
38	importance	importance	NOUN	NN	Number=Sing	36	pobj	_	_
39	both	both	PRON	DT	_	40	preconj	_	_
40	to	to	ADP	IN	_	35	prep	_	_
41	synthetic	synthetic	ADJ	JJ	Degree=Pos	43	amod	_	_
42	differential	differential	ADJ	JJ	Degree=Pos	43	amod	_	_
43	geometry	geometry	NOUN	NN	Number=Sing	40	pobj	_	_
44	and	and	CCONJ	CC	ConjType=Cmp	40	cc	_	_
45	to	to	ADP	IN	_	40	conj	_	_
46	all	all	DET	DT	_	48	det	_	_
47	existing	exist	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	48	amod	_	_
48	models	model	NOUN	NNS	Number=Plur	45	pobj	_	_
49	of	of	ADP	IN	_	48	prep	_	_
50	derived	derive	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	52	amod	_	_
51	smooth	smooth	ADJ	JJ	Degree=Pos	52	amod	_	_
52	manifolds	manifold	NOUN	NNS	Number=Plur	49	pobj	_	SpaceAfter=No
53	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 7
# text = A super Fermat theory is a natural generalization of the concept of a Fermat theory introduced by Dubuc and Kock.
1	A	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
2	super	super	ADJ	JJ	Degree=Pos	4	amod	_	_
3	Fermat	Fermat	PROPN	NNP	Number=Sing	4	compound	_	_
4	theory	theory	NOUN	NN	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	natural	natural	ADJ	JJ	Degree=Pos	8	amod	_	_
8	generalization	generalization	NOUN	NN	Number=Sing	5	attr	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	concept	concept	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	Fermat	Fermat	PROPN	NNP	Number=Sing	15	compound	_	_
15	theory	theory	NOUN	NN	Number=Sing	12	pobj	_	_
16	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
17	by	by	ADP	IN	_	16	agent	_	_
18	Dubuc	Dubuc	PROPN	NNP	Number=Sing	17	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	Kock	Kock	PROPN	NNP	Number=Sing	18	conj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 8
# text = We show that any Fermat theory admits a canonical superization, however not every super Fermat theory arises in this way.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	18	ccomp	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	any	any	DET	DT	_	6	det	_	_
5	Fermat	Fermat	PROPN	NNP	Number=Sing	6	compound	_	_
6	theory	theory	NOUN	NN	Number=Sing	7	nsubj	_	_
7	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	canonical	canonical	ADJ	JJ	Degree=Pos	10	amod	_	_
10	superization	superization	NOUN	NN	Number=Sing	7	dobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
12	however	however	ADV	RB	_	18	advmod	_	_
13	not	not	PART	RB	Polarity=Neg	17	neg	_	_
14	every	every	DET	DT	_	17	det	_	_
15	super	super	ADJ	JJ	Degree=Pos	17	amod	_	_
16	Fermat	Fermat	PROPN	NNP	Number=Sing	17	compound	_	_
17	theory	theory	NOUN	NN	Number=Sing	18	nsubj	_	_
18	arises	arise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
19	in	in	ADP	IN	_	18	prep	_	_
20	this	this	DET	DT	Number=Sing|PronType=Dem	21	det	_	_
21	way	way	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# sent_id = 9
# text = For a fixed super Fermat theory, we go on to study a special subcategory of algebras called near - point determined algebras, and derive many of their algebraic properties.
1	For	for	ADP	IN	_	9	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
3	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	amod	_	_
4	super	super	ADJ	JJ	Degree=Pos	6	amod	_	_
5	Fermat	Fermat	PROPN	NNP	Number=Sing	6	compound	_	_
6	theory	theory	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	go	go	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	on	on	ADP	RP	_	9	prt	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	study	study	VERB	VB	VerbForm=Inf	9	advcl	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	special	special	ADJ	JJ	Degree=Pos	15	amod	_	_
15	subcategory	subcategory	NOUN	NN	Number=Sing	12	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	algebras	algebra	NOUN	NNS	Number=Plur	16	pobj	_	_
18	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
19	near	near	ADJ	JJ	Degree=Pos	21	nmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	point	point	NOUN	NN	Number=Sing	23	nmod	_	_
22	determined	determined	ADJ	JJ	Degree=Pos	23	amod	_	_
23	algebras	algebra	NOUN	NNS	Number=Plur	18	oprd	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
26	derive	derive	VERB	VB	VerbForm=Inf	9	conj	_	_
27	many	many	ADJ	JJ	Degree=Pos	26	dobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	31	poss	_	_
30	algebraic	algebraic	ADJ	JJ	Degree=Pos	31	amod	_	_
31	properties	property	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 450
# sent_id = 1
# text = We introduce the notion of weakly globular double categories, a particular class of strict double categories, as a way to model weak 2 - categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	weakly	weakly	ADJ	JJ	Degree=Pos	9	amod	_	_
7	globular	globular	ADJ	JJ	Degree=Pos	9	amod	_	_
8	double	double	ADJ	JJ	Degree=Pos	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	particular	particular	ADJ	JJ	Degree=Pos	13	amod	_	_
13	class	class	NOUN	NN	Number=Sing	9	appos	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	strict	strict	ADJ	JJ	Degree=Pos	17	amod	_	_
16	double	double	ADJ	JJ	Degree=Pos	17	amod	_	_
17	categories	category	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
19	as	as	ADP	IN	_	2	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	way	way	NOUN	NN	Number=Sing	19	pobj	_	_
22	to	to	PART	TO	_	23	aux	_	_
23	model	model	VERB	VB	VerbForm=Inf	21	relcl	_	_
24	weak	weak	ADJ	JJ	Degree=Pos	27	amod	_	_
25	2	2	NUM	CD	NumType=Card	27	nummod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	categories	category	NOUN	NNS	Number=Plur	23	dobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that this model is suitably equivalent to bicategories and give an explicit description of the functors involved in this biequivalence.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	6	mark	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	model	model	NOUN	NN	Number=Sing	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
7	suitably	suitably	ADV	RB	_	8	advmod	_	_
8	equivalent	equivalent	ADJ	JJ	Degree=Pos	6	acomp	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	bicategories	bicategorie	NOUN	NNS	Number=Plur	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
12	give	give	VERB	VB	VerbForm=Inf	6	conj	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	explicit	explicit	ADJ	JJ	Degree=Pos	15	amod	_	_
15	description	description	NOUN	NN	Number=Sing	12	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	functors	functor	NOUN	NNS	Number=Plur	16	pobj	_	_
19	involved	involve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	acl	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	this	this	DET	DT	Number=Sing|PronType=Dem	22	det	_	_
22	biequivalence	biequivalence	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = As an application we show that groupoidal weakly globular double categories model homotopy 2 - types.
1	As	as	ADP	IN	_	5	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	13	det	_	_
7	groupoidal	groupoidal	NOUN	NN	Number=Sing	12	nmod	_	_
8	weakly	weakly	ADJ	JJ	Degree=Pos	12	amod	_	_
9	globular	globular	ADJ	JJ	Degree=Pos	12	amod	_	_
10	double	double	ADJ	JJ	Degree=Pos	11	amod	_	_
11	categories	category	NOUN	NNS	Number=Plur	12	compound	_	_
12	model	model	NOUN	NN	Number=Sing	13	compound	_	_
13	homotopy	homotopy	PROPN	NNP	Number=Sing	5	dobj	_	_
14	2	2	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	types	type	NOUN	NNS	Number=Plur	13	npadvmod	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 451
# sent_id = 1
# text = We define relative regular Maltsev categories and give an overview of conditions which are equivalent to the relative Maltsev axiom.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	relative	relative	ADJ	JJ	Degree=Pos	6	amod	_	_
4	regular	regular	ADJ	JJ	Degree=Pos	6	amod	_	_
5	Maltsev	Maltsev	PROPN	NNP	Number=Sing	6	amod	_	_
6	categories	category	NOUN	NNS	Number=Plur	2	dobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
8	give	give	VERB	VB	VerbForm=Inf	2	conj	_	_
9	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	overview	overview	NOUN	NN	Number=Sing	8	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	conditions	condition	NOUN	NNS	Number=Plur	11	pobj	_	_
13	which	which	PRON	WDT	_	14	nsubj	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	relcl	_	_
15	equivalent	equivalent	ADJ	JJ	Degree=Pos	14	acomp	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
18	relative	relative	ADJ	JJ	Degree=Pos	19	amod	_	_
19	Maltsev	Maltsev	PROPN	NNP	Number=Sing	20	compound	_	_
20	axiom	axiom	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = These include conditions on relations as well as conditions on simplicial objects.
1	These	these	PRON	DT	Number=Plur|PronType=Dem	2	nsubj	_	_
2	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	conditions	condition	NOUN	NNS	Number=Plur	2	dobj	_	_
4	on	on	ADP	IN	_	3	prep	_	_
5	relations	relation	NOUN	NNS	Number=Plur	4	pobj	_	_
6	as	as	ADV	RB	_	8	advmod	_	_
7	well	well	ADV	RB	Degree=Pos	8	advmod	_	_
8	as	as	ADP	IN	_	5	cc	_	_
9	conditions	condition	NOUN	NNS	Number=Plur	5	conj	_	_
10	on	on	ADP	IN	_	9	prep	_	_
11	simplicial	simplicial	ADJ	JJ	Degree=Pos	12	amod	_	_
12	objects	object	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also give various examples and counterexamples.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	various	various	ADJ	JJ	Degree=Pos	5	amod	_	_
5	examples	example	NOUN	NNS	Number=Plur	3	dobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	counterexamples	counterexample	NOUN	NNS	Number=Plur	5	conj	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 452
# sent_id = 1
# text = Cartesian differential categories abstractly capture the notion of a differentiation operation.
1	Cartesian	cartesian	ADJ	JJ	Degree=Pos	3	amod	_	_
2	differential	differential	ADJ	JJ	Degree=Pos	3	amod	_	_
3	categories	category	NOUN	NNS	Number=Plur	5	nsubj	_	_
4	abstractly	abstractly	ADV	RB	_	5	advmod	_	_
5	capture	capture	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	notion	notion	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	differentiation	differentiation	NOUN	NN	Number=Sing	11	compound	_	_
11	operation	operation	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper, we develop some of the theory of such categories by defining differential forms and exterior differentiation in this setting.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	some	some	PRON	DT	_	6	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	theory	theory	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	such	such	ADJ	JJ	Degree=Pos	13	amod	_	_
13	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
14	by	by	ADP	IN	_	6	prep	_	_
15	defining	define	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	pcomp	_	_
16	differential	differential	ADJ	JJ	Degree=Pos	17	amod	_	_
17	forms	form	NOUN	NNS	Number=Plur	15	dobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	exterior	exterior	ADJ	JJ	Degree=Pos	20	amod	_	_
20	differentiation	differentiation	NOUN	NN	Number=Sing	17	conj	_	_
21	in	in	ADP	IN	_	15	prep	_	_
22	this	this	DET	DT	Number=Sing|PronType=Dem	23	det	_	_
23	setting	setting	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that this exterior derivative, as expected, produces a cochain complex.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	11	mark	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
5	exterior	exterior	ADJ	JJ	Degree=Pos	6	amod	_	_
6	derivative	derivative	NOUN	NN	Number=Sing	11	nsubj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	as	as	SCONJ	IN	_	9	mark	_	_
9	expected	expect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	advcl	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
11	produces	produce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	cochain	cochain	NOUN	NN	Number=Sing	14	compound	_	_
14	complex	complex	NOUN	NN	Number=Sing	11	dobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 453
# sent_id = 1
# text = In this article we extend the theory of lax monoidal structures, also known as multitensors, and the monads on categories of enriched graphs that they give rise to.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	article	article	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	extend	extend	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	theory	theory	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	lax	lax	ADJ	JJ	Degree=Pos	11	amod	_	_
10	monoidal	monoidal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	structures	structure	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
13	also	also	ADV	RB	_	14	advmod	_	_
14	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	advcl	_	_
15	as	as	ADP	IN	_	14	prep	_	_
16	multitensors	multitensor	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	monads	monad	NOUN	NNS	Number=Plur	5	conj	_	_
21	on	on	ADP	IN	_	20	prep	_	_
22	categories	category	NOUN	NNS	Number=Plur	21	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	amod	_	_
25	graphs	graph	NOUN	NNS	Number=Plur	23	pobj	_	_
26	that	that	PRON	WDT	PronType=Rel	28	mark	_	_
27	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	28	nsubj	_	_
28	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	20	relcl	_	_
29	rise	rise	NOUN	NN	Number=Sing	28	dobj	_	_
30	to	to	ADP	IN	_	29	prep	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = Our first principal result—the lifting theorem for multitensors—enables us to see the Gray tensor product of 2 - categories and the Crans tensor product of Gray categories as part of this framework.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	4	poss	_	_
2	first	first	ADJ	JJ	Degree=Pos	4	amod	_	_
3	principal	principal	ADJ	JJ	Degree=Pos	4	amod	_	_
4	result	result	NOUN	NN	Number=Sing	12	nsubj	_	SpaceAfter=No
5	—	—	PUNCT	:	_	8	punct	_	SpaceAfter=No
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	lifting	lifting	NOUN	NN	Number=Sing	8	nsubj	_	_
8	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	4	acl	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	multitensors	multitensor	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
11	—	—	PUNCT	:	_	12	punct	_	SpaceAfter=No
12	enables	enable	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	12	dobj	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	see	see	VERB	VB	VerbForm=Inf	12	xcomp	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
17	Gray	Gray	PROPN	NNP	Number=Sing	19	compound	_	_
18	tensor	tensor	NOUN	NN	Number=Sing	19	compound	_	_
19	product	product	NOUN	NN	Number=Sing	15	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	2	2	NUM	CD	NumType=Card	23	nummod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	categories	category	NOUN	NNS	Number=Plur	20	pobj	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
26	Crans	Crans	PROPN	NNPS	Number=Plur	28	compound	_	_
27	tensor	tensor	NOUN	NN	Number=Sing	28	compound	_	_
28	product	product	NOUN	NN	Number=Sing	23	conj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	Gray	Gray	PROPN	NNP	Number=Sing	31	amod	_	_
31	categories	category	NOUN	NNS	Number=Plur	29	pobj	_	_
32	as	as	ADP	IN	_	15	prep	_	_
33	part	part	NOUN	NN	Number=Sing	32	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	this	this	DET	DT	Number=Sing|PronType=Dem	36	det	_	_
36	framework	framework	NOUN	NN	Number=Sing	34	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 3
# text = We define weak $ n $ - categories with strict units by means of a notion of reduced higher operad, using the theory of algebraic weak factorisation systems.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	weak	weak	ADJ	JJ	Degree=Pos	6	amod	_	_
4	$ n $	$ n $	SYM	$	_	6	compound	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	categories	category	NOUN	NNS	Number=Plur	2	dobj	_	_
7	with	with	ADP	IN	_	6	prep	_	_
8	strict	strict	ADJ	JJ	Degree=Pos	9	amod	_	_
9	units	unit	NOUN	NNS	Number=Plur	7	pobj	_	_
10	by	by	ADP	IN	_	2	prep	_	_
11	means	mean	NOUN	NNS	Number=Plur	10	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	notion	notion	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	reduced	reduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
17	higher	high	ADJ	JJR	Degree=Cmp	18	amod	_	_
18	operad	operad	ADV	RB	_	15	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
20	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	theory	theory	NOUN	NN	Number=Sing	20	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	algebraic	algebraic	ADJ	JJ	Degree=Pos	27	amod	_	_
25	weak	weak	ADJ	JJ	Degree=Pos	27	amod	_	_
26	factorisation	factorisation	NOUN	NN	Number=Sing	27	compound	_	_
27	systems	system	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = Our second principal result is to establish a lax tensor product on the category of weak $ n $ - categories with strict units, so that enriched categories with respect to this tensor product are exactly weak $ (n+1) $ - categories with strict units.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	4	poss	_	_
2	second	second	ADJ	JJ	Degree=Pos	4	amod	_	_
3	principal	principal	ADJ	JJ	Degree=Pos	4	amod	_	_
4	result	result	NOUN	NN	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	establish	establish	VERB	VB	VerbForm=Inf	5	xcomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	lax	lax	ADJ	JJ	Degree=Pos	11	amod	_	_
10	tensor	tensor	NOUN	NN	Number=Sing	11	compound	_	_
11	product	product	NOUN	NN	Number=Sing	7	dobj	_	_
12	on	on	ADP	IN	_	7	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	weak	weak	ADJ	JJ	Degree=Pos	19	amod	_	_
17	$ n $	$ n $	SYM	$	_	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	strict	strict	ADJ	JJ	Degree=Pos	22	amod	_	_
22	units	unit	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
24	so	so	SCONJ	IN	_	34	mark	_	_
25	that	that	SCONJ	IN	_	34	mark	_	_
26	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	amod	_	_
27	categories	category	NOUN	NNS	Number=Plur	34	nsubj	_	_
28	with	with	ADP	IN	_	27	prep	_	_
29	respect	respect	NOUN	NN	Number=Sing	28	pobj	_	_
30	to	to	ADP	IN	_	29	prep	_	_
31	this	this	DET	DT	Number=Sing|PronType=Dem	33	det	_	_
32	tensor	tensor	NOUN	NN	Number=Sing	33	compound	_	_
33	product	product	NOUN	NN	Number=Sing	30	pobj	_	_
34	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	advcl	_	_
35	exactly	exactly	ADV	RB	_	36	advmod	_	_
36	weak	weak	ADJ	JJ	Degree=Pos	39	amod	_	_
37	$ (n+1) $	$ (n+1) $	SYM	$	_	39	compound	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	categories	category	NOUN	NNS	Number=Plur	34	attr	_	_
40	with	with	ADP	IN	_	39	prep	_	_
41	strict	strict	ADJ	JJ	Degree=Pos	42	amod	_	_
42	units	unit	NOUN	NNS	Number=Plur	40	pobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 454
# sent_id = 1
# text = In this paper we unify the developments of Batanin, Batanin - Weber and Cheng into a single framework in which the interplay between multitensors on a category $ V $ , and monads on the category $ cal G V $ of graphs enriched in $ V $ , is taken as fundamental.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	unify	unify	VERB	VBP	Tense=Pres|VerbForm=Fin	44	csubjpass	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	developments	development	NOUN	NNS	Number=Plur	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	Batanin	Batanin	PROPN	NNP	Number=Sing	8	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	Batanin	Batanin	PROPN	NNP	Number=Sing	13	compound	_	_
12	-	-	PUNCT	:	_	13	punct	_	_
13	Weber	Weber	PROPN	NNP	Number=Sing	9	conj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	Cheng	Cheng	PROPN	NNP	Number=Sing	13	conj	_	_
16	into	into	ADP	IN	_	5	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	single	single	ADJ	JJ	Degree=Pos	19	amod	_	_
19	framework	framework	NOUN	NN	Number=Sing	16	pobj	_	_
20	in	in	ADP	IN	_	29	prep	_	_
21	which	which	PRON	WDT	_	20	pobj	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	interplay	interplay	NOUN	NN	Number=Sing	29	nsubj	_	_
24	between	between	ADP	IN	_	23	prep	_	_
25	multitensors	multitensor	NOUN	NNS	Number=Plur	24	pobj	_	_
26	on	on	ADP	IN	_	25	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	category	category	NOUN	NN	Number=Sing	26	pobj	_	_
29	$ V $	$ v $	SYM	$	_	19	relcl	_	_
30	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
32	monads	monad	NOUN	NNS	Number=Plur	5	conj	_	_
33	on	on	ADP	IN	_	32	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	category	category	NOUN	NN	Number=Sing	33	pobj	_	_
36	$ cal G V $	$ cal g v $	SYM	$	_	5	dep	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	graphs	graph	NOUN	NNS	Number=Plur	37	pobj	_	_
39	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	38	acl	_	_
40	in	in	ADP	IN	_	39	prep	_	_
41	$ V $	$ v $	SYM	$	_	40	pobj	_	_
42	,	,	PUNCT	,	PunctType=Comm	44	punct	_	_
43	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	44	auxpass	_	_
44	taken	take	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
45	as	as	ADV	RB	_	44	prep	_	_
46	fundamental	fundamental	ADJ	JJ	Degree=Pos	45	amod	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	44	punct	_	SpaceAfter=No

# sent_id = 2
# text = The material presented here is the conceptual background for subsequent work: in Batanin - Cisinski - Weber the Gray tensor product of 2 - categories and the Crans tensor product of Gray categories are exhibited as existing within our framework, and in Weber the explicit construction of the funny tensor product of categories is generalised to a large class of Batanin operads.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	material	material	NOUN	NN	Number=Sing	5	nsubj	_	_
3	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acl	_	_
4	here	here	ADV	RB	PronType=Dem	3	advmod	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	36	ccomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	conceptual	conceptual	ADJ	JJ	Degree=Pos	8	amod	_	_
8	background	background	NOUN	NN	Number=Sing	5	attr	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	subsequent	subsequent	ADJ	JJ	Degree=Pos	11	amod	_	_
11	work	work	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	:	:	PUNCT	:	_	8	punct	_	_
13	in	in	ADP	IN	_	36	prep	_	_
14	Batanin	Batanin	PROPN	NNP	Number=Sing	16	compound	_	_
15	-	-	PUNCT	:	_	16	punct	_	_
16	Cisinski	Cisinski	PROPN	NNP	Number=Sing	18	compound	_	_
17	-	-	PUNCT	:	_	18	punct	_	_
18	Weber	Weber	PROPN	NNP	Number=Sing	13	pobj	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
20	Gray	Gray	PROPN	NNP	Number=Sing	22	compound	_	_
21	tensor	tensor	NOUN	NN	Number=Sing	22	compound	_	_
22	product	product	NOUN	NN	Number=Sing	36	nsubjpass	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	2	2	NUM	CD	NumType=Card	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	categories	category	NOUN	NNS	Number=Plur	23	pobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
29	Crans	Crans	PROPN	NNPS	Number=Plur	31	compound	_	_
30	tensor	tensor	NOUN	NN	Number=Sing	31	compound	_	_
31	product	product	NOUN	NN	Number=Sing	26	conj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	Gray	Gray	PROPN	NNP	Number=Sing	34	amod	_	_
34	categories	category	NOUN	NNS	Number=Plur	32	pobj	_	_
35	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	36	auxpass	_	_
36	exhibited	exhibit	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
37	as	as	ADP	IN	_	36	prep	_	_
38	existing	exist	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	37	pcomp	_	_
39	within	within	ADP	IN	_	38	prep	_	_
40	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	41	poss	_	_
41	framework	framework	NOUN	NN	Number=Sing	39	pobj	_	SpaceAfter=No
42	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
43	and	and	CCONJ	CC	ConjType=Cmp	36	cc	_	_
44	in	in	ADP	IN	_	57	prep	_	_
45	Weber	Weber	PROPN	NNP	Number=Sing	44	pobj	_	_
46	the	the	DET	DT	Definite=Def|PronType=Art	48	det	_	_
47	explicit	explicit	ADJ	JJ	Degree=Pos	48	amod	_	_
48	construction	construction	NOUN	NN	Number=Sing	57	nsubjpass	_	_
49	of	of	ADP	IN	_	48	prep	_	_
50	the	the	DET	DT	Definite=Def|PronType=Art	53	det	_	_
51	funny	funny	ADJ	JJ	Degree=Pos	53	amod	_	_
52	tensor	tensor	NOUN	NN	Number=Sing	53	compound	_	_
53	product	product	NOUN	NN	Number=Sing	49	pobj	_	_
54	of	of	ADP	IN	_	53	prep	_	_
55	categories	category	NOUN	NNS	Number=Plur	54	pobj	_	_
56	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	57	auxpass	_	_
57	generalised	generalise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	36	conj	_	_
58	to	to	ADP	IN	_	57	prep	_	_
59	a	a	DET	DT	Definite=Ind|PronType=Art	61	det	_	_
60	large	large	ADJ	JJ	Degree=Pos	61	amod	_	_
61	class	class	NOUN	NN	Number=Sing	58	pobj	_	_
62	of	of	ADP	IN	_	61	prep	_	_
63	Batanin	Batanin	PROPN	NNP	Number=Sing	64	amod	_	_
64	operads	operad	NOUN	NNS	Number=Plur	62	pobj	_	SpaceAfter=No
65	.	.	PUNCT	.	PunctType=Peri	57	punct	_	SpaceAfter=No

# doc_id = 455
# sent_id = 1
# text = It is known that strict omega - categories are equivalent through the nerve functor to complicial sets and to sets with complicial identities.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	SCONJ	IN	_	9	mark	_	_
5	strict	strict	ADJ	JJ	Degree=Pos	8	amod	_	_
6	omega	omega	NOUN	NN	Number=Sing	8	compound	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	categories	category	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
10	equivalent	equivalent	ADJ	JJ	Degree=Pos	9	acomp	_	_
11	through	through	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	nerve	nerve	NOUN	NN	Number=Sing	14	compound	_	_
14	functor	functor	NOUN	NN	Number=Sing	11	pobj	_	_
15	to	to	ADP	IN	_	10	prep	_	_
16	complicial	complicial	ADJ	JJ	Degree=Pos	17	amod	_	_
17	sets	set	NOUN	NNS	Number=Plur	15	pobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
19	to	to	PART	TO	_	20	aux	_	_
20	sets	set	NOUN	NNS	Number=Plur	9	conj	_	_
21	with	with	ADP	IN	_	20	prep	_	_
22	complicial	complicial	ADJ	JJ	Degree=Pos	23	amod	_	_
23	identities	identity	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = It follows that complicial sets are equivalent to sets with complicial identities.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	follows	follow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	6	mark	_	_
4	complicial	complicial	ADJ	JJ	Degree=Pos	5	amod	_	_
5	sets	set	NOUN	NNS	Number=Plur	6	nsubj	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
7	equivalent	equivalent	ADJ	JJ	Degree=Pos	6	acomp	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	sets	set	NOUN	NNS	Number=Plur	7	xcomp	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	complicial	complicial	ADJ	JJ	Degree=Pos	12	amod	_	_
12	identities	identity	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We discuss these equivalences.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	discuss	discuss	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	these	these	DET	DT	Number=Plur|PronType=Dem	4	det	_	_
4	equivalences	equivalence	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
5	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = In particular we give a conceptual proof that the nerves of omega - categories are complicial sets, and a direct proof that complicial sets are sets with complicial identities.
1	In	in	ADP	IN	_	4	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	conceptual	conceptual	ADJ	JJ	Degree=Pos	7	amod	_	_
7	proof	proof	NOUN	NN	Number=Sing	4	dobj	_	_
8	that	that	SCONJ	IN	_	15	mark	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	nerves	nerve	NOUN	NNS	Number=Plur	15	nsubj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	omega	omega	NOUN	NN	Number=Sing	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	acl	_	_
16	complicial	complicial	ADJ	JJ	Degree=Pos	17	amod	_	_
17	sets	set	NOUN	NNS	Number=Plur	15	attr	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	direct	direct	ADJ	JJ	Degree=Pos	22	amod	_	_
22	proof	proof	NOUN	NN	Number=Sing	4	dobj	_	_
23	that	that	SCONJ	IN	_	26	mark	_	_
24	complicial	complicial	ADJ	JJ	Degree=Pos	25	amod	_	_
25	sets	set	NOUN	NNS	Number=Plur	26	nsubj	_	_
26	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	22	acl	_	_
27	sets	set	NOUN	NNS	Number=Plur	26	attr	_	_
28	with	with	ADP	IN	_	27	prep	_	_
29	complicial	complicial	ADJ	JJ	Degree=Pos	30	amod	_	_
30	identities	identity	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 456
# sent_id = 1
# text = We show that the nerve of a strict omega - category can be described algebraically as a simplicial set with additional operations subject to certain identities.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	14	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	nerve	nerve	NOUN	NN	Number=Sing	14	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	strict	strict	ADJ	JJ	Degree=Pos	11	amod	_	_
9	omega	omega	NOUN	NN	Number=Sing	11	compound	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
12	can	can	AUX	MD	VerbForm=Fin	14	aux	_	_
13	be	be	AUX	VB	VerbForm=Inf	14	auxpass	_	_
14	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
15	algebraically	algebraically	ADV	RB	_	14	advmod	_	_
16	as	as	SCONJ	IN	_	23	mark	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	simplicial	simplicial	NOUN	NN	Number=Sing	23	nsubj	_	_
19	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	acl	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	additional	additional	ADJ	JJ	Degree=Pos	22	amod	_	_
22	operations	operation	NOUN	NNS	Number=Plur	20	pobj	_	_
23	subject	subject	ADJ	JJ	Degree=Pos	14	advcl	_	_
24	to	to	ADP	IN	_	23	prep	_	_
25	certain	certain	ADJ	JJ	Degree=Pos	26	amod	_	_
26	identities	identity	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The resulting structures are called sets with complicial identities.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	amod	_	_
3	structures	structure	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	sets	set	NOUN	NNS	Number=Plur	5	oprd	_	_
7	with	with	ADP	IN	_	6	prep	_	_
8	complicial	complicial	ADJ	JJ	Degree=Pos	9	amod	_	_
9	identities	identity	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also construct an equivalence between the categories of strict omega - categories and of sets with complical identities.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	equivalence	equivalence	NOUN	NN	Number=Sing	3	dobj	_	_
6	between	between	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	strict	strict	ADJ	JJ	Degree=Pos	13	amod	_	_
11	omega	omega	NOUN	NN	Number=Sing	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
15	of	of	ADP	IN	_	9	conj	_	_
16	sets	set	NOUN	NNS	Number=Plur	15	pobj	_	_
17	with	with	ADP	IN	_	16	prep	_	_
18	complical	complical	ADJ	JJ	Degree=Pos	19	amod	_	_
19	identities	identity	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 457
# sent_id = 1
# text = In this paper we consider generalized metric spaces in the sense of Lawvere and the categorical Isbell completion construction.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
7	metric	metric	ADJ	JJ	Degree=Pos	8	amod	_	_
8	spaces	space	NOUN	NNS	Number=Plur	5	dobj	_	_
9	in	in	ADP	IN	_	5	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	sense	sense	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	Lawvere	Lawvere	PROPN	NNP	Number=Sing	12	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
16	categorical	categorical	ADJ	JJ	Degree=Pos	17	amod	_	_
17	Isbell	Isbell	PROPN	NNP	Number=Sing	19	compound	_	_
18	completion	completion	NOUN	NN	Number=Sing	19	compound	_	_
19	construction	construction	NOUN	NN	Number=Sing	13	conj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that this is an analogue of the tight span construction of classical metric spaces, and that the Isbell completion coincides with the directed tight span of Hirai and Koichi.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	this	this	PRON	DT	Number=Sing|PronType=Dem	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	analogue	analogue	NOUN	NN	Number=Sing	5	attr	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
10	tight	tight	ADJ	JJ	Degree=Pos	12	amod	_	_
11	span	span	NOUN	NN	Number=Sing	12	compound	_	_
12	construction	construction	NOUN	NN	Number=Sing	8	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	classical	classical	ADJ	JJ	Degree=Pos	16	amod	_	_
15	metric	metric	ADJ	JJ	Degree=Pos	16	amod	_	_
16	spaces	space	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
19	that	that	SCONJ	IN	_	23	mark	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
21	Isbell	Isbell	PROPN	NNP	Number=Sing	23	compound	_	_
22	completion	completion	NOUN	NN	Number=Sing	23	compound	_	_
23	coincides	coincide	NOUN	NNS	Number=Plur	5	conj	_	_
24	with	with	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
26	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	amod	_	_
27	tight	tight	ADJ	JJ	Degree=Pos	28	amod	_	_
28	span	span	NOUN	NN	Number=Sing	24	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	Hirai	Hirai	PROPN	NNP	Number=Sing	29	pobj	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
32	Koichi	Koichi	PROPN	NNP	Number=Sing	30	conj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The notions of categorical completion and cocompletion are related to the existence of semi - tropical module structure, and it is shown that the Isbell completion (hence the directed tight span) has two different semi - tropical module structures.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	notions	notion	NOUN	NNS	Number=Plur	9	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	categorical	categorical	ADJ	JJ	Degree=Pos	5	amod	_	_
5	completion	completion	NOUN	NN	Number=Sing	3	pobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	cocompletion	cocompletion	NOUN	NN	Number=Sing	5	conj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	existence	existence	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	semi	semi	ADJ	JJ	Degree=Pos	18	amod	_	_
15	-	-	ADJ	JJ	Degree=Pos	18	amod	_	_
16	tropical	tropical	ADJ	JJ	Degree=Pos	18	amod	_	_
17	module	module	NOUN	NN	Number=Sing	18	compound	_	_
18	structure	structure	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
21	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	23	nsubjpass	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	auxpass	_	_
23	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	conj	_	_
24	that	that	SCONJ	IN	_	35	mark	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	Isbell	Isbell	PROPN	NNP	Number=Sing	27	compound	_	_
27	completion	completion	NOUN	NN	Number=Sing	35	nsubj	_	_
28	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	33	punct	_	SpaceAfter=No
29	hence	hence	ADV	RB	_	33	advmod	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
31	directed	direct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	amod	_	_
32	tight	tight	ADJ	JJ	Degree=Pos	33	amod	_	_
33	span	span	NOUN	NN	Number=Sing	27	appos	_	SpaceAfter=No
34	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	27	punct	_	_
35	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	ccomp	_	_
36	two	two	NUM	CD	NumType=Card	42	nummod	_	_
37	different	different	ADJ	JJ	Degree=Pos	42	amod	_	_
38	semi	semi	ADJ	JJ	Degree=Pos	42	amod	_	_
39	-	-	ADJ	JJ	Degree=Pos	42	amod	_	_
40	tropical	tropical	ADJ	JJ	Degree=Pos	42	amod	_	_
41	module	module	NOUN	NN	Number=Sing	42	compound	_	_
42	structures	structure	NOUN	NNS	Number=Plur	35	dobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# doc_id = 458
# sent_id = 1
# text = We develop a theory of categories which are simultaneously (i) indexed over a base category $ S $ with finite products, and (ii) enriched over an $ S $ - indexed monoidal category $ V $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	theory	theory	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
7	which	which	PRON	WDT	_	8	nsubj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	relcl	_	_
9	simultaneously	simultaneously	ADV	RB	_	8	advmod	_	_
10	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	11	punct	_	SpaceAfter=No
11	i	i	NOUN	NN	Number=Sing	8	parataxis	_	SpaceAfter=No
12	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	11	punct	_	_
13	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acomp	_	_
14	over	over	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	base	base	NOUN	NN	Number=Sing	17	compound	_	_
17	category	category	NOUN	NN	Number=Sing	14	pobj	_	_
18	$ S $	$ s $	SYM	$	_	17	appos	_	_
19	with	with	ADP	IN	_	13	prep	_	_
20	finite	finite	ADJ	JJ	Degree=Pos	21	amod	_	_
21	products	product	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
24	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	25	punct	_	SpaceAfter=No
25	ii	ii	PROPN	NNP	Number=Sing	13	conj	_	SpaceAfter=No
26	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	25	punct	_	_
27	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	acl	_	_
28	over	over	ADP	IN	_	27	prep	_	_
29	an	an	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
30	$ S $	$ s $	SYM	$	_	32	advmod	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	34	amod	_	_
33	monoidal	monoidal	ADJ	JJ	Degree=Pos	34	amod	_	_
34	category	category	NOUN	NN	Number=Sing	28	pobj	_	_
35	$ V $	$ v $	SYM	$	_	27	npadvmod	_	_
36	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This includes classical enriched categories, indexed and fibered categories, and internal categories as special cases.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	includes	include	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	classical	classical	ADJ	JJ	Degree=Pos	5	amod	_	_
4	enriched	enriched	ADJ	JJ	Degree=Pos	5	amod	_	_
5	categories	category	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	fibered	fibere	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	conj	_	_
10	categories	category	NOUN	NNS	Number=Plur	5	conj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
13	internal	internal	ADJ	JJ	Degree=Pos	14	amod	_	_
14	categories	category	NOUN	NNS	Number=Plur	10	conj	_	_
15	as	as	ADP	IN	_	5	prep	_	_
16	special	special	ADJ	JJ	Degree=Pos	17	amod	_	_
17	cases	case	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We then describe the appropriate notion of ``limit'' for such enriched indexed categories, and show that they admit ``free cocompletions'' constructed as usual with a Yoneda embedding.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	appropriate	appropriate	ADJ	JJ	Degree=Pos	6	amod	_	_
6	notion	notion	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	10	punct	_	SpaceAfter=No
9	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	10	punct	_	SpaceAfter=No
10	limit	limit	VERB	VB	VerbForm=Inf	7	pobj	_	SpaceAfter=No
11	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	10	punct	_	_
12	for	for	ADP	IN	_	10	prep	_	_
13	such	such	ADJ	JJ	Degree=Pos	16	amod	_	_
14	enriched	enriched	ADJ	JJ	Degree=Pos	16	amod	_	_
15	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
16	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
19	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	3	conj	_	_
20	that	that	SCONJ	IN	_	22	mark	_	_
21	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	22	nsubj	_	_
22	admit	admit	VERB	VBP	Tense=Pres|VerbForm=Fin	19	ccomp	_	_
23	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	SpaceAfter=No
24	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	SpaceAfter=No
25	free	free	ADJ	JJ	Degree=Pos	26	amod	_	_
26	cocompletions	cocompletion	NOUN	NNS	Number=Plur	22	dobj	_	SpaceAfter=No
27	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	26	punct	_	_
28	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	acl	_	_
29	as	as	ADP	IN	_	28	prep	_	_
30	usual	usual	ADJ	JJ	Degree=Pos	29	amod	_	_
31	with	with	ADP	IN	_	28	prep	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
33	Yoneda	Yoneda	PROPN	NNP	Number=Sing	34	compound	_	_
34	embedding	embed	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	31	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 459
# sent_id = 1
# text = Each distributor between categories enriched over a small quantaloid $ Q $ gives rise to two adjunctions between the categories of contravariant and covariant presheaves, and hence to two monads.
1	Each	each	DET	DT	_	2	det	_	_
2	distributor	distributor	NOUN	NN	Number=Sing	11	nsubj	_	_
3	between	between	ADP	IN	_	2	prep	_	_
4	categories	category	NOUN	NNS	Number=Plur	3	pobj	_	_
5	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	acl	_	_
6	over	over	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	small	small	ADJ	JJ	Degree=Pos	9	amod	_	_
9	quantaloid	quantaloid	NOUN	NN	Number=Sing	6	pobj	_	_
10	$ Q $	$ q $	SYM	$	_	5	npadvmod	_	_
11	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	rise	rise	VERB	VB	VerbForm=Inf	11	dobj	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	two	two	NUM	CD	NumType=Card	15	nummod	_	_
15	adjunctions	adjunction	NOUN	NNS	Number=Plur	13	pobj	_	_
16	between	between	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	contravariant	contravariant	ADJ	JJ	Degree=Pos	23	amod	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	covariant	covariant	ADJ	JJ	Degree=Pos	20	conj	_	_
23	presheaves	presheave	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
26	hence	hence	ADV	RB	_	27	advmod	_	_
27	to	to	ADP	IN	_	11	conj	_	_
28	two	two	NUM	CD	NumType=Card	29	nummod	_	_
29	monads	monad	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 2
# text = These two adjunctions are respectively generalizations of Isbell adjunctions and Kan extensions in category theory.
1	These	these	DET	DT	Number=Plur|PronType=Dem	3	det	_	_
2	two	two	NUM	CD	NumType=Card	3	nummod	_	_
3	adjunctions	adjunction	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	respectively	respectively	ADV	RB	_	4	advmod	_	_
6	generalizations	generalization	NOUN	NNS	Number=Plur	4	attr	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	Isbell	Isbell	PROPN	NNP	Number=Sing	9	compound	_	_
9	adjunctions	adjunction	NOUN	NNS	Number=Plur	7	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	Kan	Kan	PROPN	NNP	Number=Sing	12	compound	_	_
12	extensions	extension	NOUN	NNS	Number=Plur	9	conj	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	category	category	NOUN	NN	Number=Sing	15	compound	_	_
15	theory	theory	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = It is proved that these two processes are functorial with infomorphisms playing as morphisms between distributors; and that the free cocompletion functor of $ Q $ - categories factors through both of these functors.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	SCONJ	IN	_	8	mark	_	_
5	these	these	DET	DT	Number=Plur|PronType=Dem	7	det	_	_
6	two	two	NUM	CD	NumType=Card	7	nummod	_	_
7	processes	process	NOUN	NNS	Number=Plur	8	nsubj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
9	functorial	functorial	ADJ	JJ	Degree=Pos	8	acomp	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	infomorphisms	infomorphism	NOUN	NNS	Number=Plur	10	pobj	_	_
12	playing	play	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	acl	_	_
13	as	as	ADP	IN	_	12	prep	_	_
14	morphisms	morphism	NOUN	NNS	Number=Plur	13	pobj	_	_
15	between	between	ADP	IN	_	12	prep	_	_
16	distributors	distributor	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
17	;	;	PUNCT	:	_	3	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
19	that	that	SCONJ	IN	_	23	mark	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
21	free	free	ADJ	JJ	Degree=Pos	22	amod	_	_
22	cocompletion	cocompletion	NOUN	NN	Number=Sing	23	compound	_	_
23	functor	functor	NOUN	NN	Number=Sing	3	conj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	$ Q $	$ q $	SYM	$	_	27	nummod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	categories	category	NOUN	NNS	Number=Plur	28	compound	_	_
28	factors	factor	NOUN	NNS	Number=Plur	24	pobj	_	_
29	through	through	ADP	IN	_	23	prep	_	_
30	both	both	PRON	DT	_	29	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	these	these	DET	DT	Number=Plur|PronType=Dem	33	det	_	_
33	functors	functor	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 460
# sent_id = 1
# text = The purpose of this text is the study of the class of homotopy types which are modelized by strict $ infty $ - groupoids.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	purpose	purpose	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	text	text	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	study	study	NOUN	NN	Number=Sing	6	attr	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	class	class	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	homotopy	homotopy	NOUN	NN	Number=Sing	14	compound	_	_
14	types	type	NOUN	NNS	Number=Plur	12	pobj	_	_
15	which	which	PRON	WDT	_	17	nsubjpass	_	_
16	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	17	auxpass	_	_
17	modelized	modelize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	relcl	_	_
18	by	by	ADP	IN	_	17	agent	_	_
19	strict	strict	ADJ	JJ	Degree=Pos	22	amod	_	_
20	$ infty $	$ infty $	SYM	$	_	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	groupoids	groupoid	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that the homotopy category of simply connected strict $ infty $ - groupoids is equivalent to the derived category in homological degree $ d ge 2 $ of abelian groups.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	14	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	homotopy	homotopy	NOUN	NN	Number=Sing	6	compound	_	_
6	category	category	NOUN	NN	Number=Sing	14	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	simply	simply	ADV	RB	_	9	advmod	_	_
9	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
10	strict	strict	ADJ	JJ	Degree=Pos	13	amod	_	_
11	$ infty $	$ infty $	SYM	$	_	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	groupoids	groupoid	NOUN	NNS	Number=Plur	7	pobj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
15	equivalent	equivalent	ADJ	JJ	Degree=Pos	14	acomp	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	derived	derive	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
19	category	category	NOUN	NN	Number=Sing	16	pobj	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	homological	homological	ADJ	JJ	Degree=Pos	22	amod	_	_
22	degree	degree	NOUN	NN	Number=Sing	20	pobj	_	_
23	$ d ge 2 $	$ d ge 2 $	SYM	$	_	19	appos	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	abelian	abelian	ADJ	JJ	Degree=Pos	26	compound	_	_
26	groups	group	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We deduce that the simply connected homotopy types modelized by strict $ infty $ - groupoids are precisely the products of Eilenberg - Mac Lane spaces.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	deduce	deduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	15	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
5	simply	simply	ADV	RB	_	6	advmod	_	_
6	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
7	homotopy	homotopy	NOUN	NN	Number=Sing	8	compound	_	_
8	types	type	NOUN	NNS	Number=Plur	15	nsubj	_	_
9	modelized	modelize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	by	by	ADP	IN	_	9	agent	_	_
11	strict	strict	ADJ	JJ	Degree=Pos	14	amod	_	_
12	$ infty $	$ infty $	SYM	$	_	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	groupoids	groupoid	NOUN	NNS	Number=Plur	10	pobj	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
16	precisely	precisely	ADV	RB	_	15	advmod	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	products	product	NOUN	NNS	Number=Plur	15	attr	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	Mac	Mac	PROPN	NNP	Number=Sing	23	compound	_	_
23	Lane	Lane	PROPN	NNP	Number=Sing	24	compound	_	_
24	spaces	space	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We also briefly study 3 - categories with weak inverses.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
2	also	also	ADV	RB	_	4	advmod	_	_
3	briefly	briefly	ADV	RB	_	4	advmod	_	_
4	study	study	VERB	VB	VerbForm=Inf	0	ROOT	_	_
5	3	3	NUM	CD	NumType=Card	7	nummod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	categories	category	NOUN	NNS	Number=Plur	4	dobj	_	_
8	with	with	ADP	IN	_	4	prep	_	_
9	weak	weak	ADJ	JJ	Degree=Pos	10	amod	_	_
10	inverses	inverse	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = We finish by two questions about the problem suggested by the title of this text.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	finish	finish	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	by	by	ADP	IN	_	2	prep	_	_
4	two	two	NUM	CD	NumType=Card	5	nummod	_	_
5	questions	question	NOUN	NNS	Number=Plur	3	pobj	_	_
6	about	about	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	problem	problem	NOUN	NN	Number=Sing	6	pobj	_	_
9	suggested	suggest	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	by	by	ADP	IN	_	9	agent	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	title	title	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	this	this	DET	DT	Number=Sing|PronType=Dem	15	det	_	_
15	text	text	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 461
# sent_id = 1
# text = Moerdijk's site description for equivariant sheaf toposes on open topological groupoids is used to give a proof for the (known, but apparently unpublished) proposition that if $ H $ is a subgroupoid of an open topological groupoid $ G $ , then the topos of equivariant sheaves on $ H $ is a subtopos of the topos of equivariant sheaves on $ G $ .
1	Moerdijk	Moerdijk	PROPN	NNP	Number=Sing	4	poss	_	SpaceAfter=No
2	's	's	PART	POS	_	1	case	_	_
3	site	site	NOUN	NN	Number=Sing	4	compound	_	_
4	description	description	NOUN	NN	Number=Sing	14	nsubjpass	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	equivariant	equivariant	ADJ	JJ	Degree=Pos	7	amod	_	_
7	sheaf	sheaf	NOUN	NN	Number=Sing	8	compound	_	_
8	toposes	topos	NOUN	NNS	Number=Plur	5	pobj	_	_
9	on	on	ADP	IN	_	8	prep	_	_
10	open	open	ADJ	JJ	Degree=Pos	12	amod	_	_
11	topological	topological	ADJ	JJ	Degree=Pos	12	amod	_	_
12	groupoids	groupoid	NOUN	NNS	Number=Plur	9	pobj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	give	give	VERB	VB	VerbForm=Inf	14	xcomp	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	proof	proof	NOUN	NN	Number=Sing	16	dobj	_	_
19	for	for	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
21	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	22	punct	_	SpaceAfter=No
22	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	amod	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	but	but	CCONJ	CC	ConjType=Cmp	22	cc	_	_
25	apparently	apparently	ADV	RB	_	26	advmod	_	_
26	unpublished	unpublished	ADJ	JJ	Degree=Pos	28	amod	_	SpaceAfter=No
27	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	28	punct	_	_
28	proposition	proposition	NOUN	NN	Number=Sing	19	pobj	_	_
29	that	that	SCONJ	IN	_	50	mark	_	_
30	if	if	SCONJ	IN	_	32	mark	_	_
31	$ H $	$ h $	SYM	$	_	32	nsubj	_	_
32	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	50	advcl	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
34	subgroupoid	subgroupoid	NOUN	NN	Number=Sing	32	attr	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	an	an	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
37	open	open	ADJ	JJ	Degree=Pos	39	amod	_	_
38	topological	topological	ADJ	JJ	Degree=Pos	39	amod	_	_
39	groupoid	groupoid	NOUN	NN	Number=Sing	35	pobj	_	_
40	$ G $	$ g $	SYM	$	_	39	appos	_	_
41	,	,	PUNCT	,	PunctType=Comm	50	punct	_	_
42	then	then	ADV	RB	PronType=Dem	50	advmod	_	_
43	the	the	DET	DT	Definite=Def|PronType=Art	44	det	_	_
44	topos	topos	NOUN	NN	Number=Sing	50	nsubj	_	_
45	of	of	ADP	IN	_	44	prep	_	_
46	equivariant	equivariant	ADJ	JJ	Degree=Pos	47	amod	_	_
47	sheaves	sheaf	NOUN	NNS	Number=Plur	45	pobj	_	_
48	on	on	ADP	IN	_	44	prep	_	_
49	$ H $	$ h $	SYM	$	_	48	pobj	_	_
50	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	28	acl	_	_
51	a	a	DET	DT	Definite=Ind|PronType=Art	52	det	_	_
52	subtopos	subtopos	NOUN	NN	Number=Sing	50	attr	_	_
53	of	of	ADP	IN	_	52	prep	_	_
54	the	the	DET	DT	Definite=Def|PronType=Art	55	det	_	_
55	topos	topos	NOUN	NN	Number=Sing	53	pobj	_	_
56	of	of	ADP	IN	_	55	prep	_	_
57	equivariant	equivariant	ADJ	JJ	Degree=Pos	58	amod	_	_
58	sheaves	sheaf	NOUN	NNS	Number=Plur	56	pobj	_	_
59	on	on	ADP	IN	_	55	prep	_	_
60	$ G $	$ g $	SYM	$	_	59	pobj	_	_
61	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 2
# text = This proposition is then applied to the study of quotient geometric theories and subtoposes.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	proposition	proposition	NOUN	NN	Number=Sing	5	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
4	then	then	ADV	RB	PronType=Dem	5	advmod	_	_
5	applied	apply	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	study	study	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	quotient	quotient	ADJ	JJ	Degree=Pos	12	amod	_	_
11	geometric	geometric	ADJ	JJ	Degree=Pos	12	amod	_	_
12	theories	theory	NOUN	NNS	Number=Plur	9	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	subtoposes	subtopose	NOUN	NNS	Number=Plur	12	conj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = In particular, an intrinsic characterization is given of those subgroupoids that are definable by quotient theories.
1	In	in	ADP	IN	_	8	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	intrinsic	intrinsic	ADJ	JJ	Degree=Pos	6	amod	_	_
6	characterization	characterization	NOUN	NN	Number=Sing	8	nsubjpass	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	those	those	DET	DT	Number=Plur|PronType=Dem	11	det	_	_
11	subgroupoids	subgroupoid	NOUN	NNS	Number=Plur	9	pobj	_	_
12	that	that	PRON	WDT	PronType=Rel	13	nsubj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	11	relcl	_	_
14	definable	definable	ADJ	JJ	Degree=Pos	13	acomp	_	_
15	by	by	ADP	IN	_	13	prep	_	_
16	quotient	quotient	ADJ	JJ	Degree=Pos	17	amod	_	_
17	theories	theory	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 462
# sent_id = 1
# text = We introduce an axiomatic framework for the parallel transport of connections on gerbes.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	axiomatic	axiomatic	ADJ	JJ	Degree=Pos	5	amod	_	_
5	framework	framework	NOUN	NN	Number=Sing	2	dobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	parallel	parallel	ADJ	JJ	Degree=Pos	9	amod	_	_
9	transport	transport	NOUN	NN	Number=Sing	6	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	connections	connection	NOUN	NNS	Number=Plur	10	pobj	_	_
12	on	on	ADP	IN	_	11	prep	_	_
13	gerbes	gerbes	PROPN	NNP	Number=Sing	12	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = It incorporates parallel transport along curves and along surfaces, and is formulated in terms of gluing axioms and smoothness conditions.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	incorporates	incorporate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	parallel	parallel	ADJ	JJ	Degree=Pos	4	amod	_	_
4	transport	transport	NOUN	NN	Number=Sing	2	dobj	_	_
5	along	along	ADP	IN	_	4	prep	_	_
6	curves	curve	NOUN	NNS	Number=Plur	5	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
8	along	along	ADP	IN	_	5	conj	_	_
9	surfaces	surface	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	formulated	formulate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	conj	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	terms	term	NOUN	NNS	Number=Plur	14	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	gluing	gluing	NOUN	NN	Number=Sing	18	compound	_	_
18	axioms	axiom	NOUN	NNS	Number=Plur	16	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	smoothness	smoothness	ADJ	JJ	Degree=Pos	21	amod	_	_
21	conditions	condition	NOUN	NNS	Number=Plur	18	conj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The smoothness conditions are imposed with respect to a strict Lie 2 - group, which plays the role of a band, or structure 2 - group.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	smoothness	smoothness	ADJ	JJ	Degree=Pos	3	amod	_	_
3	conditions	condition	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	imposed	impose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	with	with	ADP	IN	_	5	prep	_	_
7	respect	respect	NOUN	NN	Number=Sing	6	pobj	_	_
8	to	to	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
10	strict	strict	ADJ	JJ	Degree=Pos	11	amod	_	_
11	Lie	lie	NOUN	NN	Number=Sing	14	nmod	_	_
12	2	2	NUM	CD	NumType=Card	14	nummod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	group	group	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	which	which	PRON	WDT	_	17	nsubj	_	_
17	plays	play	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	role	role	NOUN	NN	Number=Sing	17	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	band	band	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
24	or	or	CCONJ	CC	ConjType=Cmp	5	cc	_	_
25	structure	structure	NOUN	NN	Number=Sing	5	conj	_	_
26	2	2	NUM	CD	NumType=Card	28	nummod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	group	group	NOUN	NN	Number=Sing	25	npadvmod	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = Upon choosing certain examples of Lie 2 - groups, our axiomatic framework reproduces in a systematical way several known concepts of gerbes with connection: non - abelian differential cocycles, Breen - Messing gerbes, abelian and non - abelian bundle gerbes.
1	Upon	upon	SCONJ	IN	_	31	prep	_	_
2	choosing	choose	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	1	pcomp	_	_
3	certain	certain	ADJ	JJ	Degree=Pos	4	amod	_	_
4	examples	example	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	Lie	lie	NOUN	NN	Number=Sing	5	pobj	_	_
7	2	2	NUM	CD	NumType=Card	9	nummod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	groups	group	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	14	poss	_	_
12	axiomatic	axiomatic	ADJ	JJ	Degree=Pos	14	amod	_	_
13	framework	framework	NOUN	NN	Number=Sing	14	compound	_	_
14	reproduces	reproduce	NOUN	NNS	Number=Plur	2	dobj	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	systematical	systematical	ADJ	JJ	Degree=Pos	18	amod	_	_
18	way	way	NOUN	NN	Number=Sing	15	pobj	_	_
19	several	several	ADJ	JJ	Degree=Pos	21	amod	_	_
20	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	amod	_	_
21	concepts	concept	NOUN	NNS	Number=Plur	14	conj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	gerbes	gerbes	PROPN	NNP	Number=Sing	22	pobj	_	_
24	with	with	ADP	IN	_	21	prep	_	_
25	connection	connection	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
26	:	:	PUNCT	:	_	31	punct	_	_
27	non	non	ADJ	JJ	Degree=Pos	31	amod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
29	abelian	abelian	ADJ	JJ	Degree=Pos	31	amod	_	_
30	differential	differential	ADJ	JJ	Degree=Pos	31	amod	_	_
31	cocycles	cocycle	NOUN	NNS	Number=Plur	0	ROOT	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
33	Breen	Breen	PROPN	NNP	Number=Sing	35	compound	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	Messing	Messing	PROPN	NNP	Number=Sing	36	compound	_	_
36	gerbes	gerbes	PROPN	NNP	Number=Sing	31	conj	_	SpaceAfter=No
37	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
38	abelian	abelian	PROPN	NNP	Number=Sing	44	nmod	_	_
39	and	and	CCONJ	CC	ConjType=Cmp	38	cc	_	_
40	non	non	PROPN	NNP	Number=Sing	42	amod	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	abelian	abelian	PROPN	NNP	Number=Sing	38	conj	_	_
43	bundle	bundle	PROPN	NNP	Number=Sing	44	compound	_	_
44	gerbes	gerbes	PROPN	NNP	Number=Sing	36	conj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	31	punct	_	SpaceAfter=No

# sent_id = 5
# text = These relationships convey a well - defined notion of surface holonomy from our axiomatic framework to each of these concrete models.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	relationships	relationship	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	convey	convey	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
5	well	well	ADV	RB	Degree=Pos	7	advmod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
8	notion	notion	NOUN	NN	Number=Sing	3	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	surface	surface	NOUN	NN	Number=Sing	11	compound	_	_
11	holonomy	holonomy	NOUN	NN	Number=Sing	9	pobj	_	_
12	from	from	ADP	IN	_	8	prep	_	_
13	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	15	poss	_	_
14	axiomatic	axiomatic	ADJ	JJ	Degree=Pos	15	amod	_	_
15	framework	framework	NOUN	NN	Number=Sing	12	pobj	_	_
16	to	to	ADP	IN	_	8	prep	_	_
17	each	each	PRON	DT	_	16	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	these	these	DET	DT	Number=Plur|PronType=Dem	21	det	_	_
20	concrete	concrete	ADJ	JJ	Degree=Pos	21	amod	_	_
21	models	model	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = Till now, holonomy was only known for abelian gerbes; our approach reproduces that known concept and extends it to non - abelian gerbes.
1	Till	till	SCONJ	IN	_	7	prep	_	_
2	now	now	ADV	RB	_	1	pcomp	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
4	holonomy	holonomy	NOUN	NN	Number=Sing	7	nsubjpass	_	_
5	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	7	auxpass	_	_
6	only	only	ADV	RB	_	7	advmod	_	_
7	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	ccomp	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	abelian	abelian	PROPN	NNP	Number=Sing	10	compound	_	_
10	gerbes	gerbes	PROPN	NNP	Number=Sing	8	pobj	_	SpaceAfter=No
11	;	;	PUNCT	:	_	14	punct	_	_
12	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	14	poss	_	_
13	approach	approach	NOUN	NN	Number=Sing	14	compound	_	_
14	reproduces	reproduce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	that	that	SCONJ	IN	_	17	det	_	_
16	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	concept	concept	NOUN	NN	Number=Sing	14	dobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
19	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	conj	_	_
20	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	19	dobj	_	_
21	to	to	ADP	IN	_	19	prep	_	_
22	non	non	ADJ	JJ	Degree=Pos	24	amod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	abelian	abelian	ADJ	JJ	Degree=Pos	25	amod	_	_
25	gerbes	gerbes	PROPN	NNP	Number=Sing	21	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 7
# text = Several new features of surface holonomy are exposed under its extension to non - abelian gerbes; for example, it carries an action of the mapping class group of the surface.
1	Several	several	ADJ	JJ	Degree=Pos	3	amod	_	_
2	new	new	ADJ	JJ	Degree=Pos	3	amod	_	_
3	features	feature	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	surface	surface	NOUN	NN	Number=Sing	6	compound	_	_
6	holonomy	holonomy	NOUN	NN	Number=Sing	4	pobj	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	exposed	expose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	ccomp	_	_
9	under	under	ADP	IN	_	8	prep	_	_
10	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	11	poss	_	_
11	extension	extension	NOUN	NN	Number=Sing	9	pobj	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	non	non	ADJ	JJ	Degree=Pos	15	amod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	abelian	abelian	ADJ	JJ	Degree=Pos	16	amod	_	_
16	gerbes	gerbes	PROPN	NNP	Number=Sing	12	pobj	_	SpaceAfter=No
17	;	;	PUNCT	:	_	22	punct	_	_
18	for	for	ADP	IN	_	22	prep	_	_
19	example	example	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
21	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	22	nsubj	_	_
22	carries	carry	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
23	an	an	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	action	action	NOUN	NN	Number=Sing	22	dobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
27	mapping	mapping	NOUN	NN	Number=Sing	28	compound	_	_
28	class	class	NOUN	NN	Number=Sing	29	compound	_	_
29	group	group	NOUN	NN	Number=Sing	25	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	surface	surface	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# doc_id = 463
# sent_id = 1
# text = By Gelfand - Neumark duality, the category $ C^*Alg $ of commutative $ C^* $ - algebras is dually equivalent to the category of compact Hausdorff spaces, which by Stone duality, is also dually equivalent to the category $ ubal $ of uniformly complete bounded Archimedean $ ell $ - algebras.
1	By	by	ADP	IN	_	15	prep	_	_
2	Gelfand	Gelfand	PROPN	NNP	Number=Sing	4	compound	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	Neumark	Neumark	PROPN	NNP	Number=Sing	5	compound	_	_
5	duality	duality	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	15	nsubj	_	_
9	$ C^*Alg $	$ c^*alg $	SYM	$	_	8	appos	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	commutative	commutative	ADJ	JJ	Degree=Pos	14	amod	_	_
12	$ C^* $	$ c^* $	SYM	$	_	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	algebras	algebras	PROPN	NNP	Number=Sing	10	pobj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	dually	dually	ADV	RB	_	17	advmod	_	_
17	equivalent	equivalent	ADJ	JJ	Degree=Pos	15	acomp	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	compact	compact	ADJ	JJ	Degree=Pos	24	amod	_	_
23	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	24	compound	_	_
24	spaces	space	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	which	which	PRON	WDT	_	31	nsubj	_	_
27	by	by	ADP	IN	_	26	prep	_	_
28	Stone	Stone	PROPN	NNP	Number=Sing	29	compound	_	_
29	duality	duality	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
31	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	relcl	_	_
32	also	also	ADV	RB	_	31	advmod	_	_
33	dually	dually	ADV	RB	_	34	advmod	_	_
34	equivalent	equivalent	ADJ	JJ	Degree=Pos	31	acomp	_	_
35	to	to	ADP	IN	_	34	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	category	category	NOUN	NN	Number=Sing	35	pobj	_	_
38	$ ubal $	$ ubal $	SYM	$	_	37	appos	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	uniformly	uniformly	ADV	RB	_	41	advmod	_	_
41	complete	complete	ADJ	JJ	Degree=Pos	43	amod	_	_
42	bounded	bound	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	43	amod	_	_
43	Archimedean	Archimedean	PROPN	NNP	Number=Sing	39	pobj	_	_
44	$ ell $	$ ell $	SYM	$	_	46	compound	_	_
45	-	-	PUNCT	HYPH	PunctType=Dash	46	punct	_	_
46	algebras	algebra	NOUN	NNS	Number=Plur	31	attr	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 2
# text = Consequently, $ C^*Alg $ is equivalent to $ ubal $ , and this equivalence can be described through complexification.
1	Consequently	consequently	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	$ C^*Alg $	$ c^*alg $	SYM	$	_	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	equivalent	equivalent	ADJ	JJ	Degree=Pos	4	acomp	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	$ ubal $	$ ubal $	SYM	$	_	6	pobj	_	_
8	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
10	this	this	DET	DT	Number=Sing|PronType=Dem	11	det	_	_
11	equivalence	equivalence	NOUN	NN	Number=Sing	14	nsubjpass	_	_
12	can	can	AUX	MD	VerbForm=Fin	14	aux	_	_
13	be	be	AUX	VB	VerbForm=Inf	14	auxpass	_	_
14	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	conj	_	_
15	through	through	ADP	IN	_	14	prep	_	_
16	complexification	complexification	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this article we study $ ubal $ within the larger category $ bal $ of bounded Archimedean $ ell $ - algebras.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	article	article	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	$ ubal $	$ ubal $	SYM	$	_	5	dobj	_	_
7	within	within	ADP	IN	_	5	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	larger	large	ADJ	JJR	Degree=Cmp	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
11	$ bal $	$ bal $	SYM	$	_	10	appos	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	bounded	bound	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
14	Archimedean	Archimedean	PROPN	NNP	Number=Sing	12	pobj	_	_
15	$ ell $	$ ell $	SYM	$	_	17	compound	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	algebras	algebra	NOUN	NNS	Number=Plur	5	dobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show that $ ubal $ is the smallest nontrivial reflective subcategory of $ bal $ , and that $ ubal $ consists of exactly those objects in $ bal $ that are epicomplete, a fact that includes a categorical formulation of the Stone - Weierstrass theorem for $ bal $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	$ ubal $	$ ubal $	SYM	$	_	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
7	smallest	small	ADJ	JJS	Degree=Sup	10	amod	_	_
8	nontrivial	nontrivial	ADJ	JJ	Degree=Pos	10	amod	_	_
9	reflective	reflective	ADJ	JJ	Degree=Pos	10	amod	_	_
10	subcategory	subcategory	NOUN	NN	Number=Sing	5	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	$ bal $	$ bal $	SYM	$	_	11	pobj	_	_
13	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
15	that	that	SCONJ	IN	_	17	mark	_	_
16	$ ubal $	$ ubal $	SYM	$	_	17	nsubj	_	_
17	consists	consist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	conj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	exactly	exactly	ADV	RB	_	21	advmod	_	_
20	those	those	DET	DT	Number=Plur|PronType=Dem	21	det	_	_
21	objects	object	NOUN	NNS	Number=Plur	18	pobj	_	_
22	in	in	ADP	IN	_	21	prep	_	_
23	$ bal $	$ bal $	SYM	$	_	22	pobj	_	_
24	that	that	PRON	WDT	PronType=Rel	25	nsubj	_	_
25	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	23	relcl	_	_
26	epicomplete	epicomplete	ADJ	JJ	Degree=Pos	25	acomp	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
29	fact	fact	NOUN	NN	Number=Sing	17	npadvmod	_	_
30	that	that	PRON	WDT	PronType=Rel	31	nsubj	_	_
31	includes	include	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	relcl	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
33	categorical	categorical	ADJ	JJ	Degree=Pos	34	amod	_	_
34	formulation	formulation	NOUN	NN	Number=Sing	31	dobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
37	Stone	Stone	PROPN	NNP	Number=Sing	39	compound	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	Weierstrass	Weierstrass	PROPN	NNP	Number=Sing	40	compound	_	_
40	theorem	theorem	NOUN	NN	Number=Sing	35	pobj	_	_
41	for	for	ADP	IN	_	34	prep	_	_
42	$ bal $	$ bal $	SYM	$	_	41	pobj	_	_
43	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = It follows that $ ubal $ is the unique nontrivial reflective epicomplete subcategory of $ bal $ .
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	follows	follow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	$ ubal $	$ ubal $	SYM	$	_	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
7	unique	unique	ADJ	JJ	Degree=Pos	11	amod	_	_
8	nontrivial	nontrivial	ADJ	JJ	Degree=Pos	11	amod	_	_
9	reflective	reflective	ADJ	JJ	Degree=Pos	11	amod	_	_
10	epicomplete	epicomplete	ADJ	JJ	Degree=Pos	11	amod	_	_
11	subcategory	subcategory	NOUN	NN	Number=Sing	5	attr	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	$ bal $	$ bal $	SYM	$	_	12	pobj	_	_
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = We also show that each nontrivial reflective subcategory of $ bal $ is both monoreflective and epireflective, and exhibit two other interesting reflective subcategories of $ bal $ involving Gelfand rings and square closed rings.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	11	mark	_	_
5	each	each	DET	DT	_	8	det	_	_
6	nontrivial	nontrivial	ADJ	JJ	Degree=Pos	8	amod	_	_
7	reflective	reflective	ADJ	JJ	Degree=Pos	8	amod	_	_
8	subcategory	subcategory	NOUN	NN	Number=Sing	11	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	$ bal $	$ bal $	SYM	$	_	9	pobj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
12	both	both	PRON	DT	_	13	preconj	_	_
13	monoreflective	monoreflective	ADJ	JJ	Degree=Pos	11	acomp	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	epireflective	epireflective	ADJ	JJ	Degree=Pos	13	conj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
18	exhibit	exhibit	VERB	VB	VerbForm=Inf	11	conj	_	_
19	two	two	NUM	CD	NumType=Card	23	nummod	_	_
20	other	other	ADJ	JJ	Degree=Pos	23	amod	_	_
21	interesting	interesting	ADJ	JJ	Degree=Pos	23	amod	_	_
22	reflective	reflective	ADJ	JJ	Degree=Pos	23	amod	_	_
23	subcategories	subcategorie	NOUN	NNS	Number=Plur	18	dobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	$ bal $	$ bal $	SYM	$	_	24	pobj	_	_
26	involving	involve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	18	advcl	_	_
27	Gelfand	Gelfand	PROPN	NNP	Number=Sing	28	compound	_	_
28	rings	ring	NOUN	NNS	Number=Plur	26	dobj	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	square	square	ADJ	JJ	Degree=Pos	32	amod	_	_
31	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	amod	_	_
32	rings	ring	NOUN	NNS	Number=Plur	28	conj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = Dually, we show that Specker $ {mathbb R} $ - algebras are precisely the co - epicomplete objects in $ bal $ .
1	Dually	Dually	PROPN	NNP	Number=Sing	4	npadvmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	10	mark	_	_
6	Specker	Specker	PROPN	NNP	Number=Sing	9	nmod	_	_
7	$ {mathbb R} $	$ {mathbb r} $	SYM	$	_	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	algebras	algebra	NOUN	NNS	Number=Plur	10	nsubj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
11	precisely	precisely	ADV	RB	_	10	advmod	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
13	co	co	ADJ	JJ	Degree=Pos	15	amod	_	_
14	-	-	ADJ	JJ	Degree=Pos	15	punct	_	_
15	epicomplete	epicomplete	ADJ	JJ	Degree=Pos	16	amod	_	_
16	objects	object	NOUN	NNS	Number=Plur	10	attr	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	$ bal $	$ bal $	SYM	$	_	17	pobj	_	_
19	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 8
# text = We prove that the category $ spec $ of Specker $ mathbb R $ - algebras is a mono - coreflective subcategory of $ bal $ that is co - epireflective in a mono - coreflective subcategory of $ bal $ consisting of what we term $ ell $ - clean rings, a version of clean rings adapted to the order - theoretic setting of $ bal $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	12	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	12	nsubj	_	_
6	$ spec $	$ spec $	SYM	$	_	5	appos	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	Specker	Specker	PROPN	NNP	Number=Sing	7	pobj	_	_
9	$ mathbb R $	$ mathbb r $	SYM	$	_	11	compound	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	algebras	algebras	PROPN	NNP	Number=Sing	7	pobj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
14	mono	mono	NOUN	NN	Number=Sing	16	npadvmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	coreflective	coreflective	ADJ	JJ	Degree=Pos	17	amod	_	_
17	subcategory	subcategory	NOUN	NN	Number=Sing	12	attr	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	$ bal $	$ bal $	SYM	$	_	18	pobj	_	_
20	that	that	PRON	WDT	PronType=Rel	21	nsubj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
22	co	co	NOUN	NN	Number=Sing	21	acomp	_	_
23	-	-	ADJ	JJ	Degree=Pos	21	attr	_	_
24	epireflective	epireflective	ADJ	JJ	Degree=Pos	21	acomp	_	_
25	in	in	ADP	IN	_	21	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
27	mono	mono	NOUN	NN	Number=Sing	29	npadvmod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	coreflective	coreflective	ADJ	JJ	Degree=Pos	30	amod	_	_
30	subcategory	subcategory	NOUN	NN	Number=Sing	25	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	$ bal $	$ bal $	SYM	$	_	31	pobj	_	_
33	consisting	consist	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	acl	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	what	what	PRON	WP	_	37	dobj	_	_
36	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	37	nsubj	_	_
37	term	term	VERB	VBP	Tense=Pres|VerbForm=Fin	34	pcomp	_	_
38	$ ell $	$ ell $	SYM	$	_	40	advmod	_	_
39	-	-	PUNCT	HYPH	PunctType=Dash	40	punct	_	_
40	clean	clean	ADJ	JJ	Degree=Pos	41	amod	_	_
41	rings	ring	NOUN	NNS	Number=Plur	37	dobj	_	SpaceAfter=No
42	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
43	a	a	DET	DT	Definite=Ind|PronType=Art	44	det	_	_
44	version	version	NOUN	NN	Number=Sing	17	appos	_	_
45	of	of	ADP	IN	_	44	prep	_	_
46	clean	clean	ADJ	JJ	Degree=Pos	47	amod	_	_
47	rings	ring	NOUN	NNS	Number=Plur	45	pobj	_	_
48	adapted	adapt	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	44	acl	_	_
49	to	to	ADP	IN	_	48	prep	_	_
50	the	the	DET	DT	Definite=Def|PronType=Art	54	det	_	_
51	order	order	NOUN	NN	Number=Sing	53	npadvmod	_	_
52	-	-	PUNCT	HYPH	PunctType=Dash	53	punct	_	_
53	theoretic	theoretic	ADJ	JJ	Degree=Pos	54	amod	_	_
54	setting	setting	NOUN	NN	Number=Sing	49	pobj	_	_
55	of	of	ADP	IN	_	54	prep	_	_
56	$ bal $	$ bal $	SYM	$	_	55	pobj	_	_
57	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 9
# text = We conclude the article by discussing the import of our results in the setting of complex $ * $ - algebras through complexification.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	conclude	conclude	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	article	article	NOUN	NN	Number=Sing	2	dobj	_	_
5	by	by	ADP	IN	_	2	prep	_	_
6	discussing	discuss	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	import	import	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	11	poss	_	_
11	results	result	NOUN	NNS	Number=Plur	9	pobj	_	_
12	in	in	ADP	IN	_	6	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	setting	setting	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	complex	complex	ADJ	JJ	Degree=Pos	19	amod	_	_
17	$ * $	$ * $	SYM	$	_	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	algebras	algebra	NOUN	NNS	Number=Plur	15	pobj	_	_
20	through	through	ADP	IN	_	6	prep	_	_
21	complexification	complexification	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 464
# sent_id = 1
# text = We exhibit sufficient conditions for a monoidal monad $ T $ on a monoidal category $ C $ to induce a monoidal structure on the Eilenberg - Moore category $ C^T $ that represents bimorphisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	exhibit	exhibit	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	sufficient	sufficient	ADJ	JJ	Degree=Pos	4	amod	_	_
4	conditions	condition	NOUN	NNS	Number=Plur	2	dobj	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	monoidal	monoidal	NOUN	NN	Number=Sing	8	amod	_	_
8	monad	monad	NOUN	NNS	Number=Plur	5	pobj	_	_
9	$ T $	$ t $	SYM	$	_	8	appos	_	_
10	on	on	ADP	IN	_	8	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	monoidal	monoidal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
14	$ C $	$ c $	SYM	$	_	10	dep	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	induce	induce	VERB	VB	VerbForm=Inf	2	advcl	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	monoidal	monoidal	ADJ	JJ	Degree=Pos	19	amod	_	_
19	structure	structure	NOUN	NN	Number=Sing	16	dobj	_	_
20	on	on	ADP	IN	_	16	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
22	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	Moore	Moore	PROPN	NNP	Number=Sing	25	compound	_	_
25	category	category	NOUN	NN	Number=Sing	20	pobj	_	_
26	$ C^T $	$ c^t $	SYM	$	_	25	appos	_	_
27	that	that	PRON	WDT	PronType=Rel	28	nsubj	_	_
28	represents	represent	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	relcl	_	_
29	bimorphisms	bimorphism	NOUN	NNS	Number=Plur	28	dobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The category of actions in $ C^T $ is then shown to be monadic over the base category $ C $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	9	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	actions	action	NOUN	NNS	Number=Plur	3	pobj	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	$ C^T $	$ c^t $	SYM	$	_	5	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
8	then	then	ADV	RB	PronType=Dem	9	advmod	_	_
9	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	be	be	AUX	VB	VerbForm=Inf	9	xcomp	_	_
12	monadic	monadic	ADJ	JJ	Degree=Pos	11	acomp	_	_
13	over	over	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	base	base	NOUN	NN	Number=Sing	16	compound	_	_
16	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
17	$ C $	$ c $	SYM	$	_	16	appos	_	_
18	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 465
# sent_id = 1
# text = In this paper, we prove that the category of vacant $ n $ - tuple groupoids is equivalent to the category of factorizations of groupoids by
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	16	mark	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	category	category	NOUN	NN	Number=Sing	16	nsubj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	vacant	vacant	ADJ	JJ	Degree=Pos	14	amod	_	_
12	$ n $	$ n $	SYM	$	_	14	quantmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	tuple	tuple	NOUN	NN	Number=Sing	15	compound	_	_
15	groupoids	groupoid	NOUN	NNS	Number=Plur	10	pobj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
17	equivalent	equivalent	ADJ	JJ	Degree=Pos	16	acomp	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	factorizations	factorization	NOUN	NNS	Number=Plur	21	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	groupoids	groupoid	NOUN	NNS	Number=Plur	23	pobj	_	_
25	by	by	ADP	IN	_	16	prep	_	SpaceAfter=No

# sent_id = 2
# text = $ n $ factors that satisfy some Yang - Baxter type equation
1	$ n $	$ n $	SYM	$	_	2	nummod	_	_
2	factors	factor	NOUN	NNS	Number=Plur	0	ROOT	_	_
3	that	that	PRON	WDT	PronType=Rel	4	nsubj	_	_
4	satisfy	satisfy	VERB	VBP	Tense=Pres|VerbForm=Fin	2	relcl	_	_
5	some	some	DET	DT	_	10	det	_	_
6	Yang	Yang	PROPN	NNP	Number=Sing	8	compound	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	Baxter	Baxter	PROPN	NNP	Number=Sing	10	compound	_	_
9	type	type	NOUN	NN	Number=Sing	10	compound	_	_
10	equation	equation	NOUN	NN	Number=Sing	4	dobj	_	SpaceAfter=No

# sent_id = 3
# text = .
1	.	.	PUNCT	.	PunctType=Peri	0	ROOT	_	SpaceAfter=No

# sent_id = 4
# text = Moreover we extend this equivalence to the category of maximally exclusive $ n $ - tuple groupoids, which we define, by dropping one assumption.
1	Moreover	moreover	ADV	RB	_	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	extend	extend	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	equivalence	equivalence	NOUN	NN	Number=Sing	3	dobj	_	_
6	to	to	ADP	IN	_	3	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	maximally	maximally	ADV	RB	_	11	advmod	_	_
11	exclusive	exclusive	ADJ	JJ	Degree=Pos	15	amod	_	_
12	$ n $	$ n $	SYM	$	_	14	quantmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	tuple	tuple	NOUN	NN	Number=Sing	15	compound	_	_
15	groupoids	groupoid	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	which	which	PRON	WDT	_	19	dobj	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	15	relcl	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
21	by	by	ADP	IN	_	3	prep	_	_
22	dropping	drop	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	21	pcomp	_	_
23	one	one	NUM	CD	NumType=Card	24	nummod	_	_
24	assumption	assumption	NOUN	NN	Number=Sing	22	dobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = The paper concludes by a note on how these results could tell us more about some Lie groups of interest.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	concludes	conclude	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	by	by	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	note	note	NOUN	NN	Number=Sing	4	pobj	_	_
7	on	on	ADP	IN	_	6	prep	_	_
8	how	how	SCONJ	WRB	_	12	advmod	_	_
9	these	these	DET	DT	Number=Plur|PronType=Dem	10	det	_	_
10	results	result	NOUN	NNS	Number=Plur	12	nsubj	_	_
11	could	could	AUX	MD	VerbForm=Fin	12	aux	_	_
12	tell	tell	VERB	VB	VerbForm=Inf	7	pcomp	_	_
13	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	12	dative	_	_
14	more	more	ADJ	JJR	Degree=Cmp	12	dobj	_	_
15	about	about	ADP	IN	_	14	prep	_	_
16	some	some	DET	DT	_	18	det	_	_
17	Lie	lie	NOUN	NN	Number=Sing	18	compound	_	_
18	groups	group	NOUN	NNS	Number=Plur	15	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	interest	interest	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 466
# sent_id = 1
# text = Suppose that $ S $ is a space.
1	Suppose	suppose	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	that	that	SCONJ	IN	_	4	mark	_	_
3	$ S $	$ s $	SYM	$	_	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	1	ccomp	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	space	space	NOUN	NN	Number=Sing	4	attr	_	SpaceAfter=No
7	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = There is an injective and a projective model structure for the resulting category of spaces with $ S $ - action, and both are easily derived.
1	There	there	PRON	EX	_	2	expl	_	_
2	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	injective	injective	ADJ	JJ	Degree=Pos	2	attr	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	projective	projective	ADJ	JJ	Degree=Pos	9	amod	_	_
8	model	model	NOUN	NN	Number=Sing	9	compound	_	_
9	structure	structure	NOUN	NN	Number=Sing	4	conj	_	_
10	for	for	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	spaces	space	NOUN	NNS	Number=Plur	14	pobj	_	_
16	with	with	ADP	IN	_	15	prep	_	_
17	$ S $	$ s $	SYM	$	_	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	action	action	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
22	both	both	PRON	DT	_	25	nsubjpass	_	_
23	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	25	auxpass	_	_
24	easily	easily	ADV	RB	_	25	advmod	_	_
25	derived	derive	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	conj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	25	punct	_	SpaceAfter=No

# sent_id = 3
# text = These model structures are special cases of model structures for presheaf - valued diagrams $ X $ defined on a fixed presheaf of categories $ E $ which is enriched in simplicial sets.
1	These	these	DET	DT	Number=Plur|PronType=Dem	3	det	_	_
2	model	model	NOUN	NN	Number=Sing	3	compound	_	_
3	structures	structure	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	special	special	ADJ	JJ	Degree=Pos	6	amod	_	_
6	cases	case	NOUN	NNS	Number=Plur	4	attr	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	model	model	NOUN	NN	Number=Sing	9	compound	_	_
9	structures	structure	NOUN	NNS	Number=Plur	7	pobj	_	_
10	for	for	ADP	IN	_	6	prep	_	_
11	presheaf	presheaf	ADV	RB	_	13	npadvmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
14	diagrams	diagram	NOUN	NNS	Number=Plur	10	pobj	_	_
15	$ X $	$ x $	SYM	$	_	6	nmod	_	_
16	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
17	on	on	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	amod	_	_
20	presheaf	presheaf	NOUN	NN	Number=Sing	17	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	categories	category	NOUN	NNS	Number=Plur	21	pobj	_	_
23	$ E $	$ e $	SYM	$	_	6	punct	_	_
24	which	which	PRON	WDT	_	26	nsubjpass	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	auxpass	_	_
26	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	relcl	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	simplicial	simplicial	ADJ	JJ	Degree=Pos	29	amod	_	_
29	sets	set	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = Varying the parameter category object $ E $ (or parameter space $ S $ ) along with the diagrams $ X $ up to weak equivalence requires model structures for $ E $ - diagrams having weak equivalences defined by homotopy colimits, and a generalization of Thomason's model structure for small categories to a model structure for presheaves of simplicial categories.
1	Varying	vary	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	csubj	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	parameter	parameter	NOUN	NN	Number=Sing	4	compound	_	_
4	category	category	NOUN	NN	Number=Sing	1	dobj	_	_
5	object	object	VERB	VBP	Tense=Pres|VerbForm=Fin	1	dep	_	_
6	$ E $	$ e $	SYM	$	_	5	advmod	_	_
7	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	6	punct	_	SpaceAfter=No
8	or	or	CCONJ	CC	ConjType=Cmp	5	cc	_	_
9	parameter	parameter	VERB	VB	VerbForm=Inf	5	conj	_	_
10	space	space	NOUN	NN	Number=Sing	9	dobj	_	_
11	$ S $	$ s $	SYM	$	_	9	npadvmod	_	_
12	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	9	punct	_	_
13	along	along	ADP	IN	_	1	prep	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	diagrams	diagram	NOUN	NNS	Number=Plur	14	pobj	_	_
17	$ X $	$ x $	SYM	$	_	16	nmod	_	_
18	up	up	ADP	IN	_	1	prep	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	weak	weak	ADJ	JJ	Degree=Pos	21	amod	_	_
21	equivalence	equivalence	NOUN	NN	Number=Sing	19	pobj	_	_
22	requires	require	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
23	model	model	NOUN	NN	Number=Sing	24	compound	_	_
24	structures	structure	NOUN	NNS	Number=Plur	22	dobj	_	_
25	for	for	ADP	IN	_	24	prep	_	_
26	$ E $	$ e $	SYM	$	_	28	compound	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	diagrams	diagram	NOUN	NNS	Number=Plur	25	pobj	_	_
29	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	28	acl	_	_
30	weak	weak	ADJ	JJ	Degree=Pos	31	amod	_	_
31	equivalences	equivalence	NOUN	NNS	Number=Plur	29	dobj	_	_
32	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	acl	_	_
33	by	by	ADP	IN	_	32	agent	_	_
34	homotopy	homotopy	PROPN	NNP	Number=Sing	35	compound	_	_
35	colimits	colimit	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
37	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
38	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
39	generalization	generalization	NOUN	NN	Number=Sing	22	conj	_	_
40	of	of	ADP	IN	_	39	prep	_	_
41	Thomason	Thomason	PROPN	NNP	Number=Sing	44	poss	_	SpaceAfter=No
42	's	's	PART	POS	_	41	case	_	_
43	model	model	NOUN	NN	Number=Sing	44	compound	_	_
44	structure	structure	NOUN	NN	Number=Sing	40	pobj	_	_
45	for	for	ADP	IN	_	44	prep	_	_
46	small	small	ADJ	JJ	Degree=Pos	47	amod	_	_
47	categories	category	NOUN	NNS	Number=Plur	45	pobj	_	_
48	to	to	ADP	IN	_	39	prep	_	_
49	a	a	DET	DT	Definite=Ind|PronType=Art	51	det	_	_
50	model	model	NOUN	NN	Number=Sing	51	compound	_	_
51	structure	structure	NOUN	NN	Number=Sing	48	pobj	_	_
52	for	for	ADP	IN	_	51	prep	_	_
53	presheaves	presheave	NOUN	NNS	Number=Plur	52	pobj	_	_
54	of	of	ADP	IN	_	53	prep	_	_
55	simplicial	simplicial	ADJ	JJ	Degree=Pos	56	amod	_	_
56	categories	category	NOUN	NNS	Number=Plur	54	pobj	_	SpaceAfter=No
57	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# doc_id = 467
# sent_id = 1
# text = We present the no - iteration version of the coherence conditions necessary to define a pseudomonad, and a description of the algebras for it in a similar fashion.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
4	no	no	DET	DT	_	6	det	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	iteration	iteration	NOUN	NN	Number=Sing	7	compound	_	_
7	version	version	NOUN	NN	Number=Sing	2	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	coherence	coherence	NOUN	NN	Number=Sing	11	compound	_	_
11	conditions	condition	NOUN	NNS	Number=Plur	8	pobj	_	_
12	necessary	necessary	ADJ	JJ	Degree=Pos	11	amod	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	define	define	VERB	VB	VerbForm=Inf	12	xcomp	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	pseudomonad	pseudomonad	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	description	description	NOUN	NN	Number=Sing	2	conj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	algebras	algebra	NOUN	NNS	Number=Plur	21	pobj	_	_
24	for	for	ADP	IN	_	20	prep	_	_
25	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	24	pobj	_	_
26	in	in	ADP	IN	_	20	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	similar	similar	ADJ	JJ	Degree=Pos	29	amod	_	_
29	fashion	fashion	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that every no - iteration pseudomonad induces a pseudomonad, and that the corresponding algebras are equivalent.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	9	mark	_	_
4	every	every	DET	DT	_	8	det	_	_
5	no	no	DET	DT	_	7	det	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	iteration	iteration	NOUN	NN	Number=Sing	8	compound	_	_
8	pseudomonad	pseudomonad	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	induces	induce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	pseudomonad	pseudomonad	NOUN	NNS	Number=Plur	9	dobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
14	that	that	SCONJ	IN	_	18	mark	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	corresponding	corresponding	ADJ	JJ	Degree=Pos	17	amod	_	_
17	algebras	algebra	NOUN	NNS	Number=Plur	18	nsubj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	conj	_	_
19	equivalent	equivalent	ADJ	JJ	Degree=Pos	18	acomp	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also show that every pseudomonad induces a no - iteration pseudomonad, and again, that the corresponding algebras are equivalent.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	7	mark	_	_
5	every	every	DET	DT	_	6	det	_	_
6	pseudomonad	pseudomonad	NOUN	NNS	Number=Plur	7	nsubj	_	_
7	induces	induce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
9	no	no	DET	DT	_	11	det	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	iteration	iteration	NOUN	NN	Number=Sing	12	compound	_	_
12	pseudomonad	pseudomonad	NOUN	NNS	Number=Plur	7	dobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
15	again	again	ADV	RB	_	21	advmod	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
17	that	that	SCONJ	IN	_	21	mark	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	corresponding	corresponding	ADJ	JJ	Degree=Pos	20	amod	_	_
20	algebras	algebra	NOUN	NNS	Number=Plur	21	nsubj	_	_
21	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	conj	_	_
22	equivalent	equivalent	ADJ	JJ	Degree=Pos	21	acomp	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = We conclude with an analysis of the algebras for the 2 - monad $ ( - )^{mathbf{2}} $ on Cat in the light of the no - iteration description of the algebras.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	conclude	conclude	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	with	with	ADP	IN	_	2	prep	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	analysis	analysis	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	algebras	algebra	NOUN	NNS	Number=Plur	6	pobj	_	_
9	for	for	ADP	IN	_	5	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	monad	monad	NOUN	NNS	Number=Plur	14	compound	_	_
14	$ ( - )^{mathbf{2}} $	$ ( - )^{mathbf{2}} $	SYM	$	_	9	pobj	_	_
15	on	on	ADP	IN	_	14	prep	_	_
16	Cat	Cat	PROPN	NNP	Number=Sing	15	pobj	_	_
17	in	in	ADP	IN	_	5	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	light	light	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
22	no	no	DET	DT	_	24	det	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	iteration	iteration	NOUN	NN	Number=Sing	25	compound	_	_
25	description	description	NOUN	NN	Number=Sing	20	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	algebras	algebra	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 468
# sent_id = 1
# text = Even a functor without an adjoint induces a monad, namely, its codensity monad; this is subject only to the existence of certain limits.
1	Even	even	ADV	RB	_	3	advmod	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	functor	functor	NOUN	NN	Number=Sing	7	nsubj	_	_
4	without	without	ADP	IN	_	3	prep	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	adjoint	adjoint	NOUN	NN	Number=Sing	4	pobj	_	_
7	induces	induce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	ccomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	monad	monad	NOUN	NNS	Number=Plur	7	dobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	namely	namely	ADV	RB	_	15	advmod	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
13	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	15	poss	_	_
14	codensity	codensity	NOUN	NN	Number=Sing	15	compound	_	_
15	monad	monad	NOUN	NNS	Number=Plur	9	appos	_	SpaceAfter=No
16	;	;	PUNCT	:	_	18	punct	_	_
17	this	this	PRON	DT	Number=Sing|PronType=Dem	18	nsubj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
19	subject	subject	ADJ	JJ	Degree=Pos	18	acomp	_	_
20	only	only	ADV	RB	_	21	advmod	_	_
21	to	to	ADP	IN	_	19	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	existence	existence	NOUN	NN	Number=Sing	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	certain	certain	ADJ	JJ	Degree=Pos	26	amod	_	_
26	limits	limit	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# sent_id = 2
# text = We clarify the sense in which codensity monads act as substitutes for monads induced by adjunctions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	clarify	clarify	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	sense	sense	NOUN	NN	Number=Sing	2	dobj	_	_
5	in	in	ADP	IN	_	9	prep	_	_
6	which	which	PRON	WDT	_	5	pobj	_	_
7	codensity	codensity	ADJ	JJ	Degree=Pos	8	amod	_	_
8	monads	monad	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	act	act	VERB	VBP	Tense=Pres|VerbForm=Fin	4	relcl	_	_
10	as	as	ADP	IN	_	9	prep	_	_
11	substitutes	substitute	NOUN	NNS	Number=Plur	10	pobj	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	monads	monad	NOUN	NNS	Number=Plur	12	pobj	_	_
14	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	acl	_	_
15	by	by	ADP	IN	_	14	agent	_	_
16	adjunctions	adjunction	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also expand on an undeservedly ignored theorem of Kennison and Gildenhuys: that the codensity monad of the inclusion of (finite sets) into (sets) is the ultrafilter monad.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	expand	expand	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	on	on	ADP	IN	_	3	prep	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
6	undeservedly	undeservedly	ADV	RB	_	7	advmod	_	_
7	ignored	ignore	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
8	theorem	theorem	ADJ	JJ	Degree=Pos	4	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Kennison	Kennison	PROPN	NNP	Number=Sing	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	Gildenhuys	gildenhuy	NOUN	NNS	Number=Plur	10	conj	_	SpaceAfter=No
13	:	:	PUNCT	:	_	3	punct	_	_
14	that	that	SCONJ	IN	_	30	mark	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	codensity	codensity	ADJ	JJ	Degree=Pos	17	compound	_	_
17	monad	monad	NOUN	NNS	Number=Plur	30	nsubj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	inclusion	inclusion	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
23	finite	finite	PROPN	NNP	Number=Sing	24	compound	_	_
24	sets	set	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
25	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	24	punct	_	_
26	into	into	ADP	IN	_	20	prep	_	_
27	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	26	punct	_	SpaceAfter=No
28	sets	set	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
29	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	17	punct	_	_
30	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	ultrafilter	ultrafilter	ADJ	JJ	Degree=Pos	33	amod	_	_
33	monad	monad	NOUN	NNS	Number=Plur	30	attr	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = This result is analogous to the correspondence between measures and integrals.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	result	result	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	analogous	analogous	ADJ	JJ	Degree=Pos	3	acomp	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	correspondence	correspondence	NOUN	NN	Number=Sing	5	pobj	_	_
8	between	between	ADP	IN	_	7	prep	_	_
9	measures	measure	NOUN	NNS	Number=Plur	8	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	integrals	integral	NOUN	NNS	Number=Plur	9	conj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = So, for example, we can speak of integration against an ultrafilter.
1	So	so	ADV	RB	_	8	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
3	for	for	ADP	IN	_	8	prep	_	_
4	example	example	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	8	nsubj	_	_
7	can	can	AUX	MD	VerbForm=Fin	8	aux	_	_
8	speak	speak	VERB	VB	VerbForm=Inf	0	ROOT	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	integration	integration	NOUN	NN	Number=Sing	9	pobj	_	_
11	against	against	ADP	IN	_	8	prep	_	_
12	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	ultrafilter	ultrafilter	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 6
# text = Using this language, we show that the codensity monad of the inclusion of (finite - dimensional vector spaces) into (vector spaces) is double dualization.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	advcl	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	language	language	NOUN	NN	Number=Sing	1	dobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	27	mark	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	codensity	codensity	ADJ	JJ	Degree=Pos	10	amod	_	_
10	monad	monad	NOUN	NNS	Number=Plur	27	nsubj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	inclusion	inclusion	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	20	punct	_	SpaceAfter=No
16	finite	finite	ADJ	JJ	Degree=Pos	18	amod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	dimensional	dimensional	ADJ	JJ	Degree=Pos	20	amod	_	_
19	vector	vector	NOUN	NN	Number=Sing	20	compound	_	_
20	spaces	space	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
21	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	20	punct	_	_
22	into	into	ADP	IN	_	13	prep	_	_
23	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	22	punct	_	SpaceAfter=No
24	vector	vector	NOUN	NN	Number=Sing	25	compound	_	_
25	spaces	space	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
26	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	10	punct	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
28	double	double	ADJ	JJ	Degree=Pos	29	amod	_	_
29	dualization	dualization	NOUN	NN	Number=Sing	27	attr	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 7
# text = From this it follows that compact Hausdorff spaces have a linear analogue: linearly compact vector spaces.
1	From	from	ADP	IN	_	4	prep	_	_
2	this	this	PRON	DT	Number=Sing|PronType=Dem	1	pobj	_	_
3	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	4	nsubj	_	_
4	follows	follow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	9	mark	_	_
6	compact	compact	ADJ	JJ	Degree=Pos	8	amod	_	_
7	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	8	compound	_	_
8	spaces	space	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	linear	linear	ADJ	JJ	Degree=Pos	12	amod	_	_
12	analogue	analogue	NOUN	NN	Number=Sing	9	dobj	_	SpaceAfter=No
13	:	:	PUNCT	:	_	4	punct	_	_
14	linearly	linearly	ADV	RB	_	17	advmod	_	_
15	compact	compact	ADJ	JJ	Degree=Pos	17	amod	_	_
16	vector	vector	NOUN	NN	Number=Sing	17	compound	_	_
17	spaces	space	NOUN	NNS	Number=Plur	12	appos	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 8
# text = Finally, we show that ultraproducts are categorically inevitable: the codensity monad of the inclusion of (finite families of sets) into (families of sets) is the ultraproduct monad.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	30	ccomp	_	_
5	that	that	SCONJ	IN	_	7	mark	_	_
6	ultraproducts	ultraproduct	NOUN	NNS	Number=Plur	7	nsubj	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
8	categorically	categorically	ADV	RB	_	7	advmod	_	_
9	inevitable	inevitable	ADJ	JJ	Degree=Pos	7	acomp	_	SpaceAfter=No
10	:	:	PUNCT	:	_	30	punct	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	codensity	codensity	ADJ	JJ	Degree=Pos	13	amod	_	_
13	monad	monad	NOUN	NNS	Number=Plur	30	nsubj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	inclusion	inclusion	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	20	punct	_	SpaceAfter=No
19	finite	finite	ADJ	JJ	Degree=Pos	20	amod	_	_
20	families	family	NOUN	NNS	Number=Plur	17	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	sets	set	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	20	punct	_	_
24	into	into	ADP	IN	_	13	prep	_	_
25	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
26	families	family	NOUN	NNS	Number=Plur	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	sets	set	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
29	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	13	punct	_	_
30	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	ultraproduct	ultraproduct	ADJ	JJ	Degree=Pos	33	amod	_	_
33	monad	monad	NOUN	NNS	Number=Plur	30	attr	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	30	punct	_	SpaceAfter=No

# doc_id = 469
# sent_id = 1
# text = The category of bisimplicial presheaves carries a model structure for which the weak equivalences are defined by the diagonal functor and the cofibrations are monomorphisms.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	bisimplicial	bisimplicial	ADJ	JJ	Degree=Pos	5	amod	_	_
5	presheaves	presheave	NOUN	NNS	Number=Plur	3	pobj	_	_
6	carries	carry	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	model	model	NOUN	NN	Number=Sing	9	compound	_	_
9	structure	structure	NOUN	NN	Number=Sing	6	dobj	_	_
10	for	for	ADP	IN	_	16	prep	_	_
11	which	which	PRON	WDT	_	10	pobj	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	weak	weak	ADJ	JJ	Degree=Pos	14	amod	_	_
14	equivalences	equivalence	NOUN	NNS	Number=Plur	16	nsubjpass	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	16	auxpass	_	_
16	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	relcl	_	_
17	by	by	ADP	IN	_	16	agent	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	diagonal	diagonal	ADJ	JJ	Degree=Pos	20	amod	_	_
20	functor	functor	NOUN	NN	Number=Sing	17	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	cofibrations	cofibration	NOUN	NNS	Number=Plur	24	nsubj	_	_
24	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	16	conj	_	_
25	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	24	attr	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# sent_id = 2
# text = This model structure has the most cofibrations of a large family of model structures with weak equivalences defined by the diagonal.
1	This	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
2	model	model	NOUN	NN	Number=Sing	3	compound	_	_
3	structure	structure	NOUN	NN	Number=Sing	4	nsubj	_	_
4	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	most	most	ADJ	JJS	Degree=Sup	7	amod	_	_
7	cofibrations	cofibration	NOUN	NNS	Number=Plur	4	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	large	large	ADJ	JJ	Degree=Pos	11	amod	_	_
11	family	family	NOUN	NN	Number=Sing	8	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	model	model	NOUN	NN	Number=Sing	14	compound	_	_
14	structures	structure	NOUN	NNS	Number=Plur	12	pobj	_	_
15	with	with	ADP	IN	_	11	prep	_	_
16	weak	weak	ADJ	JJ	Degree=Pos	17	amod	_	_
17	equivalences	equivalence	NOUN	NNS	Number=Plur	15	pobj	_	_
18	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
19	by	by	ADP	IN	_	18	agent	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	diagonal	diagonal	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = The diagonal structure for bisimplicial presheaves specializes to a diagonal model structure for bisimplicial sets, for which the fibrations are the Kan fibrations.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	diagonal	diagonal	ADJ	JJ	Degree=Pos	3	amod	_	_
3	structure	structure	NOUN	NN	Number=Sing	7	nsubj	_	_
4	for	for	ADP	IN	_	3	prep	_	_
5	bisimplicial	bisimplicial	ADJ	JJ	Degree=Pos	6	amod	_	_
6	presheaves	presheave	NOUN	NNS	Number=Plur	4	pobj	_	_
7	specializes	specialize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	to	to	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
10	diagonal	diagonal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	model	model	NOUN	NN	Number=Sing	12	compound	_	_
12	structure	structure	NOUN	NN	Number=Sing	8	pobj	_	_
13	for	for	ADP	IN	_	12	prep	_	_
14	bisimplicial	bisimplicial	ADJ	JJ	Degree=Pos	15	amod	_	_
15	sets	set	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	for	for	ADP	IN	_	21	prep	_	_
18	which	which	PRON	WDT	_	17	pobj	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	fibrations	fibration	NOUN	NNS	Number=Plur	21	nsubj	_	_
21	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	relcl	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	Kan	Kan	PROPN	NNP	Number=Sing	24	compound	_	_
24	fibrations	fibration	NOUN	NNS	Number=Plur	21	attr	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 470
# sent_id = 1
# text = We show that every geometric morphism between realizability toposes satisfies the condition that its inverse image commutes with the `constant object' functors, which was assumed by John Longley in his pioneering study of such morphisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	9	mark	_	_
4	every	every	DET	DT	_	6	det	_	_
5	geometric	geometric	ADJ	JJ	Degree=Pos	6	amod	_	_
6	morphism	morphism	NOUN	NN	Number=Sing	9	nsubj	_	_
7	between	between	ADP	IN	_	6	prep	_	_
8	realizability	realizability	NOUN	NN	Number=Sing	7	pobj	_	_
9	toposes	topos	NOUN	NNS	Number=Plur	2	ccomp	_	_
10	satisfies	satisfie	NOUN	NNS	Number=Plur	9	dobj	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	condition	condition	NOUN	NN	Number=Sing	9	dobj	_	_
13	that	that	SCONJ	IN	_	17	mark	_	_
14	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	16	poss	_	_
15	inverse	inverse	ADJ	JJ	Degree=Pos	16	amod	_	_
16	image	image	NOUN	NN	Number=Sing	17	nsubj	_	_
17	commutes	commute	NOUN	NNS	Number=Plur	12	acl	_	_
18	with	with	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
20	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	24	punct	_	SpaceAfter=No
21	constant	constant	ADJ	JJ	Degree=Pos	22	amod	_	_
22	object	object	NOUN	NN	Number=Sing	24	nmod	_	SpaceAfter=No
23	'	'	PART	POS	_	24	punct	_	_
24	functors	functor	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	which	which	PRON	WDT	_	28	nsubjpass	_	_
27	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	28	auxpass	_	_
28	assumed	assume	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	relcl	_	_
29	by	by	ADP	IN	_	28	agent	_	_
30	John	John	PROPN	NNP	Number=Sing	31	compound	_	_
31	Longley	Longley	PROPN	NNP	Number=Sing	29	pobj	_	_
32	in	in	ADP	IN	_	28	prep	_	_
33	his	his	PRON	PRP$	Gender=Masc|Number=Sing|Person=3|Poss=Yes|PronType=Prs	35	poss	_	_
34	pioneering	pioneering	ADJ	JJ	Degree=Pos	35	amod	_	_
35	study	study	NOUN	NN	Number=Sing	32	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	such	such	ADJ	JJ	Degree=Pos	38	amod	_	_
38	morphisms	morphism	NOUN	NNS	Number=Plur	36	pobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We also provide the answer to something which was stated as an open problem on Jaap van Oosten's book on realizability toposes: if a subtopos of a realizability topos is (co)complete, it must be either the topos of sets or the degenerate topos.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	38	ccomp	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	answer	answer	NOUN	NN	Number=Sing	3	dobj	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	something	something	PRON	NN	Number=Sing|PronType=Ind	6	pobj	_	_
8	which	which	PRON	WDT	_	10	nsubjpass	_	_
9	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	10	auxpass	_	_
10	stated	state	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	relcl	_	_
11	as	as	ADP	IN	_	10	prep	_	_
12	an	an	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	open	open	ADJ	JJ	Degree=Pos	14	amod	_	_
14	problem	problem	NOUN	NN	Number=Sing	11	pobj	_	_
15	on	on	ADP	IN	_	14	prep	_	_
16	Jaap	Jaap	PROPN	NNP	Number=Sing	18	compound	_	_
17	van	van	PROPN	NNP	Number=Sing	18	compound	_	_
18	Oosten	Oosten	PROPN	NNP	Number=Sing	20	poss	_	SpaceAfter=No
19	's	's	PART	POS	_	18	case	_	_
20	book	book	NOUN	NN	Number=Sing	15	pobj	_	_
21	on	on	ADP	IN	_	20	prep	_	_
22	realizability	realizability	NOUN	NN	Number=Sing	23	compound	_	_
23	toposes	topos	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	:	:	PUNCT	:	_	38	punct	_	_
25	if	if	SCONJ	IN	_	32	mark	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	subtopos	subtopos	NOUN	NN	Number=Sing	32	nsubj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	realizability	realizability	NOUN	NN	Number=Sing	31	compound	_	_
31	topos	topos	NOUN	NN	Number=Sing	28	pobj	_	_
32	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	38	advcl	_	_
33	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	32	punct	_	SpaceAfter=No
34	co)complete	co)complete	ADJ	JJ	Degree=Pos	32	acomp	_	SpaceAfter=No
35	,	,	PUNCT	,	PunctType=Comm	38	punct	_	_
36	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	38	nsubj	_	_
37	must	must	AUX	MD	VerbForm=Fin	38	aux	_	_
38	be	be	AUX	VB	VerbForm=Inf	0	ROOT	_	_
39	either	either	CCONJ	CC	ConjType=Cmp	41	preconj	_	_
40	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
41	topos	topo	NOUN	NNS	Number=Plur	38	attr	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	sets	set	NOUN	NNS	Number=Plur	42	pobj	_	_
44	or	or	CCONJ	CC	ConjType=Cmp	43	cc	_	_
45	the	the	DET	DT	Definite=Def|PronType=Art	47	det	_	_
46	degenerate	degenerate	ADJ	JJ	Degree=Pos	47	amod	_	_
47	topos	topos	NOUN	NN	Number=Sing	43	conj	_	SpaceAfter=No
48	.	.	PUNCT	.	PunctType=Peri	38	punct	_	SpaceAfter=No

# sent_id = 3
# text = And we present a new and simpler condition equivalent to the notion of computational density for applicative morphisms of Schonfinkel algebras.
1	And	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
5	new	new	ADJ	JJ	Degree=Pos	8	amod	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	simpler	simple	ADJ	JJR	Degree=Cmp	5	conj	_	_
8	condition	condition	NOUN	NN	Number=Sing	3	dobj	_	_
9	equivalent	equivalent	ADJ	JJ	Degree=Pos	8	amod	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	notion	notion	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	computational	computational	ADJ	JJ	Degree=Pos	15	amod	_	_
15	density	density	NOUN	NN	Number=Sing	13	pobj	_	_
16	for	for	ADP	IN	_	15	prep	_	_
17	applicative	applicative	ADJ	JJ	Degree=Pos	18	amod	_	_
18	morphisms	morphism	NOUN	NNS	Number=Plur	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	Schonfinkel	Schonfinkel	PROPN	NNP	Number=Sing	21	compound	_	_
21	algebras	algebra	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 471
# sent_id = 1
# text = By a `completion' on a 2 - category $ K $ we mean here an idempotent pseudomonad on $ K $ .
1	By	by	ADP	IN	_	0	ROOT	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	4	punct	_	SpaceAfter=No
4	completion	completion	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	4	punct	_	_
6	on	on	ADP	IN	_	4	prep	_	_
7	a	a	PRON	DT	Definite=Ind|PronType=Art	6	pobj	_	_
8	2	2	NUM	CD	NumType=Card	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	category	category	NOUN	NN	Number=Sing	7	nmod	_	_
11	$ K $	$ k $	SYM	$	_	10	nmod	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	mean	mean	VERB	VBP	Tense=Pres|VerbForm=Fin	17	parataxis	_	_
14	here	here	ADV	RB	PronType=Dem	17	advmod	_	_
15	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	idempotent	idempotent	ADJ	JJ	Degree=Pos	17	amod	_	_
17	pseudomonad	pseudomonad	NOUN	NNS	Number=Plur	1	pobj	_	_
18	on	on	ADP	IN	_	17	prep	_	_
19	$ K $	$ k $	SYM	$	_	18	pobj	_	_
20	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = We are particularly interested in pseudomonads that arise from $ KZ $ - doctrines.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	particularly	particularly	ADV	RB	_	4	advmod	_	_
4	interested	interested	ADJ	JJ	Degree=Pos	2	acomp	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	pseudomonads	pseudomonad	NOUN	NNS	Number=Plur	5	pobj	_	_
7	that	that	PRON	WDT	PronType=Rel	8	nsubj	_	_
8	arise	arise	VERB	VBP	Tense=Pres|VerbForm=Fin	6	relcl	_	_
9	from	from	ADP	IN	_	8	prep	_	_
10	$ KZ $	$ kz $	SYM	$	_	12	compound	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	doctrines	doctrine	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Motivated by a question of Lawvere, we compare the Cauchy completion, defined in the setting of $ V - Cat $ for $ V $ a symmetric monoidal closed category, with the Grothendieck completion, defined in the setting of $ S $ - indexed $ Cat $ for $ S $ a topos.
1	Motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	advcl	_	_
2	by	by	ADP	IN	_	1	agent	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	question	question	NOUN	NN	Number=Sing	2	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	Lawvere	Lawvere	PROPN	NNP	Number=Sing	5	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	compare	compare	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	Cauchy	Cauchy	PROPN	NNP	Number=Sing	12	compound	_	_
12	completion	completion	NOUN	NN	Number=Sing	9	dobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	setting	setting	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	$ V - Cat $	$ v - cat $	SYM	$	_	18	pobj	_	_
20	for	for	ADP	IN	_	14	prep	_	_
21	$ V $	$ v $	SYM	$	_	26	nmod	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
23	symmetric	symmetric	ADJ	JJ	Degree=Pos	24	amod	_	_
24	monoidal	monoidal	NOUN	NN	Number=Sing	26	amod	_	_
25	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
26	category	category	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
28	with	with	ADP	IN	_	14	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
30	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	31	compound	_	_
31	completion	completion	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
33	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	acl	_	_
34	in	in	ADP	IN	_	33	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	setting	setting	NOUN	NN	Number=Sing	34	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	$ S $	$ s $	SYM	$	_	40	dep	_	_
39	-	-	PUNCT	HYPH	PunctType=Dash	40	punct	_	_
40	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	37	pobj	_	_
41	$ Cat $	$ cat $	SYM	$	_	40	dep	_	_
42	for	for	ADP	IN	_	33	prep	_	_
43	$ S $	$ s $	SYM	$	_	45	nmod	_	_
44	a	a	DET	DT	Definite=Ind|PronType=Art	45	det	_	_
45	topos	topos	NOUN	NN	Number=Sing	42	pobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 4
# text = To this end we introduce a unified setting (`indexed enriched category theory') in which to formulate and study certain properties of $ KZ $ - doctrines.
1	To	to	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	end	end	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	unified	unified	ADJ	JJ	Degree=Pos	8	amod	_	_
8	setting	setting	NOUN	NN	Number=Sing	5	dobj	_	_
9	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	8	punct	_	SpaceAfter=No
10	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	14	punct	_	SpaceAfter=No
11	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
12	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	14	compound	_	_
14	theory	theory	NOUN	NN	Number=Sing	8	appos	_	SpaceAfter=No
15	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	14	punct	_	SpaceAfter=No
16	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	8	punct	_	_
17	in	in	ADP	IN	_	20	prep	_	_
18	which	which	PRON	WDT	_	17	pobj	_	_
19	to	to	PART	TO	_	20	aux	_	_
20	formulate	formulate	VERB	VB	VerbForm=Inf	8	relcl	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	study	study	VERB	VB	VerbForm=Inf	20	conj	_	_
23	certain	certain	ADJ	JJ	Degree=Pos	24	amod	_	_
24	properties	property	NOUN	NNS	Number=Plur	22	dobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	$ KZ $	$ kz $	SYM	$	_	28	compound	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	doctrines	doctrine	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = We find that, whereas all of the $ KZ $ - doctrines that are relevant to this discussion (Karoubi, Cauchy, Stack, Grothendieck) may be regarded as `bounded', only the Cauchy and the Grothendieck completions are `tightly bounded'–two notions that we introduce and study in this paper.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	find	find	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	42	mark	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	42	punct	_	_
5	whereas	whereas	SCONJ	IN	_	29	mark	_	_
6	all	all	PRON	DT	_	29	nsubjpass	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
9	$ KZ $	$ kz $	SYM	$	_	11	nmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	doctrines	doctrine	NOUN	NNS	Number=Plur	7	pobj	_	_
12	that	that	PRON	WDT	PronType=Rel	13	nsubj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	11	relcl	_	_
14	relevant	relevant	ADJ	JJ	Degree=Pos	13	acomp	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	this	this	DET	DT	Number=Sing|PronType=Dem	17	det	_	_
17	discussion	discussion	NOUN	NN	Number=Sing	15	pobj	_	_
18	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	17	punct	_	SpaceAfter=No
19	Karoubi	Karoubi	PROPN	NNP	Number=Sing	17	appos	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	Cauchy	Cauchy	PROPN	NNP	Number=Sing	19	conj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	Stack	Stack	PROPN	NNP	Number=Sing	21	conj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
25	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	23	appos	_	SpaceAfter=No
26	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	17	punct	_	_
27	may	may	AUX	MD	VerbForm=Fin	29	aux	_	_
28	be	be	AUX	VB	VerbForm=Inf	29	auxpass	_	_
29	regarded	regard	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	42	advcl	_	_
30	as	as	ADP	IN	_	29	prep	_	_
31	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	30	punct	_	SpaceAfter=No
32	bounded	bound	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	30	pobj	_	SpaceAfter=No
33	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	29	punct	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	42	punct	_	_
35	only	only	ADV	RB	_	37	advmod	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	Cauchy	Cauchy	PROPN	NNP	Number=Sing	42	nsubj	_	_
38	and	and	CCONJ	CC	ConjType=Cmp	37	cc	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
40	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	41	compound	_	_
41	completions	completion	NOUN	NNS	Number=Plur	37	conj	_	_
42	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
43	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	42	punct	_	SpaceAfter=No
44	tightly	tightly	ADV	RB	_	45	advmod	_	_
45	bounded'–two	bounded'–two	NUM	CD	NumType=Card	46	nummod	_	_
46	notions	notion	NOUN	NNS	Number=Plur	42	attr	_	_
47	that	that	SCONJ	IN	_	49	dobj	_	_
48	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	49	nsubj	_	_
49	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	46	relcl	_	_
50	and	and	CCONJ	CC	ConjType=Cmp	49	cc	_	_
51	study	study	VERB	VB	VerbForm=Inf	49	conj	_	_
52	in	in	ADP	IN	_	51	prep	_	_
53	this	this	DET	DT	Number=Sing|PronType=Dem	54	det	_	_
54	paper	paper	NOUN	NN	Number=Sing	52	pobj	_	SpaceAfter=No
55	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = Tightly bounded $ KZ $ - doctrines are shown to be idempotent.
1	Tightly	tightly	ADV	RB	_	2	advmod	_	_
2	bounded	bound	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
3	$ KZ $	$ kz $	SYM	$	_	5	nmod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	doctrines	doctrine	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	be	be	AUX	VB	VerbForm=Inf	7	xcomp	_	_
10	idempotent	idempotent	ADJ	JJ	Degree=Pos	9	acomp	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 7
# text = We also show, in a different approach to answering the motivating question, that the Cauchy completion (defined using `distributors') and the Grothendieck completion (defined using `generalized functors') are actually equivalent constructions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	in	in	ADP	IN	_	3	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	different	different	ADJ	JJ	Degree=Pos	8	amod	_	_
8	approach	approach	NOUN	NN	Number=Sing	5	pobj	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	answering	answer	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	pcomp	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	motivating	motivating	NOUN	NN	Number=Sing	13	compound	_	_
13	question	question	NOUN	NN	Number=Sing	10	dobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
15	that	that	SCONJ	IN	_	38	mark	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	Cauchy	Cauchy	PROPN	NNP	Number=Sing	18	compound	_	_
18	completion	completion	NOUN	NN	Number=Sing	38	nsubj	_	_
19	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	18	punct	_	SpaceAfter=No
20	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	acl	_	_
21	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	xcomp	_	_
22	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	21	punct	_	SpaceAfter=No
23	distributors	distributor	NOUN	NNS	Number=Plur	21	dobj	_	SpaceAfter=No
24	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	18	punct	_	SpaceAfter=No
25	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	18	punct	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	29	compound	_	_
29	completion	completion	NOUN	NN	Number=Sing	18	conj	_	_
30	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	29	punct	_	SpaceAfter=No
31	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	acl	_	_
32	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	31	xcomp	_	_
33	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	35	punct	_	SpaceAfter=No
34	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	35	amod	_	_
35	functors	functor	NOUN	NNS	Number=Plur	32	dobj	_	SpaceAfter=No
36	'	'	PART	POS	_	35	case	_	SpaceAfter=No
37	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	29	punct	_	_
38	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
39	actually	actually	ADV	RB	_	38	advmod	_	_
40	equivalent	equivalent	ADJ	JJ	Degree=Pos	41	amod	_	_
41	constructions	construction	NOUN	NNS	Number=Plur	38	attr	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 472
# sent_id = 1
# text = We show that any traced $ * $ - autonomous category is compact closed.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	10	mark	_	_
4	any	any	DET	DT	_	9	det	_	_
5	traced	trace	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	amod	_	_
6	$ * $	$ * $	SYM	$	_	8	advmod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	autonomous	autonomous	ADJ	JJ	Degree=Pos	9	amod	_	_
9	category	category	NOUN	NN	Number=Sing	10	nsubj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
11	compact	compact	ADJ	JJ	Degree=Pos	12	advmod	_	_
12	closed	closed	ADJ	JJ	Degree=Pos	10	acomp	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 473
# sent_id = 1
# text = We deeply analyse the structural organisation of the fibration of points and of the monad of internal groupoids.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	deeply	deeply	ADV	RB	_	3	advmod	_	_
3	analyse	analyse	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	structural	structural	ADJ	JJ	Degree=Pos	6	amod	_	_
6	organisation	organisation	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	fibration	fibration	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	points	point	NOUN	NNS	Number=Plur	10	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
13	of	of	ADP	IN	_	10	conj	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	monad	monad	NOUN	NNS	Number=Plur	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	internal	internal	ADJ	JJ	Degree=Pos	18	amod	_	_
18	groupoids	groupoid	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = From that we derive: (i) a new characterization of internal groupoids among reflexive graphs in the Maltsev context; (ii) a setting in which a Maltsev category is necessarily a protomodular category.
1	From	from	SCONJ	IN	_	4	mark	_	_
2	that	that	PRON	DT	Number=Sing|PronType=Dem	4	mark	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	derive	derive	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
5	:	:	PUNCT	:	_	4	punct	_	_
6	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	7	punct	_	SpaceAfter=No
7	i	i	NOUN	NN	Number=Sing	4	dep	_	SpaceAfter=No
8	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	7	punct	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	new	new	ADJ	JJ	Degree=Pos	11	amod	_	_
11	characterization	characterization	NOUN	NN	Number=Sing	7	appos	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	internal	internal	ADJ	JJ	Degree=Pos	14	amod	_	_
14	groupoids	groupoid	NOUN	NNS	Number=Plur	12	pobj	_	_
15	among	among	ADP	IN	_	11	prep	_	_
16	reflexive	reflexive	ADJ	JJ	Degree=Pos	17	amod	_	_
17	graphs	graph	NOUN	NNS	Number=Plur	15	pobj	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	Maltsev	Maltsev	PROPN	NNP	Number=Sing	21	amod	_	_
21	context	context	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
22	;	;	PUNCT	:	_	7	punct	_	_
23	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
24	ii	ii	PROPN	NNP	Number=Sing	7	appos	_	SpaceAfter=No
25	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	24	punct	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	setting	setting	NOUN	NN	Number=Sing	7	appos	_	_
28	in	in	ADP	IN	_	33	prep	_	_
29	which	which	PRON	WDT	_	28	pobj	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
31	Maltsev	Maltsev	PROPN	NNP	Number=Sing	32	compound	_	_
32	category	category	NOUN	NN	Number=Sing	33	nsubj	_	_
33	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	relcl	_	_
34	necessarily	necessarily	ADV	RB	_	33	advmod	_	_
35	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
36	protomodular	protomodular	ADJ	JJ	Degree=Pos	37	amod	_	_
37	category	category	NOUN	NN	Number=Sing	33	attr	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 474
# sent_id = 1
# text = The category $ _{A}mathbb{S}_{A} $ of bisemimodules over a semialgebra $ A, $ with the so called Takahashi's tensor - like product $ - boxtimes _{A} - , $ is semimonoidal but not monoidal.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	21	nsubj	_	_
3	$ _{A}mathbb{S}_{A} $	$ _{a}mathbb{s}_{a} $	SYM	$	_	2	appos	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	bisemimodules	bisemimodule	NOUN	NNS	Number=Plur	4	pobj	_	_
6	over	over	ADP	IN	_	2	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	semialgebra	semialgebra	NOUN	NN	Number=Sing	6	pobj	_	_
9	$ A, $	$ a, $	SYM	$	_	2	appos	_	_
10	with	with	ADP	IN	_	2	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	so	so	ADV	RB	_	13	advmod	_	_
13	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	pcomp	_	_
14	Takahashi	Takahashi	PROPN	NNP	Number=Sing	19	poss	_	SpaceAfter=No
15	's	's	PART	POS	_	14	case	_	_
16	tensor	tensor	NOUN	NN	Number=Sing	18	npadvmod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	like	like	ADJ	JJ	Degree=Pos	19	amod	_	_
19	product	product	NOUN	NN	Number=Sing	13	oprd	_	_
20	$ - boxtimes _{A} - , $	$ - boxtimes _{a} - , $	SYM	$	_	21	nsubj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
22	semimonoidal	semimonoidal	ADJ	JJ	Degree=Pos	21	acomp	_	_
23	but	but	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	not	not	PART	RB	Polarity=Neg	25	neg	_	_
25	monoidal	monoidal	ADJ	JJ	Degree=Pos	22	conj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# sent_id = 2
# text = Although not a unit in $ _{A}mathbb{S}% _{A}, $ the base semialgebra $ A $ has properties of a semiunit (in a sense which we clarify in this note).
1	Although	although	SCONJ	IN	_	4	mark	_	_
2	not	not	PART	RB	Polarity=Neg	4	neg	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	unit	unit	NOUN	NN	Number=Sing	11	nsubj	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	$ _{A}mathbb{S}% _{A}, $	$ _{a}mathbb{s}% _{a}, $	SYM	$	_	9	nsubj	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	base	base	NOUN	NN	Number=Sing	9	compound	_	_
9	semialgebra	semialgebra	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	pobj	_	_
10	$ A $	$ a $	SYM	$	_	9	dobj	_	_
11	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	properties	property	NOUN	NNS	Number=Plur	11	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	semiunit	semiunit	NOUN	NN	Number=Sing	13	pobj	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	11	punct	_	SpaceAfter=No
17	in	in	ADP	IN	_	11	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	sense	sense	NOUN	NN	Number=Sing	17	pobj	_	_
20	which	which	PRON	WDT	_	22	dobj	_	_
21	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	22	nsubj	_	_
22	clarify	clarify	VERB	VBP	Tense=Pres|VerbForm=Fin	19	relcl	_	_
23	in	in	ADP	IN	_	22	prep	_	_
24	this	this	DET	DT	Number=Sing|PronType=Dem	25	det	_	_
25	note	note	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
26	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	11	punct	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 3
# text = Motivated by this interesting example, we investigate semiunital semimonoidal categories $ (mathcal{V}% , bullet , mathbf{I}) $ as a framework for studying notions like semimonoids (semicomonoids) as well as a notion of monads (comonads) which we call $ mathbb{J} $ - monads ( $ mathbb{J} $ - comonads) with respect to the endo - functor $ mathbb{J}:=mathbf{I}bullet - simeq - bullet mathbf{I}:mathcal{V}longrightarrow mathcal{V} $ .
1	Motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	advcl	_	_
2	by	by	ADP	IN	_	1	agent	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
4	interesting	interesting	ADJ	JJ	Degree=Pos	5	amod	_	_
5	example	example	NOUN	NN	Number=Sing	2	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
7	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	8	nsubj	_	_
8	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	semiunital	semiunital	NOUN	NN	Number=Sing	11	nmod	_	_
10	semimonoidal	semimonoidal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	categories	category	NOUN	NNS	Number=Plur	8	dobj	_	_
12	$ (mathcal{V}% , bullet , mathbf{I}) $	$ (mathcal{v}% , bullet , mathbf{i}) $	SYM	$	_	8	dep	_	_
13	as	as	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	framework	framework	NOUN	NN	Number=Sing	13	pobj	_	_
16	for	for	ADP	IN	_	15	prep	_	_
17	studying	study	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	pcomp	_	_
18	notions	notion	NOUN	NNS	Number=Plur	17	dobj	_	_
19	like	like	ADP	IN	_	18	prep	_	_
20	semimonoids	semimonoid	NOUN	NNS	Number=Plur	19	pobj	_	_
21	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	20	punct	_	SpaceAfter=No
22	semicomonoids	semicomonoid	NOUN	NNS	Number=Plur	20	appos	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	20	punct	_	_
24	as	as	ADV	RB	_	26	advmod	_	_
25	well	well	ADV	RB	Degree=Pos	26	advmod	_	_
26	as	as	ADP	IN	_	15	cc	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	notion	notion	NOUN	NN	Number=Sing	15	conj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	monads	monad	NOUN	NNS	Number=Plur	29	pobj	_	_
31	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	30	punct	_	SpaceAfter=No
32	comonads	comonad	NOUN	NNS	Number=Plur	30	appos	_	SpaceAfter=No
33	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	30	punct	_	_
34	which	which	PRON	WDT	_	45	pobj	_	_
35	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	36	nsubj	_	_
36	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	28	relcl	_	_
37	$ mathbb{J} $	$ mathbb{j} $	SYM	$	_	39	compound	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	monads	monad	NOUN	NNS	Number=Plur	36	dobj	_	_
40	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	39	punct	_	_
41	$ mathbb{J} $	$ mathbb{j} $	SYM	$	_	43	compound	_	_
42	-	-	PUNCT	HYPH	PunctType=Dash	43	punct	_	_
43	comonads	comonad	NOUN	NNS	Number=Plur	39	appos	_	SpaceAfter=No
44	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	39	punct	_	_
45	with	with	ADP	IN	_	36	prep	_	_
46	respect	respect	NOUN	NN	Number=Sing	45	pobj	_	_
47	to	to	ADP	IN	_	46	prep	_	_
48	the	the	DET	DT	Definite=Def|PronType=Art	52	det	_	_
49	endo	endo	PROPN	NNP	Number=Sing	51	compound	_	_
50	-	-	PUNCT	HYPH	PunctType=Dash	51	punct	_	_
51	functor	functor	PROPN	NNP	Number=Sing	52	compound	_	_
52	$ mathbb{J}:=mathbf{I}bullet - simeq - bullet mathbf{I}:mathcal{V}longrightarrow mathcal{V} $	$ mathbb{j}:=mathbf{i}bullet - simeq - bullet mathbf{i}:mathcal{v}longrightarrow mathcal{v} $	SYM	$	_	47	pobj	_	_
53	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 4
# text = This motivated also introducing a more generalized notion of monads (comonads) in arbitrary categories with respect to arbitrary endo - functors.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	motivated	motivate	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
3	also	also	ADV	RB	_	4	advmod	_	_
4	introducing	introduce	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	xcomp	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
6	more	more	ADV	RBR	Degree=Cmp	7	advmod	_	_
7	generalized	generalized	ADJ	JJ	Degree=Pos	8	amod	_	_
8	notion	notion	NOUN	NN	Number=Sing	4	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	monads	monad	NOUN	NNS	Number=Plur	9	pobj	_	_
11	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	10	punct	_	SpaceAfter=No
12	comonads	comonad	NOUN	NNS	Number=Plur	10	appos	_	SpaceAfter=No
13	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	10	punct	_	_
14	in	in	ADP	IN	_	8	prep	_	_
15	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	16	amod	_	_
16	categories	category	NOUN	NNS	Number=Plur	14	pobj	_	_
17	with	with	ADP	IN	_	4	prep	_	_
18	respect	respect	NOUN	NN	Number=Sing	17	pobj	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	23	amod	_	_
21	endo	endo	PROPN	NNP	Number=Sing	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	functors	functor	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = Applications to the semiunital semimonoidal variety $ (_{A}mathbb{S}_{A}, boxtimes _{A}, A) $ provide us with examples of semiunital $ A $ - semirings (semicounital $ A $ - semicorings) and semiunitary semimodules (semicounitary semicomodules) which extend the classical notions of unital rings (counital corings) and unitary modules (counitary comodules).
1	Applications	application	NOUN	NNS	Number=Plur	8	nsubj	_	_
2	to	to	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
4	semiunital	semiunital	NOUN	NN	Number=Sing	6	compound	_	_
5	semimonoidal	semimonoidal	PROPN	NNP	Number=Sing	6	compound	_	_
6	variety	variety	NOUN	NN	Number=Sing	2	pobj	_	_
7	$ (_{A}mathbb{S}_{A}, boxtimes _{A}, A) $	$ (_{A}mathbb{S}_{A}, boxtimes _{A}, A) $	PROPN	NNP	Number=Sing	8	nsubj	_	_
8	provide	provide	VERB	VB	VerbForm=Inf	0	ROOT	_	_
9	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	8	dobj	_	_
10	with	with	ADP	IN	_	8	prep	_	_
11	examples	example	NOUN	NNS	Number=Plur	10	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	semiunital	semiunital	NOUN	NN	Number=Sing	16	compound	_	_
14	$ A $	$ a $	SYM	$	_	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	semirings	semiring	NOUN	NNS	Number=Plur	12	pobj	_	_
17	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	18	punct	_	SpaceAfter=No
18	semicounital	semicounital	VERB	VB	VerbForm=Inf	8	dep	_	_
19	$ A $	$ a $	SYM	$	_	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	semicorings	semicoring	NOUN	NNS	Number=Plur	18	dobj	_	SpaceAfter=No
22	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	18	punct	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
24	semiunitary	semiunitary	ADJ	JJ	Degree=Pos	25	amod	_	_
25	semimodules	semimodule	NOUN	NNS	Number=Plur	18	conj	_	_
26	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	25	punct	_	SpaceAfter=No
27	semicounitary	semicounitary	NOUN	NN	Number=Sing	28	compound	_	_
28	semicomodules	semicomodule	NOUN	NNS	Number=Plur	25	appos	_	SpaceAfter=No
29	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	25	punct	_	_
30	which	which	PRON	WDT	_	31	nsubj	_	_
31	extend	extend	VERB	VBP	Tense=Pres|VerbForm=Fin	25	relcl	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
33	classical	classical	ADJ	JJ	Degree=Pos	34	amod	_	_
34	notions	notion	NOUN	NNS	Number=Plur	31	dobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	unital	unital	PROPN	NNP	Number=Sing	37	compound	_	_
37	rings	ring	NOUN	NNS	Number=Plur	35	pobj	_	_
38	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	37	punct	_	SpaceAfter=No
39	counital	counital	NOUN	NN	Number=Sing	40	compound	_	_
40	corings	coring	NOUN	NNS	Number=Plur	37	appos	_	SpaceAfter=No
41	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	37	punct	_	_
42	and	and	CCONJ	CC	ConjType=Cmp	37	cc	_	_
43	unitary	unitary	ADJ	JJ	Degree=Pos	44	amod	_	_
44	modules	module	NOUN	NNS	Number=Plur	34	conj	_	_
45	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	44	punct	_	SpaceAfter=No
46	counitary	counitary	ADJ	JJ	Degree=Pos	47	amod	_	_
47	comodules	comodule	NOUN	NNS	Number=Plur	44	appos	_	SpaceAfter=No
48	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	44	punct	_	SpaceAfter=No
49	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 475
# sent_id = 1
# text = The main source of inspiration for the present paper is the work of Rosebrugh and Wood on constructively completely distributive lattices where the authors elegantly employ the concepts of adjunction and module.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	source	source	NOUN	NN	Number=Sing	10	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	inspiration	inspiration	NOUN	NN	Number=Sing	4	pobj	_	_
6	for	for	ADP	IN	_	3	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	present	present	ADJ	JJ	Degree=Pos	9	amod	_	_
9	paper	paper	NOUN	NN	Number=Sing	6	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	work	work	NOUN	NN	Number=Sing	10	attr	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	Rosebrugh	Rosebrugh	PROPN	NNP	Number=Sing	13	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	Wood	Wood	PROPN	NNP	Number=Sing	14	conj	_	_
17	on	on	ADP	IN	_	12	prep	_	_
18	constructively	constructively	ADV	RB	_	20	advmod	_	_
19	completely	completely	ADV	RB	_	20	advmod	_	_
20	distributive	distributive	ADJ	JJ	Degree=Pos	21	amod	_	_
21	lattices	lattice	NOUN	NNS	Number=Plur	17	pobj	_	_
22	where	where	SCONJ	WRB	_	26	advmod	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	authors	author	NOUN	NNS	Number=Plur	26	nsubj	_	_
25	elegantly	elegantly	ADV	RB	_	26	advmod	_	_
26	employ	employ	VERB	VBP	Tense=Pres|VerbForm=Fin	21	relcl	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	concepts	concept	NOUN	NNS	Number=Plur	26	dobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	adjunction	adjunction	NOUN	NN	Number=Sing	29	pobj	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
32	module	module	NOUN	NN	Number=Sing	30	conj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = Both notions (suitably adapted) are available in topology too, which permits us to investigate topological, metric and other kinds of spaces in a similar spirit.
1	Both	both	DET	DT	_	2	det	_	_
2	notions	notion	NOUN	NNS	Number=Plur	7	nsubj	_	_
3	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	5	punct	_	SpaceAfter=No
4	suitably	suitably	ADV	RB	_	5	advmod	_	_
5	adapted	adapt	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	parataxis	_	SpaceAfter=No
6	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	5	punct	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	available	available	ADJ	JJ	Degree=Pos	7	acomp	_	_
9	in	in	ADP	IN	_	7	prep	_	_
10	topology	topology	NOUN	NN	Number=Sing	9	pobj	_	_
11	too	too	ADV	RB	_	7	advmod	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
13	which	which	PRON	WDT	_	14	nsubj	_	_
14	permits	permit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	advcl	_	_
15	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	14	dobj	_	_
16	to	to	PART	TO	_	17	aux	_	_
17	investigate	investigate	VERB	VB	VerbForm=Inf	14	xcomp	_	_
18	topological	topological	ADJ	JJ	Degree=Pos	23	amod	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	metric	metric	ADJ	JJ	Degree=Pos	18	conj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	other	other	ADJ	JJ	Degree=Pos	20	conj	_	_
23	kinds	kind	NOUN	NNS	Number=Plur	17	dobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	spaces	space	NOUN	NNS	Number=Plur	24	pobj	_	_
26	in	in	ADP	IN	_	17	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	similar	similar	ADJ	JJ	Degree=Pos	29	amod	_	_
29	spirit	spirit	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = We introduce here the notion of distributive space and algebraic space and show in particular that the category of distributive spaces and colimit preserving maps is dually equivalent to the idempotent split completion of a category of spaces and convergence relations between them.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	here	here	ADV	RB	PronType=Dem	2	advmod	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	distributive	distributive	ADJ	JJ	Degree=Pos	8	amod	_	_
8	space	space	NOUN	NN	Number=Sing	6	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	algebraic	algebraic	ADJ	JJ	Degree=Pos	11	amod	_	_
11	space	space	NOUN	NN	Number=Sing	8	conj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
13	show	show	VERB	VB	VerbForm=Inf	5	conj	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	particular	particular	ADJ	JJ	Degree=Pos	14	amod	_	_
16	that	that	SCONJ	IN	_	26	mark	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	category	category	NOUN	NN	Number=Sing	26	nsubj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	distributive	distributive	ADJ	JJ	Degree=Pos	21	amod	_	_
21	spaces	space	NOUN	NNS	Number=Plur	19	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	colimit	colimit	NOUN	NN	Number=Sing	25	nmod	_	_
24	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	25	amod	_	_
25	maps	map	NOUN	NNS	Number=Plur	21	conj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
27	dually	dually	ADV	RB	_	28	advmod	_	_
28	equivalent	equivalent	ADJ	JJ	Degree=Pos	26	acomp	_	_
29	to	to	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
31	idempotent	idempotent	ADJ	JJ	Degree=Pos	32	amod	_	_
32	split	split	ADJ	JJ	Degree=Pos	33	amod	_	_
33	completion	completion	NOUN	NN	Number=Sing	29	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
36	category	category	NOUN	NN	Number=Sing	34	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	spaces	space	NOUN	NNS	Number=Plur	37	pobj	_	_
39	and	and	CCONJ	CC	ConjType=Cmp	38	cc	_	_
40	convergence	convergence	NOUN	NN	Number=Sing	41	compound	_	_
41	relations	relation	NOUN	NNS	Number=Plur	38	conj	_	_
42	between	between	ADP	IN	_	38	prep	_	_
43	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	42	pobj	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We explain the connection of this result to the well - known duality between topological spaces and frames, and deduce further duality theorems.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	explain	explain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	connection	connection	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
7	result	result	NOUN	NN	Number=Sing	5	pobj	_	_
8	to	to	ADP	IN	_	4	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
10	well	well	ADV	RB	Degree=Pos	12	advmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
13	duality	duality	NOUN	NN	Number=Sing	8	pobj	_	_
14	between	between	ADP	IN	_	13	prep	_	_
15	topological	topological	ADJ	JJ	Degree=Pos	16	amod	_	_
16	spaces	space	NOUN	NNS	Number=Plur	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	frames	frame	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
21	deduce	deduce	VERB	VB	VerbForm=Inf	2	conj	_	_
22	further	further	ADJ	JJ	Degree=Pos	24	amod	_	_
23	duality	duality	NOUN	NN	Number=Sing	24	compound	_	_
24	theorems	theorem	NOUN	NNS	Number=Plur	21	dobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 476
# sent_id = 1
# text = Given a horizontal monoid $ M $ in a duoidal category $ cal F $ , we examine the relationship between bimonoid structures on $ M $ and monoidal structures on the category $ cal F^{ast M} $ of right $ M $ - modules which lift the vertical monoidal structure of $ cal F $ .
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	horizontal	horizontal	ADJ	JJ	Degree=Pos	4	amod	_	_
4	monoid	monoid	NOUN	NN	Number=Sing	1	pobj	_	_
5	$ M $	$ m $	SYM	$	_	1	pobj	_	_
6	in	in	ADP	IN	_	1	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	duoidal	duoidal	NOUN	NN	Number=Sing	9	compound	_	_
9	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
10	$ cal F $	$ cal f $	SYM	$	_	1	advmod	_	_
11	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	examine	examine	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	relationship	relationship	NOUN	NN	Number=Sing	13	dobj	_	_
16	between	between	ADP	IN	_	15	prep	_	_
17	bimonoid	bimonoid	NOUN	NN	Number=Sing	18	compound	_	_
18	structures	structure	NOUN	NNS	Number=Plur	16	pobj	_	_
19	on	on	ADP	IN	_	18	prep	_	_
20	$ M $	$ m $	SYM	$	_	23	nmod	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	monoidal	monoidal	ADJ	JJ	Degree=Pos	20	conj	_	_
23	structures	structure	NOUN	NNS	Number=Plur	19	pobj	_	_
24	on	on	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	category	category	NOUN	NN	Number=Sing	24	pobj	_	_
27	$ cal F^{ast M} $	$ cal f^{ast m} $	SYM	$	_	13	dobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	right	right	ADJ	JJ	Degree=Pos	32	amod	_	_
30	$ M $	$ m $	SYM	$	_	32	compound	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	modules	module	NOUN	NNS	Number=Plur	28	pobj	_	_
33	which	which	PRON	WDT	_	34	nsubj	_	_
34	lift	lift	VERB	VBP	Tense=Pres|VerbForm=Fin	32	relcl	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
36	vertical	vertical	ADJ	JJ	Degree=Pos	38	amod	_	_
37	monoidal	monoidal	ADJ	JJ	Degree=Pos	38	amod	_	_
38	structure	structure	NOUN	NN	Number=Sing	34	dobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	$ cal F $	$ cal f $	SYM	$	_	39	pobj	_	_
41	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 2
# text = We obtain our result using a variant of the so - called Tannaka adjunction; that is, an adjunction inducing the equivalence which expresses Tannaka duality.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	17	ccomp	_	_
3	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	4	poss	_	_
4	result	result	NOUN	NN	Number=Sing	2	dobj	_	_
5	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	variant	variant	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
10	so	so	ADV	RB	_	12	advmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
13	Tannaka	Tannaka	PROPN	NNP	Number=Sing	14	compound	_	_
14	adjunction	adjunction	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
15	;	;	PUNCT	:	_	17	punct	_	_
16	that	that	PRON	DT	Number=Sing|PronType=Dem	17	advmod	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	an	an	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	adjunction	adjunction	NOUN	NN	Number=Sing	17	attr	_	_
21	inducing	induce	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	acl	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	equivalence	equivalence	NOUN	NN	Number=Sing	21	dobj	_	_
24	which	which	PRON	WDT	_	25	nsubj	_	_
25	expresses	express	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	relcl	_	_
26	Tannaka	Tannaka	PROPN	NNP	Number=Sing	27	compound	_	_
27	duality	duality	NOUN	NN	Number=Sing	25	dobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 3
# text = The approach taken utilizes hom - enriched categories rather than categories on which a monoidal category acts (``actegories'').
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	approach	approach	NOUN	NN	Number=Sing	4	nsubj	_	_
3	taken	take	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acl	_	_
4	utilizes	utilize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	hom	hom	VERB	VB	VerbForm=Inf	7	advmod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	4	dobj	_	_
9	rather	rather	ADV	RB	_	10	advmod	_	_
10	than	than	ADP	IN	_	8	cc	_	_
11	categories	category	NOUN	NNS	Number=Plur	8	conj	_	_
12	on	on	ADP	IN	_	17	prep	_	_
13	which	which	PRON	WDT	_	12	pobj	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	monoidal	monoidal	ADJ	JJ	Degree=Pos	16	amod	_	_
16	category	category	NOUN	NN	Number=Sing	17	nsubj	_	_
17	acts	act	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	relcl	_	_
18	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	17	punct	_	SpaceAfter=No
19	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	17	punct	_	SpaceAfter=No
20	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	17	punct	_	SpaceAfter=No
21	actegories	actegorie	NOUN	NNS	Number=Plur	17	dobj	_	SpaceAfter=No
22	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	21	punct	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	17	punct	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = The requirement of enrichment in $ cal F $ itself demands the existence of some internal homs, leading to the consideration of convolution for duoidal categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	requirement	requirement	NOUN	NN	Number=Sing	8	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	enrichment	enrichment	NOUN	NN	Number=Sing	3	pobj	_	_
5	in	in	ADP	IN	_	2	prep	_	_
6	$ cal F $	$ cal f $	SYM	$	_	7	nmod	_	_
7	itself	itself	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs|Reflex=Yes	5	pobj	_	_
8	demands	demand	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	existence	existence	NOUN	NN	Number=Sing	8	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	some	some	DET	DT	_	14	det	_	_
13	internal	internal	ADJ	JJ	Degree=Pos	14	amod	_	_
14	homs	hom	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
16	leading	lead	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	advcl	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	consideration	consideration	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	convolution	convolution	NOUN	NN	Number=Sing	20	pobj	_	_
22	for	for	ADP	IN	_	21	prep	_	_
23	duoidal	duoidal	NOUN	NN	Number=Sing	24	compound	_	_
24	categories	category	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 5
# text = Proving that certain hom - functors are monoidal, and so take monoids to monoids, unifies classical convolution in algebra and Day convolution for categories.
1	Proving	prove	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	0	ROOT	_	_
2	that	that	SCONJ	IN	_	7	mark	_	_
3	certain	certain	ADJ	JJ	Degree=Pos	6	amod	_	_
4	hom	hom	NOUN	NN	Number=Sing	6	compound	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	functors	functor	NOUN	NNS	Number=Plur	7	nsubj	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	1	ccomp	_	_
8	monoidal	monoidal	ADJ	JJ	Degree=Pos	7	acomp	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
11	so	so	ADV	RB	_	12	advmod	_	_
12	take	take	VERB	VB	VerbForm=Inf	7	conj	_	_
13	monoids	monoid	NOUN	NNS	Number=Plur	12	dobj	_	_
14	to	to	ADP	IN	_	12	prep	_	_
15	monoids	monoid	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
17	unifies	unify	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	conj	_	_
18	classical	classical	ADJ	JJ	Degree=Pos	19	amod	_	_
19	convolution	convolution	NOUN	NN	Number=Sing	17	dobj	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	algebra	algebra	NOUN	NN	Number=Sing	24	nmod	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	Day	Day	PROPN	NNP	Number=Sing	21	conj	_	_
24	convolution	convolution	NOUN	NN	Number=Sing	20	pobj	_	_
25	for	for	ADP	IN	_	24	prep	_	_
26	categories	category	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 6
# text = Hopf bimonoids are defined leading to a lifting of closed structures on $ cal F $ to $ cal F^{ast M} $ .
1	Hopf	hopf	NOUN	NN	Number=Sing	2	compound	_	_
2	bimonoids	bimonoid	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	leading	lead	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	advcl	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	lifting	lifting	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	closed	closed	ADJ	JJ	Degree=Pos	11	amod	_	_
11	structures	structure	NOUN	NNS	Number=Plur	9	pobj	_	_
12	on	on	ADP	IN	_	8	prep	_	_
13	$ cal F $	$ cal f $	SYM	$	_	12	pobj	_	_
14	to	to	ADP	IN	_	12	prep	_	_
15	$ cal F^{ast M} $	$ cal f^{ast m} $	SYM	$	_	4	dobj	_	_
16	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 7
# text = We introduce the concept of warping monoidal structures and this permits the construction of new duoidal categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	concept	concept	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	warping	warp	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	monoidal	monoidal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	structures	structure	NOUN	NNS	Number=Plur	6	dobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
10	this	this	PRON	DT	Number=Sing|PronType=Dem	11	nsubj	_	_
11	permits	permit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	construction	construction	NOUN	NN	Number=Sing	11	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	new	new	ADJ	JJ	Degree=Pos	17	amod	_	_
16	duoidal	duoidal	NOUN	NN	Number=Sing	17	compound	_	_
17	categories	category	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# doc_id = 477
# sent_id = 1
# text = One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product of 2 - categories.
1	One	one	NUM	CD	NumType=Card	10	nsubj	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	open	open	ADJ	JJ	Degree=Pos	5	amod	_	_
5	problems	problem	NOUN	NNS	Number=Plur	2	pobj	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	higher	high	ADJ	JJR	Degree=Cmp	9	amod	_	_
8	category	category	NOUN	NN	Number=Sing	9	compound	_	_
9	theory	theory	NOUN	NN	Number=Sing	6	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	systematic	systematic	ADJ	JJ	Degree=Pos	13	amod	_	_
13	construction	construction	NOUN	NN	Number=Sing	10	attr	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
16	higher	high	ADJ	JJR	Degree=Cmp	18	amod	_	_
17	dimensional	dimensional	ADJ	JJ	Degree=Pos	18	amod	_	_
18	analogues	analogue	NOUN	NNS	Number=Plur	14	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
21	Gray	Gray	PROPN	NNP	Number=Sing	23	compound	_	_
22	tensor	tensor	NOUN	NN	Number=Sing	23	compound	_	_
23	product	product	NOUN	NN	Number=Sing	19	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	2	2	NUM	CD	NumType=Card	27	nummod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	categories	category	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper we continue the developments of some other papers by understanding the natural generalisations of Gray's little brother, the funny tensor product of categories.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	continue	continue	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	developments	development	NOUN	NNS	Number=Plur	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	some	some	DET	DT	_	11	det	_	_
10	other	other	ADJ	JJ	Degree=Pos	11	amod	_	_
11	papers	paper	NOUN	NNS	Number=Plur	8	pobj	_	_
12	by	by	ADP	IN	_	5	prep	_	_
13	understanding	understand	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	pcomp	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	natural	natural	ADJ	JJ	Degree=Pos	16	amod	_	_
16	generalisations	generalisation	NOUN	NNS	Number=Plur	13	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	Gray	Gray	PROPN	NNP	Number=Sing	21	poss	_	SpaceAfter=No
19	's	's	PART	POS	_	18	case	_	_
20	little	little	ADJ	JJ	Degree=Pos	21	amod	_	_
21	brother	brother	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
24	funny	funny	ADJ	JJ	Degree=Pos	26	amod	_	_
25	tensor	tensor	NOUN	NN	Number=Sing	26	compound	_	_
26	product	product	NOUN	NN	Number=Sing	21	appos	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	categories	category	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = In fact we exhibit for any higher categorical structure definable by a normalised $ n $ - operad in the sense of Batanin, an analogous tensor product which forms a symmetric monoidal closed structure on the category of algebras of the operad.
1	In	in	ADP	IN	_	4	prep	_	_
2	fact	fact	NOUN	NN	Number=Sing	1	pobj	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	exhibit	exhibit	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	any	any	DET	DT	_	9	det	_	_
7	higher	high	ADJ	JJR	Degree=Cmp	9	amod	_	_
8	categorical	categorical	ADJ	JJ	Degree=Pos	9	amod	_	_
9	structure	structure	NOUN	NN	Number=Sing	5	pobj	_	_
10	definable	definable	ADJ	JJ	Degree=Pos	9	amod	_	_
11	by	by	ADP	IN	_	4	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
13	normalised	normalise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
14	$ n $	$ n $	SYM	$	_	13	nmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	operad	operad	ADV	RB	_	11	pobj	_	_
17	in	in	ADP	IN	_	4	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	sense	sense	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	Batanin	Batanin	PROPN	NNP	Number=Sing	20	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	an	an	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
24	analogous	analogous	ADJ	JJ	Degree=Pos	26	amod	_	_
25	tensor	tensor	NOUN	NN	Number=Sing	26	compound	_	_
26	product	product	NOUN	NN	Number=Sing	21	appos	_	_
27	which	which	PRON	WDT	_	28	nsubj	_	_
28	forms	form	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	relcl	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	symmetric	symmetric	ADJ	JJ	Degree=Pos	31	amod	_	_
31	monoidal	monoidal	NOUN	NN	Number=Sing	33	amod	_	_
32	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	33	amod	_	_
33	structure	structure	NOUN	NN	Number=Sing	28	dobj	_	_
34	on	on	ADP	IN	_	33	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	category	category	NOUN	NN	Number=Sing	34	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	algebras	algebra	NOUN	NNS	Number=Plur	37	pobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
41	operad	operad	NOUN	NN	Number=Sing	39	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 478
# sent_id = 1
# text = We study the monoidal structure of the standard strictification functor $ st : Bicat rightarrow 2Cat $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	monoidal	monoidal	ADJ	JJ	Degree=Pos	5	amod	_	_
5	structure	structure	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	standard	standard	ADJ	JJ	Degree=Pos	10	amod	_	_
9	strictification	strictification	NOUN	NN	Number=Sing	10	compound	_	_
10	functor	functor	NOUN	NN	Number=Sing	6	pobj	_	_
11	$ st : Bicat rightarrow 2Cat $	$ st : bicat rightarrow 2cat $	SYM	$	_	2	dobj	_	_
12	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In doing so, we construct monoidal structures on the 2 - category whose objects are bicategories and on the 2 - category whose objects are 2 - categories.
1	In	in	ADP	IN	_	6	prep	_	_
2	doing	do	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	1	pcomp	_	_
3	so	so	ADV	RB	_	2	advmod	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	monoidal	monoidal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	structures	structure	NOUN	NNS	Number=Plur	6	dobj	_	_
9	on	on	ADP	IN	_	6	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
14	whose	whose	DET	WP$	Poss=Yes	15	poss	_	_
15	objects	object	NOUN	NNS	Number=Plur	16	nsubj	_	_
16	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	relcl	_	_
17	bicategories	bicategorie	NOUN	NNS	Number=Plur	16	attr	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
19	on	on	ADP	IN	_	6	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
21	2	2	NUM	CD	NumType=Card	23	nummod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	category	category	NOUN	NN	Number=Sing	19	pobj	_	_
24	whose	whose	DET	WP$	Poss=Yes	25	poss	_	_
25	objects	object	NOUN	NNS	Number=Plur	26	nsubj	_	_
26	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	23	relcl	_	_
27	2	2	NUM	CD	NumType=Card	29	nummod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	categories	category	NOUN	NNS	Number=Plur	26	attr	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 479
# sent_id = 1
# text = We study the totality of categories weakly enriched in a monoidal bicategory using a notion of enriched icon as 2 - cells.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	totality	totality	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
7	weakly	weakly	ADV	RB	_	8	advmod	_	_
8	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	monoidal	monoidal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	bicategory	bicategory	NOUN	NN	Number=Sing	9	pobj	_	_
13	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	acl	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	notion	notion	NOUN	NN	Number=Sing	13	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
18	icon	icon	NOUN	NN	Number=Sing	16	pobj	_	_
19	as	as	ADP	IN	_	15	prep	_	_
20	2	2	NUM	CD	NumType=Card	22	nummod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	cells	cell	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that when the monoidal bicategory in question is symmetric then this process can be iterated.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	17	mark	_	_
4	when	when	SCONJ	WRB	_	10	advmod	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	monoidal	monoidal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	bicategory	bicategory	NOUN	NN	Number=Sing	10	nsubj	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	question	question	NOUN	NN	Number=Sing	8	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	advcl	_	_
11	symmetric	symmetric	ADJ	JJ	Degree=Pos	10	acomp	_	_
12	then	then	ADV	RB	PronType=Dem	17	advmod	_	_
13	this	this	DET	DT	Number=Sing|PronType=Dem	14	det	_	_
14	process	process	NOUN	NN	Number=Sing	17	nsubjpass	_	_
15	can	can	AUX	MD	VerbForm=Fin	17	aux	_	_
16	be	be	AUX	VB	VerbForm=Inf	17	auxpass	_	_
17	iterated	iterate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that starting from the symmetric monoidal bicategory Cat and performing the construction twice yields a convenient symmetric monoidal bicategory of partially strict tricategories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	16	mark	_	_
4	starting	start	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	csubj	_	_
5	from	from	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
7	symmetric	symmetric	ADJ	JJ	Degree=Pos	9	amod	_	_
8	monoidal	monoidal	ADJ	JJ	Degree=Pos	9	amod	_	_
9	bicategory	bicategory	NOUN	NN	Number=Sing	10	compound	_	_
10	Cat	Cat	PROPN	NNP	Number=Sing	5	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
12	performing	perform	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	conj	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	construction	construction	NOUN	NN	Number=Sing	12	dobj	_	_
15	twice	twice	ADV	RB	_	12	advmod	_	_
16	yields	yield	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
18	convenient	convenient	ADJ	JJ	Degree=Pos	21	amod	_	_
19	symmetric	symmetric	ADJ	JJ	Degree=Pos	21	amod	_	_
20	monoidal	monoidal	ADJ	JJ	Degree=Pos	21	amod	_	_
21	bicategory	bicategory	NOUN	NN	Number=Sing	16	dobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	partially	partially	ADV	RB	_	24	advmod	_	_
24	strict	strict	ADJ	JJ	Degree=Pos	25	amod	_	_
25	tricategories	tricategorie	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show that restricting to the doubly degenerate ones immediately gives the correct bicategory of `2 - tuply monoidal categories' missing from our earlier studies of the Periodic Table.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	11	mark	_	_
4	restricting	restrict	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	csubj	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
7	doubly	doubly	ADV	RB	_	8	advmod	_	_
8	degenerate	degenerate	ADJ	JJ	Degree=Pos	9	amod	_	_
9	ones	one	NOUN	NNS	Number=Plur	5	pobj	_	_
10	immediately	immediately	ADV	RB	_	11	advmod	_	_
11	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	correct	correct	ADJ	JJ	Degree=Pos	14	amod	_	_
14	bicategory	bicategory	NOUN	NN	Number=Sing	11	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	15	punct	_	SpaceAfter=No
17	2	2	NUM	CD	NumType=Card	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	tuply	tuply	NOUN	NN	Number=Sing	21	amod	_	_
20	monoidal	monoidal	NOUN	NN	Number=Sing	21	amod	_	_
21	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
22	'	'	PART	POS	_	21	case	_	_
23	missing	miss	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	21	amod	_	_
24	from	from	ADP	IN	_	11	prep	_	_
25	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	27	poss	_	_
26	earlier	early	ADJ	JJR	Degree=Cmp	27	amod	_	_
27	studies	study	NOUN	NNS	Number=Plur	24	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
30	Periodic	Periodic	PROPN	NNP	Number=Sing	31	compound	_	_
31	Table	Table	PROPN	NNP	Number=Sing	28	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = We propose a generalisation to all $ k $ - tuply monoidal $ n $ - categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	propose	propose	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	generalisation	generalisation	NOUN	NN	Number=Sing	2	dobj	_	_
5	to	to	ADP	IN	_	2	prep	_	_
6	all	all	DET	DT	_	10	det	_	_
7	$ k $	$ k $	SYM	$	_	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	tuply	tuply	NOUN	NN	Number=Sing	10	compound	_	_
10	monoidal	monoidal	NOUN	NN	Number=Sing	5	pobj	_	_
11	$ n $	$ n $	SYM	$	_	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 480
# sent_id = 1
# text = Geometric morphisms between realizability toposes are studied in terms of morphisms between partial combinatory algebras.
1	Geometric	geometric	ADJ	JJ	Degree=Pos	2	amod	_	_
2	morphisms	morphism	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
3	between	between	ADP	IN	_	2	prep	_	_
4	realizability	realizability	NOUN	NN	Number=Sing	5	compound	_	_
5	toposes	topos	NOUN	NNS	Number=Plur	3	pobj	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	studied	study	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	terms	term	NOUN	NNS	Number=Plur	8	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	morphisms	morphism	NOUN	NNS	Number=Plur	10	pobj	_	_
12	between	between	ADP	IN	_	11	prep	_	_
13	partial	partial	ADJ	JJ	Degree=Pos	15	amod	_	_
14	combinatory	combinatory	NOUN	NN	Number=Sing	15	compound	_	_
15	algebras	algebra	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 2
# text = The morphisms inducing geometric morphisms (the computationally dense ones) are seen to be the ones whose `lifts' to a kind of completion have right adjoints.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	morphisms	morphism	NOUN	NNS	Number=Plur	13	nsubjpass	_	_
3	inducing	induce	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	acl	_	_
4	geometric	geometric	ADJ	JJ	Degree=Pos	5	amod	_	_
5	morphisms	morphism	NOUN	NNS	Number=Plur	3	dobj	_	_
6	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	5	punct	_	SpaceAfter=No
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	computationally	computationally	ADV	RB	_	9	advmod	_	_
9	dense	dense	ADJ	JJ	Degree=Pos	10	amod	_	_
10	ones	one	NOUN	NNS	Number=Plur	5	appos	_	SpaceAfter=No
11	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	5	punct	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	be	be	AUX	VB	VerbForm=Inf	13	xcomp	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	ones	one	NOUN	NNS	Number=Plur	15	attr	_	_
18	whose	whose	DET	WP$	Poss=Yes	20	poss	_	_
19	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	20	punct	_	SpaceAfter=No
20	lifts	lift	NOUN	NNS	Number=Plur	27	nsubj	_	SpaceAfter=No
21	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	20	punct	_	_
22	to	to	ADP	IN	_	20	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	kind	kind	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	completion	completion	NOUN	NN	Number=Sing	25	pobj	_	_
27	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	17	relcl	_	_
28	right	right	ADJ	JJ	Degree=Pos	29	amod	_	_
29	adjoints	adjoint	NOUN	NNS	Number=Plur	27	dobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 3
# text = We characterize topos inclusions corresponding to a general form of relative computability.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	topos	topos	NOUN	NN	Number=Sing	4	compound	_	_
4	inclusions	inclusion	NOUN	NNS	Number=Plur	2	dobj	_	_
5	corresponding	corresponding	ADJ	JJ	Degree=Pos	4	amod	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	general	general	ADJ	JJ	Degree=Pos	9	amod	_	_
9	form	form	NOUN	NN	Number=Sing	6	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	relative	relative	ADJ	JJ	Degree=Pos	12	amod	_	_
12	computability	computability	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We characterize partial combinatory algebras whose realizability topos admits a geometric morphism to the effective topos.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	partial	partial	ADJ	JJ	Degree=Pos	5	amod	_	_
4	combinatory	combinatory	NOUN	NN	Number=Sing	5	compound	_	_
5	algebras	algebra	NOUN	NNS	Number=Plur	2	dobj	_	_
6	whose	whose	DET	WP$	Poss=Yes	8	poss	_	_
7	realizability	realizability	NOUN	NN	Number=Sing	8	compound	_	_
8	topos	topos	NOUN	NN	Number=Sing	9	nsubj	_	_
9	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	relcl	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	geometric	geometric	ADJ	JJ	Degree=Pos	12	amod	_	_
12	morphism	morphism	NOUN	NN	Number=Sing	9	dobj	_	_
13	to	to	ADP	IN	_	9	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	effective	effective	ADJ	JJ	Degree=Pos	16	amod	_	_
16	topos	topos	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 481
# sent_id = 1
# text = In this paper we introduce two notions—systems of fibrant objects and fibration structures—which will allow us to associate to a bicategory $ B $ a homotopy bicategory $ Ho(B) $ in such a way that $ Ho(B) $ is the universal way to add pseudo - inverses to weak equivalences in $ B $ .
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	two	two	NUM	CD	NumType=Card	7	nummod	_	_
7	notions	notion	NOUN	NNS	Number=Plur	5	dobj	_	SpaceAfter=No
8	—	—	PUNCT	:	_	7	punct	_	SpaceAfter=No
9	systems	system	NOUN	NNS	Number=Plur	7	appos	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	fibrant	fibrant	ADJ	JJ	Degree=Pos	12	amod	_	_
12	objects	object	NOUN	NNS	Number=Plur	10	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	fibration	fibration	NOUN	NN	Number=Sing	15	compound	_	_
15	structures	structure	NOUN	NNS	Number=Plur	12	conj	_	SpaceAfter=No
16	—	—	PUNCT	:	_	7	punct	_	SpaceAfter=No
17	which	which	PRON	WDT	_	19	nsubj	_	_
18	will	will	AUX	MD	VerbForm=Fin	19	aux	_	_
19	allow	allow	VERB	VB	VerbForm=Inf	7	relcl	_	_
20	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	22	nsubj	_	_
21	to	to	PART	TO	_	22	aux	_	_
22	associate	associate	VERB	VB	VerbForm=Inf	19	ccomp	_	_
23	to	to	ADP	IN	_	22	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
25	bicategory	bicategory	NOUN	NN	Number=Sing	23	pobj	_	_
26	$ B $	$ b $	SYM	$	_	29	nmod	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	homotopy	homotopy	NOUN	NN	Number=Sing	29	compound	_	_
29	bicategory	bicategory	NOUN	NN	Number=Sing	22	dobj	_	_
30	$ Ho(B) $	$ ho(b) $	SYM	$	_	22	dep	_	_
31	in	in	ADP	IN	_	30	prep	_	_
32	such	such	DET	PDT	_	34	predet	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
34	way	way	NOUN	NN	Number=Sing	31	pobj	_	_
35	that	that	PRON	WDT	PronType=Rel	37	attr	_	_
36	$ Ho(B) $	$ ho(b) $	SYM	$	_	37	nsubj	_	_
37	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	ccomp	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
39	universal	universal	ADJ	JJ	Degree=Pos	40	amod	_	_
40	way	way	NOUN	NN	Number=Sing	37	attr	_	_
41	to	to	PART	TO	_	42	aux	_	_
42	add	add	VERB	VB	VerbForm=Inf	40	relcl	_	_
43	pseudo	pseudo	NOUN	NN	Number=Sing	42	dobj	_	_
44	-	-	PUNCT	:	_	37	punct	_	_
45	inverses	inverse	NOUN	NNS	Number=Plur	37	attr	_	_
46	to	to	ADP	IN	_	45	prep	_	_
47	weak	weak	ADJ	JJ	Degree=Pos	48	amod	_	_
48	equivalences	equivalence	NOUN	NNS	Number=Plur	46	pobj	_	_
49	in	in	ADP	IN	_	48	prep	_	_
50	$ B $	$ b $	SYM	$	_	49	pobj	_	_
51	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = Furthermore, $ Ho(B) $ is locally small when $ B $ is and $ Ho(B) $ is a 2 - category when $ B $ is.
1	Furthermore	furthermore	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	$ Ho(B) $	$ ho(b) $	SYM	$	_	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	locally	locally	ADV	RB	_	6	advmod	_	_
6	small	small	ADJ	JJ	Degree=Pos	4	acomp	_	_
7	when	when	SCONJ	WRB	_	9	advmod	_	_
8	$ B $	$ b $	SYM	$	_	9	nsubj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	advcl	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	$ Ho(B) $	$ ho(b) $	SYM	$	_	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	conj	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
14	2	2	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	category	category	NOUN	NN	Number=Sing	12	attr	_	_
17	when	when	SCONJ	WRB	_	19	advmod	_	_
18	$ B $	$ b $	SYM	$	_	19	nsubj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	advcl	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = We thereby resolve two of the problems with known approaches to bicategorical localization.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	thereby	thereby	ADV	RB	_	3	advmod	_	_
3	resolve	resolve	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	two	two	NUM	CD	NumType=Card	3	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	problems	problem	NOUN	NNS	Number=Plur	5	pobj	_	_
8	with	with	ADP	IN	_	7	prep	_	_
9	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	approaches	approach	NOUN	NNS	Number=Plur	8	pobj	_	_
11	to	to	ADP	IN	_	10	prep	_	_
12	bicategorical	bicategorical	ADJ	JJ	Degree=Pos	13	amod	_	_
13	localization	localization	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = As an important example, we describe a fibration structure on the 2 - category of prestacks on a site and prove that the resulting homotopy bicategory is the 2 - category of stacks.
1	As	as	ADP	IN	_	7	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	important	important	ADJ	JJ	Degree=Pos	4	amod	_	_
4	example	example	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	fibration	fibration	NOUN	NN	Number=Sing	10	compound	_	_
10	structure	structure	NOUN	NN	Number=Sing	7	dobj	_	_
11	on	on	ADP	IN	_	7	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
13	2	2	NUM	CD	NumType=Card	15	nummod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	prestacks	prestack	NOUN	NNS	Number=Plur	16	pobj	_	_
18	on	on	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	site	site	NOUN	NN	Number=Sing	18	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
22	prove	prove	VERB	VB	VerbForm=Inf	7	conj	_	_
23	that	that	SCONJ	IN	_	28	mark	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
25	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	27	amod	_	_
26	homotopy	homotopy	NOUN	NN	Number=Sing	27	compound	_	_
27	bicategory	bicategory	NOUN	NN	Number=Sing	28	nsubj	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	ccomp	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
30	2	2	NUM	CD	NumType=Card	32	nummod	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	category	category	NOUN	NN	Number=Sing	28	attr	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	stacks	stack	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 5
# text = We also show how this example can be restricted to obtain algebraic, differentiable and topological (respectively) stacks as homotopy categories of algebraic, differential and topological (respectively) prestacks.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	how	how	SCONJ	WRB	_	9	advmod	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	example	example	NOUN	NN	Number=Sing	9	nsubjpass	_	_
7	can	can	AUX	MD	VerbForm=Fin	9	aux	_	_
8	be	be	AUX	VB	VerbForm=Inf	9	auxpass	_	_
9	restricted	restrict	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	ccomp	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	obtain	obtain	VERB	VB	VerbForm=Inf	9	advcl	_	_
12	algebraic	algebraic	ADJ	JJ	Degree=Pos	20	amod	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	differentiable	differentiable	ADJ	JJ	Degree=Pos	12	conj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	topological	topological	ADJ	JJ	Degree=Pos	14	conj	_	_
17	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	20	punct	_	SpaceAfter=No
18	respectively	respectively	ADV	RB	_	20	advmod	_	SpaceAfter=No
19	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	20	punct	_	_
20	stacks	stack	NOUN	NNS	Number=Plur	11	dobj	_	_
21	as	as	ADP	IN	_	20	prep	_	_
22	homotopy	homotopy	NOUN	NN	Number=Sing	23	compound	_	_
23	categories	category	NOUN	NNS	Number=Plur	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	algebraic	algebraic	ADJ	JJ	Degree=Pos	33	amod	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
27	differential	differential	ADJ	JJ	Degree=Pos	25	conj	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
29	topological	topological	ADJ	JJ	Degree=Pos	27	conj	_	_
30	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	33	punct	_	SpaceAfter=No
31	respectively	respectively	ADV	RB	_	33	advmod	_	SpaceAfter=No
32	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	33	punct	_	_
33	prestacks	prestack	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 482
# sent_id = 1
# text = Given a torsion bundle gerbe on a compact smooth manifold or, more generally, on a compact étale Lie groupoid $ M $ , we show that the corresponding category of gerbe modules is equivalent to the category of finitely generated projective modules over an Azumaya algebra on $ M $ .
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
3	torsion	torsion	NOUN	NN	Number=Sing	4	compound	_	_
4	bundle	bundle	NOUN	NN	Number=Sing	5	compound	_	_
5	gerbe	gerbe	NOUN	NN	Number=Sing	1	pobj	_	_
6	on	on	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	compact	compact	ADJ	JJ	Degree=Pos	10	amod	_	_
9	smooth	smooth	ADJ	JJ	Degree=Pos	10	amod	_	_
10	manifold	manifold	NOUN	NN	Number=Sing	6	pobj	_	_
11	or	or	CCONJ	CC	ConjType=Cmp	10	cc	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
13	more	more	ADV	RBR	Degree=Cmp	14	advmod	_	_
14	generally	generally	ADV	RB	_	21	advmod	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
16	on	on	ADP	IN	_	21	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
18	compact	compact	ADJ	JJ	Degree=Pos	20	amod	_	_
19	étale	étale	ADJ	JJ	Degree=Pos	20	amod	_	_
20	Lie	lie	NOUN	NN	Number=Sing	16	pobj	_	_
21	groupoid	groupoid	VERB	VB	VerbForm=Inf	25	advcl	_	_
22	$ M $	$ m $	SYM	$	_	21	dobj	_	_
23	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
24	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	25	nsubj	_	_
25	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
26	that	that	SCONJ	IN	_	33	mark	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	29	amod	_	_
29	category	category	NOUN	NN	Number=Sing	33	nsubj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	gerbe	gerbe	PROPN	NNP	Number=Sing	32	compound	_	_
32	modules	module	NOUN	NNS	Number=Plur	30	pobj	_	_
33	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	ccomp	_	_
34	equivalent	equivalent	ADJ	JJ	Degree=Pos	33	acomp	_	_
35	to	to	ADP	IN	_	34	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	category	category	NOUN	NN	Number=Sing	35	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	finitely	finitely	ADV	RB	_	40	advmod	_	_
40	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	42	amod	_	_
41	projective	projective	ADJ	JJ	Degree=Pos	42	amod	_	_
42	modules	module	NOUN	NNS	Number=Plur	38	pobj	_	_
43	over	over	ADP	IN	_	42	prep	_	_
44	an	an	DET	DT	Definite=Ind|PronType=Art	46	det	_	_
45	Azumaya	Azumaya	PROPN	NNP	Number=Sing	46	compound	_	_
46	algebra	algebra	NOUN	NN	Number=Sing	43	pobj	_	_
47	on	on	ADP	IN	_	42	prep	_	_
48	$ M $	$ m $	SYM	$	_	47	pobj	_	_
49	.	.	PUNCT	.	PunctType=Peri	25	punct	_	SpaceAfter=No

# sent_id = 2
# text = This result can be seen as an equivariant Serre - Swan theorem for twisted vector bundles.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	result	result	NOUN	NN	Number=Sing	5	nsubjpass	_	_
3	can	can	AUX	MD	VerbForm=Fin	5	aux	_	_
4	be	be	AUX	VB	VerbForm=Inf	5	auxpass	_	_
5	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	as	as	ADP	IN	_	5	prep	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	equivariant	equivariant	ADJ	JJ	Degree=Pos	11	amod	_	_
9	Serre	Serre	PROPN	NNP	Number=Sing	11	compound	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	Swan	Swan	PROPN	NNP	Number=Sing	12	nsubj	_	_
12	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	5	conj	_	_
13	for	for	ADP	IN	_	12	prep	_	_
14	twisted	twisted	ADJ	JJ	Degree=Pos	16	amod	_	_
15	vector	vector	NOUN	NN	Number=Sing	16	compound	_	_
16	bundles	bundle	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 483
# sent_id = 1
# text = Given a monad $ T $ on a suitable enriched category $ B $ equipped with a proper factorization system $ (E, M) $ , we define notions of $ T $ - completion, $ T $ - closure, and $ T $ - density.
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	monad	monad	NOUN	NNS	Number=Plur	1	pobj	_	_
4	$ T $	$ t $	SYM	$	_	3	appos	_	_
5	on	on	ADP	IN	_	1	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	suitable	suitable	ADJ	JJ	Degree=Pos	9	amod	_	_
8	enriched	enriched	ADJ	JJ	Degree=Pos	9	amod	_	_
9	category	category	NOUN	NN	Number=Sing	17	nmod	_	_
10	$ B $	$ b $	SYM	$	_	9	appos	_	_
11	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	acl	_	_
12	with	with	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
14	proper	proper	ADJ	JJ	Degree=Pos	16	amod	_	_
15	factorization	factorization	NOUN	NN	Number=Sing	16	compound	_	_
16	system	system	NOUN	NN	Number=Sing	17	nmod	_	_
17	$ (E, M) $	$ (e, m) $	SYM	$	_	5	pobj	_	_
18	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
19	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	20	nsubj	_	_
20	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
21	notions	notion	NOUN	NNS	Number=Plur	20	dobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	$ T $	$ t $	SYM	$	_	25	nummod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	completion	completion	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
27	$ T $	$ t $	SYM	$	_	20	npadvmod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	closure	closure	NOUN	NN	Number=Sing	27	amod	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
32	$ T $	$ t $	SYM	$	_	34	nummod	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	density	density	NOUN	NN	Number=Sing	20	conj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that not only the familiar notions of completion, closure, and density in normed vector spaces, but also the notions of sheafification, closure, and density with respect to a Lawvere - Tierney topology, are instances of the given abstract notions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	41	mark	_	_
4	not	not	PART	RB	Polarity=Neg	8	preconj	_	_
5	only	only	ADV	RB	_	4	advmod	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	familiar	familiar	ADJ	JJ	Degree=Pos	8	amod	_	_
8	notions	notion	NOUN	NNS	Number=Plur	41	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	completion	completion	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	closure	closure	NOUN	NN	Number=Sing	10	conj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
15	density	density	NOUN	NN	Number=Sing	12	conj	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	normed	normed	ADJ	JJ	Degree=Pos	19	amod	_	_
18	vector	vector	NOUN	NN	Number=Sing	19	compound	_	_
19	spaces	space	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
21	but	but	CCONJ	CC	ConjType=Cmp	8	cc	_	_
22	also	also	ADV	RB	_	21	advmod	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	notions	notion	NOUN	NNS	Number=Plur	8	conj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	sheafification	sheafification	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
28	closure	closure	NOUN	NN	Number=Sing	26	conj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
31	density	density	NOUN	NN	Number=Sing	28	conj	_	_
32	with	with	ADP	IN	_	31	prep	_	_
33	respect	respect	NOUN	NN	Number=Sing	32	pobj	_	_
34	to	to	ADP	IN	_	33	prep	_	_
35	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
36	Lawvere	Lawvere	PROPN	NNP	Number=Sing	38	compound	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	38	punct	_	_
38	Tierney	Tierney	PROPN	NNP	Number=Sing	39	compound	_	_
39	topology	topology	NOUN	NN	Number=Sing	34	pobj	_	SpaceAfter=No
40	,	,	PUNCT	,	PunctType=Comm	41	punct	_	_
41	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
42	instances	instance	NOUN	NNS	Number=Plur	41	attr	_	_
43	of	of	ADP	IN	_	42	prep	_	_
44	the	the	DET	DT	Definite=Def|PronType=Art	47	det	_	_
45	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	47	amod	_	_
46	abstract	abstract	ADJ	JJ	Degree=Pos	47	amod	_	_
47	notions	notion	NOUN	NNS	Number=Plur	43	pobj	_	SpaceAfter=No
48	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The process of $ T $ - completion is equally the enriched idempotent monad associated to $ T $ (which we call the idempotent core of $ T $ ), and we show that it exists as soon as every morphism in $ B $ factors as a $ T $ - dense morphism followed by a $ T $ - closed $ M $ - embedding.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	process	process	NOUN	NN	Number=Sing	7	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	$ T $	$ t $	SYM	$	_	6	compound	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	completion	completion	NOUN	NN	Number=Sing	3	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	equally	equally	ADV	RB	_	7	advmod	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
10	enriched	enriched	ADJ	JJ	Degree=Pos	12	amod	_	_
11	idempotent	idempotent	ADJ	JJ	Degree=Pos	12	amod	_	_
12	monad	monad	NOUN	NNS	Number=Plur	7	attr	_	_
13	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	$ T $	$ t $	SYM	$	_	14	pobj	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	15	punct	_	SpaceAfter=No
17	which	which	PRON	WDT	_	19	dobj	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	12	relcl	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	idempotent	idempotent	ADJ	JJ	Degree=Pos	22	amod	_	_
22	core	core	NOUN	NN	Number=Sing	19	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	$ T $	$ t $	SYM	$	_	23	pobj	_	_
25	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	7	punct	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
28	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	29	nsubj	_	_
29	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	7	conj	_	_
30	that	that	SCONJ	IN	_	32	mark	_	_
31	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	32	nsubj	_	_
32	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	ccomp	_	_
33	as	as	ADV	RB	_	34	advmod	_	_
34	soon	soon	ADV	RB	_	32	advmod	_	_
35	as	as	SCONJ	IN	_	37	mark	_	_
36	every	every	DET	DT	_	37	det	_	_
37	morphism	morphism	NOUN	NN	Number=Sing	34	advcl	_	_
38	in	in	ADP	IN	_	37	prep	_	_
39	$ B $	$ b $	SYM	$	_	40	nummod	_	_
40	factors	factor	NOUN	NNS	Number=Plur	38	pobj	_	_
41	as	as	ADP	IN	_	37	prep	_	_
42	a	a	DET	DT	Definite=Ind|PronType=Art	46	det	_	_
43	$ T $	$ t $	SYM	$	_	45	advmod	_	_
44	-	-	PUNCT	HYPH	PunctType=Dash	45	punct	_	_
45	dense	dense	ADJ	JJ	Degree=Pos	46	amod	_	_
46	morphism	morphism	NOUN	NN	Number=Sing	41	pobj	_	_
47	followed	follow	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	46	acl	_	_
48	by	by	ADP	IN	_	47	agent	_	_
49	a	a	DET	DT	Definite=Ind|PronType=Art	55	det	_	_
50	$ T $	$ t $	SYM	$	_	52	advmod	_	_
51	-	-	PUNCT	HYPH	PunctType=Dash	52	punct	_	_
52	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	55	amod	_	_
53	$ M $	$ m $	SYM	$	_	55	advmod	_	_
54	-	-	PUNCT	HYPH	PunctType=Dash	55	punct	_	_
55	embedding	embed	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	48	pobj	_	SpaceAfter=No
56	.	.	PUNCT	.	PunctType=Peri	29	punct	_	SpaceAfter=No

# sent_id = 4
# text = The latter hypothesis is satisfied as soon as $ B $ has certain pullbacks as well as wide intersections of $ M $ - embeddings.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	latter	latter	ADJ	JJ	Degree=Pos	3	amod	_	_
3	hypothesis	hypothesis	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	satisfied	satisfied	ADJ	JJ	Degree=Pos	4	acomp	_	_
6	as	as	ADV	RB	_	7	advmod	_	_
7	soon	soon	ADV	RB	_	5	advmod	_	_
8	as	as	SCONJ	IN	_	10	mark	_	_
9	$ B $	$ b $	SYM	$	_	10	nsubj	_	_
10	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	advcl	_	_
11	certain	certain	ADJ	JJ	Degree=Pos	12	amod	_	_
12	pullbacks	pullback	NOUN	NNS	Number=Plur	10	dobj	_	_
13	as	as	ADV	RB	_	15	advmod	_	_
14	well	well	ADV	RB	Degree=Pos	15	advmod	_	_
15	as	as	ADP	IN	_	12	cc	_	_
16	wide	wide	ADJ	JJ	Degree=Pos	17	amod	_	_
17	intersections	intersection	NOUN	NNS	Number=Plur	12	conj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	$ M $	$ m $	SYM	$	_	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	embeddings	embedding	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = Hence the resulting theorem on the existence of the idempotent core of an enriched monad entails Fakir's existence result in the non - enriched case, as well as adjoint functor factorization results of Applegate - Tierney and Day.
1	Hence	hence	ADV	RB	_	4	advmod	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	amod	_	_
4	theorem	theorem	ADJ	JJ	Degree=Pos	16	nsubj	_	_
5	on	on	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	existence	existence	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	idempotent	idempotent	ADJ	JJ	Degree=Pos	11	amod	_	_
11	core	core	NOUN	NN	Number=Sing	8	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	enriched	enriched	ADJ	JJ	Degree=Pos	15	amod	_	_
15	monad	monad	NOUN	NNS	Number=Plur	12	pobj	_	_
16	entails	entail	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
17	Fakir	Fakir	PROPN	NNP	Number=Sing	19	poss	_	SpaceAfter=No
18	's	's	PART	POS	_	17	case	_	_
19	existence	existence	NOUN	NN	Number=Sing	20	nsubj	_	_
20	result	result	NOUN	NN	Number=Sing	16	dobj	_	_
21	in	in	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
23	non	non	ADJ	JJ	Degree=Pos	25	advmod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
26	case	case	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
28	as	as	ADV	RB	_	30	advmod	_	_
29	well	well	ADV	RB	Degree=Pos	30	advmod	_	_
30	as	as	ADP	IN	_	20	cc	_	_
31	adjoint	adjoint	NOUN	NN	Number=Sing	32	compound	_	_
32	functor	functor	NOUN	NN	Number=Sing	33	compound	_	_
33	factorization	factorization	NOUN	NN	Number=Sing	34	compound	_	_
34	results	result	NOUN	NNS	Number=Plur	20	conj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	Applegate	Applegate	PROPN	NNP	Number=Sing	38	compound	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	38	punct	_	_
38	Tierney	Tierney	PROPN	NNP	Number=Sing	35	pobj	_	_
39	and	and	CCONJ	CC	ConjType=Cmp	38	cc	_	_
40	Day	Day	PROPN	NNP	Number=Sing	38	conj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# doc_id = 484
# sent_id = 1
# text = In this paper we consider a notion of pointwise Kan extension in double categories that naturally generalises Dubuc's notion of pointwise Kan extension along enriched functors.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	notion	notion	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	pointwise	pointwise	ADJ	JJ	Degree=Pos	11	amod	_	_
10	Kan	Kan	PROPN	NNP	Number=Sing	11	compound	_	_
11	extension	extension	NOUN	NN	Number=Sing	8	pobj	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	double	double	ADJ	JJ	Degree=Pos	14	amod	_	_
14	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	_
15	that	that	PRON	WDT	PronType=Rel	17	nsubj	_	_
16	naturally	naturally	ADV	RB	_	17	advmod	_	_
17	generalises	generalise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
18	Dubuc	Dubuc	PROPN	NNP	Number=Sing	20	poss	_	SpaceAfter=No
19	's	's	PART	POS	_	18	case	_	_
20	notion	notion	NOUN	NN	Number=Sing	17	dobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	pointwise	pointwise	ADJ	JJ	Degree=Pos	24	amod	_	_
23	Kan	Kan	PROPN	NNP	Number=Sing	24	compound	_	_
24	extension	extension	NOUN	NN	Number=Sing	21	pobj	_	_
25	along	along	ADP	IN	_	24	prep	_	_
26	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	amod	_	_
27	functors	functor	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that, when considered in equipments that admit opcartesian tabulations, it generalises Street's notion of pointwise Kan extension in 2 - categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	15	mark	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
5	when	when	SCONJ	WRB	_	6	advmod	_	_
6	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	advcl	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	equipments	equipment	NOUN	NNS	Number=Plur	7	pobj	_	_
9	that	that	PRON	WDT	PronType=Rel	10	nsubj	_	_
10	admit	admit	VERB	VBP	Tense=Pres|VerbForm=Fin	8	relcl	_	_
11	opcartesian	opcartesian	ADJ	JJ	Degree=Pos	12	amod	_	_
12	tabulations	tabulation	NOUN	NNS	Number=Plur	10	dobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
14	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	15	nsubj	_	_
15	generalises	generalise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
16	Street	Street	PROPN	NNP	Number=Sing	18	poss	_	SpaceAfter=No
17	's	's	PART	POS	_	16	case	_	_
18	notion	notion	NOUN	NN	Number=Sing	15	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	pointwise	pointwise	ADJ	JJ	Degree=Pos	22	amod	_	_
21	Kan	Kan	PROPN	NNP	Number=Sing	22	compound	_	_
22	extension	extension	NOUN	NN	Number=Sing	19	pobj	_	_
23	in	in	ADP	IN	_	22	prep	_	_
24	2	2	NUM	CD	NumType=Card	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	categories	category	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 485
# sent_id = 1
# text = We provide a diagrammatic criterion for the existence of an absolute colimit in the context of enriched category theory.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	diagrammatic	diagrammatic	ADJ	JJ	Degree=Pos	5	amod	_	_
5	criterion	criterion	NOUN	NN	Number=Sing	2	dobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	existence	existence	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	absolute	absolute	ADJ	JJ	Degree=Pos	12	amod	_	_
12	colimit	colimit	NOUN	NN	Number=Sing	9	pobj	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	context	context	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
18	category	category	NOUN	NN	Number=Sing	19	compound	_	_
19	theory	theory	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 486
# sent_id = 1
# text = We show that the category of categories fibred over a site is a generalized Quillen model category in which the weak equivalences are the local equivalences and the fibrant objects are the stacks, as they were defined by Giraud.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	8	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	8	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
8	fibred	fibre	VERB	VBD	Tense=Past|VerbForm=Fin	2	ccomp	_	_
9	over	over	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	site	site	NOUN	NN	Number=Sing	9	pobj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
14	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
15	Quillen	quillen	ADJ	JJ	Degree=Pos	17	amod	_	_
16	model	model	NOUN	NN	Number=Sing	17	compound	_	_
17	category	category	NOUN	NN	Number=Sing	12	attr	_	_
18	in	in	ADP	IN	_	23	prep	_	_
19	which	which	PRON	WDT	_	18	pobj	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	weak	weak	ADJ	JJ	Degree=Pos	22	amod	_	_
22	equivalences	equivalence	NOUN	NNS	Number=Plur	23	nsubj	_	_
23	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	17	relcl	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	local	local	ADJ	JJ	Degree=Pos	26	amod	_	_
26	equivalences	equivalence	NOUN	NNS	Number=Plur	23	attr	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
29	fibrant	fibrant	ADJ	JJ	Degree=Pos	30	amod	_	_
30	objects	object	NOUN	NNS	Number=Plur	31	nsubj	_	_
31	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	23	conj	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
33	stacks	stack	NOUN	NNS	Number=Plur	31	attr	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
35	as	as	SCONJ	IN	_	38	mark	_	_
36	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	38	nsubjpass	_	_
37	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	38	auxpass	_	_
38	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	advcl	_	_
39	by	by	ADP	IN	_	38	agent	_	_
40	Giraud	Giraud	PROPN	NNP	Number=Sing	39	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The generalized model category restricts to one on the full subcategory whose objects are the categories fibred in groupoids.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	generalized	generalized	ADJ	JJ	Degree=Pos	4	amod	_	_
3	model	model	NOUN	NN	Number=Sing	4	compound	_	_
4	category	category	NOUN	NN	Number=Sing	5	nsubj	_	_
5	restricts	restrict	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	one	one	NUM	CD	NumType=Card	6	pobj	_	_
8	on	on	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	full	full	ADJ	JJ	Degree=Pos	11	amod	_	_
11	subcategory	subcategory	NOUN	NN	Number=Sing	8	pobj	_	_
12	whose	whose	DET	WP$	Poss=Yes	13	poss	_	_
13	objects	object	NOUN	NNS	Number=Plur	14	nsubj	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	11	relcl	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	categories	category	NOUN	NNS	Number=Plur	14	attr	_	_
17	fibred	fibre	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	acl	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	groupoids	groupoid	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that the category of sheaves of categories is a model category that is Quillen equivalent to the generalized model category for stacks and to the model category for strong stacks due to Joyal and Tierney.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	10	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	10	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	sheaves	sheaf	NOUN	NNS	Number=Plur	6	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	model	model	NOUN	NN	Number=Sing	13	compound	_	_
13	category	category	NOUN	NN	Number=Sing	10	attr	_	_
14	that	that	PRON	WDT	PronType=Rel	15	nsubj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	relcl	_	_
16	Quillen	quillen	ADJ	JJ	Degree=Pos	17	amod	_	_
17	equivalent	equivalent	ADJ	JJ	Degree=Pos	15	acomp	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
20	generalized	generalized	ADJ	JJ	Degree=Pos	22	amod	_	_
21	model	model	NOUN	NN	Number=Sing	22	compound	_	_
22	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
23	for	for	ADP	IN	_	22	prep	_	_
24	stacks	stack	NOUN	NNS	Number=Plur	23	pobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
26	to	to	ADP	IN	_	23	conj	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	model	model	NOUN	NN	Number=Sing	29	compound	_	_
29	category	category	NOUN	NN	Number=Sing	26	pobj	_	_
30	for	for	ADP	IN	_	29	prep	_	_
31	strong	strong	ADJ	JJ	Degree=Pos	32	amod	_	_
32	stacks	stack	NOUN	NNS	Number=Plur	30	pobj	_	_
33	due	due	ADJ	JJ	Degree=Pos	32	amod	_	_
34	to	to	ADP	IN	_	33	pcomp	_	_
35	Joyal	Joyal	PROPN	NNP	Number=Sing	34	pobj	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
37	Tierney	Tierney	PROPN	NNP	Number=Sing	35	conj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 487
# sent_id = 1
# text = A pre - cohesive geometric morphism $ p:cal E rightarrow cal S $ satisfies Continuity if the canonical $ p_clik (X^{p^* S}) rightarrow (p_clik X)^S $ is an isomorphism for every $ X $ in $ cal E $ and $ S $ in $ cal S $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
2	pre	pre	ADJ	JJ	Degree=Pos	4	advmod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	cohesive	cohesive	ADJ	JJ	Degree=Pos	6	amod	_	_
5	geometric	geometric	ADJ	JJ	Degree=Pos	6	amod	_	_
6	morphism	morphism	NOUN	NN	Number=Sing	8	nsubj	_	_
7	$ p:cal E rightarrow cal S $	$ p:cal e rightarrow cal s $	SYM	$	_	8	nmod	_	_
8	satisfies	satisfie	NOUN	NNS	Number=Plur	0	ROOT	_	_
9	Continuity	continuity	NOUN	NN	Number=Sing	8	dobj	_	_
10	if	if	SCONJ	IN	_	14	mark	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	canonical	canonical	NOUN	NN	Number=Sing	14	nsubj	_	_
13	$ p_clik (X^{p^* S}) rightarrow (p_clik X)^S $	$ p_clik (x^{p^* s}) rightarrow (p_clik x)^s $	X	FW	Foreign=Yes	12	prep	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	advcl	_	_
15	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	isomorphism	isomorphism	NOUN	NN	Number=Sing	14	attr	_	_
17	for	for	ADP	IN	_	16	prep	_	_
18	every	every	DET	DT	_	19	det	_	_
19	$ X $	$ x $	SYM	$	_	17	pobj	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	$ cal E $	$ cal e $	SYM	$	_	20	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
23	$ S $	$ s $	SYM	$	_	17	pobj	_	_
24	in	in	ADP	IN	_	16	prep	_	_
25	$ cal S $	$ cal s $	SYM	$	_	24	pobj	_	_
26	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that if $ cal S = Set $ and $ cal E $ is a presheaf topos then, $ p $ satisfies Continuity if and only if it is a quality type.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	8	mark	_	_
4	if	if	SCONJ	IN	_	5	mark	_	_
5	$ cal S = Set $	$ cal s = set $	SYM	$	_	8	nsubj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	$ cal E $	$ cal e $	SYM	$	_	5	conj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	presheaf	presheaf	ADJ	JJ	Degree=Pos	11	amod	_	_
11	topos	topos	NOUN	NN	Number=Sing	8	attr	_	_
12	then	then	ADV	RB	PronType=Dem	8	advmod	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
14	$ p $	$ p $	SYM	$	_	15	nummod	_	_
15	satisfies	satisfie	NOUN	NNS	Number=Plur	8	attr	_	_
16	Continuity	continuity	NOUN	NN	Number=Sing	15	npadvmod	_	_
17	if	if	SCONJ	IN	_	8	dep	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	only	only	ADV	RB	_	22	advmod	_	_
20	if	if	SCONJ	IN	_	22	mark	_	_
21	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	22	nsubj	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	advcl	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	quality	quality	NOUN	NN	Number=Sing	25	compound	_	_
25	type	type	NOUN	NN	Number=Sing	22	attr	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Our proof of this characterization rests on a related result showing that Continuity and Sufficient Cohesion are incompatible for presheaf toposes.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	proof	proof	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	characterization	characterization	NOUN	NN	Number=Sing	3	pobj	_	_
6	rests	rest	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	on	on	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	related	related	ADJ	JJ	Degree=Pos	10	amod	_	_
10	result	result	NOUN	NN	Number=Sing	7	pobj	_	_
11	showing	show	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	acl	_	_
12	that	that	SCONJ	IN	_	17	mark	_	_
13	Continuity	Continuity	PROPN	NNP	Number=Sing	16	nmod	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	Sufficient	Sufficient	PROPN	NNP	Number=Sing	13	conj	_	_
16	Cohesion	Cohesion	PROPN	NNP	Number=Sing	17	nsubj	_	_
17	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	11	ccomp	_	_
18	incompatible	incompatible	ADJ	JJ	Degree=Pos	17	acomp	_	_
19	for	for	ADP	IN	_	18	prep	_	_
20	presheaf	presheaf	ADJ	JJ	Degree=Pos	21	compound	_	_
21	toposes	topos	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = This incompatibility raises the question whether Continuity and Sufficient Cohesion are ever compatible for Grothendieck toposes.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	incompatibility	incompatibility	NOUN	NN	Number=Sing	3	nsubj	_	_
3	raises	raise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	question	question	NOUN	NN	Number=Sing	3	dobj	_	_
6	whether	whether	SCONJ	IN	_	11	mark	_	_
7	Continuity	Continuity	PROPN	NNP	Number=Sing	10	nmod	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	Sufficient	Sufficient	PROPN	NNP	Number=Sing	7	conj	_	_
10	Cohesion	Cohesion	PROPN	NNP	Number=Sing	11	nsubj	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	acl	_	_
12	ever	ever	ADV	RB	_	11	advmod	_	_
13	compatible	compatible	ADJ	JJ	Degree=Pos	11	acomp	_	_
14	for	for	ADP	IN	_	13	prep	_	_
15	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	16	compound	_	_
16	toposes	topos	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = We show that the answer is positive by building some examples.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	6	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	answer	answer	NOUN	NN	Number=Sing	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
7	positive	positive	ADJ	JJ	Degree=Pos	6	acomp	_	_
8	by	by	ADP	IN	_	7	prep	_	_
9	building	build	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	pcomp	_	_
10	some	some	DET	DT	_	11	det	_	_
11	examples	example	NOUN	NNS	Number=Plur	9	dobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 488
# sent_id = 1
# text = We present a weak form of a recognition principle for Quillen model categories due to Smith.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	weak	weak	ADJ	JJ	Degree=Pos	5	amod	_	_
5	form	form	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	recognition	recognition	NOUN	NN	Number=Sing	9	compound	_	_
9	principle	principle	NOUN	NN	Number=Sing	6	pobj	_	_
10	for	for	ADP	IN	_	9	prep	_	_
11	Quillen	quillen	ADJ	JJ	Degree=Pos	13	amod	_	_
12	model	model	NOUN	NN	Number=Sing	13	compound	_	_
13	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
14	due	due	ADJ	JJ	Degree=Pos	13	amod	_	_
15	to	to	ADP	IN	_	14	pcomp	_	_
16	Smith	Smith	PROPN	NNP	Number=Sing	15	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We use it to put a model category structure on the category of small categories enriched over a suitable monoidal simplicial model category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	dobj	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	put	put	VERB	VB	VerbForm=Inf	2	xcomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	model	model	NOUN	NN	Number=Sing	9	compound	_	_
8	category	category	NOUN	NN	Number=Sing	9	compound	_	_
9	structure	structure	NOUN	NN	Number=Sing	5	dobj	_	_
10	on	on	ADP	IN	_	5	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	small	small	ADJ	JJ	Degree=Pos	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	_
16	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
17	over	over	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
19	suitable	suitable	ADJ	JJ	Degree=Pos	23	amod	_	_
20	monoidal	monoidal	ADJ	JJ	Degree=Pos	22	amod	_	_
21	simplicial	simplicial	ADJ	JJ	Degree=Pos	22	amod	_	_
22	model	model	NOUN	NN	Number=Sing	23	compound	_	_
23	category	category	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The proof uses a part of the model structure on small simplicial categories due to Bergner.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	proof	proof	NOUN	NN	Number=Sing	3	nsubj	_	_
3	uses	use	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	part	part	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	model	model	NOUN	NN	Number=Sing	9	compound	_	_
9	structure	structure	NOUN	NN	Number=Sing	6	pobj	_	_
10	on	on	ADP	IN	_	9	prep	_	_
11	small	small	ADJ	JJ	Degree=Pos	13	amod	_	_
12	simplicial	simplicial	ADJ	JJ	Degree=Pos	13	amod	_	_
13	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
14	due	due	ADJ	JJ	Degree=Pos	3	prep	_	_
15	to	to	ADP	IN	_	14	pcomp	_	_
16	Bergner	Bergner	PROPN	NNP	Number=Sing	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = We give an application of the weak form of Smith's result to left Bousfield localizations of categories of monoids in a suitable monoidal model category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	application	application	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	weak	weak	ADJ	JJ	Degree=Pos	8	amod	_	_
8	form	form	NOUN	NN	Number=Sing	5	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Smith	Smith	PROPN	NNP	Number=Sing	12	poss	_	SpaceAfter=No
11	's	's	PART	POS	_	10	case	_	_
12	result	result	NOUN	NN	Number=Sing	9	pobj	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	left	left	VERB	VB	VerbForm=Inf	12	acl	_	_
15	Bousfield	Bousfield	PROPN	NNP	Number=Sing	16	compound	_	_
16	localizations	localization	NOUN	NNS	Number=Plur	14	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	monoids	monoid	NOUN	NNS	Number=Plur	19	pobj	_	_
21	in	in	ADP	IN	_	14	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
23	suitable	suitable	ADJ	JJ	Degree=Pos	26	amod	_	_
24	monoidal	monoidal	ADJ	JJ	Degree=Pos	25	amod	_	_
25	model	model	NOUN	NN	Number=Sing	26	compound	_	_
26	category	category	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 489
# sent_id = 1
# text = We show that the composition of a homotopically meaningful `geometric realization' (or simple functor) with the simplicial replacement produces all homotopy colimits and Kan extensions in a relative category which is closed under coproducts.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	23	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	composition	composition	NOUN	NN	Number=Sing	23	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
8	homotopically	homotopically	ADV	RB	_	9	advmod	_	_
9	meaningful	meaningful	ADJ	JJ	Degree=Pos	12	amod	_	_
10	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	12	punct	_	SpaceAfter=No
11	geometric	geometric	ADJ	JJ	Degree=Pos	12	amod	_	_
12	realization	realization	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
13	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	12	punct	_	_
14	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
15	or	or	CCONJ	CC	ConjType=Cmp	12	cc	_	_
16	simple	simple	ADJ	JJ	Degree=Pos	17	amod	_	_
17	functor	functor	NOUN	NN	Number=Sing	12	conj	_	SpaceAfter=No
18	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	12	punct	_	_
19	with	with	ADP	IN	_	5	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	simplicial	simplicial	ADJ	JJ	Degree=Pos	22	amod	_	_
22	replacement	replacement	NOUN	NN	Number=Sing	19	pobj	_	_
23	produces	produce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
24	all	all	DET	DT	_	26	det	_	_
25	homotopy	homotopy	NOUN	NN	Number=Sing	26	compound	_	_
26	colimits	colimit	NOUN	NNS	Number=Plur	23	dobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	Kan	Kan	PROPN	NNP	Number=Sing	29	compound	_	_
29	extensions	extension	NOUN	NNS	Number=Plur	26	conj	_	_
30	in	in	ADP	IN	_	23	prep	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
32	relative	relative	ADJ	JJ	Degree=Pos	33	amod	_	_
33	category	category	NOUN	NN	Number=Sing	30	pobj	_	_
34	which	which	PRON	WDT	_	36	nsubjpass	_	_
35	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	36	auxpass	_	_
36	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	relcl	_	_
37	under	under	ADP	IN	_	36	prep	_	_
38	coproducts	coproduct	NOUN	NNS	Number=Plur	37	pobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Examples (and its duals) include model categories, $ Delta $ - closed classes and other concrete examples such as complexes on (AB4) abelian categories, (filtered) commutative dg algebras and mixed Hodge complexes.
1	Examples	example	NOUN	NNS	Number=Plur	7	nsubj	_	_
2	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	1	punct	_	SpaceAfter=No
3	and	and	CCONJ	CC	ConjType=Cmp	1	cc	_	_
4	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	5	poss	_	_
5	duals	dual	NOUN	NNS	Number=Plur	1	conj	_	SpaceAfter=No
6	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	5	punct	_	_
7	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	model	model	NOUN	NN	Number=Sing	9	compound	_	_
9	categories	category	NOUN	NNS	Number=Plur	7	dobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	$ Delta $	$ delta $	SYM	$	_	13	advmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
14	classes	class	NOUN	NNS	Number=Plur	9	conj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	other	other	ADJ	JJ	Degree=Pos	18	amod	_	_
17	concrete	concrete	ADJ	JJ	Degree=Pos	18	amod	_	_
18	examples	example	NOUN	NNS	Number=Plur	14	conj	_	_
19	such	such	ADJ	JJ	Degree=Pos	20	amod	_	_
20	as	as	ADP	IN	_	18	prep	_	_
21	complexes	complex	NOUN	NNS	Number=Plur	20	pobj	_	_
22	on	on	ADP	IN	_	21	prep	_	_
23	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	27	punct	_	SpaceAfter=No
24	AB4	AB4	PROPN	NNP	Number=Sing	26	nmod	_	SpaceAfter=No
25	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	26	punct	_	_
26	abelian	abelian	ADJ	JJ	Degree=Pos	27	compound	_	_
27	categories	category	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
29	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	9	punct	_	SpaceAfter=No
30	filtered	filter	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	acl	_	SpaceAfter=No
31	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	32	punct	_	_
32	commutative	commutative	PROPN	NNP	Number=Sing	9	appos	_	_
33	dg	dg	PROPN	NNP	Number=Sing	7	conj	_	_
34	algebras	algebra	NOUN	NNS	Number=Plur	7	dobj	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	34	cc	_	_
36	mixed	mixed	ADJ	JJ	Degree=Pos	38	amod	_	_
37	Hodge	Hodge	PROPN	NNP	Number=Sing	38	compound	_	_
38	complexes	complex	NOUN	NNS	Number=Plur	34	conj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = The resulting homotopy colimits satisfy the expected properties as cofinality and Fubini, and are moreover colimits in a suitable 2 - category of relative categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	amod	_	_
3	homotopy	homotopy	NOUN	NN	Number=Sing	4	compound	_	_
4	colimits	colimit	NOUN	NNS	Number=Plur	5	nsubj	_	_
5	satisfy	satisfy	VERB	VB	VerbForm=Inf	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	expected	expect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
8	properties	property	NOUN	NNS	Number=Plur	5	dobj	_	_
9	as	as	ADP	IN	_	5	prep	_	_
10	cofinality	cofinality	NOUN	NN	Number=Sing	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	Fubini	Fubini	PROPN	NNP	Number=Sing	10	conj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	conj	_	_
16	moreover	moreover	ADV	RB	_	15	advmod	_	_
17	colimits	colimit	NOUN	NNS	Number=Plur	15	attr	_	_
18	in	in	ADP	IN	_	15	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
20	suitable	suitable	ADJ	JJ	Degree=Pos	23	amod	_	_
21	2	2	NUM	CD	NumType=Card	23	nummod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	relative	relative	ADJ	JJ	Degree=Pos	26	amod	_	_
26	categories	category	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = Conversely, the existence of homotopy colimits satisfying these properties guarantees that $ hocolim_{Delta^o} $ is a simple functor.
1	Conversely	conversely	ADV	RB	_	11	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	existence	existence	NOUN	NN	Number=Sing	11	nsubj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	homotopy	homotopy	NOUN	NN	Number=Sing	7	compound	_	_
7	colimits	colimit	NOUN	NNS	Number=Plur	5	pobj	_	_
8	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	acl	_	_
9	these	these	DET	DT	Number=Plur|PronType=Dem	10	det	_	_
10	properties	property	NOUN	NNS	Number=Plur	8	dobj	_	_
11	guarantees	guarantee	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	that	that	SCONJ	IN	_	14	mark	_	_
13	$ hocolim_{Delta^o} $	$ hocolim_{delta^o} $	SYM	$	_	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	ccomp	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	simple	simple	ADJ	JJ	Degree=Pos	17	amod	_	_
17	functor	functor	NOUN	NN	Number=Sing	14	attr	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# doc_id = 490
# sent_id = 1
# text = We continue the development of the infinitesimal deformation theory of pasting diagrams of $ k $ - linear categories begun in other work.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	continue	continue	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	development	development	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
7	infinitesimal	infinitesimal	ADJ	JJ	Degree=Pos	9	amod	_	_
8	deformation	deformation	NOUN	NN	Number=Sing	9	compound	_	_
9	theory	theory	NOUN	NN	Number=Sing	5	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	pasting	paste	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	compound	_	_
12	diagrams	diagram	NOUN	NNS	Number=Plur	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	$ k $	$ k $	SYM	$	_	16	quantmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	linear	linear	ADJ	JJ	Degree=Pos	17	amod	_	_
17	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	_
18	begun	begin	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
19	in	in	ADP	IN	_	18	prep	_	_
20	other	other	ADJ	JJ	Degree=Pos	21	amod	_	_
21	work	work	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In that article the standard result that all obstructions are cocycles was established only for the elementary, composition - free parts of pasting diagrams.
1	In	in	ADP	IN	_	6	prep	_	_
2	that	that	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	article	article	NOUN	NN	Number=Sing	1	pobj	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	standard	standard	ADJ	JJ	Degree=Pos	6	nsubj	_	_
6	result	result	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	10	mark	_	_
8	all	all	DET	DT	_	9	det	_	_
9	obstructions	obstruction	NOUN	NNS	Number=Plur	10	nsubj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
11	cocycles	cocycle	NOUN	NNS	Number=Plur	13	nsubjpass	_	_
12	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	13	auxpass	_	_
13	established	establish	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	ccomp	_	_
14	only	only	ADV	RB	_	15	advmod	_	_
15	for	for	ADP	IN	_	13	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
17	elementary	elementary	ADJ	JJ	Degree=Pos	22	amod	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	composition	composition	NOUN	NN	Number=Sing	21	npadvmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	free	free	ADJ	JJ	Degree=Pos	22	amod	_	_
22	parts	part	NOUN	NNS	Number=Plur	15	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	pasting	pasting	NOUN	NN	Number=Sing	25	compound	_	_
25	diagrams	diagram	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = In the present work we give a proof for pasting diagrams in general.
1	In	in	ADP	IN	_	6	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	present	present	ADJ	JJ	Degree=Pos	4	amod	_	_
4	work	work	NOUN	NN	Number=Sing	1	pobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	proof	proof	NOUN	NN	Number=Sing	6	dobj	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	pasting	paste	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	pcomp	_	_
11	diagrams	diagram	NOUN	NNS	Number=Plur	10	dobj	_	_
12	in	in	ADP	IN	_	10	prep	_	_
13	general	general	ADJ	JJ	Degree=Pos	12	amod	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = As tools we use the method developed by Shrestha of simultaneously representing formulas for obstructions, along with the corresponding cocycle and cobounding conditions by suitably labeled polygons, giving a rigorous exposition of the previously heuristic method; and deformations of pasting diagrams in which some cells are required to be deformed trivially.
1	As	as	SCONJ	IN	_	30	mark	_	_
2	tools	tool	NOUN	NNS	Number=Plur	1	pobj	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	2	relcl	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	method	method	NOUN	NN	Number=Sing	4	dobj	_	_
7	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
8	by	by	ADP	IN	_	7	agent	_	_
9	Shrestha	Shrestha	PROPN	NNP	Number=Sing	8	pobj	_	_
10	of	of	ADP	IN	_	7	prep	_	_
11	simultaneously	simultaneously	ADV	RB	_	12	advmod	_	_
12	representing	represent	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	pcomp	_	_
13	formulas	formula	NOUN	NNS	Number=Plur	12	dobj	_	_
14	for	for	ADP	IN	_	12	prep	_	_
15	obstructions	obstruction	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	1	punct	_	_
17	along	along	ADP	IN	_	1	prep	_	_
18	with	with	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	21	amod	_	_
21	cocycle	cocycle	NOUN	NN	Number=Sing	18	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
23	cobounding	cobounde	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	conj	_	_
24	conditions	condition	NOUN	NNS	Number=Plur	23	dobj	_	_
25	by	by	ADP	IN	_	24	prep	_	_
26	suitably	suitably	ADV	RB	_	27	advmod	_	_
27	labeled	label	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	amod	_	_
28	polygons	polygon	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	1	punct	_	_
30	giving	give	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	0	ROOT	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
32	rigorous	rigorous	ADJ	JJ	Degree=Pos	33	amod	_	_
33	exposition	exposition	NOUN	NN	Number=Sing	30	dobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
36	previously	previously	ADV	RB	_	37	advmod	_	_
37	heuristic	heuristic	ADJ	JJ	Degree=Pos	38	amod	_	_
38	method	method	NOUN	NN	Number=Sing	34	pobj	_	SpaceAfter=No
39	;	;	PUNCT	:	_	30	punct	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
41	deformations	deformation	NOUN	NNS	Number=Plur	30	conj	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	pasting	paste	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	44	compound	_	_
44	diagrams	diagram	NOUN	NNS	Number=Plur	42	pobj	_	_
45	in	in	ADP	IN	_	50	prep	_	_
46	which	which	PRON	WDT	_	45	pobj	_	_
47	some	some	DET	DT	_	48	det	_	_
48	cells	cell	NOUN	NNS	Number=Plur	50	nsubjpass	_	_
49	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	50	auxpass	_	_
50	required	require	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	44	relcl	_	_
51	to	to	PART	TO	_	52	aux	_	_
52	be	be	AUX	VB	VerbForm=Inf	53	auxpass	_	_
53	deformed	deform	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	50	xcomp	_	_
54	trivially	trivially	ADV	RB	_	53	advmod	_	SpaceAfter=No
55	.	.	PUNCT	.	PunctType=Peri	30	punct	_	SpaceAfter=No

# doc_id = 491
# sent_id = 1
# text = We study the monoidal closed category of symmetric multicategories, especially in relation with its cartesian structure and with sequential multicategories (whose arrows are sequences of concurrent arrows in a given category).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	monoidal	monoidal	NOUN	NN	Number=Sing	5	nsubj	_	_
5	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	2	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	symmetric	symmetric	ADJ	JJ	Degree=Pos	9	amod	_	_
9	multicategories	multicategorie	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
11	especially	especially	ADV	RB	_	12	advmod	_	_
12	in	in	ADP	IN	_	6	prep	_	_
13	relation	relation	NOUN	NN	Number=Sing	12	pobj	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	17	poss	_	_
16	cartesian	cartesian	ADJ	JJ	Degree=Pos	17	amod	_	_
17	structure	structure	NOUN	NN	Number=Sing	14	pobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
19	with	with	ADP	IN	_	12	conj	_	_
20	sequential	sequential	ADJ	JJ	Degree=Pos	21	amod	_	_
21	multicategories	multicategorie	NOUN	NNS	Number=Plur	19	pobj	_	_
22	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	21	punct	_	SpaceAfter=No
23	whose	whose	DET	WP$	Poss=Yes	24	poss	_	_
24	arrows	arrow	NOUN	NNS	Number=Plur	25	nsubj	_	_
25	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	21	relcl	_	_
26	sequences	sequence	NOUN	NNS	Number=Plur	25	attr	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	concurrent	concurrent	ADJ	JJ	Degree=Pos	29	amod	_	_
29	arrows	arrow	NOUN	NNS	Number=Plur	27	pobj	_	_
30	in	in	ADP	IN	_	25	prep	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
32	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	amod	_	_
33	category	category	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
34	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	2	punct	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Then we consider cartesian multicategories in a similar perspective and develop some peculiar items such as algebraic products.
1	Then	then	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	cartesian	cartesian	ADJ	JJ	Degree=Pos	5	amod	_	_
5	multicategories	multicategorie	NOUN	NNS	Number=Plur	3	dobj	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	similar	similar	ADJ	JJ	Degree=Pos	9	amod	_	_
9	perspective	perspective	NOUN	NN	Number=Sing	6	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
11	develop	develop	VERB	VB	VerbForm=Inf	3	conj	_	_
12	some	some	DET	DT	_	14	det	_	_
13	peculiar	peculiar	ADJ	JJ	Degree=Pos	14	amod	_	_
14	items	item	NOUN	NNS	Number=Plur	11	dobj	_	_
15	such	such	ADJ	JJ	Degree=Pos	16	amod	_	_
16	as	as	ADP	IN	_	14	prep	_	_
17	algebraic	algebraic	ADJ	JJ	Degree=Pos	18	amod	_	_
18	products	product	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Several classical facts arise as a consequence of this analysis when some of the multicategories involved are representable.
1	Several	several	ADJ	JJ	Degree=Pos	3	amod	_	_
2	classical	classical	ADJ	JJ	Degree=Pos	3	amod	_	_
3	facts	fact	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	arise	arise	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	as	as	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	consequence	consequence	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	this	this	DET	DT	Number=Sing|PronType=Dem	10	det	_	_
10	analysis	analysis	NOUN	NN	Number=Sing	8	pobj	_	_
11	when	when	SCONJ	WRB	_	17	advmod	_	_
12	some	some	PRON	DT	_	17	nsubj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	multicategories	multicategorie	NOUN	NNS	Number=Plur	13	pobj	_	_
16	involved	involve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
17	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	advcl	_	_
18	representable	representable	ADJ	JJ	Degree=Pos	17	acomp	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 492
# sent_id = 1
# text = In a paper of 1974, Brian Day employed a notion of factorization system in the context of enriched category theory, replacing the usual diagonal lifting property with a corresponding criterion phrased in terms of hom - objects.
1	In	in	ADP	IN	_	9	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	1974	1974	NUM	CD	NumType=Card	4	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
7	Brian	Brian	PROPN	NNP	Number=Sing	8	compound	_	_
8	Day	Day	PROPN	NNP	Number=Sing	9	nsubj	_	_
9	employed	employ	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	notion	notion	NOUN	NN	Number=Sing	9	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	factorization	factorization	NOUN	NN	Number=Sing	14	compound	_	_
14	system	system	NOUN	NN	Number=Sing	12	pobj	_	_
15	in	in	ADP	IN	_	9	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	context	context	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	amod	_	_
20	category	category	NOUN	NN	Number=Sing	21	compound	_	_
21	theory	theory	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
23	replacing	replace	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	advcl	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
25	usual	usual	ADJ	JJ	Degree=Pos	28	amod	_	_
26	diagonal	diagonal	ADJ	JJ	Degree=Pos	28	amod	_	_
27	lifting	lifting	NOUN	NN	Number=Sing	28	compound	_	_
28	property	property	NOUN	NN	Number=Sing	23	dobj	_	_
29	with	with	ADP	IN	_	23	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
31	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	32	amod	_	_
32	criterion	criterion	NOUN	NN	Number=Sing	29	pobj	_	_
33	phrased	phrase	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	acl	_	_
34	in	in	ADP	IN	_	33	prep	_	_
35	terms	term	NOUN	NNS	Number=Plur	34	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	hom	hom	NOUN	NN	Number=Sing	39	amod	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	objects	object	NOUN	NNS	Number=Plur	36	pobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 2
# text = We set forth the basic theory of such enriched factorization systems.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	set	set	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
3	forth	forth	ADP	RP	_	2	prt	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	basic	basic	ADJ	JJ	Degree=Pos	6	amod	_	_
6	theory	theory	NOUN	NN	Number=Sing	2	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	such	such	ADJ	JJ	Degree=Pos	11	amod	_	_
9	enriched	enriched	ADJ	JJ	Degree=Pos	11	amod	_	_
10	factorization	factorization	NOUN	NN	Number=Sing	11	compound	_	_
11	systems	system	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = In particular, we establish stability properties for enriched prefactorization systems, we examine the relation of enriched to ordinary factorization systems, and we provide general results for obtaining enriched factorizations by means of wide (co)intersections.
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	establish	establish	VERB	VBP	Tense=Pres|VerbForm=Fin	14	ccomp	_	_
6	stability	stability	NOUN	NN	Number=Sing	7	compound	_	_
7	properties	property	NOUN	NNS	Number=Plur	5	dobj	_	_
8	for	for	ADP	IN	_	5	prep	_	_
9	enriched	enriched	ADJ	JJ	Degree=Pos	11	amod	_	_
10	prefactorization	prefactorization	NOUN	NN	Number=Sing	11	compound	_	_
11	systems	system	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	examine	examine	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	relation	relation	NOUN	NN	Number=Sing	14	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	pobj	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	ordinary	ordinary	ADJ	JJ	Degree=Pos	22	amod	_	_
21	factorization	factorization	NOUN	NN	Number=Sing	22	compound	_	_
22	systems	system	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
25	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	26	nsubj	_	_
26	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	14	conj	_	_
27	general	general	ADJ	JJ	Degree=Pos	28	amod	_	_
28	results	result	NOUN	NNS	Number=Plur	26	dobj	_	_
29	for	for	ADP	IN	_	28	prep	_	_
30	obtaining	obtain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	29	pcomp	_	_
31	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	amod	_	_
32	factorizations	factorization	NOUN	NNS	Number=Plur	30	dobj	_	_
33	by	by	ADP	IN	_	30	prep	_	_
34	means	mean	NOUN	NNS	Number=Plur	33	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	wide	wide	ADJ	JJ	Degree=Pos	38	amod	_	_
37	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	38	punct	_	SpaceAfter=No
38	co)intersections	co)intersection	NOUN	NNS	Number=Plur	35	pobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	26	punct	_	SpaceAfter=No

# sent_id = 4
# text = As a special case, we prove results on the existence of enriched factorization systems involving enriched strong monomorphisms or strong epimorphisms.
1	As	as	ADP	IN	_	7	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	special	special	ADJ	JJ	Degree=Pos	4	amod	_	_
4	case	case	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	results	result	NOUN	NNS	Number=Plur	7	dobj	_	_
9	on	on	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	existence	existence	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
14	factorization	factorization	NOUN	NN	Number=Sing	15	compound	_	_
15	systems	system	NOUN	NNS	Number=Plur	12	pobj	_	_
16	involving	involve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	acl	_	_
17	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
18	strong	strong	ADJ	JJ	Degree=Pos	19	amod	_	_
19	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	16	dobj	_	_
20	or	or	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	strong	strong	ADJ	JJ	Degree=Pos	22	amod	_	_
22	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	19	conj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 493
# sent_id = 1
# text = Any functor from the category of $ C* $ - algebras to the category of locales that assigns to each commutative $ C* $ - algebra its Gelfand spectrum must be trivial on algebras of $ n $ - by - $ n $ matrices for $ n geq 3 $ .
1	Any	any	DET	DT	_	2	det	_	_
2	functor	functor	NOUN	NN	Number=Sing	27	nsubj	_	_
3	from	from	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	$ C* $	$ c* $	SYM	$	_	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	algebras	algebra	NOUN	NNS	Number=Plur	6	pobj	_	_
10	to	to	ADP	IN	_	5	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	locales	locale	NOUN	NNS	Number=Plur	13	pobj	_	_
15	that	that	PRON	WDT	PronType=Rel	16	nsubj	_	_
16	assigns	assign	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	each	each	DET	DT	_	19	det	_	_
19	commutative	commutative	ADJ	JJ	Degree=Pos	17	pobj	_	_
20	$ C* $	$ c* $	SYM	$	_	22	nummod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	algebra	algebra	NOUN	NN	Number=Sing	2	appos	_	_
23	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	25	poss	_	_
24	Gelfand	Gelfand	PROPN	NNP	Number=Sing	25	compound	_	_
25	spectrum	spectrum	NOUN	NN	Number=Sing	2	appos	_	_
26	must	must	AUX	MD	VerbForm=Fin	27	aux	_	_
27	be	be	AUX	VB	VerbForm=Inf	0	ROOT	_	_
28	trivial	trivial	ADJ	JJ	Degree=Pos	27	acomp	_	_
29	on	on	ADP	IN	_	28	prep	_	_
30	algebras	algebra	NOUN	NNS	Number=Plur	29	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	$ n $	$ n $	SYM	$	_	37	nmod	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
34	by	by	ADP	IN	_	32	prep	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
36	$ n $	$ n $	SYM	$	_	34	pobj	_	_
37	matrices	matrix	NOUN	NNS	Number=Plur	31	pobj	_	_
38	for	for	ADP	IN	_	37	prep	_	_
39	$ n geq 3 $	$ n geq 3 $	SYM	$	_	38	pobj	_	_
40	.	.	PUNCT	.	PunctType=Peri	27	punct	_	SpaceAfter=No

# sent_id = 2
# text = This obstruction also applies to other spectra such as those named after Zariski, Stone, and Pierce.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	obstruction	obstruction	NOUN	NN	Number=Sing	4	nsubj	_	_
3	also	also	ADV	RB	_	4	advmod	_	_
4	applies	apply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	other	other	ADJ	JJ	Degree=Pos	7	amod	_	_
7	spectra	spectra	NOUN	NN	Number=Sing	5	pobj	_	_
8	such	such	ADJ	JJ	Degree=Pos	9	amod	_	_
9	as	as	ADP	IN	_	7	prep	_	_
10	those	those	PRON	DT	Number=Plur|PronType=Dem	9	pobj	_	_
11	named	name	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acl	_	_
12	after	after	ADP	IN	_	11	prep	_	_
13	Zariski	Zariski	PROPN	NNP	Number=Sing	12	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	Stone	Stone	PROPN	NNP	Number=Sing	13	conj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
18	Pierce	Pierce	PROPN	NNP	Number=Sing	15	conj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = We extend these no - go results to functors with values in (ringed) topological spaces, (ringed) toposes, schemes, and quantales.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	extend	extend	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	these	these	DET	DT	Number=Plur|PronType=Dem	7	det	_	_
4	no	no	DET	DT	_	6	det	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	go	go	VERB	VB	VerbForm=Inf	7	compound	_	_
7	results	result	NOUN	NNS	Number=Plur	2	dobj	_	_
8	to	to	ADP	IN	_	2	prep	_	_
9	functors	functor	NOUN	NNS	Number=Plur	8	pobj	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	values	value	NOUN	NNS	Number=Plur	10	pobj	_	_
12	in	in	ADP	IN	_	2	prep	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	17	punct	_	SpaceAfter=No
14	ringed	ringed	ADJ	JJ	Degree=Pos	17	amod	_	SpaceAfter=No
15	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	17	punct	_	_
16	topological	topological	ADJ	JJ	Degree=Pos	17	amod	_	_
17	spaces	space	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	17	punct	_	SpaceAfter=No
20	ringed	ring	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	SpaceAfter=No
21	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	20	punct	_	_
22	toposes	topos	NOUN	NNS	Number=Plur	17	conj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	schemes	scheme	NOUN	NNS	Number=Plur	22	conj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
27	quantales	quantale	NOUN	NNS	Number=Plur	24	conj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = The possibility of spectra in other categories is discussed.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	possibility	possibility	NOUN	NN	Number=Sing	9	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	spectra	spectra	PROPN	NNP	Number=Sing	3	pobj	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	other	other	ADJ	JJ	Degree=Pos	7	amod	_	_
7	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	discussed	discuss	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 494
# sent_id = 1
# text = We introduce a category that represents varying risk as well as ambiguity.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	category	category	NOUN	NN	Number=Sing	2	dobj	_	_
5	that	that	PRON	WDT	PronType=Rel	6	nsubj	_	_
6	represents	represent	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	relcl	_	_
7	varying	vary	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	amod	_	_
8	risk	risk	NOUN	NN	Number=Sing	6	dobj	_	_
9	as	as	ADV	RB	_	11	advmod	_	_
10	well	well	ADV	RB	Degree=Pos	11	advmod	_	_
11	as	as	ADP	IN	_	8	cc	_	_
12	ambiguity	ambiguity	NOUN	NN	Number=Sing	8	conj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We give a generalized conditional expectation as a presheaf for this category, which not only works as a traditional conditional expectation given a $ sigma $ - field but also is compatible with change of measure.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
4	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	amod	_	_
5	conditional	conditional	ADJ	JJ	Degree=Pos	6	amod	_	_
6	expectation	expectation	NOUN	NN	Number=Sing	2	dobj	_	_
7	as	as	ADP	IN	_	2	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	presheaf	presheaf	NOUN	NN	Number=Sing	7	pobj	_	_
10	for	for	ADP	IN	_	9	prep	_	_
11	this	this	DET	DT	Number=Sing|PronType=Dem	12	det	_	_
12	category	category	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	which	which	PRON	WDT	_	17	nsubj	_	_
15	not	not	PART	RB	Polarity=Neg	17	preconj	_	_
16	only	only	ADV	RB	_	15	advmod	_	_
17	works	work	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	relcl	_	_
18	as	as	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
20	traditional	traditional	ADJ	JJ	Degree=Pos	22	amod	_	_
21	conditional	conditional	ADJ	JJ	Degree=Pos	22	amod	_	_
22	expectation	expectation	NOUN	NN	Number=Sing	18	pobj	_	_
23	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
25	$ sigma $	$ sigma $	SYM	$	_	27	nmod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	field	field	NOUN	NN	Number=Sing	23	pobj	_	_
28	but	but	CCONJ	CC	ConjType=Cmp	17	cc	_	_
29	also	also	ADV	RB	_	30	advmod	_	_
30	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	conj	_	_
31	compatible	compatible	ADJ	JJ	Degree=Pos	30	acomp	_	_
32	with	with	ADP	IN	_	31	prep	_	_
33	change	change	NOUN	NN	Number=Sing	32	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	measure	measure	NOUN	NN	Number=Sing	34	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Then, we reformulate dynamic monetary value measures as a presheaf for the category.
1	Then	then	ADV	RB	PronType=Dem	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	reformulate	reformulate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	dynamic	dynamic	ADJ	JJ	Degree=Pos	8	amod	_	_
6	monetary	monetary	ADJ	JJ	Degree=Pos	7	amod	_	_
7	value	value	NOUN	NN	Number=Sing	8	compound	_	_
8	measures	measure	NOUN	NNS	Number=Plur	4	dobj	_	_
9	as	as	ADP	IN	_	4	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	presheaf	presheaf	NOUN	NN	Number=Sing	9	pobj	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	category	category	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show how some axioms of dynamic monetary value measures in the classical setting are deduced as theorems in the new formulation, which is evidence that the axioms are correct.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	how	how	SCONJ	WRB	_	16	advmod	_	_
4	some	some	DET	DT	_	5	det	_	_
5	axioms	axiom	NOUN	NNS	Number=Plur	16	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	dynamic	dynamic	ADJ	JJ	Degree=Pos	10	amod	_	_
8	monetary	monetary	ADJ	JJ	Degree=Pos	9	amod	_	_
9	value	value	NOUN	NN	Number=Sing	10	compound	_	_
10	measures	measure	NOUN	NNS	Number=Plur	6	pobj	_	_
11	in	in	ADP	IN	_	5	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	classical	classical	ADJ	JJ	Degree=Pos	14	amod	_	_
14	setting	setting	NOUN	NN	Number=Sing	11	pobj	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	16	auxpass	_	_
16	deduced	deduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
17	as	as	ADP	IN	_	16	prep	_	_
18	theorems	theorem	NOUN	NNS	Number=Plur	17	pobj	_	_
19	in	in	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	new	new	ADJ	JJ	Degree=Pos	22	amod	_	_
22	formulation	formulation	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	which	which	PRON	WDT	_	25	nsubj	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	relcl	_	_
26	evidence	evidence	NOUN	NN	Number=Sing	25	attr	_	_
27	that	that	SCONJ	IN	_	30	mark	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	axioms	axiom	NOUN	NNS	Number=Plur	30	nsubj	_	_
30	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	26	acl	_	_
31	correct	correct	ADJ	JJ	Degree=Pos	30	acomp	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = Finally, we point out the possibility of giving a theoretical criteria with which we can pick up appropriate sets of axioms required for monetary value measures to be good, using a topology - as - axioms paradigm.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	point	point	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	out	out	ADP	RP	_	4	prt	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	possibility	possibility	NOUN	NN	Number=Sing	4	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	giving	give	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	pcomp	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	theoretical	theoretical	ADJ	JJ	Degree=Pos	12	amod	_	_
12	criteria	criterion	NOUN	NNS	Number=Plur	9	dobj	_	_
13	with	with	ADP	IN	_	17	prep	_	_
14	which	which	PRON	WDT	_	13	pobj	_	_
15	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	17	nsubj	_	_
16	can	can	AUX	MD	VerbForm=Fin	17	aux	_	_
17	pick	pick	VERB	VB	VerbForm=Inf	12	relcl	_	_
18	up	up	ADP	RP	_	17	prt	_	_
19	appropriate	appropriate	ADJ	JJ	Degree=Pos	20	amod	_	_
20	sets	set	NOUN	NNS	Number=Plur	17	dobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	axioms	axiom	NOUN	NNS	Number=Plur	21	pobj	_	_
23	required	require	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	acl	_	_
24	for	for	ADP	IN	_	23	prep	_	_
25	monetary	monetary	ADJ	JJ	Degree=Pos	26	amod	_	_
26	value	value	NOUN	NN	Number=Sing	27	compound	_	_
27	measures	measure	NOUN	NNS	Number=Plur	24	pobj	_	_
28	to	to	PART	TO	_	29	aux	_	_
29	be	be	AUX	VB	VerbForm=Inf	20	relcl	_	_
30	good	good	ADJ	JJ	Degree=Pos	29	acomp	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
32	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	advcl	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
34	topology	topology	NOUN	NN	Number=Sing	39	nmod	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
36	as	as	ADP	IN	_	34	prep	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	36	punct	_	_
38	axioms	axiom	NOUN	NNS	Number=Plur	36	pobj	_	_
39	paradigm	paradigm	NOUN	NN	Number=Sing	32	dobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 495
# sent_id = 1
# text = The coordinate projective line over a field is seen as a groupoid with a further `projection' structure.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	coordinate	coordinate	NOUN	NN	Number=Sing	4	nmod	_	_
3	projective	projective	ADJ	JJ	Degree=Pos	4	amod	_	_
4	line	line	NOUN	NN	Number=Sing	9	nsubjpass	_	_
5	over	over	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	field	field	NOUN	NN	Number=Sing	5	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	as	as	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	groupoid	groupoid	NOUN	NN	Number=Sing	10	pobj	_	_
13	with	with	ADP	IN	_	9	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
15	further	further	ADJ	JJ	Degree=Pos	19	amod	_	_
16	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	19	punct	_	SpaceAfter=No
17	projection	projection	NOUN	NN	Number=Sing	19	nmod	_	SpaceAfter=No
18	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	17	case	_	_
19	structure	structure	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 2
# text = We investigate conversely to what extent such an, abstractly given, groupoid may be coordinatized by a suitable field constructed out of the geometry.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	conversely	conversely	ADV	RB	_	2	advmod	_	_
4	to	to	ADP	IN	_	16	prep	_	_
5	what	what	DET	WDT	_	6	det	_	_
6	extent	extent	NOUN	NN	Number=Sing	4	pcomp	_	_
7	such	such	DET	PDT	_	8	amod	_	_
8	an	an	PRON	DT	Definite=Ind|PronType=Art	6	dobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
10	abstractly	abstractly	ADV	RB	_	11	advmod	_	_
11	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	advcl	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
13	groupoid	groupoid	NOUN	NN	Number=Sing	16	nsubjpass	_	_
14	may	may	AUX	MD	VerbForm=Fin	16	aux	_	_
15	be	be	AUX	VB	VerbForm=Inf	16	auxpass	_	_
16	coordinatized	coordinatize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	advcl	_	_
17	by	by	ADP	IN	_	16	agent	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	suitable	suitable	ADJ	JJ	Degree=Pos	20	amod	_	_
20	field	field	NOUN	NN	Number=Sing	17	pobj	_	_
21	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	acl	_	_
22	out	out	ADP	IN	_	21	prep	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	geometry	geometry	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 496
# sent_id = 1
# text = We give a new characterization of relative entropy, also known as the Kullback - Leibler divergence.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	new	new	ADJ	JJ	Degree=Pos	5	amod	_	_
5	characterization	characterization	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	relative	relative	ADJ	JJ	Degree=Pos	8	amod	_	_
8	entropy	entropy	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
10	also	also	ADV	RB	_	11	advmod	_	_
11	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	advcl	_	_
12	as	as	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
14	Kullback	Kullback	PROPN	NNP	Number=Sing	16	compound	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	Leibler	Leibler	PROPN	NNP	Number=Sing	17	compound	_	_
17	divergence	divergence	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We use a number of interesting categories related to probability theory.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	number	number	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	interesting	interesting	ADJ	JJ	Degree=Pos	7	amod	_	_
7	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
8	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	acl	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	probability	probability	NOUN	NN	Number=Sing	11	compound	_	_
11	theory	theory	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = In particular, we consider a category FinStat where an object is a finite set equipped with a probability distribution, while a morphism is a measure - preserving function $ f maps X to Y $ together with a stochastic right inverse $ s maps Y to X $ .
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	category	category	NOUN	NN	Number=Sing	8	nsubj	_	_
8	FinStat	FinStat	PROPN	NNP	Number=Sing	5	ccomp	_	_
9	where	where	SCONJ	WRB	_	12	advmod	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	object	object	NOUN	NN	Number=Sing	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	relcl	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	finite	finite	NOUN	NN	Number=Sing	15	amod	_	_
15	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	attr	_	_
16	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
17	with	with	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	probability	probability	NOUN	NN	Number=Sing	20	compound	_	_
20	distribution	distribution	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
22	while	while	SCONJ	IN	_	25	mark	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	morphism	morphism	NOUN	NN	Number=Sing	25	nsubj	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	advcl	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
27	measure	measure	NOUN	NN	Number=Sing	29	npadvmod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	30	amod	_	_
30	function	function	NOUN	NN	Number=Sing	25	attr	_	_
31	$ f maps X to Y $	$ f maps x to y $	SYM	$	_	32	nmod	_	_
32	together	together	ADV	RB	_	25	advmod	_	_
33	with	with	ADP	IN	_	25	prep	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
35	stochastic	stochastic	ADJ	JJ	Degree=Pos	37	amod	_	_
36	right	right	ADV	RB	_	37	advmod	_	_
37	inverse	inverse	NOUN	NN	Number=Sing	33	pobj	_	_
38	$ s maps Y to X $	$ s maps y to x $	SYM	$	_	33	pobj	_	_
39	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = The function $ f $ can be thought of as a measurement process, while $ s $ provides a hypothesis about the state of the measured system given the result of a measurement.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	function	function	NOUN	NN	Number=Sing	6	nsubjpass	_	_
3	$ f $	$ f $	SYM	$	_	2	appos	_	_
4	can	can	AUX	MD	VerbForm=Fin	6	aux	_	_
5	be	be	AUX	VB	VerbForm=Inf	6	auxpass	_	_
6	thought	think	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	as	as	ADP	IN	_	6	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	measurement	measurement	NOUN	NN	Number=Sing	11	compound	_	_
11	process	process	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
13	while	while	SCONJ	IN	_	15	mark	_	_
14	$ s $	$ s $	SYM	$	_	15	nsubj	_	_
15	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	advcl	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	hypothesis	hypothesis	NOUN	NN	Number=Sing	15	dobj	_	_
18	about	about	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	state	state	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	measured	measure	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
24	system	system	NOUN	NN	Number=Sing	21	pobj	_	_
25	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	result	result	NOUN	NN	Number=Sing	25	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
30	measurement	measurement	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = Given this data we can define the entropy of the probability distribution on $ X $ relative to the `prior' given by pushing the probability distribution on $ Y $ forwards along $ s $ .
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	data	datum	NOUN	NNS	Number=Plur	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
5	can	can	AUX	MD	VerbForm=Fin	6	aux	_	_
6	define	define	VERB	VB	VerbForm=Inf	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	entropy	entropy	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	probability	probability	NOUN	NN	Number=Sing	12	compound	_	_
12	distribution	distribution	NOUN	NN	Number=Sing	9	pobj	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	$ X $	$ x $	SYM	$	_	13	pobj	_	_
15	relative	relative	ADJ	JJ	Degree=Pos	13	pobj	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	19	punct	_	SpaceAfter=No
19	prior	prior	ADV	RB	_	16	pobj	_	SpaceAfter=No
20	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	19	punct	_	_
21	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	acl	_	_
22	by	by	ADP	IN	_	21	agent	_	_
23	pushing	push	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	pcomp	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	probability	probability	NOUN	NN	Number=Sing	26	compound	_	_
26	distribution	distribution	NOUN	NN	Number=Sing	23	dobj	_	_
27	on	on	ADP	IN	_	23	prep	_	_
28	$ Y $	$ y $	SYM	$	_	27	pobj	_	_
29	forwards	forward	NOUN	NNS	Number=Plur	23	advmod	_	_
30	along	along	ADP	IN	_	23	prep	_	_
31	$ s $	$ s $	SYM	$	_	30	pobj	_	_
32	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 6
# text = We say that $ s $ is `optimal' if these distributions agree.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	say	say	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	$ s $	$ s $	SYM	$	_	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	7	punct	_	SpaceAfter=No
7	optimal	optimal	ADJ	JJ	Degree=Pos	5	acomp	_	SpaceAfter=No
8	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	5	punct	_	_
9	if	if	SCONJ	IN	_	12	mark	_	_
10	these	these	DET	DT	Number=Plur|PronType=Dem	11	det	_	_
11	distributions	distribution	NOUN	NNS	Number=Plur	12	nsubj	_	_
12	agree	agree	VERB	VBP	Tense=Pres|VerbForm=Fin	5	advcl	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = We show that any convex linear, lower semicontinuous functor from $ FinStat $ to the additive monoid $ [0, infty] $ which vanishes when $ s $ is optimal must be a scalar multiple of this relative entropy.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	10	mark	_	_
4	any	any	DET	DT	_	6	det	_	_
5	convex	convex	ADJ	JJ	Degree=Pos	6	amod	_	_
6	linear	linear	NOUN	NN	Number=Sing	10	nsubj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
8	lower	low	ADJ	JJR	Degree=Cmp	10	amod	_	_
9	semicontinuous	semicontinuous	ADJ	JJ	Degree=Pos	10	amod	_	_
10	functor	functor	NOUN	NN	Number=Sing	2	ccomp	_	_
11	from	from	ADP	IN	_	10	prep	_	_
12	$ FinStat $	$ finstat $	SYM	$	_	11	pobj	_	_
13	to	to	ADP	IN	_	11	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	additive	additive	ADJ	JJ	Degree=Pos	16	amod	_	_
16	monoid	monoid	NOUN	NN	Number=Sing	13	pobj	_	_
17	$ [0, infty] $	$ [0, infty] $	PROPN	NNP	Number=Sing	10	prep	_	_
18	which	which	DET	WDT	_	19	det	_	_
19	vanishes	vanishe	NOUN	NNS	Number=Plur	10	relcl	_	_
20	when	when	SCONJ	WRB	_	21	advmod	_	_
21	$ s $	$ s $	SYM	$	_	22	nsubj	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
23	optimal	optimal	ADJ	JJ	Degree=Pos	22	acomp	_	_
24	must	must	AUX	MD	VerbForm=Fin	25	aux	_	_
25	be	be	AUX	VB	VerbForm=Inf	2	ccomp	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
27	scalar	scalar	ADJ	JJ	Degree=Pos	28	amod	_	_
28	multiple	multiple	NOUN	NN	Number=Sing	25	attr	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	this	this	DET	DT	Number=Sing|PronType=Dem	32	det	_	_
31	relative	relative	ADJ	JJ	Degree=Pos	32	amod	_	_
32	entropy	entropy	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 8
# text = Our proof is independent of all earlier characterizations, but inspired by the work of Petz.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	proof	proof	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	independent	independent	ADJ	JJ	Degree=Pos	3	acomp	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	all	all	DET	DT	_	8	det	_	_
7	earlier	early	ADJ	JJR	Degree=Cmp	8	amod	_	_
8	characterizations	characterization	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
10	but	but	CCONJ	CC	ConjType=Cmp	3	cc	_	_
11	inspired	inspire	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	conj	_	_
12	by	by	ADP	IN	_	11	agent	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	work	work	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	Petz	Petz	PROPN	NNP	Number=Sing	15	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 497
# sent_id = 1
# text = A notion of central importance in categorical topology is that of topological functor.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	notion	notion	NOUN	NN	Number=Sing	9	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	central	central	ADJ	JJ	Degree=Pos	5	amod	_	_
5	importance	importance	NOUN	NN	Number=Sing	3	pobj	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	categorical	categorical	ADJ	JJ	Degree=Pos	8	amod	_	_
8	topology	topology	NOUN	NN	Number=Sing	6	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	that	that	PRON	DT	Number=Sing|PronType=Dem	9	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	topological	topological	ADJ	JJ	Degree=Pos	13	amod	_	_
13	functor	functor	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 2
# text = A faithful functor $ cal E to cal B $ is called topological if it admits cartesian liftings of all (possibly large) families of arrows; the basic example is the forgetful functor $ Top to Set $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	faithful	faithful	ADJ	JJ	Degree=Pos	3	amod	_	_
3	functor	functor	NOUN	NN	Number=Sing	6	nsubjpass	_	_
4	$ cal E to cal B $	$ cal e to cal b $	SYM	$	_	3	appos	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	ccomp	_	_
7	topological	topological	ADJ	JJ	Degree=Pos	6	oprd	_	_
8	if	if	SCONJ	IN	_	10	mark	_	_
9	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	10	nsubj	_	_
10	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	advcl	_	_
11	cartesian	cartesian	ADJ	JJ	Degree=Pos	12	amod	_	_
12	liftings	lifting	NOUN	NNS	Number=Plur	10	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	all	all	DET	DT	_	19	det	_	_
15	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	19	punct	_	SpaceAfter=No
16	possibly	possibly	ADV	RB	_	17	advmod	_	_
17	large	large	ADJ	JJ	Degree=Pos	19	amod	_	SpaceAfter=No
18	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	19	punct	_	_
19	families	family	NOUN	NNS	Number=Plur	13	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	arrows	arrow	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
22	;	;	PUNCT	:	_	26	punct	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	basic	basic	ADJ	JJ	Degree=Pos	25	amod	_	_
25	example	example	NOUN	NN	Number=Sing	26	nsubj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	forgetful	forgetful	ADJ	JJ	Degree=Pos	29	amod	_	_
29	functor	functor	NOUN	NN	Number=Sing	26	attr	_	_
30	$ Top to Set $	$ top to set $	SYM	$	_	29	appos	_	_
31	.	.	PUNCT	.	PunctType=Peri	26	punct	_	SpaceAfter=No

# sent_id = 3
# text = A topological functor $ cal E to 1 $ is the same thing as a (large) complete preorder, and the general topological functor $ cal E to cal B $ is intuitively thought of as a "complete preorder relative to $ cal B $ ".
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	topological	topological	ADJ	JJ	Degree=Pos	3	amod	_	_
3	functor	functor	NOUN	NN	Number=Sing	5	nsubj	_	_
4	$ cal E to 1 $	$ cal e to 1 $	SYM	$	_	3	appos	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	same	same	ADJ	JJ	Degree=Pos	8	amod	_	_
8	thing	thing	NOUN	NN	Number=Sing	5	attr	_	_
9	as	as	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
11	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	15	punct	_	SpaceAfter=No
12	large	large	ADJ	JJ	Degree=Pos	15	amod	_	SpaceAfter=No
13	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	15	punct	_	_
14	complete	complete	ADJ	JJ	Degree=Pos	15	amod	_	_
15	preorder	preorder	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
19	general	general	ADJ	JJ	Degree=Pos	21	amod	_	_
20	topological	topological	ADJ	JJ	Degree=Pos	21	amod	_	_
21	functor	functor	NOUN	NN	Number=Sing	25	nsubjpass	_	_
22	$ cal E to cal B $	$ cal e to cal b $	SYM	$	_	21	appos	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	auxpass	_	_
24	intuitively	intuitively	ADV	RB	_	25	advmod	_	_
25	thought	think	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	conj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	as	as	ADP	IN	_	25	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
29	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	31	punct	_	SpaceAfter=No
30	complete	complete	ADJ	JJ	Degree=Pos	31	amod	_	_
31	preorder	preorder	NOUN	NN	Number=Sing	27	pobj	_	_
32	relative	relative	ADJ	JJ	Degree=Pos	31	amod	_	_
33	to	to	ADP	IN	_	32	prep	_	_
34	$ cal B $	$ cal b $	SYM	$	_	33	pobj	_	_
35	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	25	punct	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = We make this intuition precise by considering an enrichment base $ cal Q_cal B $ such that $ cal Q_cal B $ - enriched categories are faithful functors into $ cal B $ , and show that, in this context, a faithful functor is topological if and only if it is total (or totally cocomplete) in the sense of Street - Walters.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	make	make	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	intuition	intuition	NOUN	NN	Number=Sing	5	nsubj	_	_
5	precise	precise	ADJ	JJ	Degree=Pos	2	ccomp	_	_
6	by	by	ADP	IN	_	2	prep	_	_
7	considering	consider	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	pcomp	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	enrichment	enrichment	NOUN	NN	Number=Sing	10	compound	_	_
10	base	base	NOUN	NN	Number=Sing	7	dobj	_	_
11	$ cal Q_cal B $	$ cal q_cal b $	SYM	$	_	10	nmod	_	_
12	such	such	ADJ	JJ	Degree=Pos	17	amod	_	_
13	that	that	SCONJ	IN	_	17	det	_	_
14	$ cal Q_cal B $	$ cal q_cal b $	SYM	$	_	16	advmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	categories	category	NOUN	NNS	Number=Plur	18	nsubj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
19	faithful	faithful	ADJ	JJ	Degree=Pos	20	amod	_	_
20	functors	functor	NOUN	NNS	Number=Plur	18	attr	_	_
21	into	into	ADP	IN	_	18	prep	_	_
22	$ cal B $	$ cal b $	SYM	$	_	21	pobj	_	_
23	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
25	show	show	VERB	VB	VerbForm=Inf	18	conj	_	_
26	that	that	SCONJ	IN	_	35	mark	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
28	in	in	ADP	IN	_	35	prep	_	_
29	this	this	DET	DT	Number=Sing|PronType=Dem	30	det	_	_
30	context	context	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
33	faithful	faithful	ADJ	JJ	Degree=Pos	34	amod	_	_
34	functor	functor	NOUN	NN	Number=Sing	35	nsubj	_	_
35	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	ccomp	_	_
36	topological	topological	ADJ	JJ	Degree=Pos	35	acomp	_	_
37	if	if	SCONJ	IN	_	42	mark	_	_
38	and	and	CCONJ	CC	ConjType=Cmp	42	cc	_	_
39	only	only	ADV	RB	_	42	advmod	_	_
40	if	if	SCONJ	IN	_	42	mark	_	_
41	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	42	nsubj	_	_
42	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	35	advcl	_	_
43	total	total	ADJ	JJ	Degree=Pos	42	acomp	_	_
44	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	43	punct	_	SpaceAfter=No
45	or	or	CCONJ	CC	ConjType=Cmp	43	cc	_	_
46	totally	totally	ADV	RB	_	47	advmod	_	_
47	cocomplete	cocomplete	ADJ	JJ	Degree=Pos	43	conj	_	SpaceAfter=No
48	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	42	punct	_	_
49	in	in	ADP	IN	_	42	prep	_	_
50	the	the	DET	DT	Definite=Def|PronType=Art	51	det	_	_
51	sense	sense	NOUN	NN	Number=Sing	49	pobj	_	_
52	of	of	ADP	IN	_	51	prep	_	_
53	Street	Street	PROPN	NNP	Number=Sing	55	compound	_	_
54	-	-	PUNCT	HYPH	PunctType=Dash	55	punct	_	_
55	Walters	Walters	PROPN	NNP	Number=Sing	52	pobj	_	SpaceAfter=No
56	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = We also consider the MacNeille completion of a faithful functor to a topological one, first described by Herrlich, and show that it may be obtained as an instance of Isbell's generalised notion of MacNeille completion for enriched categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	MacNeille	MacNeille	PROPN	NNP	Number=Sing	6	compound	_	_
6	completion	completion	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	faithful	faithful	ADJ	JJ	Degree=Pos	10	amod	_	_
10	functor	functor	NOUN	NN	Number=Sing	7	pobj	_	_
11	to	to	ADP	IN	_	3	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	topological	topological	ADJ	JJ	Degree=Pos	14	amod	_	_
14	one	one	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
16	first	first	ADV	RB	_	17	advmod	_	_
17	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	advcl	_	_
18	by	by	ADP	IN	_	17	agent	_	_
19	Herrlich	Herrlich	PROPN	NNP	Number=Sing	18	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
22	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	17	conj	_	_
23	that	that	SCONJ	IN	_	27	mark	_	_
24	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	27	nsubjpass	_	_
25	may	may	AUX	MD	VerbForm=Fin	27	aux	_	_
26	be	be	AUX	VB	VerbForm=Inf	27	auxpass	_	_
27	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	ccomp	_	_
28	as	as	ADP	IN	_	27	prep	_	_
29	an	an	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
30	instance	instance	NOUN	NN	Number=Sing	28	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	Isbell	Isbell	PROPN	NNP	Number=Sing	35	poss	_	SpaceAfter=No
33	's	's	PART	POS	_	32	case	_	_
34	generalised	generalised	ADJ	JJ	Degree=Pos	35	amod	_	_
35	notion	notion	NOUN	NN	Number=Sing	31	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	MacNeille	MacNeille	PROPN	NNP	Number=Sing	38	compound	_	_
38	completion	completion	NOUN	NN	Number=Sing	36	pobj	_	_
39	for	for	ADP	IN	_	38	prep	_	_
40	enriched	enriched	ADJ	JJ	Degree=Pos	41	amod	_	_
41	categories	category	NOUN	NNS	Number=Plur	39	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 498
# sent_id = 1
# text = We discuss various concepts of $ infty $ - homotopies, as well as the relations between them (focussing on the Leibniz type).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	discuss	discuss	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	various	various	ADJ	JJ	Degree=Pos	4	amod	_	_
4	concepts	concept	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	$ infty $	$ infty $	SYM	$	_	8	compound	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	homotopies	homotopie	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
10	as	as	ADV	RB	_	12	advmod	_	_
11	well	well	ADV	RB	Degree=Pos	12	advmod	_	_
12	as	as	ADP	IN	_	4	cc	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	relations	relation	NOUN	NNS	Number=Plur	4	conj	_	_
15	between	between	ADP	IN	_	14	prep	_	_
16	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	15	pobj	_	_
17	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	18	punct	_	SpaceAfter=No
18	focussing	focusse	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	acl	_	_
19	on	on	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	Leibniz	Leibniz	PROPN	NNP	Number=Sing	22	compound	_	_
22	type	type	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	18	punct	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In particular $ infty $ - $ n $ - homotopies appear as the $ n $ - simplices of the nerve of a complete Lie $ {infty} $ - algebra.
1	In	in	ADP	IN	_	8	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	_
3	$ infty $	$ infty $	SYM	$	_	7	nmod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
5	$ n $	$ n $	SYM	$	_	7	nummod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	homotopies	homotopie	NOUN	NNS	Number=Plur	8	nsubj	_	_
8	appear	appear	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	as	as	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
11	$ n $	$ n $	SYM	$	_	13	quantmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	simplices	simplice	NOUN	NNS	Number=Plur	9	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	nerve	nerve	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	complete	complete	ADJ	JJ	Degree=Pos	20	amod	_	_
20	Lie	lie	NOUN	NN	Number=Sing	17	pobj	_	_
21	$ {infty} $	$ {infty} $	SYM	$	_	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	algebra	algebra	NOUN	NN	Number=Sing	20	appos	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 3
# text = In the nilpotent case, this nerve is known to be a Kan complex.
1	In	in	ADP	IN	_	9	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	nilpotent	nilpotent	ADJ	JJ	Degree=Pos	4	amod	_	_
4	case	case	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
6	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
7	nerve	nerve	NOUN	NN	Number=Sing	9	nsubjpass	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	be	be	AUX	VB	VerbForm=Inf	9	xcomp	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	Kan	Kan	PROPN	NNP	Number=Sing	14	compound	_	_
14	complex	complex	NOUN	NN	Number=Sing	11	attr	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 4
# text = We argue that there is a quasi - category of $ infty $ - algebras and show that for truncated $ infty $ - algebras, that is, categorified algebras, this $ infty $ - categorical structure projects to a strict 2 - categorical one.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	argue	argue	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	there	there	PRON	EX	_	5	expl	_	_
5	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	quasi	quasi	NOUN	NN	Number=Sing	5	attr	_	_
8	-	-	NOUN	NN	Number=Sing	5	attr	_	_
9	category	category	NOUN	NN	Number=Sing	5	attr	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	$ infty $	$ infty $	SYM	$	_	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	algebras	algebra	NOUN	NNS	Number=Plur	10	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
15	show	show	VERB	VB	VerbForm=Inf	5	conj	_	_
16	that	that	SCONJ	IN	_	34	mark	_	_
17	for	for	ADP	IN	_	34	prep	_	_
18	truncated	truncate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	amod	_	_
19	$ infty $	$ infty $	SYM	$	_	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	algebras	algebra	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	34	punct	_	_
23	that	that	ADV	RB	_	24	advmod	_	_
24	is	is	ADV	RB	_	27	advmod	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
26	categorified	categorifie	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	amod	_	_
27	algebras	algebra	NOUN	NNS	Number=Plur	34	dep	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	34	punct	_	_
29	this	this	DET	DT	Number=Sing|PronType=Dem	34	det	_	_
30	$ infty $	$ infty $	SYM	$	_	32	advmod	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	categorical	categorical	ADJ	JJ	Degree=Pos	34	amod	_	_
33	structure	structure	NOUN	NN	Number=Sing	34	compound	_	_
34	projects	project	NOUN	NNS	Number=Plur	15	dobj	_	_
35	to	to	ADP	IN	_	34	prep	_	_
36	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
37	strict	strict	ADJ	JJ	Degree=Pos	41	amod	_	_
38	2	2	NUM	CD	NumType=Card	40	nummod	_	_
39	-	-	PUNCT	HYPH	PunctType=Dash	40	punct	_	_
40	categorical	categorical	ADJ	JJ	Degree=Pos	41	amod	_	_
41	one	one	NUM	CD	NumType=Card	35	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = The paper contains a shortcut to $ (infty, 1) $ - categories, as well as a review of Getzler's proof of the Kan property.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	contains	contain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	shortcut	shortcut	NOUN	NN	Number=Sing	3	dobj	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	$ (infty, 1) $	$ (infty, 1) $	SYM	$	_	9	nmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
11	as	as	ADV	RB	_	13	advmod	_	_
12	well	well	ADV	RB	Degree=Pos	13	advmod	_	_
13	as	as	ADP	IN	_	5	cc	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	review	review	NOUN	NN	Number=Sing	5	conj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	Getzler	Getzler	PROPN	NNP	Number=Sing	19	poss	_	SpaceAfter=No
18	's	's	PART	POS	_	17	case	_	_
19	proof	proof	NOUN	NN	Number=Sing	16	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	Kan	Kan	PROPN	NNP	Number=Sing	23	compound	_	_
23	property	property	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = We make the latter concrete by applying it to the 2 - term $ infty $ - algebra case, thus recovering the concept of homotopy of Baez and Crans, as well as the corresponding composition rule cite{SS07}.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	make	make	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	latter	latter	ADJ	JJ	Degree=Pos	5	amod	_	_
5	concrete	concrete	NOUN	NN	Number=Sing	2	dobj	_	_
6	by	by	ADP	IN	_	2	prep	_	_
7	applying	apply	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	pcomp	_	_
8	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	7	dobj	_	_
9	to	to	ADP	IN	_	7	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	term	term	NOUN	NN	Number=Sing	17	nmod	_	_
14	$ infty $	$ infty $	SYM	$	_	16	compound	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	algebra	algebra	NOUN	NN	Number=Sing	17	compound	_	_
17	case	case	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
19	thus	thus	ADV	RB	_	20	advmod	_	_
20	recovering	recover	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	advcl	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	concept	concept	NOUN	NN	Number=Sing	20	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	homotopy	homotopy	NOUN	NN	Number=Sing	23	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	Baez	Baez	PROPN	NNP	Number=Sing	25	pobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	Crans	Crans	PROPN	NNPS	Number=Plur	26	conj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
30	as	as	ADV	RB	_	32	advmod	_	_
31	well	well	ADV	RB	Degree=Pos	32	advmod	_	_
32	as	as	ADP	IN	_	20	cc	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
34	corresponding	corresponding	ADJ	JJ	Degree=Pos	37	amod	_	_
35	composition	composition	NOUN	NN	Number=Sing	36	compound	_	_
36	rule	rule	NOUN	NN	Number=Sing	37	compound	_	_
37	cite{SS07	cite{ss07	NOUN	NN	Number=Sing	20	dobj	_	SpaceAfter=No
38	}	}	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	2	punct	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = We also answer a question of Shoikhet about composition of $ infty $ - homotopies of $ infty $ - algebras.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	answer	answer	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	question	question	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Shoikhet	Shoikhet	PROPN	NNP	Number=Sing	6	pobj	_	_
8	about	about	ADP	IN	_	5	prep	_	_
9	composition	composition	NOUN	NN	Number=Sing	8	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	$ infty $	$ infty $	SYM	$	_	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	homotopies	homotopie	NOUN	NNS	Number=Plur	10	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	$ infty $	$ infty $	SYM	$	_	17	compound	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	algebras	algebra	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 499
# sent_id = 1
# text = The aim of this series of papers is to develop a self - dual categorical approach to some topics in non - abelian algebra, which is based on replacing the framework of a category with that of a category equipped with a functor to it.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	aim	aim	NOUN	NN	Number=Sing	8	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	series	series	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	papers	paper	NOUN	NNS	Number=Plur	6	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	develop	develop	VERB	VB	VerbForm=Inf	8	xcomp	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
12	self	self	NOUN	NN	Number=Sing	14	npadvmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	dual	dual	ADJ	JJ	Degree=Pos	16	amod	_	_
15	categorical	categorical	ADJ	JJ	Degree=Pos	16	amod	_	_
16	approach	approach	NOUN	NN	Number=Sing	10	dobj	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	some	some	DET	DT	_	19	det	_	_
19	topics	topic	NOUN	NNS	Number=Plur	17	pobj	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	non	non	ADJ	JJ	Degree=Pos	23	amod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	abelian	abelian	PROPN	NNP	Number=Sing	24	amod	_	_
24	algebra	algebra	PROPN	NNP	Number=Sing	20	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	which	which	PRON	WDT	_	28	nsubjpass	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	28	auxpass	_	_
28	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	relcl	_	_
29	on	on	ADP	IN	_	28	prep	_	_
30	replacing	replace	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	29	pcomp	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	framework	framework	NOUN	NN	Number=Sing	30	dobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
35	category	category	NOUN	NN	Number=Sing	33	pobj	_	_
36	with	with	ADP	IN	_	30	prep	_	_
37	that	that	PRON	DT	Number=Sing|PronType=Dem	36	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	a	a	DET	DT	Definite=Ind|PronType=Art	40	det	_	_
40	category	category	NOUN	NN	Number=Sing	38	pobj	_	_
41	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	40	acl	_	_
42	with	with	ADP	IN	_	41	prep	_	_
43	a	a	DET	DT	Definite=Ind|PronType=Art	44	det	_	_
44	functor	functor	NOUN	NN	Number=Sing	42	pobj	_	_
45	to	to	ADP	IN	_	41	prep	_	_
46	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	45	pobj	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = The present paper gives some preliminary steps in this direction, where several known structures on a category, which arise in the categorical treatment of these topics, are viewed as such functors; as a result, we obtain some new conceptual links between these structures.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	present	present	ADJ	JJ	Degree=Pos	3	amod	_	_
3	paper	paper	NOUN	NN	Number=Sing	4	nsubj	_	_
4	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	41	ccomp	_	_
5	some	some	DET	DT	_	7	det	_	_
6	preliminary	preliminary	ADJ	JJ	Degree=Pos	7	amod	_	_
7	steps	step	NOUN	NNS	Number=Plur	4	dobj	_	_
8	in	in	ADP	IN	_	4	prep	_	_
9	this	this	DET	DT	Number=Sing|PronType=Dem	10	det	_	_
10	direction	direction	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	where	where	SCONJ	WRB	_	31	advmod	_	_
13	several	several	ADJ	JJ	Degree=Pos	15	amod	_	_
14	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
15	structures	structure	NOUN	NNS	Number=Plur	31	nsubjpass	_	_
16	on	on	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	category	category	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	which	which	PRON	WDT	_	21	nsubj	_	_
21	arise	arise	VERB	VBP	Tense=Pres|VerbForm=Fin	18	relcl	_	_
22	in	in	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	categorical	categorical	ADJ	JJ	Degree=Pos	25	amod	_	_
25	treatment	treatment	NOUN	NN	Number=Sing	22	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	these	these	DET	DT	Number=Plur|PronType=Dem	28	det	_	_
28	topics	topic	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
30	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	31	auxpass	_	_
31	viewed	view	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	relcl	_	_
32	as	as	ADP	IN	_	31	prep	_	_
33	such	such	ADJ	JJ	Degree=Pos	34	amod	_	_
34	functors	functor	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
35	;	;	PUNCT	:	_	41	punct	_	_
36	as	as	ADP	IN	_	41	prep	_	_
37	a	a	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
38	result	result	NOUN	NN	Number=Sing	36	pobj	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	41	punct	_	_
40	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	41	nsubj	_	_
41	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
42	some	some	DET	DT	_	45	det	_	_
43	new	new	ADJ	JJ	Degree=Pos	45	amod	_	_
44	conceptual	conceptual	ADJ	JJ	Degree=Pos	45	amod	_	_
45	links	link	NOUN	NNS	Number=Plur	41	dobj	_	_
46	between	between	ADP	IN	_	45	prep	_	_
47	these	these	DET	DT	Number=Plur|PronType=Dem	48	det	_	_
48	structures	structure	NOUN	NNS	Number=Plur	46	pobj	_	SpaceAfter=No
49	.	.	PUNCT	.	PunctType=Peri	41	punct	_	SpaceAfter=No

# doc_id = 500
# sent_id = 1
# text = The goal of this paper is to demystify the role played by the Reedy category axioms in homotopy theory.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	goal	goal	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	paper	paper	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	demystify	demystify	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	role	role	NOUN	NN	Number=Sing	8	dobj	_	_
11	played	play	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acl	_	_
12	by	by	ADP	IN	_	11	agent	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	Reedy	Reedy	PROPN	NNP	Number=Sing	15	compound	_	_
15	category	category	NOUN	NN	Number=Sing	16	compound	_	_
16	axioms	axiom	NOUN	NNS	Number=Plur	12	pobj	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	homotopy	homotopy	NOUN	NN	Number=Sing	19	compound	_	_
19	theory	theory	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = With no assumed prerequisites beyond a healthy appetite for category theoretic arguments, we present streamlined proofs of a number of useful technical results, which are well known to folklore but difficult to find in the literature.
1	With	with	ADP	IN	_	15	prep	_	_
2	no	no	DET	DT	_	4	det	_	_
3	assumed	assume	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	amod	_	_
4	prerequisites	prerequisite	NOUN	NNS	Number=Plur	1	pobj	_	_
5	beyond	beyond	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	healthy	healthy	ADJ	JJ	Degree=Pos	8	amod	_	_
8	appetite	appetite	NOUN	NN	Number=Sing	5	pobj	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	category	category	NOUN	NN	Number=Sing	11	npadvmod	_	_
11	theoretic	theoretic	ADJ	JJ	Degree=Pos	12	amod	_	_
12	arguments	argument	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
14	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	15	nsubj	_	_
15	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	streamlined	streamlined	ADJ	JJ	Degree=Pos	17	amod	_	_
17	proofs	proof	NOUN	NNS	Number=Plur	15	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	number	number	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	useful	useful	ADJ	JJ	Degree=Pos	24	amod	_	_
23	technical	technical	ADJ	JJ	Degree=Pos	24	amod	_	_
24	results	result	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	which	which	PRON	WDT	_	29	nsubjpass	_	_
27	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	29	auxpass	_	_
28	well	well	ADV	RB	Degree=Pos	29	advmod	_	_
29	known	known	ADJ	JJ	Degree=Pos	24	relcl	_	_
30	to	to	PART	TO	_	31	aux	_	_
31	folklore	folklore	VERB	VB	VerbForm=Inf	29	xcomp	_	_
32	but	but	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	difficult	difficult	ADJ	JJ	Degree=Pos	31	conj	_	_
34	to	to	PART	TO	_	35	aux	_	_
35	find	find	VERB	VB	VerbForm=Inf	33	xcomp	_	_
36	in	in	ADP	IN	_	35	prep	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	literature	literature	NOUN	NN	Number=Sing	36	pobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 3
# text = While the results presented here are not new, our approach to their proofs is somewhat novel.
1	While	while	SCONJ	IN	_	6	mark	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	results	result	NOUN	NNS	Number=Plur	6	nsubj	_	_
4	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	acl	_	_
5	here	here	ADV	RB	PronType=Dem	4	advmod	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	advcl	_	_
7	not	not	PART	RB	Polarity=Neg	6	neg	_	_
8	new	new	ADJ	JJ	Degree=Pos	6	acomp	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
10	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	11	poss	_	_
11	approach	approach	NOUN	NN	Number=Sing	15	nsubj	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	14	poss	_	_
14	proofs	proof	NOUN	NNS	Number=Plur	12	pobj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	somewhat	somewhat	ADV	RB	_	17	advmod	_	_
17	novel	novel	ADJ	JJ	Degree=Pos	15	acomp	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 4
# text = Specifically, we reduce much of the hard work involved to simpler computations involving weighted colimits and Leibniz (pushout - product) constructions.
1	Specifically	specifically	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	reduce	reduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	much	much	ADJ	JJ	Degree=Pos	4	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	hard	hard	ADJ	JJ	Degree=Pos	9	amod	_	_
9	work	work	NOUN	NN	Number=Sing	6	pobj	_	_
10	involved	involve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	acl	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	simpler	simple	ADJ	JJR	Degree=Cmp	10	advcl	_	_
13	computations	computation	NOUN	NNS	Number=Plur	12	dobj	_	_
14	involving	involve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	acl	_	_
15	weighted	weighted	ADJ	JJ	Degree=Pos	16	amod	_	_
16	colimits	colimit	NOUN	NNS	Number=Plur	14	dobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	Leibniz	Leibniz	PROPN	NNP	Number=Sing	16	conj	_	_
19	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
20	pushout	pushout	NOUN	NN	Number=Sing	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	product	product	NOUN	NN	Number=Sing	24	nmod	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	24	punct	_	_
24	constructions	construction	NOUN	NNS	Number=Plur	4	dobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = The general theory is developed in parallel with examples, which we use to prove that familiar formulae for homotopy limits and colimits indeed have the desired properties.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	general	general	ADJ	JJ	Degree=Pos	3	amod	_	_
3	theory	theory	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	parallel	parallel	NOUN	NN	Number=Sing	6	pobj	_	_
8	with	with	ADP	IN	_	7	prep	_	_
9	examples	example	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	which	which	PRON	WDT	_	13	dobj	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	9	relcl	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	prove	prove	VERB	VB	VerbForm=Inf	13	xcomp	_	_
16	that	that	DET	DT	Number=Sing|PronType=Dem	18	det	_	_
17	familiar	familiar	ADJ	JJ	Degree=Pos	18	amod	_	_
18	formulae	formulae	NOUN	NN	Number=Sing	15	dobj	_	_
19	for	for	ADP	IN	_	18	prep	_	_
20	homotopy	homotopy	NOUN	NN	Number=Sing	21	compound	_	_
21	limits	limit	NOUN	NNS	Number=Plur	19	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	colimits	colimit	NOUN	NNS	Number=Plur	21	conj	_	_
24	indeed	indeed	ADV	RB	_	25	advmod	_	_
25	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	conj	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	desired	desire	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	amod	_	_
28	properties	property	NOUN	NNS	Number=Plur	25	dobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 501
# sent_id = 1
# text = This paper introduces the construction of a weakly globular double category of fractions for a category and studies its universal properties.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	introduces	introduce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	construction	construction	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	weakly	weakly	ADJ	JJ	Degree=Pos	11	amod	_	_
9	globular	globular	ADJ	JJ	Degree=Pos	11	amod	_	_
10	double	double	ADJ	JJ	Degree=Pos	11	amod	_	_
11	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	fractions	fraction	NOUN	NNS	Number=Plur	12	pobj	_	_
14	for	for	ADP	IN	_	3	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	category	category	NOUN	NN	Number=Sing	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
18	studies	study	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
19	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	21	poss	_	_
20	universal	universal	ADJ	JJ	Degree=Pos	21	amod	_	_
21	properties	property	NOUN	NNS	Number=Plur	18	dobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = It shows that this double category is locally small and considers a couple of concrete examples.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	shows	show	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
5	double	double	ADJ	JJ	Degree=Pos	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	locally	locally	ADV	RB	_	9	advmod	_	_
9	small	small	ADJ	JJ	Degree=Pos	7	acomp	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
11	considers	consider	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	conj	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	couple	couple	NOUN	NN	Number=Sing	11	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	concrete	concrete	ADJ	JJ	Degree=Pos	16	amod	_	_
16	examples	example	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 502
# sent_id = 1
# text = We develop a theory of twisted actions of categorical groups using a notion of semidirect product of categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	theory	theory	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	twisted	twisted	ADJ	JJ	Degree=Pos	7	amod	_	_
7	actions	action	NOUN	NNS	Number=Plur	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	categorical	categorical	ADJ	JJ	Degree=Pos	10	amod	_	_
10	groups	group	NOUN	NNS	Number=Plur	8	pobj	_	_
11	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	acl	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	notion	notion	NOUN	NN	Number=Sing	11	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	semidirect	semidirect	NOUN	NN	Number=Sing	16	compound	_	_
16	product	product	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We work through numerous examples to demonstrate the power of these notions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	work	work	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	through	through	ADP	IN	_	2	prep	_	_
4	numerous	numerous	ADJ	JJ	Degree=Pos	5	amod	_	_
5	examples	example	NOUN	NNS	Number=Plur	3	pobj	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	demonstrate	demonstrate	VERB	VB	VerbForm=Inf	2	advcl	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	power	power	NOUN	NN	Number=Sing	7	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	these	these	DET	DT	Number=Plur|PronType=Dem	12	det	_	_
12	notions	notion	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Turning to representations, which are actions that respect vector space structures, we establish an analog of Schur's lemma in this context.
1	Turning	turn	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	advcl	_	_
2	to	to	ADP	IN	_	1	prep	_	_
3	representations	representation	NOUN	NNS	Number=Plur	2	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	which	which	PRON	WDT	_	6	nsubj	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	relcl	_	_
7	actions	action	NOUN	NNS	Number=Plur	6	attr	_	_
8	that	that	PRON	WDT	PronType=Rel	9	nsubj	_	_
9	respect	respect	VERB	VBP	Tense=Pres|VerbForm=Fin	7	relcl	_	_
10	vector	vector	NOUN	NN	Number=Sing	12	compound	_	_
11	space	space	NOUN	NN	Number=Sing	12	compound	_	_
12	structures	structure	NOUN	NNS	Number=Plur	9	dobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
14	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	15	nsubj	_	_
15	establish	establish	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	analog	analog	NOUN	NN	Number=Sing	15	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	Schur	Schur	PROPN	NNP	Number=Sing	21	poss	_	SpaceAfter=No
20	's	's	PART	POS	_	19	case	_	_
21	lemma	lemma	NOUN	NN	Number=Sing	18	pobj	_	_
22	in	in	ADP	IN	_	15	prep	_	_
23	this	this	DET	DT	Number=Sing|PronType=Dem	24	det	_	_
24	context	context	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 4
# text = Keeping new terminology to a minimum, we concentrate on examples exploring the essential new notions introduced.
1	Keeping	keep	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	advcl	_	_
2	new	new	ADJ	JJ	Degree=Pos	3	amod	_	_
3	terminology	terminology	NOUN	NN	Number=Sing	1	dobj	_	_
4	to	to	ADP	IN	_	1	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	minimum	minimum	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	concentrate	concentrate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	on	on	ADP	IN	_	9	prep	_	_
11	examples	example	NOUN	NNS	Number=Plur	10	pobj	_	_
12	exploring	explore	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	acl	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
14	essential	essential	ADJ	JJ	Degree=Pos	16	amod	_	_
15	new	new	ADJ	JJ	Degree=Pos	16	amod	_	_
16	notions	notion	NOUN	NNS	Number=Plur	12	dobj	_	_
17	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	acl	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 503
# sent_id = 1
# text = We define the analytic spectrum of a rig category $ (A, oplus, otimes) $ , and equip it with a sheaf of categories of rational functions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	analytic	analytic	ADJ	JJ	Degree=Pos	5	amod	_	_
5	spectrum	spectrum	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	rig	rig	NOUN	NN	Number=Sing	9	compound	_	_
9	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
10	$ (A, oplus, otimes) $	$ (a, oplus, otimes) $	X	FW	Foreign=Yes	2	dep	_	_
11	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
13	equip	equip	VERB	VB	VerbForm=Inf	2	conj	_	_
14	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	13	dobj	_	_
15	with	with	ADP	IN	_	13	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	sheaf	sheaf	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	categories	category	NOUN	NNS	Number=Plur	18	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	rational	rational	ADJ	JJ	Degree=Pos	22	amod	_	_
22	functions	function	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = If the category is additive, we define a sheaf of categories of analytic functions.
1	If	if	SCONJ	IN	_	4	mark	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	category	category	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	advcl	_	_
5	additive	additive	ADJ	JJ	Degree=Pos	4	acomp	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
7	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	8	nsubj	_	_
8	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	sheaf	sheaf	NOUN	NN	Number=Sing	8	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	analytic	analytic	ADJ	JJ	Degree=Pos	15	amod	_	_
15	functions	function	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 3
# text = We relate this construction to Berkovich's analytic spaces, to Durov's generalized schemes and to Haran's $ F $ - schemes.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	relate	relate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	construction	construction	NOUN	NN	Number=Sing	2	dobj	_	_
5	to	to	ADP	IN	_	2	prep	_	_
6	Berkovich	Berkovich	PROPN	NNP	Number=Sing	9	poss	_	SpaceAfter=No
7	's	's	PART	POS	_	6	case	_	_
8	analytic	analytic	ADJ	JJ	Degree=Pos	9	amod	_	_
9	spaces	space	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	to	to	ADP	IN	_	2	prep	_	_
12	Durov	Durov	PROPN	NNP	Number=Sing	15	poss	_	SpaceAfter=No
13	's	's	PART	POS	_	12	case	_	_
14	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
15	schemes	scheme	NOUN	NNS	Number=Plur	11	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
17	to	to	ADP	IN	_	11	conj	_	_
18	Haran	Haran	PROPN	NNP	Number=Sing	22	poss	_	SpaceAfter=No
19	's	's	PART	POS	_	18	case	_	_
20	$ F $	$ f $	SYM	$	_	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	schemes	scheme	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We use these relations to define analytic versions of Arakelov compactifications of affine arithmetic varieties.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	these	these	DET	DT	Number=Plur|PronType=Dem	4	det	_	_
4	relations	relation	NOUN	NNS	Number=Plur	2	dobj	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	define	define	VERB	VB	VerbForm=Inf	2	xcomp	_	_
7	analytic	analytic	ADJ	JJ	Degree=Pos	8	amod	_	_
8	versions	version	NOUN	NNS	Number=Plur	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Arakelov	Arakelov	PROPN	NNP	Number=Sing	11	compound	_	_
11	compactifications	compactification	NOUN	NNS	Number=Plur	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	affine	affine	NOUN	NN	Number=Sing	15	nmod	_	_
14	arithmetic	arithmetic	ADJ	JJ	Degree=Pos	15	amod	_	_
15	varieties	variety	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 504
# sent_id = 1
# text = We define a mapping space for Gray - enriched categories adapted to higher gauge theory.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	mapping	mapping	NOUN	NN	Number=Sing	5	compound	_	_
5	space	space	NOUN	NN	Number=Sing	2	dobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	Gray	Gray	PROPN	NNP	Number=Sing	9	npadvmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
11	adapted	adapt	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	advcl	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	higher	high	ADJ	JJR	Degree=Cmp	14	amod	_	_
14	gauge	gauge	NOUN	NN	Number=Sing	15	compound	_	_
15	theory	theory	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Our construction differs significantly from the canonical mapping space of enriched categories in that it is much less rigid.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	construction	construction	NOUN	NN	Number=Sing	3	nsubj	_	_
3	differs	differ	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	significantly	significantly	ADV	RB	_	3	advmod	_	_
5	from	from	ADP	IN	_	3	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
7	canonical	canonical	ADJ	JJ	Degree=Pos	8	amod	_	_
8	mapping	mapping	NOUN	NN	Number=Sing	9	compound	_	_
9	space	space	NOUN	NN	Number=Sing	5	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
12	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
13	in	in	SCONJ	IN	_	16	mark	_	_
14	that	that	SCONJ	IN	_	16	mark	_	_
15	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	16	nsubj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	advcl	_	_
17	much	much	ADV	RB	_	18	advmod	_	_
18	less	less	ADV	RBR	Degree=Cmp	19	advmod	_	_
19	rigid	rigid	ADJ	JJ	Degree=Pos	16	acomp	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = The two essential ingredients are a path space construction for Gray - categories and a kind of comonadic resolution of the 1 - dimensional structure of a given Gray - category obtained by lifting the resolution of ordinary categories along the canonical fibration of $ GrayCat $ over $ Cat $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	two	two	NUM	CD	NumType=Card	4	nummod	_	_
3	essential	essential	ADJ	JJ	Degree=Pos	4	amod	_	_
4	ingredients	ingredient	NOUN	NNS	Number=Plur	5	nsubj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	path	path	NOUN	NN	Number=Sing	9	compound	_	_
8	space	space	NOUN	NN	Number=Sing	9	compound	_	_
9	construction	construction	NOUN	NN	Number=Sing	5	attr	_	_
10	for	for	ADP	IN	_	9	prep	_	_
11	Gray	Gray	PROPN	NNP	Number=Sing	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	kind	kind	NOUN	NN	Number=Sing	9	conj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	comonadic	comonadic	ADJ	JJ	Degree=Pos	19	amod	_	_
19	resolution	resolution	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
22	1	1	NUM	CD	NumType=Card	24	advmod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	dimensional	dimensional	ADJ	JJ	Degree=Pos	25	amod	_	_
25	structure	structure	NOUN	NN	Number=Sing	20	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
28	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	amod	_	_
29	Gray	Gray	PROPN	NNP	Number=Sing	31	compound	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	category	category	NOUN	NN	Number=Sing	26	pobj	_	_
32	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	acl	_	_
33	by	by	ADP	IN	_	32	agent	_	_
34	lifting	lift	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	33	pcomp	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	resolution	resolution	NOUN	NN	Number=Sing	34	dobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	ordinary	ordinary	ADJ	JJ	Degree=Pos	39	amod	_	_
39	categories	category	NOUN	NNS	Number=Plur	37	pobj	_	_
40	along	along	ADP	IN	_	36	prep	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
42	canonical	canonical	ADJ	JJ	Degree=Pos	43	amod	_	_
43	fibration	fibration	NOUN	NN	Number=Sing	40	pobj	_	_
44	of	of	ADP	IN	_	43	prep	_	_
45	$ GrayCat $	$ graycat $	SYM	$	_	47	nmod	_	_
46	over	over	ADP	IN	_	47	advmod	_	_
47	$ Cat $	$ cat $	SYM	$	_	44	pobj	_	_
48	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 505
# sent_id = 1
# text = We show that the adjunction between monoids and groups obtained via the Grothendieck group construction is admissible, relatively to surjective homomorphisms, in the sense of categorical Galois theory.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	16	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	adjunction	adjunction	NOUN	NN	Number=Sing	16	nsubj	_	_
6	between	between	ADP	IN	_	5	prep	_	_
7	monoids	monoid	NOUN	NNS	Number=Plur	6	pobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	groups	group	NOUN	NNS	Number=Plur	7	conj	_	_
10	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	acl	_	_
11	via	via	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
13	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	15	compound	_	_
14	group	group	NOUN	NN	Number=Sing	15	compound	_	_
15	construction	construction	NOUN	NN	Number=Sing	11	pobj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
17	admissible	admissible	ADJ	JJ	Degree=Pos	16	acomp	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
19	relatively	relatively	ADV	RB	_	21	advmod	_	_
20	to	to	PART	TO	_	21	aux	_	_
21	surjective	surjective	VERB	VB	VerbForm=Inf	16	acomp	_	_
22	homomorphisms	homomorphism	NOUN	NNS	Number=Plur	21	dobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
24	in	in	ADP	IN	_	16	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	sense	sense	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	categorical	categorical	ADJ	JJ	Degree=Pos	30	amod	_	_
29	Galois	Galois	PROPN	NNP	Number=Sing	30	compound	_	_
30	theory	theory	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The central extensions with respect to this Galois structure turn out to be the so - called special homogeneous surjections.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	central	central	ADJ	JJ	Degree=Pos	3	amod	_	_
3	extensions	extension	NOUN	NNS	Number=Plur	10	nsubj	_	_
4	with	with	ADP	IN	_	3	prep	_	_
5	respect	respect	NOUN	NN	Number=Sing	4	pobj	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	this	this	DET	DT	Number=Sing|PronType=Dem	9	det	_	_
8	Galois	Galois	PROPN	NNP	Number=Sing	9	compound	_	_
9	structure	structure	NOUN	NN	Number=Sing	6	pobj	_	_
10	turn	turn	VERB	VB	VerbForm=Inf	0	ROOT	_	_
11	out	out	ADP	RP	_	10	prt	_	_
12	to	to	PART	TO	_	13	aux	_	_
13	be	be	AUX	VB	VerbForm=Inf	10	xcomp	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
15	so	so	ADV	RB	_	17	advmod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	amod	_	_
18	special	special	ADJ	JJ	Degree=Pos	20	amod	_	_
19	homogeneous	homogeneous	ADJ	JJ	Degree=Pos	20	amod	_	_
20	surjections	surjection	NOUN	NNS	Number=Plur	13	attr	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# doc_id = 506
# sent_id = 1
# text = In an earlier work, we constructed the almost strict Morse $ n $ - category $ mathcal X $ which extends Cohen and Jones and Segal's flow category.
1	In	in	ADP	IN	_	7	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	earlier	early	ADJ	JJR	Degree=Cmp	4	amod	_	_
4	work	work	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	constructed	construct	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
9	almost	almost	ADV	RB	_	10	advmod	_	_
10	strict	strict	ADJ	JJ	Degree=Pos	14	amod	_	_
11	Morse	Morse	PROPN	NNP	Number=Sing	14	nmod	_	_
12	$ n $	$ n $	SYM	$	_	14	nummod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	category	category	NOUN	NN	Number=Sing	7	dobj	_	_
15	$ mathcal X $	$ mathcal x $	SYM	$	_	14	appos	_	_
16	which	which	PRON	WDT	_	17	nsubj	_	_
17	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
18	Cohen	Cohen	PROPN	NNP	Number=Sing	25	poss	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	Jones	Jones	PROPN	NNP	Number=Sing	18	conj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	Segal	Segal	PROPN	NNP	Number=Sing	25	poss	_	SpaceAfter=No
23	's	's	PART	POS	_	22	case	_	_
24	flow	flow	NOUN	NN	Number=Sing	25	compound	_	_
25	category	category	NOUN	NN	Number=Sing	17	dobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this article, we define two other almost strict $ n $ - categories $ mathcal V $ and $ mathcal W $ where $ mathcal V $ is based on homomorphisms between real vector spaces and $ mathcal W $ consists of tuples of positive integers.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	article	article	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	two	two	NUM	CD	NumType=Card	8	nummod	_	_
8	other	other	ADJ	JJ	Degree=Pos	6	dobj	_	_
9	almost	almost	ADV	RB	_	10	advmod	_	_
10	strict	strict	ADJ	JJ	Degree=Pos	13	amod	_	_
11	$ n $	$ n $	SYM	$	_	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	categories	category	NOUN	NNS	Number=Plur	14	compound	_	_
14	$ mathcal V $	$ mathcal v $	SYM	$	_	6	dep	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	$ mathcal W $	$ mathcal w $	SYM	$	_	14	conj	_	_
17	where	where	SCONJ	WRB	_	18	advmod	_	_
18	$ mathcal V $	$ mathcal v $	SYM	$	_	14	relcl	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	auxpass	_	_
20	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	conj	_	_
21	on	on	ADP	IN	_	20	prep	_	_
22	homomorphisms	homomorphism	NOUN	NNS	Number=Plur	21	pobj	_	_
23	between	between	ADP	IN	_	22	prep	_	_
24	real	real	ADJ	JJ	Degree=Pos	26	amod	_	_
25	vector	vector	NOUN	NN	Number=Sing	26	compound	_	_
26	spaces	space	NOUN	NNS	Number=Plur	23	pobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	$ mathcal W $	$ mathcal w $	SYM	$	_	29	nsubj	_	_
29	consists	consist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	conj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	tuples	tuple	NOUN	NNS	Number=Plur	30	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	positive	positive	ADJ	JJ	Degree=Pos	34	amod	_	_
34	integers	integer	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = The Morse index and the dimension of the Morse moduli spaces give rise to almost strict $ n $ - category functors $ mathcal F : mathcal X to mathcal V $ and $ mathcal G : mathcal X to mathcal W $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	Morse	Morse	PROPN	NNP	Number=Sing	3	compound	_	_
3	index	index	NOUN	NN	Number=Sing	12	nsubj	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	dimension	dimension	NOUN	NN	Number=Sing	3	conj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
9	Morse	Morse	PROPN	NNP	Number=Sing	10	compound	_	_
10	moduli	moduli	PROPN	NNP	Number=Sing	11	compound	_	_
11	spaces	space	NOUN	NNS	Number=Plur	7	pobj	_	_
12	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	rise	rise	NOUN	NN	Number=Sing	12	dobj	_	_
14	to	to	ADP	IN	_	12	prep	_	_
15	almost	almost	ADV	RB	_	16	advmod	_	_
16	strict	strict	ADJ	JJ	Degree=Pos	19	amod	_	_
17	$ n $	$ n $	SYM	$	_	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	category	category	NOUN	NN	Number=Sing	20	compound	_	_
20	functors	functor	NOUN	NNS	Number=Plur	14	pobj	_	_
21	$ mathcal F : mathcal X to mathcal V $	$ mathcal f : mathcal x to mathcal v $	SYM	$	_	12	dobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	$ mathcal G : mathcal X to mathcal W $	$ mathcal g : mathcal x to mathcal w $	SYM	$	_	21	conj	_	_
24	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# doc_id = 507
# sent_id = 1
# text = We prove that a large class of natural transformations (consisting roughly of those constructed via composition from the ``functorial'' or ``base change'' transformations) between two functors of the form $ ... f^* g_* ... $ actually has only one element, and thus that any diagram of such maps necessarily commutes.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	40	mark	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	large	large	ADJ	JJ	Degree=Pos	6	amod	_	_
6	class	class	NOUN	NN	Number=Sing	40	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	natural	natural	ADJ	JJ	Degree=Pos	9	amod	_	_
9	transformations	transformation	NOUN	NNS	Number=Plur	7	pobj	_	_
10	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	6	punct	_	SpaceAfter=No
11	consisting	consist	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	acl	_	_
12	roughly	roughly	ADV	RB	_	13	advmod	_	_
13	of	of	ADP	IN	_	11	prep	_	_
14	those	those	PRON	DT	Number=Plur|PronType=Dem	13	pobj	_	_
15	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	acl	_	_
16	via	via	ADP	IN	_	15	prep	_	_
17	composition	composition	NOUN	NN	Number=Sing	16	pobj	_	_
18	from	from	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
20	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	22	punct	_	SpaceAfter=No
21	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	22	punct	_	SpaceAfter=No
22	functorial	functorial	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
23	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	22	punct	_	_
24	or	or	CCONJ	CC	ConjType=Cmp	22	cc	_	_
25	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	28	punct	_	SpaceAfter=No
26	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	28	punct	_	SpaceAfter=No
27	base	base	NOUN	NN	Number=Sing	28	nmod	_	_
28	change	change	NOUN	NN	Number=Sing	30	nmod	_	SpaceAfter=No
29	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	30	punct	_	_
30	transformations	transformation	NOUN	NNS	Number=Plur	22	conj	_	SpaceAfter=No
31	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	30	punct	_	_
32	between	between	ADP	IN	_	22	prep	_	_
33	two	two	NUM	CD	NumType=Card	34	nummod	_	_
34	functors	functor	NOUN	NNS	Number=Plur	32	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	form	form	NOUN	NN	Number=Sing	35	pobj	_	_
38	$ ... f^* g_* ... $	$ ... f^* g_* ... $	SYM	$	_	40	nsubj	_	_
39	actually	actually	ADV	RB	_	40	advmod	_	_
40	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
41	only	only	ADV	RB	_	42	advmod	_	_
42	one	one	NUM	CD	NumType=Card	43	nummod	_	_
43	element	element	NOUN	NN	Number=Sing	40	dobj	_	SpaceAfter=No
44	,	,	PUNCT	,	PunctType=Comm	40	punct	_	_
45	and	and	CCONJ	CC	ConjType=Cmp	40	cc	_	_
46	thus	thus	ADV	RB	_	54	advmod	_	_
47	that	that	SCONJ	IN	_	54	mark	_	_
48	any	any	DET	DT	_	49	det	_	_
49	diagram	diagram	NOUN	NN	Number=Sing	54	nsubj	_	_
50	of	of	ADP	IN	_	49	prep	_	_
51	such	such	ADJ	JJ	Degree=Pos	52	amod	_	_
52	maps	map	NOUN	NNS	Number=Plur	50	pobj	_	_
53	necessarily	necessarily	ADV	RB	_	54	advmod	_	_
54	commutes	commute	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	40	conj	_	SpaceAfter=No
55	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We identify the precise axioms defining what we call a ``geofibered category'' that ensure that such a coherence theorem exists.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	identify	identify	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	precise	precise	ADJ	JJ	Degree=Pos	5	amod	_	_
5	axioms	axiom	NOUN	NNS	Number=Plur	2	dobj	_	_
6	defining	define	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	acl	_	_
7	what	what	PRON	WP	_	9	dobj	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	6	ccomp	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
11	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	14	punct	_	SpaceAfter=No
12	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	14	punct	_	SpaceAfter=No
13	geofibered	geofibere	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
14	category	category	NOUN	NN	Number=Sing	9	oprd	_	SpaceAfter=No
15	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	14	punct	_	_
16	that	that	PRON	WDT	PronType=Rel	17	nsubj	_	_
17	ensure	ensure	VERB	VBP	Tense=Pres|VerbForm=Fin	14	relcl	_	_
18	that	that	SCONJ	IN	_	23	mark	_	_
19	such	such	DET	PDT	_	23	predet	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	coherence	coherence	NOUN	NN	Number=Sing	22	compound	_	_
22	theorem	theorem	ADJ	JJ	Degree=Pos	23	amod	_	_
23	exists	exist	NOUN	NNS	Number=Plur	17	ccomp	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Our results apply to all the usual sheaf - theoretic contexts of algebraic geometry.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	results	result	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	apply	apply	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	to	to	ADP	IN	_	3	prep	_	_
5	all	all	DET	PDT	_	11	predet	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
7	usual	usual	ADJ	JJ	Degree=Pos	11	amod	_	_
8	sheaf	sheaf	NOUN	NN	Number=Sing	10	npadvmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	theoretic	theoretic	ADJ	JJ	Degree=Pos	11	amod	_	_
11	contexts	context	NOUN	NNS	Number=Plur	4	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	algebraic	algebraic	ADJ	JJ	Degree=Pos	14	amod	_	_
14	geometry	geometry	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = The analogous result that would include any other of the six functors remains unknown.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	analogous	analogous	ADJ	JJ	Degree=Pos	3	amod	_	_
3	result	result	NOUN	NN	Number=Sing	13	nsubj	_	_
4	that	that	PRON	WDT	PronType=Rel	6	nsubj	_	_
5	would	would	AUX	MD	VerbForm=Fin	6	aux	_	_
6	include	include	VERB	VB	VerbForm=Inf	3	relcl	_	_
7	any	any	DET	DT	_	8	det	_	_
8	other	other	ADJ	JJ	Degree=Pos	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	six	six	NUM	CD	NumType=Card	12	nummod	_	_
12	functors	functor	NOUN	NNS	Number=Plur	9	pobj	_	_
13	remains	remain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	unknown	unknown	ADJ	JJ	Degree=Pos	13	acomp	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# doc_id = 508
# sent_id = 1
# text = Counterexamples for two propositions in an article are given.
1	Counterexamples	counterexample	NOUN	NNS	Number=Plur	9	nsubjpass	_	_
2	for	for	ADP	IN	_	1	prep	_	_
3	two	two	NUM	CD	NumType=Card	4	nummod	_	_
4	propositions	proposition	NOUN	NNS	Number=Plur	2	pobj	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	article	article	NOUN	NN	Number=Sing	5	pobj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 2
# text = They are used in the paper only to prove a corollary.
1	They	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	3	nsubjpass	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	in	in	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	paper	paper	NOUN	NN	Number=Sing	4	pobj	_	_
7	only	only	ADV	RB	_	9	advmod	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	prove	prove	VERB	VB	VerbForm=Inf	3	xcomp	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	corollary	corollary	NOUN	NN	Number=Sing	9	dobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = A proof of this corollary is given without them.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	proof	proof	NOUN	NN	Number=Sing	7	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	corollary	corollary	ADJ	JJ	Degree=Pos	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	without	without	ADP	IN	_	7	prep	_	_
9	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	8	pobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = The proof of the fibrancy of some cubical transition systems is fixed.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	proof	proof	NOUN	NN	Number=Sing	12	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	fibrancy	fibrancy	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	some	some	DET	DT	_	10	det	_	_
8	cubical	cubical	ADJ	JJ	Degree=Pos	10	amod	_	_
9	transition	transition	NOUN	NN	Number=Sing	10	compound	_	_
10	systems	system	NOUN	NNS	Number=Plur	6	pobj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# doc_id = 509
# sent_id = 1
# text = It is proved that in any pointed category with pullbacks, coequalizers and regular epi - mono factorizations, the class of regular epimorphisms is stable under pullback along the so - called balanced effective descent morphisms.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	SCONJ	IN	_	25	mark	_	_
5	in	in	ADP	IN	_	25	prep	_	_
6	any	any	DET	DT	_	8	det	_	_
7	pointed	pointed	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	pullbacks	pullback	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	coequalizers	coequalizer	NOUN	NNS	Number=Plur	10	conj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	regular	regular	ADJ	JJ	Degree=Pos	18	amod	_	_
15	epi	epi	NOUN	NN	Number=Sing	17	compound	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	mono	mono	PROPN	NNP	Number=Sing	18	compound	_	_
18	factorizations	factorization	NOUN	NNS	Number=Plur	12	conj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	class	class	NOUN	NN	Number=Sing	25	nsubj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	regular	regular	ADJ	JJ	Degree=Pos	24	amod	_	_
24	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	22	pobj	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
26	stable	stable	ADJ	JJ	Degree=Pos	25	acomp	_	_
27	under	under	ADP	IN	_	26	prep	_	_
28	pullback	pullback	NOUN	NN	Number=Sing	27	pobj	_	_
29	along	along	ADP	IN	_	25	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
31	so	so	ADV	RB	_	33	advmod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	37	amod	_	_
34	balanced	balanced	ADJ	JJ	Degree=Pos	37	amod	_	_
35	effective	effective	ADJ	JJ	Degree=Pos	37	amod	_	_
36	descent	descent	NOUN	NN	Number=Sing	37	compound	_	_
37	morphisms	morphism	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = Here ``balanced'' can be omitted if the category is additive.
1	Here	here	ADV	RB	PronType=Dem	8	advmod	_	_
2	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	4	punct	_	SpaceAfter=No
3	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	4	punct	_	SpaceAfter=No
4	balanced	balanced	NOUN	NN	Number=Sing	8	nsubjpass	_	SpaceAfter=No
5	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	4	punct	_	_
6	can	can	AUX	MD	VerbForm=Fin	8	aux	_	_
7	be	be	AUX	VB	VerbForm=Inf	8	auxpass	_	_
8	omitted	omit	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	if	if	SCONJ	IN	_	12	mark	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	category	category	NOUN	NN	Number=Sing	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	advcl	_	_
13	additive	additive	ADJ	JJ	Degree=Pos	12	acomp	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 3
# text = A balanced effective descent morphism is defined as an effective descent morphism $ p:Erightarrow B $ such that any subobject of $ E $ is a pullback of some morphism along $ p $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
2	balanced	balanced	ADJ	JJ	Degree=Pos	5	amod	_	_
3	effective	effective	ADJ	JJ	Degree=Pos	5	amod	_	_
4	descent	descent	NOUN	NN	Number=Sing	5	compound	_	_
5	morphism	morphism	NOUN	NN	Number=Sing	7	nsubjpass	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	as	as	ADP	IN	_	7	prep	_	_
9	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
10	effective	effective	ADJ	JJ	Degree=Pos	12	amod	_	_
11	descent	descent	NOUN	NN	Number=Sing	12	compound	_	_
12	morphism	morphism	NOUN	NN	Number=Sing	8	pobj	_	_
13	$ p:Erightarrow B $	$ p:erightarrow b $	SYM	$	_	14	nmod	_	_
14	such	such	ADJ	JJ	Degree=Pos	12	appos	_	_
15	that	that	SCONJ	IN	_	20	mark	_	_
16	any	any	DET	DT	_	17	det	_	_
17	subobject	subobject	NOUN	NN	Number=Sing	20	nsubj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	$ E $	$ e $	SYM	$	_	18	pobj	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	ccomp	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	pullback	pullback	NOUN	NN	Number=Sing	20	attr	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	some	some	DET	DT	_	25	det	_	_
25	morphism	morphism	NOUN	NN	Number=Sing	23	pobj	_	_
26	along	along	ADP	IN	_	25	prep	_	_
27	$ p $	$ p $	SYM	$	_	26	pobj	_	_
28	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = It is shown that, in any category with pullbacks and coequalizers, the class of effective descent morphisms is stable under pushout if and only if any regular epimorphism is an effective descent morphism.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	SCONJ	IN	_	20	mark	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
6	in	in	ADP	IN	_	20	prep	_	_
7	any	any	DET	DT	_	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	pullbacks	pullback	NOUN	NNS	Number=Plur	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	coequalizers	coequalizer	NOUN	NNS	Number=Plur	10	conj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	class	class	NOUN	NN	Number=Sing	20	nsubj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	effective	effective	ADJ	JJ	Degree=Pos	19	amod	_	_
18	descent	descent	NOUN	NN	Number=Sing	19	compound	_	_
19	morphisms	morphism	NOUN	NNS	Number=Plur	16	pobj	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
21	stable	stable	ADJ	JJ	Degree=Pos	20	acomp	_	_
22	under	under	ADP	IN	_	20	prep	_	_
23	pushout	pushout	NOUN	NN	Number=Sing	22	pobj	_	_
24	if	if	SCONJ	IN	_	31	mark	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
26	only	only	ADV	RB	_	31	advmod	_	_
27	if	if	SCONJ	IN	_	31	mark	_	_
28	any	any	DET	DT	_	30	det	_	_
29	regular	regular	ADJ	JJ	Degree=Pos	30	amod	_	_
30	epimorphism	epimorphism	NOUN	NN	Number=Sing	31	nsubj	_	_
31	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	advcl	_	_
32	an	an	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
33	effective	effective	ADJ	JJ	Degree=Pos	35	amod	_	_
34	descent	descent	NOUN	NN	Number=Sing	35	compound	_	_
35	morphism	morphism	NOUN	NN	Number=Sing	31	attr	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = Moreover, it is shown that the class of descent morphisms is stable under pushout if and only if the class of regular epimorphisms is stable under pullback.
1	Moreover	moreover	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	that	that	SCONJ	IN	_	12	mark	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	class	class	NOUN	NN	Number=Sing	12	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	descent	descent	NOUN	NN	Number=Sing	9	pobj	_	_
11	morphisms	morphism	NOUN	NNS	Number=Plur	9	pobj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
13	stable	stable	ADJ	JJ	Degree=Pos	12	acomp	_	_
14	under	under	ADP	IN	_	12	prep	_	_
15	pushout	pushout	NOUN	NN	Number=Sing	14	pobj	_	_
16	if	if	SCONJ	IN	_	25	mark	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
18	only	only	ADV	RB	_	25	advmod	_	_
19	if	if	SCONJ	IN	_	25	mark	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	class	class	NOUN	NN	Number=Sing	25	nsubj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	regular	regular	ADJ	JJ	Degree=Pos	24	amod	_	_
24	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	22	pobj	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	advcl	_	_
26	stable	stable	ADJ	JJ	Degree=Pos	25	acomp	_	_
27	under	under	ADP	IN	_	26	prep	_	_
28	pullback	pullback	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 510
# sent_id = 1
# text = To 2 - categorify the theory of group representations, we introduce the notions of the 3 - representation of a group in a strict 3 - category and the strict 2 - categorical action of a group on a strict 2 - category.
1	To	to	AUX	IN	_	4	aux	_	_
2	2	2	NUM	CD	NumType=Card	4	nummod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	categorify	categorify	VERB	VB	VerbForm=Inf	12	advcl	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	theory	theory	NOUN	NN	Number=Sing	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	group	group	NOUN	NN	Number=Sing	9	compound	_	_
9	representations	representation	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
11	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	12	nsubj	_	_
12	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	notions	notion	NOUN	NNS	Number=Plur	12	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
17	3	3	NUM	CD	NumType=Card	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	representation	representation	NOUN	NN	Number=Sing	15	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	group	group	NOUN	NN	Number=Sing	20	pobj	_	_
23	in	in	ADP	IN	_	12	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
25	strict	strict	ADJ	JJ	Degree=Pos	28	amod	_	_
26	3	3	NUM	CD	NumType=Card	28	nummod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	category	category	NOUN	NN	Number=Sing	23	pobj	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
31	strict	strict	ADJ	JJ	Degree=Pos	35	amod	_	_
32	2	2	NUM	CD	NumType=Card	34	nummod	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	categorical	categorical	ADJ	JJ	Degree=Pos	35	amod	_	_
35	action	action	NOUN	NN	Number=Sing	12	conj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	a	a	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
38	group	group	NOUN	NN	Number=Sing	36	pobj	_	_
39	on	on	ADP	IN	_	35	prep	_	_
40	a	a	DET	DT	Definite=Ind|PronType=Art	44	det	_	_
41	strict	strict	ADJ	JJ	Degree=Pos	44	amod	_	_
42	2	2	NUM	CD	NumType=Card	44	nummod	_	_
43	-	-	PUNCT	HYPH	PunctType=Dash	44	punct	_	_
44	category	category	NOUN	NN	Number=Sing	39	pobj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 2
# text = We also 2 - categorify the concept of the trace by introducing the 2 - categorical trace of a 1 - endomorphism in a strict 3 - category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
2	also	also	ADV	RB	_	5	advmod	_	_
3	2	2	NUM	CD	NumType=Card	5	nummod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	categorify	categorify	VERB	VB	VerbForm=Inf	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	concept	concept	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	trace	trace	NOUN	NN	Number=Sing	8	pobj	_	_
11	by	by	ADP	IN	_	5	prep	_	_
12	introducing	introduce	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	pcomp	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
14	2	2	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	categorical	categorical	ADJ	JJ	Degree=Pos	17	amod	_	_
17	trace	trace	NOUN	NN	Number=Sing	12	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
20	1	1	NUM	CD	NumType=Card	22	nummod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	endomorphism	endomorphism	NOUN	NN	Number=Sing	18	pobj	_	_
23	in	in	ADP	IN	_	12	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
25	strict	strict	ADJ	JJ	Degree=Pos	28	amod	_	_
26	3	3	NUM	CD	NumType=Card	28	nummod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	category	category	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = For a 3 - representation $ rho $ of a group $ G $ and an element $ f $ of $ G $ , the 2 - categorical trace $ Tr_2rho_f $ is a category.
1	For	for	ADP	IN	_	24	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
3	3	3	NUM	CD	NumType=Card	5	nummod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	representation	representation	NOUN	NN	Number=Sing	6	compound	_	_
6	$ rho $	$ rho $	SYM	$	_	1	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	group	group	NOUN	NN	Number=Sing	7	pobj	_	_
10	$ G $	$ g $	SYM	$	_	6	appos	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
12	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	element	element	NOUN	NN	Number=Sing	6	conj	_	_
14	$ f $	$ f $	SYM	$	_	13	prep	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	$ G $	$ g $	SYM	$	_	15	pobj	_	_
17	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
19	2	2	NUM	CD	NumType=Card	21	nummod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	categorical	categorical	ADJ	JJ	Degree=Pos	22	amod	_	_
22	trace	trace	NOUN	NN	Number=Sing	24	nsubj	_	_
23	$ Tr_2rho_f $	$ tr_2rho_f $	SYM	$	_	22	appos	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
26	category	category	NOUN	NN	Number=Sing	24	attr	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# sent_id = 4
# text = Moreover, the centralizer of $ f $ in $ G $ acts categorically on this 2 - categorical trace.
1	Moreover	moreover	ADV	RB	_	9	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	centralizer	centralizer	NOUN	NN	Number=Sing	9	nsubj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	$ f $	$ f $	SYM	$	_	5	pobj	_	_
7	in	in	ADP	IN	_	4	prep	_	_
8	$ G $	$ g $	SYM	$	_	7	pobj	_	_
9	acts	act	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	categorically	categorically	ADV	RB	_	9	advmod	_	_
11	on	on	ADP	IN	_	9	prep	_	_
12	this	this	DET	DT	Number=Sing|PronType=Dem	16	det	_	_
13	2	2	NUM	CD	NumType=Card	15	nummod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	categorical	categorical	ADJ	JJ	Degree=Pos	16	amod	_	_
16	trace	trace	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 5
# text = We construct the induced strict 2 - categorical action of a finite group, and show that the 2 - categorical trace $ Tr_2 $ takes an induced strict 2 - categorical action into an induced categorical action of the initia groupoid.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
4	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	amod	_	_
5	strict	strict	ADJ	JJ	Degree=Pos	9	amod	_	_
6	2	2	NUM	CD	NumType=Card	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	categorical	categorical	ADJ	JJ	Degree=Pos	9	amod	_	_
9	action	action	NOUN	NN	Number=Sing	2	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	finite	finite	ADJ	JJ	Degree=Pos	13	amod	_	_
13	group	group	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
16	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
17	that	that	SCONJ	IN	_	24	mark	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
19	2	2	NUM	CD	NumType=Card	21	nummod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	categorical	categorical	ADJ	JJ	Degree=Pos	22	amod	_	_
22	trace	trace	NOUN	NN	Number=Sing	24	nsubj	_	_
23	$ Tr_2 $	$ tr_2 $	SYM	$	_	22	appos	_	_
24	takes	take	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	ccomp	_	_
25	an	an	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
26	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	amod	_	_
27	strict	strict	ADJ	JJ	Degree=Pos	31	amod	_	_
28	2	2	NUM	CD	NumType=Card	30	nummod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	categorical	categorical	ADJ	JJ	Degree=Pos	31	amod	_	_
31	action	action	NOUN	NN	Number=Sing	24	dobj	_	_
32	into	into	ADP	IN	_	24	prep	_	_
33	an	an	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
34	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	36	amod	_	_
35	categorical	categorical	ADJ	JJ	Degree=Pos	36	amod	_	_
36	action	action	NOUN	NN	Number=Sing	32	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
39	initia	initia	NOUN	NN	Number=Sing	40	compound	_	_
40	groupoid	groupoid	NOUN	NN	Number=Sing	37	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = As a corollary, we get the 3 - character formula of the induced strict 2 - categorical action.
1	As	as	ADP	IN	_	6	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	corollary	corollary	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	get	get	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
8	3	3	NUM	CD	NumType=Card	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	character	character	NOUN	NN	Number=Sing	11	compound	_	_
11	formula	formula	NOUN	NN	Number=Sing	6	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
14	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
15	strict	strict	ADJ	JJ	Degree=Pos	19	amod	_	_
16	2	2	NUM	CD	NumType=Card	18	nummod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	categorical	categorical	ADJ	JJ	Degree=Pos	19	amod	_	_
19	action	action	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 511
# sent_id = 1
# text = It is well known that profinite $ T_0 $ - spaces are exactly the spectral spaces.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	well	well	ADV	RB	Degree=Pos	4	advmod	_	_
4	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acomp	_	_
5	that	that	SCONJ	IN	_	10	mark	_	_
6	profinite	profinite	VERB	VBP	Tense=Pres|VerbForm=Fin	10	csubj	_	_
7	$ T_0 $	$ t_0 $	SYM	$	_	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	spaces	space	NOUN	NNS	Number=Plur	6	dobj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
11	exactly	exactly	ADV	RB	_	14	advmod	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	spectral	spectral	ADJ	JJ	Degree=Pos	14	amod	_	_
14	spaces	space	NOUN	NNS	Number=Plur	10	attr	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We generalize this result to the category of all topological spaces by showing that the following conditions are equivalent: (i) $ (X, tau) $ is a profinite topological space.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	25	ccomp	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	result	result	NOUN	NN	Number=Sing	2	dobj	_	_
5	to	to	ADP	IN	_	2	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	all	all	DET	DT	_	11	det	_	_
10	topological	topological	ADJ	JJ	Degree=Pos	11	amod	_	_
11	spaces	space	NOUN	NNS	Number=Plur	8	pobj	_	_
12	by	by	ADP	IN	_	2	prep	_	_
13	showing	show	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	pcomp	_	_
14	that	that	SCONJ	IN	_	18	mark	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	amod	_	_
17	conditions	condition	NOUN	NNS	Number=Plur	18	nsubj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
19	equivalent	equivalent	ADJ	JJ	Degree=Pos	18	acomp	_	SpaceAfter=No
20	:	:	PUNCT	:	_	25	punct	_	_
21	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	25	punct	_	SpaceAfter=No
22	i	i	NOUN	NN	Case=Nom|Number=Sing|Person=1|PronType=Prs	25	nsubj	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	22	punct	_	_
24	$ (X, tau) $	$ (X, tau) $	PROPN	NNP	Number=Sing	25	nsubj	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
27	profinite	profinite	ADJ	JJ	Degree=Pos	29	amod	_	_
28	topological	topological	ADJ	JJ	Degree=Pos	29	amod	_	_
29	space	space	NOUN	NN	Number=Sing	25	attr	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	25	punct	_	SpaceAfter=No

# sent_id = 3
# text = (ii) The $ T_0 $ - reflection of $ (X, tau) $ is a profinite $ T_0 $ - space.
1	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	2	punct	_	SpaceAfter=No
2	ii	ii	PROPN	NNP	Number=Sing	10	dep	_	SpaceAfter=No
3	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	2	punct	_	_
4	The	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	$ T_0 $	$ t_0 $	SYM	$	_	7	nummod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	reflection	reflection	NOUN	NN	Number=Sing	10	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	$ (X, tau) $	$ (x, tau) $	SYM	$	_	8	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
12	profinite	profinite	NOUN	NN	Number=Sing	15	amod	_	_
13	$ T_0 $	$ t_0 $	SYM	$	_	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	space	space	NOUN	NN	Number=Sing	10	attr	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 4
# text = (iii) $ (X, tau) $ is a quasi spectral space.
1	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	5	punct	_	SpaceAfter=No
2	iii	iii	PROPN	NNP	Number=Sing	4	nmod	_	SpaceAfter=No
3	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	4	punct	_	_
4	$ (X, tau) $	$ (X, tau) $	PROPN	NNP	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	quasi	quasi	ADJ	JJ	Degree=Pos	9	amod	_	_
8	spectral	spectral	ADJ	JJ	Degree=Pos	9	amod	_	_
9	space	space	NOUN	NN	Number=Sing	5	attr	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = (iv) $ (X, tau) $ admits a stronger Stone topology $ pi $ such that $ (X, tau, pi) $ is a bitopological quasi spectral space
1	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	5	punct	_	SpaceAfter=No
2	iv	iv	PROPN	NNP	Number=Sing	5	meta	_	SpaceAfter=No
3	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	5	punct	_	_
4	$ (X, tau) $	$ (X, tau) $	PROPN	NNP	Number=Sing	5	nsubj	_	_
5	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	stronger	strong	ADJ	JJR	Degree=Cmp	9	amod	_	_
8	Stone	Stone	PROPN	NNP	Number=Sing	9	compound	_	_
9	topology	topology	NOUN	NN	Number=Sing	5	dobj	_	_
10	$ pi $	$ pi $	SYM	$	_	9	appos	_	_
11	such	such	ADJ	JJ	Degree=Pos	10	amod	_	_
12	that	that	PRON	DT	Number=Sing|PronType=Dem	14	mark	_	_
13	$ (X, tau, pi) $	$ (X, tau, pi) $	PROPN	NNP	Number=Sing	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
16	bitopological	bitopological	ADJ	JJ	Degree=Pos	19	amod	_	_
17	quasi	quasi	ADJ	JJ	Degree=Pos	19	amod	_	_
18	spectral	spectral	ADJ	JJ	Degree=Pos	19	amod	_	_
19	space	space	NOUN	NN	Number=Sing	14	attr	_	SpaceAfter=No

# doc_id = 512
# sent_id = 1
# text = We introduce the notion of mutation pairs in pseudo - triangulated categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	mutation	mutation	NOUN	NN	Number=Sing	7	compound	_	_
7	pairs	pair	NOUN	NNS	Number=Plur	5	pobj	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	pseudo	pseudo	NOUN	NN	Number=Sing	11	npadvmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	triangulated	triangulate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
12	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Given such a mutation pair, we prove that the corresponding quotient category carries a natural triangulated structure under certain conditions.
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	prep	_	_
2	such	such	DET	PDT	_	5	predet	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	mutation	mutation	NOUN	NN	Number=Sing	5	compound	_	_
5	pair	pair	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
7	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	8	nsubj	_	_
8	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	that	that	SCONJ	IN	_	14	mark	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
11	corresponding	corresponding	ADJ	JJ	Degree=Pos	13	amod	_	_
12	quotient	quotient	NOUN	NN	Number=Sing	13	compound	_	_
13	category	category	NOUN	NN	Number=Sing	14	nsubj	_	_
14	carries	carry	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	ccomp	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
16	natural	natural	ADJ	JJ	Degree=Pos	17	advmod	_	_
17	triangulated	triangulate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
18	structure	structure	NOUN	NN	Number=Sing	14	dobj	_	_
19	under	under	ADP	IN	_	14	prep	_	_
20	certain	certain	ADJ	JJ	Degree=Pos	21	amod	_	_
21	conditions	condition	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 3
# text = This result unifies many previous constructions of quotient triangulated categories.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	result	result	NOUN	NN	Number=Sing	3	nsubj	_	_
3	unifies	unify	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	many	many	ADJ	JJ	Degree=Pos	6	amod	_	_
5	previous	previous	ADJ	JJ	Degree=Pos	6	amod	_	_
6	constructions	construction	NOUN	NNS	Number=Plur	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	quotient	quotient	ADJ	JJ	Degree=Pos	10	amod	_	_
9	triangulated	triangulate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 513
# sent_id = 1
# text = We survey the general theory of groupoids, groupoid actions, groupoid principal bundles, and various kinds of morphisms between groupoids in the framework of categories with pretopology.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	survey	survey	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	general	general	ADJ	JJ	Degree=Pos	5	amod	_	_
5	theory	theory	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	groupoids	groupoid	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
9	groupoid	groupoid	NOUN	NN	Number=Sing	10	compound	_	_
10	actions	action	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	groupoid	groupoid	NOUN	NN	Number=Sing	10	acl	_	_
13	principal	principal	ADJ	JJ	Degree=Pos	14	amod	_	_
14	bundles	bundle	NOUN	NNS	Number=Plur	12	dobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
17	various	various	ADJ	JJ	Degree=Pos	18	amod	_	_
18	kinds	kind	NOUN	NNS	Number=Plur	14	conj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	morphisms	morphism	NOUN	NNS	Number=Plur	19	pobj	_	_
21	between	between	ADP	IN	_	18	prep	_	_
22	groupoids	groupoid	NOUN	NNS	Number=Plur	21	pobj	_	_
23	in	in	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	framework	framework	NOUN	NN	Number=Sing	23	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	categories	category	NOUN	NNS	Number=Plur	26	pobj	_	_
28	with	with	ADP	IN	_	25	prep	_	_
29	pretopology	pretopology	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The categories of topological spaces and finite or infinite dimensional manifolds are examples of such categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	categories	category	NOUN	NNS	Number=Plur	12	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	topological	topological	ADJ	JJ	Degree=Pos	5	amod	_	_
5	spaces	space	NOUN	NNS	Number=Plur	3	pobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	finite	finite	PROPN	NNP	Number=Sing	5	conj	_	_
8	or	or	CCONJ	CC	ConjType=Cmp	2	cc	_	_
9	infinite	infinite	VERB	VB	VerbForm=Inf	2	conj	_	_
10	dimensional	dimensional	ADJ	JJ	Degree=Pos	11	amod	_	_
11	manifolds	manifold	NOUN	NNS	Number=Plur	9	dobj	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	examples	example	NOUN	NNS	Number=Plur	12	attr	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	such	such	ADJ	JJ	Degree=Pos	16	amod	_	_
16	categories	category	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 3
# text = We study extra assumptions on pretopologies that are needed for this theory.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	extra	extra	ADJ	JJ	Degree=Pos	4	amod	_	_
4	assumptions	assumption	NOUN	NNS	Number=Plur	2	dobj	_	_
5	on	on	ADP	IN	_	4	prep	_	_
6	pretopologies	pretopologie	NOUN	NNS	Number=Plur	5	pobj	_	_
7	that	that	PRON	WDT	PronType=Rel	9	nsubjpass	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	needed	need	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	relcl	_	_
10	for	for	ADP	IN	_	9	prep	_	_
11	this	this	DET	DT	Number=Sing|PronType=Dem	12	det	_	_
12	theory	theory	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We check these extra assumptions in several categories with pretopologies.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	check	check	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	these	these	DET	DT	Number=Plur|PronType=Dem	5	det	_	_
4	extra	extra	ADJ	JJ	Degree=Pos	5	amod	_	_
5	assumptions	assumption	NOUN	NNS	Number=Plur	2	dobj	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	several	several	ADJ	JJ	Degree=Pos	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	pretopologies	pretopologie	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = Functors between groupoids may be localised at equivalences in two ways.
1	Functors	functor	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
2	between	between	ADP	IN	_	1	prep	_	_
3	groupoids	groupoid	NOUN	NNS	Number=Plur	2	pobj	_	_
4	may	may	AUX	MD	VerbForm=Fin	6	aux	_	_
5	be	be	AUX	VB	VerbForm=Inf	6	auxpass	_	_
6	localised	localise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	at	at	ADP	IN	_	6	prep	_	_
8	equivalences	equivalence	NOUN	NNS	Number=Plur	7	pobj	_	_
9	in	in	ADP	IN	_	6	prep	_	_
10	two	two	NUM	CD	NumType=Card	11	nummod	_	_
11	ways	way	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 6
# text = One uses spans of functors, the other bibundles (commuting actions) of groupoids.
1	One	one	NUM	CD	NumType=Card	2	nsubj	_	_
2	uses	use	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	spans	span	NOUN	NNS	Number=Plur	2	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	functors	functor	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	other	other	ADJ	JJ	Degree=Pos	9	amod	_	_
9	bibundles	bibundle	NOUN	NNS	Number=Plur	2	dobj	_	_
10	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	9	punct	_	SpaceAfter=No
11	commuting	commute	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	amod	_	_
12	actions	action	NOUN	NNS	Number=Plur	9	appos	_	SpaceAfter=No
13	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	12	punct	_	_
14	of	of	ADP	IN	_	12	prep	_	_
15	groupoids	groupoid	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = We show that both approaches give equivalent bicategories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	6	mark	_	_
4	both	both	DET	DT	_	5	det	_	_
5	approaches	approach	NOUN	NNS	Number=Plur	6	nsubj	_	_
6	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
7	equivalent	equivalent	ADJ	JJ	Degree=Pos	8	amod	_	_
8	bicategories	bicategorie	NOUN	NNS	Number=Plur	6	dobj	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 8
# text = Another type of groupoid morphism, called an actor, is closely related to functors between the categories of groupoid actions.
1	Another	another	DET	DT	_	2	det	_	_
2	type	type	NOUN	NN	Number=Sing	11	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	groupoid	groupoid	NOUN	NN	Number=Sing	5	compound	_	_
5	morphism	morphism	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
7	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	2	acl	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	actor	actor	NOUN	NN	Number=Sing	7	oprd	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	closely	closely	ADV	RB	_	13	advmod	_	_
13	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acomp	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	functors	functor	NOUN	NNS	Number=Plur	14	pobj	_	_
16	between	between	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	groupoid	groupoid	NOUN	NN	Number=Sing	21	compound	_	_
21	actions	action	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 9
# text = We also generalise actors using bibundles, and show that this gives another bicategory of groupoids.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	generalise	generalise	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	actors	actor	NOUN	NNS	Number=Plur	3	dobj	_	_
5	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	acl	_	_
6	bibundles	bibundle	NOUN	NNS	Number=Plur	5	dobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
9	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	3	conj	_	_
10	that	that	SCONJ	IN	_	12	mark	_	_
11	this	this	PRON	DT	Number=Sing|PronType=Dem	12	nsubj	_	_
12	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	ccomp	_	_
13	another	another	DET	DT	_	14	det	_	_
14	bicategory	bicategory	NOUN	NN	Number=Sing	12	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	groupoids	groupoid	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 514
# sent_id = 1
# text = We call a finitely complete category algebraically coherent if the change - of - base functors of its fibration of points are coherent, which means that they preserve finite limits and jointly strongly epimorphic pairs of arrows.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
4	finitely	finitely	ADV	RB	_	5	advmod	_	_
5	complete	complete	ADJ	JJ	Degree=Pos	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	2	dobj	_	_
7	algebraically	algebraically	ADV	RB	_	8	advmod	_	_
8	coherent	coherent	ADJ	JJ	Degree=Pos	2	oprd	_	_
9	if	if	SCONJ	IN	_	22	mark	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
11	change	change	NOUN	NN	Number=Sing	16	nmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
13	of	of	ADP	IN	_	11	prep	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
15	base	base	NOUN	NN	Number=Sing	13	pobj	_	_
16	functors	functor	NOUN	NNS	Number=Plur	22	nsubj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	19	poss	_	_
19	fibration	fibration	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	points	point	NOUN	NNS	Number=Plur	20	pobj	_	_
22	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	advcl	_	_
23	coherent	coherent	ADJ	JJ	Degree=Pos	22	acomp	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
25	which	which	PRON	WDT	_	26	nsubj	_	_
26	means	mean	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	advcl	_	_
27	that	that	SCONJ	IN	_	29	mark	_	_
28	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	29	nsubj	_	_
29	preserve	preserve	VERB	VBP	Tense=Pres|VerbForm=Fin	26	ccomp	_	_
30	finite	finite	ADJ	JJ	Degree=Pos	31	compound	_	_
31	limits	limit	NOUN	NNS	Number=Plur	29	dobj	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
33	jointly	jointly	ADV	RB	_	35	advmod	_	_
34	strongly	strongly	ADV	RB	_	35	advmod	_	_
35	epimorphic	epimorphic	ADJ	JJ	Degree=Pos	36	amod	_	_
36	pairs	pair	NOUN	NNS	Number=Plur	29	dobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	arrows	arrow	NOUN	NNS	Number=Plur	37	pobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We give examples of categories satisfying this condition; for instance, coherent categories and categories of interest in the sense of Orzech.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	examples	example	NOUN	NNS	Number=Plur	2	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	_
6	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	acl	_	_
7	this	this	DET	DT	Number=Sing|PronType=Dem	8	det	_	_
8	condition	condition	NOUN	NN	Number=Sing	6	dobj	_	SpaceAfter=No
9	;	;	PUNCT	:	_	2	punct	_	_
10	for	for	ADP	IN	_	2	prep	_	_
11	instance	instance	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
13	coherent	coherent	ADJ	JJ	Degree=Pos	14	amod	_	_
14	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	categories	category	NOUN	NNS	Number=Plur	14	conj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	interest	interest	NOUN	NN	Number=Sing	17	pobj	_	_
19	in	in	ADP	IN	_	14	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	sense	sense	NOUN	NN	Number=Sing	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	Orzech	Orzech	PROPN	NNP	Number=Sing	22	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We study equivalent conditions in the context of semi - abelian categories, as well as some of its consequences: including amongst others, strong protomodularity, and normality of Higgins commutators for normal subobjects, and in the varietal case, fibre - wise algebraic cartesian closedness.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	equivalent	equivalent	ADJ	JJ	Degree=Pos	4	amod	_	_
4	conditions	condition	NOUN	NNS	Number=Plur	2	dobj	_	_
5	in	in	ADP	IN	_	2	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	context	context	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	semi	semi	ADJ	JJ	Degree=Pos	12	amod	_	_
10	-	-	ADJ	JJ	Degree=Pos	12	amod	_	_
11	abelian	abelian	ADJ	JJ	Degree=Pos	12	amod	_	_
12	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
14	as	as	ADV	RB	_	16	advmod	_	_
15	well	well	ADV	RB	Degree=Pos	16	advmod	_	_
16	as	as	ADP	IN	_	2	cc	_	_
17	some	some	PRON	DT	_	2	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	20	poss	_	_
20	consequences	consequence	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	:	:	PUNCT	:	_	17	punct	_	_
22	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	acl	_	_
23	amongst	amongst	ADP	IN	_	22	prep	_	_
24	others	other	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	strong	strong	ADJ	JJ	Degree=Pos	27	amod	_	_
27	protomodularity	protomodularity	NOUN	NN	Number=Sing	24	conj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
30	normality	normality	NOUN	NN	Number=Sing	27	conj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	Higgins	Higgins	PROPN	NNP	Number=Sing	33	compound	_	_
33	commutators	commutator	NOUN	NNS	Number=Plur	31	pobj	_	_
34	for	for	ADP	IN	_	30	prep	_	_
35	normal	normal	ADJ	JJ	Degree=Pos	36	amod	_	_
36	subobjects	subobject	NOUN	NNS	Number=Plur	34	pobj	_	SpaceAfter=No
37	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
38	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
39	in	in	ADP	IN	_	49	prep	_	_
40	the	the	DET	DT	Definite=Def|PronType=Art	42	det	_	_
41	varietal	varietal	ADJ	JJ	Degree=Pos	42	amod	_	_
42	case	case	NOUN	NN	Number=Sing	39	pobj	_	SpaceAfter=No
43	,	,	PUNCT	,	PunctType=Comm	49	punct	_	_
44	fibre	fibre	NOUN	NN	Number=Sing	46	npadvmod	_	_
45	-	-	PUNCT	HYPH	PunctType=Dash	46	punct	_	_
46	wise	wise	ADJ	JJ	Degree=Pos	49	amod	_	_
47	algebraic	algebraic	ADJ	JJ	Degree=Pos	49	amod	_	_
48	cartesian	cartesian	NOUN	NN	Number=Sing	49	compound	_	_
49	closedness	closedness	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
50	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 515
# sent_id = 1
# text = In this paper, we use the language of operads to study open dynamical systems.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	language	language	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	operads	operad	NOUN	NNS	Number=Plur	9	pobj	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	study	study	VERB	VB	VerbForm=Inf	6	xcomp	_	_
13	open	open	ADJ	JJ	Degree=Pos	15	amod	_	_
14	dynamical	dynamical	ADJ	JJ	Degree=Pos	15	amod	_	_
15	systems	system	NOUN	NNS	Number=Plur	12	dobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = More specifically, we study the algebraic nature of assembling complex dynamical systems from an interconnection of simpler ones.
1	More	more	ADV	RBR	Degree=Cmp	2	advmod	_	_
2	specifically	specifically	ADV	RB	_	5	advmod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	algebraic	algebraic	ADJ	JJ	Degree=Pos	8	amod	_	_
8	nature	nature	NOUN	NN	Number=Sing	5	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	assembling	assemble	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	pcomp	_	_
11	complex	complex	ADJ	JJ	Degree=Pos	13	amod	_	_
12	dynamical	dynamical	ADJ	JJ	Degree=Pos	13	amod	_	_
13	systems	system	NOUN	NNS	Number=Plur	10	dobj	_	_
14	from	from	ADP	IN	_	10	prep	_	_
15	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	interconnection	interconnection	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	simpler	simple	ADJ	JJR	Degree=Cmp	19	amod	_	_
19	ones	one	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = The syntactic architecture of such interconnections is encoded using the visual language of wiring diagrams.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	syntactic	syntactic	ADJ	JJ	Degree=Pos	3	amod	_	_
3	architecture	architecture	NOUN	NN	Number=Sing	8	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	such	such	ADJ	JJ	Degree=Pos	6	amod	_	_
6	interconnections	interconnection	NOUN	NNS	Number=Plur	4	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	encoded	encode	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	xcomp	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	visual	visual	ADJ	JJ	Degree=Pos	12	amod	_	_
12	language	language	NOUN	NN	Number=Sing	9	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	wiring	wiring	NOUN	NN	Number=Sing	15	compound	_	_
15	diagrams	diagram	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 4
# text = We define the symmetric monoidal category $ W $ , from which we may construct an operad $ OW $ , whose objects are black boxes with input and output ports, and whose morphisms are wiring diagrams, thus prescribing the algebraic rules for interconnection.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
4	symmetric	symmetric	ADJ	JJ	Degree=Pos	6	amod	_	_
5	monoidal	monoidal	ADJ	JJ	Degree=Pos	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	2	dobj	_	_
7	$ W $	$ w $	SYM	$	_	6	appos	_	_
8	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
9	from	from	ADP	IN	_	13	prep	_	_
10	which	which	PRON	WDT	_	9	pobj	_	_
11	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
12	may	may	AUX	MD	VerbForm=Fin	13	aux	_	_
13	construct	construct	VERB	VB	VerbForm=Inf	6	relcl	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	operad	operad	ADJ	JJ	Degree=Pos	16	amod	_	_
16	$ OW $	$ ow $	SYM	$	_	13	dobj	_	_
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	whose	whose	DET	WP$	Poss=Yes	19	poss	_	_
19	objects	object	NOUN	NNS	Number=Plur	20	nsubj	_	_
20	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	16	relcl	_	_
21	black	black	ADJ	JJ	Degree=Pos	22	amod	_	_
22	boxes	box	NOUN	NNS	Number=Plur	20	attr	_	_
23	with	with	ADP	IN	_	22	prep	_	_
24	input	input	NOUN	NN	Number=Sing	27	nmod	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	output	output	NOUN	NN	Number=Sing	24	conj	_	_
27	ports	port	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
30	whose	whose	DET	WP$	Poss=Yes	31	poss	_	_
31	morphisms	morphism	NOUN	NNS	Number=Plur	33	nsubj	_	_
32	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	33	aux	_	_
33	wiring	wiring	NOUN	NN	Number=Sing	34	compound	_	_
34	diagrams	diagram	NOUN	NNS	Number=Plur	13	conj	_	SpaceAfter=No
35	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
36	thus	thus	ADV	RB	_	37	advmod	_	_
37	prescribing	prescribe	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	advcl	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
39	algebraic	algebraic	ADJ	JJ	Degree=Pos	40	amod	_	_
40	rules	rule	NOUN	NNS	Number=Plur	37	dobj	_	_
41	for	for	ADP	IN	_	40	prep	_	_
42	interconnection	interconnection	NOUN	NN	Number=Sing	41	pobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = We then define two $ W $ - algebras} $ G $ and $ L $ , which associate semantic content to the structures in $ W $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	two	two	NUM	CD	NumType=Card	7	nummod	_	_
5	$ W $	$ w $	SYM	$	_	7	nmod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	algebras	algebra	NOUN	NNS	Number=Plur	3	dobj	_	SpaceAfter=No
8	}	}	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	7	punct	_	_
9	$ G $	$ g $	SYM	$	_	7	appos	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	$ L $	$ l $	SYM	$	_	9	conj	_	_
12	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
13	which	which	PRON	WDT	_	14	nsubj	_	_
14	associate	associate	VERB	VBP	Tense=Pres|VerbForm=Fin	7	relcl	_	_
15	semantic	semantic	ADJ	JJ	Degree=Pos	16	amod	_	_
16	content	content	NOUN	NN	Number=Sing	14	dobj	_	_
17	to	to	ADP	IN	_	14	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	structures	structure	NOUN	NNS	Number=Plur	17	pobj	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	$ W $	$ w $	SYM	$	_	20	pobj	_	_
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = Respectively, they correspond to general and to linear systems of differential equations, in which an internal state is controlled by inputs and produces outputs.
1	Respectively	respectively	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	4	nsubj	_	_
4	correspond	correspond	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	general	general	ADJ	JJ	Degree=Pos	5	amod	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
8	to	to	ADP	IN	_	5	conj	_	_
9	linear	linear	ADJ	JJ	Degree=Pos	10	compound	_	_
10	systems	system	NOUN	NNS	Number=Plur	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	differential	differential	ADJ	JJ	Degree=Pos	13	amod	_	_
13	equations	equation	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
15	in	in	ADP	IN	_	21	prep	_	_
16	which	which	PRON	WDT	_	15	pobj	_	_
17	an	an	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	internal	internal	ADJ	JJ	Degree=Pos	19	amod	_	_
19	state	state	NOUN	NN	Number=Sing	21	nsubjpass	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	21	auxpass	_	_
21	controlled	control	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	relcl	_	_
22	by	by	ADP	IN	_	21	agent	_	_
23	inputs	input	NOUN	NNS	Number=Plur	22	pobj	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
25	produces	produce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	21	conj	_	_
26	outputs	output	NOUN	NNS	Number=Plur	25	dobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 7
# text = As an example, we use these algebras to formalize the classical problem of systems of tanks interconnected by pipes, and hence make explicit the algebraic relationships among systems at different levels of granularity.
1	As	as	ADP	IN	_	6	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	example	example	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	these	these	DET	DT	Number=Plur|PronType=Dem	8	det	_	_
8	algebras	algebra	NOUN	NNS	Number=Plur	6	dobj	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	formalize	formalize	VERB	VB	VerbForm=Inf	6	xcomp	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	classical	classical	ADJ	JJ	Degree=Pos	13	amod	_	_
13	problem	problem	NOUN	NN	Number=Sing	10	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	systems	system	NOUN	NNS	Number=Plur	14	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	tanks	tank	NOUN	NNS	Number=Plur	16	pobj	_	_
18	interconnected	interconnect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
19	by	by	ADP	IN	_	18	agent	_	_
20	pipes	pipe	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
23	hence	hence	ADV	RB	_	24	advmod	_	_
24	make	make	VERB	VBP	Tense=Pres|VerbForm=Fin	6	conj	_	_
25	explicit	explicit	ADJ	JJ	Degree=Pos	24	ccomp	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	algebraic	algebraic	ADJ	JJ	Degree=Pos	28	amod	_	_
28	relationships	relationship	NOUN	NNS	Number=Plur	25	dobj	_	_
29	among	among	ADP	IN	_	28	prep	_	_
30	systems	system	NOUN	NNS	Number=Plur	29	pobj	_	_
31	at	at	ADP	IN	_	30	prep	_	_
32	different	different	ADJ	JJ	Degree=Pos	33	amod	_	_
33	levels	level	NOUN	NNS	Number=Plur	31	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	granularity	granularity	NOUN	NN	Number=Sing	34	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 516
# sent_id = 1
# text = Inspired by recent work of Batanin and Berger on the homotopy theory of operads, a general monad - theoretic context for speaking about structures within structures is presented, and the problem of constructing the universal ambient structure containing the prescribed internal structure is studied.
1	Inspired	inspire	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	advcl	_	_
2	by	by	ADP	IN	_	1	agent	_	_
3	recent	recent	ADJ	JJ	Degree=Pos	4	amod	_	_
4	work	work	NOUN	NN	Number=Sing	2	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	Batanin	Batanin	PROPN	NNP	Number=Sing	5	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	Berger	Berger	PROPN	NNP	Number=Sing	6	conj	_	_
9	on	on	ADP	IN	_	4	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	homotopy	homotopy	NOUN	NN	Number=Sing	12	compound	_	_
12	theory	theory	NOUN	NN	Number=Sing	9	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	operads	operad	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
17	general	general	ADJ	JJ	Degree=Pos	21	amod	_	_
18	monad	monad	NOUN	NNS	Number=Plur	20	npadvmod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	theoretic	theoretic	ADJ	JJ	Degree=Pos	21	amod	_	_
21	context	context	NOUN	NN	Number=Sing	29	nsubjpass	_	_
22	for	for	ADP	IN	_	21	prep	_	_
23	speaking	speak	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	pcomp	_	_
24	about	about	ADP	IN	_	23	prep	_	_
25	structures	structure	NOUN	NNS	Number=Plur	29	nsubjpass	_	_
26	within	within	ADP	IN	_	25	prep	_	_
27	structures	structure	NOUN	NNS	Number=Plur	26	pobj	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	auxpass	_	_
29	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
33	problem	problem	NOUN	NN	Number=Sing	46	nsubjpass	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	constructing	construct	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	34	pcomp	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
37	universal	universal	ADJ	JJ	Degree=Pos	39	amod	_	_
38	ambient	ambient	ADJ	JJ	Degree=Pos	39	amod	_	_
39	structure	structure	NOUN	NN	Number=Sing	35	dobj	_	_
40	containing	contain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	39	acl	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	44	det	_	_
42	prescribed	prescribed	ADJ	JJ	Degree=Pos	44	amod	_	_
43	internal	internal	ADJ	JJ	Degree=Pos	44	amod	_	_
44	structure	structure	NOUN	NN	Number=Sing	40	dobj	_	_
45	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	46	auxpass	_	_
46	studied	study	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	conj	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	46	punct	_	SpaceAfter=No

# sent_id = 2
# text = Following the work of Lack, these universal objects must be constructed from simplicial objects arising from our monad - theoretic framework, as certain 2 - categorical colimits called codescent objects.
1	Following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	work	work	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	Lack	Lack	PROPN	NNP	Number=Sing	4	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
7	these	these	DET	DT	Number=Plur|PronType=Dem	9	det	_	_
8	universal	universal	ADJ	JJ	Degree=Pos	9	amod	_	_
9	objects	object	NOUN	NNS	Number=Plur	12	nsubjpass	_	_
10	must	must	AUX	MD	VerbForm=Fin	12	aux	_	_
11	be	be	AUX	VB	VerbForm=Inf	12	auxpass	_	_
12	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
13	from	from	ADP	IN	_	12	prep	_	_
14	simplicial	simplicial	ADJ	JJ	Degree=Pos	15	amod	_	_
15	objects	object	NOUN	NNS	Number=Plur	13	pobj	_	_
16	arising	arise	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	acl	_	_
17	from	from	ADP	IN	_	16	prep	_	_
18	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	22	poss	_	_
19	monad	monad	NOUN	NNS	Number=Plur	21	npadvmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	theoretic	theoretic	NOUN	NN	Number=Sing	22	amod	_	_
22	framework	framework	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
24	as	as	SCONJ	IN	_	30	mark	_	_
25	certain	certain	ADJ	JJ	Degree=Pos	29	amod	_	_
26	2	2	NUM	CD	NumType=Card	28	nummod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	categorical	categorical	ADJ	JJ	Degree=Pos	29	amod	_	_
29	colimits	colimit	NOUN	NNS	Number=Plur	30	nsubj	_	_
30	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	advcl	_	_
31	codescent	codescent	NOUN	NN	Number=Sing	32	compound	_	_
32	objects	object	NOUN	NNS	Number=Plur	30	oprd	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 3
# text = We isolate the extra structure present on these simplicial objects which enable their codescent objects to be computed.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	isolate	isolate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	extra	extra	ADJ	JJ	Degree=Pos	5	amod	_	_
5	structure	structure	NOUN	NN	Number=Sing	2	dobj	_	_
6	present	present	ADJ	JJ	Degree=Pos	5	amod	_	_
7	on	on	ADP	IN	_	6	prep	_	_
8	these	these	DET	DT	Number=Plur|PronType=Dem	10	det	_	_
9	simplicial	simplicial	ADJ	JJ	Degree=Pos	10	amod	_	_
10	objects	object	NOUN	NNS	Number=Plur	7	pobj	_	_
11	which	which	PRON	WDT	_	12	nsubj	_	_
12	enable	enable	VERB	VBP	Tense=Pres|VerbForm=Fin	10	relcl	_	_
13	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	15	poss	_	_
14	codescent	codescent	NOUN	NN	Number=Sing	15	compound	_	_
15	objects	object	NOUN	NNS	Number=Plur	12	dobj	_	_
16	to	to	PART	TO	_	18	aux	_	_
17	be	be	AUX	VB	VerbForm=Inf	18	auxpass	_	_
18	computed	compute	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	xcomp	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = These are the crossed internal categories of the title, and generalise the crossed simplicial groups of Loday and Fiedorowicz.
1	These	these	PRON	DT	Number=Plur|PronType=Dem	2	nsubj	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
4	crossed	crossed	ADJ	JJ	Degree=Pos	6	amod	_	_
5	internal	internal	ADJ	JJ	Degree=Pos	6	amod	_	_
6	categories	category	NOUN	NNS	Number=Plur	2	attr	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	title	title	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
12	generalise	generalise	VERB	VB	VerbForm=Inf	2	conj	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
14	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
15	simplicial	simplicial	ADJ	JJ	Degree=Pos	16	amod	_	_
16	groups	group	NOUN	NNS	Number=Plur	12	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	Loday	Loday	PROPN	NNP	Number=Sing	17	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	Fiedorowicz	Fiedorowicz	PROPN	NNP	Number=Sing	18	conj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = The most general results of this article are concerned with how to compute such codescent objects in 2 - categories of internal categories, and on isolating conditions on the monad - theoretic situation which enable these results to apply.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	most	most	ADV	RBS	Degree=Sup	3	advmod	_	_
3	general	general	ADJ	JJ	Degree=Pos	4	amod	_	_
4	results	result	NOUN	NNS	Number=Plur	9	nsubjpass	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
7	article	article	NOUN	NN	Number=Sing	5	pobj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	concerned	concern	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	how	how	SCONJ	WRB	_	13	advmod	_	_
12	to	to	PART	TO	_	13	aux	_	_
13	compute	compute	VERB	VB	VerbForm=Inf	10	pcomp	_	_
14	such	such	ADJ	JJ	Degree=Pos	16	amod	_	_
15	codescent	codescent	NOUN	NN	Number=Sing	16	compound	_	_
16	objects	object	NOUN	NNS	Number=Plur	13	dobj	_	_
17	in	in	ADP	IN	_	13	prep	_	_
18	2	2	NUM	CD	NumType=Card	20	nummod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	internal	internal	ADJ	JJ	Degree=Pos	23	amod	_	_
23	categories	category	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
26	on	on	ADP	IN	_	9	conj	_	_
27	isolating	isolate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	26	pcomp	_	_
28	conditions	condition	NOUN	NNS	Number=Plur	27	dobj	_	_
29	on	on	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
31	monad	monad	NOUN	NNS	Number=Plur	33	npadvmod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	theoretic	theoretic	ADJ	JJ	Degree=Pos	34	amod	_	_
34	situation	situation	NOUN	NN	Number=Sing	29	pobj	_	_
35	which	which	PRON	WDT	_	36	nsubj	_	_
36	enable	enable	VERB	VBP	Tense=Pres|VerbForm=Fin	34	relcl	_	_
37	these	these	DET	DT	Number=Plur|PronType=Dem	38	det	_	_
38	results	result	NOUN	NNS	Number=Plur	36	dobj	_	_
39	to	to	PART	TO	_	40	aux	_	_
40	apply	apply	VERB	VB	VerbForm=Inf	36	xcomp	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 6
# text = Combined with earlier work of the author in which operads are seen as polynomial 2 - monads, our results are then applied to the theory of non - symmetric, symmetric and braided operads.
1	Combined	combine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	advcl	_	_
2	with	with	ADP	IN	_	1	prep	_	_
3	earlier	early	ADJ	JJR	Degree=Cmp	4	amod	_	_
4	work	work	NOUN	NN	Number=Sing	2	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	author	author	NOUN	NN	Number=Sing	5	pobj	_	_
8	in	in	ADP	IN	_	12	prep	_	_
9	which	which	PRON	WDT	_	8	pobj	_	_
10	operads	operad	NOUN	NNS	Number=Plur	12	nsubjpass	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	relcl	_	_
13	as	as	ADP	IN	_	12	prep	_	_
14	polynomial	polynomial	ADJ	JJ	Degree=Pos	17	amod	_	_
15	2	2	NUM	CD	NumType=Card	17	nummod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	monads	monad	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
19	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	20	poss	_	_
20	results	result	NOUN	NNS	Number=Plur	23	nsubjpass	_	_
21	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	23	auxpass	_	_
22	then	then	ADV	RB	PronType=Dem	23	advmod	_	_
23	applied	apply	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
24	to	to	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	theory	theory	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	non	non	ADJ	JJ	Degree=Pos	30	amod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	symmetric	symmetric	ADJ	JJ	Degree=Pos	35	amod	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
32	symmetric	symmetric	ADJ	JJ	Degree=Pos	35	amod	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
34	braided	braid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	conj	_	_
35	operads	operad	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# sent_id = 7
# text = In particular, the well - known construction of a PROP from an operad is recovered, as an illustration of our techniques.
1	In	in	ADP	IN	_	16	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
5	well	well	ADV	RB	Degree=Pos	7	advmod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
8	construction	construction	NOUN	NN	Number=Sing	16	nsubjpass	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	PROP	prop	NOUN	NN	Number=Sing	9	pobj	_	_
12	from	from	ADP	IN	_	8	prep	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	operad	operad	NOUN	NN	Number=Sing	12	pobj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	auxpass	_	_
16	recovered	recover	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	as	as	ADP	IN	_	16	prep	_	_
19	an	an	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	illustration	illustration	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	23	poss	_	_
23	techniques	technique	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# doc_id = 517
# sent_id = 1
# text = We show that the category of abstract elementary classes and concrete functors is closed under constructions of ``limit type, " which generalizes the approach of Mariano, Zambrano and Villaveces away from the syntactically oriented framework of institutions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	14	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	14	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	abstract	abstract	ADJ	JJ	Degree=Pos	9	amod	_	_
8	elementary	elementary	ADJ	JJ	Degree=Pos	9	compound	_	_
9	classes	class	NOUN	NNS	Number=Plur	6	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	concrete	concrete	ADJ	JJ	Degree=Pos	12	amod	_	_
12	functors	functor	NOUN	NNS	Number=Plur	9	conj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
15	under	under	ADP	IN	_	14	prep	_	_
16	constructions	construction	NOUN	NNS	Number=Plur	15	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	17	punct	_	SpaceAfter=No
19	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	17	punct	_	SpaceAfter=No
20	limit	limit	VERB	VB	VerbForm=Inf	21	compound	_	_
21	type	type	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	21	punct	_	_
24	which	which	PRON	WDT	_	25	nsubj	_	_
25	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	21	relcl	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	approach	approach	NOUN	NN	Number=Sing	25	dobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	Mariano	Mariano	PROPN	NNP	Number=Sing	28	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
31	Zambrano	Zambrano	PROPN	NNP	Number=Sing	29	conj	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	Villaveces	Villaveces	PROPN	NNPS	Number=Plur	31	conj	_	_
34	away	away	ADV	RB	_	25	advmod	_	_
35	from	from	ADP	IN	_	34	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
37	syntactically	syntactically	ADV	RB	_	38	advmod	_	_
38	oriented	orient	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	39	amod	_	_
39	framework	framework	NOUN	NN	Number=Sing	35	pobj	_	_
40	of	of	ADP	IN	_	39	prep	_	_
41	institutions	institution	NOUN	NNS	Number=Plur	40	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Moreover, we provide a broader view of this closure phenomenon, considering a variety of categories of accessible categories with additional structure, and relaxing the assumption that the morphisms be concrete functors.
1	Moreover	moreover	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	broader	broad	ADJ	JJR	Degree=Cmp	7	amod	_	_
7	view	view	NOUN	NN	Number=Sing	4	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	this	this	DET	DT	Number=Sing|PronType=Dem	11	det	_	_
10	closure	closure	NOUN	NN	Number=Sing	11	amod	_	_
11	phenomenon	phenomenon	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
13	considering	consider	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	advcl	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	variety	variety	NOUN	NN	Number=Sing	13	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	accessible	accessible	ADJ	JJ	Degree=Pos	20	amod	_	_
20	categories	category	NOUN	NNS	Number=Plur	18	pobj	_	_
21	with	with	ADP	IN	_	15	prep	_	_
22	additional	additional	ADJ	JJ	Degree=Pos	23	amod	_	_
23	structure	structure	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
26	relaxing	relax	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	conj	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	assumption	assumption	NOUN	NN	Number=Sing	26	dobj	_	_
29	that	that	SCONJ	IN	_	32	mark	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	morphisms	morphism	NOUN	NNS	Number=Plur	32	nsubj	_	_
32	be	be	AUX	VB	VerbForm=Inf	28	acl	_	_
33	concrete	concrete	ADJ	JJ	Degree=Pos	34	amod	_	_
34	functors	functor	NOUN	NNS	Number=Plur	32	attr	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 518
# sent_id = 1
# text = In this article we give a construction of a polynomial 2 - monad from an operad and describe the algebras of the 2 - monads which then arise.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	article	article	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	construction	construction	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
10	polynomial	polynomial	ADJ	JJ	Degree=Pos	13	amod	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	monad	monad	NOUN	NNS	Number=Plur	8	pobj	_	_
14	from	from	ADP	IN	_	5	prep	_	_
15	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	operad	operad	NOUN	NN	Number=Sing	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
18	describe	describe	VERB	VB	VerbForm=Inf	5	conj	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	algebras	algebra	NOUN	NNS	Number=Plur	18	dobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
23	2	2	NUM	CD	NumType=Card	25	nummod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	monads	monad	NOUN	NNS	Number=Plur	21	pobj	_	_
26	which	which	PRON	WDT	_	28	nsubj	_	_
27	then	then	ADV	RB	PronType=Dem	28	advmod	_	_
28	arise	arise	VERB	VBP	Tense=Pres|VerbForm=Fin	25	relcl	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = This construction is different from the standard construction of a monad from an operad in that the algebras of our associated 2 - monad are the categorified algebras of the original operad.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	construction	construction	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	different	different	ADJ	JJ	Degree=Pos	3	acomp	_	_
5	from	from	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	standard	standard	ADJ	JJ	Degree=Pos	8	amod	_	_
8	construction	construction	NOUN	NN	Number=Sing	5	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	monad	monad	NOUN	NNS	Number=Plur	9	pobj	_	_
12	from	from	ADP	IN	_	11	prep	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	operad	operad	NOUN	NN	Number=Sing	12	pobj	_	_
15	in	in	SCONJ	IN	_	25	mark	_	_
16	that	that	SCONJ	IN	_	25	mark	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	algebras	algebra	NOUN	NNS	Number=Plur	25	nsubj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	24	poss	_	_
21	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
22	2	2	NUM	CD	NumType=Card	24	nummod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	monad	monad	NOUN	NNS	Number=Plur	19	pobj	_	_
25	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	advcl	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	categorified	categorified	ADJ	JJ	Degree=Pos	28	amod	_	_
28	algebras	algebra	NOUN	NNS	Number=Plur	25	attr	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	original	original	ADJ	JJ	Degree=Pos	32	amod	_	_
32	operad	operad	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Moreover it enables us to characterise operads as categorical polynomial monads in a canonical way.
1	Moreover	moreover	ADV	RB	_	3	advmod	_	_
2	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubj	_	_
3	enables	enable	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	3	dobj	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	characterise	characterise	VERB	VB	VerbForm=Inf	3	xcomp	_	_
7	operads	operad	NOUN	NNS	Number=Plur	6	dobj	_	_
8	as	as	ADP	IN	_	6	prep	_	_
9	categorical	categorical	ADJ	JJ	Degree=Pos	11	amod	_	_
10	polynomial	polynomial	ADJ	JJ	Degree=Pos	11	amod	_	_
11	monads	monad	NOUN	NNS	Number=Plur	8	pobj	_	_
12	in	in	ADP	IN	_	6	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	canonical	canonical	ADJ	JJ	Degree=Pos	15	amod	_	_
15	way	way	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = This point of view reveals categorical polynomial monads as a unifying environment for operads, $ Cat $ - operads and clubs.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	point	point	NOUN	NN	Number=Sing	5	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	view	view	NOUN	NN	Number=Sing	3	pobj	_	_
5	reveals	reveal	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	categorical	categorical	ADJ	JJ	Degree=Pos	8	amod	_	_
7	polynomial	polynomial	ADJ	JJ	Degree=Pos	8	amod	_	_
8	monads	monad	NOUN	NNS	Number=Plur	5	dobj	_	_
9	as	as	ADP	IN	_	5	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	unifying	unifying	ADJ	JJ	Degree=Pos	12	amod	_	_
12	environment	environment	NOUN	NN	Number=Sing	9	pobj	_	_
13	for	for	ADP	IN	_	12	prep	_	_
14	operads	operad	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
16	$ Cat $	$ cat $	SYM	$	_	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	operads	operad	NOUN	NNS	Number=Plur	12	conj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	clubs	club	NOUN	NNS	Number=Plur	18	conj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = We recover the standard construction of a monad from an operad in a 2 - categorical way from our associated 2 - monad as a coidentifier of 2 - monads, and understand the algebras of both as weak morphisms of operads into a $ Cat $ - operad of categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	recover	recover	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	standard	standard	ADJ	JJ	Degree=Pos	5	amod	_	_
5	construction	construction	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	monad	monad	NOUN	NNS	Number=Plur	6	pobj	_	_
9	from	from	ADP	IN	_	8	prep	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	operad	operad	NOUN	NN	Number=Sing	9	pobj	_	_
12	in	in	ADP	IN	_	2	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
14	2	2	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	categorical	categorical	ADJ	JJ	Degree=Pos	17	amod	_	_
17	way	way	NOUN	NN	Number=Sing	12	pobj	_	_
18	from	from	ADP	IN	_	17	prep	_	_
19	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	23	poss	_	_
20	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	amod	_	_
21	2	2	NUM	CD	NumType=Card	23	nummod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	monad	monad	NOUN	NNS	Number=Plur	18	pobj	_	_
24	as	as	ADP	IN	_	2	prep	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
26	coidentifier	coidentifier	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	2	2	NUM	CD	NumType=Card	30	nummod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	monads	monad	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
33	understand	understand	VERB	VB	VerbForm=Inf	2	conj	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	algebras	algebra	NOUN	NNS	Number=Plur	33	dobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	both	both	PRON	DT	_	36	pobj	_	_
38	as	as	ADP	IN	_	33	prep	_	_
39	weak	weak	ADJ	JJ	Degree=Pos	40	amod	_	_
40	morphisms	morphism	NOUN	NNS	Number=Plur	38	pobj	_	_
41	of	of	ADP	IN	_	40	prep	_	_
42	operads	operad	NOUN	NNS	Number=Plur	41	pobj	_	_
43	into	into	ADP	IN	_	33	prep	_	_
44	a	a	DET	DT	Definite=Ind|PronType=Art	47	det	_	_
45	$ Cat $	$ cat $	SYM	$	_	47	nmod	_	_
46	-	-	PUNCT	HYPH	PunctType=Dash	47	punct	_	_
47	operad	operad	NOUN	NN	Number=Sing	43	pobj	_	_
48	of	of	ADP	IN	_	47	prep	_	_
49	categories	category	NOUN	NNS	Number=Plur	48	pobj	_	SpaceAfter=No
50	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = Algebras of operads within general symmetric monoidal categories arise from our new associated 2 - monad in a canonical way.
1	Algebras	algebra	NOUN	NNS	Number=Plur	9	nsubj	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	operads	operad	NOUN	NNS	Number=Plur	2	pobj	_	_
4	within	within	ADP	IN	_	3	prep	_	_
5	general	general	ADJ	JJ	Degree=Pos	8	amod	_	_
6	symmetric	symmetric	ADJ	JJ	Degree=Pos	8	amod	_	_
7	monoidal	monoidal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	_
9	arise	arise	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	from	from	ADP	IN	_	9	prep	_	_
11	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	16	poss	_	_
12	new	new	ADJ	JJ	Degree=Pos	16	amod	_	_
13	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
14	2	2	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	monad	monad	NOUN	NNS	Number=Plur	10	pobj	_	_
17	in	in	ADP	IN	_	9	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	canonical	canonical	ADJ	JJ	Degree=Pos	20	amod	_	_
20	way	way	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 7
# text = When the operad is sigma - free, we establish a Quillen equivalence, with respect to the model structures on algebras of 2 - monads found by Lack, between the strict algebras of our associated 2 - monad, and those of the standard one.
1	When	when	SCONJ	WRB	_	4	advmod	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	operad	operad	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	advcl	_	_
5	sigma	sigma	PROPN	NNP	Number=Sing	7	npadvmod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	free	free	ADJ	JJ	Degree=Pos	4	acomp	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
9	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
10	establish	establish	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	Quillen	quillen	ADJ	JJ	Degree=Pos	13	amod	_	_
13	equivalence	equivalence	NOUN	NN	Number=Sing	10	dobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
15	with	with	ADP	IN	_	10	prep	_	_
16	respect	respect	NOUN	NN	Number=Sing	15	pobj	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	model	model	NOUN	NN	Number=Sing	20	compound	_	_
20	structures	structure	NOUN	NNS	Number=Plur	17	pobj	_	_
21	on	on	ADP	IN	_	20	prep	_	_
22	algebras	algebra	NOUN	NNS	Number=Plur	21	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	2	2	NUM	CD	NumType=Card	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	monads	monad	NOUN	NNS	Number=Plur	23	pobj	_	_
27	found	find	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	acl	_	_
28	by	by	ADP	IN	_	27	agent	_	_
29	Lack	Lack	PROPN	NNP	Number=Sing	28	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
31	between	between	ADP	IN	_	20	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
33	strict	strict	ADJ	JJ	Degree=Pos	34	amod	_	_
34	algebras	algebra	NOUN	NNS	Number=Plur	31	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	40	poss	_	_
37	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	40	amod	_	_
38	2	2	NUM	CD	NumType=Card	40	nummod	_	_
39	-	-	PUNCT	HYPH	PunctType=Dash	40	punct	_	_
40	monad	monad	NOUN	NNS	Number=Plur	35	pobj	_	SpaceAfter=No
41	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
42	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
43	those	those	PRON	DT	Number=Plur|PronType=Dem	10	conj	_	_
44	of	of	ADP	IN	_	43	prep	_	_
45	the	the	DET	DT	Definite=Def|PronType=Art	47	det	_	_
46	standard	standard	ADJ	JJ	Degree=Pos	47	amod	_	_
47	one	one	NUM	CD	NumType=Card	44	pobj	_	SpaceAfter=No
48	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# doc_id = 519
# sent_id = 1
# text = For any total category $ K $ , with defining adjunction $ sup ladj Y : K rightarrow set^{K^{op}} $ , the expression $ W(a)(k)= set^{set^{K^{op}}}(K(a, sup - ), [k, - ]) $ , where $ [k, - ] $ is evaluation at $ k $ , provides a well - defined functor $ W : K rightarrow hat{K} = set^{K^{op}} $ .
1	For	for	ADP	IN	_	23	prep	_	_
2	any	any	DET	DT	_	4	det	_	_
3	total	total	ADJ	JJ	Degree=Pos	4	amod	_	_
4	category	category	NOUN	NN	Number=Sing	1	pobj	_	_
5	$ K $	$ k $	SYM	$	_	1	pcomp	_	_
6	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
7	with	with	ADP	IN	_	23	prep	_	_
8	defining	define	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	pcomp	_	_
9	adjunction	adjunction	NOUN	NN	Number=Sing	8	dobj	_	_
10	$ sup ladj Y : K rightarrow set^{K^{op}} $	$ sup ladj y : k rightarrow set^{k^{op}} $	SYM	$	_	8	dobj	_	_
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	expression	expression	NOUN	NN	Number=Sing	10	appos	_	_
14	$ W(a)(k)= set^{set^{K^{op}}}(K(a, sup - ), [k, - ]) $	$ w(a)(k)= set^{set^{k^{op}}}(k(a, sup - ), [k, - ]) $	SYM	$	_	13	appos	_	_
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	where	where	SCONJ	WRB	_	18	advmod	_	_
17	$ [k, - ] $	$ [k, - ] $	SYM	$	_	18	nsubj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
19	evaluation	evaluation	NOUN	NN	Number=Sing	18	attr	_	_
20	at	at	ADP	IN	_	19	prep	_	_
21	$ k $	$ k $	SYM	$	_	20	pobj	_	_
22	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
23	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
25	well	well	ADV	RB	Degree=Pos	27	advmod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	amod	_	_
28	functor	functor	NOUN	NN	Number=Sing	23	dobj	_	_
29	$ W : K rightarrow hat{K} = set^{K^{op}} $	$ w : k rightarrow hat{k} = set^{k^{op}} $	SYM	$	_	23	dobj	_	_
30	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# sent_id = 2
# text = Also, there are natural transformations $ beta : Wsup rightarrow 1_{hat{K}} $ and $ gamma : sup W rightarrow 1_K $ satisfying $ supbeta =gammasup $ and $ beta W =Wgamma $ .
1	Also	also	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	there	there	PRON	EX	_	4	expl	_	_
4	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	natural	natural	ADJ	JJ	Degree=Pos	6	amod	_	_
6	transformations	transformation	NOUN	NNS	Number=Plur	4	attr	_	_
7	$ beta : Wsup rightarrow 1_{hat{K}} $	$ beta : wsup rightarrow 1_{hat{k}} $	SYM	$	_	6	appos	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	$ gamma : sup W rightarrow 1_K $	$ gamma : sup w rightarrow 1_k $	SYM	$	_	4	dep	_	_
10	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	advcl	_	_
11	$ supbeta =gammasup $	$ supbeta =gammasup $	SYM	$	_	10	dobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	$ beta W =Wgamma $	$ beta w =wgamma $	SYM	$	_	11	conj	_	_
14	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = A total $ K $ is totally distributive if $ sup $ has a left adjoint.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	total	total	NOUN	NN	Number=Sing	3	amod	_	_
3	$ K $	$ k $	SYM	$	_	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	totally	totally	ADV	RB	_	6	advmod	_	_
6	distributive	distributive	ADJ	JJ	Degree=Pos	4	acomp	_	_
7	if	if	SCONJ	IN	_	9	mark	_	_
8	$ sup $	$ sup $	SYM	$	_	9	nsubj	_	_
9	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	advcl	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	left	left	ADJ	JJ	Degree=Pos	12	amod	_	_
12	adjoint	adjoint	NOUN	NN	Number=Sing	9	dobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show that $ K $ is totally distributive iff $ gamma $ is invertible iff $ W ladj sup $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	$ K $	$ k $	SYM	$	_	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	totally	totally	ADV	RB	_	7	advmod	_	_
7	distributive	distributive	ADJ	JJ	Degree=Pos	5	acomp	_	_
8	iff	iff	PROPN	NNP	Number=Sing	7	prep	_	_
9	$ gamma $	$ gamma $	X	XX	_	10	nsubj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	conj	_	_
11	invertible	invertible	ADJ	JJ	Degree=Pos	10	acomp	_	_
12	iff	iff	PROPN	NNP	Number=Sing	10	npadvmod	_	_
13	$ W ladj sup $	$ w ladj sup $	SYM	$	_	10	attr	_	_
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = The elements of $ W(a)(k) $ are called waves from $ k $ to $ a $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	elements	element	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	$ W(a)(k) $	$ w(a)(k) $	SYM	$	_	3	pobj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	waves	wave	NOUN	NNS	Number=Plur	6	oprd	_	_
8	from	from	ADP	IN	_	6	prep	_	_
9	$ k $	$ k $	SYM	$	_	8	pobj	_	_
10	to	to	PART	TO	_	8	prep	_	_
11	$ a $	$ a $	SYM	$	_	10	pobj	_	_
12	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 6
# text = Write $ tilde{K}(k, a) $ for $ W(a)(k) $ .
1	Write	write	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ tilde{K}(k, a) $	$ tilde{k}(k, a) $	SYM	$	_	1	dobj	_	_
3	for	for	ADP	IN	_	2	prep	_	_
4	$ W(a)(k) $	$ w(a)(k) $	SYM	$	_	3	pobj	_	_
5	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 7
# text = For any total $ K $ there is an associative composition of waves.
1	For	for	ADP	IN	_	6	prep	_	_
2	any	any	DET	DT	_	3	det	_	_
3	total	total	ADJ	JJ	Degree=Pos	1	pobj	_	_
4	$ K $	$ k $	SYM	$	_	3	prep	_	_
5	there	there	PRON	EX	_	6	expl	_	_
6	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	associative	associative	ADJ	JJ	Degree=Pos	9	amod	_	_
9	composition	composition	NOUN	NN	Number=Sing	6	attr	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	waves	wave	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 8
# text = Composition becomes an arrow $ bullet : tilde{K}circ_{K}tilde{K} rightarrow tilde{K} $ .
1	Composition	composition	NOUN	NN	Number=Sing	2	nsubj	_	_
2	becomes	become	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	arrow	arrow	NOUN	NN	Number=Sing	5	compound	_	_
5	$ bullet : tilde{K}circ_{K}tilde{K} rightarrow tilde{K} $	$ bullet : tilde{k}circ_{k}tilde{k} rightarrow tilde{k} $	SYM	$	_	2	attr	_	_
6	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 9
# text = Also, there is an augmentation $ tilde{K}( - , - ) rightarrow K( - , - ) $ corresponding to a natural $ delta : W rightarrow Y $ constructed via $ beta $ .
1	Also	also	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	there	there	PRON	EX	_	4	expl	_	_
4	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	augmentation	augmentation	NOUN	NN	Number=Sing	4	attr	_	_
7	$ tilde{K}( - , - ) rightarrow K( - , - ) $	$ tilde{k}( - , - ) rightarrow k( - , - ) $	SYM	$	_	8	nsubj	_	_
8	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	conj	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	natural	natural	ADJ	JJ	Degree=Pos	12	amod	_	_
12	$ delta : W rightarrow Y $	$ delta : w rightarrow y $	SYM	$	_	9	pobj	_	_
13	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
14	via	via	ADP	IN	_	13	prep	_	_
15	$ beta $	$ beta $	SYM	$	_	14	pobj	_	_
16	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 10
# text = We show that if $ K $ is totally distributive then $ bullet $ is invertible and then $ tilde{K} $ supports an idempotent comonad structure.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	11	mark	_	_
4	if	if	SCONJ	IN	_	6	mark	_	_
5	$ K $	$ k $	SYM	$	_	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	advcl	_	_
7	totally	totally	ADV	RB	_	8	advmod	_	_
8	distributive	distributive	ADJ	JJ	Degree=Pos	6	acomp	_	_
9	then	then	ADV	RB	PronType=Dem	10	advmod	_	_
10	$ bullet $	$ bullet $	SYM	$	_	11	nsubj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
12	invertible	invertible	ADJ	JJ	Degree=Pos	11	acomp	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
14	then	then	ADV	RB	PronType=Dem	16	advmod	_	_
15	$ tilde{K} $	$ tilde{k} $	SYM	$	_	16	nsubj	_	_
16	supports	support	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	conj	_	_
17	an	an	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
18	idempotent	idempotent	ADJ	JJ	Degree=Pos	20	amod	_	_
19	comonad	comonad	NOUN	NNS	Number=Plur	20	compound	_	_
20	structure	structure	NOUN	NN	Number=Sing	16	dobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 11
# text = In fact, $ tilde{K} circ_{K} tilde{K} = tilde{K} circ_{tilde{K}} tilde{K} $ so that $ bullet $ is the coequalizer of $ bullet K $ and $ K bullet $ , making $ tilde{K} $ a taxon in the sense of Koslowski.
1	In	in	ADP	IN	_	8	prep	_	_
2	fact	fact	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
4	$ tilde{K} circ_{K} tilde{K} = tilde{K} circ_{tilde{K}} tilde{K} $	$ tilde{k} circ_{k} tilde{k} = tilde{k} circ_{tilde{k}} tilde{k} $	SYM	$	_	8	nsubj	_	_
5	so	so	SCONJ	IN	_	8	mark	_	_
6	that	that	SCONJ	IN	_	8	mark	_	_
7	$ bullet $	$ bullet $	SYM	$	_	8	nsubj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	coequalizer	coequalizer	NOUN	NN	Number=Sing	8	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	$ bullet K $	$ bullet k $	SYM	$	_	11	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
14	$ K bullet $	$ k bullet $	SYM	$	_	10	conj	_	_
15	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
16	making	make	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	advcl	_	_
17	$ tilde{K} $	$ tilde{k} $	SYM	$	_	19	predet	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	taxon	taxon	NOUN	NN	Number=Sing	16	ccomp	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	sense	sense	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	Koslowski	Koslowski	PROPN	NNP	Number=Sing	23	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 12
# text = For a small taxon $ T $ , the category of interpolative modules $ iMod(1, T) $ is totally distributive.
1	For	for	ADP	IN	_	13	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	small	small	ADJ	JJ	Degree=Pos	4	amod	_	_
4	taxon	taxon	NOUN	NN	Number=Sing	1	pobj	_	_
5	$ T $	$ t $	SYM	$	_	1	pobj	_	_
6	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	13	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	interpolative	interpolative	ADJ	JJ	Degree=Pos	11	amod	_	_
11	modules	module	NOUN	NNS	Number=Plur	9	pobj	_	_
12	$ iMod(1, T) $	$ imod(1, t) $	SYM	$	_	8	appos	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	totally	totally	ADV	RB	_	15	advmod	_	_
15	distributive	distributive	ADJ	JJ	Degree=Pos	13	acomp	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 13
# text = Here we show, for any totally distributive $ K $ , that there is an equivalence $ K rightarrow iMod(1, tilde{K}) $ .
1	Here	here	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	for	for	ADP	IN	_	3	prep	_	_
6	any	any	DET	DT	_	9	det	_	_
7	totally	totally	ADV	RB	_	8	advmod	_	_
8	distributive	distributive	ADJ	JJ	Degree=Pos	9	amod	_	_
9	$ K $	$ k $	SYM	$	_	5	pobj	_	_
10	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
11	that	that	SCONJ	IN	_	13	mark	_	_
12	there	there	PRON	EX	_	13	expl	_	_
13	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	equivalence	equivalence	NOUN	NN	Number=Sing	13	attr	_	_
16	$ K rightarrow iMod(1, tilde{K}) $	$ k rightarrow imod(1, tilde{k}) $	SYM	$	_	15	appos	_	_
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 520
# sent_id = 1
# text = We show that morphisms from n homotopy unital $ A_infty $ - algebras to a single one are maps over an operad module with $ n+1 $ commuting actions of the operad $ A_infty^hu $ , whose algebras are homotopy unital $ A_infty $ - algebras.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	16	mark	_	_
4	morphisms	morphism	NOUN	NNS	Number=Plur	8	nsubj	_	_
5	from	from	ADP	IN	_	4	prep	_	_
6	n	n	NOUN	NN	Number=Sing	5	pobj	_	_
7	homotopy	homotopy	PROPN	NNP	Number=Sing	5	pobj	_	_
8	unital	unital	PROPN	NNP	Number=Sing	3	nmod	_	_
9	$ A_infty $	$ a_infty $	SYM	$	_	11	compound	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	algebras	algebra	NOUN	NNS	Number=Plur	8	dobj	_	_
12	to	to	ADP	IN	_	8	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	single	single	ADJ	JJ	Degree=Pos	15	amod	_	_
15	one	one	NUM	CD	NumType=Card	12	pobj	_	_
16	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
17	maps	map	NOUN	NNS	Number=Plur	16	attr	_	_
18	over	over	ADP	IN	_	17	prep	_	_
19	an	an	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	operad	operad	ADJ	JJ	Degree=Pos	21	amod	_	_
21	module	module	NOUN	NN	Number=Sing	18	pobj	_	_
22	with	with	ADP	IN	_	21	prep	_	_
23	$ n+1 $	$ n+1 $	SYM	$	_	24	nsubj	_	_
24	commuting	commute	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	25	compound	_	_
25	actions	action	NOUN	NNS	Number=Plur	22	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	operad	operad	ADJ	JJ	Degree=Pos	29	amod	_	_
29	$ A_infty^hu $	$ a_infty^hu $	SYM	$	_	26	pobj	_	_
30	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
31	whose	whose	DET	WP$	Poss=Yes	32	poss	_	_
32	algebras	algebra	NOUN	NNS	Number=Plur	33	nsubj	_	_
33	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	25	relcl	_	_
34	homotopy	homotopy	PROPN	NNP	Number=Sing	33	attr	_	_
35	unital	unital	PROPN	NNP	Number=Sing	2	ccomp	_	_
36	$ A_infty $	$ a_infty $	SYM	$	_	38	compound	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	38	punct	_	_
38	algebras	algebra	NOUN	NNS	Number=Plur	35	dobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The operad $ A_infty $ and modules over it have two useful gradings related by isomorphisms which change the degree.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	operad	operad	ADJ	JJ	Degree=Pos	8	nsubj	_	_
3	$ A_infty $	$ a_infty $	SYM	$	_	2	prt	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
5	modules	module	NOUN	NNS	Number=Plur	2	conj	_	_
6	over	over	ADP	IN	_	5	prep	_	_
7	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	6	pobj	_	_
8	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	two	two	NUM	CD	NumType=Card	11	nummod	_	_
10	useful	useful	ADJ	JJ	Degree=Pos	11	amod	_	_
11	gradings	grading	NOUN	NNS	Number=Plur	8	dobj	_	_
12	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acl	_	_
13	by	by	ADP	IN	_	12	agent	_	_
14	isomorphisms	isomorphism	NOUN	NNS	Number=Plur	13	pobj	_	_
15	which	which	PRON	WDT	_	16	nsubj	_	_
16	change	change	VERB	VBP	Tense=Pres|VerbForm=Fin	14	relcl	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	degree	degree	NOUN	NN	Number=Sing	16	dobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 3
# text = The composition of $ A_infty^hu $  $ n $ - morphisms with several entries is presented as a convolution of a coalgebra - like and an algebra - like structures.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	composition	composition	NOUN	NN	Number=Sing	13	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	$ A_infty^hu $	$ a_infty^hu $	SYM	$	_	8	nmod	_	_
5	 	 	SPACE	_SP	_	4	dep	_	SpaceAfter=No
6	$ n $	$ n $	SYM	$	_	8	quantmod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	morphisms	morphism	NOUN	NNS	Number=Plur	3	pobj	_	_
9	with	with	ADP	IN	_	2	prep	_	_
10	several	several	ADJ	JJ	Degree=Pos	11	amod	_	_
11	entries	entry	NOUN	NNS	Number=Plur	9	pobj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
14	as	as	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	convolution	convolution	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
19	coalgebra	coalgebra	NOUN	NN	Number=Sing	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	like	like	ADJ	JJ	Degree=Pos	17	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	an	an	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
24	algebra	algebra	NOUN	NN	Number=Sing	26	npadvmod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
26	like	like	ADJ	JJ	Degree=Pos	27	amod	_	_
27	structures	structure	NOUN	NNS	Number=Plur	21	conj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# doc_id = 521
# sent_id = 1
# text = We show that morphisms from n $ A_infty $ - algebras to a single one are maps over an operad module with $ n+1 $ commuting actions of the operad $ A_infty $ , whose algebras are conventional $ A_infty $ - algebras.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	14	mark	_	_
4	morphisms	morphism	NOUN	NNS	Number=Plur	14	nsubj	_	_
5	from	from	ADP	IN	_	4	prep	_	_
6	n	n	ADP	IN	_	9	nmod	_	_
7	$ A_infty $	$ a_infty $	SYM	$	_	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	algebras	algebra	NOUN	NNS	Number=Plur	5	pobj	_	_
10	to	to	ADP	IN	_	5	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	single	single	ADJ	JJ	Degree=Pos	13	amod	_	_
13	one	one	NUM	CD	NumType=Card	10	pobj	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
15	maps	map	NOUN	NNS	Number=Plur	14	attr	_	_
16	over	over	ADP	IN	_	15	prep	_	_
17	an	an	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	operad	operad	ADJ	JJ	Degree=Pos	19	amod	_	_
19	module	module	NOUN	NN	Number=Sing	16	pobj	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	$ n+1 $	$ n+1 $	SYM	$	_	22	nsubj	_	_
22	commuting	commute	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	23	compound	_	_
23	actions	action	NOUN	NNS	Number=Plur	20	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	operad	operad	ADJ	JJ	Degree=Pos	27	amod	_	_
27	$ A_infty $	$ a_infty $	SYM	$	_	24	pobj	_	_
28	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
29	whose	whose	DET	WP$	Poss=Yes	30	poss	_	_
30	algebras	algebra	NOUN	NNS	Number=Plur	31	nsubj	_	_
31	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	23	relcl	_	_
32	conventional	conventional	ADJ	JJ	Degree=Pos	31	acomp	_	_
33	$ A_infty $	$ a_infty $	SYM	$	_	35	compound	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	algebras	algebra	NOUN	NNS	Number=Plur	31	npadvmod	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The composition of $ A_infty $ - morphisms with several entries is presented as a convolution of a coalgebra - like and an algebra - like structures.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	composition	composition	NOUN	NN	Number=Sing	11	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	$ A_infty $	$ a_infty $	SYM	$	_	6	compound	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	morphisms	morphism	NOUN	NNS	Number=Plur	3	pobj	_	_
7	with	with	ADP	IN	_	2	prep	_	_
8	several	several	ADJ	JJ	Degree=Pos	9	amod	_	_
9	entries	entry	NOUN	NNS	Number=Plur	7	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
12	as	as	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	convolution	convolution	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
17	coalgebra	coalgebra	NOUN	NN	Number=Sing	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	like	like	ADJ	JJ	Degree=Pos	15	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
22	algebra	algebra	NOUN	NN	Number=Sing	24	npadvmod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
24	like	like	ADJ	JJ	Degree=Pos	25	amod	_	_
25	structures	structure	NOUN	NNS	Number=Plur	19	conj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 3
# text = Under these notions lie two examples of $ Cat $ - operads: that of graded modules and of complexes.
1	Under	under	ADP	IN	_	4	prep	_	_
2	these	these	DET	DT	Number=Plur|PronType=Dem	3	det	_	_
3	notions	notion	NOUN	NNS	Number=Plur	1	pobj	_	_
4	lie	lie	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	two	two	NUM	CD	NumType=Card	6	nummod	_	_
6	examples	example	NOUN	NNS	Number=Plur	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	$ Cat $	$ cat $	SYM	$	_	10	nmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	operads	operad	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
11	:	:	PUNCT	:	_	6	punct	_	_
12	that	that	PRON	DT	Number=Sing|PronType=Dem	6	appos	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	graded	grade	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
15	modules	module	NOUN	NNS	Number=Plur	13	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	of	of	ADP	IN	_	15	prep	_	_
18	complexes	complex	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 522
# sent_id = 1
# text = We generalize the concept of a strong inclusion on a biframe to that of a proximity on a biframe, which is related to the concept of a strong bi - inclusion on a frame introduced by Picado and Pultr.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	concept	concept	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	strong	strong	ADJ	JJ	Degree=Pos	8	amod	_	_
8	inclusion	inclusion	NOUN	NN	Number=Sing	5	pobj	_	_
9	on	on	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	biframe	biframe	NOUN	NN	Number=Sing	9	pobj	_	_
12	to	to	ADP	IN	_	8	prep	_	_
13	that	that	PRON	DT	Number=Sing|PronType=Dem	12	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	proximity	proximity	NOUN	NN	Number=Sing	14	pobj	_	_
17	on	on	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	biframe	biframe	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	which	which	PRON	WDT	_	23	nsubjpass	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	auxpass	_	_
23	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	relcl	_	_
24	to	to	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	concept	concept	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
29	strong	strong	ADJ	JJ	Degree=Pos	32	amod	_	_
30	bi	bi	NOUN	NN	Number=Sing	32	compound	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	inclusion	inclusion	NOUN	NN	Number=Sing	27	pobj	_	_
33	on	on	ADP	IN	_	32	prep	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
35	frame	frame	NOUN	NN	Number=Sing	33	pobj	_	_
36	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	35	acl	_	_
37	by	by	ADP	IN	_	36	agent	_	_
38	Picado	Picado	PROPN	NNP	Number=Sing	37	pobj	_	_
39	and	and	CCONJ	CC	ConjType=Cmp	38	cc	_	_
40	Pultr	Pultr	PROPN	NNP	Number=Sing	38	conj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We also generalize the concept of a bi - compactification of a biframe to that of a compactification of a biframe, and prove that the poset of compactifications of a biframe $ L $ is isomorphic to the poset of proximities on $ L $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	concept	concept	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	bi	bi	NOUN	NN	Number=Sing	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	compactification	compactification	NOUN	NN	Number=Sing	6	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	biframe	biframe	NOUN	NN	Number=Sing	11	pobj	_	_
14	to	to	ADP	IN	_	10	prep	_	_
15	that	that	PRON	DT	Number=Sing|PronType=Dem	14	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	compactification	compactification	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	biframe	biframe	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
24	prove	prove	VERB	VB	VerbForm=Inf	3	conj	_	_
25	that	that	SCONJ	IN	_	34	mark	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	poset	poset	NOUN	NN	Number=Sing	34	nsubj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	compactifications	compactification	NOUN	NNS	Number=Plur	28	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
32	biframe	biframe	NOUN	NN	Number=Sing	30	pobj	_	_
33	$ L $	$ l $	SYM	$	_	27	appos	_	_
34	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	ccomp	_	_
35	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	34	acomp	_	_
36	to	to	ADP	IN	_	35	prep	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	poset	poset	NOUN	NN	Number=Sing	36	pobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	proximities	proximity	NOUN	NNS	Number=Plur	39	pobj	_	_
41	on	on	ADP	IN	_	40	prep	_	_
42	$ L $	$ l $	SYM	$	_	41	pobj	_	_
43	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = As a corollary, we obtain Schauerte's characterization of bi - compactifications of a biframe.
1	As	as	ADP	IN	_	6	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	corollary	corollary	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	Schauerte	Schauerte	PROPN	NNP	Number=Sing	9	poss	_	SpaceAfter=No
8	's	's	PART	POS	_	7	case	_	_
9	characterization	characterization	NOUN	NN	Number=Sing	6	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	bi	bi	NOUN	NN	Number=Sing	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	compactifications	compactification	NOUN	NNS	Number=Plur	10	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	biframe	biframe	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = In the spatial case this yields Blatter and Seever's characterization of compactifications of completely regular ordered spaces and a characterization of bi - compactifications of completely regular bispaces.
1	In	in	ADP	IN	_	6	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	spatial	spatial	ADJ	JJ	Degree=Pos	4	amod	_	_
4	case	case	NOUN	NN	Number=Sing	1	pobj	_	_
5	this	this	PRON	DT	Number=Sing|PronType=Dem	6	nsubj	_	_
6	yields	yield	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	Blatter	Blatter	PROPN	NNP	Number=Sing	6	dobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	Seever	Seever	PROPN	NNP	Number=Sing	11	poss	_	SpaceAfter=No
10	's	's	PART	POS	_	9	case	_	_
11	characterization	characterization	NOUN	NN	Number=Sing	7	conj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	compactifications	compactification	NOUN	NNS	Number=Plur	12	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	completely	completely	ADV	RB	_	16	advmod	_	_
16	regular	regular	ADJ	JJ	Degree=Pos	18	amod	_	_
17	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
18	spaces	space	NOUN	NNS	Number=Plur	14	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	characterization	characterization	NOUN	NN	Number=Sing	7	conj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	bi	bi	NOUN	NN	Number=Sing	25	compound	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	compactifications	compactification	NOUN	NNS	Number=Plur	22	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	completely	completely	ADV	RB	_	28	advmod	_	_
28	regular	regular	ADJ	JJ	Degree=Pos	29	amod	_	_
29	bispaces	bispace	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 523
# sent_id = 1
# text = Transformation groupoids associated to group actions capture the interplay between global and local symmetries of structures described in set - theoretic terms.
1	Transformation	transformation	NOUN	NN	Number=Sing	2	compound	_	_
2	groupoids	groupoid	NOUN	NNS	Number=Plur	7	nsubj	_	_
3	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acl	_	_
4	to	to	ADP	IN	_	3	prep	_	_
5	group	group	NOUN	NN	Number=Sing	6	compound	_	_
6	actions	action	NOUN	NNS	Number=Plur	4	pobj	_	_
7	capture	capture	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	interplay	interplay	NOUN	NN	Number=Sing	7	dobj	_	_
10	between	between	ADP	IN	_	9	prep	_	_
11	global	global	ADJ	JJ	Degree=Pos	14	amod	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	local	local	ADJ	JJ	Degree=Pos	11	conj	_	_
14	symmetries	symmetry	NOUN	NNS	Number=Plur	10	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	structures	structure	NOUN	NNS	Number=Plur	15	pobj	_	_
17	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	acl	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	set	set	NOUN	NN	Number=Sing	21	amod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	theoretic	theoretic	ADJ	JJ	Degree=Pos	22	amod	_	_
22	terms	term	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 2
# text = This paper examines the analogous situation for structures described in category - theoretic terms, where symmetry is expressed as the action of a 2 - group $ G $ (equivalently, a categorical group) on a category $ C $ .
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	examines	examine	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	analogous	analogous	ADJ	JJ	Degree=Pos	6	amod	_	_
6	situation	situation	NOUN	NN	Number=Sing	3	dobj	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	structures	structure	NOUN	NNS	Number=Plur	7	pobj	_	_
9	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	category	category	NOUN	NN	Number=Sing	13	npadvmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	theoretic	theoretic	ADJ	JJ	Degree=Pos	14	amod	_	_
14	terms	term	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	where	where	SCONJ	WRB	_	19	advmod	_	_
17	symmetry	symmetry	NOUN	NN	Number=Sing	19	nsubjpass	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	auxpass	_	_
19	expressed	express	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	relcl	_	_
20	as	as	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	action	action	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
25	2	2	NUM	CD	NumType=Card	27	nummod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	group	group	NOUN	NN	Number=Sing	28	compound	_	_
28	$ G $	$ g $	SYM	$	_	23	pobj	_	_
29	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	28	punct	_	SpaceAfter=No
30	equivalently	equivalently	ADV	RB	_	34	advmod	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	34	punct	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
33	categorical	categorical	ADJ	JJ	Degree=Pos	34	amod	_	_
34	group	group	NOUN	NN	Number=Sing	19	npadvmod	_	SpaceAfter=No
35	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	34	punct	_	_
36	on	on	ADP	IN	_	34	prep	_	_
37	a	a	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
38	category	category	NOUN	NN	Number=Sing	36	pobj	_	_
39	$ C $	$ c $	SYM	$	_	36	pobj	_	_
40	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = It describes the construction of a transformation groupoid in diagrammatic terms, and considers this construction internal to $ Cat $ , the category of categories.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	describes	describe	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	construction	construction	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	transformation	transformation	NOUN	NN	Number=Sing	8	compound	_	_
8	groupoid	groupoid	NOUN	NN	Number=Sing	5	pobj	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	diagrammatic	diagrammatic	ADJ	JJ	Degree=Pos	11	amod	_	_
11	terms	term	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
14	considers	consider	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
15	this	this	DET	DT	Number=Sing|PronType=Dem	16	det	_	_
16	construction	construction	NOUN	NN	Number=Sing	17	nsubj	_	_
17	internal	internal	ADJ	JJ	Degree=Pos	14	ccomp	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	$ Cat $	$ cat $	SYM	$	_	18	pobj	_	_
20	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	category	category	NOUN	NN	Number=Sing	14	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	categories	category	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = The result is a double category $ C//G $ which describes the local symmetries of $ C $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	result	result	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	double	double	ADJ	JJ	Degree=Pos	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	3	attr	_	_
7	$ C//G $	$ c//g $	SYM	$	_	6	appos	_	_
8	which	which	PRON	WDT	_	9	nsubj	_	_
9	describes	describe	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	relcl	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	local	local	ADJ	JJ	Degree=Pos	12	amod	_	_
12	symmetries	symmetry	NOUN	NNS	Number=Plur	9	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	$ C $	$ c $	SYM	$	_	13	pobj	_	_
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = We define this and describe some of its structure, with the adjoint action of $ G $ on itself as a guiding example.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	this	this	PRON	DT	Number=Sing|PronType=Dem	2	dobj	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
5	describe	describe	VERB	VB	VerbForm=Inf	2	conj	_	_
6	some	some	PRON	DT	_	5	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	9	poss	_	_
9	structure	structure	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
11	with	with	ADP	IN	_	5	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	adjoint	adjoint	NOUN	NN	Number=Sing	14	compound	_	_
14	action	action	NOUN	NN	Number=Sing	11	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	$ G $	$ g $	SYM	$	_	15	pobj	_	_
17	on	on	ADP	IN	_	14	prep	_	_
18	itself	itself	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs|Reflex=Yes	17	pobj	_	_
19	as	as	ADP	IN	_	14	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	guiding	guide	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	amod	_	_
22	example	example	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 524
# sent_id = 1
# text = There are few known computable examples of non - abelian surface holonomy.
1	There	there	PRON	EX	_	2	expl	_	_
2	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	few	few	ADJ	JJ	Degree=Pos	6	amod	_	_
4	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	amod	_	_
5	computable	computable	ADJ	JJ	Degree=Pos	6	amod	_	_
6	examples	example	NOUN	NNS	Number=Plur	2	attr	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	non	non	ADJ	JJ	Degree=Pos	10	amod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	abelian	abelian	ADJ	JJ	Degree=Pos	12	amod	_	_
11	surface	surface	NOUN	NN	Number=Sing	12	compound	_	_
12	holonomy	holonomy	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper, we give several examples whose structure 2 - groups are covering 2 - groups and show that the surface holonomies can be computed via a simple formula in terms of paths of 1 - dimensional holonomies inspired by earlier work of Chan Hong - Mo and Tsou Sheung Tsun on magnetic monopoles.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	several	several	ADJ	JJ	Degree=Pos	8	amod	_	_
8	examples	example	NOUN	NNS	Number=Plur	6	dobj	_	_
9	whose	whose	DET	WP$	Poss=Yes	10	poss	_	_
10	structure	structure	NOUN	NN	Number=Sing	15	nsubj	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	groups	group	NOUN	NNS	Number=Plur	15	nsubj	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	aux	_	_
15	covering	cover	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	relcl	_	_
16	2	2	NUM	CD	NumType=Card	18	nummod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	groups	group	NOUN	NNS	Number=Plur	15	dobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
20	show	show	VERB	VB	VerbForm=Inf	15	conj	_	_
21	that	that	SCONJ	IN	_	27	mark	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	surface	surface	NOUN	NN	Number=Sing	24	compound	_	_
24	holonomies	holonomie	NOUN	NNS	Number=Plur	27	nsubjpass	_	_
25	can	can	AUX	MD	VerbForm=Fin	27	aux	_	_
26	be	be	AUX	VB	VerbForm=Inf	27	auxpass	_	_
27	computed	compute	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	ccomp	_	_
28	via	via	ADP	IN	_	27	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	simple	simple	ADJ	JJ	Degree=Pos	31	amod	_	_
31	formula	formula	NOUN	NN	Number=Sing	28	pobj	_	_
32	in	in	ADP	IN	_	31	prep	_	_
33	terms	term	NOUN	NNS	Number=Plur	32	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	paths	path	NOUN	NNS	Number=Plur	34	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	1	1	NUM	CD	NumType=Card	39	advmod	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	dimensional	dimensional	ADJ	JJ	Degree=Pos	40	amod	_	_
40	holonomies	holonomie	NOUN	NNS	Number=Plur	36	pobj	_	_
41	inspired	inspire	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	40	acl	_	_
42	by	by	ADP	IN	_	41	agent	_	_
43	earlier	early	ADJ	JJR	Degree=Cmp	44	amod	_	_
44	work	work	NOUN	NN	Number=Sing	42	pobj	_	_
45	of	of	ADP	IN	_	44	prep	_	_
46	Chan	Chan	PROPN	NNP	Number=Sing	49	compound	_	_
47	Hong	Hong	PROPN	NNP	Number=Sing	49	compound	_	_
48	-	-	PUNCT	HYPH	PunctType=Dash	49	punct	_	_
49	Mo	Mo	PROPN	NNP	Number=Sing	45	pobj	_	_
50	and	and	CCONJ	CC	ConjType=Cmp	49	cc	_	_
51	Tsou	Tsou	PROPN	NNP	Number=Sing	53	compound	_	_
52	Sheung	Sheung	PROPN	NNP	Number=Sing	53	compound	_	_
53	Tsun	Tsun	PROPN	NNP	Number=Sing	49	conj	_	_
54	on	on	ADP	IN	_	44	prep	_	_
55	magnetic	magnetic	ADJ	JJ	Degree=Pos	56	amod	_	_
56	monopoles	monopole	NOUN	NNS	Number=Plur	54	pobj	_	SpaceAfter=No
57	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = As a consequence of our work and that of Schreiber and Waldorf, this formula gives a rigorous meaning to non - abelian magnetic flux for magnetic monopoles.
1	As	as	ADP	IN	_	16	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	consequence	consequence	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	6	poss	_	_
6	work	work	NOUN	NN	Number=Sing	4	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
8	that	that	PRON	DT	Number=Sing|PronType=Dem	3	conj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Schreiber	Schreiber	PROPN	NNP	Number=Sing	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	Waldorf	Waldorf	PROPN	NNP	Number=Sing	10	conj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
14	this	this	DET	DT	Number=Sing|PronType=Dem	15	det	_	_
15	formula	formula	NOUN	NN	Number=Sing	16	nsubj	_	_
16	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	rigorous	rigorous	ADJ	JJ	Degree=Pos	19	amod	_	_
19	meaning	meaning	NOUN	NN	Number=Sing	16	dobj	_	_
20	to	to	ADP	IN	_	16	dative	_	_
21	non	non	ADJ	JJ	Degree=Pos	25	amod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	25	amod	_	_
23	abelian	abelian	ADJ	JJ	Degree=Pos	25	amod	_	_
24	magnetic	magnetic	ADJ	JJ	Degree=Pos	25	amod	_	_
25	flux	flux	PROPN	NNP	Number=Sing	20	pobj	_	_
26	for	for	ADP	IN	_	25	prep	_	_
27	magnetic	magnetic	ADJ	JJ	Degree=Pos	28	amod	_	_
28	monopoles	monopole	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 4
# text = In the process, we discuss gauge covariance of surface holonomies for spheres for any 2 - group, therefore generalizing the notion of the reduced group introduced by Schreiber and Waldorf.
1	In	in	ADP	IN	_	6	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	process	process	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	discuss	discuss	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	gauge	gauge	NOUN	NN	Number=Sing	8	compound	_	_
8	covariance	covariance	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	surface	surface	NOUN	NN	Number=Sing	11	compound	_	_
11	holonomies	holonomie	NOUN	NNS	Number=Plur	9	pobj	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	spheres	sphere	NOUN	NNS	Number=Plur	12	pobj	_	_
14	for	for	ADP	IN	_	13	prep	_	_
15	any	any	DET	DT	_	18	det	_	_
16	2	2	NUM	CD	NumType=Card	18	nummod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	group	group	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
20	therefore	therefore	ADV	RB	_	21	advmod	_	_
21	generalizing	generalize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	advcl	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	notion	notion	NOUN	NN	Number=Sing	21	dobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	reduced	reduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	amod	_	_
27	group	group	NOUN	NN	Number=Sing	24	pobj	_	_
28	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	acl	_	_
29	by	by	ADP	IN	_	28	agent	_	_
30	Schreiber	Schreiber	PROPN	NNP	Number=Sing	29	pobj	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
32	Waldorf	Waldorf	PROPN	NNP	Number=Sing	30	conj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = Using these ideas, we also prove that magnetic monopoles form an abelian group.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	advcl	_	_
2	these	these	DET	DT	Number=Plur|PronType=Dem	3	det	_	_
3	ideas	idea	NOUN	NNS	Number=Plur	1	dobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
6	also	also	ADV	RB	_	7	advmod	_	_
7	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	that	that	SCONJ	IN	_	11	mark	_	_
9	magnetic	magnetic	ADJ	JJ	Degree=Pos	10	amod	_	_
10	monopoles	monopole	NOUN	NNS	Number=Plur	11	nsubj	_	_
11	form	form	VERB	VBP	Tense=Pres|VerbForm=Fin	7	ccomp	_	_
12	an	an	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	abelian	abelian	ADJ	JJ	Degree=Pos	14	compound	_	_
14	group	group	NOUN	NN	Number=Sing	11	dobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 525
# sent_id = 1
# text = We introduce a 3 - dimensional categorical structure which we call intercategory.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
4	3	3	NUM	CD	NumType=Card	6	advmod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	dimensional	dimensional	ADJ	JJ	Degree=Pos	8	amod	_	_
7	categorical	categorical	ADJ	JJ	Degree=Pos	8	amod	_	_
8	structure	structure	NOUN	NN	Number=Sing	2	dobj	_	_
9	which	which	PRON	WDT	_	11	dobj	_	_
10	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	11	nsubj	_	_
11	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	8	relcl	_	_
12	intercategory	intercategory	NOUN	NN	Number=Sing	11	oprd	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This is a kind of weak triple category with three kinds of arrows, three kinds of 2 - dimensional cells and one kind of 3 - dimensional cells.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	kind	kind	NOUN	NN	Number=Sing	2	attr	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	weak	weak	ADJ	JJ	Degree=Pos	8	amod	_	_
7	triple	triple	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
9	with	with	ADP	IN	_	4	prep	_	_
10	three	three	NUM	CD	NumType=Card	11	nummod	_	_
11	kinds	kind	NOUN	NNS	Number=Plur	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	arrows	arrow	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
15	three	three	NUM	CD	NumType=Card	16	nummod	_	_
16	kinds	kind	NOUN	NNS	Number=Plur	11	appos	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	2	2	NUM	CD	NumType=Card	20	advmod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	dimensional	dimensional	ADJ	JJ	Degree=Pos	21	amod	_	_
21	cells	cell	NOUN	NNS	Number=Plur	17	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
23	one	one	NUM	CD	NumType=Card	24	nummod	_	_
24	kind	kind	NOUN	NN	Number=Sing	16	conj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	3	3	NUM	CD	NumType=Card	28	advmod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	dimensional	dimensional	ADJ	JJ	Degree=Pos	29	amod	_	_
29	cells	cell	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = In one dimension, the compositions are strictly associative and unitary, whereas in the other two, these laws only hold up to coherent isomorphism.
1	In	in	ADP	IN	_	7	prep	_	_
2	one	one	NUM	CD	NumType=Card	3	nummod	_	_
3	dimension	dimension	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	compositions	composition	NOUN	NNS	Number=Plur	7	nsubj	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	strictly	strictly	ADV	RB	_	7	advmod	_	_
9	associative	associative	ADJ	JJ	Degree=Pos	7	acomp	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	unitary	unitary	ADJ	JJ	Degree=Pos	9	conj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
13	whereas	whereas	SCONJ	IN	_	22	mark	_	_
14	in	in	ADP	IN	_	22	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	other	other	ADJ	JJ	Degree=Pos	17	amod	_	_
17	two	two	NUM	CD	NumType=Card	14	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
19	these	these	DET	DT	Number=Plur|PronType=Dem	20	det	_	_
20	laws	law	NOUN	NNS	Number=Plur	22	nsubj	_	_
21	only	only	ADV	RB	_	22	advmod	_	_
22	hold	hold	VERB	VBP	Tense=Pres|VerbForm=Fin	7	advcl	_	_
23	up	up	ADP	RP	_	22	prt	_	_
24	to	to	ADP	IN	_	22	prep	_	_
25	coherent	coherent	ADJ	JJ	Degree=Pos	26	amod	_	_
26	isomorphism	isomorphism	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = The main feature is that the interchange law between the second and third compositions does not hold, but rather there is a non - invertible comparison cell which satisfies some coherence conditions.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	feature	feature	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	17	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	interchange	interchange	ADJ	JJ	Degree=Pos	8	compound	_	_
8	law	law	NOUN	NN	Number=Sing	17	nsubj	_	_
9	between	between	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
11	second	second	ADJ	JJ	Degree=Pos	14	amod	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	third	third	ADJ	JJ	Degree=Pos	11	conj	_	_
14	compositions	composition	NOUN	NNS	Number=Plur	9	pobj	_	_
15	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	aux	_	_
16	not	not	PART	RB	Polarity=Neg	17	neg	_	_
17	hold	hold	VERB	VB	VerbForm=Inf	4	ccomp	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	but	but	CCONJ	CC	ConjType=Cmp	17	cc	_	_
20	rather	rather	ADV	RB	_	17	cc	_	_
21	there	there	PRON	EX	_	22	expl	_	_
22	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	conj	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
24	non	non	ADJ	JJ	Degree=Pos	26	npadvmod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	invertible	invertible	ADJ	JJ	Degree=Pos	28	amod	_	_
27	comparison	comparison	NOUN	NN	Number=Sing	28	compound	_	_
28	cell	cell	NOUN	NN	Number=Sing	22	attr	_	_
29	which	which	PRON	WDT	_	30	nsubj	_	_
30	satisfies	satisfy	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	28	relcl	_	_
31	some	some	DET	DT	_	33	det	_	_
32	coherence	coherence	NOUN	NN	Number=Sing	33	compound	_	_
33	conditions	condition	NOUN	NNS	Number=Plur	30	dobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = We introduce appropriate morphisms of intercategory, of which there are three types, and cells relating these.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	appropriate	appropriate	ADJ	JJ	Degree=Pos	4	amod	_	_
4	morphisms	morphism	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	intercategory	intercategory	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
8	of	of	ADP	IN	_	11	dep	_	_
9	which	which	PRON	WDT	_	8	pobj	_	_
10	there	there	PRON	EX	_	11	expl	_	_
11	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	relcl	_	_
12	three	three	NUM	CD	NumType=Card	13	nummod	_	_
13	types	type	NOUN	NNS	Number=Plur	11	attr	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
16	cells	cell	NOUN	NNS	Number=Plur	11	conj	_	_
17	relating	relate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	acl	_	_
18	these	these	PRON	DT	Number=Plur|PronType=Dem	17	dobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = We show that these fit together to produce a strict triple category of intercategories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	these	these	PRON	DT	Number=Plur|PronType=Dem	5	nsubj	_	_
5	fit	fit	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	together	together	ADV	RB	_	5	advmod	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	produce	produce	VERB	VB	VerbForm=Inf	5	advcl	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
10	strict	strict	ADJ	JJ	Degree=Pos	12	amod	_	_
11	triple	triple	ADJ	JJ	Degree=Pos	12	amod	_	_
12	category	category	NOUN	NN	Number=Sing	8	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	intercategories	intercategorie	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 526
# sent_id = 1
# text = We show that ann - categories admit a presentation by crossed bimodules, and prove that morphisms between them can be expressed by special kinds spans between the presentations.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	ann	ann	PROPN	NNP	Number=Sing	6	compound	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	categories	category	NOUN	NNS	Number=Plur	7	nsubj	_	_
7	admit	admit	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	presentation	presentation	NOUN	NN	Number=Sing	7	dobj	_	_
10	by	by	ADP	IN	_	9	prep	_	_
11	crossed	crossed	ADJ	JJ	Degree=Pos	12	amod	_	_
12	bimodules	bimodule	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
15	prove	prove	VERB	VB	VerbForm=Inf	7	conj	_	_
16	that	that	SCONJ	IN	_	22	mark	_	_
17	morphisms	morphism	NOUN	NNS	Number=Plur	22	nsubjpass	_	_
18	between	between	ADP	IN	_	17	prep	_	_
19	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	18	pobj	_	_
20	can	can	AUX	MD	VerbForm=Fin	22	aux	_	_
21	be	be	AUX	VB	VerbForm=Inf	22	auxpass	_	_
22	expressed	express	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	ccomp	_	_
23	by	by	ADP	IN	_	22	agent	_	_
24	special	special	ADJ	JJ	Degree=Pos	25	amod	_	_
25	kinds	kind	NOUN	NNS	Number=Plur	26	compound	_	_
26	spans	span	NOUN	NNS	Number=Plur	23	pobj	_	_
27	between	between	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	presentations	presentation	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = More precisely, we prove the groupoid of morphisms between two ann - categories is equivalent to that of bimodule butterflies between the presentations.
1	More	more	ADV	RBR	Degree=Cmp	2	advmod	_	_
2	precisely	precisely	ADV	RB	_	5	advmod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	groupoid	groupoid	NOUN	NN	Number=Sing	15	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	morphisms	morphism	NOUN	NNS	Number=Plur	8	pobj	_	_
10	between	between	ADP	IN	_	7	prep	_	_
11	two	two	NUM	CD	NumType=Card	14	nummod	_	_
12	ann	ann	PROPN	NNP	Number=Sing	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
16	equivalent	equivalent	ADJ	JJ	Degree=Pos	15	acomp	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	that	that	PRON	DT	Number=Sing|PronType=Dem	17	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	bimodule	bimodule	NOUN	NN	Number=Sing	21	compound	_	_
21	butterflies	butterfly	NOUN	NNS	Number=Plur	19	pobj	_	_
22	between	between	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	presentations	presentation	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = A bimodule butterfly is a specialization of a butterfly, that is, a special kind of span or fraction, between the underlying complexes
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	bimodule	bimodule	NOUN	NN	Number=Sing	3	compound	_	_
3	butterfly	butterfly	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	specialization	specialization	NOUN	NN	Number=Sing	4	attr	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	butterfly	butterfly	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
11	that	that	ADV	RB	_	12	advmod	_	_
12	is	is	ADV	RB	_	16	advmod	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	special	special	ADJ	JJ	Degree=Pos	16	amod	_	_
16	kind	kind	NOUN	NN	Number=Sing	4	attr	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	span	span	NOUN	NN	Number=Sing	17	pobj	_	_
19	or	or	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	fraction	fraction	NOUN	NN	Number=Sing	18	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
22	between	between	ADP	IN	_	16	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	underlying	underlie	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	25	amod	_	_
25	complexes	complex	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No

# doc_id = 527
# sent_id = 1
# text = In this paper, we unify various approaches to generalized covering space theory by introducing a categorical framework in which coverings are defined purely in terms of unique lifting properties.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	unify	unify	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	various	various	ADJ	JJ	Degree=Pos	8	amod	_	_
8	approaches	approach	NOUN	NNS	Number=Plur	6	dobj	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
11	covering	cover	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	pobj	_	_
12	space	space	NOUN	NN	Number=Sing	13	compound	_	_
13	theory	theory	NOUN	NN	Number=Sing	11	dobj	_	_
14	by	by	ADP	IN	_	6	prep	_	_
15	introducing	introduce	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	pcomp	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	categorical	categorical	ADJ	JJ	Degree=Pos	18	amod	_	_
18	framework	framework	NOUN	NN	Number=Sing	15	dobj	_	_
19	in	in	ADP	IN	_	23	prep	_	_
20	which	which	PRON	WDT	_	19	pobj	_	_
21	coverings	covering	NOUN	NNS	Number=Plur	23	nsubjpass	_	_
22	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	23	auxpass	_	_
23	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	relcl	_	_
24	purely	purely	ADV	RB	_	23	advmod	_	_
25	in	in	ADP	IN	_	23	prep	_	_
26	terms	term	NOUN	NNS	Number=Plur	25	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	unique	unique	ADJ	JJ	Degree=Pos	30	amod	_	_
29	lifting	lifting	NOUN	NN	Number=Sing	30	compound	_	_
30	properties	property	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = For each category $ C $ of path - connected spaces having the unit disk as an object, we construct a category of $ C $ - coverings over a given space $ X $ that embeds in the category of $ pi_1(X, x_0) $ - sets via the usual monodromy action on fibers.
1	For	for	ADP	IN	_	19	prep	_	_
2	each	each	DET	DT	_	3	det	_	_
3	category	category	NOUN	NN	Number=Sing	1	pobj	_	_
4	$ C $	$ c $	SYM	$	_	1	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	path	path	NOUN	NN	Number=Sing	8	npadvmod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	amod	_	_
9	spaces	space	NOUN	NNS	Number=Plur	5	pobj	_	_
10	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	acl	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	unit	unit	NOUN	NN	Number=Sing	13	compound	_	_
13	disk	disk	NOUN	NN	Number=Sing	10	dobj	_	_
14	as	as	ADP	IN	_	10	prep	_	_
15	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	object	object	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	category	category	NOUN	NN	Number=Sing	19	dobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	$ C $	$ c $	SYM	$	_	25	compound	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	coverings	covering	NOUN	NNS	Number=Plur	22	pobj	_	_
26	over	over	ADP	IN	_	19	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	amod	_	_
29	space	space	NOUN	NN	Number=Sing	26	pobj	_	_
30	$ X $	$ x $	SYM	$	_	29	appos	_	_
31	that	that	PRON	WDT	PronType=Rel	32	nsubj	_	_
32	embeds	embed	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	relcl	_	_
33	in	in	ADP	IN	_	32	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	category	category	NOUN	NN	Number=Sing	33	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	$ pi_1(X, x_0) $	$ pi_1(x, x_0) $	SYM	$	_	39	compound	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	sets	set	NOUN	NNS	Number=Plur	36	pobj	_	_
40	via	via	ADP	IN	_	32	prep	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	44	det	_	_
42	usual	usual	ADJ	JJ	Degree=Pos	44	amod	_	_
43	monodromy	monodromy	NOUN	NN	Number=Sing	44	compound	_	_
44	action	action	NOUN	NN	Number=Sing	40	pobj	_	_
45	on	on	ADP	IN	_	44	prep	_	_
46	fibers	fiber	NOUN	NNS	Number=Plur	45	pobj	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 3
# text = When $ C $ is extended to its coreflective hull $ H(C) $ , the resulting category of based $ H(C) $ - coverings is complete, has an initial object, and often characterizes more of the subgroup lattice of $ pi_1(X, x_0) $ than traditional covering spaces.
1	When	when	SCONJ	WRB	_	4	advmod	_	_
2	$ C $	$ c $	SYM	$	_	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	advcl	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	8	poss	_	_
7	coreflective	coreflective	ADJ	JJ	Degree=Pos	8	amod	_	_
8	hull	hull	NOUN	NN	Number=Sing	5	pobj	_	_
9	$ H(C) $	$ h(c) $	SYM	$	_	8	appos	_	_
10	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	19	nsubj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
16	$ H(C) $	$ h(c) $	SYM	$	_	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	coverings	covering	NOUN	NNS	Number=Plur	14	pobj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	complete	complete	ADJ	JJ	Degree=Pos	19	acomp	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
22	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	conj	_	_
23	an	an	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	initial	initial	ADJ	JJ	Degree=Pos	25	amod	_	_
25	object	object	NOUN	NN	Number=Sing	22	dobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
28	often	often	ADV	RB	_	29	advmod	_	_
29	characterizes	characterize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	conj	_	_
30	more	more	ADJ	JJR	Degree=Cmp	29	dobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
33	subgroup	subgroup	NOUN	NN	Number=Sing	34	compound	_	_
34	lattice	lattice	NOUN	NN	Number=Sing	31	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	$ pi_1(X, x_0) $	$ pi_1(x, x_0) $	SYM	$	_	35	pobj	_	_
37	than	than	ADP	IN	_	29	prep	_	_
38	traditional	traditional	ADJ	JJ	Degree=Pos	40	amod	_	_
39	covering	covering	NOUN	NN	Number=Sing	40	compound	_	_
40	spaces	space	NOUN	NNS	Number=Plur	37	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 4
# text = We apply our results to three special coreflective subcategories: (i) The category of $ Delta $ - coverings employs the convenient category of $ Delta $ - generated spaces and is universal in the sense that it contains every other generalized covering category as a subcategory.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	apply	apply	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	4	poss	_	_
4	results	result	NOUN	NNS	Number=Plur	2	dobj	_	_
5	to	to	ADP	IN	_	2	prep	_	_
6	three	three	NUM	CD	NumType=Card	9	nummod	_	_
7	special	special	ADJ	JJ	Degree=Pos	9	amod	_	_
8	coreflective	coreflective	ADJ	JJ	Degree=Pos	9	amod	_	_
9	subcategories	subcategorie	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
10	:	:	PUNCT	:	_	9	punct	_	_
11	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
12	i	i	NOUN	NN	Number=Sing	9	appos	_	SpaceAfter=No
13	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	12	punct	_	_
14	The	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	category	category	NOUN	NN	Number=Sing	20	nsubj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	$ Delta $	$ delta $	SYM	$	_	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	coverings	covering	NOUN	NNS	Number=Plur	16	pobj	_	_
20	employs	employ	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	convenient	convenient	ADJ	JJ	Degree=Pos	23	amod	_	_
23	category	category	NOUN	NN	Number=Sing	20	dobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	$ Delta $	$ delta $	SYM	$	_	27	advmod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	amod	_	_
28	spaces	space	NOUN	NNS	Number=Plur	24	pobj	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
30	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	conj	_	_
31	universal	universal	ADJ	JJ	Degree=Pos	30	acomp	_	_
32	in	in	ADP	IN	_	30	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
34	sense	sense	NOUN	NN	Number=Sing	32	pobj	_	_
35	that	that	SCONJ	IN	_	37	mark	_	_
36	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	37	nsubj	_	_
37	contains	contain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	ccomp	_	_
38	every	every	DET	DT	_	42	det	_	_
39	other	other	ADJ	JJ	Degree=Pos	42	amod	_	_
40	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	42	amod	_	_
41	covering	covering	NOUN	NN	Number=Sing	42	compound	_	_
42	category	category	NOUN	NN	Number=Sing	37	dobj	_	_
43	as	as	ADP	IN	_	42	prep	_	_
44	a	a	DET	DT	Definite=Ind|PronType=Art	45	det	_	_
45	subcategory	subcategory	NOUN	NN	Number=Sing	43	pobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 5
# text = (ii) In the locally path - connected category, we preserve notion of generalized covering due to Fischer and Zastrow and characterize the topology of such coverings using the standard whisker topology.
1	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	2	punct	_	SpaceAfter=No
2	ii	ii	PROPN	NNP	Number=Sing	13	dep	_	SpaceAfter=No
3	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	2	punct	_	_
4	In	in	ADP	IN	_	13	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
6	locally	locally	ADV	RB	_	10	amod	_	_
7	path	path	NOUN	NN	Number=Sing	9	npadvmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	preserve	preserve	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	notion	notion	NOUN	NN	Number=Sing	13	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	covering	covering	NOUN	NN	Number=Sing	15	pobj	_	_
18	due	due	ADP	IN	_	13	prep	_	_
19	to	to	ADP	IN	_	18	pcomp	_	_
20	Fischer	Fischer	PROPN	NNP	Number=Sing	18	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	Zastrow	Zastrow	PROPN	NNP	Number=Sing	20	conj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
24	characterize	characterize	VERB	VB	VerbForm=Inf	13	conj	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	topology	topology	NOUN	NN	Number=Sing	24	dobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	such	such	ADJ	JJ	Degree=Pos	29	amod	_	_
29	coverings	covering	NOUN	NNS	Number=Plur	27	pobj	_	_
30	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	24	advcl	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
32	standard	standard	ADJ	JJ	Degree=Pos	34	amod	_	_
33	whisker	whisker	NOUN	NN	Number=Sing	34	compound	_	_
34	topology	topology	NOUN	NN	Number=Sing	30	dobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 6
# text = (iii) By employing the coreflective hull Fan of the category of all contractible spaces, we characterize the notion of continuous lifting of paths and identify the topology of Fan - coverings as the natural quotient topology inherited from the path space.
1	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	2	punct	_	SpaceAfter=No
2	iii	iii	NOUN	NN	Number=Sing	19	meta	_	SpaceAfter=No
3	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	2	punct	_	_
4	By	by	ADP	IN	_	19	prep	_	_
5	employing	employ	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	pcomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	coreflective	coreflective	ADJ	JJ	Degree=Pos	8	amod	_	_
8	hull	hull	NOUN	NN	Number=Sing	5	dobj	_	_
9	Fan	Fan	PROPN	NNP	Number=Sing	5	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	all	all	DET	DT	_	16	det	_	_
15	contractible	contractible	ADJ	JJ	Degree=Pos	16	amod	_	_
16	spaces	space	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	notion	notion	NOUN	NN	Number=Sing	19	dobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	continuous	continuous	ADJ	JJ	Degree=Pos	24	amod	_	_
24	lifting	lifting	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	paths	path	NOUN	NNS	Number=Plur	25	pobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
28	identify	identify	VERB	VB	VerbForm=Inf	19	conj	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	topology	topology	NOUN	NN	Number=Sing	28	dobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	Fan	Fan	PROPN	NNP	Number=Sing	34	compound	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	coverings	covering	NOUN	NNS	Number=Plur	31	pobj	_	_
35	as	as	ADP	IN	_	28	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
37	natural	natural	ADJ	JJ	Degree=Pos	38	amod	_	_
38	quotient	quotient	NOUN	NN	Number=Sing	39	compound	_	_
39	topology	topology	NOUN	NN	Number=Sing	35	pobj	_	_
40	inherited	inherit	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	39	acl	_	_
41	from	from	ADP	IN	_	40	prep	_	_
42	the	the	DET	DT	Definite=Def|PronType=Art	44	det	_	_
43	path	path	NOUN	NN	Number=Sing	44	compound	_	_
44	space	space	NOUN	NN	Number=Sing	41	pobj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# doc_id = 528
# sent_id = 1
# text = This is the third paper in a series.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	third	third	ADJ	JJ	Degree=Pos	5	amod	_	_
5	paper	paper	NOUN	NN	Number=Sing	2	attr	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	series	series	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In it we construct a $ C $ - system $ CC(C, p) $ starting from a category $ C $ together with a morphism $ p:tilde{U} to U $ , a choice of pull - back squares based on $ p $ for all morphisms to $ U $ and a choice of a final object of $ C $ .
1	In	in	ADP	IN	_	4	prep	_	_
2	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	1	pobj	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
6	$ C $	$ c $	SYM	$	_	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	system	system	NOUN	NN	Number=Sing	4	dobj	_	_
9	$ CC(C, p) $	$ cc(c, p) $	SYM	$	_	10	nsubj	_	_
10	starting	start	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	advcl	_	_
11	from	from	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
14	$ C $	$ c $	SYM	$	_	15	nmod	_	_
15	together	together	ADV	RB	_	10	advmod	_	_
16	with	with	ADP	IN	_	10	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	morphism	morphism	NOUN	NN	Number=Sing	16	pobj	_	_
19	$ p:tilde{U} to U $	$ p:tilde{u} to u $	SYM	$	_	18	appos	_	_
20	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	choice	choice	NOUN	NN	Number=Sing	18	appos	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	pull	pull	VERB	VB	VerbForm=Inf	27	amod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
26	back	back	NOUN	NN	Number=Sing	24	prt	_	_
27	squares	square	NOUN	NNS	Number=Plur	23	pobj	_	_
28	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	acl	_	_
29	on	on	ADP	IN	_	28	prep	_	_
30	$ p $	$ p $	SYM	$	_	29	pobj	_	_
31	for	for	ADP	IN	_	22	prep	_	_
32	all	all	DET	DT	_	33	det	_	_
33	morphisms	morphism	NOUN	NNS	Number=Plur	31	pobj	_	_
34	to	to	ADP	IN	_	22	prep	_	_
35	$ U $	$ u $	SYM	$	_	34	pobj	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
37	a	a	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
38	choice	choice	NOUN	NN	Number=Sing	22	conj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	a	a	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
41	final	final	ADJ	JJ	Degree=Pos	42	amod	_	_
42	object	object	NOUN	NN	Number=Sing	39	pobj	_	_
43	of	of	ADP	IN	_	42	prep	_	_
44	$ C $	$ c $	SYM	$	_	43	pobj	_	_
45	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = Such a quadruple is called a universe category.
1	Such	such	DET	PDT	_	3	predet	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	quadruple	quadruple	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	universe	universe	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	5	oprd	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = We then define universe category functors and construct homomorphisms of $ C $ - systems $ CC(C, p) $ defined by universe category functors.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	universe	universe	ADJ	JJ	Degree=Pos	6	compound	_	_
5	category	category	NOUN	NN	Number=Sing	6	compound	_	_
6	functors	functor	NOUN	NNS	Number=Plur	3	dobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
8	construct	construct	VERB	VB	VerbForm=Inf	3	conj	_	_
9	homomorphisms	homomorphism	NOUN	NNS	Number=Plur	8	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	$ C $	$ c $	SYM	$	_	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	systems	system	NOUN	NNS	Number=Plur	10	pobj	_	_
14	$ CC(C, p) $	$ cc(c, p) $	SYM	$	_	8	dobj	_	_
15	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	advcl	_	_
16	by	by	ADP	IN	_	15	agent	_	_
17	universe	universe	ADJ	JJ	Degree=Pos	19	compound	_	_
18	category	category	NOUN	NN	Number=Sing	19	compound	_	_
19	functors	functor	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = In the sections before the last section we give, for any $ C $ - system $ CC $ , three different constructions of pairs $ ((C, p), H) $ where $ (C, p) $ is a universe category and $ H : CC to CC(C, p) $ is an isomorphism.
1	In	in	ADP	IN	_	32	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	sections	section	NOUN	NNS	Number=Plur	1	pobj	_	_
4	before	before	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	last	last	ADJ	JJ	Degree=Pos	7	amod	_	_
7	section	section	NOUN	NN	Number=Sing	4	pobj	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	7	relcl	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
11	for	for	ADP	IN	_	32	prep	_	_
12	any	any	DET	DT	_	15	det	_	_
13	$ C $	$ c $	SYM	$	_	15	nmod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	system	system	NOUN	NN	Number=Sing	11	pobj	_	_
16	$ CC $	$ cc $	SYM	$	_	15	nmod	_	_
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	three	three	NUM	CD	NumType=Card	20	nummod	_	_
19	different	different	ADJ	JJ	Degree=Pos	20	amod	_	_
20	constructions	construction	NOUN	NNS	Number=Plur	32	nsubj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	pairs	pair	NOUN	NNS	Number=Plur	21	pobj	_	_
23	$ ((C, p), H) $	$ ((C, p), H) $	PROPN	NNP	Number=Sing	20	appos	_	_
24	where	where	SCONJ	WRB	_	26	advmod	_	_
25	$ (C, p) $	$ (c, p) $	SYM	$	_	26	nsubj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	relcl	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	universe	universe	ADJ	JJ	Degree=Pos	29	amod	_	_
29	category	category	NOUN	NN	Number=Sing	26	attr	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
31	$ H : CC to CC(C, p) $	$ h : cc to cc(c, p) $	SYM	$	_	32	nsubj	_	_
32	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
33	an	an	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
34	isomorphism	isomorphism	NOUN	NN	Number=Sing	32	attr	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	32	punct	_	SpaceAfter=No

# sent_id = 6
# text = In the last section we construct for any (set) category $ C $ with a choice of a final object and fiber products a $ C $ - system and an equivalence between $ C $ and the precategory underlying $ CC $ .
1	In	in	ADP	IN	_	6	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	last	last	ADJ	JJ	Degree=Pos	4	amod	_	_
4	section	section	NOUN	NN	Number=Sing	1	pobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	any	any	DET	DT	_	12	det	_	_
9	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	10	punct	_	SpaceAfter=No
10	set	set	NOUN	NN	Number=Sing	12	nmod	_	SpaceAfter=No
11	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	12	punct	_	_
12	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
13	$ C $	$ c $	SYM	$	_	6	dep	_	_
14	with	with	ADP	IN	_	6	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	choice	choice	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
19	final	final	ADJ	JJ	Degree=Pos	23	amod	_	_
20	object	object	NOUN	NN	Number=Sing	23	nmod	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	fiber	fiber	NOUN	NN	Number=Sing	20	conj	_	_
23	products	product	NOUN	NNS	Number=Plur	17	pobj	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
25	$ C $	$ c $	SYM	$	_	27	compound	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	system	system	NOUN	NN	Number=Sing	6	dobj	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
29	an	an	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
30	equivalence	equivalence	NOUN	NN	Number=Sing	27	conj	_	_
31	between	between	ADP	IN	_	30	prep	_	_
32	$ C $	$ c $	SYM	$	_	31	pobj	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	precategory	precategory	NOUN	NN	Number=Sing	30	conj	_	_
36	underlying	underlie	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	35	acl	_	_
37	$ CC $	$ cc $	SYM	$	_	36	dobj	_	_
38	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 529
# sent_id = 1
# text = The purpose of this note is to understand the two out of three property of the model category in terms of the weak factorization systems.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	purpose	purpose	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	note	note	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	understand	understand	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	two	two	NUM	CD	NumType=Card	14	nummod	_	_
11	out	out	ADP	IN	_	13	quantmod	_	_
12	of	of	ADP	IN	_	13	quantmod	_	_
13	three	three	NUM	CD	NumType=Card	14	nummod	_	_
14	property	property	NOUN	NN	Number=Sing	8	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	model	model	NOUN	NN	Number=Sing	18	compound	_	_
18	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
19	in	in	ADP	IN	_	14	prep	_	_
20	terms	term	NOUN	NNS	Number=Plur	19	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
23	weak	weak	ADJ	JJ	Degree=Pos	25	amod	_	_
24	factorization	factorization	NOUN	NN	Number=Sing	25	compound	_	_
25	systems	system	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = We will show that if a category with classes of trivial cofibrations, cofibrations, trivial fibrations, and fibrations is given a simplicial structure similar to that of the simplicial model category, then the full subcategory of cofibrant and fibrant objects has the two out of three property, and we will give a list of necessary and sufficient conditions in terms of the simplicial structure for the associated canonical "weak equivalence class" to have the two out of three property.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	will	will	AUX	MD	VerbForm=Fin	3	aux	_	_
3	show	show	VERB	VB	VerbForm=Inf	0	ROOT	_	_
4	that	that	SCONJ	IN	_	44	mark	_	_
5	if	if	SCONJ	IN	_	22	mark	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	category	category	NOUN	NN	Number=Sing	5	nmod	_	_
8	with	with	ADP	IN	_	7	prep	_	_
9	classes	class	NOUN	NNS	Number=Plur	8	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	trivial	trivial	ADJ	JJ	Degree=Pos	12	amod	_	_
12	cofibrations	cofibration	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	cofibrations	cofibration	NOUN	NNS	Number=Plur	12	conj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	trivial	trivial	ADJ	JJ	Degree=Pos	17	amod	_	_
17	fibrations	fibration	NOUN	NNS	Number=Plur	14	conj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
20	fibrations	fibration	NOUN	NNS	Number=Plur	22	nsubjpass	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	auxpass	_	_
22	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	44	advcl	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	simplicial	simplicial	ADJ	JJ	Degree=Pos	25	amod	_	_
25	structure	structure	NOUN	NN	Number=Sing	22	dobj	_	_
26	similar	similar	ADJ	JJ	Degree=Pos	25	amod	_	_
27	to	to	ADP	IN	_	26	prep	_	_
28	that	that	PRON	DT	Number=Sing|PronType=Dem	27	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
31	simplicial	simplicial	ADJ	JJ	Degree=Pos	32	amod	_	_
32	model	model	NOUN	NN	Number=Sing	33	compound	_	_
33	category	category	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	44	punct	_	_
35	then	then	ADV	RB	PronType=Dem	44	advmod	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
37	full	full	ADJ	JJ	Degree=Pos	38	amod	_	_
38	subcategory	subcategory	NOUN	NN	Number=Sing	44	nsubj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	cofibrant	cofibrant	NOUN	NN	Number=Sing	43	nmod	_	_
41	and	and	CCONJ	CC	ConjType=Cmp	40	cc	_	_
42	fibrant	fibrant	ADJ	JJ	Degree=Pos	40	conj	_	_
43	objects	object	NOUN	NNS	Number=Plur	39	pobj	_	_
44	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
45	the	the	DET	DT	Definite=Def|PronType=Art	50	det	_	_
46	two	two	NUM	CD	NumType=Card	50	nummod	_	_
47	out	out	ADP	IN	_	49	quantmod	_	_
48	of	of	ADP	IN	_	49	quantmod	_	_
49	three	three	NUM	CD	NumType=Card	50	nummod	_	_
50	property	property	NOUN	NN	Number=Sing	44	dobj	_	SpaceAfter=No
51	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
52	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
53	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	55	nsubj	_	_
54	will	will	AUX	MD	VerbForm=Fin	55	aux	_	_
55	give	give	VERB	VB	VerbForm=Inf	3	conj	_	_
56	a	a	DET	DT	Definite=Ind|PronType=Art	57	det	_	_
57	list	list	NOUN	NN	Number=Sing	55	dobj	_	_
58	of	of	ADP	IN	_	57	prep	_	_
59	necessary	necessary	ADJ	JJ	Degree=Pos	62	amod	_	_
60	and	and	CCONJ	CC	ConjType=Cmp	59	cc	_	_
61	sufficient	sufficient	ADJ	JJ	Degree=Pos	59	conj	_	_
62	conditions	condition	NOUN	NNS	Number=Plur	58	pobj	_	_
63	in	in	ADP	IN	_	62	prep	_	_
64	terms	term	NOUN	NNS	Number=Plur	63	pobj	_	_
65	of	of	ADP	IN	_	64	prep	_	_
66	the	the	DET	DT	Definite=Def|PronType=Art	68	det	_	_
67	simplicial	simplicial	ADJ	JJ	Degree=Pos	68	amod	_	_
68	structure	structure	NOUN	NN	Number=Sing	65	pobj	_	_
69	for	for	ADP	IN	_	68	prep	_	_
70	the	the	DET	DT	Definite=Def|PronType=Art	76	det	_	_
71	associated	associated	ADJ	JJ	Degree=Pos	72	amod	_	_
72	canonical	canonical	NOUN	NN	Number=Sing	76	amod	_	_
73	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	76	punct	_	SpaceAfter=No
74	weak	weak	ADJ	JJ	Degree=Pos	76	amod	_	_
75	equivalence	equivalence	NOUN	NN	Number=Sing	76	compound	_	_
76	class	class	NOUN	NN	Number=Sing	69	pobj	_	SpaceAfter=No
77	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	76	punct	_	_
78	to	to	PART	TO	_	79	aux	_	_
79	have	have	VERB	VB	VerbForm=Inf	55	xcomp	_	_
80	the	the	DET	DT	Definite=Def|PronType=Art	81	det	_	_
81	two	two	NUM	CD	NumType=Card	85	nummod	_	_
82	out	out	ADP	IN	_	84	quantmod	_	_
83	of	of	ADP	IN	_	84	quantmod	_	_
84	three	three	NUM	CD	NumType=Card	85	nummod	_	_
85	property	property	NOUN	NN	Number=Sing	79	dobj	_	SpaceAfter=No
86	.	.	PUNCT	.	PunctType=Peri	55	punct	_	SpaceAfter=No

# doc_id = 530
# sent_id = 1
# text = We study transport of algebraic structures and prove a theorem which subsumes results of Comfort and Ross on topological group structures on Stone - Cech compactifications, of Chevalley and of Gil de Lamadrid and Jans on topological group and ring structures on universal covering spaces, and of Gleason on topological group structures on universal locally connected refinements.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	transport	transport	NOUN	NN	Number=Sing	2	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	algebraic	algebraic	ADJ	JJ	Degree=Pos	6	amod	_	_
6	structures	structure	NOUN	NNS	Number=Plur	4	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
8	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	theorem	theorem	NOUN	NN	Number=Sing	8	dobj	_	_
11	which	which	PRON	WDT	_	12	nsubj	_	_
12	subsumes	subsume	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	relcl	_	_
13	results	result	NOUN	NNS	Number=Plur	12	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	Comfort	Comfort	PROPN	NNP	Number=Sing	14	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	Ross	Ross	PROPN	NNP	Number=Sing	15	conj	_	_
18	on	on	ADP	IN	_	13	prep	_	_
19	topological	topological	ADJ	JJ	Degree=Pos	21	amod	_	_
20	group	group	NOUN	NN	Number=Sing	21	compound	_	_
21	structures	structure	NOUN	NNS	Number=Plur	18	pobj	_	_
22	on	on	ADP	IN	_	21	prep	_	_
23	Stone	Stone	PROPN	NNP	Number=Sing	25	compound	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	Cech	Cech	PROPN	NNP	Number=Sing	26	compound	_	_
26	compactifications	compactification	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
28	of	of	ADP	IN	_	26	prep	_	_
29	Chevalley	Chevalley	PROPN	NNP	Number=Sing	28	pobj	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
31	of	of	ADP	IN	_	21	prep	_	_
32	Gil	Gil	PROPN	NNP	Number=Sing	34	compound	_	_
33	de	de	PROPN	NNP	Number=Sing	34	nmod	_	_
34	Lamadrid	Lamadrid	PROPN	NNP	Number=Sing	31	pobj	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	34	cc	_	_
36	Jans	Jans	PROPN	NNPS	Number=Plur	34	conj	_	_
37	on	on	ADP	IN	_	34	prep	_	_
38	topological	topological	ADJ	JJ	Degree=Pos	39	amod	_	_
39	group	group	NOUN	NN	Number=Sing	37	pobj	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
41	ring	ring	NOUN	NN	Number=Sing	12	conj	_	_
42	structures	structure	NOUN	NNS	Number=Plur	41	dobj	_	_
43	on	on	ADP	IN	_	41	prep	_	_
44	universal	universal	ADJ	JJ	Degree=Pos	46	amod	_	_
45	covering	covering	NOUN	NN	Number=Sing	46	compound	_	_
46	spaces	space	NOUN	NNS	Number=Plur	43	pobj	_	SpaceAfter=No
47	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
48	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
49	of	of	ADP	IN	_	8	conj	_	_
50	Gleason	Gleason	PROPN	NNP	Number=Sing	49	pobj	_	_
51	on	on	ADP	IN	_	50	prep	_	_
52	topological	topological	ADJ	JJ	Degree=Pos	54	amod	_	_
53	group	group	NOUN	NN	Number=Sing	54	compound	_	_
54	structures	structure	NOUN	NNS	Number=Plur	51	pobj	_	_
55	on	on	ADP	IN	_	8	prep	_	_
56	universal	universal	ADJ	JJ	Degree=Pos	59	amod	_	_
57	locally	locally	ADV	RB	_	58	advmod	_	_
58	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	59	amod	_	_
59	refinements	refinement	NOUN	NNS	Number=Plur	55	pobj	_	SpaceAfter=No
60	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 531
# sent_id = 1
# text = Let $ C $ be a category with finite colimits, writing its coproduct $ + $ , and let $ (D, otimes) $ be a braided monoidal category.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ C $	$ c $	SYM	$	_	3	nsubj	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	3	attr	_	_
6	with	with	ADP	IN	_	5	prep	_	_
7	finite	finite	ADJ	JJ	Degree=Pos	8	compound	_	_
8	colimits	colimit	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
10	writing	write	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	advcl	_	_
11	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	12	poss	_	_
12	coproduct	coproduct	NOUN	NN	Number=Sing	10	dobj	_	_
13	$ + $	$ + $	SYM	$	_	10	dobj	_	_
14	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
16	let	let	VERB	VB	VerbForm=Inf	3	conj	_	_
17	$ (D, otimes) $	$ (d, otimes) $	SYM	$	_	18	nsubj	_	_
18	be	be	AUX	VB	VerbForm=Inf	16	ccomp	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
20	braided	braid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	amod	_	_
21	monoidal	monoidal	ADJ	JJ	Degree=Pos	22	amod	_	_
22	category	category	NOUN	NN	Number=Sing	18	attr	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = We describe a method of producing a symmetric monoidal category from a lax braided monoidal functor $ F : (C, +) to (D, otimes) $ , and of producing a strong monoidal functor between such categories from a monoidal natural transformation between such functors.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	method	method	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	producing	produce	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	symmetric	symmetric	ADJ	JJ	Degree=Pos	10	amod	_	_
9	monoidal	monoidal	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	6	dobj	_	_
11	from	from	ADP	IN	_	6	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
13	lax	lax	ADJ	JJ	Degree=Pos	14	advmod	_	_
14	braided	braid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
15	monoidal	monoidal	ADJ	JJ	Degree=Pos	16	amod	_	_
16	functor	functor	NOUN	NN	Number=Sing	11	pobj	_	_
17	$ F : (C, +) to (D, otimes) $	$ f : (c, +) to (d, otimes) $	SYM	$	_	2	dep	_	_
18	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
20	of	of	ADP	IN	_	2	prep	_	_
21	producing	produce	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	pcomp	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
23	strong	strong	ADJ	JJ	Degree=Pos	25	amod	_	_
24	monoidal	monoidal	ADJ	JJ	Degree=Pos	25	amod	_	_
25	functor	functor	NOUN	NN	Number=Sing	21	dobj	_	_
26	between	between	ADP	IN	_	25	prep	_	_
27	such	such	ADJ	JJ	Degree=Pos	28	amod	_	_
28	categories	category	NOUN	NNS	Number=Plur	26	pobj	_	_
29	from	from	ADP	IN	_	28	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
31	monoidal	monoidal	ADJ	JJ	Degree=Pos	33	amod	_	_
32	natural	natural	ADJ	JJ	Degree=Pos	33	amod	_	_
33	transformation	transformation	NOUN	NN	Number=Sing	29	pobj	_	_
34	between	between	ADP	IN	_	33	prep	_	_
35	such	such	ADJ	JJ	Degree=Pos	36	amod	_	_
36	functors	functor	NOUN	NNS	Number=Plur	34	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The objects of these categories, our so - called `decorated cospan categories', are simply the objects of $ C $ , while the morphisms are pairs comprising a cospan $ X rightarrow N leftarrow Y $ in $ C $ together with an element $ 1 to FN $ in $ D $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	objects	object	NOUN	NNS	Number=Plur	17	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	these	these	DET	DT	Number=Plur|PronType=Dem	5	det	_	_
5	categories	category	NOUN	NNS	Number=Plur	3	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
7	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	14	poss	_	_
8	so	so	ADV	RB	_	10	advmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
11	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	14	punct	_	SpaceAfter=No
12	decorated	decorate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
13	cospan	cospan	NOUN	NN	Number=Sing	14	compound	_	_
14	categories	category	NOUN	NNS	Number=Plur	2	appos	_	SpaceAfter=No
15	'	'	PART	POS	_	14	punct	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
17	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
18	simply	simply	ADV	RB	_	17	advmod	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	objects	object	NOUN	NNS	Number=Plur	17	attr	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	$ C $	$ c $	SYM	$	_	21	pobj	_	_
23	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
24	while	while	SCONJ	IN	_	27	mark	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	morphisms	morphism	NOUN	NNS	Number=Plur	27	nsubj	_	_
27	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	17	advcl	_	_
28	pairs	pair	NOUN	NNS	Number=Plur	27	attr	_	_
29	comprising	comprise	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	28	acl	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
31	cospan	cospan	NOUN	NN	Number=Sing	29	dobj	_	_
32	$ X rightarrow N leftarrow Y $	$ x rightarrow n leftarrow y $	SYM	$	_	29	dep	_	_
33	in	in	ADP	IN	_	29	prep	_	_
34	$ C $	$ c $	SYM	$	_	33	pobj	_	_
35	together	together	ADV	RB	_	33	advmod	_	_
36	with	with	ADP	IN	_	29	prep	_	_
37	an	an	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
38	element	element	NOUN	NN	Number=Sing	36	pobj	_	_
39	$ 1 to FN $	$ 1 to fn $	SYM	$	_	38	appos	_	_
40	in	in	ADP	IN	_	38	prep	_	_
41	$ D $	$ d $	SYM	$	_	40	pobj	_	_
42	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 4
# text = Moreover, decorated cospan categories are hypergraph categories—each object is equipped with a special commutative Frobenius monoid—and their functors preserve this structure.
1	Moreover	moreover	ADV	RB	_	6	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
3	decorated	decorate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	amod	_	_
4	cospan	cospan	NOUN	NN	Number=Sing	5	compound	_	_
5	categories	category	NOUN	NNS	Number=Plur	6	nsubj	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
7	hypergraph	hypergraph	ADJ	JJ	Degree=Pos	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	6	attr	_	SpaceAfter=No
9	—	—	PUNCT	:	_	13	punct	_	SpaceAfter=No
10	each	each	DET	DT	_	11	det	_	_
11	object	object	NOUN	NN	Number=Sing	13	nsubjpass	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
16	special	special	ADJ	JJ	Degree=Pos	19	amod	_	_
17	commutative	commutative	ADJ	JJ	Degree=Pos	19	compound	_	_
18	Frobenius	Frobenius	PROPN	NNP	Number=Sing	19	compound	_	_
19	monoid	monoid	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
20	—	—	PUNCT	:	_	13	punct	_	SpaceAfter=No
21	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
22	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	23	poss	_	_
23	functors	functor	NOUN	NNS	Number=Plur	24	nsubj	_	_
24	preserve	preserve	VERB	VBP	Tense=Pres|VerbForm=Fin	13	conj	_	_
25	this	this	DET	DT	Number=Sing|PronType=Dem	26	det	_	_
26	structure	structure	NOUN	NN	Number=Sing	24	dobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# doc_id = 532
# sent_id = 1
# text = Given a monad and a comonad, one obtains a distributive law between them from lifts of one through an adjunction for the other.
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	monad	monad	NOUN	NNS	Number=Plur	1	pobj	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	comonad	comonad	NOUN	NNS	Number=Plur	3	conj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
8	one	one	PRON	PRP	PronType=Prs	9	nsubj	_	_
9	obtains	obtain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	distributive	distributive	ADJ	JJ	Degree=Pos	12	amod	_	_
12	law	law	NOUN	NN	Number=Sing	9	dobj	_	_
13	between	between	ADP	IN	_	12	prep	_	_
14	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	13	pobj	_	_
15	from	from	ADP	IN	_	9	prep	_	_
16	lifts	lift	NOUN	NNS	Number=Plur	15	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	one	one	NUM	CD	NumType=Card	17	pobj	_	_
19	through	through	ADP	IN	_	9	prep	_	_
20	an	an	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	adjunction	adjunction	NOUN	NN	Number=Sing	19	pobj	_	_
22	for	for	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	other	other	ADJ	JJ	Degree=Pos	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 2
# text = In particular, this yields for any bialgebroid the Yetter - Drinfel'd distributive law between the comonad given by a module coalgebra and the monad given by a comodule algebra.
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	yields	yield	NOUN	NNS	Number=Plur	0	ROOT	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	any	any	DET	DT	_	8	det	_	_
8	bialgebroid	bialgebroid	NOUN	NN	Number=Sing	6	pobj	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
10	Yetter	Yetter	PROPN	NNP	Number=Sing	12	compound	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	Drinfel'd	drinfel'd	NOUN	NN	Number=Sing	14	nmod	_	_
13	distributive	distributive	ADJ	JJ	Degree=Pos	14	amod	_	_
14	law	law	NOUN	NN	Number=Sing	8	dobj	_	_
15	between	between	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	comonad	comonad	NOUN	NNS	Number=Plur	15	pobj	_	_
18	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
19	by	by	ADP	IN	_	18	agent	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	module	module	NOUN	NN	Number=Sing	22	compound	_	_
22	coalgebra	coalgebra	NOUN	NNS	Number=Plur	19	pobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	monad	monad	NOUN	NNS	Number=Plur	22	conj	_	_
26	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	acl	_	_
27	by	by	ADP	IN	_	26	agent	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
29	comodule	comodule	NOUN	NN	Number=Sing	30	compound	_	_
30	algebra	algebra	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = It is this self - dual setting that reproduces the cyclic homology of associative and of Hopf algebras in the monadic framework of Böhm and Stefan.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
4	self	self	NOUN	NN	Number=Sing	6	npadvmod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	dual	dual	ADJ	JJ	Degree=Pos	7	amod	_	_
7	setting	setting	NOUN	NN	Number=Sing	2	attr	_	_
8	that	that	PRON	WDT	PronType=Rel	9	nsubj	_	_
9	reproduces	reproduce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	relcl	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	cyclic	cyclic	ADJ	JJ	Degree=Pos	12	amod	_	_
12	homology	homology	NOUN	NN	Number=Sing	9	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	associative	associative	NOUN	NN	Number=Sing	13	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	of	of	ADP	IN	_	14	conj	_	_
17	Hopf	Hopf	PROPN	NNP	Number=Sing	18	compound	_	_
18	algebras	algebra	NOUN	NNS	Number=Plur	13	pobj	_	_
19	in	in	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	monadic	monadic	ADJ	JJ	Degree=Pos	22	amod	_	_
22	framework	framework	NOUN	NN	Number=Sing	19	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	Böhm	Böhm	PROPN	NNP	Number=Sing	23	pobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	Stefan	Stefan	PROPN	NNP	Number=Sing	24	conj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = In fact, their approach generates two duplicial objects and morphisms between them which are mutual inverses if and only if the duplicial objects are cyclic.
1	In	in	ADP	IN	_	6	prep	_	_
2	fact	fact	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
4	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	5	poss	_	_
5	approach	approach	NOUN	NN	Number=Sing	6	nsubj	_	_
6	generates	generate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	two	two	NUM	CD	NumType=Card	9	nummod	_	_
8	duplicial	duplicial	ADJ	JJ	Degree=Pos	9	amod	_	_
9	objects	object	NOUN	NNS	Number=Plur	6	dobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	morphisms	morphism	NOUN	NNS	Number=Plur	9	conj	_	_
12	between	between	ADP	IN	_	9	prep	_	_
13	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	12	pobj	_	_
14	which	which	PRON	WDT	_	15	nsubj	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	relcl	_	_
16	mutual	mutual	ADJ	JJ	Degree=Pos	17	amod	_	_
17	inverses	inverse	NOUN	NNS	Number=Plur	15	attr	_	_
18	if	if	SCONJ	IN	_	25	mark	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	only	only	ADV	RB	_	25	advmod	_	_
21	if	if	SCONJ	IN	_	25	mark	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	duplicial	duplicial	ADJ	JJ	Degree=Pos	24	amod	_	_
24	objects	object	NOUN	NNS	Number=Plur	25	nsubj	_	_
25	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	advcl	_	_
26	cyclic	cyclic	ADJ	JJ	Degree=Pos	25	acomp	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = A 2 - categorical perspective on the process of twisting coefficients is provided and the role of the two notions of bimonad studied in the literature is clarified.
1	A	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
2	2	2	NUM	CD	NumType=Card	4	nummod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	categorical	categorical	ADJ	JJ	Degree=Pos	5	amod	_	_
5	perspective	perspective	NOUN	NN	Number=Sing	13	nsubjpass	_	_
6	on	on	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	process	process	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	twisting	twisting	NOUN	NN	Number=Sing	11	compound	_	_
11	coefficients	coefficient	NOUN	NNS	Number=Plur	9	pobj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	provided	provide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	role	role	NOUN	NN	Number=Sing	28	nsubjpass	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	two	two	NUM	CD	NumType=Card	20	nummod	_	_
20	notions	notion	NOUN	NNS	Number=Plur	17	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	bimonad	bimonad	NOUN	NNS	Number=Plur	21	pobj	_	_
23	studied	study	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	acl	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	literature	literature	NOUN	NN	Number=Sing	24	pobj	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	28	auxpass	_	_
28	clarified	clarify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	conj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	28	punct	_	SpaceAfter=No

# doc_id = 533
# sent_id = 1
# text = An arbitrary Lie groupoid gives rise to a groupoid of germs of local diffeomorphisms over its base manifold, known as its effect.
1	An	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
2	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	4	amod	_	_
3	Lie	lie	NOUN	NN	Number=Sing	4	compound	_	_
4	groupoid	groupoid	NOUN	NN	Number=Sing	5	nsubj	_	_
5	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	rise	rise	VERB	VB	VerbForm=Inf	5	dobj	_	_
7	to	to	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	groupoid	groupoid	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	germs	germ	NOUN	NNS	Number=Plur	10	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	local	local	ADJ	JJ	Degree=Pos	14	amod	_	_
14	diffeomorphisms	diffeomorphism	NOUN	NNS	Number=Plur	12	pobj	_	_
15	over	over	ADP	IN	_	11	prep	_	_
16	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	18	poss	_	_
17	base	base	NOUN	NN	Number=Sing	18	compound	_	_
18	manifold	manifold	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	acl	_	_
21	as	as	ADP	IN	_	20	prep	_	_
22	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	23	poss	_	_
23	effect	effect	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = The effect of any bundle of Lie groups is trivial.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	effect	effect	NOUN	NN	Number=Sing	9	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	any	any	DET	DT	_	5	det	_	_
5	bundle	bundle	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Lie	lie	NOUN	NN	Number=Sing	8	compound	_	_
8	groups	group	NOUN	NNS	Number=Plur	6	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	trivial	trivial	ADJ	JJ	Degree=Pos	9	acomp	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 3
# text = All quotients of a given Lie groupoid determine the same effect.
1	All	all	DET	DT	_	2	det	_	_
2	quotients	quotient	NOUN	NNS	Number=Plur	8	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
6	Lie	lie	NOUN	NN	Number=Sing	7	compound	_	_
7	groupoid	groupoid	NOUN	NN	Number=Sing	3	pobj	_	_
8	determine	determine	VERB	VB	VerbForm=Inf	0	ROOT	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	same	same	ADJ	JJ	Degree=Pos	11	amod	_	_
11	effect	effect	NOUN	NN	Number=Sing	8	dobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 4
# text = It is natural to regard the effects of any two Morita equivalent Lie groupoids as being ``equivalent''.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	natural	natural	ADJ	JJ	Degree=Pos	2	acomp	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	regard	regard	VERB	VB	VerbForm=Inf	2	xcomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	effects	effect	NOUN	NNS	Number=Plur	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	any	any	DET	DT	_	14	det	_	_
10	two	two	NUM	CD	NumType=Card	14	nummod	_	_
11	Morita	Morita	PROPN	NNP	Number=Sing	14	nmod	_	_
12	equivalent	equivalent	ADJ	JJ	Degree=Pos	14	amod	_	_
13	Lie	lie	NOUN	NN	Number=Sing	14	compound	_	_
14	groupoids	groupoid	NOUN	NNS	Number=Plur	8	pobj	_	_
15	as	as	ADP	IN	_	5	prep	_	_
16	being	be	AUX	VBG	VerbForm=Ger	15	pcomp	_	_
17	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	16	punct	_	SpaceAfter=No
18	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	16	punct	_	SpaceAfter=No
19	equivalent	equivalent	ADJ	JJ	Degree=Pos	16	acomp	_	SpaceAfter=No
20	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	2	punct	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = In this paper we shall describe a systematic way of comparing the effects of different Lie groupoids.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
5	shall	shall	AUX	MD	VerbType=Mod	6	aux	_	_
6	describe	describe	VERB	VB	VerbForm=Inf	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	systematic	systematic	ADJ	JJ	Degree=Pos	9	amod	_	_
9	way	way	NOUN	NN	Number=Sing	6	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	comparing	compare	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	pcomp	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	effects	effect	NOUN	NNS	Number=Plur	11	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	different	different	ADJ	JJ	Degree=Pos	17	amod	_	_
16	Lie	lie	NOUN	NN	Number=Sing	17	compound	_	_
17	groupoids	groupoid	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 6
# text = In particular, we shall rigorously define what it means for two arbitrary Lie groupoids to give rise to ``equivalent'' effects.
1	In	in	ADP	IN	_	7	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
5	shall	shall	AUX	MD	VerbType=Mod	7	aux	_	_
6	rigorously	rigorously	ADV	RB	_	7	advmod	_	_
7	define	define	VERB	VB	VerbForm=Inf	0	ROOT	_	_
8	what	what	PRON	WP	_	10	dobj	_	_
9	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	10	nsubj	_	_
10	means	mean	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	ccomp	_	_
11	for	for	SCONJ	IN	_	17	mark	_	_
12	two	two	NUM	CD	NumType=Card	15	nummod	_	_
13	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	15	amod	_	_
14	Lie	lie	NOUN	NN	Number=Sing	15	compound	_	_
15	groupoids	groupoid	NOUN	NNS	Number=Plur	17	nsubj	_	_
16	to	to	PART	TO	_	17	aux	_	_
17	give	give	VERB	VB	VerbForm=Inf	10	advcl	_	_
18	rise	rise	NOUN	NN	Number=Sing	17	dobj	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	24	punct	_	SpaceAfter=No
21	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	24	punct	_	SpaceAfter=No
22	equivalent	equivalent	ADJ	JJ	Degree=Pos	24	amod	_	SpaceAfter=No
23	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	24	punct	_	_
24	effects	effect	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 7
# text = For effective orbifold groupoids, the new notion of equivalence turns out to coincide with the traditional notion of Morita equivalence.
1	For	for	ADP	IN	_	11	prep	_	_
2	effective	effective	ADJ	JJ	Degree=Pos	4	amod	_	_
3	orbifold	orbifold	ADJ	JJ	Degree=Pos	4	amod	_	_
4	groupoids	groupoid	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	new	new	ADJ	JJ	Degree=Pos	8	amod	_	_
8	notion	notion	NOUN	NN	Number=Sing	11	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	equivalence	equivalence	NOUN	NN	Number=Sing	9	pobj	_	_
11	turns	turn	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	out	out	ADP	RP	_	11	prt	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	coincide	coincide	VERB	VB	VerbForm=Inf	11	xcomp	_	_
15	with	with	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	traditional	traditional	ADJ	JJ	Degree=Pos	18	amod	_	_
18	notion	notion	NOUN	NN	Number=Sing	15	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	Morita	Morita	PROPN	NNP	Number=Sing	21	compound	_	_
21	equivalence	equivalence	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 8
# text = Our analysis is relevant to the presentation theory of proper smooth stacks.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	analysis	analysis	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	relevant	relevant	ADJ	JJ	Degree=Pos	3	acomp	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	presentation	presentation	NOUN	NN	Number=Sing	8	compound	_	_
8	theory	theory	NOUN	NN	Number=Sing	5	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	proper	proper	ADJ	JJ	Degree=Pos	12	amod	_	_
11	smooth	smooth	ADJ	JJ	Degree=Pos	12	amod	_	_
12	stacks	stack	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 534
# sent_id = 1
# text = This paper extends the Day Reflection Theorem to skew monoidal categories.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	Day	Day	PROPN	NNP	Number=Sing	6	compound	_	_
6	Reflection	Reflection	PROPN	NNP	Number=Sing	7	compound	_	_
7	Theorem	Theorem	PROPN	NNP	Number=Sing	3	dobj	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	skew	skew	VERB	VB	VerbForm=Inf	3	xcomp	_	_
10	monoidal	monoidal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	categories	category	NOUN	NNS	Number=Plur	9	dobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = We also provide conditions under which a skew monoidal structure can be lifted to the category of Eilenberg - Moore coalgebras for a comonad.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	conditions	condition	NOUN	NNS	Number=Plur	3	dobj	_	_
5	under	under	ADP	IN	_	13	prep	_	_
6	which	which	PRON	WDT	_	5	pobj	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	skew	skew	NOUN	NN	Number=Sing	10	amod	_	_
9	monoidal	monoidal	ADJ	JJ	Degree=Pos	10	amod	_	_
10	structure	structure	NOUN	NN	Number=Sing	13	nsubjpass	_	_
11	can	can	AUX	MD	VerbForm=Fin	13	aux	_	_
12	be	be	AUX	VB	VerbForm=Inf	13	auxpass	_	_
13	lifted	lift	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	relcl	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	category	category	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	20	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	Moore	Moore	PROPN	NNP	Number=Sing	21	compound	_	_
21	coalgebras	coalgebra	NOUN	NNS	Number=Plur	17	pobj	_	_
22	for	for	ADP	IN	_	13	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	comonad	comonad	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 535
# sent_id = 1
# text = Let $ C $ be a finite category.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ C $	$ c $	SYM	$	_	1	ccomp	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	finite	finite	ADJ	JJ	Degree=Pos	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	3	attr	_	SpaceAfter=No
7	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = For an object $ X $ of $ C $ one has the hom - functor $ Hom( - , X) $ of $ C $ to $ Set $ .
1	For	for	ADP	IN	_	8	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	object	object	NOUN	NN	Number=Sing	1	pobj	_	_
4	$ X $	$ x $	SYM	$	_	3	prep	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	$ C $	$ c $	SYM	$	_	7	nmod	_	_
7	one	one	NUM	CD	NumType=Card	5	pobj	_	_
8	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	hom	hom	NOUN	NN	Number=Sing	17	nsubj	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	functor	functor	PROPN	NNP	Number=Sing	10	prep	_	_
13	$ Hom( - , X) $	$ hom( - , x) $	SYM	$	_	10	appos	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	$ C $	$ c $	SYM	$	_	14	pobj	_	_
16	to	to	PART	TO	_	10	prep	_	_
17	$ Set $	$ set $	SYM	$	_	8	dobj	_	_
18	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 3
# text = If $ G $ is a subgroup of $ Aut(X) $ , one has the quotient functor $ Hom( - , X)/G $ .
1	If	if	SCONJ	IN	_	3	mark	_	_
2	$ G $	$ g $	SYM	$	_	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	advcl	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	subgroup	subgroup	NOUN	NN	Number=Sing	3	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	$ Aut(X) $	$ aut(x) $	SYM	$	_	6	pobj	_	_
8	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
9	one	one	PRON	PRP	PronType=Prs	10	nsubj	_	_
10	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	quotient	quotient	ADJ	JJ	Degree=Pos	13	compound	_	_
13	functor	functor	NOUN	NN	Number=Sing	10	dobj	_	_
14	$ Hom( - , X)/G $	$ hom( - , x)/g $	SYM	$	_	13	appos	_	_
15	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show that any finite product of hom - functors of $ C $ is a sum of hom - functors if and only if $ C $ has pushouts and coequalizers and that any finite product of hom - functors of $ C $ is a sum of functors of the form $ Hom( - , X)/G $ if and only if $ C $ has pushouts.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	13	mark	_	_
4	any	any	DET	DT	_	6	det	_	_
5	finite	finite	ADJ	JJ	Degree=Pos	6	amod	_	_
6	product	product	NOUN	NN	Number=Sing	13	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	hom	hom	NOUN	NN	Number=Sing	10	amod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	functors	functor	NOUN	NNS	Number=Plur	7	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	$ C $	$ c $	SYM	$	_	11	pobj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	sum	sum	NOUN	NN	Number=Sing	13	attr	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	hom	hom	NOUN	NN	Number=Sing	16	pobj	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	functors	functor	NOUN	NNS	Number=Plur	16	pobj	_	_
20	if	if	SCONJ	IN	_	13	dep	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	only	only	ADV	RB	_	25	advmod	_	_
23	if	if	SCONJ	IN	_	25	mark	_	_
24	$ C $	$ c $	SYM	$	_	25	nsubj	_	_
25	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	advcl	_	_
26	pushouts	pushout	NOUN	NNS	Number=Plur	25	dobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	coequalizers	coequalizer	NOUN	NNS	Number=Plur	26	conj	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
30	that	that	SCONJ	IN	_	40	mark	_	_
31	any	any	DET	DT	_	33	det	_	_
32	finite	finite	ADJ	JJ	Degree=Pos	33	amod	_	_
33	product	product	NOUN	NN	Number=Sing	40	nsubj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	hom	hom	NOUN	NN	Number=Sing	37	amod	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	functors	functor	NOUN	NNS	Number=Plur	34	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	$ C $	$ c $	SYM	$	_	38	pobj	_	_
40	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	conj	_	_
41	a	a	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
42	sum	sum	NOUN	NN	Number=Sing	40	attr	_	_
43	of	of	ADP	IN	_	42	prep	_	_
44	functors	functor	NOUN	NNS	Number=Plur	43	pobj	_	_
45	of	of	ADP	IN	_	44	prep	_	_
46	the	the	DET	DT	Definite=Def|PronType=Art	47	det	_	_
47	form	form	NOUN	NN	Number=Sing	45	pobj	_	_
48	$ Hom( - , X)/G $	$ hom( - , x)/g $	SYM	$	_	47	appos	_	_
49	if	if	SCONJ	IN	_	40	dep	_	_
50	and	and	CCONJ	CC	ConjType=Cmp	49	cc	_	_
51	only	only	ADV	RB	_	54	advmod	_	_
52	if	if	SCONJ	IN	_	54	mark	_	_
53	$ C $	$ c $	SYM	$	_	54	nsubj	_	_
54	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	40	advcl	_	_
55	pushouts	pushout	NOUN	NNS	Number=Plur	54	dobj	_	SpaceAfter=No
56	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = These are variations of the fact that a finite category has products if and only if it has coproducts.
1	These	these	PRON	DT	Number=Plur|PronType=Dem	2	nsubj	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	variations	variation	NOUN	NNS	Number=Plur	2	attr	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	fact	fact	NOUN	NN	Number=Sing	4	pobj	_	_
7	that	that	SCONJ	IN	_	11	mark	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	finite	finite	ADJ	JJ	Degree=Pos	10	compound	_	_
10	category	category	NOUN	NN	Number=Sing	11	nsubj	_	_
11	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	acl	_	_
12	products	product	NOUN	NNS	Number=Plur	11	dobj	_	_
13	if	if	SCONJ	IN	_	11	prep	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	only	only	ADV	RB	_	18	advmod	_	_
16	if	if	SCONJ	IN	_	18	mark	_	_
17	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	18	nsubj	_	_
18	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	advcl	_	_
19	coproducts	coproduct	NOUN	NNS	Number=Plur	18	dobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 536
# sent_id = 1
# text = We show that for a differential graded Lie algebra $ g $ whose components vanish in degrees below - 1 the nerve of the Deligne 2 - groupoid is homotopy equivalent to the simplicial set of $ g $ - valued differential forms introduced by Hinich.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	27	mark	_	_
4	for	for	ADP	IN	_	27	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
6	differential	differential	ADJ	JJ	Degree=Pos	7	advmod	_	_
7	graded	grade	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	amod	_	_
8	Lie	lie	NOUN	NN	Number=Sing	9	compound	_	_
9	algebra	algebra	NOUN	NN	Number=Sing	4	pobj	_	_
10	$ g $	$ g $	SYM	$	_	9	prep	_	_
11	whose	whose	DET	WP$	Poss=Yes	12	poss	_	_
12	components	component	NOUN	NNS	Number=Plur	13	nsubj	_	_
13	vanish	vanish	VERB	VBP	Tense=Pres|VerbForm=Fin	10	relcl	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	degrees	degree	NOUN	NNS	Number=Plur	14	pobj	_	_
16	below	below	ADP	IN	_	9	prep	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
18	1	1	NUM	CD	NumType=Card	4	pobj	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	nerve	nerve	NOUN	NN	Number=Sing	27	nsubj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
23	Deligne	Deligne	PROPN	NNP	Number=Sing	26	compound	_	_
24	2	2	NUM	CD	NumType=Card	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	groupoid	groupoid	NOUN	NN	Number=Sing	21	pobj	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
28	homotopy	homotopy	ADV	RB	_	27	acomp	_	_
29	equivalent	equivalent	ADJ	JJ	Degree=Pos	28	oprd	_	_
30	to	to	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	simplicial	simplicial	ADJ	JJ	Degree=Pos	33	amod	_	_
33	set	set	NOUN	NN	Number=Sing	30	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	$ g $	$ g $	SYM	$	_	37	advmod	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	39	amod	_	_
38	differential	differential	ADJ	JJ	Degree=Pos	39	amod	_	_
39	forms	form	NOUN	NNS	Number=Plur	34	pobj	_	_
40	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	39	acl	_	_
41	by	by	ADP	IN	_	40	agent	_	_
42	Hinich	Hinich	PROPN	NNP	Number=Sing	41	pobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 537
# sent_id = 1
# text = We introduce the second cohomology categorical group of a categorical group $ G $ with coefficients in a symmetric $ G $ - categorical group and we show that it classifies extensions of $ G $ with symmetric kernel and a functorial section.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
4	second	second	ADJ	JJ	Degree=Pos	7	amod	_	_
5	cohomology	cohomology	NOUN	NN	Number=Sing	7	nmod	_	_
6	categorical	categorical	ADJ	JJ	Degree=Pos	7	amod	_	_
7	group	group	NOUN	NN	Number=Sing	2	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	categorical	categorical	ADJ	JJ	Degree=Pos	11	amod	_	_
11	group	group	NOUN	NN	Number=Sing	8	pobj	_	_
12	$ G $	$ g $	SYM	$	_	2	dep	_	_
13	with	with	ADP	IN	_	2	prep	_	_
14	coefficients	coefficient	NOUN	NNS	Number=Plur	13	pobj	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
17	symmetric	symmetric	ADJ	JJ	Degree=Pos	21	amod	_	_
18	$ G $	$ g $	SYM	$	_	20	advmod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	categorical	categorical	ADJ	JJ	Degree=Pos	21	amod	_	_
21	group	group	NOUN	NN	Number=Sing	15	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
23	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	24	nsubj	_	_
24	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
25	that	that	SCONJ	IN	_	27	mark	_	_
26	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	27	nsubj	_	_
27	classifies	classify	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	ccomp	_	_
28	extensions	extension	NOUN	NNS	Number=Plur	27	dobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	$ G $	$ g $	SYM	$	_	29	pobj	_	_
31	with	with	ADP	IN	_	27	prep	_	_
32	symmetric	symmetric	ADJ	JJ	Degree=Pos	33	amod	_	_
33	kernel	kernel	NOUN	NN	Number=Sing	31	pobj	_	_
34	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
35	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
36	functorial	functorial	ADJ	JJ	Degree=Pos	37	amod	_	_
37	section	section	NOUN	NN	Number=Sing	33	conj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# sent_id = 2
# text = Moreover, from an essentially surjective homomorphism of categorical groups we get 2 - exact sequences a la Hochschild - Serre connecting the categorical groups of derivations and the first and the second cohomology categorical groups.
1	Moreover	moreover	ADV	RB	_	12	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
3	from	from	ADP	IN	_	12	prep	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	essentially	essentially	ADV	RB	_	6	advmod	_	_
6	surjective	surjective	ADJ	JJ	Degree=Pos	7	amod	_	_
7	homomorphism	homomorphism	NOUN	NN	Number=Sing	3	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	categorical	categorical	ADJ	JJ	Degree=Pos	10	amod	_	_
10	groups	group	NOUN	NNS	Number=Plur	8	pobj	_	_
11	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	12	nsubj	_	_
12	get	get	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	2	2	NUM	CD	NumType=Card	15	nummod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	exact	exact	ADJ	JJ	Degree=Pos	16	amod	_	_
16	sequences	sequence	NOUN	NNS	Number=Plur	12	dobj	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
18	la	la	X	FW	Foreign=Yes	21	compound	_	_
19	Hochschild	Hochschild	PROPN	NNP	Number=Sing	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	Serre	Serre	PROPN	NNP	Number=Sing	12	dobj	_	_
22	connecting	connect	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	21	acl	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	categorical	categorical	ADJ	JJ	Degree=Pos	25	amod	_	_
25	groups	group	NOUN	NNS	Number=Plur	22	dobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	derivations	derivation	NOUN	NNS	Number=Plur	26	pobj	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	first	first	ADJ	JJ	Degree=Pos	21	conj	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
33	second	second	ADJ	JJ	Degree=Pos	36	amod	_	_
34	cohomology	cohomology	NOUN	NN	Number=Sing	36	nmod	_	_
35	categorical	categorical	ADJ	JJ	Degree=Pos	36	amod	_	_
36	groups	group	NOUN	NNS	Number=Plur	30	conj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# doc_id = 538
# sent_id = 1
# text = The "linear dual" of a cocomplete linear category $ C $ is the category of all cocontinuous linear functors $ C to Vect $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	4	punct	_	SpaceAfter=No
3	linear	linear	ADJ	JJ	Degree=Pos	4	compound	_	_
4	dual	dual	ADJ	JJ	Degree=Pos	12	nsubj	_	SpaceAfter=No
5	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	4	punct	_	_
6	of	of	ADP	IN	_	4	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	cocomplete	cocomplete	ADJ	JJ	Degree=Pos	10	amod	_	_
9	linear	linear	ADJ	JJ	Degree=Pos	10	compound	_	_
10	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
11	$ C $	$ c $	SYM	$	_	4	appos	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	category	category	NOUN	NN	Number=Sing	12	attr	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	all	all	DET	DT	_	19	det	_	_
17	cocontinuous	cocontinuous	ADJ	JJ	Degree=Pos	19	amod	_	_
18	linear	linear	ADJ	JJ	Degree=Pos	19	compound	_	_
19	functors	functor	NOUN	NNS	Number=Plur	15	pobj	_	_
20	$ C to Vect $	$ c to vect $	SYM	$	_	14	appos	_	_
21	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 2
# text = We study the questions of when a cocomplete linear category is reflexive (equivalent to its double dual) or dualizable (the pairing with its dual comes with a corresponding copairing).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	questions	question	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	when	when	SCONJ	WRB	_	11	advmod	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	cocomplete	cocomplete	ADJ	JJ	Degree=Pos	10	amod	_	_
9	linear	linear	ADJ	JJ	Degree=Pos	10	compound	_	_
10	category	category	NOUN	NN	Number=Sing	11	nsubj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	pcomp	_	_
12	reflexive	reflexive	ADJ	JJ	Degree=Pos	11	acomp	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	11	punct	_	SpaceAfter=No
14	equivalent	equivalent	ADJ	JJ	Degree=Pos	11	acomp	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	18	poss	_	_
17	double	double	ADJ	JJ	Degree=Pos	18	amod	_	_
18	dual	dual	ADJ	JJ	Degree=Pos	15	pobj	_	SpaceAfter=No
19	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	14	punct	_	_
20	or	or	CCONJ	CC	ConjType=Cmp	11	cc	_	_
21	dualizable	dualizable	ADJ	JJ	Degree=Pos	11	conj	_	_
22	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	21	punct	_	SpaceAfter=No
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	pairing	pairing	NOUN	NN	Number=Sing	28	nsubj	_	_
25	with	with	ADP	IN	_	24	prep	_	_
26	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	27	poss	_	_
27	dual	dual	ADJ	JJ	Degree=Pos	25	pobj	_	_
28	comes	come	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
29	with	with	ADP	IN	_	28	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
31	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	32	amod	_	_
32	copairing	copairing	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
33	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	28	punct	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Our main results are that the category of comodules for a countable - dimensional coassociative coalgebra is always reflexive, but
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	3	poss	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	results	result	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	17	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	category	category	NOUN	NN	Number=Sing	17	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	comodules	comodule	NOUN	NNS	Number=Plur	8	pobj	_	_
10	for	for	ADP	IN	_	7	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
12	countable	countable	ADJ	JJ	Degree=Pos	14	amod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	dimensional	dimensional	ADJ	JJ	Degree=Pos	16	amod	_	_
15	coassociative	coassociative	ADJ	JJ	Degree=Pos	16	amod	_	_
16	coalgebra	coalgebra	NOUN	NNS	Number=Plur	10	pobj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
18	always	always	ADV	RB	_	17	advmod	_	_
19	reflexive	reflexive	ADJ	JJ	Degree=Pos	17	acomp	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
21	but	but	CCONJ	CC	ConjType=Cmp	4	cc	_	SpaceAfter=No

# sent_id = 4
# text = (without any dimension hypothesis) dualizable if and only if it has enough projectives, which rarely happens.
1	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	7	punct	_	SpaceAfter=No
2	without	without	ADP	IN	_	7	prep	_	_
3	any	any	DET	DT	_	5	det	_	_
4	dimension	dimension	NOUN	NN	Number=Sing	5	compound	_	_
5	hypothesis	hypothesis	NOUN	NN	Number=Sing	2	pobj	_	SpaceAfter=No
6	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	2	punct	_	_
7	dualizable	dualizable	ADJ	JJ	Degree=Pos	0	ROOT	_	_
8	if	if	SCONJ	IN	_	7	prep	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	only	only	ADV	RB	_	13	advmod	_	_
11	if	if	SCONJ	IN	_	13	mark	_	_
12	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	13	nsubj	_	_
13	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	conj	_	_
14	enough	enough	ADJ	JJ	Degree=Pos	15	amod	_	_
15	projectives	projective	NOUN	NNS	Number=Plur	13	dobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	which	which	PRON	WDT	_	19	nsubj	_	_
18	rarely	rarely	ADV	RB	_	19	advmod	_	_
19	happens	happen	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	relcl	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 5
# text = Along the way, we prove that the category $ QCoh(X) $ of quasi - coherent sheaves on a stack $ X $ is not dualizable if $ X $ is the classifying stack of a semisimple algebraic group in positive characteristic or if $ X $ is a scheme containing a closed projective subscheme of positive dimension, but is dualizable if $ X $ is the quotient of an affine scheme by a virtually linearly reductive group.
1	Along	along	ADP	IN	_	6	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	way	way	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	20	mark	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	category	category	NOUN	NN	Number=Sing	20	nsubj	_	_
10	$ QCoh(X) $	$ qcoh(x) $	SYM	$	_	9	appos	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	quasi	quasi	ADJ	JJ	Degree=Pos	15	amod	_	_
13	-	-	ADJ	JJ	Degree=Pos	15	amod	_	_
14	coherent	coherent	ADJ	JJ	Degree=Pos	15	amod	_	_
15	sheaves	sheaf	NOUN	NNS	Number=Plur	11	pobj	_	_
16	on	on	ADP	IN	_	9	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	stack	stack	NOUN	NN	Number=Sing	16	pobj	_	_
19	$ X $	$ x $	SYM	$	_	9	appos	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
21	not	not	PART	RB	Polarity=Neg	20	neg	_	_
22	dualizable	dualizable	ADJ	JJ	Degree=Pos	20	acomp	_	_
23	if	if	SCONJ	IN	_	25	mark	_	_
24	$ X $	$ x $	SYM	$	_	25	nsubj	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	advcl	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	classifying	classify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	28	amod	_	_
28	stack	stack	NOUN	NN	Number=Sing	25	attr	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
31	semisimple	semisimple	ADJ	JJ	Degree=Pos	33	amod	_	_
32	algebraic	algebraic	ADJ	JJ	Degree=Pos	33	amod	_	_
33	group	group	NOUN	NN	Number=Sing	29	pobj	_	_
34	in	in	ADP	IN	_	33	prep	_	_
35	positive	positive	ADJ	JJ	Degree=Pos	36	amod	_	_
36	characteristic	characteristic	NOUN	NN	Number=Sing	34	pobj	_	_
37	or	or	CCONJ	CC	ConjType=Cmp	34	cc	_	_
38	if	if	SCONJ	IN	_	40	mark	_	_
39	$ X $	$ x $	SYM	$	_	40	nsubj	_	_
40	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	conj	_	_
41	a	a	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
42	scheme	scheme	NOUN	NN	Number=Sing	40	attr	_	_
43	containing	contain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	42	acl	_	_
44	a	a	DET	DT	Definite=Ind|PronType=Art	47	det	_	_
45	closed	closed	ADJ	JJ	Degree=Pos	47	amod	_	_
46	projective	projective	ADJ	JJ	Degree=Pos	47	amod	_	_
47	subscheme	subscheme	NOUN	NN	Number=Sing	43	dobj	_	_
48	of	of	ADP	IN	_	47	prep	_	_
49	positive	positive	ADJ	JJ	Degree=Pos	50	amod	_	_
50	dimension	dimension	NOUN	NN	Number=Sing	48	pobj	_	SpaceAfter=No
51	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
52	but	but	CCONJ	CC	ConjType=Cmp	6	cc	_	_
53	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	conj	_	_
54	dualizable	dualizable	ADJ	JJ	Degree=Pos	53	acomp	_	_
55	if	if	SCONJ	IN	_	57	mark	_	_
56	$ X $	$ x $	SYM	$	_	57	nsubj	_	_
57	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	53	advcl	_	_
58	the	the	DET	DT	Definite=Def|PronType=Art	59	det	_	_
59	quotient	quotient	NOUN	NN	Number=Sing	57	attr	_	_
60	of	of	ADP	IN	_	59	prep	_	_
61	an	an	DET	DT	Definite=Ind|PronType=Art	63	det	_	_
62	affine	affine	NOUN	NN	Number=Sing	63	compound	_	_
63	scheme	scheme	NOUN	NN	Number=Sing	60	pobj	_	_
64	by	by	ADP	IN	_	59	prep	_	_
65	a	a	DET	DT	Definite=Ind|PronType=Art	69	det	_	_
66	virtually	virtually	ADV	RB	_	67	advmod	_	_
67	linearly	linearly	ADV	RB	_	68	advmod	_	_
68	reductive	reductive	ADJ	JJ	Degree=Pos	69	amod	_	_
69	group	group	NOUN	NN	Number=Sing	64	pobj	_	SpaceAfter=No
70	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 6
# text = Finally we prove tensoriality (a type of Tannakian duality) for affine ind - schemes with countable indexing poset.
1	Finally	finally	ADV	RB	_	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	tensoriality	tensoriality	NOUN	NN	Number=Sing	3	dobj	_	_
5	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	4	punct	_	SpaceAfter=No
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	type	type	NOUN	NN	Number=Sing	4	appos	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	Tannakian	tannakian	ADJ	JJ	Degree=Pos	10	amod	_	_
10	duality	duality	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
11	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	7	punct	_	_
12	for	for	ADP	IN	_	7	prep	_	_
13	affine	affine	PROPN	NNP	Number=Sing	16	compound	_	_
14	ind	ind	NOUN	NN	Number=Sing	16	compound	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	schemes	scheme	NOUN	NNS	Number=Plur	12	pobj	_	_
17	with	with	ADP	IN	_	16	prep	_	_
18	countable	countable	ADJ	JJ	Degree=Pos	20	amod	_	_
19	indexing	indexing	NOUN	NN	Number=Sing	20	compound	_	_
20	poset	poset	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 539
# sent_id = 1
# text = We introduce an apparent strengthening of Sufficient Cohesion that we call stable connected codiscreteness and show that if $ p: E - - > S $ is cohesive and satisfies stable connected codiscreteness then the internal axiom of choice holds in $ S $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	apparent	apparent	ADJ	JJ	Degree=Pos	5	amod	_	_
5	strengthening	strengthening	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Sufficient	Sufficient	PROPN	NNP	Number=Sing	8	compound	_	_
8	Cohesion	Cohesion	PROPN	NNP	Number=Sing	6	pobj	_	_
9	that	that	PRON	WDT	PronType=Rel	11	dobj	_	_
10	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	11	nsubj	_	_
11	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	8	relcl	_	_
12	stable	stable	ADJ	JJ	Degree=Pos	14	amod	_	_
13	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
14	codiscreteness	codiscreteness	NOUN	NN	Number=Sing	11	dobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
16	show	show	VERB	VB	VerbForm=Inf	11	conj	_	_
17	that	that	SCONJ	IN	_	33	mark	_	_
18	if	if	SCONJ	IN	_	20	mark	_	_
19	$ p: E - - > S $	$ p: e - - > s $	SYM	$	_	20	nsubj	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	33	advcl	_	_
21	cohesive	cohesive	ADJ	JJ	Degree=Pos	20	acomp	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
23	satisfies	satisfie	NOUN	NNS	Number=Plur	20	conj	_	_
24	stable	stable	ADJ	JJ	Degree=Pos	26	amod	_	_
25	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
26	codiscreteness	codiscreteness	NOUN	NN	Number=Sing	20	attr	_	_
27	then	then	ADV	RB	PronType=Dem	33	advmod	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
29	internal	internal	ADJ	JJ	Degree=Pos	30	amod	_	_
30	axiom	axiom	NOUN	NN	Number=Sing	33	nsubj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	choice	choice	NOUN	NN	Number=Sing	31	pobj	_	_
33	holds	hold	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	ccomp	_	_
34	in	in	ADP	IN	_	33	prep	_	_
35	$ S $	$ s $	SYM	$	_	34	pobj	_	_
36	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Moreover, in this case, $ p^clik: S - - > E $ is equivalent to the inclusion $ E_{negneg} - - > E $ .
1	Moreover	moreover	ADV	RB	_	8	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
3	in	in	ADP	IN	_	8	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	case	case	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
7	$ p^clik: S - - > E $	$ p^clik: s - - > e $	SYM	$	_	8	nsubj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	equivalent	equivalent	ADJ	JJ	Degree=Pos	8	acomp	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	inclusion	inclusion	NOUN	NN	Number=Sing	10	pobj	_	_
13	$ E_{negneg} - - > E $	$ e_{negneg} - - > e $	SYM	$	_	8	dep	_	_
14	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 540
# sent_id = 1
# text = The existence of the split extension classifier of a crossed module in the category of associative algebras is investigated.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	existence	existence	NOUN	NN	Number=Sing	19	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	split	split	NOUN	NN	Number=Sing	7	compound	_	_
6	extension	extension	NOUN	NN	Number=Sing	7	compound	_	_
7	classifier	classifier	NOUN	NN	Number=Sing	3	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	crossed	crossed	ADJ	JJ	Degree=Pos	11	amod	_	_
11	module	module	NOUN	NN	Number=Sing	8	pobj	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	associative	associative	ADJ	JJ	Degree=Pos	17	amod	_	_
17	algebras	algebra	NOUN	NNS	Number=Plur	15	pobj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	auxpass	_	_
19	investigated	investigate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 2
# text = According to the equivalence of categories $ XAss simeq Cat^1 - Ass $ we consider this problem in $ Cat^1 - Ass $ .
1	According	accord	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	prep	_	_
2	to	to	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	equivalence	equivalence	NOUN	NN	Number=Sing	2	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
7	$ XAss simeq Cat^1 - Ass $	$ xass simeq cat^1 - ass $	SYM	$	_	9	dep	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	this	this	DET	DT	Number=Sing|PronType=Dem	11	det	_	_
11	problem	problem	NOUN	NN	Number=Sing	9	dobj	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	$ Cat^1 - Ass $	$ cat^1 - ass $	SYM	$	_	12	pobj	_	_
14	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 3
# text = This category is not a category of interest, it satisfies its all axioms except one.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	ccomp	_	_
4	not	not	PART	RB	Polarity=Neg	3	neg	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	category	category	NOUN	NN	Number=Sing	3	attr	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	interest	interest	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
10	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	11	nsubj	_	_
11	satisfies	satisfy	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	14	poss	_	_
13	all	all	DET	DT	_	14	det	_	_
14	axioms	axiom	NOUN	NNS	Number=Plur	11	dobj	_	_
15	except	except	SCONJ	IN	_	14	prep	_	_
16	one	one	NUM	CD	NumType=Card	15	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 4
# text = The action theory developed in the category of interest is adapted to the new type of category, which will be called modified category of interest.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	action	action	NOUN	NN	Number=Sing	3	compound	_	_
3	theory	theory	NOUN	NN	Number=Sing	4	nsubj	_	_
4	developed	develop	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	interest	interest	NOUN	NN	Number=Sing	8	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	adapted	adapt	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	conj	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	new	new	ADJ	JJ	Degree=Pos	15	amod	_	_
15	type	type	NOUN	NN	Number=Sing	12	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	category	category	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
19	which	which	PRON	WDT	_	22	nsubjpass	_	_
20	will	will	AUX	MD	VerbForm=Fin	22	aux	_	_
21	be	be	AUX	VB	VerbForm=Inf	22	auxpass	_	_
22	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	relcl	_	_
23	modified	modified	ADJ	JJ	Degree=Pos	24	amod	_	_
24	category	category	NOUN	NN	Number=Sing	22	oprd	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	interest	interest	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 5
# text = Applying the results obtained in this direction and the equivalence of categories we find a condition under which there exists the split extension classifier of a crossed module and give the corresponding construction.
1	Applying	apply	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	advcl	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	results	result	NOUN	NNS	Number=Plur	1	dobj	_	_
4	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	acl	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
7	direction	direction	NOUN	NN	Number=Sing	5	pobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	equivalence	equivalence	NOUN	NN	Number=Sing	3	conj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	find	find	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	condition	condition	NOUN	NN	Number=Sing	14	dobj	_	_
17	under	under	ADP	IN	_	20	prep	_	_
18	which	which	PRON	WDT	_	17	pobj	_	_
19	there	there	PRON	EX	_	20	expl	_	_
20	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	relcl	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
22	split	split	NOUN	NN	Number=Sing	24	compound	_	_
23	extension	extension	NOUN	NN	Number=Sing	24	compound	_	_
24	classifier	classifier	NOUN	NN	Number=Sing	20	dobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
27	crossed	crossed	ADJ	JJ	Degree=Pos	28	amod	_	_
28	module	module	NOUN	NN	Number=Sing	25	pobj	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
30	give	give	VERB	VB	VerbForm=Inf	20	conj	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	corresponding	corresponding	ADJ	JJ	Degree=Pos	33	amod	_	_
33	construction	construction	NOUN	NN	Number=Sing	30	dobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# doc_id = 541
# sent_id = 1
# text = Control theory uses `signal - flow diagrams' to describe processes where real - valued functions of time are added, multiplied by scalars, differentiated and integrated, duplicated and deleted.
1	Control	control	NOUN	NN	Number=Sing	2	compound	_	_
2	theory	theory	NOUN	NN	Number=Sing	3	nsubj	_	_
3	uses	use	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	8	punct	_	SpaceAfter=No
5	signal	signal	NOUN	NN	Number=Sing	7	amod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	flow	flow	NOUN	NN	Number=Sing	8	compound	_	_
8	diagrams	diagram	NOUN	NNS	Number=Plur	3	dobj	_	SpaceAfter=No
9	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	8	punct	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	describe	describe	VERB	VB	VerbForm=Inf	3	xcomp	_	_
12	processes	process	NOUN	NNS	Number=Plur	11	dobj	_	_
13	where	where	SCONJ	WRB	_	21	advmod	_	_
14	real	real	ADV	RB	_	16	advmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	functions	function	NOUN	NNS	Number=Plur	21	nsubjpass	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	time	time	NOUN	NN	Number=Sing	18	pobj	_	_
20	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	21	auxpass	_	_
21	added	add	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	relcl	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	multiplied	multiply	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	advcl	_	_
24	by	by	ADP	IN	_	23	agent	_	_
25	scalars	scalar	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
27	differentiated	differentiate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	acl	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
29	integrated	integrate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	conj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
31	duplicated	duplicate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	acl	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	deleted	delete	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	conj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = These diagrams can be seen as string diagrams for the symmetric monoidal category FinVectk of finite - dimensional vector spaces over the field of rational functions $ k = R(s) $ , where the variable $ s $ acts as differentiation and the monoidal structure is direct sum rather than the usual tensor product of vector spaces.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	diagrams	diagram	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
3	can	can	AUX	MD	VerbForm=Fin	5	aux	_	_
4	be	be	AUX	VB	VerbForm=Inf	5	auxpass	_	_
5	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	as	as	ADP	IN	_	5	prep	_	_
7	string	string	NOUN	NN	Number=Sing	8	compound	_	_
8	diagrams	diagram	NOUN	NNS	Number=Plur	6	pobj	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
11	symmetric	symmetric	ADJ	JJ	Degree=Pos	13	amod	_	_
12	monoidal	monoidal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
14	FinVectk	FinVectk	PROPN	NNP	Number=Sing	13	appos	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	finite	finite	ADJ	JJ	Degree=Pos	18	amod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	dimensional	dimensional	ADJ	JJ	Degree=Pos	20	amod	_	_
19	vector	vector	NOUN	NN	Number=Sing	20	compound	_	_
20	spaces	space	NOUN	NNS	Number=Plur	15	pobj	_	_
21	over	over	ADP	IN	_	8	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	field	field	NOUN	NN	Number=Sing	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	rational	rational	ADJ	JJ	Degree=Pos	26	amod	_	_
26	functions	function	NOUN	NNS	Number=Plur	24	pobj	_	_
27	$ k = R(s) $	$ k = r(s) $	SYM	$	_	8	appos	_	_
28	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
29	where	where	SCONJ	WRB	_	33	advmod	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
31	variable	variable	ADJ	JJ	Degree=Pos	32	amod	_	_
32	$ s $	$ s $	SYM	$	_	33	nmod	_	_
33	acts	act	NOUN	NNS	Number=Plur	27	relcl	_	_
34	as	as	ADP	IN	_	33	prep	_	_
35	differentiation	differentiation	NOUN	NN	Number=Sing	34	pobj	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
38	monoidal	monoidal	ADJ	JJ	Degree=Pos	39	amod	_	_
39	structure	structure	NOUN	NN	Number=Sing	40	nsubj	_	_
40	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	conj	_	_
41	direct	direct	ADJ	JJ	Degree=Pos	42	amod	_	_
42	sum	sum	NOUN	NN	Number=Sing	40	attr	_	_
43	rather	rather	ADV	RB	_	44	advmod	_	_
44	than	than	ADP	IN	_	42	cc	_	_
45	the	the	DET	DT	Definite=Def|PronType=Art	48	det	_	_
46	usual	usual	ADJ	JJ	Degree=Pos	48	amod	_	_
47	tensor	tensor	NOUN	NN	Number=Sing	48	compound	_	_
48	product	product	NOUN	NN	Number=Sing	42	conj	_	_
49	of	of	ADP	IN	_	48	prep	_	_
50	vector	vector	NOUN	NN	Number=Sing	51	compound	_	_
51	spaces	space	NOUN	NNS	Number=Plur	49	pobj	_	SpaceAfter=No
52	.	.	PUNCT	.	PunctType=Peri	40	punct	_	SpaceAfter=No

# sent_id = 3
# text = For any field $ k $ we give a presentation of $ FinVectk $ in terms of the generators used in signal - flow diagrams.
1	For	for	ADP	IN	_	6	prep	_	_
2	any	any	DET	DT	_	3	det	_	_
3	field	field	NOUN	NN	Number=Sing	1	pobj	_	_
4	$ k $	$ k $	SYM	$	_	3	prep	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	presentation	presentation	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	$ FinVectk $	$ finvectk $	SYM	$	_	9	pobj	_	_
11	in	in	ADP	IN	_	6	prep	_	_
12	terms	term	NOUN	NNS	Number=Plur	11	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	generators	generator	NOUN	NNS	Number=Plur	13	pobj	_	_
16	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	signal	signal	ADJ	JJ	Degree=Pos	20	amod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	flow	flow	NOUN	NN	Number=Sing	21	compound	_	_
21	diagrams	diagram	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = A broader class of signal - flow diagrams also includes `caps' and `cups' to model feedback.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	broader	broad	ADJ	JJR	Degree=Cmp	3	amod	_	_
3	class	class	NOUN	NN	Number=Sing	10	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	signal	signal	NOUN	NN	Number=Sing	7	amod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	flow	flow	NOUN	NN	Number=Sing	8	compound	_	_
8	diagrams	diagram	NOUN	NNS	Number=Plur	4	pobj	_	_
9	also	also	ADV	RB	_	10	advmod	_	_
10	includes	include	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	10	punct	_	SpaceAfter=No
12	caps	cap	NOUN	NNS	Number=Plur	10	dobj	_	SpaceAfter=No
13	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	12	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
15	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	16	punct	_	SpaceAfter=No
16	cups	cup	NOUN	NNS	Number=Plur	12	conj	_	SpaceAfter=No
17	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	16	punct	_	_
18	to	to	PART	TO	_	19	aux	_	_
19	model	model	VERB	VB	VerbForm=Inf	10	xcomp	_	_
20	feedback	feedback	NOUN	NN	Number=Sing	19	dobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 5
# text = We show these diagrams can be seen as string diagrams for the symmetric monoidal category $ FinRelk $ , where objects are still finite - dimensional vector spaces but the morphisms are linear relations.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	these	these	DET	DT	Number=Plur|PronType=Dem	4	det	_	_
4	diagrams	diagram	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
5	can	can	AUX	MD	VerbForm=Fin	7	aux	_	_
6	be	be	AUX	VB	VerbForm=Inf	7	auxpass	_	_
7	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
8	as	as	ADP	IN	_	7	prep	_	_
9	string	string	NOUN	NN	Number=Sing	10	compound	_	_
10	diagrams	diagram	NOUN	NNS	Number=Plur	8	pobj	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
13	symmetric	symmetric	ADJ	JJ	Degree=Pos	15	amod	_	_
14	monoidal	monoidal	ADJ	JJ	Degree=Pos	15	amod	_	_
15	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
16	$ FinRelk $	$ finrelk $	SYM	$	_	15	appos	_	_
17	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
18	where	where	SCONJ	WRB	_	20	advmod	_	_
19	objects	object	NOUN	NNS	Number=Plur	20	nsubj	_	_
20	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	relcl	_	_
21	still	still	ADV	RB	_	20	advmod	_	_
22	finite	finite	ADJ	JJ	Degree=Pos	24	npadvmod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	dimensional	dimensional	ADJ	JJ	Degree=Pos	26	amod	_	_
25	vector	vector	NOUN	NN	Number=Sing	26	compound	_	_
26	spaces	space	NOUN	NNS	Number=Plur	20	attr	_	_
27	but	but	CCONJ	CC	ConjType=Cmp	2	cc	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	morphisms	morphism	NOUN	NNS	Number=Plur	30	nsubj	_	_
30	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	conj	_	_
31	linear	linear	ADJ	JJ	Degree=Pos	32	compound	_	_
32	relations	relation	NOUN	NNS	Number=Plur	30	attr	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	30	punct	_	SpaceAfter=No

# sent_id = 6
# text = We also give a presentation for $ FinRelk $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	presentation	presentation	NOUN	NN	Number=Sing	3	dobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	$ FinRelk $	$ finrelk $	SYM	$	_	6	pobj	_	_
8	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = The relations say, among other things, that the 1 - dimensional vector space $ k $ has two special commutative dagger - Frobenius structures, such that the multiplication and unit of either one and the comultiplication and counit of the other fit together to form a bimonoid.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	relations	relation	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	say	say	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	among	among	ADP	IN	_	3	prep	_	_
6	other	other	ADJ	JJ	Degree=Pos	7	amod	_	_
7	things	thing	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
9	that	that	SCONJ	IN	_	17	mark	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
11	1	1	NUM	CD	NumType=Card	13	advmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	dimensional	dimensional	ADJ	JJ	Degree=Pos	15	amod	_	_
14	vector	vector	NOUN	NN	Number=Sing	15	compound	_	_
15	space	space	NOUN	NN	Number=Sing	17	nsubj	_	_
16	$ k $	$ k $	SYM	$	_	15	appos	_	_
17	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
18	two	two	NUM	CD	NumType=Card	24	nummod	_	_
19	special	special	ADJ	JJ	Degree=Pos	24	amod	_	_
20	commutative	commutative	ADJ	JJ	Degree=Pos	24	amod	_	_
21	dagger	dagger	PROPN	NNP	Number=Sing	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	Frobenius	Frobenius	PROPN	NNP	Number=Sing	24	compound	_	_
24	structures	structure	NOUN	NNS	Number=Plur	17	dobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	such	such	ADJ	JJ	Degree=Pos	27	amod	_	_
27	that	that	SCONJ	IN	_	17	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	multiplication	multiplication	NOUN	NN	Number=Sing	27	pobj	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
31	unit	unit	NOUN	NN	Number=Sing	29	conj	_	_
32	of	of	ADP	IN	_	29	prep	_	_
33	either	either	PRON	DT	_	34	preconj	_	_
34	one	one	NUM	CD	NumType=Card	32	pobj	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	34	cc	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	comultiplication	comultiplication	NOUN	NN	Number=Sing	34	conj	_	_
38	and	and	CCONJ	CC	ConjType=Cmp	37	cc	_	_
39	counit	counit	NOUN	NN	Number=Sing	37	conj	_	_
40	of	of	ADP	IN	_	37	prep	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
42	other	other	ADJ	JJ	Degree=Pos	43	amod	_	_
43	fit	fit	NOUN	NN	Number=Sing	40	pobj	_	_
44	together	together	ADV	RB	_	43	advmod	_	_
45	to	to	PART	TO	_	46	aux	_	_
46	form	form	VERB	VB	VerbForm=Inf	29	acl	_	_
47	a	a	DET	DT	Definite=Ind|PronType=Art	48	det	_	_
48	bimonoid	bimonoid	NOUN	NN	Number=Sing	46	dobj	_	SpaceAfter=No
49	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 8
# text = This sort of structure, but with tensor product replacing direct sum, is familiar from the `ZX - calculus' obeyed by a finite - dimensional Hilbert space with two mutually unbiased bases.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	sort	sort	NOUN	NN	Number=Sing	14	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	structure	structure	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
6	but	but	CCONJ	CC	ConjType=Cmp	2	cc	_	_
7	with	with	ADP	IN	_	14	prep	_	_
8	tensor	tensor	NOUN	NN	Number=Sing	9	compound	_	_
9	product	product	NOUN	NN	Number=Sing	10	nsubj	_	_
10	replacing	replace	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	pcomp	_	_
11	direct	direct	ADJ	JJ	Degree=Pos	12	amod	_	_
12	sum	sum	NOUN	NN	Number=Sing	10	dobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	familiar	familiar	ADJ	JJ	Degree=Pos	14	acomp	_	_
16	from	from	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
18	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	21	punct	_	SpaceAfter=No
19	ZX	ZX	PROPN	NNP	Number=Sing	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	calculus	calculus	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
22	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	21	case	_	_
23	obeyed	obey	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	advcl	_	_
24	by	by	ADP	IN	_	23	agent	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
26	finite	finite	ADJ	JJ	Degree=Pos	28	npadvmod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	dimensional	dimensional	ADJ	JJ	Degree=Pos	30	amod	_	_
29	Hilbert	Hilbert	PROPN	NNP	Number=Sing	30	compound	_	_
30	space	space	NOUN	NN	Number=Sing	24	pobj	_	_
31	with	with	ADP	IN	_	30	prep	_	_
32	two	two	NUM	CD	NumType=Card	35	nummod	_	_
33	mutually	mutually	ADV	RB	_	34	advmod	_	_
34	unbiased	unbiased	ADJ	JJ	Degree=Pos	35	amod	_	_
35	bases	basis	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# doc_id = 542
# sent_id = 1
# text = In this paper we define a sequence of monads $ T^{(infty, n)} (ninmathbb{N}) $ on the category $ infty - Gr $ of $ infty $ - graphs.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	sequence	sequence	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	monads	monad	NOUN	NNS	Number=Plur	8	pobj	_	_
10	$ T^{(infty, n)} (ninmathbb{N}) $	$ t^{(infty, n)} (ninmathbb{n}) $	SYM	$	_	5	dep	_	_
11	on	on	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
14	$ infty - Gr $	$ infty - gr $	SYM	$	_	10	appos	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	$ infty $	$ infty $	SYM	$	_	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	graphs	graph	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = We conjecture that algebras for $ T^{(infty, 0)} $ , which are defined in a purely algebraic setting, are models of $ infty $ - groupoids.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	conjecture	conjecture	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	4	nsubj	_	_
4	algebras	algebra	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	$ T^{(infty, 0)} $	$ t^{(infty, 0)} $	SYM	$	_	5	pobj	_	_
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	which	which	PRON	WDT	_	10	nsubjpass	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	relcl	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	purely	purely	ADV	RB	_	14	advmod	_	_
14	algebraic	algebraic	ADJ	JJ	Degree=Pos	15	amod	_	_
15	setting	setting	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
17	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
18	models	model	NOUN	NNS	Number=Plur	17	attr	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	$ infty $	$ infty $	SYM	$	_	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	groupoids	groupoid	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = More generally, we conjecture that $ T^{(infty, n)} $ - algebras are models for $ (infty, n) $ - categories.
1	More	more	ADV	RBR	Degree=Cmp	2	advmod	_	_
2	generally	generally	ADV	RB	_	5	advmod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	conjecture	conjecture	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	10	mark	_	_
7	$ T^{(infty, n)} $	$ t^{(infty, n)} $	SYM	$	_	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	algebras	algebra	NOUN	NNS	Number=Plur	10	nsubj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
11	models	model	NOUN	NNS	Number=Plur	10	attr	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	$ (infty, n) $	$ (infty, n) $	SYM	$	_	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = We prove that our $ (infty, 0) $ - categories are bigroupoids when truncated at level 2.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	8	mark	_	_
4	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	7	poss	_	_
5	$ (infty, 0) $	$ (infty, 0) $	SYM	$	_	7	compound	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	categories	category	NOUN	NNS	Number=Plur	8	nsubj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
9	bigroupoids	bigroupoid	NOUN	NNS	Number=Plur	8	attr	_	_
10	when	when	SCONJ	WRB	_	11	advmod	_	_
11	truncated	truncate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	advcl	_	_
12	at	at	ADP	IN	_	11	prep	_	_
13	level	level	NOUN	NN	Number=Sing	12	pobj	_	_
14	2	2	NUM	CD	NumType=Card	13	nummod	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 543
# sent_id = 1
# text = Are all subcategories of locally finitely presentable categories that are closed under limits and $ lambda $ - filtered colimits also locally presentable?
1	Are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
2	all	all	PRON	DT	_	1	advmod	_	_
3	subcategories	subcategorie	NOUN	NNS	Number=Plur	1	attr	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	locally	locally	ADV	RB	_	6	advmod	_	_
6	finitely	finitely	ADV	RB	_	8	amod	_	_
7	presentable	presentable	ADJ	JJ	Degree=Pos	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	_
9	that	that	PRON	WDT	PronType=Rel	11	nsubjpass	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	relcl	_	_
12	under	under	ADP	IN	_	11	prep	_	_
13	limits	limit	NOUN	NNS	Number=Plur	12	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	$ lambda $	$ lambda $	SYM	$	_	17	advmod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	filtered	filter	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
18	colimits	colimit	NOUN	NNS	Number=Plur	13	conj	_	_
19	also	also	ADV	RB	_	21	advmod	_	_
20	locally	locally	ADV	RB	_	21	advmod	_	_
21	presentable	presentable	ADJ	JJ	Degree=Pos	1	acomp	_	SpaceAfter=No
22	?	?	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = For full subcategories the answer is affirmative.
1	For	for	ADP	IN	_	6	prep	_	_
2	full	full	ADJ	JJ	Degree=Pos	3	amod	_	_
3	subcategories	subcategorie	NOUN	NNS	Number=Plur	1	pobj	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	answer	answer	NOUN	NN	Number=Sing	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	affirmative	affirmative	ADJ	JJ	Degree=Pos	6	acomp	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = Makkai and Pitts proved that in the case $ lambda = aleph_0 $ the answer is affirmative also for all iso - full subcategories, that is, those containing with every pair of objects all isomorphisms between them.
1	Makkai	Makkai	PROPN	NNP	Number=Sing	4	nsubj	_	_
2	and	and	CCONJ	CC	ConjType=Cmp	1	cc	_	_
3	Pitts	Pitts	PROPN	NNP	Number=Sing	1	conj	_	_
4	proved	prove	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	12	mark	_	_
6	in	in	ADP	IN	_	12	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	case	case	NOUN	NN	Number=Sing	6	pobj	_	_
9	$ lambda = aleph_0 $	$ lambda = aleph_0 $	SYM	$	_	11	nmod	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	answer	answer	NOUN	NN	Number=Sing	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
13	affirmative	affirmative	ADJ	JJ	Degree=Pos	12	acomp	_	_
14	also	also	ADV	RB	_	12	advmod	_	_
15	for	for	ADP	IN	_	12	prep	_	_
16	all	all	DET	DT	_	20	det	_	_
17	iso	iso	NOUN	NN	Number=Sing	19	npadvmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	full	full	ADJ	JJ	Degree=Pos	20	amod	_	_
20	subcategories	subcategorie	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	that	that	ADV	RB	_	23	advmod	_	_
23	is	is	ADV	RB	_	25	advmod	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
25	those	those	PRON	DT	Number=Plur|PronType=Dem	12	attr	_	_
26	containing	contain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	25	acl	_	_
27	with	with	ADP	IN	_	26	prep	_	_
28	every	every	DET	DT	_	29	det	_	_
29	pair	pair	NOUN	NN	Number=Sing	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	objects	object	NOUN	NNS	Number=Plur	30	pobj	_	_
32	all	all	DET	DT	_	33	det	_	_
33	isomorphisms	isomorphism	NOUN	NNS	Number=Plur	27	pobj	_	_
34	between	between	ADP	IN	_	26	prep	_	_
35	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	34	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = We discuss a possible generalization of this from $ aleph_0 $ to an arbitrary $ lambda $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	discuss	discuss	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	possible	possible	ADJ	JJ	Degree=Pos	5	amod	_	_
5	generalization	generalization	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	this	this	PRON	DT	Number=Sing|PronType=Dem	6	pobj	_	_
8	from	from	ADP	IN	_	2	prep	_	_
9	$ aleph_0 $	$ aleph_0 $	SYM	$	_	8	pobj	_	_
10	to	to	ADP	IN	_	8	prep	_	_
11	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	13	amod	_	_
13	$ lambda $	$ lambda $	SYM	$	_	10	pobj	_	_
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 544
# sent_id = 1
# text = We define a model category structure on a slice category of simplicial spaces, called the "Segal group action" structure, whose fibrant - cofibrant objects may be viewed as representing spaces $ X $ with an action of a fixed Segal group (that is, a group - like, reduced Segal space).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
4	model	model	NOUN	NN	Number=Sing	6	compound	_	_
5	category	category	NOUN	NN	Number=Sing	6	compound	_	_
6	structure	structure	NOUN	NN	Number=Sing	2	dobj	_	_
7	on	on	ADP	IN	_	2	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	slice	slice	NOUN	NN	Number=Sing	10	compound	_	_
10	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	simplicial	simplicial	ADJ	JJ	Degree=Pos	13	amod	_	_
13	spaces	space	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
15	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	2	dep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
17	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	22	punct	_	SpaceAfter=No
18	Segal	Segal	PROPN	NNP	Number=Sing	20	nmod	_	_
19	group	group	NOUN	NN	Number=Sing	20	nmod	_	_
20	action	action	NOUN	NN	Number=Sing	22	nmod	_	SpaceAfter=No
21	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	22	punct	_	_
22	structure	structure	NOUN	NN	Number=Sing	15	oprd	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	whose	whose	DET	WP$	Poss=Yes	28	poss	_	_
25	fibrant	fibrant	NOUN	NN	Number=Sing	27	amod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	cofibrant	cofibrant	NOUN	NN	Number=Sing	28	amod	_	_
28	objects	object	NOUN	NNS	Number=Plur	31	nsubjpass	_	_
29	may	may	AUX	MD	VerbForm=Fin	31	aux	_	_
30	be	be	AUX	VB	VerbForm=Inf	31	auxpass	_	_
31	viewed	view	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	relcl	_	_
32	as	as	ADP	IN	_	31	prep	_	_
33	representing	represent	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	32	pcomp	_	_
34	spaces	space	NOUN	NNS	Number=Plur	33	dobj	_	_
35	$ X $	$ x $	SYM	$	_	34	appos	_	_
36	with	with	ADP	IN	_	33	prep	_	_
37	an	an	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
38	action	action	NOUN	NN	Number=Sing	36	pobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	a	a	DET	DT	Definite=Ind|PronType=Art	43	det	_	_
41	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	43	amod	_	_
42	Segal	Segal	PROPN	NNP	Number=Sing	43	compound	_	_
43	group	group	NOUN	NN	Number=Sing	39	pobj	_	_
44	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	43	punct	_	SpaceAfter=No
45	that	that	ADV	RB	_	46	advmod	_	_
46	is	is	ADV	RB	_	43	parataxis	_	SpaceAfter=No
47	,	,	PUNCT	,	PunctType=Comm	46	punct	_	_
48	a	a	DET	DT	Definite=Ind|PronType=Art	55	det	_	_
49	group	group	NOUN	NN	Number=Sing	51	npadvmod	_	_
50	-	-	PUNCT	HYPH	PunctType=Dash	51	punct	_	_
51	like	like	ADJ	JJ	Degree=Pos	55	amod	_	SpaceAfter=No
52	,	,	PUNCT	,	PunctType=Comm	55	punct	_	_
53	reduced	reduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	55	amod	_	_
54	Segal	segal	ADJ	JJ	Degree=Pos	55	amod	_	_
55	space	space	NOUN	NN	Number=Sing	43	appos	_	SpaceAfter=No
56	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	31	punct	_	SpaceAfter=No
57	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that this model structure is Quillen equivalent to the projective model structure on $ G $ - spaces, $ S^BG} $ , where $ G $ is a simplicial group corresponding to the Segal group.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
5	model	model	NOUN	NN	Number=Sing	6	compound	_	_
6	structure	structure	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	Quillen	quillen	ADJ	JJ	Degree=Pos	7	acomp	_	_
9	equivalent	equivalent	ADJ	JJ	Degree=Pos	8	advmod	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
12	projective	projective	ADJ	JJ	Degree=Pos	14	amod	_	_
13	model	model	NOUN	NN	Number=Sing	14	compound	_	_
14	structure	structure	NOUN	NN	Number=Sing	10	pobj	_	_
15	on	on	ADP	IN	_	14	prep	_	_
16	$ G $	$ g $	SYM	$	_	18	nmod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	spaces	space	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	$ S^BG} $	$ s^bg} $	SYM	$	_	18	appos	_	_
21	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
22	where	where	SCONJ	WRB	_	23	advmod	_	_
23	$ G $	$ g $	SYM	$	_	18	relcl	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
26	simplicial	simplicial	ADJ	JJ	Degree=Pos	27	amod	_	_
27	group	group	NOUN	NN	Number=Sing	24	attr	_	_
28	corresponding	corresponding	NOUN	NN	Number=Sing	27	amod	_	_
29	to	to	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	Segal	Segal	PROPN	NNP	Number=Sing	32	compound	_	_
32	group	group	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = One advantage of this model is that if we start with an ordinary group action $ Xin S^BG $ and apply a weakly monoidal functor of spaces $ L: S to S $ (such as localization or completion) on each simplicial degree of its associated Segal group action, we get a new Segal group action of $ LG $ on $ LX $ which can then be rigidified via the above - mentioned Quillen equivalence.
1	One	one	NUM	CD	NumType=Card	2	nummod	_	_
2	advantage	advantage	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	model	model	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	45	mark	_	_
8	if	if	SCONJ	IN	_	10	mark	_	_
9	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
10	start	start	VERB	VBP	Tense=Pres|VerbForm=Fin	45	advcl	_	_
11	with	with	ADP	IN	_	10	prep	_	_
12	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	ordinary	ordinary	ADJ	JJ	Degree=Pos	15	amod	_	_
14	group	group	NOUN	NN	Number=Sing	15	compound	_	_
15	action	action	NOUN	NN	Number=Sing	11	pobj	_	_
16	$ Xin S^BG $	$ xin s^bg $	X	XX	_	10	advmod	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
18	apply	apply	VERB	VB	VerbForm=Inf	10	conj	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
20	weakly	weakly	ADJ	JJ	Degree=Pos	22	amod	_	_
21	monoidal	monoidal	ADJ	JJ	Degree=Pos	22	amod	_	_
22	functor	functor	NOUN	NN	Number=Sing	18	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	spaces	space	NOUN	NNS	Number=Plur	23	pobj	_	_
25	$ L: S to S $	$ l: s to s $	SYM	$	_	18	npadvmod	_	_
26	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	18	punct	_	SpaceAfter=No
27	such	such	ADJ	JJ	Degree=Pos	28	amod	_	_
28	as	as	ADP	IN	_	18	prep	_	_
29	localization	localization	NOUN	NN	Number=Sing	28	pobj	_	_
30	or	or	CCONJ	CC	ConjType=Cmp	29	cc	_	_
31	completion	completion	NOUN	NN	Number=Sing	29	conj	_	SpaceAfter=No
32	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	18	punct	_	_
33	on	on	ADP	IN	_	18	prep	_	_
34	each	each	DET	DT	_	36	det	_	_
35	simplicial	simplicial	ADJ	JJ	Degree=Pos	36	amod	_	_
36	degree	degree	NOUN	NN	Number=Sing	33	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	42	poss	_	_
39	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	42	amod	_	_
40	Segal	Segal	PROPN	NNP	Number=Sing	41	compound	_	_
41	group	group	NOUN	NN	Number=Sing	42	compound	_	_
42	action	action	NOUN	NN	Number=Sing	37	pobj	_	SpaceAfter=No
43	,	,	PUNCT	,	PunctType=Comm	45	punct	_	_
44	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	45	nsubj	_	_
45	get	get	VERB	VBP	Tense=Pres|VerbForm=Fin	6	ccomp	_	_
46	a	a	DET	DT	Definite=Ind|PronType=Art	50	det	_	_
47	new	new	ADJ	JJ	Degree=Pos	50	amod	_	_
48	Segal	Segal	PROPN	NNP	Number=Sing	49	compound	_	_
49	group	group	NOUN	NN	Number=Sing	50	compound	_	_
50	action	action	NOUN	NN	Number=Sing	45	dobj	_	_
51	of	of	ADP	IN	_	50	prep	_	_
52	$ LG $	$ lg $	SYM	$	_	51	pobj	_	_
53	on	on	ADP	IN	_	50	prep	_	_
54	$ LX $	$ lx $	SYM	$	_	53	pobj	_	_
55	which	which	PRON	WDT	_	59	nsubjpass	_	_
56	can	can	AUX	MD	VerbForm=Fin	59	aux	_	_
57	then	then	ADV	RB	PronType=Dem	59	advmod	_	_
58	be	be	AUX	VB	VerbForm=Inf	59	auxpass	_	_
59	rigidified	rigidify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	50	relcl	_	_
60	via	via	ADP	IN	_	59	prep	_	_
61	the	the	DET	DT	Definite=Def|PronType=Art	66	det	_	_
62	above	above	ADV	RB	_	64	advmod	_	_
63	-	-	PUNCT	HYPH	PunctType=Dash	64	punct	_	_
64	mentioned	mention	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	66	amod	_	_
65	Quillen	quillen	ADJ	JJ	Degree=Pos	66	amod	_	_
66	equivalence	equivalence	NOUN	NN	Number=Sing	60	pobj	_	SpaceAfter=No
67	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 545
# sent_id = 1
# text = Given a small quantaloid $ Q $ with a set of objects $ Q_0 $ , it is proved that complete skeletal $ Q $ - categories, completely distributive skeletal $ Q $ - categories, and $ Q $ - powersets of $ Q $ - typed sets are all monadic over athe slice category of $ Set $ over $ Q_0 $ .
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	small	small	ADJ	JJ	Degree=Pos	4	amod	_	_
4	quantaloid	quantaloid	NOUN	NN	Number=Sing	1	pobj	_	_
5	$ Q $	$ q $	SYM	$	_	1	dep	_	_
6	with	with	ADP	IN	_	1	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	set	set	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	objects	object	NOUN	NNS	Number=Plur	9	pobj	_	_
11	$ Q_0 $	$ q_0 $	SYM	$	_	1	pobj	_	_
12	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
13	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	15	nsubjpass	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
16	that	that	PRON	DT	Number=Sing|PronType=Dem	17	nsubj	_	_
17	complete	complete	ADJ	JJ	Degree=Pos	15	oprd	_	_
18	skeletal	skeletal	ADJ	JJ	Degree=Pos	21	amod	_	_
19	$ Q $	$ q $	SYM	$	_	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	categories	category	NOUN	NNS	Number=Plur	17	dobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	completely	completely	ADV	RB	_	24	advmod	_	_
24	distributive	distributive	ADJ	JJ	Degree=Pos	28	amod	_	_
25	skeletal	skeletal	ADJ	JJ	Degree=Pos	28	amod	_	_
26	$ Q $	$ q $	SYM	$	_	28	nmod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	categories	category	NOUN	NNS	Number=Plur	39	nsubj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
31	$ Q $	$ q $	SYM	$	_	33	nummod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	powersets	powerset	NOUN	NNS	Number=Plur	28	conj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	$ Q $	$ q $	SYM	$	_	37	advmod	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	typed	type	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	38	amod	_	_
38	sets	set	NOUN	NNS	Number=Plur	34	pobj	_	_
39	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	conj	_	_
40	all	all	ADV	RB	_	39	advmod	_	_
41	monadic	monadic	ADJ	JJ	Degree=Pos	39	acomp	_	_
42	over	over	ADP	IN	_	41	prep	_	_
43	athe	athe	DET	DT	_	45	det	_	_
44	slice	slice	NOUN	NN	Number=Sing	45	compound	_	_
45	category	category	NOUN	NN	Number=Sing	42	pobj	_	_
46	of	of	ADP	IN	_	45	prep	_	_
47	$ Set $	$ set $	SYM	$	_	46	pobj	_	_
48	over	over	ADP	IN	_	41	prep	_	_
49	$ Q_0 $	$ q_0 $	SYM	$	_	48	pobj	_	_
50	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# doc_id = 546
# sent_id = 1
# text = We put a model structure on the category of categories internal to simplicial sets.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	put	put	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	model	model	NOUN	NN	Number=Sing	5	compound	_	_
5	structure	structure	NOUN	NN	Number=Sing	2	dobj	_	_
6	on	on	ADP	IN	_	2	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	_
11	internal	internal	ADJ	JJ	Degree=Pos	10	amod	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	simplicial	simplicial	ADJ	JJ	Degree=Pos	14	amod	_	_
14	sets	set	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The weak equivalences in this model structure are preserved and reflected by the nerve functor to bisimplicial sets with the complete Segal space model structure.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	weak	weak	ADJ	JJ	Degree=Pos	3	amod	_	_
3	equivalences	equivalence	NOUN	NNS	Number=Plur	9	nsubjpass	_	_
4	in	in	ADP	IN	_	3	prep	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
6	model	model	NOUN	NN	Number=Sing	7	compound	_	_
7	structure	structure	NOUN	NN	Number=Sing	4	pobj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	preserved	preserve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	reflected	reflect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	conj	_	_
12	by	by	ADP	IN	_	11	agent	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	nerve	nerve	NOUN	NN	Number=Sing	15	compound	_	_
15	functor	functor	NOUN	NN	Number=Sing	12	pobj	_	_
16	to	to	ADP	IN	_	11	prep	_	_
17	bisimplicial	bisimplicial	ADJ	JJ	Degree=Pos	18	amod	_	_
18	sets	set	NOUN	NNS	Number=Plur	16	pobj	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
21	complete	complete	ADJ	JJ	Degree=Pos	25	amod	_	_
22	Segal	Segal	PROPN	NNP	Number=Sing	24	compound	_	_
23	space	space	NOUN	NN	Number=Sing	24	compound	_	_
24	model	model	NOUN	NN	Number=Sing	25	compound	_	_
25	structure	structure	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 3
# text = This model structure is shown to be a model for the homotopy theory of infinity categories.
1	This	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
2	model	model	NOUN	NN	Number=Sing	3	compound	_	_
3	structure	structure	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	be	be	AUX	VB	VerbForm=Inf	5	xcomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	model	model	NOUN	NN	Number=Sing	7	attr	_	_
10	for	for	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	homotopy	homotopy	NOUN	NN	Number=Sing	13	compound	_	_
13	theory	theory	NOUN	NN	Number=Sing	10	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	infinity	infinity	NOUN	NN	Number=Sing	16	compound	_	_
16	categories	category	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = We also study the homotopy theory of internal presheaves over an internal category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	homotopy	homotopy	NOUN	NN	Number=Sing	6	compound	_	_
6	theory	theory	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	internal	internal	ADJ	JJ	Degree=Pos	9	amod	_	_
9	presheaves	presheave	NOUN	NNS	Number=Plur	7	pobj	_	_
10	over	over	ADP	IN	_	3	prep	_	_
11	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	internal	internal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 547
# sent_id = 1
# text = We study the accessibility properties of trivial cofibrations and weak equivalences in a combinatorial model category and prove an estimate for the accessibility rank of weak equivalences.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	accessibility	accessibility	NOUN	NN	Number=Sing	5	compound	_	_
5	properties	property	NOUN	NNS	Number=Plur	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	trivial	trivial	ADJ	JJ	Degree=Pos	8	amod	_	_
8	cofibrations	cofibration	NOUN	NNS	Number=Plur	6	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	weak	weak	ADJ	JJ	Degree=Pos	11	amod	_	_
11	equivalences	equivalence	NOUN	NNS	Number=Plur	8	conj	_	_
12	in	in	ADP	IN	_	2	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
14	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	16	amod	_	_
15	model	model	NOUN	NN	Number=Sing	16	compound	_	_
16	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
18	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
19	an	an	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	estimate	estimate	NOUN	NN	Number=Sing	18	dobj	_	_
21	for	for	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	accessibility	accessibility	NOUN	NN	Number=Sing	24	compound	_	_
24	rank	rank	NOUN	NN	Number=Sing	21	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	weak	weak	ADJ	JJ	Degree=Pos	27	amod	_	_
27	equivalences	equivalence	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In particular, we show that the class of weak equivalences between simplicial sets is finitely accessible.
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	15	mark	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	class	class	NOUN	NN	Number=Sing	15	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	weak	weak	ADJ	JJ	Degree=Pos	11	amod	_	_
11	equivalences	equivalence	NOUN	NNS	Number=Plur	9	pobj	_	_
12	between	between	ADP	IN	_	11	prep	_	_
13	simplicial	simplicial	ADJ	JJ	Degree=Pos	14	amod	_	_
14	sets	set	NOUN	NNS	Number=Plur	12	pobj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
16	finitely	finitely	ADV	RB	_	17	advmod	_	_
17	accessible	accessible	ADJ	JJ	Degree=Pos	15	acomp	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 548
# sent_id = 1
# text = It is well known how to compute the number of orbits of a group action.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	well	well	ADV	RB	Degree=Pos	4	advmod	_	_
4	known	known	ADJ	JJ	Degree=Pos	2	acomp	_	_
5	how	how	SCONJ	WRB	_	7	advmod	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	compute	compute	VERB	VB	VerbForm=Inf	4	xcomp	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	number	number	NOUN	NN	Number=Sing	7	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	orbits	orbit	NOUN	NNS	Number=Plur	10	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	group	group	NOUN	NN	Number=Sing	15	compound	_	_
15	action	action	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = A related problem, apparently not in the literature, is to determine the number of elements in an orbit.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	related	related	ADJ	JJ	Degree=Pos	3	amod	_	_
3	problem	problem	NOUN	NN	Number=Sing	11	nsubj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	apparently	apparently	ADV	RB	_	7	advmod	_	_
6	not	not	PART	RB	Polarity=Neg	7	neg	_	_
7	in	in	ADP	IN	_	3	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	literature	literature	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	to	to	PART	TO	_	13	aux	_	_
13	determine	determine	VERB	VB	VerbForm=Inf	11	xcomp	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	number	number	NOUN	NN	Number=Sing	13	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	elements	element	NOUN	NNS	Number=Plur	16	pobj	_	_
18	in	in	ADP	IN	_	15	prep	_	_
19	an	an	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	orbit	orbit	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 3
# text = The theory that addresses this question leads to orbital extensive categories and to combinatorial aspects of such categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	theory	theory	NOUN	NN	Number=Sing	7	nsubj	_	_
3	that	that	PRON	WDT	PronType=Rel	4	nsubj	_	_
4	addresses	address	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	relcl	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	question	question	NOUN	NN	Number=Sing	4	dobj	_	_
7	leads	lead	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	to	to	ADP	IN	_	7	prep	_	_
9	orbital	orbital	ADJ	JJ	Degree=Pos	11	amod	_	_
10	extensive	extensive	ADJ	JJ	Degree=Pos	11	amod	_	_
11	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
13	to	to	ADP	IN	_	8	conj	_	_
14	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	15	amod	_	_
15	aspects	aspect	NOUN	NNS	Number=Plur	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	such	such	ADJ	JJ	Degree=Pos	18	amod	_	_
18	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 549
# sent_id = 1
# text = Monoidal differential categories provide the framework for categorical models of differential linear logic.
1	Monoidal	monoidal	ADJ	JJ	Degree=Pos	3	amod	_	_
2	differential	differential	ADJ	JJ	Degree=Pos	3	amod	_	_
3	categories	category	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	framework	framework	NOUN	NN	Number=Sing	4	dobj	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	categorical	categorical	ADJ	JJ	Degree=Pos	9	amod	_	_
9	models	model	NOUN	NNS	Number=Plur	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	differential	differential	ADJ	JJ	Degree=Pos	13	amod	_	_
12	linear	linear	ADJ	JJ	Degree=Pos	13	compound	_	_
13	logic	logic	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = The coKleisli category of any monoidal differential category is always a Cartesian differential category.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	coKleisli	cokleisli	ADJ	JJ	Degree=Pos	3	amod	_	_
3	category	category	NOUN	NN	Number=Sing	9	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	any	any	DET	DT	_	8	det	_	_
6	monoidal	monoidal	ADJ	JJ	Degree=Pos	8	amod	_	_
7	differential	differential	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	always	always	ADV	RB	_	9	advmod	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
12	Cartesian	cartesian	ADJ	JJ	Degree=Pos	14	amod	_	_
13	differential	differential	ADJ	JJ	Degree=Pos	14	amod	_	_
14	category	category	NOUN	NN	Number=Sing	9	attr	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 3
# text = Cartesian differential categories, besides arising in this manner as coKleisli categories, occur in many different and quite independent ways.
1	Cartesian	cartesian	ADJ	JJ	Degree=Pos	3	amod	_	_
2	differential	differential	ADJ	JJ	Degree=Pos	3	amod	_	_
3	categories	category	NOUN	NNS	Number=Plur	14	nsubj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	besides	besides	SCONJ	IN	_	3	prep	_	_
6	arising	arise	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	this	this	DET	DT	Number=Sing|PronType=Dem	9	det	_	_
9	manner	manner	NOUN	NN	Number=Sing	7	pobj	_	_
10	as	as	ADP	IN	_	6	prep	_	_
11	coKleisli	cokleisli	ADJ	JJ	Degree=Pos	12	amod	_	_
12	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
14	occur	occur	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	many	many	ADJ	JJ	Degree=Pos	21	amod	_	_
17	different	different	ADJ	JJ	Degree=Pos	21	amod	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	quite	quite	ADV	RB	_	20	advmod	_	_
20	independent	independent	ADJ	JJ	Degree=Pos	17	conj	_	_
21	ways	way	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 4
# text = Thus, it was not obvious how to pass from Cartesian differential categories back to monoidal differential categories.
1	Thus	thus	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	4	nsubj	_	_
4	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	0	ROOT	_	_
5	not	not	PART	RB	Polarity=Neg	4	neg	_	_
6	obvious	obvious	ADJ	JJ	Degree=Pos	4	acomp	_	_
7	how	how	SCONJ	WRB	_	9	advmod	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	pass	pass	VERB	VB	VerbForm=Inf	6	xcomp	_	_
10	from	from	ADP	IN	_	9	prep	_	_
11	Cartesian	cartesian	ADJ	JJ	Degree=Pos	13	amod	_	_
12	differential	differential	ADJ	JJ	Degree=Pos	13	amod	_	_
13	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
14	back	back	ADV	RB	_	9	advmod	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	monoidal	monoidal	ADJ	JJ	Degree=Pos	18	amod	_	_
17	differential	differential	ADJ	JJ	Degree=Pos	18	amod	_	_
18	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = This paper provides natural conditions under which the linear maps of a Cartesian differential category form a monoidal differential category.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	natural	natural	ADJ	JJ	Degree=Pos	5	amod	_	_
5	conditions	condition	NOUN	NNS	Number=Plur	3	dobj	_	_
6	under	under	ADP	IN	_	16	prep	_	_
7	which	which	PRON	WDT	_	6	pobj	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	linear	linear	ADJ	JJ	Degree=Pos	10	compound	_	_
10	maps	map	NOUN	NNS	Number=Plur	16	nsubj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	Cartesian	cartesian	ADJ	JJ	Degree=Pos	15	amod	_	_
14	differential	differential	ADJ	JJ	Degree=Pos	15	amod	_	_
15	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
16	form	form	VERB	VBP	Tense=Pres|VerbForm=Fin	5	relcl	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
18	monoidal	monoidal	ADJ	JJ	Degree=Pos	20	amod	_	_
19	differential	differential	ADJ	JJ	Degree=Pos	20	amod	_	_
20	category	category	NOUN	NN	Number=Sing	16	dobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = This is a question of some practical importance as much of the machinery of modern differential geometry is based on models which implicitly allow such a passage, and thus the results and tools of the area tend to freely assume access to this structure.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	question	question	NOUN	NN	Number=Sing	2	attr	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	some	some	DET	DT	_	8	det	_	_
7	practical	practical	ADJ	JJ	Degree=Pos	8	amod	_	_
8	importance	importance	NOUN	NN	Number=Sing	5	pobj	_	_
9	as	as	ADP	IN	_	10	advmod	_	_
10	much	much	ADJ	JJ	Degree=Pos	19	nsubjpass	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	machinery	machinery	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	modern	modern	ADJ	JJ	Degree=Pos	17	amod	_	_
16	differential	differential	ADJ	JJ	Degree=Pos	17	amod	_	_
17	geometry	geometry	NOUN	NN	Number=Sing	14	pobj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	auxpass	_	_
19	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	conj	_	_
20	on	on	ADP	IN	_	19	prep	_	_
21	models	model	NOUN	NNS	Number=Plur	20	pobj	_	_
22	which	which	PRON	WDT	_	24	nsubj	_	_
23	implicitly	implicitly	ADV	RB	_	24	advmod	_	_
24	allow	allow	VERB	VBP	Tense=Pres|VerbForm=Fin	21	relcl	_	_
25	such	such	DET	PDT	_	27	predet	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	passage	passage	NOUN	NN	Number=Sing	24	dobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
30	thus	thus	ADV	RB	_	32	advmod	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	results	result	NOUN	NNS	Number=Plur	38	nsubj	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
34	tools	tool	NOUN	NNS	Number=Plur	32	conj	_	_
35	of	of	ADP	IN	_	32	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	area	area	NOUN	NN	Number=Sing	35	pobj	_	_
38	tend	tend	VERB	VBP	Tense=Pres|VerbForm=Fin	19	conj	_	_
39	to	to	PART	TO	_	41	aux	_	_
40	freely	freely	ADV	RB	_	41	advmod	_	_
41	assume	assume	VERB	VB	VerbForm=Inf	38	xcomp	_	_
42	access	access	NOUN	NN	Number=Sing	41	dobj	_	_
43	to	to	ADP	IN	_	42	prep	_	_
44	this	this	DET	DT	Number=Sing|PronType=Dem	45	det	_	_
45	structure	structure	NOUN	NN	Number=Sing	43	pobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = The purpose of this paper is to make precise the connection between the two types of differential categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	purpose	purpose	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	paper	paper	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	make	make	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	precise	precise	ADJ	JJ	Degree=Pos	8	ccomp	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	connection	connection	NOUN	NN	Number=Sing	8	dobj	_	_
12	between	between	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	two	two	NUM	CD	NumType=Card	15	nummod	_	_
15	types	type	NOUN	NNS	Number=Plur	12	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	differential	differential	ADJ	JJ	Degree=Pos	18	amod	_	_
18	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 8
# text = As a prelude to this, however, it is convenient to have available a general theory which relates the behaviour of "linear" maps in Cartesian categories to the structure of Seely categories.
1	As	as	ADP	IN	_	10	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	prelude	prelude	NOUN	NN	Number=Sing	1	pobj	_	_
4	to	to	ADP	IN	_	3	prep	_	_
5	this	this	PRON	DT	Number=Sing|PronType=Dem	4	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
7	however	however	ADV	RB	_	10	advmod	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
9	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	10	nsubj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	convenient	convenient	ADJ	JJ	Degree=Pos	10	acomp	_	_
12	to	to	PART	TO	_	13	aux	_	_
13	have	have	AUX	VB	VerbForm=Inf	14	aux	_	_
14	available	available	ADJ	JJ	Degree=Pos	10	xcomp	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	general	general	ADJ	JJ	Degree=Pos	17	amod	_	_
17	theory	theory	NOUN	NN	Number=Sing	14	dobj	_	_
18	which	which	PRON	WDT	_	19	nsubj	_	_
19	relates	relate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	behaviour	behaviour	NOUN	NN	Number=Sing	19	dobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	SpaceAfter=No
24	linear	linear	ADJ	JJ	Degree=Pos	26	nmod	_	SpaceAfter=No
25	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	26	punct	_	_
26	maps	map	NOUN	NNS	Number=Plur	22	pobj	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	Cartesian	cartesian	ADJ	JJ	Degree=Pos	29	amod	_	_
29	categories	category	NOUN	NNS	Number=Plur	27	pobj	_	_
30	to	to	ADP	IN	_	19	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	structure	structure	NOUN	NN	Number=Sing	30	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	Seely	Seely	PROPN	NNP	Number=Sing	35	amod	_	_
35	categories	category	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 9
# text = The latter were developed to provide the categorical semantics for (fragments of) linear logic which use a "storage" modality.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	latter	latter	ADJ	JJ	Degree=Pos	4	nsubjpass	_	_
3	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	4	auxpass	_	_
4	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	provide	provide	VERB	VB	VerbForm=Inf	4	xcomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	categorical	categorical	ADJ	JJ	Degree=Pos	9	amod	_	_
9	semantics	semantic	NOUN	NNS	Number=Plur	6	dobj	_	_
10	for	for	ADP	IN	_	6	prep	_	_
11	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	10	punct	_	SpaceAfter=No
12	fragments	fragment	NOUN	NNS	Number=Plur	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	SpaceAfter=No
14	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	16	punct	_	_
15	linear	linear	ADJ	JJ	Degree=Pos	16	amod	_	_
16	logic	logic	NOUN	NN	Number=Sing	13	pobj	_	_
17	which	which	PRON	WDT	_	18	nsubj	_	_
18	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	16	relcl	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
20	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	23	punct	_	SpaceAfter=No
21	storage	storage	NOUN	NN	Number=Sing	23	nmod	_	SpaceAfter=No
22	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	23	punct	_	_
23	modality	modality	NOUN	NN	Number=Sing	18	dobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 10
# text = The general theory of storage, which underlies the results mentioned above, is developed in the opening sections of the paper and is then applied to the case of differential categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	general	general	ADJ	JJ	Degree=Pos	3	amod	_	_
3	theory	theory	NOUN	NN	Number=Sing	15	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	storage	storage	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
7	which	which	PRON	WDT	_	8	nsubj	_	_
8	underlies	underlie	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	relcl	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	results	result	NOUN	NNS	Number=Plur	8	dobj	_	_
11	mentioned	mention	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acl	_	_
12	above	above	ADV	RB	_	11	advmod	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	opening	opening	NOUN	NN	Number=Sing	19	compound	_	_
19	sections	section	NOUN	NNS	Number=Plur	16	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	paper	paper	NOUN	NN	Number=Sing	20	pobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	auxpass	_	_
25	then	then	ADV	RB	PronType=Dem	26	advmod	_	_
26	applied	apply	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	conj	_	_
27	to	to	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	case	case	NOUN	NN	Number=Sing	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	differential	differential	ADJ	JJ	Degree=Pos	32	amod	_	_
32	categories	category	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# doc_id = 550
# sent_id = 1
# text = The theory developed by Gambino and Kock, of polynomials over a locally cartesian closed category $ E $ , is generalised for $ E $ just having pullbacks.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	theory	theory	NOUN	NN	Number=Sing	20	nsubjpass	_	_
3	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acl	_	_
4	by	by	ADP	IN	_	3	agent	_	_
5	Gambino	Gambino	PROPN	NNP	Number=Sing	4	pobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	Kock	Kock	PROPN	NNP	Number=Sing	5	conj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
9	of	of	ADP	IN	_	5	prep	_	_
10	polynomials	polynomial	NOUN	NNS	Number=Plur	9	pobj	_	_
11	over	over	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
13	locally	locally	ADV	RB	_	14	advmod	_	_
14	cartesian	cartesian	ADJ	JJ	Degree=Pos	16	amod	_	_
15	closed	closed	ADJ	JJ	Degree=Pos	16	amod	_	_
16	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
17	$ E $	$ e $	SYM	$	_	2	appos	_	_
18	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	auxpass	_	_
20	generalised	generalise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
21	for	for	ADP	IN	_	20	prep	_	_
22	$ E $	$ e $	SYM	$	_	21	pobj	_	_
23	just	just	ADV	RB	_	24	advmod	_	_
24	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	advcl	_	_
25	pullbacks	pullback	NOUN	NNS	Number=Plur	24	dobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 2
# text = The 2 - categorical analogue of the theory of polynomials and polynomial functors is given, and its relationship with Street's theory of fibrations within 2 - categories is explored.
1	The	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
2	2	2	NUM	CD	NumType=Card	4	nummod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	categorical	categorical	ADJ	JJ	Degree=Pos	5	amod	_	_
5	analogue	analogue	NOUN	NN	Number=Sing	15	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	theory	theory	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	polynomials	polynomial	NOUN	NNS	Number=Plur	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	polynomial	polynomial	ADJ	JJ	Degree=Pos	13	amod	_	_
13	functors	functor	NOUN	NNS	Number=Plur	10	conj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
18	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	19	poss	_	_
19	relationship	relationship	NOUN	NN	Number=Sing	31	nsubjpass	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	Street	Street	PROPN	NNP	Number=Sing	23	poss	_	SpaceAfter=No
22	's	's	PART	POS	_	21	case	_	_
23	theory	theory	NOUN	NN	Number=Sing	20	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	fibrations	fibration	NOUN	NNS	Number=Plur	24	pobj	_	_
26	within	within	ADP	IN	_	25	prep	_	_
27	2	2	NUM	CD	NumType=Card	29	nummod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	categories	category	NOUN	NNS	Number=Plur	26	pobj	_	_
30	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	31	auxpass	_	_
31	explored	explore	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	conj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	31	punct	_	SpaceAfter=No

# sent_id = 3
# text = Johnstone's notion of "bagdomain data" is adapted to the present framework to make it easier to completely exhibit examples of polynomial monads.
1	Johnstone	Johnstone	PROPN	NNP	Number=Sing	3	poss	_	SpaceAfter=No
2	's	's	PART	POS	_	1	case	_	_
3	notion	notion	NOUN	NN	Number=Sing	10	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	4	punct	_	SpaceAfter=No
6	bagdomain	bagdomain	NOUN	NN	Number=Sing	7	compound	_	_
7	data	datum	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
8	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	3	punct	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	adapted	adapt	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	to	to	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	present	present	ADJ	JJ	Degree=Pos	14	amod	_	_
14	framework	framework	NOUN	NN	Number=Sing	11	pobj	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	make	make	VERB	VB	VerbForm=Inf	10	advcl	_	_
17	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	18	nsubj	_	_
18	easier	easy	ADJ	JJR	Degree=Cmp	16	ccomp	_	_
19	to	to	PART	TO	_	21	aux	_	_
20	completely	completely	ADV	RB	_	21	advmod	_	_
21	exhibit	exhibit	VERB	VB	VerbForm=Inf	18	xcomp	_	_
22	examples	example	NOUN	NNS	Number=Plur	21	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	polynomial	polynomial	ADJ	JJ	Degree=Pos	25	amod	_	_
25	monads	monad	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# doc_id = 551
# sent_id = 1
# text = We show that there are infinitely many distinct closed classes of colimits (in the sense of the Galois connection induced by commutation of limits and colimits in $ Set $ ) which are intermediate between the class of pseudo - filtered colimits and that of all (small) colimits.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	there	there	PRON	EX	_	5	expl	_	_
5	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	infinitely	infinitely	ADV	RB	_	7	advmod	_	_
7	many	many	ADJ	JJ	Degree=Pos	10	amod	_	_
8	distinct	distinct	ADJ	JJ	Degree=Pos	10	amod	_	_
9	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	classes	class	NOUN	NNS	Number=Plur	5	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	colimits	colimit	NOUN	NNS	Number=Plur	11	pobj	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	10	punct	_	SpaceAfter=No
14	in	in	ADP	IN	_	5	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	sense	sense	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	Galois	Galois	PROPN	NNP	Number=Sing	20	compound	_	_
20	connection	connection	NOUN	NN	Number=Sing	17	pobj	_	_
21	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	acl	_	_
22	by	by	ADP	IN	_	21	agent	_	_
23	commutation	commutation	NOUN	NN	Number=Sing	22	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	limits	limit	NOUN	NNS	Number=Plur	24	pobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	colimits	colimit	NOUN	NNS	Number=Plur	25	conj	_	_
28	in	in	ADP	IN	_	25	prep	_	_
29	$ Set $	$ set $	SYM	$	_	28	pobj	_	_
30	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	20	punct	_	_
31	which	which	PRON	WDT	_	32	nsubj	_	_
32	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	20	relcl	_	_
33	intermediate	intermediate	ADJ	JJ	Degree=Pos	32	acomp	_	_
34	between	between	ADP	IN	_	33	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	class	class	NOUN	NN	Number=Sing	34	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	pseudo	pseudo	NOUN	NN	Number=Sing	40	npadvmod	_	_
39	-	-	PUNCT	HYPH	PunctType=Dash	40	punct	_	_
40	filtered	filter	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	41	amod	_	_
41	colimits	colimit	NOUN	NNS	Number=Plur	37	pobj	_	_
42	and	and	CCONJ	CC	ConjType=Cmp	36	cc	_	_
43	that	that	PRON	DT	Number=Sing|PronType=Dem	36	conj	_	_
44	of	of	ADP	IN	_	43	prep	_	_
45	all	all	DET	DT	_	49	det	_	_
46	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	49	punct	_	SpaceAfter=No
47	small	small	ADJ	JJ	Degree=Pos	49	amod	_	SpaceAfter=No
48	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	49	punct	_	_
49	colimits	colimit	NOUN	NNS	Number=Plur	44	pobj	_	SpaceAfter=No
50	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = On the other hand, if the corresponding class of limits contains either pullbacks or equalizers, then the class of colimits is contained in that of pseudo - filtered colimits.
1	On	on	ADP	IN	_	24	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	other	other	ADJ	JJ	Degree=Pos	4	amod	_	_
4	hand	hand	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
6	if	if	SCONJ	IN	_	12	mark	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	amod	_	_
9	class	class	NOUN	NN	Number=Sing	12	nsubj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	limits	limit	NOUN	NNS	Number=Plur	10	pobj	_	_
12	contains	contain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	advcl	_	_
13	either	either	CCONJ	CC	ConjType=Cmp	14	preconj	_	_
14	pullbacks	pullback	NOUN	NNS	Number=Plur	12	dobj	_	_
15	or	or	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	equalizers	equalizer	NOUN	NNS	Number=Plur	14	conj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
18	then	then	ADV	RB	PronType=Dem	24	advmod	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	class	class	NOUN	NN	Number=Sing	24	nsubjpass	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	colimits	colimit	NOUN	NNS	Number=Plur	21	pobj	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	auxpass	_	_
24	contained	contain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
25	in	in	ADP	IN	_	24	prep	_	_
26	that	that	PRON	DT	Number=Sing|PronType=Dem	25	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	pseudo	pseudo	NOUN	NN	Number=Sing	30	npadvmod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	filtered	filter	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	amod	_	_
31	colimits	colimit	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# doc_id = 552
# sent_id = 1
# text = A factorization system $ (E, M) $ on a category $ A $ gives rise to the covariant category - valued pseudofunctor $ P $ of $ A $ sending each object to its slice category over $ M $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	factorization	factorization	NOUN	NN	Number=Sing	3	compound	_	_
3	system	system	NOUN	NN	Number=Sing	9	nsubj	_	_
4	$ (E, M) $	$ (e, m) $	SYM	$	_	3	appos	_	_
5	on	on	ADP	IN	_	3	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
8	$ A $	$ a $	SYM	$	_	3	appos	_	_
9	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	rise	rise	NOUN	NN	Number=Sing	9	dobj	_	_
11	to	to	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
13	covariant	covariant	ADJ	JJ	Degree=Pos	17	amod	_	_
14	category	category	NOUN	NN	Number=Sing	16	npadvmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	pseudofunctor	pseudofunctor	NOUN	NN	Number=Sing	11	pobj	_	_
18	$ P $	$ p $	SYM	$	_	17	appos	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	$ A $	$ a $	SYM	$	_	19	pobj	_	_
21	sending	send	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	advcl	_	_
22	each	each	DET	DT	_	23	det	_	_
23	object	object	NOUN	NN	Number=Sing	21	dobj	_	_
24	to	to	ADP	IN	_	21	prep	_	_
25	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	27	poss	_	_
26	slice	slice	NOUN	NN	Number=Sing	27	compound	_	_
27	category	category	NOUN	NN	Number=Sing	24	pobj	_	_
28	over	over	ADP	IN	_	21	prep	_	_
29	$ M $	$ m $	SYM	$	_	28	pobj	_	_
30	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 2
# text = This article characterizes the $ P $ so obtained as follows: their object images have terminal objects, and they admit bicategorically cartesian liftings, up to equivalence, of slice - category projections.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	article	article	NOUN	NN	Number=Sing	3	nsubj	_	_
3	characterizes	characterize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	ccomp	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	$ P $	$ p $	SYM	$	_	6	nmod	_	_
6	so	so	ADV	RB	_	7	advmod	_	_
7	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	ccomp	_	_
8	as	as	SCONJ	IN	_	9	mark	_	_
9	follows	follow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	advcl	_	SpaceAfter=No
10	:	:	PUNCT	:	_	14	punct	_	_
11	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	13	poss	_	_
12	object	object	NOUN	NN	Number=Sing	13	compound	_	_
13	images	image	NOUN	NNS	Number=Plur	14	nsubj	_	_
14	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	terminal	terminal	ADJ	JJ	Degree=Pos	16	amod	_	_
16	objects	object	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
19	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	20	nsubj	_	_
20	admit	admit	VERB	VBP	Tense=Pres|VerbForm=Fin	14	conj	_	_
21	bicategorically	bicategorically	ADV	RB	_	22	advmod	_	_
22	cartesian	cartesian	ADJ	JJ	Degree=Pos	23	amod	_	_
23	liftings	lifting	NOUN	NNS	Number=Plur	20	dobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
25	up	up	ADP	IN	_	20	advmod	_	_
26	to	to	ADP	IN	_	25	prep	_	_
27	equivalence	equivalence	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
29	of	of	ADP	IN	_	25	prep	_	_
30	slice	slice	NOUN	NN	Number=Sing	32	compound	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	category	category	NOUN	NN	Number=Sing	33	compound	_	_
33	projections	projection	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 3
# text = It is clear that, and how, $ (E, M) $ can be recovered from such a $ P $ .
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	clear	clear	ADJ	JJ	Degree=Pos	2	acomp	_	_
4	that	that	SCONJ	IN	_	12	mark	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
7	how	how	SCONJ	WRB	_	12	advmod	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
9	$ (E, M) $	$ (e, m) $	SYM	$	_	12	nsubjpass	_	_
10	can	can	AUX	MD	VerbForm=Fin	12	aux	_	_
11	be	be	AUX	VB	VerbForm=Inf	12	auxpass	_	_
12	recovered	recover	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
13	from	from	ADP	IN	_	12	prep	_	_
14	such	such	DET	PDT	_	16	predet	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	$ P $	$ p $	SYM	$	_	13	pobj	_	_
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = The correspondence thus described is actually the second of three similar ones between certain $ (E, M) $ and certain $ P $ that the article presents.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	correspondence	correspondence	NOUN	NN	Number=Sing	4	nsubj	_	_
3	thus	thus	ADV	RB	_	4	advmod	_	_
4	described	describe	VERB	VBD	Tense=Past|VerbForm=Fin	5	csubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	actually	actually	ADV	RB	_	5	advmod	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	second	second	ADJ	JJ	Degree=Pos	5	attr	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	three	three	NUM	CD	NumType=Card	12	nummod	_	_
11	similar	similar	ADJ	JJ	Degree=Pos	12	amod	_	_
12	ones	one	NOUN	NNS	Number=Plur	9	pobj	_	_
13	between	between	ADP	IN	_	12	prep	_	_
14	certain	certain	ADJ	JJ	Degree=Pos	15	amod	_	_
15	$ (E, M) $	$ (e, m) $	SYM	$	_	13	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	certain	certain	ADJ	JJ	Degree=Pos	18	amod	_	_
18	$ P $	$ p $	SYM	$	_	15	conj	_	_
19	that	that	SCONJ	IN	_	22	mark	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	article	article	NOUN	NN	Number=Sing	22	nsubj	_	_
22	presents	present	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	relcl	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = In the first one the characterization of the $ P $ has all ultimately bicategorical ingredients replaced with their categorical analogues.
1	In	in	ADP	IN	_	10	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	first	first	ADJ	JJ	Degree=Pos	4	amod	_	_
4	one	one	NUM	CD	NumType=Card	1	pobj	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	characterization	characterization	NOUN	NN	Number=Sing	10	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	$ P $	$ p $	SYM	$	_	7	pobj	_	_
10	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	all	all	DET	DT	_	14	det	_	_
12	ultimately	ultimately	ADV	RB	_	13	advmod	_	_
13	bicategorical	bicategorical	ADJ	JJ	Degree=Pos	14	amod	_	_
14	ingredients	ingredient	NOUN	NNS	Number=Plur	10	dobj	_	_
15	replaced	replace	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	acl	_	_
16	with	with	ADP	IN	_	15	prep	_	_
17	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	19	poss	_	_
18	categorical	categorical	ADJ	JJ	Degree=Pos	19	amod	_	_
19	analogues	analogue	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 6
# text = A category $ A $ with such a $ P $ is precisely what the author has called a `slicing site'.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	8	nsubj	_	_
3	$ A $	$ a $	SYM	$	_	2	appos	_	_
4	with	with	ADP	IN	_	2	prep	_	_
5	such	such	DET	PDT	_	7	predet	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	$ P $	$ p $	SYM	$	_	4	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	precisely	precisely	ADV	RB	_	10	advmod	_	_
10	what	what	PRON	WP	_	14	dobj	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	author	author	NOUN	NN	Number=Sing	14	nsubj	_	_
13	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	aux	_	_
14	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	ccomp	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
16	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	18	punct	_	SpaceAfter=No
17	slicing	slicing	NOUN	NN	Number=Sing	18	compound	_	_
18	site	site	NOUN	NN	Number=Sing	14	oprd	_	SpaceAfter=No
19	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	8	punct	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 7
# text = In the article's terms the associated $ (E, M) $ are again factorization systems—but the concept conveyed extends the standard one by not obliging isomorphisms to belong to either factor class, namely those that are `right semireplete' (isomorphisms do belong to $ M $ and `left semistrict' (morphisms in $ M $ are monic relative to $ E $ ).
1	In	in	ADP	IN	_	9	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	article	article	NOUN	NN	Number=Sing	5	poss	_	SpaceAfter=No
4	's	's	PART	POS	_	3	case	_	_
5	terms	term	NOUN	NNS	Number=Plur	1	pobj	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	associated	associated	ADJ	JJ	Degree=Pos	8	amod	_	_
8	$ (E, M) $	$ (E, M) $	PROPN	NNP	Number=Sing	9	nsubj	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	again	again	ADV	RB	_	9	advmod	_	_
11	factorization	factorization	NOUN	NN	Number=Sing	12	compound	_	_
12	systems	system	NOUN	NNS	Number=Plur	9	attr	_	SpaceAfter=No
13	—	—	PUNCT	:	_	9	punct	_	SpaceAfter=No
14	but	but	CCONJ	CC	ConjType=Cmp	9	cc	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	concept	concept	NOUN	NN	Number=Sing	18	nsubj	_	_
17	conveyed	convey	VERB	VBD	Tense=Past|VerbForm=Fin	16	acl	_	_
18	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	44	ccomp	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	standard	standard	ADJ	JJ	Degree=Pos	21	amod	_	_
21	one	one	NUM	CD	NumType=Card	18	dobj	_	_
22	by	by	ADP	IN	_	18	prep	_	_
23	not	not	PART	RB	Polarity=Neg	24	neg	_	_
24	obliging	oblige	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	pcomp	_	_
25	isomorphisms	isomorphism	NOUN	NNS	Number=Plur	24	dobj	_	_
26	to	to	PART	TO	_	27	aux	_	_
27	belong	belong	VERB	VB	VerbForm=Inf	18	xcomp	_	_
28	to	to	ADP	IN	_	27	prep	_	_
29	either	either	CCONJ	CC	ConjType=Cmp	31	det	_	_
30	factor	factor	NOUN	NN	Number=Sing	31	compound	_	_
31	class	class	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
33	namely	namely	ADV	RB	_	34	advmod	_	_
34	those	those	PRON	DT	Number=Plur|PronType=Dem	31	appos	_	_
35	that	that	PRON	WDT	PronType=Rel	36	nsubj	_	_
36	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	34	relcl	_	_
37	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	39	punct	_	SpaceAfter=No
38	right	right	ADJ	JJ	Degree=Pos	39	amod	_	_
39	semireplete	semireplete	NOUN	NN	Number=Sing	36	attr	_	SpaceAfter=No
40	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	39	punct	_	_
41	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	44	punct	_	SpaceAfter=No
42	isomorphisms	isomorphism	NOUN	NNS	Number=Plur	44	nsubj	_	_
43	do	do	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	44	aux	_	_
44	belong	belong	VERB	VB	VerbForm=Inf	9	conj	_	_
45	to	to	ADP	IN	_	44	prep	_	_
46	$ M $	$ m $	SYM	$	_	45	pobj	_	_
47	and	and	CCONJ	CC	ConjType=Cmp	44	cc	_	_
48	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	49	punct	_	SpaceAfter=No
49	left	leave	VERB	VBD	Tense=Past|VerbForm=Fin	44	conj	_	_
50	semistrict	semistrict	NOUN	NN	Number=Sing	49	dobj	_	SpaceAfter=No
51	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	49	punct	_	_
52	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	56	punct	_	SpaceAfter=No
53	morphisms	morphism	NOUN	NNS	Number=Plur	56	nsubj	_	_
54	in	in	ADP	IN	_	53	prep	_	_
55	$ M $	$ m $	SYM	$	_	54	pobj	_	_
56	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	44	conj	_	_
57	monic	monic	ADJ	JJ	Degree=Pos	58	amod	_	_
58	relative	relative	NOUN	NN	Number=Sing	56	attr	_	_
59	to	to	ADP	IN	_	58	prep	_	_
60	$ E $	$ e $	SYM	$	_	59	pobj	_	_
61	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	56	punct	_	SpaceAfter=No
62	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 8
# text = The third correspondence subsumes the other two; here the $ (E, M) $ are all right - semireplete factorization systems.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	third	third	ADJ	JJ	Degree=Pos	3	amod	_	_
3	correspondence	correspondence	NOUN	NN	Number=Sing	4	nsubj	_	_
4	subsumes	subsume	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	ccomp	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	other	other	ADJ	JJ	Degree=Pos	7	amod	_	_
7	two	two	NUM	CD	NumType=Card	4	dobj	_	SpaceAfter=No
8	;	;	PUNCT	:	_	12	punct	_	_
9	here	here	ADV	RB	PronType=Dem	12	advmod	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	$ (E, M) $	$ (e, m) $	SYM	$	_	12	nsubj	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	all	all	ADV	RB	_	12	advmod	_	_
14	right	right	ADV	RB	_	16	advmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	semireplete	semireplete	NOUN	NN	Number=Sing	18	amod	_	_
17	factorization	factorization	NOUN	NN	Number=Sing	18	compound	_	_
18	systems	system	NOUN	NNS	Number=Plur	12	attr	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# doc_id = 553
# sent_id = 1
# text = This paper concerns the relationships between notions of weak $ n $ - category defined as algebras for $ n $ - globular operads, as well as their coherence properties.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	concerns	concern	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	relationships	relationship	NOUN	NNS	Number=Plur	3	dobj	_	_
6	between	between	ADP	IN	_	5	prep	_	_
7	notions	notion	NOUN	NNS	Number=Plur	6	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	weak	weak	ADJ	JJ	Degree=Pos	12	amod	_	_
10	$ n $	$ n $	SYM	$	_	12	nummod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
13	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
14	as	as	ADP	IN	_	13	prep	_	_
15	algebras	algebra	NOUN	NNS	Number=Plur	14	pobj	_	_
16	for	for	ADP	IN	_	15	prep	_	_
17	$ n $	$ n $	SYM	$	_	19	advmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	globular	globular	ADJ	JJ	Degree=Pos	20	amod	_	_
20	operads	operad	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
22	as	as	ADV	RB	_	24	advmod	_	_
23	well	well	ADV	RB	Degree=Pos	24	advmod	_	_
24	as	as	ADP	IN	_	5	cc	_	_
25	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	27	poss	_	_
26	coherence	coherence	NOUN	NN	Number=Sing	27	compound	_	_
27	properties	property	NOUN	NNS	Number=Plur	5	conj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = We focus primarily on the definitions due to Batanin and Leinster.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	focus	focus	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	primarily	primarily	ADV	RB	_	2	advmod	_	_
4	on	on	ADP	IN	_	2	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	definitions	definition	NOUN	NNS	Number=Plur	4	pobj	_	_
7	due	due	ADJ	JJ	Degree=Pos	2	prep	_	_
8	to	to	ADP	IN	_	7	pcomp	_	_
9	Batanin	Batanin	PROPN	NNP	Number=Sing	7	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	Leinster	Leinster	PROPN	NNP	Number=Sing	9	conj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = A correspondence between the contractions and systems of compositions used in Batanin's definition, and the unbiased contractions used in Leinster's definition, has long been suspected, and we prove a conjecture of Leinster that shows that the two notions are in some sense equivalent.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	correspondence	correspondence	NOUN	NN	Number=Sing	29	nsubjpass	_	_
3	between	between	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	contractions	contraction	NOUN	NNS	Number=Plur	3	pobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	systems	system	NOUN	NNS	Number=Plur	5	conj	_	_
8	of	of	ADP	IN	_	5	prep	_	_
9	compositions	composition	NOUN	NNS	Number=Plur	8	pobj	_	_
10	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	acl	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	Batanin	Batanin	PROPN	NNP	Number=Sing	14	poss	_	SpaceAfter=No
13	's	's	PART	POS	_	12	case	_	_
14	definition	definition	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	unbiased	unbiased	ADJ	JJ	Degree=Pos	19	amod	_	_
19	contractions	contraction	NOUN	NNS	Number=Plur	2	conj	_	_
20	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	acl	_	_
21	in	in	ADP	IN	_	20	prep	_	_
22	Leinster	Leinster	PROPN	NNP	Number=Sing	24	poss	_	SpaceAfter=No
23	's	's	PART	POS	_	22	case	_	_
24	definition	definition	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
26	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	aux	_	_
27	long	long	ADV	RB	_	29	advmod	_	_
28	been	be	AUX	VBN	Tense=Past|VerbForm=Part	29	auxpass	_	_
29	suspected	suspect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
32	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	33	nsubj	_	_
33	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	29	conj	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
35	conjecture	conjecture	NOUN	NN	Number=Sing	33	dobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	Leinster	Leinster	PROPN	NNP	Number=Sing	36	pobj	_	_
38	that	that	PRON	WDT	PronType=Rel	39	nsubj	_	_
39	shows	show	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	35	relcl	_	_
40	that	that	SCONJ	IN	_	44	mark	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
42	two	two	NUM	CD	NumType=Card	43	nummod	_	_
43	notions	notion	NOUN	NNS	Number=Plur	44	nsubj	_	_
44	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	39	ccomp	_	_
45	in	in	ADP	IN	_	44	prep	_	_
46	some	some	DET	DT	_	47	det	_	_
47	sense	sense	NOUN	NN	Number=Sing	45	pobj	_	_
48	equivalent	equivalent	ADJ	JJ	Degree=Pos	44	acomp	_	SpaceAfter=No
49	.	.	PUNCT	.	PunctType=Peri	33	punct	_	SpaceAfter=No

# sent_id = 4
# text = We then prove several coherence theorems which apply to algebras for any operad with a contraction and system of compositions or with an unbiased contraction; these coherence theorems thus apply to weak $ n $ - categories in the senses of Batanin, Leinster, Penon and Trimble.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	31	ccomp	_	_
4	several	several	ADJ	JJ	Degree=Pos	6	amod	_	_
5	coherence	coherence	NOUN	NN	Number=Sing	6	compound	_	_
6	theorems	theorem	NOUN	NNS	Number=Plur	3	dobj	_	_
7	which	which	PRON	WDT	_	8	nsubj	_	_
8	apply	apply	VERB	VBP	Tense=Pres|VerbForm=Fin	6	relcl	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	algebras	algebra	NOUN	NNS	Number=Plur	9	pobj	_	_
11	for	for	ADP	IN	_	8	prep	_	_
12	any	any	DET	DT	_	13	det	_	_
13	operad	operad	NOUN	NN	Number=Sing	11	pobj	_	_
14	with	with	ADP	IN	_	8	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	contraction	contraction	NOUN	NN	Number=Sing	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	system	system	NOUN	NN	Number=Sing	16	conj	_	_
19	of	of	ADP	IN	_	16	prep	_	_
20	compositions	composition	NOUN	NNS	Number=Plur	19	pobj	_	_
21	or	or	CCONJ	CC	ConjType=Cmp	14	cc	_	_
22	with	with	ADP	IN	_	14	conj	_	_
23	an	an	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	unbiased	unbiased	ADJ	JJ	Degree=Pos	25	amod	_	_
25	contraction	contraction	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
26	;	;	PUNCT	:	_	31	punct	_	_
27	these	these	DET	DT	Number=Plur|PronType=Dem	29	det	_	_
28	coherence	coherence	NOUN	NN	Number=Sing	29	compound	_	_
29	theorems	theorem	NOUN	NNS	Number=Plur	31	nsubj	_	_
30	thus	thus	ADV	RB	_	31	advmod	_	_
31	apply	apply	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
32	to	to	ADP	IN	_	31	prep	_	_
33	weak	weak	ADJ	JJ	Degree=Pos	36	amod	_	_
34	$ n $	$ n $	SYM	$	_	36	nummod	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	36	punct	_	_
36	categories	category	NOUN	NNS	Number=Plur	32	pobj	_	_
37	in	in	ADP	IN	_	36	prep	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
39	senses	sense	NOUN	NNS	Number=Plur	37	pobj	_	_
40	of	of	ADP	IN	_	39	prep	_	_
41	Batanin	Batanin	PROPN	NNP	Number=Sing	40	pobj	_	SpaceAfter=No
42	,	,	PUNCT	,	PunctType=Comm	41	punct	_	_
43	Leinster	Leinster	PROPN	NNP	Number=Sing	41	conj	_	SpaceAfter=No
44	,	,	PUNCT	,	PunctType=Comm	43	punct	_	_
45	Penon	Penon	PROPN	NNP	Number=Sing	43	conj	_	_
46	and	and	CCONJ	CC	ConjType=Cmp	45	cc	_	_
47	Trimble	Trimble	PROPN	NNP	Number=Sing	45	conj	_	SpaceAfter=No
48	.	.	PUNCT	.	PunctType=Peri	31	punct	_	SpaceAfter=No

# sent_id = 5
# text = We then take some steps towards a comparison between Batanin weak $ n $ - categories and Leinster weak $ n $ - categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	take	take	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	some	some	DET	DT	_	5	det	_	_
5	steps	step	NOUN	NNS	Number=Plur	3	dobj	_	_
6	towards	towards	ADP	IN	_	3	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	comparison	comparison	NOUN	NN	Number=Sing	6	pobj	_	_
9	between	between	ADP	IN	_	8	prep	_	_
10	Batanin	Batanin	PROPN	NNP	Number=Sing	9	pobj	_	_
11	weak	weak	ADJ	JJ	Degree=Pos	14	amod	_	_
12	$ n $	$ n $	SYM	$	_	14	nummod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	categories	category	NOUN	NNS	Number=Plur	10	appos	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	Leinster	leinster	NOUN	NN	Number=Sing	14	conj	_	_
17	weak	weak	ADJ	JJ	Degree=Pos	20	amod	_	_
18	$ n $	$ n $	SYM	$	_	20	nummod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = We describe a canonical adjunction between the categories of these, giving a construction of the left adjoint, which is applicable in more generality to a class of functors induced by monad morphisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	canonical	canonical	ADJ	JJ	Degree=Pos	5	amod	_	_
5	adjunction	adjunction	NOUN	NN	Number=Sing	2	dobj	_	_
6	between	between	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	these	these	PRON	DT	Number=Plur|PronType=Dem	9	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
12	giving	give	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	construction	construction	NOUN	NN	Number=Sing	12	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	left	left	ADJ	JJ	Degree=Pos	18	amod	_	_
18	adjoint	adjoint	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	which	which	PRON	WDT	_	21	nsubj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	relcl	_	_
22	applicable	applicable	ADJ	JJ	Degree=Pos	21	acomp	_	_
23	in	in	ADP	IN	_	22	prep	_	_
24	more	more	ADJ	JJR	Degree=Cmp	25	amod	_	_
25	generality	generality	NOUN	NN	Number=Sing	23	pobj	_	_
26	to	to	ADP	IN	_	21	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	class	class	NOUN	NN	Number=Sing	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	functors	functor	NOUN	NNS	Number=Plur	29	pobj	_	_
31	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	30	acl	_	_
32	by	by	ADP	IN	_	31	agent	_	_
33	monad	monad	NOUN	NNS	Number=Plur	34	compound	_	_
34	morphisms	morphism	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = We conclude with some preliminary statements about a possible weak equivalence of some sort between these categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	conclude	conclude	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	with	with	ADP	IN	_	2	prep	_	_
4	some	some	DET	DT	_	6	det	_	_
5	preliminary	preliminary	ADJ	JJ	Degree=Pos	6	amod	_	_
6	statements	statement	NOUN	NNS	Number=Plur	3	pobj	_	_
7	about	about	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	possible	possible	ADJ	JJ	Degree=Pos	11	amod	_	_
10	weak	weak	ADJ	JJ	Degree=Pos	11	amod	_	_
11	equivalence	equivalence	NOUN	NN	Number=Sing	7	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	some	some	DET	DT	_	14	det	_	_
14	sort	sort	NOUN	NN	Number=Sing	12	pobj	_	_
15	between	between	ADP	IN	_	14	prep	_	_
16	these	these	DET	DT	Number=Plur|PronType=Dem	17	det	_	_
17	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 554
# sent_id = 1
# text = We give several reformulations of action accessibility in the sense of Bourn and Janelidze.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	several	several	ADJ	JJ	Degree=Pos	4	amod	_	_
4	reformulations	reformulation	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	action	action	NOUN	NN	Number=Sing	7	compound	_	_
7	accessibility	accessibility	NOUN	NN	Number=Sing	5	pobj	_	_
8	in	in	ADP	IN	_	2	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	sense	sense	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	Bourn	Bourn	PROPN	NNP	Number=Sing	11	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	Janelidze	Janelidze	PROPN	NNP	Number=Sing	12	conj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In particular we prove that a pointed exact protomodular category is action accessible if and only if for each normal monomorphism $ kappa:Xto A $ the normalizer of $ < kappa, kappa>: Xto Atimes A $ exists.
1	In	in	ADP	IN	_	4	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	11	mark	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
7	pointed	pointed	ADJ	JJ	Degree=Pos	10	amod	_	_
8	exact	exact	ADJ	JJ	Degree=Pos	10	amod	_	_
9	protomodular	protomodular	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	11	nsubj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
12	action	action	NOUN	NN	Number=Sing	11	attr	_	_
13	accessible	accessible	ADJ	JJ	Degree=Pos	12	amod	_	_
14	if	if	SCONJ	IN	_	4	prep	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	only	only	ADV	RB	_	17	advmod	_	_
17	if	if	SCONJ	IN	_	14	conj	_	_
18	for	for	ADP	IN	_	17	prep	_	_
19	each	each	DET	DT	_	21	det	_	_
20	normal	normal	ADJ	JJ	Degree=Pos	21	amod	_	_
21	monomorphism	monomorphism	NOUN	NN	Number=Sing	18	pobj	_	_
22	$ kappa:Xto A $	$ kappa:xto a $	SYM	$	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	normalizer	normalizer	NOUN	NN	Number=Sing	21	appos	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	$ < kappa, kappa>: Xto Atimes A $	$ < kappa, kappa>: xto atimes a $	SYM	$	_	25	pobj	_	_
27	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = This clarifies the connection between normalizers and action accessible categories established in a joint paper of Bourn and the author, in which it is proved that for pointed exact protomodular categories the existence of normalizers implies action accessibility.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	clarifies	clarify	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	connection	connection	NOUN	NN	Number=Sing	2	dobj	_	_
5	between	between	ADP	IN	_	4	prep	_	_
6	normalizers	normalizer	NOUN	NNS	Number=Plur	5	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	action	action	NOUN	NN	Number=Sing	10	nmod	_	_
9	accessible	accessible	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	6	conj	_	_
11	established	establish	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	joint	joint	ADJ	JJ	Degree=Pos	15	amod	_	_
15	paper	paper	NOUN	NN	Number=Sing	12	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	Bourn	Bourn	PROPN	NNP	Number=Sing	16	pobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	author	author	NOUN	NN	Number=Sing	15	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	in	in	ADP	IN	_	26	prep	_	_
23	which	which	PRON	WDT	_	22	pobj	_	_
24	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	26	nsubjpass	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	auxpass	_	_
26	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	relcl	_	_
27	that	that	SCONJ	IN	_	37	mark	_	_
28	for	for	ADP	IN	_	37	prep	_	_
29	pointed	pointed	ADJ	JJ	Degree=Pos	32	amod	_	_
30	exact	exact	ADJ	JJ	Degree=Pos	32	amod	_	_
31	protomodular	protomodular	ADJ	JJ	Degree=Pos	32	amod	_	_
32	categories	category	NOUN	NNS	Number=Plur	28	pobj	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
34	existence	existence	NOUN	NN	Number=Sing	37	nsubj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	normalizers	normalizer	NOUN	NNS	Number=Plur	35	pobj	_	_
37	implies	imply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	ccomp	_	_
38	action	action	NOUN	NN	Number=Sing	39	compound	_	_
39	accessibility	accessibility	NOUN	NN	Number=Sing	37	dobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = In addition we prove a pointed exact protomodular category with coequalizers is action accessible if centralizers of normal monomorphisms exist, and the normality of unions holds.
1	In	in	ADP	IN	_	4	prep	_	_
2	addition	addition	NOUN	NN	Number=Sing	1	pobj	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	27	ccomp	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
6	pointed	pointed	ADJ	JJ	Degree=Pos	9	amod	_	_
7	exact	exact	ADJ	JJ	Degree=Pos	9	amod	_	_
8	protomodular	protomodular	ADJ	JJ	Degree=Pos	9	amod	_	_
9	category	category	NOUN	NN	Number=Sing	4	dobj	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	coequalizers	coequalizer	NOUN	NNS	Number=Plur	10	pobj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
13	action	action	NOUN	NN	Number=Sing	12	attr	_	_
14	accessible	accessible	ADJ	JJ	Degree=Pos	13	amod	_	_
15	if	if	SCONJ	IN	_	20	mark	_	_
16	centralizers	centralizer	NOUN	NNS	Number=Plur	20	nsubj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	normal	normal	ADJ	JJ	Degree=Pos	19	amod	_	_
19	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	17	pobj	_	_
20	exist	exist	VERB	VBP	Tense=Pres|VerbForm=Fin	12	advcl	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	normality	normality	NOUN	NN	Number=Sing	27	nsubj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	unions	union	NOUN	NNS	Number=Plur	25	pobj	_	_
27	holds	hold	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	27	punct	_	SpaceAfter=No

# doc_id = 555
# sent_id = 1
# text = It was argued by Crans that it is too much to ask that the category of Gray - categories admit a well behaved monoidal biclosed structure.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	3	auxpass	_	_
3	argued	argue	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	by	by	ADP	IN	_	3	agent	_	_
5	Crans	Crans	PROPN	NNPS	Number=Plur	4	pobj	_	_
6	that	that	SCONJ	IN	_	8	mark	_	_
7	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	8	nsubj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
9	too	too	ADV	RB	_	10	advmod	_	_
10	much	much	ADJ	JJ	Degree=Pos	8	acomp	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	ask	ask	VERB	VB	VerbForm=Inf	8	xcomp	_	_
13	that	that	SCONJ	IN	_	20	mark	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	category	category	NOUN	NN	Number=Sing	20	nsubj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	Gray	Gray	PROPN	NNP	Number=Sing	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	_
20	admit	admit	VERB	VBP	Tense=Pres|VerbForm=Fin	12	ccomp	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
22	well	well	ADV	RB	Degree=Pos	23	advmod	_	_
23	behaved	behave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
24	monoidal	monoidal	ADJ	JJ	Degree=Pos	25	amod	_	_
25	biclosed	biclose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
26	structure	structure	NOUN	NN	Number=Sing	20	dobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = We make this precise by establishing undesirable properties that any such monoidal biclosed structure must have.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	make	make	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	this	this	PRON	DT	Number=Sing|PronType=Dem	4	nsubj	_	_
4	precise	precise	ADJ	JJ	Degree=Pos	2	ccomp	_	_
5	by	by	ADP	IN	_	2	prep	_	_
6	establishing	establish	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	undesirable	undesirable	ADJ	JJ	Degree=Pos	8	amod	_	_
8	properties	property	NOUN	NNS	Number=Plur	6	dobj	_	_
9	that	that	SCONJ	IN	_	16	dobj	_	_
10	any	any	DET	DT	_	14	det	_	_
11	such	such	ADJ	JJ	Degree=Pos	14	amod	_	_
12	monoidal	monoidal	ADJ	JJ	Degree=Pos	14	amod	_	_
13	biclosed	biclose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
14	structure	structure	NOUN	NN	Number=Sing	16	nsubj	_	_
15	must	must	AUX	MD	VerbForm=Fin	16	aux	_	_
16	have	have	VERB	VB	VerbForm=Inf	8	relcl	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = In particular we show that there does not exist any tensor product making the model category of Gray - categories into a monoidal model category.
1	In	in	ADP	IN	_	4	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	9	mark	_	_
6	there	there	PRON	EX	_	9	expl	_	_
7	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	aux	_	_
8	not	not	PART	RB	Polarity=Neg	9	neg	_	_
9	exist	exist	VERB	VB	VerbForm=Inf	4	ccomp	_	_
10	any	any	DET	DT	_	12	det	_	_
11	tensor	tensor	NOUN	NN	Number=Sing	12	compound	_	_
12	product	product	NOUN	NN	Number=Sing	9	dobj	_	_
13	making	make	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	acl	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	model	model	NOUN	NN	Number=Sing	16	compound	_	_
16	category	category	NOUN	NN	Number=Sing	13	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	Gray	Gray	PROPN	NNP	Number=Sing	20	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	_
21	into	into	ADP	IN	_	13	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
23	monoidal	monoidal	ADJ	JJ	Degree=Pos	25	amod	_	_
24	model	model	NOUN	NN	Number=Sing	25	compound	_	_
25	category	category	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 556
# sent_id = 1
# text = Generalized operads, also called generalized multicategories and $ T $ - monoids, are defined as monads within a Kleisli bicategory.
1	Generalized	generalized	ADJ	JJ	Degree=Pos	2	amod	_	_
2	operads	operad	NOUN	NNS	Number=Plur	5	nsubj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
4	also	also	ADV	RB	_	5	advmod	_	_
5	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	14	advcl	_	_
6	generalized	generalized	ADJ	JJ	Degree=Pos	7	amod	_	_
7	multicategories	multicategorie	NOUN	NNS	Number=Plur	5	dobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	$ T $	$ t $	SYM	$	_	11	compound	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	monoids	monoid	NOUN	NNS	Number=Plur	7	conj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
15	as	as	ADP	IN	_	14	prep	_	_
16	monads	monad	NOUN	NNS	Number=Plur	15	pobj	_	_
17	within	within	ADP	IN	_	14	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	Kleisli	Kleisli	PROPN	NNP	Number=Sing	20	compound	_	_
20	bicategory	bicategory	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 2
# text = With or without emphasizing their monoidal nature, generalized operads have been considered by numerous authors in different contexts, with examples including symmetric multicategories, topological spaces, globular operads and Lawvere theories.
1	With	with	ADP	IN	_	13	prep	_	_
2	or	or	CCONJ	CC	ConjType=Cmp	1	cc	_	_
3	without	without	ADP	IN	_	1	conj	_	_
4	emphasizing	emphasize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	pcomp	_	_
5	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	7	poss	_	_
6	monoidal	monoidal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	nature	nature	NOUN	NN	Number=Sing	4	dobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
9	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	operads	operad	NOUN	NNS	Number=Plur	13	nsubjpass	_	_
11	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	aux	_	_
12	been	be	AUX	VBN	Tense=Past|VerbForm=Part	13	auxpass	_	_
13	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
14	by	by	ADP	IN	_	13	agent	_	_
15	numerous	numerous	ADJ	JJ	Degree=Pos	16	amod	_	_
16	authors	author	NOUN	NNS	Number=Plur	14	pobj	_	_
17	in	in	ADP	IN	_	13	prep	_	_
18	different	different	ADJ	JJ	Degree=Pos	19	amod	_	_
19	contexts	context	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
21	with	with	ADP	IN	_	13	prep	_	_
22	examples	example	NOUN	NNS	Number=Plur	21	pobj	_	_
23	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	prep	_	_
24	symmetric	symmetric	ADJ	JJ	Degree=Pos	25	amod	_	_
25	multicategories	multicategorie	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
27	topological	topological	ADJ	JJ	Degree=Pos	28	amod	_	_
28	spaces	space	NOUN	NNS	Number=Plur	25	conj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
30	globular	globular	ADJ	JJ	Degree=Pos	31	amod	_	_
31	operads	operad	NOUN	NNS	Number=Plur	28	conj	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	Lawvere	Lawvere	PROPN	NNP	Number=Sing	34	compound	_	_
34	theories	theory	NOUN	NNS	Number=Plur	31	conj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this paper we study functoriality of the Kleisli construction, and correspondingly that of generalized operads.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	functoriality	functoriality	NOUN	NN	Number=Sing	5	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	Kleisli	Kleisli	PROPN	NNP	Number=Sing	10	compound	_	_
10	construction	construction	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
13	correspondingly	correspondingly	ADV	RB	_	14	advmod	_	_
14	that	that	PRON	DT	Number=Sing|PronType=Dem	5	conj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	operads	operad	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = Motivated by this problem we develop a lax version of the formal theory of monads, and study its connection to bicategorical structures.
1	Motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	advcl	_	_
2	by	by	ADP	IN	_	1	agent	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	problem	problem	NOUN	NN	Number=Sing	2	pobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	lax	lax	ADJ	JJ	Degree=Pos	9	amod	_	_
9	version	version	NOUN	NN	Number=Sing	6	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	formal	formal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	theory	theory	NOUN	NN	Number=Sing	10	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	monads	monad	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
18	study	study	VERB	VB	VerbForm=Inf	6	conj	_	_
19	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	20	poss	_	_
20	connection	connection	NOUN	NN	Number=Sing	18	dobj	_	_
21	to	to	ADP	IN	_	18	prep	_	_
22	bicategorical	bicategorical	ADJ	JJ	Degree=Pos	23	amod	_	_
23	structures	structure	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 557
# sent_id = 1
# text = We study and, in a number of cases, classify completely the limit closures in the category of commutative rings of subcategories of integral domains.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
5	in	in	ADP	IN	_	11	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	number	number	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	cases	case	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
11	classify	classify	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
12	completely	completely	ADV	RB	_	11	advmod	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	limit	limit	NOUN	NN	Number=Sing	15	compound	_	_
15	closures	closure	NOUN	NNS	Number=Plur	11	dobj	_	_
16	in	in	ADP	IN	_	11	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	category	category	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	commutative	commutative	ADJ	JJ	Degree=Pos	21	amod	_	_
21	rings	ring	NOUN	NNS	Number=Plur	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	subcategories	subcategorie	NOUN	NNS	Number=Plur	22	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	integral	integral	ADJ	JJ	Degree=Pos	26	amod	_	_
26	domains	domain	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# doc_id = 558
# sent_id = 1
# text = The study of sup lattices teaches us the important distinction between the algebraic part of the structure (in this case suprema) and the coincidental part of the structure (in this case infima).
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	study	study	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	sup	sup	NOUN	NN	Number=Sing	5	compound	_	_
5	lattices	lattice	NOUN	NNS	Number=Plur	3	pobj	_	_
6	teaches	teach	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	6	dative	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	important	important	ADJ	JJ	Degree=Pos	10	amod	_	_
10	distinction	distinction	NOUN	NN	Number=Sing	6	dobj	_	_
11	between	between	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	algebraic	algebraic	ADJ	JJ	Degree=Pos	14	amod	_	_
14	part	part	NOUN	NN	Number=Sing	11	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	structure	structure	NOUN	NN	Number=Sing	15	pobj	_	_
18	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	10	punct	_	SpaceAfter=No
19	in	in	ADP	IN	_	22	prep	_	_
20	this	this	DET	DT	Number=Sing|PronType=Dem	21	det	_	_
21	case	case	NOUN	NN	Number=Sing	19	pobj	_	_
22	suprema	suprema	ADV	RB	_	10	appos	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	10	punct	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	coincidental	coincidental	ADJ	JJ	Degree=Pos	27	amod	_	_
27	part	part	NOUN	NN	Number=Sing	10	conj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	structure	structure	NOUN	NN	Number=Sing	28	pobj	_	_
31	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	27	punct	_	SpaceAfter=No
32	in	in	ADP	IN	_	35	prep	_	_
33	this	this	DET	DT	Number=Sing|PronType=Dem	34	det	_	_
34	case	case	NOUN	NN	Number=Sing	32	pobj	_	_
35	infima	infima	PROPN	NNP	Number=Sing	27	appos	_	SpaceAfter=No
36	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	27	punct	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = While a sup lattice happens to have all infima, only the suprema are part of the algebraic structure.
1	While	while	SCONJ	IN	_	5	mark	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	sup	sup	NOUN	NN	Number=Sing	4	compound	_	_
4	lattice	lattice	NOUN	NN	Number=Sing	5	nsubj	_	_
5	happens	happen	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	advcl	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	have	have	VERB	VB	VerbForm=Inf	5	xcomp	_	_
8	all	all	DET	DT	_	9	det	_	_
9	infima	infima	PROPN	NNP	Number=Sing	7	dobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
11	only	only	ADV	RB	_	13	advmod	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	suprema	suprema	PROPN	NNP	Number=Sing	14	nsubj	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	part	part	NOUN	NN	Number=Sing	14	attr	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	algebraic	algebraic	ADJ	JJ	Degree=Pos	19	amod	_	_
19	structure	structure	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 3
# text = Extending this idea, we look at posets that happen to have all suprema (and therefore all infima), but we will only declare some of them to be part of the algebraic structure (which we will call joins).
1	Extending	extend	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	advcl	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	idea	idea	NOUN	NN	Number=Sing	1	dobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	look	look	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	at	at	ADP	IN	_	6	prep	_	_
8	posets	poset	NOUN	NNS	Number=Plur	7	pobj	_	_
9	that	that	PRON	WDT	PronType=Rel	10	nsubj	_	_
10	happen	happen	VERB	VBP	Tense=Pres|VerbForm=Fin	8	relcl	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	have	have	VERB	VB	VerbForm=Inf	10	xcomp	_	_
13	all	all	DET	DT	_	14	det	_	_
14	suprema	suprema	PROPN	NNP	Number=Sing	12	dobj	_	_
15	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
16	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
17	therefore	therefore	ADV	RB	_	19	advmod	_	_
18	all	all	DET	DT	_	19	det	_	_
19	infima	infima	PROPN	NNP	Number=Sing	14	conj	_	SpaceAfter=No
20	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	14	punct	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
22	but	but	CCONJ	CC	ConjType=Cmp	6	cc	_	_
23	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	26	nsubj	_	_
24	will	will	AUX	MD	VerbForm=Fin	26	aux	_	_
25	only	only	ADV	RB	_	26	advmod	_	_
26	declare	declare	VERB	VB	VerbForm=Inf	6	conj	_	_
27	some	some	PRON	DT	_	31	nsubj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	28	pobj	_	_
30	to	to	PART	TO	_	31	aux	_	_
31	be	be	AUX	VB	VerbForm=Inf	26	ccomp	_	_
32	part	part	NOUN	NN	Number=Sing	31	attr	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
35	algebraic	algebraic	ADJ	JJ	Degree=Pos	36	amod	_	_
36	structure	structure	NOUN	NN	Number=Sing	33	pobj	_	_
37	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	36	punct	_	SpaceAfter=No
38	which	which	PRON	WDT	_	41	dobj	_	_
39	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	41	nsubj	_	_
40	will	will	AUX	MD	VerbForm=Fin	41	aux	_	_
41	call	call	VERB	VB	VerbForm=Inf	36	relcl	_	_
42	joins	join	NOUN	NNS	Number=Plur	41	oprd	_	SpaceAfter=No
43	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	26	punct	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	26	punct	_	SpaceAfter=No

# sent_id = 4
# text = We find that a lot of the theory of complete distributivity for sup lattices can be extended to this context.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	find	find	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	17	mark	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	lot	lot	NOUN	NN	Number=Sing	17	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	theory	theory	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	complete	complete	ADJ	JJ	Degree=Pos	11	amod	_	_
11	distributivity	distributivity	NOUN	NN	Number=Sing	9	pobj	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	sup	sup	NOUN	NN	Number=Sing	14	compound	_	_
14	lattices	lattice	NOUN	NNS	Number=Plur	12	pobj	_	_
15	can	can	AUX	MD	VerbForm=Fin	17	aux	_	_
16	be	be	AUX	VB	VerbForm=Inf	17	auxpass	_	_
17	extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	this	this	DET	DT	Number=Sing|PronType=Dem	20	det	_	_
20	context	context	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = There are a lot of natural examples of completely join - distributive partial lattice complete partial orders, including for example, the lattice of all equivalence relations on a set $ X $ , and the lattice of all subgroups of a group $ G $ .
1	There	there	PRON	EX	_	2	expl	_	_
2	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	lot	lot	NOUN	NN	Number=Sing	2	attr	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	natural	natural	ADJ	JJ	Degree=Pos	7	amod	_	_
7	examples	example	NOUN	NNS	Number=Plur	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	completely	completely	ADV	RB	_	12	advmod	_	_
10	join	join	VERB	VB	VerbForm=Inf	12	amod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	distributive	distributive	ADJ	JJ	Degree=Pos	14	amod	_	_
13	partial	partial	ADJ	JJ	Degree=Pos	14	amod	_	_
14	lattice	lattice	NOUN	NN	Number=Sing	8	pobj	_	_
15	complete	complete	ADJ	JJ	Degree=Pos	17	amod	_	_
16	partial	partial	ADJ	JJ	Degree=Pos	17	amod	_	_
17	orders	order	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	prep	_	_
20	for	for	ADP	IN	_	19	prep	_	_
21	example	example	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	lattice	lattice	NOUN	NN	Number=Sing	4	appos	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	all	all	DET	DT	_	28	det	_	_
27	equivalence	equivalence	NOUN	NN	Number=Sing	28	compound	_	_
28	relations	relation	NOUN	NNS	Number=Plur	25	pobj	_	_
29	on	on	ADP	IN	_	28	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
31	set	set	NOUN	NN	Number=Sing	32	amod	_	_
32	$ X $	$ x $	SYM	$	_	29	pobj	_	_
33	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
34	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	lattice	lattice	NOUN	NN	Number=Sing	24	conj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	all	all	DET	DT	_	39	det	_	_
39	subgroups	subgroup	NOUN	NNS	Number=Plur	37	pobj	_	_
40	of	of	ADP	IN	_	39	prep	_	_
41	a	a	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
42	group	group	NOUN	NN	Number=Sing	40	pobj	_	_
43	$ G $	$ g $	SYM	$	_	2	attr	_	_
44	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = In both cases we define the join operation as union.
1	In	in	ADP	IN	_	5	prep	_	_
2	both	both	DET	DT	_	3	det	_	_
3	cases	case	NOUN	NNS	Number=Plur	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	join	join	NOUN	NN	Number=Sing	8	compound	_	_
8	operation	operation	NOUN	NN	Number=Sing	5	dobj	_	_
9	as	as	ADP	IN	_	5	prep	_	_
10	union	union	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 7
# text = This is a partial operation, because for example, the union of subgroups of a group is not necessarily a subgroup.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	partial	partial	ADJ	JJ	Degree=Pos	5	amod	_	_
5	operation	operation	NOUN	NN	Number=Sing	2	attr	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
7	because	because	SCONJ	IN	_	18	mark	_	_
8	for	for	ADP	IN	_	18	prep	_	_
9	example	example	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	union	union	NOUN	NN	Number=Sing	18	nsubj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	subgroups	subgroup	NOUN	NNS	Number=Plur	13	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	group	group	NOUN	NN	Number=Sing	15	pobj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	advcl	_	_
19	not	not	PART	RB	Polarity=Neg	18	neg	_	_
20	necessarily	necessarily	ADV	RB	_	18	advmod	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	subgroup	subgroup	NOUN	NN	Number=Sing	18	attr	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 8
# text = However, sometimes it is, and keeping track of this can help with topics such as the inclusion - exclusion principle.
1	However	however	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	sometimes	sometimes	ADV	RB	_	5	advmod	_	_
4	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
8	keeping	keep	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	csubj	_	_
9	track	track	NOUN	NN	Number=Sing	8	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	this	this	PRON	DT	Number=Sing|PronType=Dem	10	pobj	_	_
12	can	can	AUX	MD	VerbForm=Fin	13	aux	_	_
13	help	help	VERB	VB	VerbForm=Inf	5	conj	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	topics	topic	NOUN	NNS	Number=Plur	14	pobj	_	_
16	such	such	ADJ	JJ	Degree=Pos	17	amod	_	_
17	as	as	ADP	IN	_	15	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
19	inclusion	inclusion	NOUN	NN	Number=Sing	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	exclusion	exclusion	NOUN	NN	Number=Sing	22	compound	_	_
22	principle	principle	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 9
# text = Another motivation for the study of sup lattices is as a simplified model for the study of presheaf categories.
1	Another	another	DET	DT	_	2	det	_	_
2	motivation	motivation	NOUN	NN	Number=Sing	9	nsubj	_	_
3	for	for	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	study	study	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	sup	sup	NOUN	NN	Number=Sing	8	compound	_	_
8	lattices	lattice	NOUN	NNS	Number=Plur	6	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	as	as	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	simplified	simplified	ADJ	JJ	Degree=Pos	13	amod	_	_
13	model	model	NOUN	NN	Number=Sing	10	pobj	_	_
14	for	for	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	study	study	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	presheaf	presheaf	ADJ	JJ	Degree=Pos	19	amod	_	_
19	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 10
# text = The construction of downsets is a form of the Yoneda embedding, and the study of downset lattices can be a useful guide for the study of presheaf categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	construction	construction	NOUN	NN	Number=Sing	5	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	downsets	downset	NOUN	NNS	Number=Plur	3	pobj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	form	form	NOUN	NN	Number=Sing	5	attr	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	Yoneda	Yoneda	PROPN	NNP	Number=Sing	11	compound	_	_
11	embedding	embed	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	study	study	NOUN	NN	Number=Sing	20	nsubj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	downset	downset	NOUN	NN	Number=Sing	18	compound	_	_
18	lattices	lattice	NOUN	NNS	Number=Plur	16	pobj	_	_
19	can	can	AUX	MD	VerbForm=Fin	20	aux	_	_
20	be	be	AUX	VB	VerbForm=Inf	5	conj	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	useful	useful	ADJ	JJ	Degree=Pos	23	amod	_	_
23	guide	guide	NOUN	NN	Number=Sing	20	attr	_	_
24	for	for	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	study	study	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	presheaf	presheaf	ADJ	JJ	Degree=Pos	29	amod	_	_
29	categories	category	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 11
# text = In this context, partial lattices can be viewed as a simplified model for the study of sheaf categories.
1	In	in	ADP	IN	_	9	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	context	context	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
5	partial	partial	ADJ	JJ	Degree=Pos	6	amod	_	_
6	lattices	lattice	NOUN	NNS	Number=Plur	9	nsubjpass	_	_
7	can	can	AUX	MD	VerbForm=Fin	9	aux	_	_
8	be	be	AUX	VB	VerbForm=Inf	9	auxpass	_	_
9	viewed	view	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	as	as	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	simplified	simplified	ADJ	JJ	Degree=Pos	13	amod	_	_
13	model	model	NOUN	NN	Number=Sing	10	pobj	_	_
14	for	for	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	study	study	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	sheaf	sheaf	NOUN	NN	Number=Sing	19	compound	_	_
19	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 559
# sent_id = 1
# text = The homotopy theory of higher categorical structures has become a relevant part of the machinery of algebraic topology and algebraic $ K $ - theory, and this paper contains contributions to the study of the relationship between Benabou's bicategories and the homotopy types of their classifying spaces.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	homotopy	homotopy	NOUN	NN	Number=Sing	3	compound	_	_
3	theory	theory	NOUN	NN	Number=Sing	9	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	higher	high	ADJ	JJR	Degree=Cmp	7	amod	_	_
6	categorical	categorical	ADJ	JJ	Degree=Pos	7	amod	_	_
7	structures	structure	NOUN	NNS	Number=Plur	4	pobj	_	_
8	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	aux	_	_
9	become	become	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	relevant	relevant	ADJ	JJ	Degree=Pos	12	amod	_	_
12	part	part	NOUN	NN	Number=Sing	9	attr	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	machinery	machinery	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	algebraic	algebraic	ADJ	JJ	Degree=Pos	18	amod	_	_
18	topology	topology	NOUN	NN	Number=Sing	16	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
20	algebraic	algebraic	ADJ	JJ	Degree=Pos	23	amod	_	_
21	$ K $	$ k $	SYM	$	_	23	nmod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	theory	theory	NOUN	NN	Number=Sing	15	conj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
26	this	this	DET	DT	Number=Sing|PronType=Dem	27	det	_	_
27	paper	paper	NOUN	NN	Number=Sing	28	nsubj	_	_
28	contains	contain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	conj	_	_
29	contributions	contribution	NOUN	NNS	Number=Plur	28	dobj	_	_
30	to	to	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	study	study	NOUN	NN	Number=Sing	30	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	relationship	relationship	NOUN	NN	Number=Sing	33	pobj	_	_
36	between	between	ADP	IN	_	35	prep	_	_
37	Benabou	Benabou	PROPN	NNP	Number=Sing	39	poss	_	SpaceAfter=No
38	's	's	PART	POS	_	37	case	_	_
39	bicategories	bicategorie	NOUN	NNS	Number=Plur	36	pobj	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	39	cc	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
42	homotopy	homotopy	NOUN	NN	Number=Sing	43	compound	_	_
43	types	type	NOUN	NNS	Number=Plur	39	conj	_	_
44	of	of	ADP	IN	_	43	prep	_	_
45	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	47	poss	_	_
46	classifying	classify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	47	amod	_	_
47	spaces	space	NOUN	NNS	Number=Plur	44	pobj	_	SpaceAfter=No
48	.	.	PUNCT	.	PunctType=Peri	28	punct	_	SpaceAfter=No

# sent_id = 2
# text = Mainly, we state and prove an extension of Quillen's Theorem B by showing, under reasonable necessary conditions, a bicategory - theoretical interpretation of the homotopy - fibre product of the continuous maps induced on classifying spaces by a diagram of bicategories $ Ato B leftarrow A' $ .
1	Mainly	mainly	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	state	state	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	prove	prove	VERB	VB	VerbForm=Inf	4	conj	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	extension	extension	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Quillen	Quillen	PROPN	NNP	Number=Sing	13	poss	_	SpaceAfter=No
11	's	's	PART	POS	_	10	case	_	_
12	Theorem	Theorem	PROPN	NNP	Number=Sing	13	compound	_	_
13	B	B	PROPN	NNP	Number=Sing	9	pobj	_	_
14	by	by	ADP	IN	_	6	prep	_	_
15	showing	show	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	pcomp	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
17	under	under	ADP	IN	_	6	prep	_	_
18	reasonable	reasonable	ADJ	JJ	Degree=Pos	20	amod	_	_
19	necessary	necessary	ADJ	JJ	Degree=Pos	20	amod	_	_
20	conditions	condition	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
23	bicategory	bicategory	ADJ	JJ	Degree=Pos	25	amod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	theoretical	theoretical	ADJ	JJ	Degree=Pos	26	amod	_	_
26	interpretation	interpretation	NOUN	NN	Number=Sing	4	dobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
29	homotopy	homotopy	NOUN	NN	Number=Sing	31	compound	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	fibre	fibre	NOUN	NN	Number=Sing	32	compound	_	_
32	product	product	NOUN	NN	Number=Sing	27	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
35	continuous	continuous	ADJ	JJ	Degree=Pos	36	amod	_	_
36	maps	map	NOUN	NNS	Number=Plur	33	pobj	_	_
37	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	36	acl	_	_
38	on	on	ADP	IN	_	37	prep	_	_
39	classifying	classify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	38	pcomp	_	_
40	spaces	space	NOUN	NNS	Number=Plur	39	dobj	_	_
41	by	by	ADP	IN	_	39	prep	_	_
42	a	a	DET	DT	Definite=Ind|PronType=Art	43	det	_	_
43	diagram	diagram	NOUN	NN	Number=Sing	41	pobj	_	_
44	of	of	ADP	IN	_	43	prep	_	_
45	bicategories	bicategorie	NOUN	NNS	Number=Plur	44	pobj	_	_
46	$ Ato B leftarrow A' $	$ ato b leftarrow a' $	SYM	$	_	38	pobj	_	_
47	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = Applications are given for the study of homotopy pullbacks of monoidal categories and of crossed modules.
1	Applications	application	NOUN	NNS	Number=Plur	3	nsubjpass	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	for	for	ADP	IN	_	3	dative	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	study	study	NOUN	NN	Number=Sing	4	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	homotopy	homotopy	NOUN	NN	Number=Sing	9	compound	_	_
9	pullbacks	pullback	NOUN	NNS	Number=Plur	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	monoidal	monoidal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
14	of	of	ADP	IN	_	10	conj	_	_
15	crossed	crossed	ADJ	JJ	Degree=Pos	16	amod	_	_
16	modules	module	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 560
# sent_id = 1
# text = We extend to semi - abelian categories the notion of characteristic subobject, which is widely used in group theory and in the theory of Lie algebras.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	extend	extend	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	semi	semi	ADJ	JJ	Degree=Pos	7	amod	_	_
5	-	-	ADJ	JJ	Degree=Pos	7	amod	_	_
6	abelian	abelian	ADJ	JJ	Degree=Pos	7	amod	_	_
7	categories	category	NOUN	NNS	Number=Plur	3	pobj	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	characteristic	characteristic	ADJ	JJ	Degree=Pos	12	amod	_	_
12	subobject	subobject	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	which	which	PRON	WDT	_	17	nsubjpass	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	auxpass	_	_
16	widely	widely	ADV	RB	_	17	advmod	_	_
17	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	relcl	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	group	group	NOUN	NN	Number=Sing	20	compound	_	_
20	theory	theory	NOUN	NN	Number=Sing	18	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
22	in	in	ADP	IN	_	9	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	theory	theory	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	Lie	Lie	PROPN	NNP	Number=Sing	27	compound	_	_
27	algebras	algebra	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Moreover, we show that many of the classical properties of characteristic subgroups of a group hold in the general semi - abelian context, or in stronger ones.
1	Moreover	moreover	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	6	mark	_	_
6	many	many	ADJ	JJ	Degree=Pos	4	ccomp	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	classical	classical	ADJ	JJ	Degree=Pos	10	amod	_	_
10	properties	property	NOUN	NNS	Number=Plur	7	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	characteristic	characteristic	ADJ	JJ	Degree=Pos	13	amod	_	_
13	subgroups	subgroup	NOUN	NNS	Number=Plur	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	group	group	NOUN	NN	Number=Sing	17	compound	_	_
17	hold	hold	NOUN	NN	Number=Sing	14	pobj	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
20	general	general	ADJ	JJ	Degree=Pos	24	amod	_	_
21	semi	semi	ADJ	JJ	Degree=Pos	24	amod	_	_
22	-	-	ADJ	JJ	Degree=Pos	24	amod	_	_
23	abelian	abelian	ADJ	JJ	Degree=Pos	24	amod	_	_
24	context	context	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
26	or	or	CCONJ	CC	ConjType=Cmp	6	cc	_	_
27	in	in	ADP	IN	_	6	prep	_	_
28	stronger	strong	ADJ	JJR	Degree=Cmp	29	amod	_	_
29	ones	one	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 561
# sent_id = 1
# text = We study Kan extensions in three weakenings of the Eilenberg - Moore double category associated to a double monad, that was introduced by Grandis and Paré.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	Kan	Kan	PROPN	NNP	Number=Sing	4	compound	_	_
4	extensions	extension	NOUN	NNS	Number=Plur	2	dobj	_	_
5	in	in	ADP	IN	_	2	prep	_	_
6	three	three	NUM	CD	NumType=Card	7	nummod	_	_
7	weakenings	weakening	NOUN	NNS	Number=Plur	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
10	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	12	compound	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	Moore	Moore	PROPN	NNP	Number=Sing	14	nmod	_	_
13	double	double	ADJ	JJ	Degree=Pos	14	amod	_	_
14	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
15	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	acl	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	double	double	ADJ	JJ	Degree=Pos	19	amod	_	_
19	monad	monad	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
21	that	that	PRON	WDT	PronType=Rel	23	nsubjpass	_	_
22	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	23	auxpass	_	_
23	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	relcl	_	_
24	by	by	ADP	IN	_	23	agent	_	_
25	Grandis	Grandis	PROPN	NNP	Number=Sing	24	pobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	Paré	Paré	PROPN	NNP	Number=Sing	25	conj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = To be precise, given a normal oplax double monad $ T $ on a double category $ K $ , we consider the double categories consisting of pseudo $ T $ - algebras, `weak' vertical $ T $ - morphisms, horizontal $ T $ - morphisms and $ T $ - cells, where `weak' means either `lax', `colax' or `pseudo'.
1	To	to	PART	TO	_	2	aux	_	_
2	be	be	AUX	VB	VerbForm=Inf	19	advcl	_	_
3	precise	precise	ADJ	JJ	Degree=Pos	2	acomp	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
5	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	normal	normal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	oplax	oplax	NOUN	NN	Number=Sing	10	nmod	_	_
9	double	double	PROPN	NNP	Number=Sing	10	amod	_	_
10	monad	monad	NOUN	NNS	Number=Plur	5	pobj	_	_
11	$ T $	$ t $	SYM	$	_	5	pcomp	_	_
12	on	on	ADP	IN	_	5	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	double	double	ADJ	JJ	Degree=Pos	15	amod	_	_
15	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
16	$ K $	$ k $	SYM	$	_	5	pcomp	_	_
17	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	double	double	ADJ	JJ	Degree=Pos	22	amod	_	_
22	categories	category	NOUN	NNS	Number=Plur	23	nsubj	_	_
23	consisting	consist	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	ccomp	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	pseudo	pseudo	NOUN	NN	Number=Sing	24	pobj	_	_
26	$ T $	$ t $	SYM	$	_	28	compound	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	algebras	algebra	NOUN	NNS	Number=Plur	23	dobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
30	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	28	punct	_	SpaceAfter=No
31	weak	weak	ADJ	JJ	Degree=Pos	36	amod	_	SpaceAfter=No
32	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	36	punct	_	_
33	vertical	vertical	ADJ	JJ	Degree=Pos	36	amod	_	_
34	$ T $	$ t $	SYM	$	_	36	nmod	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	36	punct	_	_
36	morphisms	morphism	NOUN	NNS	Number=Plur	28	appos	_	SpaceAfter=No
37	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
38	horizontal	horizontal	ADJ	JJ	Degree=Pos	41	amod	_	_
39	$ T $	$ t $	SYM	$	_	41	nmod	_	_
40	-	-	PUNCT	HYPH	PunctType=Dash	41	punct	_	_
41	morphisms	morphism	NOUN	NNS	Number=Plur	36	conj	_	_
42	and	and	CCONJ	CC	ConjType=Cmp	41	cc	_	_
43	$ T $	$ t $	SYM	$	_	45	compound	_	_
44	-	-	PUNCT	HYPH	PunctType=Dash	45	punct	_	_
45	cells	cell	NOUN	NNS	Number=Plur	41	conj	_	SpaceAfter=No
46	,	,	PUNCT	,	PunctType=Comm	45	punct	_	_
47	where	where	SCONJ	WRB	_	51	advmod	_	_
48	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	51	punct	_	SpaceAfter=No
49	weak	weak	ADJ	JJ	Degree=Pos	51	nsubj	_	SpaceAfter=No
50	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	51	punct	_	_
51	means	mean	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	28	relcl	_	_
52	either	either	CCONJ	CC	ConjType=Cmp	54	preconj	_	_
53	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	54	punct	_	SpaceAfter=No
54	lax	lax	PROPN	NNP	Number=Sing	51	dobj	_	SpaceAfter=No
55	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	51	punct	_	SpaceAfter=No
56	,	,	PUNCT	,	PunctType=Comm	51	punct	_	_
57	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	58	punct	_	SpaceAfter=No
58	colax	colax	PROPN	NNP	Number=Sing	51	dep	_	SpaceAfter=No
59	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	58	punct	_	_
60	or	or	CCONJ	CC	ConjType=Cmp	58	cc	_	_
61	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	62	punct	_	SpaceAfter=No
62	pseudo	pseudo	NOUN	NN	Number=Sing	58	conj	_	SpaceAfter=No
63	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	19	punct	_	SpaceAfter=No
64	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 3
# text = Denoting these double categories by $ Alg_w(T) $ , where $ w = l $ , $ c $ or $ ps $ accordingly, our main result gives, in each of these cases, conditions ensuring that (pointwise) Kan extensions can be lifted along the forgetful double functor $ Alg_w(T) - - > K $ .
1	Denoting	denote	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	0	ROOT	_	_
2	these	these	DET	DT	Number=Plur|PronType=Dem	4	det	_	_
3	double	double	ADJ	JJ	Degree=Pos	4	amod	_	_
4	categories	category	NOUN	NNS	Number=Plur	1	dobj	_	_
5	by	by	ADP	IN	_	1	prep	_	_
6	$ Alg_w(T) $	$ alg_w(t) $	SYM	$	_	5	pobj	_	_
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	where	where	SCONJ	WRB	_	9	advmod	_	_
9	$ w = l $	$ w = l $	SYM	$	_	6	relcl	_	_
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	$ c $	$ c $	SYM	$	_	9	appos	_	_
12	or	or	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	$ ps $	$ ps $	SYM	$	_	11	conj	_	_
14	accordingly	accordingly	ADV	RB	_	9	advmod	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
16	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	18	poss	_	_
17	main	main	ADJ	JJ	Degree=Pos	18	amod	_	_
18	result	result	NOUN	NN	Number=Sing	19	nsubj	_	_
19	gives	gives	AUX	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	1	aux	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	in	in	ADP	IN	_	19	prep	_	_
22	each	each	PRON	DT	_	21	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	these	these	DET	DT	Number=Plur|PronType=Dem	25	det	_	_
25	cases	case	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
27	conditions	condition	NOUN	NNS	Number=Plur	1	dobj	_	_
28	ensuring	ensure	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	27	acl	_	_
29	that	that	SCONJ	IN	_	37	mark	_	_
30	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	31	punct	_	SpaceAfter=No
31	pointwise	pointwise	NOUN	NN	Number=Sing	34	nmod	_	SpaceAfter=No
32	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	34	punct	_	_
33	Kan	Kan	PROPN	NNP	Number=Sing	34	compound	_	_
34	extensions	extension	NOUN	NNS	Number=Plur	37	nsubjpass	_	_
35	can	can	AUX	MD	VerbForm=Fin	37	aux	_	_
36	be	be	AUX	VB	VerbForm=Inf	37	auxpass	_	_
37	lifted	lift	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	ccomp	_	_
38	along	along	ADP	IN	_	37	prep	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	42	det	_	_
40	forgetful	forgetful	ADJ	JJ	Degree=Pos	42	amod	_	_
41	double	double	ADJ	JJ	Degree=Pos	42	amod	_	_
42	functor	functor	NOUN	NN	Number=Sing	38	pobj	_	_
43	$ Alg_w(T) - - > K $	$ alg_w(t) - - > k $	SYM	$	_	1	dep	_	_
44	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 4
# text = As an application we recover and generalise a result by Getzler, on the lifting of pointwise left Kan extensions along symmetric monoidal enriched functors.
1	As	as	SCONJ	IN	_	18	mark	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	18	nsubj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	recover	recover	VERB	VBP	Tense=Pres|VerbForm=Fin	3	relcl	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	generalise	generalise	VERB	VB	VerbForm=Inf	5	conj	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	result	result	NOUN	NN	Number=Sing	7	dobj	_	_
10	by	by	ADP	IN	_	7	prep	_	_
11	Getzler	Getzler	PROPN	NNP	Number=Sing	10	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
13	on	on	ADP	IN	_	7	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	lifting	lifting	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	pointwise	pointwise	NOUN	NN	Number=Sing	16	pobj	_	_
18	left	leave	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
19	Kan	Kan	PROPN	NNP	Number=Sing	20	compound	_	_
20	extensions	extension	NOUN	NNS	Number=Plur	18	dobj	_	_
21	along	along	ADP	IN	_	20	prep	_	_
22	symmetric	symmetric	ADJ	JJ	Degree=Pos	25	amod	_	_
23	monoidal	monoidal	ADJ	JJ	Degree=Pos	25	amod	_	_
24	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	amod	_	_
25	functors	functor	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# sent_id = 5
# text = As an application of Getzler's result we prove, in suitable symmetric monoidal categories, the existence of bicommutative Hopf monoids that are freely generated by cocommutative comonoids.
1	As	as	ADP	IN	_	9	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	Getzler	Getzler	PROPN	NNP	Number=Sing	7	poss	_	SpaceAfter=No
6	's	's	PART	POS	_	5	case	_	_
7	result	result	NOUN	NN	Number=Sing	4	pobj	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	18	advcl	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	in	in	ADP	IN	_	9	prep	_	_
12	suitable	suitable	ADJ	JJ	Degree=Pos	15	amod	_	_
13	symmetric	symmetric	ADJ	JJ	Degree=Pos	15	amod	_	_
14	monoidal	monoidal	ADJ	JJ	Degree=Pos	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	existence	existence	NOUN	NN	Number=Sing	0	ROOT	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	bicommutative	bicommutative	ADJ	JJ	Degree=Pos	22	amod	_	_
21	Hopf	hopf	NOUN	NN	Number=Sing	22	compound	_	_
22	monoids	monoid	NOUN	NNS	Number=Plur	19	pobj	_	_
23	that	that	PRON	WDT	PronType=Rel	26	nsubjpass	_	_
24	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	26	auxpass	_	_
25	freely	freely	ADV	RB	_	26	advmod	_	_
26	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	relcl	_	_
27	by	by	ADP	IN	_	26	agent	_	_
28	cocommutative	cocommutative	ADJ	JJ	Degree=Pos	29	amod	_	_
29	comonoids	comonoid	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# doc_id = 562
# sent_id = 1
# text = We generalize Quillen's Theorem A to triangles of lax 2 - functors which commute up to transformation.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	Quillen	Quillen	PROPN	NNP	Number=Sing	6	poss	_	SpaceAfter=No
4	's	's	PART	POS	_	3	case	_	_
5	Theorem	Theorem	PROPN	NNP	Number=Sing	6	compound	_	_
6	A	A	PROPN	NNP	Number=Sing	2	dobj	_	_
7	to	to	ADP	IN	_	2	prep	_	_
8	triangles	triangle	NOUN	NNS	Number=Plur	7	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	lax	lax	ADJ	JJ	Degree=Pos	13	amod	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	functors	functor	NOUN	NNS	Number=Plur	9	pobj	_	_
14	which	which	PRON	WDT	_	15	nsubj	_	_
15	commute	commute	VERB	VBP	Tense=Pres|VerbForm=Fin	13	relcl	_	_
16	up	up	ADP	RP	_	15	prt	_	_
17	to	to	ADP	IN	_	15	prep	_	_
18	transformation	transformation	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = It follows from a special case of this result that 2 - categories are models for homotopy types.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	follows	follow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	from	from	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	special	special	ADJ	JJ	Degree=Pos	6	amod	_	_
6	case	case	NOUN	NN	Number=Sing	3	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	this	this	DET	DT	Number=Sing|PronType=Dem	9	det	_	_
9	result	result	NOUN	NN	Number=Sing	7	pobj	_	_
10	that	that	SCONJ	IN	_	14	mark	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	categories	category	NOUN	NNS	Number=Plur	14	nsubj	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
15	models	model	NOUN	NNS	Number=Plur	14	attr	_	_
16	for	for	ADP	IN	_	15	prep	_	_
17	homotopy	homotopy	NOUN	NN	Number=Sing	18	compound	_	_
18	types	type	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 563
# sent_id = 1
# text = We show that the homotopy colimit construction for diagrams of categories with an operad action, recently introduced by Fiedorowicz, Stelzer and Vogt, has the desired homotopy type for diagrams of weak braided monoidal categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	26	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	homotopy	homotopy	NOUN	NN	Number=Sing	6	compound	_	_
6	colimit	colimit	NOUN	NN	Number=Sing	7	compound	_	_
7	construction	construction	NOUN	NN	Number=Sing	26	nsubj	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	diagrams	diagram	NOUN	NNS	Number=Plur	8	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
12	with	with	ADP	IN	_	7	prep	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	operad	operad	ADJ	JJ	Degree=Pos	15	amod	_	_
15	action	action	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
17	recently	recently	ADV	RB	_	18	advmod	_	_
18	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	acl	_	_
19	by	by	ADP	IN	_	18	agent	_	_
20	Fiedorowicz	Fiedorowicz	PROPN	NNP	Number=Sing	19	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	Stelzer	Stelzer	PROPN	NNP	Number=Sing	20	conj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	Vogt	Vogt	PROPN	NNP	Number=Sing	22	conj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
26	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
28	desired	desire	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	30	amod	_	_
29	homotopy	homotopy	NOUN	NN	Number=Sing	30	compound	_	_
30	type	type	NOUN	NN	Number=Sing	26	dobj	_	_
31	for	for	ADP	IN	_	30	prep	_	_
32	diagrams	diagram	NOUN	NNS	Number=Plur	31	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	weak	weak	ADJ	JJ	Degree=Pos	37	amod	_	_
35	braided	braid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	37	amod	_	_
36	monoidal	monoidal	ADJ	JJ	Degree=Pos	37	amod	_	_
37	categories	category	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This provides a more flexible way to realize $ E_2 $ spaces categorically.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
4	more	more	ADV	RBR	Degree=Cmp	5	advmod	_	_
5	flexible	flexible	ADJ	JJ	Degree=Pos	6	amod	_	_
6	way	way	NOUN	NN	Number=Sing	2	dobj	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	realize	realize	VERB	VB	VerbForm=Inf	6	relcl	_	_
9	$ E_2 $	$ e_2 $	SYM	$	_	10	nummod	_	_
10	spaces	space	NOUN	NNS	Number=Plur	8	dobj	_	_
11	categorically	categorically	ADV	RB	_	8	advmod	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 564
# sent_id = 1
# text = In the present article we describe constructions of model structures on general bicomplete categories.
1	In	in	ADP	IN	_	6	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	present	present	ADJ	JJ	Degree=Pos	4	amod	_	_
4	article	article	NOUN	NN	Number=Sing	1	pobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	constructions	construction	NOUN	NNS	Number=Plur	6	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	model	model	NOUN	NN	Number=Sing	10	compound	_	_
10	structures	structure	NOUN	NNS	Number=Plur	8	pobj	_	_
11	on	on	ADP	IN	_	7	prep	_	_
12	general	general	ADJ	JJ	Degree=Pos	14	amod	_	_
13	bicomplete	bicomplete	ADJ	JJ	Degree=Pos	14	amod	_	_
14	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = We are motivated by the following question: given a category $ C $ with a suitable subcategory $ wC $ , when is there a model structure on $ C $ with $ wC $ as the subcategory of weak equivalences?
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubjpass	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	by	by	ADP	IN	_	3	agent	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	amod	_	_
7	question	question	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
8	:	:	PUNCT	:	_	7	punct	_	_
9	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
12	$ C $	$ c $	SYM	$	_	11	appos	_	_
13	with	with	ADP	IN	_	9	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	suitable	suitable	ADJ	JJ	Degree=Pos	17	amod	_	_
16	subcategory	subcategory	NOUN	NN	Number=Sing	17	amod	_	_
17	$ wC $	$ wc $	SYM	$	_	13	pobj	_	_
18	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
19	when	when	SCONJ	WRB	_	20	advmod	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
21	there	there	PRON	EX	_	20	expl	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
23	model	model	NOUN	NN	Number=Sing	24	compound	_	_
24	structure	structure	NOUN	NN	Number=Sing	20	attr	_	_
25	on	on	ADP	IN	_	24	prep	_	_
26	$ C $	$ c $	SYM	$	_	25	pobj	_	_
27	with	with	ADP	IN	_	24	prep	_	_
28	$ wC $	$ wc $	SYM	$	_	27	pobj	_	_
29	as	as	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	subcategory	subcategory	NOUN	NN	Number=Sing	29	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	weak	weak	ADJ	JJ	Degree=Pos	34	amod	_	_
34	equivalences	equivalence	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
35	?	?	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 3
# text = We .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	0	ROOT	_	_
2	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# doc_id = 565
# sent_id = 1
# text = A quasi - schemoid is a small category with a particular partition of the set of morphisms.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	quasi	quasi	ADJ	JJ	Degree=Pos	4	amod	_	_
3	-	-	NOUN	NN	Number=Sing	4	amod	_	_
4	schemoid	schemoid	NOUN	NN	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	small	small	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	5	attr	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	particular	particular	ADJ	JJ	Degree=Pos	12	amod	_	_
12	partition	partition	NOUN	NN	Number=Sing	9	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	set	set	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	morphisms	morphism	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = We define a homotopy relation on the category of quasi - schemoids and study its fundamental properties.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	homotopy	homotopy	NOUN	NN	Number=Sing	5	compound	_	_
5	relation	relation	NOUN	NN	Number=Sing	2	dobj	_	_
6	on	on	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	quasi	quasi	NOUN	NNS	Number=Plur	9	pobj	_	_
11	-	-	NOUN	NNS	Number=Plur	10	punct	_	_
12	schemoids	schemoid	NOUN	NNS	Number=Plur	10	conj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
14	study	study	VERB	VB	VerbForm=Inf	2	conj	_	_
15	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	17	poss	_	_
16	fundamental	fundamental	ADJ	JJ	Degree=Pos	17	amod	_	_
17	properties	property	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The homotopy set of self - homotopy equivalences on a quasi - schemoid is used as a homotopy invariant in the study.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	homotopy	homotopy	NOUN	NN	Number=Sing	15	nsubjpass	_	_
3	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acl	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	self	self	NOUN	NN	Number=Sing	7	compound	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	homotopy	homotopy	NOUN	NN	Number=Sing	8	compound	_	_
8	equivalences	equivalence	NOUN	NNS	Number=Plur	4	pobj	_	_
9	on	on	ADP	IN	_	3	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	quasi	quasi	NOUN	NN	Number=Sing	9	pobj	_	_
12	-	-	NOUN	NNS	Number=Plur	9	pobj	_	_
13	schemoid	schemoid	NOUN	NN	Number=Sing	15	nsubjpass	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
16	as	as	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	homotopy	homotopy	NOUN	NN	Number=Sing	19	compound	_	_
19	invariant	invariant	NOUN	NN	Number=Sing	16	pobj	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	study	study	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 4
# text = The main theorem enables us to deduce that the homotopy invariant for the quasi - schemoid induced by a finite group is isomorphic to the automorphism group of the given group.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	theorem	theorem	NOUN	NN	Number=Sing	4	nsubj	_	_
4	enables	enable	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	4	dobj	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	deduce	deduce	VERB	VB	VerbForm=Inf	4	xcomp	_	_
8	that	that	SCONJ	IN	_	22	mark	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	homotopy	homotopy	NOUN	NN	Number=Sing	11	compound	_	_
11	invariant	invariant	ADJ	JJ	Degree=Pos	22	nsubj	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
14	quasi	quasi	ADJ	JJ	Degree=Pos	16	compound	_	_
15	-	-	ADJ	JJ	Degree=Pos	16	punct	_	_
16	schemoid	schemoid	NOUN	NN	Number=Sing	12	pobj	_	_
17	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	acl	_	_
18	by	by	ADP	IN	_	17	agent	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	finite	finite	ADJ	JJ	Degree=Pos	21	compound	_	_
21	group	group	NOUN	NN	Number=Sing	18	pobj	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	ccomp	_	_
23	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	22	acomp	_	_
24	to	to	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	automorphism	automorphism	NOUN	NN	Number=Sing	27	compound	_	_
27	group	group	NOUN	NN	Number=Sing	24	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
30	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	amod	_	_
31	group	group	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = These considerations are the first step to develop homotopy theory for quasi - schemoids.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	considerations	consideration	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	first	first	ADJ	JJ	Degree=Pos	6	amod	_	_
6	step	step	NOUN	NN	Number=Sing	3	attr	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	develop	develop	VERB	VB	VerbForm=Inf	6	relcl	_	_
9	homotopy	homotopy	NOUN	NN	Number=Sing	10	compound	_	_
10	theory	theory	NOUN	NN	Number=Sing	8	dobj	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	quasi	quasi	NOUN	NNS	Number=Plur	11	pobj	_	_
13	-	-	NOUN	NNS	Number=Plur	11	pobj	_	_
14	schemoids	schemoid	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 566
# sent_id = 1
# text = It is proved that for any small Grothendieck site $ X $ , there exists a coreflection (called cosheafification) from the category of precosheaves on $ X $ with values in a category $ K $ , to the full subcategory of cosheaves, provided either $ K $ or $ K^{op} $ is locally presentable.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	SCONJ	IN	_	13	mark	_	_
5	for	for	ADP	IN	_	13	prep	_	_
6	any	any	DET	DT	_	9	det	_	_
7	small	small	ADJ	JJ	Degree=Pos	8	amod	_	_
8	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	9	compound	_	_
9	site	site	NOUN	NN	Number=Sing	5	pobj	_	_
10	$ X $	$ x $	SYM	$	_	5	pobj	_	_
11	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
12	there	there	PRON	EX	_	13	expl	_	_
13	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	coreflection	coreflection	NOUN	NN	Number=Sing	13	dobj	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	15	punct	_	SpaceAfter=No
17	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
18	cosheafification	cosheafification	NOUN	NN	Number=Sing	17	oprd	_	SpaceAfter=No
19	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	15	punct	_	_
20	from	from	ADP	IN	_	15	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	category	category	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	precosheaves	precosheave	NOUN	NNS	Number=Plur	23	pobj	_	_
25	on	on	ADP	IN	_	22	prep	_	_
26	$ X $	$ x $	SYM	$	_	25	pobj	_	_
27	with	with	ADP	IN	_	22	prep	_	_
28	values	value	NOUN	NNS	Number=Plur	27	pobj	_	_
29	in	in	ADP	IN	_	28	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
31	category	category	NOUN	NN	Number=Sing	29	pobj	_	_
32	$ K $	$ k $	SYM	$	_	15	appos	_	_
33	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
34	to	to	ADP	IN	_	15	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
36	full	full	ADJ	JJ	Degree=Pos	37	amod	_	_
37	subcategory	subcategory	NOUN	NN	Number=Sing	34	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	cosheaves	cosheave	NOUN	NNS	Number=Plur	38	pobj	_	SpaceAfter=No
40	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
41	provided	provide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
42	either	either	CCONJ	CC	ConjType=Cmp	43	preconj	_	_
43	$ K $	$ k $	SYM	$	_	45	nmod	_	_
44	or	or	CCONJ	CC	ConjType=Cmp	43	cc	_	_
45	$ K^{op} $	$ k^{op} $	SYM	$	_	41	dobj	_	_
46	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	conj	_	_
47	locally	locally	ADV	RB	_	48	advmod	_	_
48	presentable	presentable	ADJ	JJ	Degree=Pos	46	acomp	_	SpaceAfter=No
49	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = If $ K $ is cocomplete, such a coreflection is built explicitly for the (pre)cosheaves with values in the category $ Pro(K) $ of pro - objects in $ K $ .
1	If	if	SCONJ	IN	_	3	mark	_	_
2	$ K $	$ k $	SYM	$	_	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	advcl	_	_
4	cocomplete	cocomplete	ADJ	JJ	Degree=Pos	3	acomp	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
6	such	such	DET	PDT	_	8	predet	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	coreflection	coreflection	NOUN	NN	Number=Sing	10	nsubjpass	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	built	build	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	explicitly	explicitly	ADV	RB	_	10	advmod	_	_
12	for	for	ADP	IN	_	10	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	15	punct	_	SpaceAfter=No
15	pre)cosheaves	pre)cosheave	NOUN	NNS	Number=Plur	12	pobj	_	_
16	with	with	ADP	IN	_	15	prep	_	_
17	values	value	NOUN	NNS	Number=Plur	16	pobj	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	category	category	NOUN	NN	Number=Sing	21	nmod	_	_
21	$ Pro(K) $	$ pro(k) $	SYM	$	_	18	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	pro	pro	ADJ	JJ	Degree=Pos	25	amod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	objects	object	NOUN	NNS	Number=Plur	22	pobj	_	_
26	in	in	ADP	IN	_	25	prep	_	_
27	$ K $	$ k $	SYM	$	_	26	pobj	_	_
28	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 3
# text = In the case of precosheaves on topological spaces, it is proved that any precosheaf with values in $ Pro(K) $ is smooth, that is, is strongly locally isomorphic to a cosheaf.
1	In	in	ADP	IN	_	12	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	case	case	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	precosheaves	precosheave	NOUN	NNS	Number=Plur	4	pobj	_	_
6	on	on	ADP	IN	_	3	prep	_	_
7	topological	topological	ADJ	JJ	Degree=Pos	8	amod	_	_
8	spaces	space	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
10	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	12	nsubjpass	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
13	that	that	SCONJ	IN	_	20	mark	_	_
14	any	any	DET	DT	_	15	det	_	_
15	precosheaf	precosheaf	NOUN	NN	Number=Sing	20	nsubj	_	_
16	with	with	ADP	IN	_	15	prep	_	_
17	values	value	NOUN	NNS	Number=Plur	16	pobj	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	$ Pro(K) $	$ pro(k) $	SYM	$	_	20	nsubj	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	ccomp	_	_
21	smooth	smooth	ADJ	JJ	Degree=Pos	20	acomp	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
23	that	that	ADV	RB	_	24	advmod	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	advmod	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	conj	_	_
27	strongly	strongly	ADV	RB	_	26	advmod	_	_
28	locally	locally	ADV	RB	_	29	advmod	_	_
29	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	26	acomp	_	_
30	to	to	ADP	IN	_	29	prep	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
32	cosheaf	cosheaf	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 4
# text = Constant cosheaves are constructed, and there are established connections with shape theory.
1	Constant	constant	ADJ	JJ	Degree=Pos	2	amod	_	_
2	cosheaves	cosheave	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
7	there	there	PRON	EX	_	8	expl	_	_
8	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	conj	_	_
9	established	establish	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	connections	connection	NOUN	NNS	Number=Plur	8	attr	_	_
11	with	with	ADP	IN	_	10	prep	_	_
12	shape	shape	NOUN	NN	Number=Sing	13	compound	_	_
13	theory	theory	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 567
# sent_id = 1
# text = Unlike the uniform completion, the Dedekind completion of a vector lattice is not functorial.
1	Unlike	unlike	ADP	IN	_	13	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	uniform	uniform	ADJ	JJ	Degree=Pos	4	compound	_	_
4	completion	completion	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	Dedekind	Dedekind	PROPN	NNP	Number=Sing	8	compound	_	_
8	completion	completion	NOUN	NN	Number=Sing	13	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	vector	vector	NOUN	NN	Number=Sing	12	compound	_	_
12	lattice	lattice	NOUN	NN	Number=Sing	9	pobj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	not	not	PART	RB	Polarity=Neg	13	neg	_	_
15	functorial	functorial	ADJ	JJ	Degree=Pos	13	acomp	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 2
# text = In order to repair the lack of functoriality of Dedekind completions, we enrich the signature of vector lattices with a proximity relation, thus arriving at the category $ pdv $ of proximity Dedekind vector lattices.
1	In	in	ADP	IN	_	14	prep	_	_
2	order	order	NOUN	NN	Number=Sing	1	pobj	_	_
3	to	to	PART	TO	_	4	aux	_	_
4	repair	repair	VERB	VB	VerbForm=Inf	2	acl	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	lack	lack	NOUN	NN	Number=Sing	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	functoriality	functoriality	NOUN	NN	Number=Sing	7	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Dedekind	Dedekind	PROPN	NNP	Number=Sing	11	compound	_	_
11	completions	completion	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	enrich	enrich	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	signature	signature	NOUN	NN	Number=Sing	14	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	vector	vector	NOUN	NN	Number=Sing	19	compound	_	_
19	lattices	lattice	NOUN	NNS	Number=Plur	17	pobj	_	_
20	with	with	ADP	IN	_	14	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	proximity	proximity	NOUN	NN	Number=Sing	23	compound	_	_
23	relation	relation	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
25	thus	thus	ADV	RB	_	26	advmod	_	_
26	arriving	arrive	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	advcl	_	_
27	at	at	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	category	category	NOUN	NN	Number=Sing	27	pobj	_	_
30	$ pdv $	$ pdv $	SYM	$	_	29	appos	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	proximity	proximity	NOUN	NN	Number=Sing	33	compound	_	_
33	Dedekind	Dedekind	PROPN	NNP	Number=Sing	35	compound	_	_
34	vector	vector	NOUN	NN	Number=Sing	35	compound	_	_
35	lattices	lattice	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 3
# text = We prove that the Dedekind completion induces a functor from the category $ bav $ of bounded archimedean vector lattices to $ pdv $ , which in fact is an equivalence.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	Dedekind	Dedekind	PROPN	NNP	Number=Sing	6	compound	_	_
6	completion	completion	NOUN	NN	Number=Sing	7	nsubj	_	_
7	induces	induce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	functor	functor	NOUN	NN	Number=Sing	7	dobj	_	_
10	from	from	ADP	IN	_	7	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
13	$ bav $	$ bav $	SYM	$	_	12	appos	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	bounded	bound	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
16	archimedean	archimedean	ADJ	JJ	Degree=Pos	17	compound	_	_
17	vector	vector	NOUN	NN	Number=Sing	18	compound	_	_
18	lattices	lattice	NOUN	NNS	Number=Plur	14	pobj	_	_
19	to	to	ADP	IN	_	7	prep	_	_
20	$ pdv $	$ pdv $	SYM	$	_	19	pobj	_	_
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	which	which	PRON	WDT	_	25	nsubj	_	_
23	in	in	ADP	IN	_	25	prep	_	_
24	fact	fact	NOUN	NN	Number=Sing	23	pobj	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	advcl	_	_
26	an	an	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	equivalence	equivalence	NOUN	NN	Number=Sing	25	attr	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We utilize the results of Dilworth to show that every proximity Dedekind vector lattice $ D $ is represented as the normal real - valued functions on the compact Hausdorff space associated with $ D $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	utilize	utilize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	results	result	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	Dilworth	Dilworth	PROPN	NNP	Number=Sing	5	pobj	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	show	show	VERB	VB	VerbForm=Inf	2	xcomp	_	_
9	that	that	SCONJ	IN	_	17	mark	_	_
10	every	every	DET	DT	_	11	det	_	_
11	proximity	proximity	NOUN	NN	Number=Sing	17	nsubjpass	_	_
12	Dedekind	Dedekind	PROPN	NNP	Number=Sing	13	compound	_	_
13	vector	vector	NOUN	NN	Number=Sing	14	nsubj	_	_
14	lattice	lattice	VERB	VBP	Tense=Pres|VerbForm=Fin	11	appos	_	_
15	$ D $	$ d $	SYM	$	_	11	appos	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	auxpass	_	_
17	represented	represent	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	ccomp	_	_
18	as	as	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
20	normal	normal	ADJ	JJ	Degree=Pos	24	amod	_	_
21	real	real	ADV	RB	_	23	advmod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
24	functions	function	NOUN	NNS	Number=Plur	18	pobj	_	_
25	on	on	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
27	compact	compact	ADJ	JJ	Degree=Pos	29	amod	_	_
28	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	29	compound	_	_
29	space	space	NOUN	NN	Number=Sing	25	pobj	_	_
30	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	acl	_	_
31	with	with	ADP	IN	_	30	prep	_	_
32	$ D $	$ d $	SYM	$	_	31	pobj	_	_
33	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = This yields a contravariant adjunction between $ pdv $ and the category $ KHaus $ of compact Hausdorff spaces, which restricts to a dual equivalence between $ KHaus $ and the proper subcategory of $ pdv $ consisting of those proximity Dedekind vector lattices in which the proximity is uniformly closed.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	yields	yield	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	contravariant	contravariant	ADJ	JJ	Degree=Pos	5	amod	_	_
5	adjunction	adjunction	NOUN	NN	Number=Sing	2	dobj	_	_
6	between	between	ADP	IN	_	5	prep	_	_
7	$ pdv $	$ pdv $	SYM	$	_	6	pobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	category	category	NOUN	NN	Number=Sing	5	conj	_	_
11	$ KHaus $	$ khaus $	SYM	$	_	10	appos	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	compact	compact	ADJ	JJ	Degree=Pos	15	amod	_	_
14	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	15	compound	_	_
15	spaces	space	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	which	which	PRON	WDT	_	18	nsubj	_	_
18	restricts	restrict	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	relcl	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	dual	dual	ADJ	JJ	Degree=Pos	22	amod	_	_
22	equivalence	equivalence	NOUN	NN	Number=Sing	19	pobj	_	_
23	between	between	ADP	IN	_	22	prep	_	_
24	$ KHaus $	$ khaus $	SYM	$	_	23	pobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	proper	proper	ADJ	JJ	Degree=Pos	28	amod	_	_
28	subcategory	subcategory	NOUN	NN	Number=Sing	22	conj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	$ pdv $	$ pdv $	SYM	$	_	29	pobj	_	_
31	consisting	consist	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	28	acl	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	those	those	DET	DT	Number=Plur|PronType=Dem	34	det	_	_
34	proximity	proximity	NOUN	NN	Number=Sing	37	compound	_	_
35	Dedekind	Dedekind	PROPN	NNP	Number=Sing	37	compound	_	_
36	vector	vector	NOUN	NN	Number=Sing	37	compound	_	_
37	lattices	lattice	NOUN	NNS	Number=Plur	32	pobj	_	_
38	in	in	ADP	IN	_	42	prep	_	_
39	which	which	PRON	WDT	_	38	pobj	_	_
40	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
41	proximity	proximity	NOUN	NN	Number=Sing	42	nsubj	_	_
42	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	37	relcl	_	_
43	uniformly	uniformly	ADV	RB	_	44	advmod	_	_
44	closed	closed	ADJ	JJ	Degree=Pos	42	acomp	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = We show how to derive the classic Yosida Representation, Kakutani - Krein Duality, Stone - Gelfand - Naimark Duality, and Stone - Nakano Theorem from our approach.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	how	how	SCONJ	WRB	_	5	advmod	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	derive	derive	VERB	VB	VerbForm=Inf	2	xcomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
7	classic	classic	ADJ	JJ	Degree=Pos	9	amod	_	_
8	Yosida	Yosida	PROPN	NNP	Number=Sing	9	compound	_	_
9	Representation	Representation	PROPN	NNP	Number=Sing	5	dobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	Kakutani	Kakutani	PROPN	NNP	Number=Sing	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	Krein	Krein	PROPN	NNP	Number=Sing	14	compound	_	_
14	Duality	Duality	PROPN	NNP	Number=Sing	9	conj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	Stone	Stone	PROPN	NNP	Number=Sing	20	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	Gelfand	Gelfand	PROPN	NNP	Number=Sing	20	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	Naimark	Naimark	PROPN	NNP	Number=Sing	21	compound	_	_
21	Duality	Duality	PROPN	NNP	Number=Sing	14	conj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
24	Stone	Stone	PROPN	NNP	Number=Sing	26	compound	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	Nakano	Nakano	PROPN	NNP	Number=Sing	27	compound	_	_
27	Theorem	Theorem	PROPN	NNP	Number=Sing	21	conj	_	_
28	from	from	ADP	IN	_	5	prep	_	_
29	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	30	poss	_	_
30	approach	approach	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 568
# sent_id = 1
# text = In this paper we continue, following the pioneering works by Cartmell and Streicher, the study of the most important structures on $ C $ - systems, the structures that correspond, in the case of the syntactic $ C $ - systems, to the $ (Pi, lambda, app, beta, eta) $ - system of inference rules.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	continue	continue	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	pioneering	pioneering	ADJ	JJ	Degree=Pos	10	amod	_	_
10	works	work	NOUN	NNS	Number=Plur	7	pobj	_	_
11	by	by	ADP	IN	_	10	prep	_	_
12	Cartmell	Cartmell	PROPN	NNP	Number=Sing	11	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	Streicher	Streicher	PROPN	NNP	Number=Sing	12	conj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	study	study	NOUN	NN	Number=Sing	5	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
20	most	most	ADV	RBS	Degree=Sup	21	advmod	_	_
21	important	important	ADJ	JJ	Degree=Pos	22	amod	_	_
22	structures	structure	NOUN	NNS	Number=Plur	18	pobj	_	_
23	on	on	ADP	IN	_	22	prep	_	_
24	$ C $	$ c $	SYM	$	_	26	compound	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	systems	system	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	structures	structure	NOUN	NNS	Number=Plur	17	appos	_	_
30	that	that	PRON	WDT	PronType=Rel	31	nsubj	_	_
31	correspond	correspond	VERB	VBP	Tense=Pres|VerbForm=Fin	29	relcl	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
33	in	in	ADP	IN	_	29	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	case	case	NOUN	NN	Number=Sing	33	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
38	syntactic	syntactic	ADJ	JJ	Degree=Pos	41	amod	_	_
39	$ C $	$ c $	SYM	$	_	41	compound	_	_
40	-	-	PUNCT	HYPH	PunctType=Dash	41	punct	_	_
41	systems	system	NOUN	NNS	Number=Plur	36	pobj	_	SpaceAfter=No
42	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
43	to	to	ADP	IN	_	17	prep	_	_
44	the	the	DET	DT	Definite=Def|PronType=Art	47	det	_	_
45	$ (Pi, lambda, app, beta, eta) $	$ (Pi, lambda, app, beta, eta) $	PROPN	NNP	Number=Sing	47	nmod	_	_
46	-	-	PUNCT	HYPH	PunctType=Dash	47	punct	_	_
47	system	system	NOUN	NN	Number=Sing	43	pobj	_	_
48	of	of	ADP	IN	_	47	prep	_	_
49	inference	inference	NOUN	NN	Number=Sing	50	compound	_	_
50	rules	rule	NOUN	NNS	Number=Plur	48	pobj	_	SpaceAfter=No
51	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = One such structure was introduced by Cartmell and later studied by Streicher under the name of the products of families of types.
1	One	one	NUM	CD	NumType=Card	3	nummod	_	_
2	such	such	ADJ	JJ	Degree=Pos	3	amod	_	_
3	structure	structure	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	5	auxpass	_	_
5	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	by	by	ADP	IN	_	5	agent	_	_
7	Cartmell	Cartmell	PROPN	NNP	Number=Sing	6	pobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
9	later	later	ADV	RB	_	10	advmod	_	_
10	studied	study	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	conj	_	_
11	by	by	ADP	IN	_	10	agent	_	_
12	Streicher	Streicher	PROPN	NNP	Number=Sing	11	pobj	_	_
13	under	under	ADP	IN	_	10	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	name	name	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	products	product	NOUN	NNS	Number=Plur	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	families	family	NOUN	NNS	Number=Plur	19	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	types	type	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = We introduce the notion of a $ (Pi, lambda) $ - structure and construct a bijection, for a given $ C $ - system, between the set of $ (Pi, lambda) $ - structures and the set of Cartmell - Streicher structures.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	$ (Pi, lambda) $	$ (pi, lambda) $	X	LS	NumType=Ord	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	structure	structure	NOUN	NN	Number=Sing	5	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
11	construct	construct	VERB	VB	VerbForm=Inf	2	conj	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	bijection	bijection	NOUN	NN	Number=Sing	11	dobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
15	for	for	ADP	IN	_	11	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
17	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	amod	_	_
18	$ C $	$ c $	SYM	$	_	20	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	system	system	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	between	between	ADP	IN	_	20	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	set	set	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	$ (Pi, lambda) $	$ (pi, lambda) $	SYM	$	_	28	compound	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	structures	structure	NOUN	NNS	Number=Plur	25	pobj	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	set	set	NOUN	NN	Number=Sing	28	conj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	Cartmell	Cartmell	PROPN	NNP	Number=Sing	35	compound	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	Streicher	Streicher	PROPN	NNP	Number=Sing	36	compound	_	_
36	structures	structure	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = In the following paper we will show how to construct, and in some cases fully classify, the $ (Pi, lambda) $ - structures on the $ C $ - systems that correspond to universe categories.
1	In	in	ADP	IN	_	7	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	amod	_	_
4	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
6	will	will	AUX	MD	VerbForm=Fin	7	aux	_	_
7	show	show	VERB	VB	VerbForm=Inf	0	ROOT	_	_
8	how	how	SCONJ	WRB	_	10	advmod	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	construct	construct	VERB	VB	VerbForm=Inf	7	xcomp	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
13	in	in	ADP	IN	_	17	prep	_	_
14	some	some	DET	DT	_	15	det	_	_
15	cases	case	NOUN	NNS	Number=Plur	13	pobj	_	_
16	fully	fully	ADV	RB	_	17	advmod	_	_
17	classify	classify	VERB	VBP	Tense=Pres|VerbForm=Fin	7	conj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
20	$ (Pi, lambda) $	$ (pi, lambda) $	SYM	$	_	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	structures	structure	NOUN	NNS	Number=Plur	17	npadvmod	_	_
23	on	on	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
25	$ C $	$ c $	SYM	$	_	27	compound	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	systems	system	NOUN	NNS	Number=Plur	23	pobj	_	_
28	that	that	PRON	WDT	PronType=Rel	29	nsubj	_	_
29	correspond	correspond	VERB	VBP	Tense=Pres|VerbForm=Fin	27	relcl	_	_
30	to	to	PART	TO	_	31	aux	_	_
31	universe	universe	VERB	VB	VerbForm=Inf	29	advcl	_	_
32	categories	category	NOUN	NNS	Number=Plur	31	dobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 5
# text = The first section of the paper provides careful proofs of many of the properties of general $ C $ - systems.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	first	first	ADJ	JJ	Degree=Pos	3	amod	_	_
3	section	section	NOUN	NN	Number=Sing	7	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	paper	paper	NOUN	NN	Number=Sing	4	pobj	_	_
7	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	careful	careful	ADJ	JJ	Degree=Pos	9	amod	_	_
9	proofs	proof	NOUN	NNS	Number=Plur	7	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	many	many	ADJ	JJ	Degree=Pos	10	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	properties	property	NOUN	NNS	Number=Plur	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	general	general	ADJ	JJ	Degree=Pos	19	amod	_	_
17	$ C $	$ c $	SYM	$	_	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	systems	system	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 6
# text = Methods of the paper are fully constructive, that is, neither the axiom of excluded middle nor the axiom of choice are used.
1	Methods	method	NOUN	NNS	Number=Plur	5	nsubj	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	paper	paper	NOUN	NN	Number=Sing	2	pobj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	24	ccomp	_	_
6	fully	fully	ADV	RB	_	7	advmod	_	_
7	constructive	constructive	ADJ	JJ	Degree=Pos	5	acomp	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
9	that	that	ADV	RB	_	10	advmod	_	_
10	is	is	ADV	RB	_	24	advmod	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
12	neither	neither	CCONJ	CC	ConjType=Cmp	14	preconj	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	axiom	axiom	NOUN	NN	Number=Sing	24	nsubjpass	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	excluded	exclude	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	middle	middle	NOUN	NN	Number=Sing	15	pobj	_	_
18	nor	nor	CCONJ	CC	ConjType=Cmp	14	cc	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	axiom	axiom	NOUN	NN	Number=Sing	14	conj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	choice	choice	NOUN	NN	Number=Sing	21	pobj	_	_
23	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	24	auxpass	_	_
24	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# doc_id = 569
# sent_id = 1
# text = The theory of monads on categories equipped with a dagger (a contravariant identity - on - objects involutive endofunctor) works best when all structure respects the dagger: the monad and adjunctions should preserve the dagger, and the monad and its algebras should satisfy the so - called Frobenius law.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	theory	theory	NOUN	NN	Number=Sing	22	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	monads	monad	NOUN	NNS	Number=Plur	3	pobj	_	_
5	on	on	ADP	IN	_	4	prep	_	_
6	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
7	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
8	with	with	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	dagger	dagger	NOUN	NN	Number=Sing	8	pobj	_	_
11	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	10	punct	_	SpaceAfter=No
12	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
13	contravariant	contravariant	ADJ	JJ	Degree=Pos	20	amod	_	_
14	identity	identity	NOUN	NN	Number=Sing	20	nmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
16	on	on	ADP	IN	_	14	prep	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
18	objects	object	NOUN	NNS	Number=Plur	16	pobj	_	_
19	involutive	involutive	ADJ	JJ	Degree=Pos	20	amod	_	_
20	endofunctor	endofunctor	PROPN	NNP	Number=Sing	10	appos	_	SpaceAfter=No
21	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	10	punct	_	_
22	works	work	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
23	best	well	ADV	RB	_	22	advmod	_	_
24	when	when	SCONJ	WRB	_	27	advmod	_	_
25	all	all	DET	DT	_	26	det	_	_
26	structure	structure	NOUN	NN	Number=Sing	27	nsubj	_	_
27	respects	respect	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	advcl	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	dagger	dagger	NOUN	NN	Number=Sing	27	dobj	_	SpaceAfter=No
30	:	:	PUNCT	:	_	29	punct	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	monad	monad	NOUN	NNS	Number=Plur	36	nsubj	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
34	adjunctions	adjunction	NOUN	NNS	Number=Plur	32	conj	_	_
35	should	should	AUX	MD	VerbForm=Fin	36	aux	_	_
36	preserve	preserve	VERB	VB	VerbForm=Inf	22	conj	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	dagger	dagger	NOUN	NN	Number=Sing	36	dobj	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	36	cc	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	42	det	_	_
42	monad	monad	NOUN	NNS	Number=Plur	47	nsubj	_	_
43	and	and	CCONJ	CC	ConjType=Cmp	42	cc	_	_
44	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	45	poss	_	_
45	algebras	algebra	NOUN	NNS	Number=Plur	42	conj	_	_
46	should	should	AUX	MD	VerbForm=Fin	47	aux	_	_
47	satisfy	satisfy	VERB	VB	VerbForm=Inf	36	conj	_	_
48	the	the	DET	DT	Definite=Def|PronType=Art	53	det	_	_
49	so	so	ADV	RB	_	51	advmod	_	_
50	-	-	PUNCT	HYPH	PunctType=Dash	51	punct	_	_
51	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	53	amod	_	_
52	Frobenius	Frobenius	PROPN	NNP	Number=Sing	53	compound	_	_
53	law	law	NOUN	NN	Number=Sing	47	dobj	_	SpaceAfter=No
54	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# sent_id = 2
# text = Then any monad resolves as an adjunction, with extremal solutions given by the categories of Kleisli and Frobenius - Eilenberg - Moore algebras, which again have a dagger.
1	Then	then	ADV	RB	PronType=Dem	4	advmod	_	_
2	any	any	DET	DT	_	3	det	_	_
3	monad	monad	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	resolves	resolve	NOUN	NNS	Number=Plur	0	ROOT	_	_
5	as	as	ADP	IN	_	4	prep	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	adjunction	adjunction	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
9	with	with	ADP	IN	_	4	prep	_	_
10	extremal	extremal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	solutions	solution	NOUN	NNS	Number=Plur	9	pobj	_	_
12	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acl	_	_
13	by	by	ADP	IN	_	12	agent	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	Kleisli	Kleisli	PROPN	NNP	Number=Sing	24	nmod	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	Frobenius	Frobenius	PROPN	NNP	Number=Sing	23	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
21	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	Moore	Moore	PROPN	NNP	Number=Sing	17	conj	_	_
24	algebras	algebra	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	which	which	PRON	WDT	_	28	nsubj	_	_
27	again	again	ADV	RB	_	28	advmod	_	_
28	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	24	relcl	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
30	dagger	dagger	NOUN	NN	Number=Sing	28	dobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = We characterize the Frobenius law as a coherence property between dagger and closure, and characterize strong such monads as being induced by Frobenius monoids.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	Frobenius	Frobenius	PROPN	NNP	Number=Sing	5	compound	_	_
5	law	law	NOUN	NN	Number=Sing	2	dobj	_	_
6	as	as	ADP	IN	_	2	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	coherence	coherence	NOUN	NN	Number=Sing	9	compound	_	_
9	property	property	NOUN	NN	Number=Sing	6	pobj	_	_
10	between	between	ADP	IN	_	9	prep	_	_
11	dagger	dagger	NOUN	NN	Number=Sing	10	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	closure	closure	NOUN	NN	Number=Sing	11	conj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
16	characterize	characterize	VERB	VB	VerbForm=Inf	2	conj	_	_
17	strong	strong	ADJ	JJ	Degree=Pos	19	amod	_	_
18	such	such	ADJ	JJ	Degree=Pos	19	amod	_	_
19	monads	monad	NOUN	NNS	Number=Plur	16	dobj	_	_
20	as	as	ADP	IN	_	19	prep	_	_
21	being	be	AUX	VBG	VerbForm=Ger	22	auxpass	_	_
22	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	pcomp	_	_
23	by	by	ADP	IN	_	22	agent	_	_
24	Frobenius	Frobenius	PROPN	NNP	Number=Sing	25	compound	_	_
25	monoids	monoid	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 570
# sent_id = 1
# text = We provide a more economical refined version of Evrard's categorical cocylinder factorization of a functor.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
4	more	more	ADV	RBR	Degree=Cmp	5	advmod	_	_
5	economical	economical	ADJ	JJ	Degree=Pos	7	amod	_	_
6	refined	refined	ADJ	JJ	Degree=Pos	7	amod	_	_
7	version	version	NOUN	NN	Number=Sing	2	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	Evrard	Evrard	PROPN	NNP	Number=Sing	13	poss	_	SpaceAfter=No
10	's	's	PART	POS	_	9	case	_	_
11	categorical	categorical	ADJ	JJ	Degree=Pos	12	amod	_	_
12	cocylinder	cocylinder	NOUN	NN	Number=Sing	13	compound	_	_
13	factorization	factorization	NOUN	NN	Number=Sing	8	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	functor	functor	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that any functor between small categories can be factored into a homotopy equivalence followed by a (co)fibred functor which satisfies the (dual) assumption of Quillen's Theorem B.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	11	mark	_	_
4	any	any	DET	DT	_	5	det	_	_
5	functor	functor	NOUN	NN	Number=Sing	11	nsubjpass	_	_
6	between	between	ADP	IN	_	5	prep	_	_
7	small	small	ADJ	JJ	Degree=Pos	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
9	can	can	AUX	MD	VerbForm=Fin	11	aux	_	_
10	be	be	AUX	VB	VerbForm=Inf	11	auxpass	_	_
11	factored	factor	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
12	into	into	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	homotopy	homotopy	NOUN	NN	Number=Sing	15	compound	_	_
15	equivalence	equivalence	NOUN	NN	Number=Sing	12	pobj	_	_
16	followed	follow	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
17	by	by	ADP	IN	_	16	agent	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
19	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	21	punct	_	SpaceAfter=No
20	co)fibred	co)fibred	ADJ	JJ	Degree=Pos	21	amod	_	_
21	functor	functor	NOUN	NN	Number=Sing	17	pobj	_	_
22	which	which	PRON	WDT	_	23	nsubj	_	_
23	satisfies	satisfy	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	21	relcl	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
25	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	28	punct	_	SpaceAfter=No
26	dual	dual	ADJ	JJ	Degree=Pos	28	amod	_	SpaceAfter=No
27	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	28	punct	_	_
28	assumption	assumption	NOUN	NN	Number=Sing	23	dobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	Quillen	Quillen	PROPN	NNP	Number=Sing	33	poss	_	SpaceAfter=No
31	's	's	PART	POS	_	30	case	_	_
32	Theorem	Theorem	PROPN	NNP	Number=Sing	33	compound	_	_
33	B.	B.	PROPN	NNP	Number=Sing	29	pobj	_	SpaceAfter=No

# doc_id = 571
# sent_id = 1
# text = Sheaves are objects of a local nature: a global section is determined by how it looks locally.
1	Sheaves	sheaf	NOUN	NNS	Number=Plur	2	nsubj	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
3	objects	object	NOUN	NNS	Number=Plur	2	attr	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	local	local	ADJ	JJ	Degree=Pos	7	amod	_	_
7	nature	nature	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
8	:	:	PUNCT	:	_	13	punct	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	global	global	ADJ	JJ	Degree=Pos	11	amod	_	_
11	section	section	NOUN	NN	Number=Sing	13	nsubjpass	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	determined	determine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
14	by	by	ADP	IN	_	13	agent	_	_
15	how	how	SCONJ	WRB	_	17	advmod	_	_
16	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	17	nsubj	_	_
17	looks	look	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	pcomp	_	_
18	locally	locally	ADV	RB	_	17	advmod	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 2
# text = Hence, a sheaf cannot describe mathematical structures which contain global or nonlocal geometric information.
1	Hence	hence	ADV	RB	_	7	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	sheaf	sheaf	NOUN	NN	Number=Sing	7	nsubj	_	_
5	can	can	AUX	MD	VerbForm=Fin	7	aux	_	SpaceAfter=No
6	not	not	PART	RB	Polarity=Neg	7	neg	_	_
7	describe	describe	VERB	VB	VerbForm=Inf	0	ROOT	_	_
8	mathematical	mathematical	ADJ	JJ	Degree=Pos	9	amod	_	_
9	structures	structure	NOUN	NNS	Number=Plur	7	dobj	_	_
10	which	which	PRON	WDT	_	11	nsubj	_	_
11	contain	contain	VERB	VBP	Tense=Pres|VerbForm=Fin	9	relcl	_	_
12	global	global	ADJ	JJ	Degree=Pos	16	amod	_	_
13	or	or	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	nonlocal	nonlocal	ADJ	JJ	Degree=Pos	12	conj	_	_
15	geometric	geometric	ADJ	JJ	Degree=Pos	16	amod	_	_
16	information	information	NOUN	NN	Number=Sing	11	dobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = To fill this gap, we introduce the theory of ``gleaves'', which are presheaves equipped with an additional ``gluing operation'' of compatible pairs of local sections.
1	To	to	PART	TO	_	2	aux	_	_
2	fill	fill	VERB	VB	VerbForm=Inf	7	advcl	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	gap	gap	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	theory	theory	NOUN	NN	Number=Sing	7	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	13	punct	_	SpaceAfter=No
12	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	13	punct	_	SpaceAfter=No
13	gleaves	gleave	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
14	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	13	punct	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
16	which	which	PRON	WDT	_	17	nsubj	_	_
17	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	relcl	_	_
18	presheaves	presheave	NOUN	NNS	Number=Plur	17	attr	_	_
19	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	acl	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
22	additional	additional	ADJ	JJ	Degree=Pos	26	amod	_	_
23	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	SpaceAfter=No
24	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	26	punct	_	SpaceAfter=No
25	gluing	glue	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	26	amod	_	_
26	operation	operation	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
27	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	26	punct	_	_
28	of	of	ADP	IN	_	26	prep	_	_
29	compatible	compatible	ADJ	JJ	Degree=Pos	30	amod	_	_
30	pairs	pair	NOUN	NNS	Number=Plur	28	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	local	local	ADJ	JJ	Degree=Pos	33	amod	_	_
33	sections	section	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = This generalizes the conditional product structures of Dawid and Studeny, which correspond to gleaves on distributive lattices.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
4	conditional	conditional	ADJ	JJ	Degree=Pos	6	amod	_	_
5	product	product	NOUN	NN	Number=Sing	6	compound	_	_
6	structures	structure	NOUN	NNS	Number=Plur	2	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	Dawid	Dawid	PROPN	NNP	Number=Sing	7	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	Studeny	Studeny	PROPN	NNP	Number=Sing	8	conj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
12	which	which	PRON	WDT	_	13	nsubj	_	_
13	correspond	correspond	VERB	VBP	Tense=Pres|VerbForm=Fin	6	relcl	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	gleaves	gleave	NOUN	NNS	Number=Plur	14	pobj	_	_
16	on	on	ADP	IN	_	15	prep	_	_
17	distributive	distributive	ADJ	JJ	Degree=Pos	18	amod	_	_
18	lattices	lattice	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = Our examples include the gleaf of metric spaces and the gleaf of joint probability distributions.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	examples	example	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	gleaf	gleaf	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	metric	metric	ADJ	JJ	Degree=Pos	8	amod	_	_
8	spaces	space	NOUN	NNS	Number=Plur	6	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	gleaf	gleaf	NOUN	NN	Number=Sing	5	conj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	joint	joint	ADJ	JJ	Degree=Pos	14	amod	_	_
14	probability	probability	NOUN	NN	Number=Sing	15	compound	_	_
15	distributions	distribution	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = A result of Johnstone shows that a category of gleaves can have a subobject classifier despite not being cartesian closed.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	result	result	NOUN	NN	Number=Sing	5	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	Johnstone	Johnstone	PROPN	NNP	Number=Sing	3	pobj	_	_
5	shows	show	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	12	mark	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	12	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	gleaves	gleave	NOUN	NNS	Number=Plur	9	pobj	_	_
11	can	can	AUX	MD	VerbForm=Fin	12	aux	_	_
12	have	have	VERB	VB	VerbForm=Inf	5	ccomp	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	subobject	subobject	NOUN	NN	Number=Sing	15	compound	_	_
15	classifier	classifier	NOUN	NN	Number=Sing	12	dobj	_	_
16	despite	despite	SCONJ	IN	_	12	prep	_	_
17	not	not	PART	RB	Polarity=Neg	18	neg	_	_
18	being	be	AUX	VBG	VerbForm=Ger	16	pcomp	_	_
19	cartesian	cartesian	ADJ	JJ	Degree=Pos	18	acomp	_	_
20	closed	closed	ADJ	JJ	Degree=Pos	18	acomp	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 7
# text = Gleaves over the simplex category $ Delta $ , which we call compositories, can be interpreted as a new kind of higher category in which the composition of an $ m $ - morphism and an $ n $ - morphism along a common $ k $ - morphism face results in an $ (m+n - k) $ - morphism.
1	Gleaves	gleave	NOUN	NNS	Number=Plur	15	nsubjpass	_	_
2	over	over	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	simplex	simplex	NOUN	NN	Number=Sing	5	compound	_	_
5	category	category	NOUN	NN	Number=Sing	2	pobj	_	_
6	$ Delta $	$ delta $	SYM	$	_	5	appos	_	_
7	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
8	which	which	PRON	WDT	_	10	dobj	_	_
9	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
10	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	1	relcl	_	_
11	compositories	compositorie	NOUN	NNS	Number=Plur	10	dobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
13	can	can	AUX	MD	VerbForm=Fin	15	aux	_	_
14	be	be	AUX	VB	VerbForm=Inf	15	auxpass	_	_
15	interpreted	interpret	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
16	as	as	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	new	new	ADJ	JJ	Degree=Pos	19	amod	_	_
19	kind	kind	NOUN	NN	Number=Sing	16	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	higher	high	ADJ	JJR	Degree=Cmp	22	amod	_	_
22	category	category	NOUN	NN	Number=Sing	20	pobj	_	_
23	in	in	ADP	IN	_	43	prep	_	_
24	which	which	PRON	WDT	_	23	pobj	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	composition	composition	NOUN	NN	Number=Sing	43	nsubj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	an	an	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
29	$ m $	$ m $	SYM	$	_	31	compound	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	morphism	morphism	NOUN	NN	Number=Sing	27	pobj	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	an	an	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
34	$ n $	$ n $	SYM	$	_	36	compound	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	36	punct	_	_
36	morphism	morphism	NOUN	NN	Number=Sing	31	conj	_	_
37	along	along	ADP	IN	_	36	prep	_	_
38	a	a	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
39	common	common	ADJ	JJ	Degree=Pos	42	amod	_	_
40	$ k $	$ k $	SYM	$	_	42	nummod	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	morphism	morphism	NOUN	NN	Number=Sing	37	pobj	_	_
43	face	face	NOUN	NN	Number=Sing	22	relcl	_	_
44	results	result	NOUN	NNS	Number=Plur	43	dobj	_	_
45	in	in	ADP	IN	_	43	prep	_	_
46	an	an	DET	DT	Definite=Ind|PronType=Art	49	det	_	_
47	$ (m+n - k) $	$ (m+n - k) $	SYM	$	_	49	compound	_	_
48	-	-	PUNCT	HYPH	PunctType=Dash	49	punct	_	_
49	morphism	morphism	NOUN	NN	Number=Sing	45	pobj	_	SpaceAfter=No
50	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 8
# text = The distinctive feature of this composition operation is that the original morphisms can be recovered from the composite morphism as initial and final faces.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	distinctive	distinctive	ADJ	JJ	Degree=Pos	3	amod	_	_
3	feature	feature	NOUN	NN	Number=Sing	8	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
6	composition	composition	NOUN	NN	Number=Sing	7	compound	_	_
7	operation	operation	NOUN	NN	Number=Sing	4	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	that	that	SCONJ	IN	_	15	mark	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	original	original	ADJ	JJ	Degree=Pos	12	amod	_	_
12	morphisms	morphism	NOUN	NNS	Number=Plur	15	nsubjpass	_	_
13	can	can	AUX	MD	VerbForm=Fin	15	aux	_	_
14	be	be	AUX	VB	VerbForm=Inf	15	auxpass	_	_
15	recovered	recover	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	ccomp	_	_
16	from	from	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	composite	composite	ADJ	JJ	Degree=Pos	19	amod	_	_
19	morphism	morphism	NOUN	NN	Number=Sing	16	pobj	_	_
20	as	as	ADP	IN	_	15	prep	_	_
21	initial	initial	ADJ	JJ	Degree=Pos	24	amod	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	final	final	ADJ	JJ	Degree=Pos	21	conj	_	_
24	faces	face	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 9
# text = Examples of compositories include nerves of categories and compositories of higher spans.
1	Examples	example	NOUN	NNS	Number=Plur	4	nsubj	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	compositories	compositorie	NOUN	NNS	Number=Plur	2	pobj	_	_
4	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	nerves	nerve	NOUN	NNS	Number=Plur	4	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	compositories	compositorie	NOUN	NNS	Number=Plur	7	conj	_	_
10	of	of	ADP	IN	_	7	prep	_	_
11	higher	high	ADJ	JJR	Degree=Cmp	12	amod	_	_
12	spans	span	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 572
# sent_id = 1
# text = We study the theory of representations of a 2 - group $ G $ in Baez - Crans 2 - vector spaces over a field $ k $ of arbitrary characteristic, and the corresponding 2 - vector spaces of intertwiners.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	theory	theory	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	representations	representation	NOUN	NNS	Number=Plur	5	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
9	2	2	NUM	CD	NumType=Card	11	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	group	group	NOUN	NN	Number=Sing	12	compound	_	_
12	$ G $	$ g $	SYM	$	_	7	pobj	_	_
13	in	in	ADP	IN	_	6	prep	_	_
14	Baez	Baez	PROPN	NNP	Number=Sing	16	nmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	Crans	Crans	PROPN	NNPS	Number=Plur	20	nmod	_	_
17	2	2	NUM	CD	NumType=Card	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	vector	vector	NOUN	NN	Number=Sing	20	compound	_	_
20	spaces	space	NOUN	NNS	Number=Plur	13	pobj	_	_
21	over	over	ADP	IN	_	20	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
23	field	field	NOUN	NN	Number=Sing	21	pobj	_	_
24	$ k $	$ k $	SYM	$	_	23	appos	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	27	amod	_	_
27	characteristic	characteristic	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
31	corresponding	corresponding	ADJ	JJ	Degree=Pos	35	amod	_	_
32	2	2	NUM	CD	NumType=Card	34	nummod	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	vector	vector	NOUN	NN	Number=Sing	35	compound	_	_
35	spaces	space	NOUN	NNS	Number=Plur	2	conj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	intertwiners	intertwiner	NOUN	NNS	Number=Plur	36	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We also characterize the irreducible and indecomposable representations.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
5	irreducible	irreducible	ADJ	JJ	Degree=Pos	8	amod	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	indecomposable	indecomposable	ADJ	JJ	Degree=Pos	5	conj	_	_
8	representations	representation	NOUN	NNS	Number=Plur	3	dobj	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Finally, it is shown that when the 2 - group is finite and the base field $ k $ is of characteristic zero or coprime to the orders of the homotopy groups of $ G $ , the theory essentially reduces to the theory of $ k $ - linear representations of the first homotopy group of $ G $ , the remaining homotopy invariants of $ G $ playing no role.
1	Finally	finally	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	38	ccomp	_	_
6	that	that	SCONJ	IN	_	19	mark	_	_
7	when	when	SCONJ	WRB	_	12	advmod	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
9	2	2	NUM	CD	NumType=Card	11	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	group	group	NOUN	NN	Number=Sing	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	advcl	_	_
13	finite	finite	ADJ	JJ	Degree=Pos	12	acomp	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	base	base	NOUN	NN	Number=Sing	17	compound	_	_
17	field	field	NOUN	NN	Number=Sing	19	nsubj	_	_
18	$ k $	$ k $	SYM	$	_	17	appos	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	characteristic	characteristic	ADJ	JJ	Degree=Pos	22	amod	_	_
22	zero	zero	NUM	CD	NumType=Card	20	pobj	_	_
23	or	or	CCONJ	CC	ConjType=Cmp	20	cc	_	_
24	coprime	coprime	ADV	RB	_	20	conj	_	_
25	to	to	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	orders	order	NOUN	NNS	Number=Plur	25	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
30	homotopy	homotopy	NOUN	NN	Number=Sing	31	compound	_	_
31	groups	group	NOUN	NNS	Number=Plur	28	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	$ G $	$ g $	SYM	$	_	32	pobj	_	_
34	,	,	PUNCT	,	PunctType=Comm	38	punct	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	theory	theory	NOUN	NN	Number=Sing	38	nsubj	_	_
37	essentially	essentially	ADV	RB	_	38	advmod	_	_
38	reduces	reduce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
39	to	to	ADP	IN	_	38	prep	_	_
40	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
41	theory	theory	NOUN	NN	Number=Sing	39	pobj	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	$ k $	$ k $	SYM	$	_	45	quantmod	_	_
44	-	-	PUNCT	HYPH	PunctType=Dash	45	punct	_	_
45	linear	linear	ADJ	JJ	Degree=Pos	46	amod	_	_
46	representations	representation	NOUN	NNS	Number=Plur	42	pobj	_	_
47	of	of	ADP	IN	_	46	prep	_	_
48	the	the	DET	DT	Definite=Def|PronType=Art	51	det	_	_
49	first	first	ADJ	JJ	Degree=Pos	51	amod	_	_
50	homotopy	homotopy	NOUN	NN	Number=Sing	51	compound	_	_
51	group	group	NOUN	NN	Number=Sing	47	pobj	_	_
52	of	of	ADP	IN	_	51	prep	_	_
53	$ G $	$ g $	SYM	$	_	52	pobj	_	_
54	,	,	PUNCT	,	PunctType=Comm	38	punct	_	_
55	the	the	DET	DT	Definite=Def|PronType=Art	58	det	_	_
56	remaining	remain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	58	amod	_	_
57	homotopy	homotopy	NOUN	NN	Number=Sing	58	compound	_	_
58	invariants	invariant	NOUN	NNS	Number=Plur	38	dobj	_	_
59	of	of	ADP	IN	_	58	prep	_	_
60	$ G $	$ g $	SYM	$	_	59	pobj	_	_
61	playing	play	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	58	acl	_	_
62	no	no	DET	DT	_	63	det	_	_
63	role	role	NOUN	NN	Number=Sing	61	dobj	_	SpaceAfter=No
64	.	.	PUNCT	.	PunctType=Peri	38	punct	_	SpaceAfter=No

# doc_id = 573
# sent_id = 1
# text = We consider locales $ B $ as algebras in the tensor category $ sl $ of sup - lattices.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	locales	locale	NOUN	NNS	Number=Plur	2	dobj	_	_
4	$ B $	$ b $	SYM	$	_	3	dep	_	_
5	as	as	ADP	IN	_	3	prep	_	_
6	algebras	algebra	NOUN	NNS	Number=Plur	5	pobj	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	tensor	tensor	NOUN	NN	Number=Sing	10	compound	_	_
10	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
11	$ sl $	$ sl $	SYM	$	_	10	appos	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	sup	sup	NOUN	NN	Number=Sing	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	lattices	lattice	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show the equivalence between the Joyal - Tierney descent theorem for open localic surjections $ q : shB - - > E $ in Galois theory and a Tannakian recognition theorem over $ sl $ for the $ sl $ - functor $ Rel (q^*) : Rel(E) - - > Rel(shB) cong (B - Mod)_0 $ into the sl - category of discrete $ B $ - modules.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	equivalence	equivalence	NOUN	NN	Number=Sing	11	nsubj	_	_
5	between	between	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
7	Joyal	Joyal	PROPN	NNP	Number=Sing	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	Tierney	Tierney	PROPN	NNP	Number=Sing	10	compound	_	_
10	descent	descent	NOUN	NN	Number=Sing	5	pobj	_	_
11	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	2	ccomp	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	open	open	ADJ	JJ	Degree=Pos	15	amod	_	_
14	localic	localic	ADJ	JJ	Degree=Pos	15	amod	_	_
15	surjections	surjection	NOUN	NNS	Number=Plur	12	pobj	_	_
16	$ q : shB - - > E $	$ q : shb - - > e $	SYM	$	_	11	dep	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	Galois	Galois	PROPN	NNP	Number=Sing	19	compound	_	_
19	theory	theory	NOUN	NN	Number=Sing	17	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	Tannakian	tannakian	ADJ	JJ	Degree=Pos	23	amod	_	_
23	recognition	recognition	NOUN	NN	Number=Sing	24	nsubj	_	_
24	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	11	conj	_	_
25	over	over	ADP	IN	_	26	quantmod	_	_
26	$ sl $	$ sl $	SYM	$	_	24	dobj	_	_
27	for	for	ADP	IN	_	24	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
29	$ sl $	$ sl $	SYM	$	_	31	compound	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	functor	functor	NOUN	NN	Number=Sing	27	pobj	_	_
32	$ Rel (q^*) : Rel(E) - - > Rel(shB) cong (B - Mod)_0 $	$ rel (q^*) : rel(e) - - > rel(shb) cong (b - mod)_0 $	SYM	$	_	27	dep	_	_
33	into	into	ADP	IN	_	24	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
35	sl	sl	NOUN	NN	Number=Sing	37	compound	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	category	category	NOUN	NN	Number=Sing	33	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	discrete	discrete	ADJ	JJ	Degree=Pos	42	amod	_	_
40	$ B $	$ b $	SYM	$	_	42	compound	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	modules	module	NOUN	NNS	Number=Plur	38	pobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Thus, a new Tannaka recognition theorem is obtained, essentially different from those known so far.
1	Thus	thus	ADV	RB	_	9	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
4	new	new	ADJ	JJ	Degree=Pos	7	amod	_	_
5	Tannaka	Tannaka	PROPN	NNP	Number=Sing	6	compound	_	_
6	recognition	recognition	NOUN	NN	Number=Sing	7	compound	_	_
7	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	9	nsubjpass	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	essentially	essentially	ADV	RB	_	12	advmod	_	_
12	different	different	ADJ	JJ	Degree=Pos	9	advmod	_	_
13	from	from	ADP	IN	_	12	prep	_	_
14	those	those	PRON	DT	Number=Plur|PronType=Dem	13	pobj	_	_
15	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	acl	_	_
16	so	so	ADV	RB	_	17	advmod	_	_
17	far	far	ADV	RB	_	12	advmod	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 4
# text = This equivalence follows from two independent results.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	equivalence	equivalence	NOUN	NN	Number=Sing	3	nsubj	_	_
3	follows	follow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	from	from	ADP	IN	_	3	prep	_	_
5	two	two	NUM	CD	NumType=Card	7	nummod	_	_
6	independent	independent	ADJ	JJ	Degree=Pos	7	amod	_	_
7	results	result	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = We develop an explicit construction of the localic groupoid $ G $ associated by Joyal - Tierney to $ q $ , and do an exhaustive comparison with the Deligne Tannakian construction of the Hopf algebroid $ L $ associated to $ Rel(q^*) $ , and show they are isomorphic, that is, $ L cong O(G) $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	explicit	explicit	ADJ	JJ	Degree=Pos	5	amod	_	_
5	construction	construction	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	localic	localic	ADJ	JJ	Degree=Pos	9	amod	_	_
9	groupoid	groupoid	NOUN	NN	Number=Sing	6	pobj	_	_
10	$ G $	$ g $	SYM	$	_	9	appos	_	_
11	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	acl	_	_
12	by	by	ADP	IN	_	11	agent	_	_
13	Joyal	Joyal	PROPN	NNP	Number=Sing	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	Tierney	Tierney	PROPN	NNP	Number=Sing	12	pobj	_	_
16	to	to	ADP	IN	_	11	prep	_	_
17	$ q $	$ q $	SYM	$	_	16	pobj	_	_
18	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
20	do	do	VERB	VB	VerbForm=Inf	2	conj	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	exhaustive	exhaustive	ADJ	JJ	Degree=Pos	23	amod	_	_
23	comparison	comparison	NOUN	NN	Number=Sing	20	dobj	_	_
24	with	with	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
26	Deligne	Deligne	PROPN	NNP	Number=Sing	27	compound	_	_
27	Tannakian	Tannakian	PROPN	NNP	Number=Sing	28	compound	_	_
28	construction	construction	NOUN	NN	Number=Sing	24	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	Hopf	Hopf	PROPN	NNP	Number=Sing	32	compound	_	_
32	algebroid	algebroid	NOUN	NN	Number=Sing	29	pobj	_	_
33	$ L $	$ l $	SYM	$	_	32	appos	_	_
34	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	acl	_	_
35	to	to	ADP	IN	_	34	prep	_	_
36	$ Rel(q^*) $	$ rel(q^*) $	SYM	$	_	35	pobj	_	_
37	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
38	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
39	show	show	VERB	VB	VerbForm=Inf	20	conj	_	_
40	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	41	nsubj	_	_
41	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	39	ccomp	_	_
42	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	41	acomp	_	SpaceAfter=No
43	,	,	PUNCT	,	PunctType=Comm	39	punct	_	_
44	that	that	ADV	RB	_	45	advmod	_	_
45	is	is	ADV	RB	_	47	advmod	_	SpaceAfter=No
46	,	,	PUNCT	,	PunctType=Comm	47	punct	_	_
47	$ L cong O(G) $	$ l cong o(g) $	SYM	$	_	39	dobj	_	_
48	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = On the other hand, we show that the $ sl $ - category of relations of the classifying topos of any localic groupoid $ G $ , is equivalent to the $ sl $ - category of $ L $ - comodules with discrete subjacent $ B $ - module, where $ L = O(G) $ .
1	On	on	ADP	IN	_	7	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	other	other	ADJ	JJ	Degree=Pos	4	amod	_	_
4	hand	hand	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	that	that	SCONJ	IN	_	25	mark	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
10	$ sl $	$ sl $	SYM	$	_	12	amod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	category	category	NOUN	NN	Number=Sing	25	nsubj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	relations	relation	NOUN	NNS	Number=Plur	13	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	classifying	classify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	18	amod	_	_
18	topos	topos	NOUN	NN	Number=Sing	15	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	any	any	DET	DT	_	22	det	_	_
21	localic	localic	ADJ	JJ	Degree=Pos	22	amod	_	_
22	groupoid	groupoid	NOUN	NN	Number=Sing	19	pobj	_	_
23	$ G $	$ g $	SYM	$	_	22	appos	_	_
24	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	ccomp	_	_
26	equivalent	equivalent	ADJ	JJ	Degree=Pos	25	acomp	_	_
27	to	to	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
29	$ sl $	$ sl $	SYM	$	_	31	nummod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	category	category	NOUN	NN	Number=Sing	27	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	$ L $	$ l $	SYM	$	_	35	nmod	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	comodules	comodule	NOUN	NNS	Number=Plur	32	pobj	_	_
36	with	with	ADP	IN	_	31	prep	_	_
37	discrete	discrete	ADJ	JJ	Degree=Pos	38	amod	_	_
38	subjacent	subjacent	NOUN	NN	Number=Sing	36	pobj	_	_
39	$ B $	$ b $	SYM	$	_	41	nummod	_	_
40	-	-	PUNCT	HYPH	PunctType=Dash	41	punct	_	_
41	module	module	NOUN	NN	Number=Sing	31	appos	_	SpaceAfter=No
42	,	,	PUNCT	,	PunctType=Comm	41	punct	_	_
43	where	where	SCONJ	WRB	_	44	advmod	_	_
44	$ L = O(G) $	$ l = o(g) $	SYM	$	_	31	relcl	_	_
45	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 7
# text = We are forced to work over an arbitrary base topos because, contrary to the neutral case which can be developed completely over $ Sets $ , here change of base techniques are unavoidable.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubjpass	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	forced	force	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	work	work	VERB	VB	VerbForm=Inf	3	xcomp	_	_
6	over	over	ADP	IN	_	5	prep	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	10	amod	_	_
9	base	base	NOUN	NN	Number=Sing	10	compound	_	_
10	topos	topos	NOUN	NN	Number=Sing	6	pobj	_	_
11	because	because	SCONJ	IN	_	31	mark	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
13	contrary	contrary	ADV	RB	_	31	advmod	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	neutral	neutral	ADJ	JJ	Degree=Pos	17	amod	_	_
17	case	case	NOUN	NN	Number=Sing	14	pobj	_	_
18	which	which	PRON	WDT	_	21	nsubjpass	_	_
19	can	can	AUX	MD	VerbForm=Fin	21	aux	_	_
20	be	be	AUX	VB	VerbForm=Inf	21	auxpass	_	_
21	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	relcl	_	_
22	completely	completely	ADV	RB	_	21	advmod	_	_
23	over	over	ADP	IN	_	21	prep	_	_
24	$ Sets $	$ sets $	SYM	$	_	23	pobj	_	_
25	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
26	here	here	ADV	RB	PronType=Dem	31	advmod	_	_
27	change	change	NOUN	NN	Number=Sing	31	nsubj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	base	base	NOUN	NN	Number=Sing	30	compound	_	_
30	techniques	technique	NOUN	NNS	Number=Plur	28	pobj	_	_
31	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	advcl	_	_
32	unavoidable	unavoidable	ADJ	JJ	Degree=Pos	31	acomp	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 574
# sent_id = 1
# text = Projectivity, continuity and adjointness: quantales, $ Q $ - posets and $ Q $ - modules In this paper, projective modules over a quantale are characterized by distributivity, continuity, and adjointness conditions.
1	Projectivity	projectivity	NOUN	NN	Number=Sing	26	nsubjpass	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	1	punct	_	_
3	continuity	continuity	NOUN	NN	Number=Sing	1	conj	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	adjointness	adjointness	NOUN	NN	Number=Sing	3	conj	_	SpaceAfter=No
6	:	:	PUNCT	:	_	1	punct	_	_
7	quantales	quantale	NOUN	NNS	Number=Plur	1	appos	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	$ Q $	$ q $	SYM	$	_	11	compound	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	posets	poset	NOUN	NNS	Number=Plur	7	appos	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	$ Q $	$ q $	SYM	$	_	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	modules	module	NOUN	NNS	Number=Plur	1	appos	_	_
16	In	in	ADP	IN	_	1	prep	_	_
17	this	this	DET	DT	Number=Sing|PronType=Dem	18	det	_	_
18	paper	paper	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	1	punct	_	_
20	projective	projective	ADJ	JJ	Degree=Pos	21	amod	_	_
21	modules	module	NOUN	NNS	Number=Plur	1	appos	_	_
22	over	over	ADP	IN	_	21	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	quantale	quantale	NOUN	NN	Number=Sing	22	pobj	_	_
25	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	26	auxpass	_	_
26	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
27	by	by	ADP	IN	_	26	agent	_	_
28	distributivity	distributivity	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
30	continuity	continuity	NOUN	NN	Number=Sing	28	conj	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
33	adjointness	adjointness	NOUN	NN	Number=Sing	34	compound	_	_
34	conditions	condition	NOUN	NNS	Number=Plur	30	conj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	26	punct	_	SpaceAfter=No

# sent_id = 2
# text = It is then shown that a morphism $ Q - - > A $ of commutative quantales is coexponentiable if and only if the corresponding $ Q $ - module is projective, and hence, satisfies these equivalent conditions.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	4	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
3	then	then	ADV	RB	PronType=Dem	4	advmod	_	_
4	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	that	that	SCONJ	IN	_	12	mark	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	morphism	morphism	NOUN	NN	Number=Sing	12	nsubj	_	_
8	$ Q - - > A $	$ q - - > a $	SYM	$	_	12	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	commutative	commutative	ADJ	JJ	Degree=Pos	11	amod	_	_
11	quantales	quantale	NOUN	NNS	Number=Plur	9	pobj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
13	coexponentiable	coexponentiable	ADJ	JJ	Degree=Pos	12	acomp	_	_
14	if	if	SCONJ	IN	_	29	mark	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
16	only	only	ADV	RB	_	23	advmod	_	_
17	if	if	SCONJ	IN	_	23	mark	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
19	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	amod	_	_
20	$ Q $	$ q $	SYM	$	_	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	module	module	NOUN	NN	Number=Sing	23	nsubj	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	advcl	_	_
24	projective	projective	ADJ	JJ	Degree=Pos	23	acomp	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
27	hence	hence	ADV	RB	_	23	conj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
29	satisfies	satisfy	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	advcl	_	_
30	these	these	DET	DT	Number=Plur|PronType=Dem	32	det	_	_
31	equivalent	equivalent	ADJ	JJ	Degree=Pos	32	amod	_	_
32	conditions	condition	NOUN	NNS	Number=Plur	29	dobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 575
# sent_id = 1
# text = We present a version of the enriched Yoneda lemma for conventional (not $ infty $ - ) categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	version	version	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
7	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	amod	_	_
8	Yoneda	Yoneda	PROPN	NNP	Number=Sing	9	compound	_	_
9	lemma	lemma	NOUN	NN	Number=Sing	5	pobj	_	_
10	for	for	ADP	IN	_	4	prep	_	_
11	conventional	conventional	ADJ	JJ	Degree=Pos	17	amod	_	_
12	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	17	punct	_	SpaceAfter=No
13	not	not	PART	RB	Polarity=Neg	17	neg	_	_
14	$ infty $	$ infty $	SYM	$	_	17	nmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
16	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	17	punct	_	_
17	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We do not require the base monoidal category $ M $ to be closed or symmetric monoidal.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
2	do	do	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	aux	_	_
3	not	not	PART	RB	Polarity=Neg	4	neg	_	_
4	require	require	VERB	VB	VerbForm=Inf	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
6	base	base	ADJ	JJ	Degree=Pos	8	amod	_	_
7	monoidal	monoidal	NOUN	NN	Number=Sing	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	4	dobj	_	_
9	$ M $	$ m $	SYM	$	_	8	appos	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	be	be	AUX	VB	VerbForm=Inf	4	xcomp	_	_
12	closed	closed	ADJ	JJ	Degree=Pos	11	acomp	_	_
13	or	or	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	symmetric	symmetric	ADJ	JJ	Degree=Pos	15	amod	_	_
15	monoidal	monoidal	NOUN	NN	Number=Sing	12	conj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = In the case $ M $ has colimits and the monoidal structure in $ M $ preserves colimits in each argument, we prove that the Yoneda embedding $ A $ to $ P_M(A) $ is a universal functor from $ A $ to a category with colimits, left - tensored over $ M $ .
1	In	in	ADP	IN	_	5	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	case	case	NOUN	NN	Number=Sing	1	pobj	_	_
4	$ M $	$ m $	SYM	$	_	5	nsubj	_	_
5	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	advcl	_	_
6	colimits	colimit	NOUN	NNS	Number=Plur	5	dobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	monoidal	monoidal	ADJ	JJ	Degree=Pos	10	amod	_	_
10	structure	structure	NOUN	NN	Number=Sing	6	conj	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	$ M $	$ m $	SYM	$	_	11	pobj	_	_
13	preserves	preserve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	conj	_	_
14	colimits	colimit	NOUN	NNS	Number=Plur	13	dobj	_	_
15	in	in	ADP	IN	_	13	prep	_	_
16	each	each	DET	DT	_	17	det	_	_
17	argument	argument	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
19	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	20	nsubj	_	_
20	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
21	that	that	SCONJ	IN	_	28	mark	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	Yoneda	Yoneda	PROPN	NNP	Number=Sing	24	nsubj	_	_
24	embedding	embed	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	28	csubj	_	_
25	$ A $	$ a $	SYM	$	_	24	dobj	_	_
26	to	to	PART	TO	_	24	prep	_	_
27	$ P_M(A) $	$ p_m(a) $	SYM	$	_	26	pobj	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	ccomp	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	universal	universal	ADJ	JJ	Degree=Pos	31	amod	_	_
31	functor	functor	NOUN	NN	Number=Sing	28	attr	_	_
32	from	from	ADP	IN	_	28	prep	_	_
33	$ A $	$ a $	SYM	$	_	32	pobj	_	_
34	to	to	ADP	IN	_	32	prep	_	_
35	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
36	category	category	NOUN	NN	Number=Sing	34	pobj	_	_
37	with	with	ADP	IN	_	36	prep	_	_
38	colimits	colimit	NOUN	NNS	Number=Plur	37	pobj	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
40	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	42	amod	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	tensored	tensore	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	44	amod	_	_
43	over	over	ADP	IN	_	44	quantmod	_	_
44	$ M $	$ m $	SYM	$	_	28	dep	_	_
45	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# doc_id = 576
# sent_id = 1
# text = In this paper, we use some basic quasi - topos theory to study two functors: one adding infinitesimals of Fermat reals to diffeological spaces (which generalize smooth manifolds including singular spaces and infinite - dimensional spaces), and the other deleting infinitesimals on Fermat spaces.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	some	some	DET	DT	_	12	det	_	_
8	basic	basic	ADJ	JJ	Degree=Pos	12	amod	_	_
9	quasi	quasi	ADJ	JJ	Degree=Pos	12	amod	_	_
10	-	-	NOUN	NNS	Number=Plur	12	amod	_	_
11	topos	topos	ADJ	JJ	Degree=Pos	12	compound	_	_
12	theory	theory	NOUN	NN	Number=Sing	6	dobj	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	study	study	VERB	VB	VerbForm=Inf	6	xcomp	_	_
15	two	two	NUM	CD	NumType=Card	16	nummod	_	_
16	functors	functor	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
17	:	:	PUNCT	:	_	16	punct	_	_
18	one	one	NUM	CD	NumType=Card	19	nummod	_	_
19	adding	add	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	conj	_	_
20	infinitesimals	infinitesimal	NOUN	NNS	Number=Plur	19	dobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	Fermat	Fermat	PROPN	NNP	Number=Sing	23	amod	_	_
23	reals	real	NOUN	NNS	Number=Plur	21	pobj	_	_
24	to	to	ADP	IN	_	20	prep	_	_
25	diffeological	diffeological	ADJ	JJ	Degree=Pos	26	amod	_	_
26	spaces	space	NOUN	NNS	Number=Plur	24	pobj	_	_
27	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	26	punct	_	SpaceAfter=No
28	which	which	PRON	WDT	_	29	nsubj	_	_
29	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	26	relcl	_	_
30	smooth	smooth	ADJ	JJ	Degree=Pos	31	amod	_	_
31	manifolds	manifold	NOUN	NNS	Number=Plur	29	dobj	_	_
32	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	31	prep	_	_
33	singular	singular	ADJ	JJ	Degree=Pos	34	amod	_	_
34	spaces	space	NOUN	NNS	Number=Plur	32	pobj	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	34	cc	_	_
36	infinite	infinite	ADJ	JJ	Degree=Pos	38	amod	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	38	punct	_	_
38	dimensional	dimensional	ADJ	JJ	Degree=Pos	39	amod	_	_
39	spaces	space	NOUN	NNS	Number=Plur	34	conj	_	SpaceAfter=No
40	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	26	punct	_	SpaceAfter=No
41	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
42	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
43	the	the	DET	DT	Definite=Def|PronType=Art	46	det	_	_
44	other	other	ADJ	JJ	Degree=Pos	46	amod	_	_
45	deleting	delete	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	46	amod	_	_
46	infinitesimals	infinitesimal	NOUN	NNS	Number=Plur	19	conj	_	_
47	on	on	ADP	IN	_	46	prep	_	_
48	Fermat	Fermat	PROPN	NNP	Number=Sing	49	compound	_	_
49	spaces	space	NOUN	NNS	Number=Plur	47	pobj	_	SpaceAfter=No
50	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = We study the properties of these functors, and calculate some examples.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	properties	property	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	these	these	DET	DT	Number=Plur|PronType=Dem	7	det	_	_
7	functors	functor	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
10	calculate	calculate	VERB	VB	VerbForm=Inf	2	conj	_	_
11	some	some	DET	DT	_	12	det	_	_
12	examples	example	NOUN	NNS	Number=Plur	10	dobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = These serve as fundamentals for developing differential geometry on diffeological spaces using infinitesimals in a future paper.
1	These	these	PRON	DT	Number=Plur|PronType=Dem	2	nsubj	_	_
2	serve	serve	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	as	as	ADP	IN	_	2	prep	_	_
4	fundamentals	fundamental	NOUN	NNS	Number=Plur	3	pobj	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	developing	develop	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	differential	differential	ADJ	JJ	Degree=Pos	8	amod	_	_
8	geometry	geometry	NOUN	NN	Number=Sing	6	dobj	_	_
9	on	on	ADP	IN	_	6	prep	_	_
10	diffeological	diffeological	ADJ	JJ	Degree=Pos	11	amod	_	_
11	spaces	space	NOUN	NNS	Number=Plur	9	pobj	_	_
12	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	acl	_	_
13	infinitesimals	infinitesimal	NOUN	NNS	Number=Plur	12	dobj	_	_
14	in	in	ADP	IN	_	12	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	future	future	ADJ	JJ	Degree=Pos	17	amod	_	_
17	paper	paper	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 577
# sent_id = 1
# text = We give a direct proof that the category of strict $ omega $ - categories is monadic over the category of polygraphs.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	direct	direct	ADJ	JJ	Degree=Pos	5	amod	_	_
5	proof	proof	NOUN	NN	Number=Sing	2	dobj	_	_
6	that	that	SCONJ	IN	_	14	mark	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	14	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	strict	strict	ADJ	JJ	Degree=Pos	13	amod	_	_
11	$ omega $	$ omega $	SYM	$	_	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	acl	_	_
15	monadic	monadic	ADJ	JJ	Degree=Pos	14	acomp	_	_
16	over	over	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	category	category	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	polygraphs	polygraphs	PROPN	NNP	Number=Sing	19	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 578
# sent_id = 1
# text = A compact closed bicategory is a symmetric monoidal bicategory where every object is equipped with a weak dual.
1	A	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
2	compact	compact	ADJ	JJ	Degree=Pos	3	advmod	_	_
3	closed	closed	ADJ	JJ	Degree=Pos	4	amod	_	_
4	bicategory	bicategory	NOUN	NN	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	symmetric	symmetric	ADJ	JJ	Degree=Pos	9	amod	_	_
8	monoidal	monoidal	ADJ	JJ	Degree=Pos	9	amod	_	_
9	bicategory	bicategory	NOUN	NN	Number=Sing	5	attr	_	_
10	where	where	SCONJ	WRB	_	14	advmod	_	_
11	every	every	DET	DT	_	12	det	_	_
12	object	object	NOUN	NN	Number=Sing	14	nsubjpass	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	relcl	_	_
15	with	with	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	weak	weak	ADJ	JJ	Degree=Pos	18	amod	_	_
18	dual	dual	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = The unit and counit satisfy the usual ``zig - zag'' identities of a compact closed category only up to natural isomorphism, and the isomorphism is subject to a coherence law.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	unit	unit	NOUN	NN	Number=Sing	5	nsubj	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	counit	counit	PROPN	NNP	Number=Sing	2	conj	_	_
5	satisfy	satisfy	PROPN	NNP	Number=Sing	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
7	usual	usual	ADJ	JJ	Degree=Pos	14	amod	_	_
8	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	12	punct	_	SpaceAfter=No
9	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	12	punct	_	SpaceAfter=No
10	zig	zig	VERB	VB	VerbForm=Inf	12	compound	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	zag	zag	NOUN	NN	Number=Sing	7	nmod	_	SpaceAfter=No
13	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	14	punct	_	_
14	identities	identity	NOUN	NNS	Number=Plur	5	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
17	compact	compact	ADJ	JJ	Degree=Pos	18	advmod	_	_
18	closed	closed	ADJ	JJ	Degree=Pos	19	amod	_	_
19	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
20	only	only	ADV	RB	_	21	advmod	_	_
21	up	up	ADP	IN	_	5	prep	_	_
22	to	to	ADP	IN	_	21	prep	_	_
23	natural	natural	ADJ	JJ	Degree=Pos	24	amod	_	_
24	isomorphism	isomorphism	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	isomorphism	isomorphism	NOUN	NN	Number=Sing	29	nsubj	_	_
29	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	conj	_	_
30	subject	subject	ADJ	JJ	Degree=Pos	29	acomp	_	_
31	to	to	ADP	IN	_	30	prep	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
33	coherence	coherence	NOUN	NN	Number=Sing	34	compound	_	_
34	law	law	NOUN	NN	Number=Sing	31	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	29	punct	_	SpaceAfter=No

# sent_id = 3
# text = We give several examples of compact closed bicategories, then review previous work.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	several	several	ADJ	JJ	Degree=Pos	4	amod	_	_
4	examples	example	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	compact	compact	ADJ	JJ	Degree=Pos	8	amod	_	_
7	closed	closed	ADJ	JJ	Degree=Pos	8	amod	_	_
8	bicategories	bicategorie	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
10	then	then	ADV	RB	PronType=Dem	11	advmod	_	_
11	review	review	VERB	VB	VerbForm=Inf	2	conj	_	_
12	previous	previous	ADJ	JJ	Degree=Pos	13	amod	_	_
13	work	work	NOUN	NN	Number=Sing	11	dobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = In particular, Day and Street defined compact closed bicategories indirectly via Gray monoids and then appealed to a coherence theorem to extend the concept to bicategories; we restate the definition directly.
1	In	in	ADP	IN	_	7	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
4	Day	Day	PROPN	NNP	Number=Sing	3	nmod	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	Street	Street	PROPN	NNP	Number=Sing	4	conj	_	_
7	defined	define	VERB	VBD	Tense=Past|VerbForm=Fin	30	ccomp	_	_
8	compact	compact	ADJ	JJ	Degree=Pos	10	amod	_	_
9	closed	closed	ADJ	JJ	Degree=Pos	10	amod	_	_
10	bicategories	bicategorie	NOUN	NNS	Number=Plur	7	dobj	_	_
11	indirectly	indirectly	ADV	RB	_	7	advmod	_	_
12	via	via	ADP	IN	_	7	prep	_	_
13	Gray	Gray	PROPN	NNP	Number=Sing	14	compound	_	_
14	monoids	monoid	NOUN	NNS	Number=Plur	12	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
16	then	then	ADV	RB	PronType=Dem	17	advmod	_	_
17	appealed	appeal	VERB	VBD	Tense=Past|VerbForm=Fin	7	conj	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	coherence	coherence	NOUN	NN	Number=Sing	18	pobj	_	_
21	theorem	theorem	ADJ	JJ	Degree=Pos	17	ccomp	_	_
22	to	to	PART	TO	_	23	aux	_	_
23	extend	extend	VERB	VB	VerbForm=Inf	21	xcomp	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	concept	concept	NOUN	NN	Number=Sing	23	dobj	_	_
26	to	to	ADP	IN	_	23	prep	_	_
27	bicategories	bicategorie	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
28	;	;	PUNCT	:	_	30	punct	_	_
29	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	30	nsubj	_	_
30	restate	restate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	definition	definition	NOUN	NN	Number=Sing	30	dobj	_	_
33	directly	directly	ADV	RB	_	30	advmod	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	30	punct	_	SpaceAfter=No

# sent_id = 5
# text = We prove that given a 2 - category $ T $ with finite products and weak pullbacks, the bicategory of objects of $ C $ , spans, and isomorphism classes of maps of spans is compact closed.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	33	mark	_	_
4	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
6	2	2	NUM	CD	NumType=Card	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	category	category	NOUN	NN	Number=Sing	9	compound	_	_
9	$ T $	$ t $	SYM	$	_	4	pobj	_	_
10	with	with	ADP	IN	_	4	prep	_	_
11	finite	finite	ADJ	JJ	Degree=Pos	12	amod	_	_
12	products	product	NOUN	NNS	Number=Plur	10	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	weak	weak	ADJ	JJ	Degree=Pos	15	amod	_	_
15	pullbacks	pullback	NOUN	NNS	Number=Plur	12	conj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	bicategory	bicategory	NOUN	NN	Number=Sing	33	nsubj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	objects	object	NOUN	NNS	Number=Plur	19	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	$ C $	$ c $	SYM	$	_	21	pobj	_	_
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	spans	span	NOUN	NNS	Number=Plur	22	conj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
27	isomorphism	isomorphism	NOUN	NN	Number=Sing	28	compound	_	_
28	classes	class	NOUN	NNS	Number=Plur	24	conj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	maps	map	NOUN	NNS	Number=Plur	29	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	spans	span	NOUN	NNS	Number=Plur	31	pobj	_	_
33	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
34	compact	compact	ADJ	JJ	Degree=Pos	35	advmod	_	_
35	closed	closed	ADJ	JJ	Degree=Pos	33	acomp	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = As corollaries, the bicategory of spans of sets and certain bicategories of ``resistor networks'' are compact closed.
1	As	as	ADP	IN	_	19	prep	_	_
2	corollaries	corollary	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	bicategory	bicategory	NOUN	NN	Number=Sing	19	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	spans	span	NOUN	NNS	Number=Plur	6	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	sets	set	NOUN	NNS	Number=Plur	8	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
11	certain	certain	ADJ	JJ	Degree=Pos	12	amod	_	_
12	bicategories	bicategorie	NOUN	NNS	Number=Plur	5	conj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	17	punct	_	SpaceAfter=No
15	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	17	punct	_	SpaceAfter=No
16	resistor	resistor	NOUN	NN	Number=Sing	17	compound	_	_
17	networks	network	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
18	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	17	punct	_	_
19	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	compact	compact	ADJ	JJ	Degree=Pos	21	advmod	_	_
21	closed	closed	ADJ	JJ	Degree=Pos	19	acomp	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# doc_id = 579
# sent_id = 1
# text = We develop a homotopy theory of categories enriched in a monoidal model category $ V $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	homotopy	homotopy	NOUN	NN	Number=Sing	5	compound	_	_
5	theory	theory	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
8	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	acl	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	monoidal	monoidal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	model	model	NOUN	NN	Number=Sing	9	pobj	_	_
13	category	category	NOUN	NN	Number=Sing	2	prep	_	_
14	$ V $	$ v $	SYM	$	_	2	dep	_	_
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In particular, we deal with homotopy weighted limits and colimits, and homotopy local presentability.
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	deal	deal	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	with	with	ADP	IN	_	5	prep	_	_
7	homotopy	homotopy	PROPN	NNP	Number=Sing	6	pobj	_	_
8	weighted	weight	VERB	VBD	Tense=Past|VerbForm=Fin	5	conj	_	_
9	limits	limit	NOUN	NNS	Number=Plur	8	dobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	colimits	colimit	NOUN	NNS	Number=Plur	9	conj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
14	homotopy	homotopy	VERB	VB	VerbForm=Inf	8	conj	_	_
15	local	local	ADJ	JJ	Degree=Pos	16	amod	_	_
16	presentability	presentability	NOUN	NN	Number=Sing	14	dobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = The main result, which was known for simplicially - enriched categories, links homotopy locally presentable $ V $ - categories with combinatorial model $ V $ - categories, in the case where all objects of $ V $ are cofibrant.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	result	result	NOUN	NN	Number=Sing	15	nsubj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	which	which	PRON	WDT	_	7	nsubjpass	_	_
6	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	7	auxpass	_	_
7	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	relcl	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	simplicially	simplicially	ADV	RB	_	11	advmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
12	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
14	links	link	NOUN	NNS	Number=Plur	15	nsubj	_	_
15	homotopy	homotopy	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	locally	locally	ADV	RB	_	17	advmod	_	_
17	presentable	presentable	ADJ	JJ	Degree=Pos	20	amod	_	_
18	$ V $	$ v $	SYM	$	_	20	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	categories	category	NOUN	NNS	Number=Plur	15	dobj	_	_
21	with	with	ADP	IN	_	15	prep	_	_
22	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	23	amod	_	_
23	model	model	NOUN	NN	Number=Sing	21	pobj	_	_
24	$ V $	$ v $	SYM	$	_	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	categories	category	NOUN	NNS	Number=Plur	23	appos	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
28	in	in	ADP	IN	_	15	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	case	case	NOUN	NN	Number=Sing	28	pobj	_	_
31	where	where	SCONJ	WRB	_	36	advmod	_	_
32	all	all	DET	DT	_	33	det	_	_
33	objects	object	NOUN	NNS	Number=Plur	36	nsubj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	$ V $	$ v $	SYM	$	_	34	pobj	_	_
36	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	30	relcl	_	_
37	cofibrant	cofibrant	NOUN	NN	Number=Sing	36	attr	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# doc_id = 580
# sent_id = 1
# text = The Joyal model structure on simplicial sets is extended to a model structure on the simplicial presheaves on a small site, in which the cofibrations are monomorphisms and the weak equivalences are local (or stalkwise) Joyal equivalences.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	Joyal	Joyal	PROPN	NNP	Number=Sing	4	amod	_	_
3	model	model	NOUN	NN	Number=Sing	4	compound	_	_
4	structure	structure	NOUN	NN	Number=Sing	9	nsubjpass	_	_
5	on	on	ADP	IN	_	4	prep	_	_
6	simplicial	simplicial	ADJ	JJ	Degree=Pos	7	amod	_	_
7	sets	set	NOUN	NNS	Number=Plur	5	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	model	model	NOUN	NN	Number=Sing	13	compound	_	_
13	structure	structure	NOUN	NN	Number=Sing	10	pobj	_	_
14	on	on	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	simplicial	simplicial	ADJ	JJ	Degree=Pos	17	amod	_	_
17	presheaves	presheave	NOUN	NNS	Number=Plur	14	pobj	_	_
18	on	on	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	small	small	ADJ	JJ	Degree=Pos	21	amod	_	_
21	site	site	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	in	in	ADP	IN	_	27	prep	_	_
24	which	which	PRON	WDT	_	23	pobj	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	cofibrations	cofibration	NOUN	NNS	Number=Plur	27	nsubj	_	_
27	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	21	relcl	_	_
28	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	27	attr	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	weak	weak	ADJ	JJ	Degree=Pos	32	amod	_	_
32	equivalences	equivalence	NOUN	NNS	Number=Plur	33	nsubj	_	_
33	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	conj	_	_
34	local	local	ADJ	JJ	Degree=Pos	40	amod	_	_
35	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	34	punct	_	SpaceAfter=No
36	or	or	CCONJ	CC	ConjType=Cmp	34	cc	_	_
37	stalkwise	stalkwise	ADJ	JJ	Degree=Pos	34	conj	_	SpaceAfter=No
38	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	40	punct	_	_
39	Joyal	joyal	ADJ	JJ	Degree=Pos	40	amod	_	_
40	equivalences	equivalence	NOUN	NNS	Number=Plur	33	attr	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	33	punct	_	SpaceAfter=No

# sent_id = 2
# text = The model structure is shown to be left proper.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	model	model	NOUN	NN	Number=Sing	3	compound	_	_
3	structure	structure	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	to	to	PART	TO	_	8	aux	_	_
7	be	be	AUX	VB	VerbForm=Inf	8	auxpass	_	_
8	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	xcomp	_	_
9	proper	proper	ADJ	JJ	Degree=Pos	8	oprd	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 581
# sent_id = 1
# text = We show that in any symmetric monoidal category, if a weight for colimits is absolute, then the resulting colimit of any diagram of dualizable objects is again dualizable.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	28	mark	_	_
4	in	in	ADP	IN	_	28	prep	_	_
5	any	any	DET	DT	_	8	det	_	_
6	symmetric	symmetric	ADJ	JJ	Degree=Pos	8	amod	_	_
7	monoidal	monoidal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
10	if	if	SCONJ	IN	_	15	mark	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	weight	weight	NOUN	NN	Number=Sing	15	nsubj	_	_
13	for	for	ADP	IN	_	12	prep	_	_
14	colimits	colimit	NOUN	NNS	Number=Plur	13	pobj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	28	advcl	_	_
16	absolute	absolute	ADJ	JJ	Degree=Pos	15	acomp	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
18	then	then	ADV	RB	PronType=Dem	28	advmod	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	21	amod	_	_
21	colimit	colimit	NOUN	NN	Number=Sing	28	nsubj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	any	any	DET	DT	_	24	det	_	_
24	diagram	diagram	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	dualizable	dualizable	ADJ	JJ	Degree=Pos	27	amod	_	_
27	objects	object	NOUN	NNS	Number=Plur	25	pobj	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
29	again	again	ADV	RB	_	30	advmod	_	_
30	dualizable	dualizable	ADJ	JJ	Degree=Pos	28	acomp	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Moreover, in this case, if an endomorphism of the colimit is induced by an endomorphism of the diagram, then its trace can be calculated as a linear combination of traces on the objects in the diagram.
1	Moreover	moreover	ADV	RB	_	27	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
3	in	in	ADP	IN	_	27	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	case	case	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
7	if	if	SCONJ	IN	_	14	mark	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	endomorphism	endomorphism	NOUN	NN	Number=Sing	14	nsubjpass	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	colimit	colimit	NOUN	NN	Number=Sing	10	pobj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	advcl	_	_
15	by	by	ADP	IN	_	14	agent	_	_
16	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	endomorphism	endomorphism	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	diagram	diagram	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
22	then	then	ADV	RB	PronType=Dem	27	advmod	_	_
23	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	24	poss	_	_
24	trace	trace	NOUN	NN	Number=Sing	27	nsubjpass	_	_
25	can	can	AUX	MD	VerbForm=Fin	27	aux	_	_
26	be	be	AUX	VB	VerbForm=Inf	27	auxpass	_	_
27	calculated	calculate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
28	as	as	ADP	IN	_	27	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	linear	linear	ADJ	JJ	Degree=Pos	31	amod	_	_
31	combination	combination	NOUN	NN	Number=Sing	28	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	traces	trace	NOUN	NNS	Number=Plur	32	pobj	_	_
34	on	on	ADP	IN	_	33	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	objects	object	NOUN	NNS	Number=Plur	34	pobj	_	_
37	in	in	ADP	IN	_	36	prep	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
39	diagram	diagram	NOUN	NN	Number=Sing	37	pobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	27	punct	_	SpaceAfter=No

# sent_id = 3
# text = The formal nature of this result makes it easy to generalize to traces in homotopical contexts (using derivators) and traces in bicategories.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	formal	formal	ADJ	JJ	Degree=Pos	3	amod	_	_
3	nature	nature	NOUN	NN	Number=Sing	7	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	result	result	NOUN	NN	Number=Sing	4	pobj	_	_
7	makes	make	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	9	nsubj	_	_
9	easy	easy	ADJ	JJ	Degree=Pos	7	ccomp	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	generalize	generalize	VERB	VB	VerbForm=Inf	9	xcomp	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	traces	trace	NOUN	NNS	Number=Plur	12	pobj	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	homotopical	homotopical	ADJ	JJ	Degree=Pos	16	amod	_	_
16	contexts	context	NOUN	NNS	Number=Plur	14	pobj	_	_
17	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	18	punct	_	SpaceAfter=No
18	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	advcl	_	_
19	derivators	derivator	NOUN	NNS	Number=Plur	18	dobj	_	SpaceAfter=No
20	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	18	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
22	traces	trace	NOUN	NNS	Number=Plur	18	conj	_	_
23	in	in	ADP	IN	_	22	prep	_	_
24	bicategories	bicategorie	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = These generalizations include the familiar additivity of the Euler characteristic and Lefschetz number along cofiber sequences, as well as an analogous result for the Reidemeister trace, but also the orbit - counting theorem for sets with a group action, and a general formula for homotopy colimits over $ EI $ - categories.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	generalizations	generalization	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	familiar	familiar	ADJ	JJ	Degree=Pos	6	amod	_	_
6	additivity	additivity	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	Euler	Euler	PROPN	NNP	Number=Sing	10	compound	_	_
10	characteristic	characteristic	ADJ	JJ	Degree=Pos	7	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
12	Lefschetz	lefschetz	ADJ	JJ	Degree=Pos	13	amod	_	_
13	number	number	NOUN	NN	Number=Sing	6	conj	_	_
14	along	along	ADP	IN	_	13	prep	_	_
15	cofiber	cofiber	NOUN	NN	Number=Sing	16	compound	_	_
16	sequences	sequence	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
18	as	as	ADV	RB	_	20	advmod	_	_
19	well	well	ADV	RB	Degree=Pos	20	advmod	_	_
20	as	as	ADP	IN	_	13	cc	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	analogous	analogous	ADJ	JJ	Degree=Pos	23	amod	_	_
23	result	result	NOUN	NN	Number=Sing	13	conj	_	_
24	for	for	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	Reidemeister	Reidemeister	PROPN	NNP	Number=Sing	27	compound	_	_
27	trace	trace	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
29	but	but	CCONJ	CC	ConjType=Cmp	13	cc	_	_
30	also	also	ADV	RB	_	29	advmod	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
32	orbit	orbit	NOUN	NN	Number=Sing	34	compound	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	counting	counting	NOUN	NN	Number=Sing	35	compound	_	_
35	theorem	theorem	NOUN	NN	Number=Sing	13	conj	_	_
36	for	for	ADP	IN	_	35	prep	_	_
37	sets	set	NOUN	NNS	Number=Plur	36	pobj	_	_
38	with	with	ADP	IN	_	37	prep	_	_
39	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
40	group	group	NOUN	NN	Number=Sing	41	compound	_	_
41	action	action	NOUN	NN	Number=Sing	38	pobj	_	SpaceAfter=No
42	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
43	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
44	a	a	DET	DT	Definite=Ind|PronType=Art	46	det	_	_
45	general	general	ADJ	JJ	Degree=Pos	46	amod	_	_
46	formula	formula	NOUN	NN	Number=Sing	35	conj	_	_
47	for	for	ADP	IN	_	46	prep	_	_
48	homotopy	homotopy	NOUN	NN	Number=Sing	49	compound	_	_
49	colimits	colimit	NOUN	NNS	Number=Plur	47	pobj	_	_
50	over	over	ADP	IN	_	49	prep	_	_
51	$ EI $	$ ei $	SYM	$	_	53	compound	_	_
52	-	-	PUNCT	HYPH	PunctType=Dash	53	punct	_	_
53	categories	category	NOUN	NNS	Number=Plur	50	pobj	_	SpaceAfter=No
54	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 582
# sent_id = 1
# text = We show that every abstract Krivine structure in the sense of Streicher can be obtained, up to equivalence of the resulting tripos, from a filtered opca $ (A, A') $ and a subobject of 1 in the relative realizability topos $ RT(A', A) $ ; the topos is always a Boolean subtopos of $ RT(A', A) $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	44	ccomp	_	_
3	that	that	SCONJ	IN	_	15	mark	_	_
4	every	every	DET	DT	_	7	det	_	_
5	abstract	abstract	ADJ	JJ	Degree=Pos	7	amod	_	_
6	Krivine	Krivine	PROPN	NNP	Number=Sing	7	compound	_	_
7	structure	structure	NOUN	NN	Number=Sing	15	nsubjpass	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	sense	sense	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	Streicher	Streicher	PROPN	NNP	Number=Sing	11	pobj	_	_
13	can	can	AUX	MD	VerbForm=Fin	15	aux	_	_
14	be	be	AUX	VB	VerbForm=Inf	15	auxpass	_	_
15	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	up	up	ADP	IN	_	15	prep	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	equivalence	equivalence	NOUN	NN	Number=Sing	18	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	23	amod	_	_
23	tripos	tripo	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
25	from	from	ADP	IN	_	15	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
27	filtered	filter	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	amod	_	_
28	opca	opca	NOUN	NN	Number=Sing	25	pobj	_	_
29	$ (A, A') $	$ (a, a') $	SYM	$	_	28	appos	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
32	subobject	subobject	NOUN	NN	Number=Sing	29	conj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	1	1	NUM	CD	NumType=Card	33	pobj	_	_
35	in	in	ADP	IN	_	29	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
37	relative	relative	ADJ	JJ	Degree=Pos	38	amod	_	_
38	realizability	realizability	NOUN	NN	Number=Sing	35	pobj	_	_
39	topos	topos	NOUN	NN	Number=Sing	29	appos	_	_
40	$ RT(A', A) $	$ rt(a', a) $	SYM	$	_	28	conj	_	_
41	;	;	PUNCT	:	_	44	punct	_	_
42	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
43	topos	topos	NOUN	NN	Number=Sing	44	nsubj	_	_
44	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
45	always	always	ADV	RB	_	44	advmod	_	_
46	a	a	DET	DT	Definite=Ind|PronType=Art	48	det	_	_
47	Boolean	boolean	ADJ	JJ	Degree=Pos	48	amod	_	_
48	subtopos	subtopos	NOUN	NN	Number=Sing	44	attr	_	_
49	of	of	ADP	IN	_	48	prep	_	_
50	$ RT(A', A) $	$ rt(a', a) $	SYM	$	_	49	pobj	_	_
51	.	.	PUNCT	.	PunctType=Peri	44	punct	_	SpaceAfter=No

# sent_id = 2
# text = We exhibit a range of non - localic Boolean subtriposes of the Kleene - Vesley tripos.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	exhibit	exhibit	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	range	range	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	non	non	ADJ	JJ	Degree=Pos	10	amod	_	_
7	-	-	ADJ	JJ	Degree=Pos	10	amod	_	_
8	localic	localic	ADJ	JJ	Degree=Pos	10	amod	_	_
9	Boolean	Boolean	PROPN	NNP	Number=Sing	10	amod	_	_
10	subtriposes	subtripose	NOUN	NNS	Number=Plur	5	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
13	Kleene	Kleene	PROPN	NNP	Number=Sing	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	Vesley	Vesley	PROPN	NNP	Number=Sing	16	compound	_	_
16	tripos	tripos	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 583
# sent_id = 1
# text = We study the gerbal representations of a finite group $ G $ or, equivalently, module categories over Ostrik's category $ Vec_G^alpha $ for a 3 - cocycle $ alpha $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	gerbal	gerbal	ADJ	JJ	Degree=Pos	5	amod	_	_
5	representations	representation	NOUN	NNS	Number=Plur	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	finite	finite	ADJ	JJ	Degree=Pos	9	compound	_	_
9	group	group	NOUN	NN	Number=Sing	6	pobj	_	_
10	$ G $	$ g $	SYM	$	_	9	appos	_	_
11	or	or	CCONJ	CC	ConjType=Cmp	5	cc	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
13	equivalently	equivalently	ADV	RB	_	2	advmod	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
15	module	module	NOUN	NN	Number=Sing	16	compound	_	_
16	categories	category	NOUN	NNS	Number=Plur	2	dep	_	_
17	over	over	ADP	IN	_	16	prep	_	_
18	Ostrik	Ostrik	PROPN	NNP	Number=Sing	20	poss	_	SpaceAfter=No
19	's	's	PART	POS	_	18	case	_	_
20	category	category	NOUN	NN	Number=Sing	17	pobj	_	_
21	$ Vec_G^alpha $	$ vec_g^alpha $	SYM	$	_	16	appos	_	_
22	for	for	ADP	IN	_	16	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
24	3	3	NUM	CD	NumType=Card	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	cocycle	cocycle	NOUN	NN	Number=Sing	27	compound	_	_
27	$ alpha $	$ alpha $	SYM	$	_	22	pobj	_	_
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We adapt Bartlett's string diagram formalism to this situation to prove that the categorical character of a gerbal representation is a representation of the inertia groupoid of a categorical group.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	adapt	adapt	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	Bartlett	Bartlett	PROPN	NNP	Number=Sing	7	poss	_	SpaceAfter=No
4	's	's	PART	POS	_	3	case	_	_
5	string	string	NOUN	NN	Number=Sing	6	compound	_	_
6	diagram	diagram	NOUN	NN	Number=Sing	7	compound	_	_
7	formalism	formalism	NOUN	NN	Number=Sing	2	dobj	_	_
8	to	to	ADP	IN	_	2	prep	_	_
9	this	this	DET	DT	Number=Sing|PronType=Dem	10	det	_	_
10	situation	situation	NOUN	NN	Number=Sing	8	pobj	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	prove	prove	VERB	VB	VerbForm=Inf	2	advcl	_	_
13	that	that	SCONJ	IN	_	21	mark	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	categorical	categorical	ADJ	JJ	Degree=Pos	16	amod	_	_
16	character	character	NOUN	NN	Number=Sing	21	nsubj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	gerbal	gerbal	ADJ	JJ	Degree=Pos	20	amod	_	_
20	representation	representation	NOUN	NN	Number=Sing	17	pobj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	ccomp	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
23	representation	representation	NOUN	NN	Number=Sing	21	attr	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	inertia	inertia	NOUN	NN	Number=Sing	27	compound	_	_
27	groupoid	groupoid	NOUN	NN	Number=Sing	24	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	categorical	categorical	ADJ	JJ	Degree=Pos	31	amod	_	_
31	group	group	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We interpret such a representation as a module over the twisted Drinfeld double $ D^alpha(G) $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	interpret	interpret	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	such	such	DET	PDT	_	5	predet	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	representation	representation	NOUN	NN	Number=Sing	2	dobj	_	_
6	as	as	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	module	module	NOUN	NN	Number=Sing	6	pobj	_	_
9	over	over	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	twisted	twisted	ADJ	JJ	Degree=Pos	12	amod	_	_
12	Drinfeld	Drinfeld	PROPN	NNP	Number=Sing	9	pobj	_	_
13	double	double	DET	PDT	_	14	amod	_	_
14	$ D^alpha(G) $	$ d^alpha(g) $	SYM	$	_	2	dobj	_	_
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 584
# sent_id = 1
# text = We define a notion of morphism for quotient vector bundles that yields both a category $ QVBun $ and a contravariant global sections functor $ C:QVBun^{op} to Vect $ whose restriction to trivial vector bundles with fiber $ F $ coincides with the contravariant functor $ Top^{op} to Vect $ of $ F $ - valued continuous functions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	morphism	morphism	NOUN	NN	Number=Sing	5	pobj	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	quotient	quotient	ADJ	JJ	Degree=Pos	10	amod	_	_
9	vector	vector	NOUN	NN	Number=Sing	10	compound	_	_
10	bundles	bundle	NOUN	NNS	Number=Plur	7	pobj	_	_
11	that	that	PRON	WDT	PronType=Rel	12	nsubj	_	_
12	yields	yield	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	relcl	_	_
13	both	both	CCONJ	CC	ConjType=Cmp	15	preconj	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	category	category	NOUN	NN	Number=Sing	12	dobj	_	_
16	$ QVBun $	$ qvbun $	SYM	$	_	15	appos	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
19	contravariant	contravariant	ADJ	JJ	Degree=Pos	21	amod	_	_
20	global	global	ADJ	JJ	Degree=Pos	21	amod	_	_
21	sections	section	NOUN	NNS	Number=Plur	15	conj	_	_
22	functor	functor	VERB	VBP	Tense=Pres|VerbForm=Fin	15	appos	_	_
23	$ C:QVBun^{op} to Vect $	$ c:qvbun^{op} to vect $	SYM	$	_	12	dep	_	_
24	whose	whose	DET	WP$	Poss=Yes	25	poss	_	_
25	restriction	restriction	NOUN	NN	Number=Sing	12	dobj	_	_
26	to	to	ADP	IN	_	25	prep	_	_
27	trivial	trivial	ADJ	JJ	Degree=Pos	29	amod	_	_
28	vector	vector	NOUN	NN	Number=Sing	29	compound	_	_
29	bundles	bundle	NOUN	NNS	Number=Plur	26	pobj	_	_
30	with	with	ADP	IN	_	25	prep	_	_
31	fiber	fiber	NOUN	NN	Number=Sing	30	pobj	_	_
32	$ F $	$ f $	SYM	$	_	33	nmod	_	_
33	coincides	coincide	NOUN	NNS	Number=Plur	12	dobj	_	_
34	with	with	ADP	IN	_	12	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
36	contravariant	contravariant	ADJ	JJ	Degree=Pos	37	amod	_	_
37	functor	functor	NOUN	NN	Number=Sing	34	pobj	_	_
38	$ Top^{op} to Vect $	$ top^{op} to vect $	SYM	$	_	37	appos	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	$ F $	$ f $	SYM	$	_	42	advmod	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	44	amod	_	_
43	continuous	continuous	ADJ	JJ	Degree=Pos	44	amod	_	_
44	functions	function	NOUN	NNS	Number=Plur	39	pobj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Based on this we obtain a linear extension of the adjunction between the categories of topological spaces and locales: (i) a linearized topological space is a spectral vector bundle, by which is meant a mildly restricted type of quotient vector bundle; (ii) a linearized locale is a locale $ Delta $ equipped with both a topological vector space $ A $ and a $ Delta $ - valued support map for the elements of $ A $ satisfying a continuity condition relative to the spectrum of $ Delta $ and the lower Vietoris topology on $ Sub A $ ; (iii) we obtain an adjunction between the full subcategory of spectral vector bundles $ QVBun_Sigma $ and the category of linearized locales $ LinLoc $ , which restricts to an equivalence of categories between sober spectral vector bundles and spatial linearized locales.
1	Based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	prep	_	_
2	on	on	ADP	IN	_	1	prep	_	_
3	this	this	PRON	DT	Number=Sing|PronType=Dem	2	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	22	ccomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	linear	linear	ADJ	JJ	Degree=Pos	8	amod	_	_
8	extension	extension	NOUN	NN	Number=Sing	5	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	adjunction	adjunction	NOUN	NN	Number=Sing	9	pobj	_	_
12	between	between	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	topological	topological	ADJ	JJ	Degree=Pos	17	amod	_	_
17	spaces	space	NOUN	NNS	Number=Plur	15	pobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	locales	locale	NOUN	NNS	Number=Plur	17	conj	_	SpaceAfter=No
20	:	:	PUNCT	:	_	22	punct	_	_
21	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	22	punct	_	SpaceAfter=No
22	i	i	NOUN	NN	Case=Nom|Number=Sing|Person=1|PronType=Prs	28	nsubj	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	22	punct	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
25	linearized	linearize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	amod	_	_
26	topological	topological	ADJ	JJ	Degree=Pos	27	amod	_	_
27	space	space	NOUN	NN	Number=Sing	28	nsubj	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	53	ccomp	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
30	spectral	spectral	ADJ	JJ	Degree=Pos	32	amod	_	_
31	vector	vector	NOUN	NN	Number=Sing	32	compound	_	_
32	bundle	bundle	NOUN	NN	Number=Sing	28	attr	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
34	by	by	ADP	IN	_	37	prep	_	_
35	which	which	PRON	WDT	_	34	pobj	_	_
36	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	37	auxpass	_	_
37	meant	mean	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	relcl	_	_
38	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
39	mildly	mildly	ADV	RB	_	40	advmod	_	_
40	restricted	restrict	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	41	amod	_	_
41	type	type	NOUN	NN	Number=Sing	37	dobj	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	quotient	quotient	ADJ	JJ	Degree=Pos	45	amod	_	_
44	vector	vector	NOUN	NN	Number=Sing	45	compound	_	_
45	bundle	bundle	NOUN	NN	Number=Sing	42	pobj	_	SpaceAfter=No
46	;	;	PUNCT	:	_	53	punct	_	_
47	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	48	punct	_	SpaceAfter=No
48	ii	ii	PROPN	NNP	Number=Sing	53	dep	_	SpaceAfter=No
49	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	48	punct	_	_
50	a	a	DET	DT	Definite=Ind|PronType=Art	52	det	_	_
51	linearized	linearize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	52	amod	_	_
52	locale	locale	NOUN	NN	Number=Sing	53	nsubj	_	_
53	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
54	a	a	DET	DT	Definite=Ind|PronType=Art	55	det	_	_
55	locale	locale	NOUN	NN	Number=Sing	53	attr	_	_
56	$ Delta $	$ delta $	SYM	$	_	55	appos	_	_
57	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	56	acl	_	_
58	with	with	ADP	IN	_	57	prep	_	_
59	both	both	CCONJ	CC	ConjType=Cmp	63	preconj	_	_
60	a	a	DET	DT	Definite=Ind|PronType=Art	63	det	_	_
61	topological	topological	ADJ	JJ	Degree=Pos	63	amod	_	_
62	vector	vector	NOUN	NN	Number=Sing	63	compound	_	_
63	space	space	NOUN	NN	Number=Sing	58	pobj	_	_
64	$ A $	$ a $	SYM	$	_	63	nummod	_	_
65	and	and	CCONJ	CC	ConjType=Cmp	63	cc	_	_
66	a	a	DET	DT	Definite=Ind|PronType=Art	71	det	_	_
67	$ Delta $	$ delta $	SYM	$	_	69	advmod	_	_
68	-	-	PUNCT	HYPH	PunctType=Dash	69	punct	_	_
69	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	71	amod	_	_
70	support	support	NOUN	NN	Number=Sing	71	compound	_	_
71	map	map	NOUN	NN	Number=Sing	63	conj	_	_
72	for	for	ADP	IN	_	71	prep	_	_
73	the	the	DET	DT	Definite=Def|PronType=Art	74	det	_	_
74	elements	element	NOUN	NNS	Number=Plur	72	pobj	_	_
75	of	of	ADP	IN	_	74	prep	_	_
76	$ A $	$ a $	SYM	$	_	75	pobj	_	_
77	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	53	advcl	_	_
78	a	a	DET	DT	Definite=Ind|PronType=Art	80	det	_	_
79	continuity	continuity	NOUN	NN	Number=Sing	80	compound	_	_
80	condition	condition	NOUN	NN	Number=Sing	77	dobj	_	_
81	relative	relative	ADJ	JJ	Degree=Pos	80	amod	_	_
82	to	to	ADP	IN	_	81	prep	_	_
83	the	the	DET	DT	Definite=Def|PronType=Art	84	det	_	_
84	spectrum	spectrum	NOUN	NN	Number=Sing	82	pobj	_	_
85	of	of	ADP	IN	_	84	prep	_	_
86	$ Delta $	$ delta $	SYM	$	_	85	pobj	_	_
87	and	and	CCONJ	CC	ConjType=Cmp	84	cc	_	_
88	the	the	DET	DT	Definite=Def|PronType=Art	91	det	_	_
89	lower	low	ADJ	JJR	Degree=Cmp	91	amod	_	_
90	Vietoris	Vietoris	PROPN	NNP	Number=Sing	91	compound	_	_
91	topology	topology	NOUN	NN	Number=Sing	84	conj	_	_
92	on	on	ADP	IN	_	91	prep	_	_
93	$ Sub A $	$ sub a $	SYM	$	_	92	pobj	_	_
94	;	;	PUNCT	:	_	99	punct	_	_
95	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	96	punct	_	SpaceAfter=No
96	iii	iii	NOUN	NN	Number=Sing	99	meta	_	SpaceAfter=No
97	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	96	punct	_	_
98	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	99	nsubj	_	_
99	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	53	conj	_	_
100	an	an	DET	DT	Definite=Ind|PronType=Art	101	det	_	_
101	adjunction	adjunction	NOUN	NN	Number=Sing	99	dobj	_	_
102	between	between	ADP	IN	_	101	prep	_	_
103	the	the	DET	DT	Definite=Def|PronType=Art	105	det	_	_
104	full	full	ADJ	JJ	Degree=Pos	105	amod	_	_
105	subcategory	subcategory	NOUN	NN	Number=Sing	102	pobj	_	_
106	of	of	ADP	IN	_	105	prep	_	_
107	spectral	spectral	ADJ	JJ	Degree=Pos	108	amod	_	_
108	vector	vector	NOUN	NN	Number=Sing	109	compound	_	_
109	bundles	bundle	NOUN	NNS	Number=Plur	106	pobj	_	_
110	$ QVBun_Sigma $	$ qvbun_sigma $	SYM	$	_	105	nmod	_	_
111	and	and	CCONJ	CC	ConjType=Cmp	105	cc	_	_
112	the	the	DET	DT	Definite=Def|PronType=Art	113	det	_	_
113	category	category	NOUN	NN	Number=Sing	105	conj	_	_
114	of	of	ADP	IN	_	113	prep	_	_
115	linearized	linearized	ADJ	JJ	Degree=Pos	116	amod	_	_
116	locales	locale	NOUN	NNS	Number=Plur	114	pobj	_	_
117	$ LinLoc $	$ linloc $	SYM	$	_	116	appos	_	_
118	,	,	PUNCT	,	PunctType=Comm	116	punct	_	_
119	which	which	PRON	WDT	_	120	nsubj	_	_
120	restricts	restrict	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	116	relcl	_	_
121	to	to	ADP	IN	_	120	prep	_	_
122	an	an	DET	DT	Definite=Ind|PronType=Art	123	det	_	_
123	equivalence	equivalence	NOUN	NN	Number=Sing	121	pobj	_	_
124	of	of	ADP	IN	_	123	prep	_	_
125	categories	category	NOUN	NNS	Number=Plur	124	pobj	_	_
126	between	between	ADP	IN	_	123	prep	_	_
127	sober	sober	ADJ	JJ	Degree=Pos	130	amod	_	_
128	spectral	spectral	ADJ	JJ	Degree=Pos	129	amod	_	_
129	vector	vector	NOUN	NN	Number=Sing	130	compound	_	_
130	bundles	bundle	NOUN	NNS	Number=Plur	126	pobj	_	_
131	and	and	CCONJ	CC	ConjType=Cmp	130	cc	_	_
132	spatial	spatial	ADJ	JJ	Degree=Pos	134	amod	_	_
133	linearized	linearize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	134	amod	_	_
134	locales	locale	NOUN	NNS	Number=Plur	130	conj	_	SpaceAfter=No
135	.	.	PUNCT	.	PunctType=Peri	99	punct	_	SpaceAfter=No

# sent_id = 3
# text = The spectral vector bundles are classified by a finer topology on $ Sub A $ , called the open support topology, but there is no notion of universal spectral vector bundle for an arbitrary topological vector space $ A $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	spectral	spectral	ADJ	JJ	Degree=Pos	4	amod	_	_
3	vector	vector	NOUN	NN	Number=Sing	4	compound	_	_
4	bundles	bundle	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	classified	classify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	by	by	ADP	IN	_	6	agent	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	finer	finer	ADJ	JJ	Degree=Pos	10	amod	_	_
10	topology	topology	NOUN	NN	Number=Sing	7	pobj	_	_
11	on	on	ADP	IN	_	6	prep	_	_
12	$ Sub A $	$ sub a $	SYM	$	_	11	pobj	_	_
13	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
14	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	6	advcl	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
16	open	open	ADJ	JJ	Degree=Pos	17	amod	_	_
17	support	support	NOUN	NN	Number=Sing	18	compound	_	_
18	topology	topology	NOUN	NN	Number=Sing	14	oprd	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
20	but	but	CCONJ	CC	ConjType=Cmp	6	cc	_	_
21	there	there	PRON	EX	_	22	expl	_	_
22	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	conj	_	_
23	no	no	DET	DT	_	24	det	_	_
24	notion	notion	NOUN	NN	Number=Sing	22	attr	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	universal	universal	ADJ	JJ	Degree=Pos	29	amod	_	_
27	spectral	spectral	ADJ	JJ	Degree=Pos	29	amod	_	_
28	vector	vector	NOUN	NN	Number=Sing	29	compound	_	_
29	bundle	bundle	NOUN	NN	Number=Sing	25	pobj	_	_
30	for	for	ADP	IN	_	29	prep	_	_
31	an	an	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
32	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	35	amod	_	_
33	topological	topological	ADJ	JJ	Degree=Pos	34	amod	_	_
34	vector	vector	NOUN	NN	Number=Sing	35	compound	_	_
35	space	space	NOUN	NN	Number=Sing	30	pobj	_	_
36	$ A $	$ a $	SYM	$	_	25	pobj	_	_
37	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# doc_id = 585
# sent_id = 1
# text = The classical snake lemma produces a six terms exact sequence starting from a commutative square with one of the edge being a regular epimorphism.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	classical	classical	ADJ	JJ	Degree=Pos	4	amod	_	_
3	snake	snake	NOUN	NN	Number=Sing	4	compound	_	_
4	lemma	lemma	NOUN	NN	Number=Sing	5	nsubj	_	_
5	produces	produce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
7	six	six	NUM	CD	NumType=Card	8	nummod	_	_
8	terms	term	NOUN	NNS	Number=Plur	10	nmod	_	_
9	exact	exact	ADJ	JJ	Degree=Pos	10	amod	_	_
10	sequence	sequence	NOUN	NN	Number=Sing	5	dobj	_	_
11	starting	start	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	acl	_	_
12	from	from	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	commutative	commutative	ADJ	JJ	Degree=Pos	15	amod	_	_
15	square	square	NOUN	NN	Number=Sing	12	pobj	_	_
16	with	with	ADP	IN	_	15	prep	_	_
17	one	one	NUM	CD	NumType=Card	16	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	edge	edge	NOUN	NN	Number=Sing	18	pobj	_	_
21	being	be	AUX	VBG	VerbForm=Ger	10	acl	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
23	regular	regular	ADJ	JJ	Degree=Pos	24	amod	_	_
24	epimorphism	epimorphism	NOUN	NN	Number=Sing	21	attr	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = We establish a new diagram lemma, that we call snail lemma, removing such a condition.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	establish	establish	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
4	new	new	ADJ	JJ	Degree=Pos	6	amod	_	_
5	diagram	diagram	NOUN	NN	Number=Sing	6	compound	_	_
6	lemma	lemma	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
8	that	that	SCONJ	IN	_	10	mark	_	_
9	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
10	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	2	advcl	_	_
11	snail	snail	NOUN	NN	Number=Sing	12	compound	_	_
12	lemma	lemma	NOUN	NN	Number=Sing	10	dobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
14	removing	remove	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	advcl	_	_
15	such	such	DET	PDT	_	17	predet	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	condition	condition	NOUN	NN	Number=Sing	14	dobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also show that the snail lemma subsumes the snake lemma and we give an interpretation of the snail lemma in terms of strong homotopy kernels.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	8	mark	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	snail	snail	NOUN	NN	Number=Sing	7	compound	_	_
7	lemma	lemma	NOUN	NN	Number=Sing	8	nsubj	_	_
8	subsumes	subsume	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	snake	snake	NOUN	NN	Number=Sing	11	compound	_	_
11	lemma	lemma	NOUN	NN	Number=Sing	8	dobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	8	conj	_	_
15	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	interpretation	interpretation	NOUN	NN	Number=Sing	14	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	snail	snail	NOUN	NN	Number=Sing	20	compound	_	_
20	lemma	lemma	NOUN	NN	Number=Sing	17	pobj	_	_
21	in	in	ADP	IN	_	14	prep	_	_
22	terms	term	NOUN	NNS	Number=Plur	21	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	strong	strong	ADJ	JJ	Degree=Pos	26	amod	_	_
25	homotopy	homotopy	NOUN	NN	Number=Sing	26	compound	_	_
26	kernels	kernel	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = Our results hold in any pointed regular protomodular category.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	results	result	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	hold	hold	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	in	in	ADP	RP	_	3	prep	_	_
5	any	any	DET	DT	_	9	det	_	_
6	pointed	point	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	amod	_	_
7	regular	regular	ADJ	JJ	Degree=Pos	9	amod	_	_
8	protomodular	protomodular	ADJ	JJ	Degree=Pos	9	amod	_	_
9	category	category	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 586
# sent_id = 1
# text = We show that the morphism axiom for $ n $ - angulated categories is redundant.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	6	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	morphism	morphism	NOUN	NN	Number=Sing	6	nsubj	_	_
6	axiom	axiom	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	$ n $	$ n $	SYM	$	_	10	advmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	angulated	angulate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
11	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
13	redundant	redundant	ADJ	JJ	Degree=Pos	12	acomp	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 587
# sent_id = 1
# text = Model categories have long been a useful tool in homotopy theory, allowing many generalizations of results in topological spaces to other categories.
1	Model	Model	PROPN	NNP	Number=Sing	2	compound	_	_
2	categories	category	NOUN	NNS	Number=Plur	5	nsubj	_	_
3	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	aux	_	_
4	long	long	ADV	RB	_	5	advmod	_	_
5	been	be	AUX	VBN	Tense=Past|VerbForm=Part	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	useful	useful	ADJ	JJ	Degree=Pos	8	amod	_	_
8	tool	tool	NOUN	NN	Number=Sing	5	attr	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	homotopy	homotopy	NOUN	NN	Number=Sing	11	compound	_	_
11	theory	theory	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
13	allowing	allow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	advcl	_	_
14	many	many	ADJ	JJ	Degree=Pos	15	amod	_	_
15	generalizations	generalization	NOUN	NNS	Number=Plur	13	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	results	result	NOUN	NNS	Number=Plur	16	pobj	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	topological	topological	ADJ	JJ	Degree=Pos	20	amod	_	_
20	spaces	space	NOUN	NNS	Number=Plur	18	pobj	_	_
21	to	to	ADP	IN	_	20	prep	_	_
22	other	other	ADJ	JJ	Degree=Pos	23	amod	_	_
23	categories	category	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = Giving a localization of a model category provides an additional model category structure on the same base category, which alters what objects are being considered equivalent by increasing the class of weak equivalences.
1	Giving	give	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	csubj	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	localization	localization	NOUN	NN	Number=Sing	1	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	model	model	NOUN	NN	Number=Sing	7	compound	_	_
7	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
8	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
10	additional	additional	ADJ	JJ	Degree=Pos	13	amod	_	_
11	model	model	NOUN	NN	Number=Sing	13	compound	_	_
12	category	category	NOUN	NN	Number=Sing	13	compound	_	_
13	structure	structure	NOUN	NN	Number=Sing	8	dobj	_	_
14	on	on	ADP	IN	_	8	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
16	same	same	ADJ	JJ	Degree=Pos	18	amod	_	_
17	base	base	NOUN	NN	Number=Sing	18	compound	_	_
18	category	category	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	which	which	PRON	WDT	_	21	nsubj	_	_
21	alters	alter	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	relcl	_	_
22	what	what	PRON	WP	_	23	det	_	_
23	objects	object	NOUN	NNS	Number=Plur	26	nsubjpass	_	_
24	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	26	aux	_	_
25	being	be	AUX	VBG	VerbForm=Ger	26	auxpass	_	_
26	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	ccomp	_	_
27	equivalent	equivalent	ADJ	JJ	Degree=Pos	26	oprd	_	_
28	by	by	ADP	IN	_	27	prep	_	_
29	increasing	increase	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	28	pcomp	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	class	class	NOUN	NN	Number=Sing	29	dobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	weak	weak	ADJ	JJ	Degree=Pos	34	amod	_	_
34	equivalences	equivalence	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 3
# text = In some situations, a model category where the class of weak equivalences is restricted from the original one could be more desirable.
1	In	in	ADP	IN	_	21	prep	_	_
2	some	some	DET	DT	_	3	det	_	_
3	situations	situation	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	model	model	NOUN	NN	Number=Sing	7	compound	_	_
7	category	category	NOUN	NN	Number=Sing	21	nsubj	_	_
8	where	where	SCONJ	WRB	_	15	advmod	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	class	class	NOUN	NN	Number=Sing	15	nsubjpass	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	weak	weak	ADJ	JJ	Degree=Pos	13	amod	_	_
13	equivalences	equivalence	NOUN	NNS	Number=Plur	11	pobj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	restricted	restrict	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	relcl	_	_
16	from	from	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	original	original	ADJ	JJ	Degree=Pos	19	amod	_	_
19	one	one	NOUN	NN	Number=Sing	16	pobj	_	_
20	could	could	AUX	MD	VerbForm=Fin	21	aux	_	_
21	be	be	AUX	VB	VerbForm=Inf	0	ROOT	_	_
22	more	more	ADV	RBR	Degree=Cmp	23	advmod	_	_
23	desirable	desirable	ADJ	JJ	Degree=Pos	21	acomp	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# sent_id = 4
# text = In this situation we need the notion of a delocalization.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	situation	situation	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	need	need	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	notion	notion	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	delocalization	delocalization	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = In this paper, right Bousfield delocalization is defined, we provide examples of right Bousfield delocalization as well as an existence theorem.
1	In	in	ADP	IN	_	9	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
5	right	right	INTJ	UH	_	9	advmod	_	_
6	Bousfield	Bousfield	PROPN	NNP	Number=Sing	7	compound	_	_
7	delocalization	delocalization	NOUN	NN	Number=Sing	9	nsubjpass	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	advcl	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
11	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	12	nsubj	_	_
12	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	examples	example	NOUN	NNS	Number=Plur	12	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	right	right	ADJ	JJ	Degree=Pos	17	amod	_	_
16	Bousfield	Bousfield	PROPN	NNP	Number=Sing	17	compound	_	_
17	delocalization	delocalization	NOUN	NN	Number=Sing	14	pobj	_	_
18	as	as	ADV	RB	_	20	advmod	_	_
19	well	well	ADV	RB	Degree=Pos	20	advmod	_	_
20	as	as	ADP	IN	_	13	cc	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	existence	existence	NOUN	NN	Number=Sing	23	nsubj	_	_
23	theorem	theorem	ADJ	JJ	Degree=Pos	12	ccomp	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 6
# text = In particular, we show that given two model category structures $ MO $ and $ MT $ we can define an additional model category structure $ MO cap MT $ by defining the class of weak equivalences to be the intersection of the $ MO $ and $ MT $ weak equivalences.
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	17	mark	_	_
7	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	prep	_	_
8	two	two	NUM	CD	NumType=Card	10	nummod	_	_
9	model	model	NOUN	NN	Number=Sing	10	compound	_	_
10	category	category	NOUN	NN	Number=Sing	11	compound	_	_
11	structures	structure	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	dative	_	_
12	$ MO $	$ mo $	SYM	$	_	11	dobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
14	$ MT $	$ mt $	SYM	$	_	11	conj	_	_
15	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	17	nsubj	_	_
16	can	can	AUX	MD	VerbForm=Fin	17	aux	_	_
17	define	define	VERB	VB	VerbForm=Inf	5	ccomp	_	_
18	an	an	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
19	additional	additional	ADJ	JJ	Degree=Pos	22	amod	_	_
20	model	model	NOUN	NN	Number=Sing	22	compound	_	_
21	category	category	NOUN	NN	Number=Sing	22	compound	_	_
22	structure	structure	NOUN	NN	Number=Sing	17	dobj	_	_
23	$ MO cap MT $	$ mo cap mt $	SYM	$	_	17	dep	_	_
24	by	by	ADP	IN	_	17	prep	_	_
25	defining	define	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	24	pcomp	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	class	class	NOUN	NN	Number=Sing	25	dobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	weak	weak	ADJ	JJ	Degree=Pos	30	amod	_	_
30	equivalences	equivalence	NOUN	NNS	Number=Plur	28	pobj	_	_
31	to	to	PART	TO	_	32	aux	_	_
32	be	be	AUX	VB	VerbForm=Inf	25	xcomp	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
34	intersection	intersection	NOUN	NN	Number=Sing	32	attr	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	$ MO $	$ mo $	SYM	$	_	35	pobj	_	_
38	and	and	CCONJ	CC	ConjType=Cmp	34	cc	_	_
39	$ MT $	$ mt $	SYM	$	_	41	poss	_	_
40	weak	weak	ADJ	JJ	Degree=Pos	41	amod	_	_
41	equivalences	equivalence	NOUN	NNS	Number=Plur	34	conj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 7
# text = In addition we consider the model category on diagram categories over a base category (which is endowed with a model category structure) and show that delocalization is often preserved by the diagram model category structure.
1	In	in	ADP	IN	_	4	prep	_	_
2	addition	addition	NOUN	NN	Number=Sing	1	pobj	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	model	model	NOUN	NN	Number=Sing	7	compound	_	_
7	category	category	NOUN	NN	Number=Sing	4	dobj	_	_
8	on	on	ADP	IN	_	7	prep	_	_
9	diagram	diagram	NOUN	NN	Number=Sing	10	compound	_	_
10	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	_
11	over	over	ADP	IN	_	7	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	base	base	NOUN	NN	Number=Sing	14	compound	_	_
14	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
15	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
16	which	which	PRON	WDT	_	18	nsubjpass	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	auxpass	_	_
18	endowed	endow	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	relcl	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
21	model	model	NOUN	NN	Number=Sing	23	compound	_	_
22	category	category	NOUN	NN	Number=Sing	23	compound	_	_
23	structure	structure	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
24	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	4	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
26	show	show	VERB	VB	VerbForm=Inf	4	conj	_	_
27	that	that	SCONJ	IN	_	31	mark	_	_
28	delocalization	delocalization	NOUN	NN	Number=Sing	31	nsubjpass	_	_
29	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	31	auxpass	_	_
30	often	often	ADV	RB	_	31	advmod	_	_
31	preserved	preserve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	ccomp	_	_
32	by	by	ADP	IN	_	31	agent	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
34	diagram	diagram	PROPN	NNP	Number=Sing	35	compound	_	_
35	model	model	NOUN	NN	Number=Sing	37	compound	_	_
36	category	category	NOUN	NN	Number=Sing	37	compound	_	_
37	structure	structure	NOUN	NN	Number=Sing	32	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 588
# sent_id = 1
# text = For a relative exact homological category $ (C, E) $ , we define relative points over an arbitrary object in $ C $ , and show that they form an exact homological category.
1	For	for	ADP	IN	_	10	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
3	relative	relative	ADJ	JJ	Degree=Pos	6	amod	_	_
4	exact	exact	ADJ	JJ	Degree=Pos	6	amod	_	_
5	homological	homological	ADJ	JJ	Degree=Pos	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	1	pobj	_	_
7	$ (C, E) $	$ (c, e) $	X	FW	Foreign=Yes	6	appos	_	_
8	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
9	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
10	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	relative	relative	ADJ	JJ	Degree=Pos	12	amod	_	_
12	points	point	NOUN	NNS	Number=Plur	10	dobj	_	_
13	over	over	ADP	IN	_	10	prep	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	16	amod	_	_
16	object	object	NOUN	NN	Number=Sing	13	pobj	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	$ C $	$ c $	SYM	$	_	17	pobj	_	_
19	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
21	show	show	VERB	VB	VerbForm=Inf	10	conj	_	_
22	that	that	SCONJ	IN	_	24	mark	_	_
23	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	24	nsubj	_	_
24	form	form	VERB	VBP	Tense=Pres|VerbForm=Fin	21	ccomp	_	_
25	an	an	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
26	exact	exact	ADJ	JJ	Degree=Pos	28	amod	_	_
27	homological	homological	ADJ	JJ	Degree=Pos	28	amod	_	_
28	category	category	NOUN	NN	Number=Sing	24	dobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = In particular, it follows that the full subcategory of nilpotent objects in an exact homological category is an exact homological category.
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	5	nsubj	_	_
5	follows	follow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	18	mark	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	full	full	ADJ	JJ	Degree=Pos	9	amod	_	_
9	subcategory	subcategory	NOUN	NN	Number=Sing	18	nsubj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	nilpotent	nilpotent	ADJ	JJ	Degree=Pos	12	amod	_	_
12	objects	object	NOUN	NNS	Number=Plur	10	pobj	_	_
13	in	in	ADP	IN	_	9	prep	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	exact	exact	ADJ	JJ	Degree=Pos	17	amod	_	_
16	homological	homological	ADJ	JJ	Degree=Pos	17	amod	_	_
17	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
19	an	an	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
20	exact	exact	ADJ	JJ	Degree=Pos	22	amod	_	_
21	homological	homological	ADJ	JJ	Degree=Pos	22	amod	_	_
22	category	category	NOUN	NN	Number=Sing	18	attr	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = These nilpotent objects are defined with respect to a Birkhoff subcategory in $ C $ as defined by Everaert and Van der Linden.
1	These	these	DET	DT	Number=Plur|PronType=Dem	3	det	_	_
2	nilpotent	nilpotent	ADJ	JJ	Degree=Pos	3	amod	_	_
3	objects	object	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	with	with	ADP	IN	_	5	prep	_	_
7	respect	respect	NOUN	NN	Number=Sing	6	pobj	_	_
8	to	to	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	Birkhoff	Birkhoff	PROPN	NNP	Number=Sing	11	compound	_	_
11	subcategory	subcategory	NOUN	NN	Number=Sing	8	pobj	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	$ C $	$ c $	SYM	$	_	12	pobj	_	_
14	as	as	SCONJ	IN	_	15	mark	_	_
15	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	advcl	_	_
16	by	by	ADP	IN	_	15	agent	_	_
17	Everaert	Everaert	PROPN	NNP	Number=Sing	20	nmod	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	Van	Van	PROPN	NNP	Number=Sing	17	conj	_	_
20	der	der	NOUN	NN	Number=Sing	21	compound	_	_
21	Linden	Linden	PROPN	NNP	Number=Sing	16	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = In addition, we introduce relative internal actions and show that, just as in the classical case, there is an equivalence of categories between the category of relative points over an object and the category of relative internal actions for the same object.
1	In	in	ADP	IN	_	5	prep	_	_
2	addition	addition	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	relative	relative	ADJ	JJ	Degree=Pos	8	amod	_	_
7	internal	internal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	actions	action	NOUN	NNS	Number=Plur	5	dobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
10	show	show	VERB	VB	VerbForm=Inf	5	conj	_	_
11	that	that	SCONJ	IN	_	21	mark	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
13	just	just	ADV	RB	_	14	advmod	_	_
14	as	as	ADP	IN	_	21	prep	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	classical	classical	ADJ	JJ	Degree=Pos	18	amod	_	_
18	case	case	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
20	there	there	PRON	EX	_	21	expl	_	_
21	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	ccomp	_	_
22	an	an	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
23	equivalence	equivalence	NOUN	NN	Number=Sing	21	attr	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	categories	category	NOUN	NNS	Number=Plur	24	pobj	_	_
26	between	between	ADP	IN	_	23	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	category	category	NOUN	NN	Number=Sing	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	relative	relative	ADJ	JJ	Degree=Pos	31	amod	_	_
31	points	point	NOUN	NNS	Number=Plur	29	pobj	_	_
32	over	over	ADP	IN	_	23	prep	_	_
33	an	an	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
34	object	object	NOUN	NN	Number=Sing	32	pobj	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	34	cc	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	category	category	NOUN	NN	Number=Sing	34	conj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	relative	relative	ADJ	JJ	Degree=Pos	41	amod	_	_
40	internal	internal	ADJ	JJ	Degree=Pos	41	amod	_	_
41	actions	action	NOUN	NNS	Number=Plur	38	pobj	_	_
42	for	for	ADP	IN	_	41	prep	_	_
43	the	the	DET	DT	Definite=Def|PronType=Art	45	det	_	_
44	same	same	ADJ	JJ	Degree=Pos	45	amod	_	_
45	object	object	NOUN	NN	Number=Sing	42	pobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 589
# sent_id = 1
# text = We introduced in a previous article a notion of Maltsevness relative to a specific class $ Sigma $ of split epimorphisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduced	introduce	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	previous	previous	ADJ	JJ	Degree=Pos	6	amod	_	_
6	article	article	NOUN	NN	Number=Sing	3	pobj	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Maltsevness	Maltsevness	PROPN	NNP	Number=Sing	9	pobj	_	_
11	relative	relative	ADJ	JJ	Degree=Pos	8	amod	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	specific	specific	ADJ	JJ	Degree=Pos	15	amod	_	_
15	class	class	NOUN	NN	Number=Sing	12	pobj	_	_
16	$ Sigma $	$ sigma $	SYM	$	_	15	appos	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	split	split	ADJ	JJ	Degree=Pos	19	amod	_	_
19	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We investigate here the induced relative notion of natural Maltsevness, with a special attention to the example of quandles.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	here	here	ADV	RB	PronType=Dem	2	advmod	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
6	relative	relative	ADJ	JJ	Degree=Pos	7	amod	_	_
7	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	natural	natural	ADJ	JJ	Degree=Pos	10	amod	_	_
10	Maltsevness	Maltsevness	PROPN	NNP	Number=Sing	8	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
12	with	with	ADP	IN	_	7	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	special	special	ADJ	JJ	Degree=Pos	15	amod	_	_
15	attention	attention	NOUN	NN	Number=Sing	12	pobj	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	example	example	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	quandles	quandle	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 590
# sent_id = 1
# text = A categorical principal bundle is a structure comprised of categories that is analogous to a classical principal bundle; examples arise from geometric contexts involving bundles over path spaces.
1	A	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
2	categorical	categorical	ADJ	JJ	Degree=Pos	4	amod	_	_
3	principal	principal	ADJ	JJ	Degree=Pos	4	amod	_	_
4	bundle	bundle	NOUN	NN	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	21	ccomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	structure	structure	NOUN	NN	Number=Sing	5	attr	_	_
8	comprised	comprise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	acl	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	_
11	that	that	PRON	WDT	PronType=Rel	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	relcl	_	_
13	analogous	analogous	ADJ	JJ	Degree=Pos	12	acomp	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
16	classical	classical	ADJ	JJ	Degree=Pos	18	amod	_	_
17	principal	principal	ADJ	JJ	Degree=Pos	18	amod	_	_
18	bundle	bundle	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
19	;	;	PUNCT	:	_	21	punct	_	_
20	examples	example	NOUN	NNS	Number=Plur	21	nsubj	_	_
21	arise	arise	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
22	from	from	ADP	IN	_	21	prep	_	_
23	geometric	geometric	ADJ	JJ	Degree=Pos	24	amod	_	_
24	contexts	context	NOUN	NNS	Number=Plur	22	pobj	_	_
25	involving	involve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	21	advcl	_	_
26	bundles	bundle	NOUN	NNS	Number=Plur	25	dobj	_	_
27	over	over	ADP	IN	_	26	prep	_	_
28	path	path	NOUN	NN	Number=Sing	29	compound	_	_
29	spaces	space	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show how a categorical principal bundle can be constructed from local data specified through transition functors and natural transformations.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	how	how	SCONJ	WRB	_	10	advmod	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	categorical	categorical	ADJ	JJ	Degree=Pos	7	amod	_	_
6	principal	principal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	bundle	bundle	NOUN	NN	Number=Sing	10	nsubjpass	_	_
8	can	can	AUX	MD	VerbForm=Fin	10	aux	_	_
9	be	be	AUX	VB	VerbForm=Inf	10	auxpass	_	_
10	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
11	from	from	ADP	IN	_	10	prep	_	_
12	local	local	ADJ	JJ	Degree=Pos	13	amod	_	_
13	data	datum	NOUN	NNS	Number=Plur	11	pobj	_	_
14	specified	specify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	acl	_	_
15	through	through	ADP	IN	_	14	prep	_	_
16	transition	transition	NOUN	NN	Number=Sing	17	compound	_	_
17	functors	functor	NOUN	NNS	Number=Plur	15	pobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	natural	natural	ADJ	JJ	Degree=Pos	20	amod	_	_
20	transformations	transformation	NOUN	NNS	Number=Plur	17	conj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 591
# sent_id = 1
# text = We present a brief and simple cotriple description of the simplicial algebra used in Bloch's construction of the higher Chow groups.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
4	brief	brief	ADJ	JJ	Degree=Pos	8	amod	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	simple	simple	ADJ	JJ	Degree=Pos	4	conj	_	_
7	cotriple	cotriple	ADJ	JJ	Degree=Pos	8	amod	_	_
8	description	description	NOUN	NN	Number=Sing	2	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	simplicial	simplicial	ADJ	JJ	Degree=Pos	12	amod	_	_
12	algebra	algebra	NOUN	NN	Number=Sing	9	pobj	_	_
13	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	Bloch	Bloch	PROPN	NNP	Number=Sing	17	poss	_	SpaceAfter=No
16	's	's	PART	POS	_	15	case	_	_
17	construction	construction	NOUN	NN	Number=Sing	14	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
20	higher	high	ADJ	JJR	Degree=Cmp	22	amod	_	_
21	Chow	Chow	PROPN	NNP	Number=Sing	22	compound	_	_
22	groups	group	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 592
# sent_id = 1
# text = By Isbell duality, each compact regular frame $ L $ is isomorphic to the frame of opens of a compact Hausdorff space $ X $ .
1	By	by	ADP	IN	_	10	prep	_	_
2	Isbell	Isbell	PROPN	NNP	Number=Sing	3	compound	_	_
3	duality	duality	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
5	each	each	DET	DT	_	8	det	_	_
6	compact	compact	ADJ	JJ	Degree=Pos	8	amod	_	_
7	regular	regular	ADJ	JJ	Degree=Pos	8	amod	_	_
8	frame	frame	NOUN	NN	Number=Sing	10	nsubj	_	_
9	$ L $	$ l $	SYM	$	_	8	appos	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	10	acomp	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	frame	frame	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	opens	open	NOUN	NNS	Number=Plur	15	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
19	compact	compact	ADJ	JJ	Degree=Pos	21	amod	_	_
20	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	21	compound	_	_
21	space	space	NOUN	NN	Number=Sing	17	pobj	_	_
22	$ X $	$ x $	SYM	$	_	15	pobj	_	_
23	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this note we study the spectrum $ Spec(L) $ of prime filters of a compact regular frame $ L $ .
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	note	note	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	spectrum	spectrum	NOUN	NN	Number=Sing	5	dobj	_	_
8	$ Spec(L) $	$ spec(l) $	SYM	$	_	17	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	prime	prime	ADJ	JJ	Degree=Pos	11	amod	_	_
11	filters	filter	NOUN	NNS	Number=Plur	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
14	compact	compact	ADJ	JJ	Degree=Pos	16	amod	_	_
15	regular	regular	ADJ	JJ	Degree=Pos	16	amod	_	_
16	frame	frame	NOUN	NN	Number=Sing	12	pobj	_	_
17	$ L $	$ l $	SYM	$	_	5	advcl	_	_
18	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = We prove that $ X $ is realized as the minimum of $ Spec(L) $ and the Gleason cover of $ X $ as the maximum of $ Spec(L) $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	6	mark	_	_
4	$ X $	$ x $	SYM	$	_	6	nsubjpass	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	realized	realize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
7	as	as	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	minimum	minimum	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	$ Spec(L) $	$ spec(l) $	SYM	$	_	10	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	Gleason	Gleason	PROPN	NNP	Number=Sing	15	compound	_	_
15	cover	cover	NOUN	NN	Number=Sing	11	conj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	$ X $	$ x $	SYM	$	_	16	pobj	_	_
18	as	as	ADP	IN	_	9	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	maximum	maximum	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	$ Spec(L) $	$ spec(l) $	SYM	$	_	21	pobj	_	_
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We also characterize zero - dimensional, extremally disconnected, and scattered compact regular frames by means of $ Spec(L) $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	zero	zero	NUM	CD	NumType=Card	6	npadvmod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	dimensional	dimensional	ADJ	JJ	Degree=Pos	9	amod	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
8	extremally	extremally	ADV	RB	_	9	advmod	_	_
9	disconnected	disconnected	ADJ	JJ	Degree=Pos	3	ccomp	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
12	scattered	scatter	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	conj	_	_
13	compact	compact	ADJ	JJ	Degree=Pos	15	amod	_	_
14	regular	regular	ADJ	JJ	Degree=Pos	15	amod	_	_
15	frames	frame	NOUN	NNS	Number=Plur	12	dobj	_	_
16	by	by	ADP	IN	_	12	prep	_	_
17	means	mean	NOUN	NNS	Number=Plur	16	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	$ Spec(L) $	$ spec(l) $	SYM	$	_	18	pobj	_	_
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 593
# sent_id = 1
# text = We revisit what we call the fibred topology on a fibred category over a site and we prove a few basic results concerning this topology.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	revisit	revisit	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	what	what	PRON	WP	_	5	dobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	fibred	fibred	ADJ	JJ	Degree=Pos	8	amod	_	_
8	topology	topology	NOUN	NN	Number=Sing	5	oprd	_	_
9	on	on	ADP	IN	_	5	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	fibred	fibred	ADJ	JJ	Degree=Pos	12	amod	_	_
12	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
13	over	over	ADP	IN	_	5	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	site	site	NOUN	NN	Number=Sing	13	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
17	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	18	nsubj	_	_
18	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	quantmod	_	_
20	few	few	ADJ	JJ	Degree=Pos	22	amod	_	_
21	basic	basic	ADJ	JJ	Degree=Pos	22	amod	_	_
22	results	result	NOUN	NNS	Number=Plur	18	dobj	_	_
23	concerning	concern	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	acl	_	_
24	this	this	DET	DT	Number=Sing|PronType=Dem	25	det	_	_
25	topology	topology	NOUN	NN	Number=Sing	23	dobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# sent_id = 2
# text = We give a general result concerning the invariance of a 2 - category of stacks under change of base.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	general	general	ADJ	JJ	Degree=Pos	5	amod	_	_
5	result	result	NOUN	NN	Number=Sing	2	dobj	_	_
6	concerning	concern	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	acl	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	invariance	invariance	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	stacks	stack	NOUN	NNS	Number=Plur	14	pobj	_	_
16	under	under	ADP	IN	_	6	prep	_	_
17	change	change	NOUN	NN	Number=Sing	16	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	base	base	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 594
# sent_id = 1
# text = In this paper we investigate the construction of bicategories of fractions originally described by Pronk: given any bicategory $ C $ together with a suitable class of morphisms $ W $ , one can construct a bicategory $ C[W^{ - 1}] $ , where all the morphisms of $ W $ are turned into internal equivalences, and that is universal with respect to this property.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	32	ccomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	construction	construction	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	bicategories	bicategorie	NOUN	NNS	Number=Plur	8	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	fractions	fraction	NOUN	NNS	Number=Plur	10	pobj	_	_
12	originally	originally	ADV	RB	_	13	advmod	_	_
13	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acl	_	_
14	by	by	ADP	IN	_	13	agent	_	_
15	Pronk	Pronk	PROPN	NNP	Number=Sing	14	pobj	_	SpaceAfter=No
16	:	:	PUNCT	:	_	5	punct	_	_
17	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	prep	_	_
18	any	any	DET	DT	_	19	det	_	_
19	bicategory	bicategory	NOUN	NN	Number=Sing	17	pobj	_	_
20	$ C $	$ c $	SYM	$	_	21	nmod	_	_
21	together	together	ADV	RB	_	17	advmod	_	_
22	with	with	ADP	IN	_	17	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	suitable	suitable	ADJ	JJ	Degree=Pos	25	amod	_	_
25	class	class	NOUN	NN	Number=Sing	22	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	morphisms	morphism	NOUN	NNS	Number=Plur	26	pobj	_	_
28	$ W $	$ w $	SYM	$	_	25	appos	_	_
29	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
30	one	one	PRON	PRP	PronType=Prs	32	nsubj	_	_
31	can	can	AUX	MD	VerbForm=Fin	32	aux	_	_
32	construct	construct	VERB	VB	VerbForm=Inf	0	ROOT	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
34	bicategory	bicategory	NOUN	NN	Number=Sing	35	compound	_	_
35	$ C[W^{ - 1}] $	$ c[w^{ - 1}] $	SYM	$	_	32	dobj	_	_
36	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
37	where	where	SCONJ	WRB	_	44	advmod	_	_
38	all	all	DET	PDT	_	40	predet	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
40	morphisms	morphism	NOUN	NNS	Number=Plur	44	nsubjpass	_	_
41	of	of	ADP	IN	_	40	prep	_	_
42	$ W $	$ w $	SYM	$	_	41	pobj	_	_
43	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	44	auxpass	_	_
44	turned	turn	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	35	relcl	_	_
45	into	into	ADP	IN	_	44	prep	_	_
46	internal	internal	ADJ	JJ	Degree=Pos	47	amod	_	_
47	equivalences	equivalence	NOUN	NNS	Number=Plur	45	pobj	_	SpaceAfter=No
48	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
49	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
50	that	that	PRON	DT	Number=Sing|PronType=Dem	51	nsubj	_	_
51	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	32	conj	_	_
52	universal	universal	ADJ	JJ	Degree=Pos	51	acomp	_	_
53	with	with	ADP	IN	_	52	prep	_	_
54	respect	respect	NOUN	NN	Number=Sing	53	pobj	_	_
55	to	to	ADP	IN	_	54	prep	_	_
56	this	this	DET	DT	Number=Sing|PronType=Dem	57	det	_	_
57	property	property	NOUN	NN	Number=Sing	55	pobj	_	SpaceAfter=No
58	.	.	PUNCT	.	PunctType=Peri	51	punct	_	SpaceAfter=No

# sent_id = 2
# text = Most of the descriptions leading to this construction were long and heavily based on the axiom of choice.
1	Most	Most	ADJ	JJS	Degree=Sup	9	nsubj	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	descriptions	description	NOUN	NNS	Number=Plur	2	pobj	_	_
5	leading	lead	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	acl	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	this	this	DET	DT	Number=Sing|PronType=Dem	8	det	_	_
8	construction	construction	NOUN	NN	Number=Sing	6	pobj	_	_
9	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	0	ROOT	_	_
10	long	long	ADJ	JJ	Degree=Pos	9	acomp	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	heavily	heavily	ADV	RB	_	13	advmod	_	_
13	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	conj	_	_
14	on	on	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	axiom	axiom	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	choice	choice	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this paper we considerably simplify the description of the equivalence relation on 2 - morphisms and the constructions of associators, vertical and horizontal compositions in $ C[W^{ - 1}] $ , thus proving that the axiom of choice is not needed under certain conditions.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
5	considerably	considerably	ADV	RB	_	6	advmod	_	_
6	simplify	simplify	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	description	description	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	equivalence	equivalence	NOUN	NN	Number=Sing	12	compound	_	_
12	relation	relation	NOUN	NN	Number=Sing	9	pobj	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	2	2	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	morphisms	morphism	NOUN	NNS	Number=Plur	13	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	constructions	construction	NOUN	NNS	Number=Plur	16	conj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	associators	associator	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	vertical	vertical	ADJ	JJ	Degree=Pos	26	amod	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	horizontal	horizontal	ADJ	JJ	Degree=Pos	23	conj	_	_
26	compositions	composition	NOUN	NNS	Number=Plur	13	pobj	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	$ C[W^{ - 1}] $	$ c[w^{ - 1}] $	SYM	$	_	27	pobj	_	_
29	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
30	thus	thus	ADV	RB	_	31	advmod	_	_
31	proving	prove	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	advcl	_	_
32	that	that	SCONJ	IN	_	39	mark	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
34	axiom	axiom	NOUN	NN	Number=Sing	39	nsubjpass	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	choice	choice	NOUN	NN	Number=Sing	35	pobj	_	_
37	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	39	auxpass	_	_
38	not	not	PART	RB	Polarity=Neg	39	neg	_	_
39	needed	need	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	ccomp	_	_
40	under	under	ADP	IN	_	39	prep	_	_
41	certain	certain	ADJ	JJ	Degree=Pos	42	amod	_	_
42	conditions	condition	NOUN	NNS	Number=Plur	40	pobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = The simplified description of associators and compositions will also play a crucial role in two forthcoming papers about pseudofunctors and equivalences between bicategories of fractions.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	simplified	simplified	ADJ	JJ	Degree=Pos	3	amod	_	_
3	description	description	NOUN	NN	Number=Sing	10	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	associators	associator	NOUN	NNS	Number=Plur	4	pobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	compositions	composition	NOUN	NNS	Number=Plur	5	conj	_	_
8	will	will	AUX	MD	VerbForm=Fin	10	aux	_	_
9	also	also	ADV	RB	_	10	advmod	_	_
10	play	play	VERB	VB	VerbForm=Inf	0	ROOT	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	crucial	crucial	ADJ	JJ	Degree=Pos	13	amod	_	_
13	role	role	NOUN	NN	Number=Sing	10	dobj	_	_
14	in	in	ADP	IN	_	10	prep	_	_
15	two	two	NUM	CD	NumType=Card	17	nummod	_	_
16	forthcoming	forthcoming	ADJ	JJ	Degree=Pos	17	amod	_	_
17	papers	paper	NOUN	NNS	Number=Plur	14	pobj	_	_
18	about	about	ADP	IN	_	17	prep	_	_
19	pseudofunctors	pseudofunctor	NOUN	NNS	Number=Plur	18	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	equivalences	equivalence	NOUN	NNS	Number=Plur	19	conj	_	_
22	between	between	ADP	IN	_	17	prep	_	_
23	bicategories	bicategorie	NOUN	NNS	Number=Plur	22	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	fractions	fraction	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# doc_id = 595
# sent_id = 1
# text = We prove a biadjoint triangle theorem and its strict version, which are 2 - dimensional analogues of the adjoint triangle theorem of Dubuc.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	biadjoint	biadjoint	NOUN	NN	Number=Sing	5	compound	_	_
5	triangle	triangle	NOUN	NN	Number=Sing	2	dobj	_	_
6	theorem	theorem	ADJ	JJ	Degree=Pos	5	amod	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
8	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	10	poss	_	_
9	strict	strict	ADJ	JJ	Degree=Pos	10	amod	_	_
10	version	version	NOUN	NN	Number=Sing	5	conj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	which	which	PRON	WDT	_	13	nsubj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	10	relcl	_	_
14	2	2	NUM	CD	NumType=Card	16	advmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	dimensional	dimensional	ADJ	JJ	Degree=Pos	17	amod	_	_
17	analogues	analogue	NOUN	NNS	Number=Plur	13	attr	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	adjoint	adjoint	NOUN	NN	Number=Sing	21	compound	_	_
21	triangle	triangle	NOUN	NN	Number=Sing	18	pobj	_	_
22	theorem	theorem	ADJ	JJ	Degree=Pos	21	amod	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	Dubuc	Dubuc	PROPN	NNP	Number=Sing	23	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Similarly to the 1 - dimensional case, we demonstrate how we can apply our results to get the pseudomonadicity characterization (due to Le Creurer, Marmolejo and Vitale).
1	Similarly	similarly	ADV	RB	_	2	advmod	_	_
2	to	to	ADP	IN	_	10	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
4	1	1	NUM	CD	NumType=Card	6	advmod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	dimensional	dimensional	ADJ	JJ	Degree=Pos	7	amod	_	_
7	case	case	NOUN	NN	Number=Sing	2	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
9	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
10	demonstrate	demonstrate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	how	how	SCONJ	WRB	_	14	advmod	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
13	can	can	AUX	MD	VerbForm=Fin	14	aux	_	_
14	apply	apply	VERB	VB	VerbForm=Inf	10	ccomp	_	_
15	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	16	poss	_	_
16	results	result	NOUN	NNS	Number=Plur	14	dobj	_	_
17	to	to	PART	TO	_	18	aux	_	_
18	get	get	VERB	VB	VerbForm=Inf	14	advcl	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	pseudomonadicity	pseudomonadicity	NOUN	NN	Number=Sing	21	compound	_	_
21	characterization	characterization	NOUN	NN	Number=Sing	18	dobj	_	_
22	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	21	punct	_	SpaceAfter=No
23	due	due	ADP	IN	_	18	prep	_	_
24	to	to	ADP	IN	_	23	pcomp	_	_
25	Le	Le	PROPN	NNP	Number=Sing	26	compound	_	_
26	Creurer	Creurer	PROPN	NNP	Number=Sing	23	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
28	Marmolejo	Marmolejo	PROPN	NNP	Number=Sing	26	conj	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	Vitale	Vitale	PROPN	NNP	Number=Sing	28	conj	_	SpaceAfter=No
31	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	10	punct	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 3
# text = Furthermore, we study applications of our main theorems in the context of the 2 - monadic approach to coherence.
1	Furthermore	furthermore	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	applications	application	NOUN	NNS	Number=Plur	4	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	9	poss	_	_
8	main	main	ADJ	JJ	Degree=Pos	9	amod	_	_
9	theorems	theorem	NOUN	NNS	Number=Plur	6	pobj	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	context	context	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
15	2	2	NUM	CD	NumType=Card	17	nummod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	monadic	monadic	ADJ	JJ	Degree=Pos	18	amod	_	_
18	approach	approach	NOUN	NN	Number=Sing	13	pobj	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	coherence	coherence	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = As a direct consequence of our strict biadjoint triangle theorem, we give the construction (due to Lack) of the left 2 - adjoint to the inclusion of the strict algebras into the pseudoalgebras.
1	As	as	SCONJ	IN	_	10	mark	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	direct	direct	ADJ	JJ	Degree=Pos	4	amod	_	_
4	consequence	consequence	NOUN	NN	Number=Sing	1	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	9	poss	_	_
7	strict	strict	ADJ	JJ	Degree=Pos	9	amod	_	_
8	biadjoint	biadjoint	NOUN	NN	Number=Sing	9	compound	_	_
9	triangle	triangle	NOUN	NN	Number=Sing	5	pobj	_	_
10	theorem	theorem	ADJ	JJ	Degree=Pos	13	advcl	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	construction	construction	NOUN	NN	Number=Sing	13	dobj	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	13	punct	_	SpaceAfter=No
17	due	due	ADP	IN	_	13	prep	_	_
18	to	to	ADP	IN	_	17	pcomp	_	_
19	Lack	Lack	PROPN	NNP	Number=Sing	17	pobj	_	SpaceAfter=No
20	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	17	punct	_	_
21	of	of	ADP	IN	_	13	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
23	left	left	ADJ	JJ	Degree=Pos	26	amod	_	_
24	2	2	NUM	CD	NumType=Card	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	adjoint	adjoint	NOUN	NN	Number=Sing	21	pobj	_	_
27	to	to	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	inclusion	inclusion	NOUN	NN	Number=Sing	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	strict	strict	ADJ	JJ	Degree=Pos	33	amod	_	_
33	algebras	algebra	NOUN	NNS	Number=Plur	30	pobj	_	_
34	into	into	ADP	IN	_	29	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	pseudoalgebras	pseudoalgebra	NOUN	NNS	Number=Plur	34	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 5
# text = In the last section, we give two brief applications on lifting biadjunctions and pseudo - Kan extensions.
1	In	in	ADP	IN	_	7	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	last	last	ADJ	JJ	Degree=Pos	4	amod	_	_
4	section	section	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	two	two	NUM	CD	NumType=Card	10	nummod	_	_
9	brief	brief	ADJ	JJ	Degree=Pos	10	amod	_	_
10	applications	application	NOUN	NNS	Number=Plur	7	dobj	_	_
11	on	on	ADP	IN	_	10	prep	_	_
12	lifting	lift	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	amod	_	_
13	biadjunctions	biadjunction	NOUN	NNS	Number=Plur	11	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	pseudo	pseudo	NOUN	NN	Number=Sing	17	compound	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	Kan	Kan	PROPN	NNP	Number=Sing	18	compound	_	_
18	extensions	extension	NOUN	NNS	Number=Plur	13	conj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 596
# sent_id = 1
# text = The category of symmetric quandles is a Maltsev variety whose subvariety of abelian symmetric quandles is the category of abelian algebras.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	symmetric	symmetric	ADJ	JJ	Degree=Pos	5	amod	_	_
5	quandles	quandle	NOUN	NNS	Number=Plur	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	Maltsev	Maltsev	PROPN	NNP	Number=Sing	9	compound	_	_
9	variety	variety	NOUN	NN	Number=Sing	6	attr	_	_
10	whose	whose	DET	WP$	Poss=Yes	11	poss	_	_
11	subvariety	subvariety	NOUN	NN	Number=Sing	16	nsubj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	abelian	abelian	ADJ	JJ	Degree=Pos	15	nmod	_	_
14	symmetric	symmetric	ADJ	JJ	Degree=Pos	15	amod	_	_
15	quandles	quandle	NOUN	NNS	Number=Plur	12	pobj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	relcl	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	category	category	NOUN	NN	Number=Sing	16	attr	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	abelian	abelian	PROPN	NNP	Number=Sing	21	compound	_	_
21	algebras	algebras	PROPN	NNP	Number=Sing	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = We give an algebraic description of the quandle extensions that are central for the adjunction between the variety of quandles and its subvariety of abelian symmetric quandles.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	algebraic	algebraic	ADJ	JJ	Degree=Pos	5	amod	_	_
5	description	description	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	quandle	quandle	NOUN	NN	Number=Sing	9	compound	_	_
9	extensions	extension	NOUN	NNS	Number=Plur	6	pobj	_	_
10	that	that	PRON	WDT	PronType=Rel	11	nsubj	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	relcl	_	_
12	central	central	ADJ	JJ	Degree=Pos	11	acomp	_	_
13	for	for	ADP	IN	_	11	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	adjunction	adjunction	NOUN	NN	Number=Sing	13	pobj	_	_
16	between	between	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	variety	variety	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	quandles	quandle	NOUN	NNS	Number=Plur	19	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
22	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	23	poss	_	_
23	subvariety	subvariety	NOUN	NN	Number=Sing	18	conj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	abelian	abelian	ADJ	JJ	Degree=Pos	27	amod	_	_
26	symmetric	symmetric	ADJ	JJ	Degree=Pos	27	amod	_	_
27	quandles	quandle	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 597
# sent_id = 1
# text = For a coherent site we construct a canonically associated enlarged coherent site, such that cohomology of bounded below complexes is preserved by the enlargement.
1	For	for	ADP	IN	_	6	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	coherent	coherent	ADJ	JJ	Degree=Pos	4	amod	_	_
4	site	site	NOUN	NN	Number=Sing	1	pobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
8	canonically	canonically	ADV	RB	_	9	advmod	_	_
9	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
10	enlarged	enlarge	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
11	coherent	coherent	ADJ	JJ	Degree=Pos	12	amod	_	_
12	site	site	NOUN	NN	Number=Sing	6	dobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	such	such	ADJ	JJ	Degree=Pos	16	amod	_	_
15	that	that	DET	DT	Number=Sing|PronType=Dem	16	det	_	_
16	cohomology	cohomology	NOUN	NN	Number=Sing	22	nsubjpass	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	bounded	bound	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	pobj	_	_
19	below	below	ADP	IN	_	18	prep	_	_
20	complexes	complex	NOUN	NNS	Number=Plur	19	pobj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	auxpass	_	_
22	preserved	preserve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	relcl	_	_
23	by	by	ADP	IN	_	22	agent	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	enlargement	enlargement	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = In the topos associated to the enlarged site transfinite compositions of epimorphisms are epimorphisms and a weak analog of the concept of the algebraic closure exists.
1	In	in	ADP	IN	_	13	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	topos	topos	NOUN	NN	Number=Sing	1	pobj	_	_
4	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	acl	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
7	enlarged	enlarge	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
8	site	site	NOUN	NN	Number=Sing	9	compound	_	_
9	transfinite	transfinite	NOUN	NN	Number=Sing	10	compound	_	_
10	compositions	composition	NOUN	NNS	Number=Plur	5	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	11	pobj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	26	nsubj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	weak	weak	ADJ	JJ	Degree=Pos	18	amod	_	_
18	analog	analog	NOUN	NN	Number=Sing	14	conj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	concept	concept	NOUN	NN	Number=Sing	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	algebraic	algebraic	ADJ	JJ	Degree=Pos	25	amod	_	_
25	closure	closure	NOUN	NN	Number=Sing	22	pobj	_	_
26	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	attr	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 3
# text = The construction is a variant of the work of Bhatt and Scholze on the pro - etale topology.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	construction	construction	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	variant	variant	NOUN	NN	Number=Sing	3	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	work	work	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Bhatt	Bhatt	PROPN	NNP	Number=Sing	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	Scholze	Scholze	PROPN	NNP	Number=Sing	10	conj	_	_
13	on	on	ADP	IN	_	5	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
15	pro	pro	ADJ	JJ	Degree=Pos	17	amod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	etale	etale	ADJ	JJ	Degree=Pos	18	amod	_	_
18	topology	topology	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 598
# sent_id = 1
# text = There is a general notion of the magnitude of an enriched category, defined subject to hypotheses.
1	There	there	PRON	EX	_	2	expl	_	_
2	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	general	general	ADJ	JJ	Degree=Pos	5	amod	_	_
5	notion	notion	NOUN	NN	Number=Sing	2	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	magnitude	magnitude	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	enriched	enriched	ADJ	JJ	Degree=Pos	12	amod	_	_
12	category	category	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
14	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
15	subject	subject	NOUN	NN	Number=Sing	5	appos	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	hypotheses	hypothesis	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In topological and geometric contexts, magnitude is already known to be closely related to classical invariants such as Euler characteristic and dimension.
1	In	in	ADP	IN	_	10	prep	_	_
2	topological	topological	ADJ	JJ	Degree=Pos	5	amod	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	geometric	geometric	ADJ	JJ	Degree=Pos	2	conj	_	_
5	contexts	context	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
7	magnitude	magnitude	NOUN	NN	Number=Sing	10	nsubjpass	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
9	already	already	ADV	RB	_	10	advmod	_	_
10	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	to	to	PART	TO	_	14	aux	_	_
12	be	be	AUX	VB	VerbForm=Inf	14	auxpass	_	_
13	closely	closely	ADV	RB	_	14	advmod	_	_
14	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	xcomp	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	classical	classical	ADJ	JJ	Degree=Pos	17	amod	_	_
17	invariants	invariant	NOUN	NNS	Number=Plur	15	pobj	_	_
18	such	such	ADJ	JJ	Degree=Pos	19	amod	_	_
19	as	as	ADP	IN	_	17	prep	_	_
20	Euler	Euler	PROPN	NNP	Number=Sing	19	pobj	_	_
21	characteristic	characteristic	ADJ	JJ	Degree=Pos	20	amod	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	dimension	dimension	NOUN	NN	Number=Sing	21	conj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 3
# text = Here we establish its significance in an algebraic context.
1	Here	here	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	establish	establish	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	5	poss	_	_
5	significance	significance	NOUN	NN	Number=Sing	3	dobj	_	_
6	in	in	ADP	IN	_	3	prep	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	algebraic	algebraic	ADJ	JJ	Degree=Pos	9	amod	_	_
9	context	context	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = Specifically, in the representation theory of an associative algebra $ A $ , a central role is played by the indecomposable projective $ A $ - modules, which form a category enriched in vector spaces.
1	Specifically	specifically	ADV	RB	_	17	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
3	in	in	ADP	IN	_	17	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	representation	representation	NOUN	NN	Number=Sing	6	compound	_	_
6	theory	theory	NOUN	NN	Number=Sing	3	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	associative	associative	ADJ	JJ	Degree=Pos	10	amod	_	_
10	algebra	algebra	NOUN	NN	Number=Sing	7	pobj	_	_
11	$ A $	$ a $	SYM	$	_	10	appos	_	_
12	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	central	central	ADJ	JJ	Degree=Pos	15	amod	_	_
15	role	role	NOUN	NN	Number=Sing	17	nsubjpass	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	auxpass	_	_
17	played	play	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
18	by	by	ADP	IN	_	17	agent	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
20	indecomposable	indecomposable	ADJ	JJ	Degree=Pos	24	amod	_	_
21	projective	projective	NOUN	NN	Number=Sing	24	amod	_	_
22	$ A $	$ a $	SYM	$	_	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	modules	module	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	which	which	PRON	WDT	_	27	nsubj	_	_
27	form	form	VERB	VBP	Tense=Pres|VerbForm=Fin	24	relcl	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
29	category	category	NOUN	NN	Number=Sing	27	dobj	_	_
30	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	acl	_	_
31	in	in	ADP	IN	_	30	prep	_	_
32	vector	vector	NOUN	NN	Number=Sing	33	compound	_	_
33	spaces	space	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 5
# text = We show that the magnitude of that category is a known homological invariant of the algebra: writing $ chi_A $ for the Euler form of $ A $ and $ S $ for the direct sum of the simple $ A $ - modules, it is $ chi_A(S, S) $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	9	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	magnitude	magnitude	NOUN	NN	Number=Sing	9	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	that	that	DET	DT	Number=Sing|PronType=Dem	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
12	homological	homological	ADJ	JJ	Degree=Pos	13	amod	_	_
13	invariant	invariant	NOUN	NN	Number=Sing	9	attr	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	algebra	algebra	PROPN	NNP	Number=Sing	14	pobj	_	SpaceAfter=No
17	:	:	PUNCT	:	_	9	punct	_	_
18	writing	write	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	advcl	_	_
19	$ chi_A $	$ chi_a $	SYM	$	_	18	dobj	_	_
20	for	for	ADP	IN	_	18	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	Euler	Euler	PROPN	NNP	Number=Sing	23	compound	_	_
23	form	form	NOUN	NN	Number=Sing	20	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	$ A $	$ a $	SYM	$	_	24	pobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	$ S $	$ s $	SYM	$	_	24	pobj	_	_
28	for	for	ADP	IN	_	18	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
30	direct	direct	ADJ	JJ	Degree=Pos	31	amod	_	_
31	sum	sum	NOUN	NN	Number=Sing	28	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
34	simple	simple	ADJ	JJ	Degree=Pos	37	amod	_	_
35	$ A $	$ a $	SYM	$	_	37	compound	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	modules	module	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
38	,	,	PUNCT	,	PunctType=Comm	40	punct	_	_
39	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	40	nsubj	_	_
40	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
41	$ chi_A(S, S) $	$ chi_a(s, s) $	SYM	$	_	40	attr	_	_
42	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 599
# sent_id = 1
# text = Symmetric monoidal closed categories may be related to one another not only by the functors between them but also by enrichment of one in another, and it was known to Kelly in the 1960s that there is a very close connection between these phenomena.
1	Symmetric	symmetric	ADJ	JJ	Degree=Pos	2	amod	_	_
2	monoidal	monoidal	NOUN	NN	Number=Sing	3	nsubj	_	_
3	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	4	amod	_	_
4	categories	category	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
5	may	may	AUX	MD	VerbForm=Fin	7	aux	_	_
6	be	be	AUX	VB	VerbForm=Inf	7	auxpass	_	_
7	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	to	to	ADP	IN	_	7	prep	_	_
9	one	one	NUM	CD	NumType=Card	8	pobj	_	_
10	another	another	DET	DT	_	9	det	_	_
11	not	not	PART	RB	Polarity=Neg	13	preconj	_	_
12	only	only	ADV	RB	_	11	advmod	_	_
13	by	by	ADP	IN	_	7	agent	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	functors	functor	NOUN	NNS	Number=Plur	13	pobj	_	_
16	between	between	ADP	IN	_	15	prep	_	_
17	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	16	pobj	_	_
18	but	but	CCONJ	CC	ConjType=Cmp	16	cc	_	_
19	also	also	ADV	RB	_	18	advmod	_	_
20	by	by	ADP	IN	_	7	prep	_	_
21	enrichment	enrichment	NOUN	NN	Number=Sing	20	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	one	one	NUM	CD	NumType=Card	22	pobj	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	another	another	PRON	DT	_	24	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
28	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	30	nsubjpass	_	_
29	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	30	auxpass	_	_
30	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	conj	_	_
31	to	to	ADP	IN	_	30	prep	_	_
32	Kelly	Kelly	PROPN	NNP	Number=Sing	31	pobj	_	_
33	in	in	ADP	IN	_	30	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
35	1960s	1960	NOUN	NNS	Number=Plur	33	pobj	_	_
36	that	that	SCONJ	IN	_	38	mark	_	_
37	there	there	PRON	EX	_	38	expl	_	_
38	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	ccomp	_	_
39	a	a	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
40	very	very	ADV	RB	_	41	advmod	_	_
41	close	close	ADJ	JJ	Degree=Pos	42	amod	_	_
42	connection	connection	NOUN	NN	Number=Sing	38	attr	_	_
43	between	between	ADP	IN	_	42	prep	_	_
44	these	these	DET	DT	Number=Plur|PronType=Dem	45	det	_	_
45	phenomena	phenomenon	NOUN	NNS	Number=Plur	43	pobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	30	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this first part of a two - part series on this subject, we show that the assignment to each symmetric monoidal closed category $ V $ its associated $ V $ - enriched category $ underline{V} $ extends to a 2 - functor valued in an op - 2 - fibred 2 - category of symmetric monoidal closed categories enriched over various bases.
1	In	in	ADP	IN	_	16	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
3	first	first	ADJ	JJ	Degree=Pos	4	amod	_	_
4	part	part	NOUN	NN	Number=Sing	1	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
7	two	two	NUM	CD	NumType=Card	9	nummod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	part	part	NOUN	NN	Number=Sing	10	compound	_	_
10	series	series	NOUN	NN	Number=Sing	5	pobj	_	_
11	on	on	ADP	IN	_	10	prep	_	_
12	this	this	DET	DT	Number=Sing|PronType=Dem	13	det	_	_
13	subject	subject	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
15	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	16	nsubj	_	_
16	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
17	that	that	SCONJ	IN	_	24	mark	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	assignment	assignment	NOUN	NN	Number=Sing	24	nsubj	_	_
20	to	to	ADP	IN	_	19	prep	_	_
21	each	each	DET	DT	_	23	det	_	_
22	symmetric	symmetric	ADJ	JJ	Degree=Pos	23	amod	_	_
23	monoidal	monoidal	NOUN	NN	Number=Sing	20	pobj	_	_
24	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	16	ccomp	_	_
25	category	category	NOUN	NN	Number=Sing	24	dobj	_	_
26	$ V $	$ v $	SYM	$	_	25	nummod	_	_
27	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	32	poss	_	_
28	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	amod	_	_
29	$ V $	$ v $	SYM	$	_	31	advmod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	amod	_	_
32	category	category	NOUN	NN	Number=Sing	34	nsubj	_	_
33	$ underline{V} $	$ underline{v} $	SYM	$	_	34	nsubj	_	_
34	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	ccomp	_	_
35	to	to	ADP	IN	_	34	prep	_	_
36	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
37	2	2	NUM	CD	NumType=Card	39	nummod	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	functor	functor	NOUN	NN	Number=Sing	35	pobj	_	_
40	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	39	acl	_	_
41	in	in	ADP	IN	_	40	prep	_	_
42	an	an	DET	DT	Definite=Ind|PronType=Art	50	det	_	_
43	op	op	NOUN	NN	Number=Sing	47	npadvmod	_	_
44	-	-	PUNCT	HYPH	PunctType=Dash	43	punct	_	_
45	2	2	NUM	CD	NumType=Card	43	nummod	_	_
46	-	-	PUNCT	HYPH	PunctType=Dash	47	punct	_	_
47	fibred	fibre	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	50	amod	_	_
48	2	2	NUM	CD	NumType=Card	50	nummod	_	_
49	-	-	PUNCT	HYPH	PunctType=Dash	50	punct	_	_
50	category	category	NOUN	NN	Number=Sing	41	pobj	_	_
51	of	of	ADP	IN	_	50	prep	_	_
52	symmetric	symmetric	ADJ	JJ	Degree=Pos	53	amod	_	_
53	monoidal	monoidal	NOUN	NN	Number=Sing	51	pobj	_	_
54	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	55	amod	_	_
55	categories	category	NOUN	NNS	Number=Plur	34	dobj	_	_
56	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	55	acl	_	_
57	over	over	ADP	IN	_	56	prep	_	_
58	various	various	ADJ	JJ	Degree=Pos	59	amod	_	_
59	bases	basis	NOUN	NNS	Number=Plur	57	pobj	_	SpaceAfter=No
60	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 3
# text = For a fixed $ V $ , we show that this induces a 2 - functorial passage from symmetric monoidal closed categories over $ V $ (that is, equipped with a morphism to $ V $ ) to symmetric monoidal closed $ V $ - categories over $ underline{V} $ .
1	For	for	ADP	IN	_	7	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	amod	_	_
4	$ V $	$ v $	SYM	$	_	1	pobj	_	_
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	that	that	SCONJ	IN	_	10	mark	_	_
9	this	this	PRON	DT	Number=Sing|PronType=Dem	10	nsubj	_	_
10	induces	induce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	ccomp	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
12	2	2	NUM	CD	NumType=Card	14	nummod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	functorial	functorial	NOUN	NN	Number=Sing	15	compound	_	_
15	passage	passage	NOUN	NN	Number=Sing	19	nsubj	_	_
16	from	from	ADP	IN	_	15	prep	_	_
17	symmetric	symmetric	ADJ	JJ	Degree=Pos	18	amod	_	_
18	monoidal	monoidal	NOUN	NN	Number=Sing	16	pobj	_	_
19	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	10	ccomp	_	_
20	categories	category	NOUN	NNS	Number=Plur	19	dobj	_	_
21	over	over	ADP	IN	_	19	prep	_	_
22	$ V $	$ v $	SYM	$	_	21	pobj	_	_
23	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	27	punct	_	SpaceAfter=No
24	that	that	ADV	RB	_	25	advmod	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	auxpass	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
27	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	parataxis	_	_
28	with	with	ADP	IN	_	27	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
30	morphism	morphism	NOUN	NN	Number=Sing	28	pobj	_	_
31	to	to	ADP	IN	_	27	prep	_	_
32	$ V $	$ v $	SYM	$	_	31	pobj	_	_
33	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	27	punct	_	_
34	to	to	AUX	IN	_	37	aux	_	_
35	symmetric	symmetric	ADJ	JJ	Degree=Pos	36	amod	_	_
36	monoidal	monoidal	NOUN	NN	Number=Sing	37	nsubj	_	_
37	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	10	advcl	_	_
38	$ V $	$ v $	SYM	$	_	40	compound	_	_
39	-	-	PUNCT	HYPH	PunctType=Dash	40	punct	_	_
40	categories	category	NOUN	NNS	Number=Plur	37	dobj	_	_
41	over	over	ADP	IN	_	37	prep	_	_
42	$ underline{V} $	$ underline{v} $	SYM	$	_	41	pobj	_	_
43	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = As a consequence, we find that the enriched adjunction determined a symmetric monoidal closed adjunction can be obtained by applying a 2 - functor and, consequently, is an adjunction in the 2 - category of symmetric monoidal closed $ V $ - categories.
1	As	as	ADP	IN	_	6	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	consequence	consequence	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	find	find	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	11	mark	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	adjunction	adjunction	NOUN	NN	Number=Sing	11	nsubj	_	_
11	determined	determine	VERB	VBD	Tense=Past|VerbForm=Fin	6	ccomp	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	symmetric	symmetric	ADJ	JJ	Degree=Pos	14	amod	_	_
14	monoidal	monoidal	NOUN	NN	Number=Sing	15	nsubj	_	_
15	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
16	adjunction	adjunction	NOUN	NN	Number=Sing	19	nsubjpass	_	_
17	can	can	AUX	MD	VerbForm=Fin	19	aux	_	_
18	be	be	AUX	VB	VerbForm=Inf	19	auxpass	_	_
19	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	ccomp	_	_
20	by	by	ADP	IN	_	19	prep	_	_
21	applying	apply	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	pcomp	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
23	2	2	NUM	CD	NumType=Card	25	nummod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	functor	functor	NOUN	NN	Number=Sing	21	dobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
28	consequently	consequently	ADV	RB	_	30	advmod	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
30	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	conj	_	_
31	an	an	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
32	adjunction	adjunction	NOUN	NN	Number=Sing	30	attr	_	_
33	in	in	ADP	IN	_	32	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
35	2	2	NUM	CD	NumType=Card	37	nummod	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	category	category	NOUN	NN	Number=Sing	33	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	symmetric	symmetric	ADJ	JJ	Degree=Pos	40	amod	_	_
40	monoidal	monoidal	NOUN	NN	Number=Sing	38	pobj	_	_
41	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	6	ccomp	_	_
42	$ V $	$ v $	SYM	$	_	44	nmod	_	_
43	-	-	PUNCT	HYPH	PunctType=Dash	44	punct	_	_
44	categories	category	NOUN	NNS	Number=Plur	41	dobj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 600
# sent_id = 1
# text = Under a minimum of assumptions, we develop in generality the basic theory of universal algebra in a symmetric monoidal closed category $ V $ with respect to a specified system of arities $ j:J hookrightarrow V $ .
1	Under	under	ADP	IN	_	8	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	minimum	minimum	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	assumptions	assumption	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
7	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	8	nsubj	_	_
8	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	generality	generality	NOUN	NN	Number=Sing	9	pobj	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	basic	basic	ADJ	JJ	Degree=Pos	13	amod	_	_
13	theory	theory	NOUN	NN	Number=Sing	21	nsubj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	universal	universal	ADJ	JJ	Degree=Pos	16	amod	_	_
16	algebra	algebra	NOUN	NN	Number=Sing	14	pobj	_	_
17	in	in	ADP	IN	_	13	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	symmetric	symmetric	ADJ	JJ	Degree=Pos	20	amod	_	_
20	monoidal	monoidal	NOUN	NN	Number=Sing	17	pobj	_	_
21	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	8	conj	_	_
22	category	category	NOUN	NN	Number=Sing	21	dobj	_	_
23	$ V $	$ v $	SYM	$	_	21	dep	_	_
24	with	with	ADP	IN	_	21	prep	_	_
25	respect	respect	NOUN	NN	Number=Sing	24	pobj	_	_
26	to	to	ADP	IN	_	25	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	specified	specify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	amod	_	_
29	system	system	NOUN	NN	Number=Sing	26	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	arities	arity	NOUN	NNS	Number=Plur	30	pobj	_	_
32	$ j:J hookrightarrow V $	$ j:j hookrightarrow v $	SYM	$	_	29	appos	_	_
33	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = Lawvere's notion of algebraic theory generalizes to this context, resulting in the notion of single - sorted $ V $ - enriched $ J $ - cotensor theory, or $ J $ - theory for short.
1	Lawvere	Lawvere	PROPN	NNP	Number=Sing	3	poss	_	SpaceAfter=No
2	's	's	PART	POS	_	1	case	_	_
3	notion	notion	NOUN	NN	Number=Sing	7	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	algebraic	algebraic	ADJ	JJ	Degree=Pos	6	amod	_	_
6	theory	theory	NOUN	NN	Number=Sing	4	pobj	_	_
7	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	to	to	ADP	IN	_	7	prep	_	_
9	this	this	DET	DT	Number=Sing|PronType=Dem	10	det	_	_
10	context	context	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
12	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	advcl	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	notion	notion	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	single	single	ADJ	JJ	Degree=Pos	19	advmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	sorted	sorted	ADJ	JJ	Degree=Pos	26	amod	_	_
20	$ V $	$ v $	SYM	$	_	22	advmod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
23	$ J $	$ j $	SYM	$	_	25	det	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	cotensor	cotensor	NOUN	NN	Number=Sing	26	compound	_	_
26	theory	theory	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
28	or	or	CCONJ	CC	ConjType=Cmp	26	cc	_	_
29	$ J $	$ j $	SYM	$	_	31	compound	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	theory	theory	NOUN	NN	Number=Sing	26	conj	_	_
32	for	for	ADP	IN	_	31	prep	_	_
33	short	short	ADJ	JJ	Degree=Pos	32	amod	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = For suitable choices of $ V $ and $ J $ , such $ J $ - theories include the enriched algebraic theories of Borceux and Day, the enriched Lawvere theories of Power, the equational theories of Linton's 1965 work, and the $ V $ - theories of Dubuc, which are recovered by taking $ J = V $ and correspond to arbitrary $ V $ - monads on $ V $ .
1	For	for	ADP	IN	_	13	prep	_	_
2	suitable	suitable	ADJ	JJ	Degree=Pos	3	amod	_	_
3	choices	choice	NOUN	NNS	Number=Plur	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	$ V $	$ v $	SYM	$	_	4	pobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	$ J $	$ j $	SYM	$	_	5	conj	_	_
8	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
9	such	such	ADJ	JJ	Degree=Pos	12	amod	_	_
10	$ J $	$ j $	SYM	$	_	12	compound	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	theories	theory	NOUN	NNS	Number=Plur	13	nsubj	_	_
13	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
15	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
16	algebraic	algebraic	ADJ	JJ	Degree=Pos	17	amod	_	_
17	theories	theory	NOUN	NNS	Number=Plur	13	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	Borceux	Borceux	PROPN	NNP	Number=Sing	18	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	Day	Day	PROPN	NNP	Number=Sing	19	conj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
24	enriched	enriched	ADJ	JJ	Degree=Pos	26	amod	_	_
25	Lawvere	Lawvere	PROPN	NNP	Number=Sing	26	compound	_	_
26	theories	theory	NOUN	NNS	Number=Plur	17	appos	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	Power	Power	PROPN	NNP	Number=Sing	27	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	equational	equational	ADJ	JJ	Degree=Pos	32	amod	_	_
32	theories	theory	NOUN	NNS	Number=Plur	26	conj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	Linton	Linton	PROPN	NNP	Number=Sing	37	poss	_	SpaceAfter=No
35	's	's	PART	POS	_	34	case	_	_
36	1965	1965	NUM	CD	NumType=Card	37	nummod	_	_
37	work	work	NOUN	NN	Number=Sing	33	pobj	_	SpaceAfter=No
38	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
39	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
40	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
41	$ V $	$ v $	SYM	$	_	43	compound	_	_
42	-	-	PUNCT	HYPH	PunctType=Dash	43	punct	_	_
43	theories	theory	NOUN	NNS	Number=Plur	32	conj	_	_
44	of	of	ADP	IN	_	43	prep	_	_
45	Dubuc	Dubuc	PROPN	NNP	Number=Sing	44	pobj	_	SpaceAfter=No
46	,	,	PUNCT	,	PunctType=Comm	45	punct	_	_
47	which	which	PRON	WDT	_	49	nsubjpass	_	_
48	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	49	auxpass	_	_
49	recovered	recover	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	45	relcl	_	_
50	by	by	ADP	IN	_	49	prep	_	_
51	taking	take	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	50	pcomp	_	_
52	$ J = V $	$ j = v $	SYM	$	_	51	dobj	_	_
53	and	and	CCONJ	CC	ConjType=Cmp	51	cc	_	_
54	correspond	correspond	VERB	VB	VerbForm=Inf	51	conj	_	_
55	to	to	ADP	IN	_	54	prep	_	_
56	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	59	amod	_	_
57	$ V $	$ v $	SYM	$	_	59	compound	_	_
58	-	-	PUNCT	HYPH	PunctType=Dash	59	punct	_	_
59	monads	monad	NOUN	NNS	Number=Plur	55	pobj	_	_
60	on	on	ADP	IN	_	59	prep	_	_
61	$ V $	$ v $	SYM	$	_	60	pobj	_	_
62	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 4
# text = We identify a modest condition on $ j $ that entails that the $ V $ - category of $ T $ - algebras exists and is monadic over $ V $ for every $ J $ - theory $ T $ , even when $ T $ is not small and $ V $ is neither complete nor cocomplete.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	identify	identify	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	modest	modest	ADJ	JJ	Degree=Pos	5	amod	_	_
5	condition	condition	NOUN	NN	Number=Sing	2	dobj	_	_
6	on	on	ADP	IN	_	5	prep	_	_
7	$ j $	$ j $	SYM	$	_	6	pobj	_	_
8	that	that	PRON	WDT	PronType=Rel	9	nsubj	_	_
9	entails	entail	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	relcl	_	_
10	that	that	SCONJ	IN	_	19	mark	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
12	$ V $	$ v $	SYM	$	_	14	nmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	category	category	NOUN	NN	Number=Sing	19	nsubj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	$ T $	$ t $	SYM	$	_	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	algebras	algebras	PROPN	NNP	Number=Sing	15	pobj	_	_
19	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	ccomp	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	conj	_	_
22	monadic	monadic	ADJ	JJ	Degree=Pos	21	acomp	_	_
23	over	over	ADP	IN	_	22	prep	_	_
24	$ V $	$ v $	SYM	$	_	23	pobj	_	_
25	for	for	ADP	IN	_	21	prep	_	_
26	every	every	DET	DT	_	29	det	_	_
27	$ J $	$ j $	SYM	$	_	29	compound	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	theory	theory	NOUN	NN	Number=Sing	25	pobj	_	_
30	$ T $	$ t $	SYM	$	_	29	appos	_	_
31	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
32	even	even	ADV	RB	_	33	advmod	_	_
33	when	when	SCONJ	WRB	_	35	advmod	_	_
34	$ T $	$ t $	SYM	$	_	35	nsubj	_	_
35	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	21	advcl	_	_
36	not	not	PART	RB	Polarity=Neg	35	neg	_	_
37	small	small	ADJ	JJ	Degree=Pos	35	acomp	_	_
38	and	and	CCONJ	CC	ConjType=Cmp	37	cc	_	_
39	$ V $	$ v $	SYM	$	_	40	nsubj	_	_
40	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
41	neither	neither	ADV	RB	_	42	preconj	_	_
42	complete	complete	ADJ	JJ	Degree=Pos	40	acomp	_	_
43	nor	nor	CCONJ	CC	ConjType=Cmp	42	cc	_	_
44	cocomplete	cocomplete	ADJ	JJ	Degree=Pos	42	conj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = We show that $ j $ satisfies this condition if and only if $ j $ presents $ V $ as a free cocompletion of $ J $ with respect to the weights for left Kan extensions along $ j $ , and so we call such systems of arities eleutheric.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	$ j $	$ j $	SYM	$	_	5	nmod	_	_
5	satisfies	satisfie	NOUN	NNS	Number=Plur	2	ccomp	_	_
6	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
7	condition	condition	NOUN	NN	Number=Sing	5	npadvmod	_	_
8	if	if	SCONJ	IN	_	2	prep	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	only	only	ADV	RB	_	13	advmod	_	_
11	if	if	SCONJ	IN	_	13	mark	_	_
12	$ j $	$ j $	SYM	$	_	13	nsubj	_	_
13	presents	present	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	advcl	_	_
14	$ V $	$ v $	SYM	$	_	13	dep	_	_
15	as	as	ADP	IN	_	13	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	free	free	ADJ	JJ	Degree=Pos	18	amod	_	_
18	cocompletion	cocompletion	NOUN	NN	Number=Sing	15	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	$ J $	$ j $	SYM	$	_	19	pobj	_	_
21	with	with	ADP	IN	_	13	prep	_	_
22	respect	respect	NOUN	NN	Number=Sing	21	pobj	_	_
23	to	to	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	weights	weight	NOUN	NNS	Number=Plur	23	pobj	_	_
26	for	for	ADP	IN	_	25	prep	_	_
27	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	amod	_	_
28	Kan	Kan	PROPN	NNP	Number=Sing	29	compound	_	_
29	extensions	extension	NOUN	NNS	Number=Plur	26	pobj	_	_
30	along	along	ADP	IN	_	29	prep	_	_
31	$ j $	$ j $	SYM	$	_	30	pobj	_	_
32	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
34	so	so	ADV	RB	_	36	advmod	_	_
35	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	36	nsubj	_	_
36	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	13	conj	_	_
37	such	such	ADJ	JJ	Degree=Pos	38	amod	_	_
38	systems	system	NOUN	NNS	Number=Plur	36	dobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	arities	arity	NOUN	NNS	Number=Plur	39	pobj	_	_
41	eleutheric	eleutheric	ADJ	JJ	Degree=Pos	40	amod	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	36	punct	_	SpaceAfter=No

# sent_id = 6
# text = We show that $ J $ - theories for an eleutheric system may be equivalently described as (i) monads in a certain one - object bicategory of profunctors on $ J $ , and (ii) $ V $ - monads on $ V $ satisfying a certain condition.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	14	mark	_	_
4	$ J $	$ j $	SYM	$	_	6	compound	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	theories	theory	NOUN	NNS	Number=Plur	14	nsubjpass	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	eleutheric	eleutheric	ADJ	JJ	Degree=Pos	10	amod	_	_
10	system	system	NOUN	NN	Number=Sing	7	pobj	_	_
11	may	may	AUX	MD	VerbForm=Fin	14	aux	_	_
12	be	be	AUX	VB	VerbForm=Inf	14	auxpass	_	_
13	equivalently	equivalently	ADV	RB	_	14	advmod	_	_
14	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
15	as	as	ADP	IN	_	14	prep	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	15	punct	_	SpaceAfter=No
17	i	i	NOUN	NN	Case=Acc|Number=Sing|Person=1|PronType=Prs	15	pobj	_	SpaceAfter=No
18	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	15	punct	_	_
19	monads	monad	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	pobj	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
22	certain	certain	ADJ	JJ	Degree=Pos	26	amod	_	_
23	one	one	NUM	CD	NumType=Card	25	nummod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	object	object	NOUN	NN	Number=Sing	26	compound	_	_
26	bicategory	bicategory	NOUN	NN	Number=Sing	20	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	profunctors	profunctor	NOUN	NNS	Number=Plur	27	pobj	_	_
29	on	on	ADP	IN	_	26	prep	_	_
30	$ J $	$ j $	SYM	$	_	29	pobj	_	_
31	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
33	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	34	punct	_	SpaceAfter=No
34	ii	ii	PROPN	NNP	Number=Sing	38	dep	_	SpaceAfter=No
35	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	38	punct	_	_
36	$ V $	$ v $	SYM	$	_	38	nummod	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	38	punct	_	_
38	monads	monad	NOUN	NNS	Number=Plur	14	conj	_	_
39	on	on	ADP	IN	_	38	prep	_	_
40	$ V $	$ v $	SYM	$	_	39	pobj	_	_
41	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	advcl	_	_
42	a	a	DET	DT	Definite=Ind|PronType=Art	44	det	_	_
43	certain	certain	ADJ	JJ	Degree=Pos	44	amod	_	_
44	condition	condition	NOUN	NN	Number=Sing	41	dobj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = We prove a characterization theorem for the categories of algebras of $ J $ - theories, considered as $ V $ - categories $ A $ equipped with a specified $ V $ - functor $ A rightarrow V $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	characterization	characterization	NOUN	NN	Number=Sing	5	nsubj	_	_
5	theorem	theorem	ADJ	JJ	Degree=Pos	2	ccomp	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	algebras	algebra	NOUN	NNS	Number=Plur	9	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	$ J $	$ j $	SYM	$	_	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	theories	theory	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
16	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	advcl	_	_
17	as	as	ADP	IN	_	16	prep	_	_
18	$ V $	$ v $	SYM	$	_	20	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	_
21	$ A $	$ a $	SYM	$	_	16	npadvmod	_	_
22	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	advcl	_	_
23	with	with	ADP	IN	_	22	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
25	specified	specify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	amod	_	_
26	$ V $	$ v $	SYM	$	_	28	compound	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	functor	functor	NOUN	NN	Number=Sing	29	compound	_	_
29	$ A rightarrow V $	$ a rightarrow v $	SYM	$	_	23	pobj	_	_
30	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 601
# sent_id = 1
# text = Birkhoff's variety theorem from universal algebra characterises equational subcategories of varieties.
1	Birkhoff	Birkhoff	PROPN	NNP	Number=Sing	3	poss	_	SpaceAfter=No
2	's	's	PART	POS	_	1	case	_	_
3	variety	variety	NOUN	NN	Number=Sing	4	nsubj	_	_
4	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
5	from	from	ADP	IN	_	4	prep	_	_
6	universal	universal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	algebra	algebra	NOUN	NN	Number=Sing	5	pobj	_	_
8	characterises	characterise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	conj	_	_
9	equational	equational	ADJ	JJ	Degree=Pos	10	amod	_	_
10	subcategories	subcategorie	NOUN	NNS	Number=Plur	8	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	varieties	variety	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = We give an analogue of Birkhoff's theorem in the setting of enrichment in categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	analogue	analogue	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	Birkhoff	Birkhoff	PROPN	NNP	Number=Sing	8	poss	_	SpaceAfter=No
7	's	's	PART	POS	_	6	case	_	_
8	theorem	theorem	ADJ	JJ	Degree=Pos	5	pobj	_	_
9	in	in	ADP	IN	_	2	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	setting	setting	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	enrichment	enrichment	NOUN	NN	Number=Sing	12	pobj	_	_
14	in	in	ADP	IN	_	11	prep	_	_
15	categories	category	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = For a suitable notion of an equational subcategory we characterise these subcategories by their closure properties in the ambient algebraic category.
1	For	for	ADP	IN	_	0	ROOT	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	suitable	suitable	ADJ	JJ	Degree=Pos	4	amod	_	_
4	notion	notion	NOUN	NN	Number=Sing	1	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	equational	equational	ADJ	JJ	Degree=Pos	8	amod	_	_
8	subcategory	subcategory	NOUN	NN	Number=Sing	5	pobj	_	_
9	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
10	characterise	characterise	VERB	VBP	Tense=Pres|VerbForm=Fin	8	relcl	_	_
11	these	these	DET	DT	Number=Plur|PronType=Dem	12	det	_	_
12	subcategories	subcategorie	NOUN	NNS	Number=Plur	10	dobj	_	_
13	by	by	ADP	IN	_	10	prep	_	_
14	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	16	poss	_	_
15	closure	closure	NOUN	NN	Number=Sing	16	compound	_	_
16	properties	property	NOUN	NNS	Number=Plur	13	pobj	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
19	ambient	ambient	ADJ	JJ	Degree=Pos	21	amod	_	_
20	algebraic	algebraic	ADJ	JJ	Degree=Pos	21	amod	_	_
21	category	category	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# doc_id = 602
# sent_id = 1
# text = We show that every small model category that satisfies certain size conditions can be completed to yield a combinatorial model category, and conversely, every combinatorial model category arises in this way.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	15	mark	_	_
4	every	every	DET	DT	_	7	det	_	_
5	small	small	ADJ	JJ	Degree=Pos	6	amod	_	_
6	model	model	NOUN	NN	Number=Sing	7	compound	_	_
7	category	category	NOUN	NN	Number=Sing	15	nsubjpass	_	_
8	that	that	PRON	WDT	PronType=Rel	9	nsubj	_	_
9	satisfies	satisfy	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	relcl	_	_
10	certain	certain	ADJ	JJ	Degree=Pos	12	amod	_	_
11	size	size	NOUN	NN	Number=Sing	12	compound	_	_
12	conditions	condition	NOUN	NNS	Number=Plur	15	nsubjpass	_	_
13	can	can	AUX	MD	VerbForm=Fin	15	aux	_	_
14	be	be	AUX	VB	VerbForm=Inf	15	auxpass	_	_
15	completed	complete	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
16	to	to	PART	TO	_	17	aux	_	_
17	yield	yield	VERB	VB	VerbForm=Inf	15	xcomp	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
19	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	21	amod	_	_
20	model	model	NOUN	NN	Number=Sing	21	compound	_	_
21	category	category	NOUN	NN	Number=Sing	17	dobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
24	conversely	conversely	ADV	RB	_	30	advmod	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
26	every	every	DET	DT	_	29	det	_	_
27	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	28	amod	_	_
28	model	model	NOUN	NN	Number=Sing	29	compound	_	_
29	category	category	NOUN	NN	Number=Sing	30	nsubj	_	_
30	arises	arise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	conj	_	_
31	in	in	ADP	IN	_	30	prep	_	_
32	this	this	DET	DT	Number=Sing|PronType=Dem	33	det	_	_
33	way	way	NOUN	NN	Number=Sing	31	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We will also see that these constructions preserve right properness and compatibility with simplicial enrichment.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
2	will	will	AUX	MD	VerbForm=Fin	4	aux	_	_
3	also	also	ADV	RB	_	4	advmod	_	_
4	see	see	VERB	VB	VerbForm=Inf	0	ROOT	_	_
5	that	that	SCONJ	IN	_	8	mark	_	_
6	these	these	DET	DT	Number=Plur|PronType=Dem	7	det	_	_
7	constructions	construction	NOUN	NNS	Number=Plur	8	nsubj	_	_
8	preserve	preserve	VERB	VBP	Tense=Pres|VerbForm=Fin	4	ccomp	_	_
9	right	right	ADJ	JJ	Degree=Pos	10	amod	_	_
10	properness	properness	NOUN	NN	Number=Sing	8	dobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	compatibility	compatibility	NOUN	NN	Number=Sing	10	conj	_	_
13	with	with	ADP	IN	_	10	prep	_	_
14	simplicial	simplicial	ADJ	JJ	Degree=Pos	15	amod	_	_
15	enrichment	enrichment	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = Along the way, we establish some technical results on the index of accessibility of various constructions on accessible categories, which may be of independent interest.
1	Along	along	ADP	IN	_	6	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	way	way	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	establish	establish	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	some	some	DET	DT	_	9	det	_	_
8	technical	technical	ADJ	JJ	Degree=Pos	9	amod	_	_
9	results	result	NOUN	NNS	Number=Plur	6	dobj	_	_
10	on	on	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	index	index	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	accessibility	accessibility	NOUN	NN	Number=Sing	13	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	various	various	ADJ	JJ	Degree=Pos	17	amod	_	_
17	constructions	construction	NOUN	NNS	Number=Plur	15	pobj	_	_
18	on	on	ADP	IN	_	17	prep	_	_
19	accessible	accessible	ADJ	JJ	Degree=Pos	20	amod	_	_
20	categories	category	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	which	which	PRON	WDT	_	24	nsubj	_	_
23	may	may	AUX	MD	VerbForm=Fin	24	aux	_	_
24	be	be	AUX	VB	VerbForm=Inf	20	relcl	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	independent	independent	ADJ	JJ	Degree=Pos	27	amod	_	_
27	interest	interest	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 603
# sent_id = 1
# text = We develop the homotopy theory of Euler characteristic (magnitude) of a category enriched in a monoidal model category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	homotopy	homotopy	NOUN	NN	Number=Sing	5	compound	_	_
5	theory	theory	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Euler	Euler	PROPN	NNP	Number=Sing	8	compound	_	_
8	characteristic	characteristic	ADJ	JJ	Degree=Pos	6	pobj	_	_
9	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	10	punct	_	SpaceAfter=No
10	magnitude	magnitude	NOUN	NN	Number=Sing	8	parataxis	_	SpaceAfter=No
11	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	10	punct	_	_
12	of	of	ADP	IN	_	10	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
15	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	acl	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
18	monoidal	monoidal	ADJ	JJ	Degree=Pos	20	amod	_	_
19	model	model	NOUN	NN	Number=Sing	20	compound	_	_
20	category	category	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = If a monoidal model category $ V $ is equipped with an Euler characteristic that is compatible with weak equivalences and fibrations in $ V $ , then our Euler characteristic of $ V $ - enriched categories is also compatible with weak equivalences and fibrations in the canonical model structure on the category of $ V $ - enriched categories.
1	If	if	SCONJ	IN	_	8	mark	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
3	monoidal	monoidal	ADJ	JJ	Degree=Pos	4	amod	_	_
4	model	model	NOUN	NN	Number=Sing	5	compound	_	_
5	category	category	NOUN	NN	Number=Sing	8	nsubjpass	_	_
6	$ V $	$ v $	SYM	$	_	5	appos	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	advcl	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	Euler	Euler	PROPN	NNP	Number=Sing	12	compound	_	_
12	characteristic	characteristic	NOUN	NN	Number=Sing	9	pobj	_	_
13	that	that	PRON	WDT	PronType=Rel	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	relcl	_	_
15	compatible	compatible	ADJ	JJ	Degree=Pos	14	acomp	_	_
16	with	with	ADP	IN	_	15	prep	_	_
17	weak	weak	ADJ	JJ	Degree=Pos	18	amod	_	_
18	equivalences	equivalence	NOUN	NNS	Number=Plur	16	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	fibrations	fibration	NOUN	NNS	Number=Plur	18	conj	_	_
21	in	in	ADP	IN	_	20	prep	_	_
22	$ V $	$ v $	SYM	$	_	21	pobj	_	_
23	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
24	then	then	ADV	RB	PronType=Dem	27	advmod	_	_
25	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	26	poss	_	_
26	Euler	Euler	PROPN	NNP	Number=Sing	27	compound	_	_
27	characteristic	characteristic	NOUN	NN	Number=Sing	33	nsubj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	$ V $	$ v $	SYM	$	_	31	advmod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	amod	_	_
32	categories	category	NOUN	NNS	Number=Plur	28	pobj	_	_
33	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
34	also	also	ADV	RB	_	33	advmod	_	_
35	compatible	compatible	ADJ	JJ	Degree=Pos	33	acomp	_	_
36	with	with	ADP	IN	_	35	prep	_	_
37	weak	weak	ADJ	JJ	Degree=Pos	38	amod	_	_
38	equivalences	equivalence	NOUN	NNS	Number=Plur	36	pobj	_	_
39	and	and	CCONJ	CC	ConjType=Cmp	38	cc	_	_
40	fibrations	fibration	NOUN	NNS	Number=Plur	38	conj	_	_
41	in	in	ADP	IN	_	40	prep	_	_
42	the	the	DET	DT	Definite=Def|PronType=Art	45	det	_	_
43	canonical	canonical	ADJ	JJ	Degree=Pos	44	amod	_	_
44	model	model	NOUN	NN	Number=Sing	45	compound	_	_
45	structure	structure	NOUN	NN	Number=Sing	41	pobj	_	_
46	on	on	ADP	IN	_	45	prep	_	_
47	the	the	DET	DT	Definite=Def|PronType=Art	48	det	_	_
48	category	category	NOUN	NN	Number=Sing	46	pobj	_	_
49	of	of	ADP	IN	_	48	prep	_	_
50	$ V $	$ v $	SYM	$	_	52	advmod	_	_
51	-	-	PUNCT	HYPH	PunctType=Dash	52	punct	_	_
52	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	53	amod	_	_
53	categories	category	NOUN	NNS	Number=Plur	49	pobj	_	SpaceAfter=No
54	.	.	PUNCT	.	PunctType=Peri	33	punct	_	SpaceAfter=No

# sent_id = 3
# text = In particular, we focus on the case of topological categories; that is, categories enriched in the category of topological spaces.
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	focus	focus	VERB	VBP	Tense=Pres|VerbForm=Fin	14	ccomp	_	_
6	on	on	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	case	case	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	topological	topological	ADJ	JJ	Degree=Pos	11	amod	_	_
11	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
12	;	;	PUNCT	:	_	14	punct	_	_
13	that	that	PRON	DT	Number=Sing|PronType=Dem	14	advmod	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	categories	category	NOUN	NNS	Number=Plur	14	attr	_	_
17	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	acl	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	topological	topological	ADJ	JJ	Degree=Pos	23	amod	_	_
23	spaces	space	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 4
# text = As its application, we obtain the ordinary Euler characteristic of a cellular stratified space $ X $ by computing the Euler characteristic of the face category $ C(X) $ .
1	As	as	ADP	IN	_	6	prep	_	_
2	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	3	poss	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	ordinary	ordinary	ADJ	JJ	Degree=Pos	10	amod	_	_
9	Euler	Euler	PROPN	NNP	Number=Sing	10	compound	_	_
10	characteristic	characteristic	ADJ	JJ	Degree=Pos	6	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	cellular	cellular	ADJ	JJ	Degree=Pos	15	amod	_	_
14	stratified	stratify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
15	space	space	NOUN	NN	Number=Sing	11	pobj	_	_
16	$ X $	$ x $	SYM	$	_	15	appos	_	_
17	by	by	ADP	IN	_	6	prep	_	_
18	computing	compute	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	pcomp	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	Euler	Euler	PROPN	NNP	Number=Sing	21	compound	_	_
21	characteristic	characteristic	NOUN	NN	Number=Sing	18	dobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	face	face	NOUN	NN	Number=Sing	25	compound	_	_
25	category	category	NOUN	NN	Number=Sing	22	pobj	_	_
26	$ C(X) $	$ c(x) $	SYM	$	_	18	dobj	_	_
27	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 604
# sent_id = 1
# text = We study a categorical commutator, introduced by Huq, defined for a pair of coterminal morphisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	categorical	categorical	ADJ	JJ	Degree=Pos	5	amod	_	_
5	commutator	commutator	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	acl	_	_
8	by	by	ADP	IN	_	7	agent	_	_
9	Huq	Huq	PROPN	NNP	Number=Sing	8	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
11	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	acl	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	pair	pair	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	coterminal	coterminal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	morphisms	morphism	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that in a normal unital category $ C $ with finite colimits, the normal closure of the regular image of the Huq commutator of a pair of subobjects under an arbitrary morphism is the same as the Huq commutator of their respective regular images.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	34	mark	_	_
4	in	in	ADP	IN	_	34	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
6	normal	normal	ADJ	JJ	Degree=Pos	8	amod	_	_
7	unital	unital	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
9	$ C $	$ c $	SYM	$	_	4	dep	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	finite	finite	ADJ	JJ	Degree=Pos	12	amod	_	_
12	colimits	colimit	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	34	punct	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	normal	normal	ADJ	JJ	Degree=Pos	16	amod	_	_
16	closure	closure	NOUN	NN	Number=Sing	34	nsubj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	regular	regular	ADJ	JJ	Degree=Pos	20	amod	_	_
20	image	image	NOUN	NN	Number=Sing	17	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	Huq	Huq	PROPN	NNP	Number=Sing	24	compound	_	_
24	commutator	commutator	NOUN	NN	Number=Sing	21	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	pair	pair	NOUN	NN	Number=Sing	25	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	subobjects	subobject	NOUN	NNS	Number=Plur	28	pobj	_	_
30	under	under	ADP	IN	_	27	prep	_	_
31	an	an	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
32	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	33	amod	_	_
33	morphism	morphism	NOUN	NN	Number=Sing	30	pobj	_	_
34	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	same	same	ADJ	JJ	Degree=Pos	34	attr	_	_
37	as	as	ADP	IN	_	36	prep	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
39	Huq	Huq	PROPN	NNP	Number=Sing	40	compound	_	_
40	commutator	commutator	NOUN	NN	Number=Sing	37	pobj	_	_
41	of	of	ADP	IN	_	40	prep	_	_
42	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	45	poss	_	_
43	respective	respective	ADJ	JJ	Degree=Pos	45	amod	_	_
44	regular	regular	ADJ	JJ	Degree=Pos	45	amod	_	_
45	images	image	NOUN	NNS	Number=Plur	41	pobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Then we use this property to characterize the Huq commutator as the largest commutator satisfying certain properties.
1	Then	then	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	property	property	NOUN	NN	Number=Sing	3	dobj	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	characterize	characterize	VERB	VB	VerbForm=Inf	3	xcomp	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	Huq	Huq	PROPN	NNP	Number=Sing	10	compound	_	_
10	commutator	commutator	NOUN	NN	Number=Sing	7	dobj	_	_
11	as	as	ADP	IN	_	7	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	largest	large	ADJ	JJS	Degree=Sup	14	amod	_	_
14	commutator	commutator	NOUN	NN	Number=Sing	11	pobj	_	_
15	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	acl	_	_
16	certain	certain	ADJ	JJ	Degree=Pos	17	amod	_	_
17	properties	property	NOUN	NNS	Number=Plur	15	dobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 605
# sent_id = 1
# text = The purpose of this paper is two - fold.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	purpose	purpose	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	paper	paper	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	two	two	NUM	CD	NumType=Card	9	nummod	_	_
8	-	-	ADJ	JJ	Degree=Pos	9	punct	_	_
9	fold	fold	ADJ	JJ	Degree=Pos	6	acomp	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = A first and more concrete aim is to characterise $ n $ - permutable categories through certain stability properties of regular epimorphisms.
1	A	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
2	first	first	ADJ	JJ	Degree=Pos	6	amod	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	more	more	ADV	RBR	Degree=Cmp	2	conj	_	_
5	concrete	concrete	ADJ	JJ	Degree=Pos	2	conj	_	_
6	aim	aim	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	characterise	characterise	VERB	VB	VerbForm=Inf	7	xcomp	_	_
10	$ n $	$ n $	SYM	$	_	12	advmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	permutable	permutable	ADJ	JJ	Degree=Pos	13	amod	_	_
13	categories	category	NOUN	NNS	Number=Plur	9	dobj	_	_
14	through	through	ADP	IN	_	9	prep	_	_
15	certain	certain	ADJ	JJ	Degree=Pos	17	amod	_	_
16	stability	stability	NOUN	NN	Number=Sing	17	compound	_	_
17	properties	property	NOUN	NNS	Number=Plur	14	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	regular	regular	ADJ	JJ	Degree=Pos	20	amod	_	_
20	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = These characterisations allow us to recover the ternary terms and the $ (n+1) $ - ary terms describing $ n $ - permutable varieties of universal algebras.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	characterisations	characterisation	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	allow	allow	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	recover	recover	VERB	VB	VerbForm=Inf	3	ccomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	ternary	ternary	NOUN	NN	Number=Sing	9	compound	_	_
9	terms	term	NOUN	NNS	Number=Plur	6	dobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
12	$ (n+1) $	$ (n+1) $	SYM	$	_	14	nmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	ary	ary	ADJ	JJ	Degree=Pos	15	amod	_	_
15	terms	term	NOUN	NNS	Number=Plur	9	conj	_	_
16	describing	describe	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	acl	_	_
17	$ n $	$ n $	SYM	$	_	19	advmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	permutable	permutable	ADJ	JJ	Degree=Pos	20	amod	_	_
20	varieties	variety	NOUN	NNS	Number=Plur	16	dobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	universal	universal	ADJ	JJ	Degree=Pos	23	amod	_	_
23	algebras	algebra	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = A second and more abstract aim is to explain two proof techniques, by using the above characterisation as an opportunity to provide explicit new examples of their use: (i) an embedding theorem for $ n $ - permutable categories which allows us to follow the varietal proof to show that an $ n $ - permutable category has certain properties; (ii) the theory of unconditional exactness properties which allows us to remove the assumption of the existence of colimits, in particular when we use the approximate co - operations approach to show that a regular category is $ n $ - permutable.
1	A	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
2	second	second	ADJ	JJ	Degree=Pos	6	amod	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	more	more	ADV	RBR	Degree=Cmp	2	conj	_	_
5	abstract	abstract	ADJ	JJ	Degree=Pos	2	conj	_	_
6	aim	aim	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	explain	explain	VERB	VB	VerbForm=Inf	7	xcomp	_	_
10	two	two	NUM	CD	NumType=Card	12	nummod	_	_
11	proof	proof	NOUN	NN	Number=Sing	12	compound	_	_
12	techniques	technique	NOUN	NNS	Number=Plur	9	dobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
14	by	by	ADP	IN	_	9	prep	_	_
15	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	pcomp	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	above	above	ADJ	JJ	Degree=Pos	18	amod	_	_
18	characterisation	characterisation	NOUN	NN	Number=Sing	15	dobj	_	_
19	as	as	ADP	IN	_	15	prep	_	_
20	an	an	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	opportunity	opportunity	NOUN	NN	Number=Sing	19	pobj	_	_
22	to	to	PART	TO	_	23	aux	_	_
23	provide	provide	VERB	VB	VerbForm=Inf	21	acl	_	_
24	explicit	explicit	ADJ	JJ	Degree=Pos	26	amod	_	_
25	new	new	ADJ	JJ	Degree=Pos	26	amod	_	_
26	examples	example	NOUN	NNS	Number=Plur	23	dobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	29	poss	_	_
29	use	use	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
30	:	:	PUNCT	:	_	32	punct	_	_
31	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	32	punct	_	SpaceAfter=No
32	i	i	NOUN	NN	Number=Sing	6	appos	_	SpaceAfter=No
33	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	32	punct	_	_
34	an	an	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
35	embedding	embed	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	36	amod	_	_
36	theorem	theorem	NOUN	NN	Number=Sing	32	appos	_	_
37	for	for	ADP	IN	_	36	prep	_	_
38	$ n $	$ n $	SYM	$	_	40	advmod	_	_
39	-	-	PUNCT	HYPH	PunctType=Dash	40	punct	_	_
40	permutable	permutable	ADJ	JJ	Degree=Pos	41	amod	_	_
41	categories	category	NOUN	NNS	Number=Plur	37	pobj	_	_
42	which	which	PRON	WDT	_	43	nsubj	_	_
43	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	41	relcl	_	_
44	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	46	nsubj	_	_
45	to	to	PART	TO	_	46	aux	_	_
46	follow	follow	VERB	VB	VerbForm=Inf	43	ccomp	_	_
47	the	the	DET	DT	Definite=Def|PronType=Art	49	det	_	_
48	varietal	varietal	ADJ	JJ	Degree=Pos	49	amod	_	_
49	proof	proof	NOUN	NN	Number=Sing	46	dobj	_	_
50	to	to	PART	TO	_	51	aux	_	_
51	show	show	VERB	VB	VerbForm=Inf	49	acl	_	_
52	that	that	SCONJ	IN	_	58	mark	_	_
53	an	an	DET	DT	Definite=Ind|PronType=Art	57	det	_	_
54	$ n $	$ n $	SYM	$	_	56	advmod	_	_
55	-	-	PUNCT	HYPH	PunctType=Dash	56	punct	_	_
56	permutable	permutable	ADJ	JJ	Degree=Pos	57	amod	_	_
57	category	category	NOUN	NN	Number=Sing	58	nsubj	_	_
58	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	51	ccomp	_	_
59	certain	certain	ADJ	JJ	Degree=Pos	60	amod	_	_
60	properties	property	NOUN	NNS	Number=Plur	58	dobj	_	SpaceAfter=No
61	;	;	PUNCT	:	_	32	punct	_	_
62	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	63	punct	_	SpaceAfter=No
63	ii	ii	PROPN	NNP	Number=Sing	32	appos	_	SpaceAfter=No
64	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	63	punct	_	_
65	the	the	DET	DT	Definite=Def|PronType=Art	66	det	_	_
66	theory	theory	NOUN	NN	Number=Sing	32	appos	_	_
67	of	of	ADP	IN	_	66	prep	_	_
68	unconditional	unconditional	ADJ	JJ	Degree=Pos	70	amod	_	_
69	exactness	exactness	NOUN	NN	Number=Sing	70	compound	_	_
70	properties	property	NOUN	NNS	Number=Plur	67	pobj	_	_
71	which	which	PRON	WDT	_	72	nsubj	_	_
72	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	70	relcl	_	_
73	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	75	nsubj	_	_
74	to	to	PART	TO	_	75	aux	_	_
75	remove	remove	VERB	VB	VerbForm=Inf	72	ccomp	_	_
76	the	the	DET	DT	Definite=Def|PronType=Art	77	det	_	_
77	assumption	assumption	NOUN	NN	Number=Sing	75	dobj	_	_
78	of	of	ADP	IN	_	77	prep	_	_
79	the	the	DET	DT	Definite=Def|PronType=Art	80	det	_	_
80	existence	existence	NOUN	NN	Number=Sing	78	pobj	_	_
81	of	of	ADP	IN	_	80	prep	_	_
82	colimits	colimit	NOUN	NNS	Number=Plur	81	pobj	_	SpaceAfter=No
83	,	,	PUNCT	,	PunctType=Comm	75	punct	_	_
84	in	in	ADP	IN	_	75	prep	_	_
85	particular	particular	ADJ	JJ	Degree=Pos	84	amod	_	_
86	when	when	SCONJ	WRB	_	88	advmod	_	_
87	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	88	nsubj	_	_
88	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	75	advcl	_	_
89	the	the	DET	DT	Definite=Def|PronType=Art	94	det	_	_
90	approximate	approximate	ADJ	JJ	Degree=Pos	93	amod	_	_
91	co	co	NOUN	NN	Number=Sing	93	compound	_	_
92	-	-	PUNCT	HYPH	PunctType=Dash	93	punct	_	_
93	operations	operation	NOUN	NNS	Number=Plur	94	compound	_	_
94	approach	approach	VERB	VBP	Tense=Pres|VerbForm=Fin	88	dobj	_	_
95	to	to	PART	TO	_	96	aux	_	_
96	show	show	VERB	VB	VerbForm=Inf	88	xcomp	_	_
97	that	that	SCONJ	IN	_	101	mark	_	_
98	a	a	DET	DT	Definite=Ind|PronType=Art	100	det	_	_
99	regular	regular	ADJ	JJ	Degree=Pos	100	amod	_	_
100	category	category	NOUN	NN	Number=Sing	101	nsubj	_	_
101	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	96	ccomp	_	_
102	$ n $	$ n $	SYM	$	_	104	advmod	_	_
103	-	-	PUNCT	HYPH	PunctType=Dash	104	punct	_	_
104	permutable	permutable	ADJ	JJ	Degree=Pos	101	acomp	_	SpaceAfter=No
105	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 606
# sent_id = 1
# text = In this paper we introduce a notion of Maltsev object, and the dual notion of co - Maltsev object, in a general category.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	notion	notion	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	Maltsev	Maltsev	PROPN	NNP	Number=Sing	10	compound	_	_
10	object	object	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	dual	dual	ADJ	JJ	Degree=Pos	15	amod	_	_
15	notion	notion	NOUN	NN	Number=Sing	5	conj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	co	co	PROPN	NNP	Number=Sing	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	Maltsev	Maltsev	PROPN	NNP	Number=Sing	20	compound	_	_
20	object	object	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
22	in	in	ADP	IN	_	15	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	general	general	ADJ	JJ	Degree=Pos	25	amod	_	_
25	category	category	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = In particular, a category $ C $ is a Maltsev category if and only if every object in $ C $ is a Maltsev object.
1	In	in	ADP	IN	_	7	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	7	nsubj	_	_
6	$ C $	$ c $	SYM	$	_	5	appos	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	Maltsev	Maltsev	PROPN	NNP	Number=Sing	10	compound	_	_
10	category	category	NOUN	NN	Number=Sing	7	attr	_	_
11	if	if	SCONJ	IN	_	7	dep	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	only	only	ADV	RB	_	19	advmod	_	_
14	if	if	SCONJ	IN	_	19	mark	_	_
15	every	every	DET	DT	_	16	det	_	_
16	object	object	NOUN	NN	Number=Sing	19	nsubj	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	$ C $	$ c $	SYM	$	_	17	pobj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	advcl	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	Maltsev	Maltsev	PROPN	NNP	Number=Sing	22	compound	_	_
22	object	object	NOUN	NN	Number=Sing	19	attr	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that for a well - powered regular category $ C $ which admits coproducts, the full subcategory of Maltsev objects is coreflective in $ C $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	22	mark	_	_
4	for	for	ADP	IN	_	22	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
6	well	well	ADV	RB	Degree=Pos	8	advmod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	powered	power	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
9	regular	regular	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
11	$ C $	$ c $	SYM	$	_	4	dep	_	_
12	which	which	PRON	WDT	_	13	nsubj	_	_
13	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	pcomp	_	_
14	coproducts	coproduct	NOUN	NNS	Number=Plur	13	dobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	full	full	ADJ	JJ	Degree=Pos	18	amod	_	_
18	subcategory	subcategory	NOUN	NN	Number=Sing	22	nsubj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	Maltsev	Maltsev	PROPN	NNP	Number=Sing	21	amod	_	_
21	objects	object	NOUN	NNS	Number=Plur	19	pobj	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
23	coreflective	coreflective	ADJ	JJ	Degree=Pos	22	acomp	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	$ C $	$ c $	SYM	$	_	24	pobj	_	_
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show that the co - Maltsev objects in the category of topological spaces and continuous maps are precisely the $ R_1 $ - spaces, and that the co - Maltsev objects in the category of metric spaces and short maps are precisely the ultrametric spaces.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	18	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
5	co	co	ADJ	JJ	Degree=Pos	7	compound	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	Maltsev	Maltsev	PROPN	NNP	Number=Sing	8	amod	_	_
8	objects	object	NOUN	NNS	Number=Plur	18	nsubj	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	topological	topological	ADJ	JJ	Degree=Pos	14	amod	_	_
14	spaces	space	NOUN	NNS	Number=Plur	12	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	continuous	continuous	ADJ	JJ	Degree=Pos	17	amod	_	_
17	maps	map	NOUN	NNS	Number=Plur	14	conj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
19	precisely	precisely	ADV	RB	_	23	advmod	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
21	$ R_1 $	$ r_1 $	SYM	$	_	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	spaces	space	NOUN	NNS	Number=Plur	18	attr	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
26	that	that	SCONJ	IN	_	41	mark	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
28	co	co	ADJ	JJ	Degree=Pos	30	compound	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	Maltsev	Maltsev	PROPN	NNP	Number=Sing	31	amod	_	_
31	objects	object	NOUN	NNS	Number=Plur	41	nsubj	_	_
32	in	in	ADP	IN	_	31	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
34	category	category	NOUN	NN	Number=Sing	32	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	metric	metric	ADJ	JJ	Degree=Pos	37	amod	_	_
37	spaces	space	NOUN	NNS	Number=Plur	35	pobj	_	_
38	and	and	CCONJ	CC	ConjType=Cmp	37	cc	_	_
39	short	short	ADJ	JJ	Degree=Pos	40	amod	_	_
40	maps	map	NOUN	NNS	Number=Plur	37	conj	_	_
41	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	18	conj	_	_
42	precisely	precisely	ADV	RB	_	41	advmod	_	_
43	the	the	DET	DT	Definite=Def|PronType=Art	45	det	_	_
44	ultrametric	ultrametric	ADJ	JJ	Degree=Pos	45	amod	_	_
45	spaces	space	NOUN	NNS	Number=Plur	41	attr	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 607
# sent_id = 1
# text = We consider notions of metrized categories, and then approximate categorical structures defined by a function of three variables generalizing the notion of 2 - metric space.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	notions	notion	NOUN	NNS	Number=Plur	2	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	metrized	metrize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	amod	_	_
6	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
9	then	then	ADV	RB	PronType=Dem	10	advmod	_	_
10	approximate	approximate	ADJ	JJ	Degree=Pos	2	conj	_	_
11	categorical	categorical	ADJ	JJ	Degree=Pos	12	amod	_	_
12	structures	structure	NOUN	NNS	Number=Plur	10	dobj	_	_
13	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
14	by	by	ADP	IN	_	13	agent	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	function	function	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	three	three	NUM	CD	NumType=Card	19	nummod	_	_
19	variables	variable	NOUN	NNS	Number=Plur	17	pobj	_	_
20	generalizing	generalize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	acl	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	notion	notion	NOUN	NN	Number=Sing	20	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	2	2	NUM	CD	NumType=Card	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	metric	metric	ADJ	JJ	Degree=Pos	27	amod	_	_
27	space	space	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We prove an embedding theorem giving sufficient conditions for an approximate categorical structure to come from an inclusion into a metrized category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	embedding	embed	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	amod	_	_
5	theorem	theorem	ADJ	JJ	Degree=Pos	2	dobj	_	_
6	giving	give	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	acl	_	_
7	sufficient	sufficient	ADJ	JJ	Degree=Pos	8	amod	_	_
8	conditions	condition	NOUN	NNS	Number=Plur	6	dobj	_	_
9	for	for	SCONJ	IN	_	15	mark	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	approximate	approximate	ADJ	JJ	Degree=Pos	13	amod	_	_
12	categorical	categorical	ADJ	JJ	Degree=Pos	13	amod	_	_
13	structure	structure	NOUN	NN	Number=Sing	15	nsubj	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	come	come	VERB	VB	VerbForm=Inf	6	advcl	_	_
16	from	from	ADP	IN	_	15	prep	_	_
17	an	an	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	inclusion	inclusion	NOUN	NN	Number=Sing	16	pobj	_	_
19	into	into	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	metrized	metrize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	amod	_	_
22	category	category	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 608
# sent_id = 1
# text = We give several reformulations of action representability of a category as well as action representability of its category of morphisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	several	several	ADJ	JJ	Degree=Pos	4	amod	_	_
4	reformulations	reformulation	NOUN	NNS	Number=Plur	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	action	action	NOUN	NN	Number=Sing	7	compound	_	_
7	representability	representability	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
11	as	as	ADV	RB	_	13	advmod	_	_
12	well	well	ADV	RB	Degree=Pos	13	advmod	_	_
13	as	as	ADP	IN	_	4	cc	_	_
14	action	action	NOUN	NN	Number=Sing	15	compound	_	_
15	representability	representability	NOUN	NN	Number=Sing	4	conj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	18	poss	_	_
18	category	category	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	morphisms	morphism	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In particular we show that for a semi - abelian category $ C $ , its category of morphisms is action representable if and only if the functor from the category of split extensions in $ C $ to $ C $ , sending a split extension to its kernel, is a prefibration.
1	In	in	ADP	IN	_	4	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	18	mark	_	_
6	for	for	ADP	IN	_	18	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	semi	semi	ADJ	JJ	Degree=Pos	11	amod	_	_
9	-	-	ADJ	JJ	Degree=Pos	11	amod	_	_
10	abelian	abelian	ADJ	JJ	Degree=Pos	11	amod	_	_
11	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
12	$ C $	$ c $	SYM	$	_	11	nummod	_	_
13	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
14	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	15	poss	_	_
15	category	category	NOUN	NN	Number=Sing	18	nsubj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	morphisms	morphism	NOUN	NNS	Number=Plur	16	pobj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
19	action	action	NOUN	NN	Number=Sing	20	npadvmod	_	_
20	representable	representable	ADJ	JJ	Degree=Pos	18	acomp	_	_
21	if	if	SCONJ	IN	_	46	mark	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	46	cc	_	_
23	only	only	ADV	RB	_	46	advmod	_	_
24	if	if	SCONJ	IN	_	46	mark	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	functor	functor	NOUN	NN	Number=Sing	46	nsubj	_	_
27	from	from	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	category	category	NOUN	NN	Number=Sing	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	split	split	ADJ	JJ	Degree=Pos	32	amod	_	_
32	extensions	extension	NOUN	NNS	Number=Plur	30	pobj	_	_
33	in	in	ADP	IN	_	32	prep	_	_
34	$ C $	$ c $	SYM	$	_	33	pobj	_	_
35	to	to	ADP	IN	_	27	prep	_	_
36	$ C $	$ c $	SYM	$	_	35	pobj	_	_
37	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
38	sending	send	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	26	acl	_	_
39	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
40	split	split	ADJ	JJ	Degree=Pos	41	amod	_	_
41	extension	extension	NOUN	NN	Number=Sing	38	dobj	_	_
42	to	to	ADP	IN	_	41	prep	_	_
43	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	44	poss	_	_
44	kernel	kernel	NOUN	NN	Number=Sing	42	pobj	_	SpaceAfter=No
45	,	,	PUNCT	,	PunctType=Comm	46	punct	_	_
46	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	advcl	_	_
47	a	a	DET	DT	Definite=Ind|PronType=Art	48	det	_	_
48	prefibration	prefibration	NOUN	NN	Number=Sing	46	attr	_	SpaceAfter=No
49	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = To obtain these reformulations we show that certain conditions are equivalent for right regular spans of categories.
1	To	to	PART	TO	_	2	aux	_	_
2	obtain	obtain	VERB	VB	VerbForm=Inf	6	advcl	_	_
3	these	these	DET	DT	Number=Plur|PronType=Dem	4	det	_	_
4	reformulations	reformulation	NOUN	NNS	Number=Plur	2	dobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	10	mark	_	_
8	certain	certain	ADJ	JJ	Degree=Pos	9	amod	_	_
9	conditions	condition	NOUN	NNS	Number=Plur	10	nsubj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
11	equivalent	equivalent	ADJ	JJ	Degree=Pos	10	acomp	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	right	right	ADJ	JJ	Degree=Pos	14	advmod	_	_
14	regular	regular	ADJ	JJ	Degree=Pos	15	amod	_	_
15	spans	span	NOUN	NNS	Number=Plur	12	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 609
# sent_id = 1
# text = We construct an operad Phyl whose operations are the edge - labelled trees used in phylogenetics.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	operad	operad	ADJ	JJ	Degree=Pos	5	amod	_	_
5	Phyl	Phyl	PROPN	NNP	Number=Sing	2	dobj	_	_
6	whose	whose	DET	WP$	Poss=Yes	7	poss	_	_
7	operations	operation	NOUN	NNS	Number=Plur	8	nsubj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	relcl	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
10	edge	edge	NOUN	NN	Number=Sing	12	npadvmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	labelled	label	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
13	trees	tree	NOUN	NNS	Number=Plur	8	attr	_	_
14	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	acl	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	phylogenetics	phylogenetic	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This operad is the coproduct of $ Com $ , the operad for commutative semigroups, and $ [0, infty) $ , the operad with unary operations corresponding to nonnegative real numbers, where composition is addition.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	operad	operad	ADV	RB	_	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	coproduct	coproduct	NOUN	NN	Number=Sing	3	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	$ Com $	$ com $	SYM	$	_	6	pobj	_	_
8	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	operad	operad	NOUN	NN	Number=Sing	5	appos	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	commutative	commutative	ADJ	JJ	Degree=Pos	13	amod	_	_
13	semigroups	semigroup	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
16	$ [0, infty) $	$ [0, infty) $	SYM	$	_	10	conj	_	_
17	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	operad	operad	NOUN	NN	Number=Sing	10	appos	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	unary	unary	ADJ	JJ	Degree=Pos	22	amod	_	_
22	operations	operation	NOUN	NNS	Number=Plur	23	nsubj	_	_
23	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	acl	_	_
24	to	to	ADP	IN	_	23	prep	_	_
25	nonnegative	nonnegative	ADJ	JJ	Degree=Pos	27	amod	_	_
26	real	real	ADJ	JJ	Degree=Pos	27	amod	_	_
27	numbers	number	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
29	where	where	SCONJ	WRB	_	31	advmod	_	_
30	composition	composition	NOUN	NN	Number=Sing	31	nsubj	_	_
31	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	relcl	_	_
32	addition	addition	NOUN	NN	Number=Sing	31	attr	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that there is a homeomorphism between the space of $ n $ - ary operations of $ Phyl $ and $ T_ntimes [0, infty)^{n+1} $ , where $ T_n $ is the space of metric $ n $ - trees introduced by Billera, Holmes and Vogtmann.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	there	there	PRON	EX	_	5	expl	_	_
5	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	homeomorphism	homeomorphism	NOUN	NN	Number=Sing	5	attr	_	_
8	between	between	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	space	space	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	$ n $	$ n $	SYM	$	_	14	quantmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	ary	ary	ADJ	JJ	Degree=Pos	15	amod	_	_
15	operations	operation	NOUN	NNS	Number=Plur	11	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	$ Phyl $	$ phyl $	SYM	$	_	16	pobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
19	$ T_ntimes [0, infty)^{n+1} $	$ t_ntimes [0, infty)^{n+1} $	SYM	$	_	15	conj	_	_
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	where	where	SCONJ	WRB	_	23	advmod	_	_
22	$ T_n $	$ t_n $	SYM	$	_	23	nsubj	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	relcl	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	space	space	NOUN	NN	Number=Sing	23	attr	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	metric	metric	ADJ	JJ	Degree=Pos	30	amod	_	_
28	$ n $	$ n $	SYM	$	_	30	compound	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	trees	tree	NOUN	NNS	Number=Plur	26	pobj	_	_
31	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	30	acl	_	_
32	by	by	ADP	IN	_	31	agent	_	_
33	Billera	Billera	PROPN	NNP	Number=Sing	32	pobj	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
35	Holmes	Holmes	PROPN	NNP	Number=Sing	33	conj	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
37	Vogtmann	Vogtmann	PROPN	NNP	Number=Sing	35	conj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = Furthermore, we show that the Markov models used to reconstruct phylogenetic trees from genome data give coalgebras of $ Phyl $ .
1	Furthermore	furthermore	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	17	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	Markov	Markov	PROPN	NNP	Number=Sing	8	compound	_	_
8	models	model	NOUN	NNS	Number=Plur	17	nsubj	_	_
9	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	reconstruct	reconstruct	VERB	VB	VerbForm=Inf	9	xcomp	_	_
12	phylogenetic	phylogenetic	ADJ	JJ	Degree=Pos	13	amod	_	_
13	trees	tree	NOUN	NNS	Number=Plur	11	dobj	_	_
14	from	from	ADP	IN	_	11	prep	_	_
15	genome	genome	ADJ	JJ	Degree=Pos	16	amod	_	_
16	data	datum	NOUN	NNS	Number=Plur	14	pobj	_	_
17	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	4	ccomp	_	_
18	coalgebras	coalgebra	NOUN	NNS	Number=Plur	17	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	$ Phyl $	$ phyl $	SYM	$	_	19	pobj	_	_
21	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = These always extend to coalgebras of the larger operad $ Com + [0, infty] $ , since Markov processes on finite sets converge to an equilibrium as time approaches infinity.
1	These	these	PRON	DT	Number=Plur|PronType=Dem	3	nsubj	_	_
2	always	always	ADV	RB	_	3	advmod	_	_
3	extend	extend	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	to	to	ADP	IN	_	3	prep	_	_
5	coalgebras	coalgebra	NOUN	NNS	Number=Plur	4	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	larger	large	ADJ	JJR	Degree=Cmp	10	amod	_	_
9	operad	operad	NOUN	NN	Number=Sing	10	amod	_	_
10	$ Com + [0, infty] $	$ com + [0, infty] $	SYM	$	_	6	pobj	_	_
11	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
12	since	since	SCONJ	IN	_	18	mark	_	_
13	Markov	Markov	PROPN	NNP	Number=Sing	14	nsubj	_	_
14	processes	process	NOUN	NNS	Number=Plur	18	nsubj	_	_
15	on	on	ADP	IN	_	14	prep	_	_
16	finite	finite	ADJ	JJ	Degree=Pos	17	compound	_	_
17	sets	set	NOUN	NNS	Number=Plur	15	pobj	_	_
18	converge	converge	VERB	VBP	Tense=Pres|VerbForm=Fin	3	advcl	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	an	an	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	equilibrium	equilibrium	NOUN	NN	Number=Sing	19	pobj	_	_
22	as	as	ADP	IN	_	21	prep	_	_
23	time	time	NOUN	NN	Number=Sing	24	compound	_	_
24	approaches	approach	NOUN	NNS	Number=Plur	25	compound	_	_
25	infinity	infinity	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = We show that for any operad O, its coproduct with $ [0, infty] $ contains the operad $ W(O) $ constructed by Boardman and Vogt.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	13	mark	_	_
4	for	for	ADP	IN	_	13	prep	_	_
5	any	any	DET	DT	_	7	det	_	_
6	operad	operad	ADJ	JJ	Degree=Pos	7	amod	_	_
7	O	o	INTJ	UH	_	4	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
9	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	10	poss	_	_
10	coproduct	coproduct	NOUN	NN	Number=Sing	13	nsubj	_	_
11	with	with	ADP	IN	_	10	prep	_	_
12	$ [0, infty] $	$ [0, infty] $	SYM	$	_	13	nsubj	_	_
13	contains	contain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	operad	operad	ADJ	JJ	Degree=Pos	16	amod	_	_
16	$ W(O) $	$ w(o) $	SYM	$	_	13	dobj	_	_
17	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	acl	_	_
18	by	by	ADP	IN	_	17	agent	_	_
19	Boardman	Boardman	PROPN	NNP	Number=Sing	18	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	Vogt	Vogt	PROPN	NNP	Number=Sing	19	conj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = To prove these results, we explicitly describe the coproduct of operads in terms of labelled trees.
1	To	to	PART	TO	_	2	aux	_	_
2	prove	prove	VERB	VB	VerbForm=Inf	8	advcl	_	_
3	these	these	DET	DT	Number=Plur|PronType=Dem	4	det	_	_
4	results	result	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	8	nsubj	_	_
7	explicitly	explicitly	ADV	RB	_	8	advmod	_	_
8	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	coproduct	coproduct	NOUN	NN	Number=Sing	8	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	operads	operad	NOUN	NNS	Number=Plur	11	pobj	_	_
13	in	in	ADP	IN	_	8	prep	_	_
14	terms	term	NOUN	NNS	Number=Plur	13	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	labelled	label	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	trees	tree	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 610
# sent_id = 1
# text = We define a right Cartan - Eilenberg structure on the category of Kan's combinatorial spectra, and the category of sheaves of such spectra, assuming some conditions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
4	right	right	ADJ	JJ	Degree=Pos	8	amod	_	_
5	Cartan	Cartan	PROPN	NNP	Number=Sing	7	compound	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	8	compound	_	_
8	structure	structure	NOUN	NN	Number=Sing	2	dobj	_	_
9	on	on	ADP	IN	_	2	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	Kan	Kan	PROPN	NNP	Number=Sing	16	poss	_	SpaceAfter=No
14	's	's	PART	POS	_	13	case	_	_
15	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	16	amod	_	_
16	spectra	spectra	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	category	category	NOUN	NN	Number=Sing	2	conj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	sheaves	sheaf	NOUN	NNS	Number=Plur	21	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	such	such	ADJ	JJ	Degree=Pos	25	amod	_	_
25	spectra	spectra	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
27	assuming	assume	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	acl	_	_
28	some	some	DET	DT	_	29	det	_	_
29	conditions	condition	NOUN	NNS	Number=Plur	27	dobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In both structures, we use the geometric concept of homotopy equivalence as the strong equivalence.
1	In	in	ADP	IN	_	6	prep	_	_
2	both	both	DET	DT	_	3	det	_	_
3	structures	structure	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	geometric	geometric	ADJ	JJ	Degree=Pos	9	amod	_	_
9	concept	concept	NOUN	NN	Number=Sing	6	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	homotopy	homotopy	NOUN	NN	Number=Sing	12	compound	_	_
12	equivalence	equivalence	NOUN	NN	Number=Sing	10	pobj	_	_
13	as	as	ADP	IN	_	9	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	strong	strong	ADJ	JJ	Degree=Pos	16	amod	_	_
16	equivalence	equivalence	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = In the case of sheaves, we use local equivalence as the weak equivalence.
1	In	in	ADP	IN	_	8	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	case	case	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	sheaves	sheaf	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
7	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	8	nsubj	_	_
8	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	local	local	ADJ	JJ	Degree=Pos	10	amod	_	_
10	equivalence	equivalence	NOUN	NN	Number=Sing	8	dobj	_	_
11	as	as	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	weak	weak	ADJ	JJ	Degree=Pos	14	amod	_	_
14	equivalence	equivalence	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 4
# text = This paper is the first step in a larger - scale program of investigating sheaves of spectra from a geometric viewpoint.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	first	first	ADJ	JJ	Degree=Pos	6	amod	_	_
6	step	step	NOUN	NN	Number=Sing	3	attr	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
9	larger	large	ADJ	JJR	Degree=Cmp	11	amod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	scale	scale	NOUN	NN	Number=Sing	12	compound	_	_
12	program	program	NOUN	NN	Number=Sing	7	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	investigating	investigate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	pcomp	_	_
15	sheaves	sheaf	NOUN	NNS	Number=Plur	14	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	spectra	spectra	PROPN	NNP	Number=Sing	16	pobj	_	_
18	from	from	ADP	IN	_	14	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	geometric	geometric	ADJ	JJ	Degree=Pos	21	amod	_	_
21	viewpoint	viewpoint	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 611
# sent_id = 1
# text = The theory of derivators enhances and simplifies the theory of triangulated categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	theory	theory	NOUN	NN	Number=Sing	7	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	derivators	derivator	NOUN	NNS	Number=Plur	5	compound	_	_
5	enhances	enhance	NOUN	NNS	Number=Plur	3	pobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	simplifies	simplify	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	theory	theory	NOUN	NN	Number=Sing	7	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	triangulated	triangulate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
12	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this article a notion of fibered (multi)derivator is developed, which similarly enhances fibrations of (monoidal) triangulated categories.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	article	article	NOUN	NN	Number=Sing	1	pobj	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	notion	notion	NOUN	NN	Number=Sing	0	ROOT	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	fibered	fibere	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	pobj	_	_
8	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	11	punct	_	SpaceAfter=No
9	multi)derivator	multi)derivator	NOUN	NN	Number=Sing	11	nsubjpass	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	acl	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	which	which	PRON	WDT	_	15	nsubj	_	_
14	similarly	similarly	ADV	RB	_	15	advmod	_	_
15	enhances	enhance	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	relcl	_	_
16	fibrations	fibration	NOUN	NNS	Number=Plur	15	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	17	punct	_	SpaceAfter=No
19	monoidal	monoidal	NOUN	NN	Number=Sing	22	amod	_	SpaceAfter=No
20	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	22	punct	_	_
21	triangulated	triangulate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	amod	_	_
22	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = We present a theory of cohomological as well as homological descent in this language.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	theory	theory	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	cohomological	cohomological	ADJ	JJ	Degree=Pos	11	amod	_	_
7	as	as	ADV	RB	_	9	advmod	_	_
8	well	well	ADV	RB	Degree=Pos	9	advmod	_	_
9	as	as	ADP	IN	_	6	cc	_	_
10	homological	homological	ADJ	JJ	Degree=Pos	11	amod	_	_
11	descent	descent	NOUN	NN	Number=Sing	5	pobj	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	this	this	DET	DT	Number=Sing|PronType=Dem	14	det	_	_
14	language	language	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = The main motivation is a descent theory for Grothendieck's six operations.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	motivation	motivation	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	descent	descent	NOUN	NN	Number=Sing	7	compound	_	_
7	theory	theory	NOUN	NN	Number=Sing	4	attr	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	12	poss	_	SpaceAfter=No
10	's	's	PART	POS	_	9	case	_	_
11	six	six	NUM	CD	NumType=Card	12	nummod	_	_
12	operations	operation	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 612
# sent_id = 1
# text = We associate, in a functorial way, a monoidal bicategory $ Span|V $ to any monoidal bicategory $ V $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	associate	associate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
4	in	in	ADP	IN	_	17	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	functorial	functorial	ADJ	JJ	Degree=Pos	7	amod	_	_
7	way	way	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	monoidal	monoidal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	bicategory	bicategory	NOUN	NN	Number=Sing	17	nsubj	_	_
12	$ Span|V $	$ span|v $	SYM	$	_	11	appos	_	_
13	to	to	ADP	IN	_	11	prep	_	_
14	any	any	DET	DT	_	16	det	_	_
15	monoidal	monoidal	ADJ	JJ	Degree=Pos	16	amod	_	_
16	bicategory	bicategory	NOUN	NN	Number=Sing	13	pobj	_	_
17	$ V $	$ v $	SYM	$	_	2	dep	_	_
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Two examples of this construction are of particular interest: Hopf polyads of Bruguieres can be seen as Hopf monads in $ Span|Cat $ while Hopf group monoids in the spirit of Zunino and Turaev in a braided monoidal category $ V $ , and Hopf categories of Batista - Caenepeel - Vercruysse over $ V $ both turn out to be Hopf monads in $ Span|V $ .
1	Two	two	NUM	CD	NumType=Card	2	nummod	_	_
2	examples	example	NOUN	NNS	Number=Plur	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	construction	construction	NOUN	NN	Number=Sing	3	pobj	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	17	ccomp	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	particular	particular	ADJ	JJ	Degree=Pos	9	amod	_	_
9	interest	interest	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
10	:	:	PUNCT	:	_	17	punct	_	_
11	Hopf	hopf	NOUN	NN	Number=Sing	12	compound	_	_
12	polyads	polyad	NOUN	NNS	Number=Plur	17	nsubjpass	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	Bruguieres	Bruguieres	PROPN	NNPS	Number=Plur	13	pobj	_	_
15	can	can	AUX	MD	VerbForm=Fin	17	aux	_	_
16	be	be	AUX	VB	VerbForm=Inf	17	auxpass	_	_
17	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
18	as	as	SCONJ	IN	_	20	mark	_	_
19	Hopf	hopf	NOUN	NN	Number=Sing	20	nsubj	_	_
20	monads	monad	NOUN	NNS	Number=Plur	17	advcl	_	_
21	in	in	ADP	IN	_	20	prep	_	_
22	$ Span|Cat $	$ span|cat $	SYM	$	_	21	pobj	_	_
23	while	while	SCONJ	IN	_	26	mark	_	_
24	Hopf	hopf	NOUN	NN	Number=Sing	25	compound	_	_
25	group	group	NOUN	NN	Number=Sing	26	nsubj	_	_
26	monoids	monoid	NOUN	NNS	Number=Plur	17	advcl	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	spirit	spirit	NOUN	NN	Number=Sing	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	Zunino	Zunino	PROPN	NNP	Number=Sing	30	pobj	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	Turaev	Turaev	PROPN	NNP	Number=Sing	31	conj	_	_
34	in	in	ADP	IN	_	26	prep	_	_
35	a	a	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
36	braided	braid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	38	amod	_	_
37	monoidal	monoidal	NOUN	NN	Number=Sing	38	amod	_	_
38	category	category	NOUN	NN	Number=Sing	34	pobj	_	_
39	$ V $	$ v $	SYM	$	_	17	dep	_	_
40	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
41	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
42	Hopf	Hopf	PROPN	NNP	Number=Sing	43	compound	_	_
43	categories	category	NOUN	NNS	Number=Plur	53	nsubj	_	_
44	of	of	ADP	IN	_	43	prep	_	_
45	Batista	Batista	PROPN	NNP	Number=Sing	49	compound	_	_
46	-	-	PUNCT	HYPH	PunctType=Dash	49	punct	_	_
47	Caenepeel	Caenepeel	PROPN	NNP	Number=Sing	49	compound	_	_
48	-	-	PUNCT	HYPH	PunctType=Dash	49	punct	_	_
49	Vercruysse	Vercruysse	PROPN	NNP	Number=Sing	44	pobj	_	_
50	over	over	ADP	IN	_	51	advmod	_	_
51	$ V $	$ v $	SYM	$	_	52	nmod	_	_
52	both	both	PRON	DT	_	43	appos	_	_
53	turn	turn	VERB	VBP	Tense=Pres|VerbForm=Fin	17	conj	_	_
54	out	out	ADP	RP	_	53	prt	_	_
55	to	to	PART	TO	_	56	aux	_	_
56	be	be	AUX	VB	VerbForm=Inf	53	xcomp	_	_
57	Hopf	hopf	NOUN	NN	Number=Sing	58	compound	_	_
58	monads	monad	NOUN	NNS	Number=Plur	56	attr	_	_
59	in	in	ADP	IN	_	58	prep	_	_
60	$ Span|V $	$ span|v $	SYM	$	_	59	pobj	_	_
61	.	.	PUNCT	.	PunctType=Peri	53	punct	_	SpaceAfter=No

# sent_id = 3
# text = Hopf group monoids and Hopf categories are Hopf monads on a distinguished type of monoidales fitting the framework of Bohm - Lack.
1	Hopf	hopf	NOUN	NN	Number=Sing	2	compound	_	_
2	group	group	NOUN	NN	Number=Sing	3	compound	_	_
3	monoids	monoid	NOUN	NNS	Number=Plur	7	nsubj	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	Hopf	hopf	NOUN	NN	Number=Sing	6	compound	_	_
6	categories	category	NOUN	NNS	Number=Plur	3	conj	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	Hopf	hopf	NOUN	NN	Number=Sing	9	compound	_	_
9	monads	monad	NOUN	NNS	Number=Plur	7	attr	_	_
10	on	on	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	distinguished	distinguished	ADJ	JJ	Degree=Pos	13	amod	_	_
13	type	type	NOUN	NN	Number=Sing	10	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	monoidales	monoidale	NOUN	NNS	Number=Plur	14	pobj	_	_
16	fitting	fit	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	acl	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	framework	framework	NOUN	NN	Number=Sing	16	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	Bohm	Bohm	PROPN	NNP	Number=Sing	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	Lack	Lack	PROPN	NNP	Number=Sing	19	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = These examples are related by a monoidal pseudofunctor $ V - > Cat $ .
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	examples	example	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	by	by	ADP	IN	_	4	agent	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	monoidal	monoidal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	pseudofunctor	pseudofunctor	NOUN	NN	Number=Sing	5	pobj	_	_
9	$ V - > Cat $	$ v - > cat $	SYM	$	_	4	dep	_	_
10	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 613
# sent_id = 1
# text = The invertibility hypothesis for a monoidal model category $ S $ asks that localizing an $ S $ - enriched category with respect to an equivalence results in an weakly equivalent enriched category.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	invertibility	invertibility	NOUN	NN	Number=Sing	3	compound	_	_
3	hypothesis	hypothesis	NOUN	NN	Number=Sing	10	nsubj	_	_
4	for	for	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
6	monoidal	monoidal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	model	model	NOUN	NN	Number=Sing	8	compound	_	_
8	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
9	$ S $	$ s $	SYM	$	_	3	appos	_	_
10	asks	ask	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	that	that	SCONJ	IN	_	12	mark	_	_
12	localizing	localize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	ccomp	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
14	$ S $	$ s $	SYM	$	_	16	advmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	category	category	NOUN	NN	Number=Sing	12	dobj	_	_
18	with	with	ADP	IN	_	12	prep	_	_
19	respect	respect	NOUN	NN	Number=Sing	18	pobj	_	_
20	to	to	ADP	IN	_	19	prep	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	equivalence	equivalence	NOUN	NN	Number=Sing	23	compound	_	_
23	results	result	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	pobj	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	an	an	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
26	weakly	weakly	ADJ	JJ	Degree=Pos	29	amod	_	_
27	equivalent	equivalent	ADJ	JJ	Degree=Pos	29	amod	_	_
28	enriched	enriched	ADJ	JJ	Degree=Pos	29	amod	_	_
29	category	category	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = This is the most technical among the axioms for $ S $ to be an excellent model category in the sense of Lurie, who showed that the category $ Cat_S $ of $ S $ - enriched categories then has a model structure with characterizable fibrant objects.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	most	most	ADV	RBS	Degree=Sup	5	advmod	_	_
5	technical	technical	ADJ	JJ	Degree=Pos	2	attr	_	_
6	among	among	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	axioms	axiom	NOUN	NNS	Number=Plur	6	pobj	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	$ S $	$ s $	SYM	$	_	9	pobj	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	be	be	AUX	VB	VerbForm=Inf	2	xcomp	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
14	excellent	excellent	ADJ	JJ	Degree=Pos	16	amod	_	_
15	model	model	NOUN	NN	Number=Sing	16	compound	_	_
16	category	category	NOUN	NN	Number=Sing	12	attr	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	sense	sense	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	Lurie	Lurie	PROPN	NNP	Number=Sing	20	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	who	who	PRON	WP	_	24	nsubj	_	_
24	showed	show	VERB	VBD	Tense=Past|VerbForm=Fin	21	relcl	_	_
25	that	that	SCONJ	IN	_	35	mark	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	category	category	NOUN	NN	Number=Sing	35	nsubj	_	_
28	$ Cat_S $	$ cat_s $	SYM	$	_	27	appos	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	$ S $	$ s $	SYM	$	_	32	advmod	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	amod	_	_
33	categories	category	NOUN	NNS	Number=Plur	29	pobj	_	_
34	then	then	ADV	RB	PronType=Dem	35	advmod	_	_
35	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	ccomp	_	_
36	a	a	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
37	model	model	NOUN	NN	Number=Sing	38	compound	_	_
38	structure	structure	NOUN	NN	Number=Sing	35	dobj	_	_
39	with	with	ADP	IN	_	38	prep	_	_
40	characterizable	characterizable	ADJ	JJ	Degree=Pos	42	amod	_	_
41	fibrant	fibrant	NOUN	NN	Number=Sing	42	amod	_	_
42	objects	object	NOUN	NNS	Number=Plur	39	pobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We use a universal property of cubical sets, as a monoidal model category, to show that the invertibility hypothesis is a consequence of the other axioms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	universal	universal	ADJ	JJ	Degree=Pos	5	amod	_	_
5	property	property	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	cubical	cubical	ADJ	JJ	Degree=Pos	8	amod	_	_
8	sets	set	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
10	as	as	ADP	IN	_	2	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
12	monoidal	monoidal	ADJ	JJ	Degree=Pos	14	amod	_	_
13	model	model	NOUN	NN	Number=Sing	14	compound	_	_
14	category	category	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
16	to	to	PART	TO	_	17	aux	_	_
17	show	show	VERB	VB	VerbForm=Inf	2	xcomp	_	_
18	that	that	SCONJ	IN	_	22	mark	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	invertibility	invertibility	NOUN	NN	Number=Sing	21	compound	_	_
21	hypothesis	hypothesis	NOUN	NN	Number=Sing	22	nsubj	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	ccomp	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	consequence	consequence	NOUN	NN	Number=Sing	22	attr	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	other	other	ADJ	JJ	Degree=Pos	28	amod	_	_
28	axioms	axiom	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 614
# sent_id = 1
# text = We introduce and study hypercrossed complexes of Lie algebras, that is, non - negatively graded chain complexes of Lie algebras $ L=(L_n, partial_n) $ endowed with an additional structure by means of a suitable set of bilinear maps $ L_rtimes L_srightarrow L_n $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	study	study	NOUN	NN	Number=Sing	2	conj	_	_
5	hypercrossed	hypercrosse	VERB	VBD	Tense=Past|VerbForm=Fin	6	amod	_	_
6	complexes	complex	NOUN	NNS	Number=Plur	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	Lie	Lie	PROPN	NNP	Number=Sing	9	compound	_	_
9	algebras	algebra	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	that	that	ADV	RB	_	12	advmod	_	_
12	is	is	ADV	RB	_	17	advmod	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
14	non	non	ADV	RB	_	17	nsubj	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
16	negatively	negatively	ADV	RB	_	17	advmod	_	_
17	graded	grade	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
18	chain	chain	NOUN	NN	Number=Sing	19	compound	_	_
19	complexes	complex	NOUN	NNS	Number=Plur	22	nsubj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	Lie	Lie	PROPN	NNP	Number=Sing	20	pobj	_	_
22	algebras	algebra	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
23	$ L=(L_n, partial_n) $	$ l=(l_n, partial_n) $	SYM	$	_	22	dobj	_	_
24	endowed	endow	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	acl	_	_
25	with	with	ADP	IN	_	24	prep	_	_
26	an	an	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
27	additional	additional	ADJ	JJ	Degree=Pos	28	amod	_	_
28	structure	structure	NOUN	NN	Number=Sing	25	pobj	_	_
29	by	by	ADP	IN	_	24	agent	_	_
30	means	mean	NOUN	NNS	Number=Plur	29	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
33	suitable	suitable	ADJ	JJ	Degree=Pos	34	amod	_	_
34	set	set	NOUN	NN	Number=Sing	31	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	bilinear	bilinear	NOUN	NN	Number=Sing	37	compound	_	_
37	maps	map	NOUN	NNS	Number=Plur	35	pobj	_	_
38	$ L_rtimes L_srightarrow L_n $	$ l_rtimes l_srightarrow l_n $	SYM	$	_	34	appos	_	_
39	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The Moore complex of any simplicial Lie algebra acquires such a structure and, in this way, we prove a Dold - Kan type equivalence between the category of simplicial Lie algebras and the category of hypercrossed complexes of Lie algebras.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	Moore	Moore	PROPN	NNP	Number=Sing	3	compound	_	_
3	complex	complex	NOUN	NN	Number=Sing	9	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	any	any	DET	DT	_	8	det	_	_
6	simplicial	simplicial	ADJ	JJ	Degree=Pos	8	amod	_	_
7	Lie	lie	NOUN	NN	Number=Sing	8	compound	_	_
8	algebra	algebra	NOUN	NN	Number=Sing	4	pobj	_	_
9	acquires	acquire	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	such	such	DET	PDT	_	12	predet	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	structure	structure	NOUN	NN	Number=Sing	9	dobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
15	in	in	ADP	IN	_	20	prep	_	_
16	this	this	DET	DT	Number=Sing|PronType=Dem	17	det	_	_
17	way	way	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
19	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	20	nsubj	_	_
20	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	9	conj	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
22	Dold	Dold	PROPN	NNP	Number=Sing	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	Kan	Kan	PROPN	NNP	Number=Sing	26	compound	_	_
25	type	type	NOUN	NN	Number=Sing	26	compound	_	_
26	equivalence	equivalence	NOUN	NN	Number=Sing	20	dobj	_	_
27	between	between	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	category	category	NOUN	NN	Number=Sing	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	simplicial	simplicial	ADJ	JJ	Degree=Pos	32	amod	_	_
32	Lie	lie	NOUN	NN	Number=Sing	33	compound	_	_
33	algebras	algebra	NOUN	NNS	Number=Plur	30	pobj	_	_
34	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	category	category	NOUN	NN	Number=Sing	29	conj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	hypercrossed	hypercrossed	ADJ	JJ	Degree=Pos	39	amod	_	_
39	complexes	complex	NOUN	NNS	Number=Plur	37	pobj	_	_
40	of	of	ADP	IN	_	39	prep	_	_
41	Lie	Lie	PROPN	NNP	Number=Sing	42	compound	_	_
42	algebras	algebra	NOUN	NNS	Number=Plur	40	pobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 3
# text = Several consequences of examining particular classes of hypercrossed complexes of Lie algebras are presented.
1	Several	several	ADJ	JJ	Degree=Pos	2	amod	_	_
2	consequences	consequence	NOUN	NNS	Number=Plur	14	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	examining	examine	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	pcomp	_	_
5	particular	particular	ADJ	JJ	Degree=Pos	6	amod	_	_
6	classes	class	NOUN	NNS	Number=Plur	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	hypercrossed	hypercrossed	ADJ	JJ	Degree=Pos	9	amod	_	_
9	complexes	complex	NOUN	NNS	Number=Plur	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	Lie	Lie	PROPN	NNP	Number=Sing	12	compound	_	_
12	algebras	algebra	NOUN	NNS	Number=Plur	10	pobj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# doc_id = 615
# sent_id = 1
# text = We show that a commutative monoid $ A $ is coexponentiable in $ CMon(V) $ if and only if $ - otimes A : V to V $ has a left adjoint, when $ V $ is a cocomplete symmetric monoidal closed category with finite biproducts and in which every object is a quotient of a free object.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	8	mark	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	commutative	commutative	ADJ	JJ	Degree=Pos	6	amod	_	_
6	monoid	monoid	NOUN	NN	Number=Sing	7	compound	_	_
7	$ A $	$ a $	SYM	$	_	8	nsubj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
9	coexponentiable	coexponentiable	ADJ	JJ	Degree=Pos	8	acomp	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	$ CMon(V) $	$ cmon(v) $	SYM	$	_	10	pobj	_	_
12	if	if	SCONJ	IN	_	24	mark	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	only	only	ADV	RB	_	17	advmod	_	_
15	if	if	SCONJ	IN	_	17	mark	_	_
16	$ - otimes A : V to V $	$ - otimes a : v to v $	SYM	$	_	17	nsubj	_	_
17	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	conj	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	left	left	ADJ	JJ	Degree=Pos	20	amod	_	_
20	adjoint	adjoint	NOUN	NN	Number=Sing	17	dobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	when	when	SCONJ	WRB	_	24	advmod	_	_
23	$ V $	$ v $	SYM	$	_	24	nsubj	_	_
24	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	advcl	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
26	cocomplete	cocomplete	ADJ	JJ	Degree=Pos	28	amod	_	_
27	symmetric	symmetric	ADJ	JJ	Degree=Pos	28	amod	_	_
28	monoidal	monoidal	NOUN	NN	Number=Sing	29	nsubj	_	_
29	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	24	ccomp	_	_
30	category	category	NOUN	NN	Number=Sing	29	dobj	_	_
31	with	with	ADP	IN	_	29	prep	_	_
32	finite	finite	ADJ	JJ	Degree=Pos	33	compound	_	_
33	biproducts	biproduct	NOUN	NNS	Number=Plur	31	pobj	_	_
34	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
35	in	in	ADP	IN	_	39	prep	_	_
36	which	which	PRON	WDT	_	35	pobj	_	_
37	every	every	DET	DT	_	38	det	_	_
38	object	object	NOUN	NN	Number=Sing	39	nsubj	_	_
39	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	conj	_	_
40	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
41	quotient	quotient	NOUN	NN	Number=Sing	39	attr	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	a	a	DET	DT	Definite=Ind|PronType=Art	45	det	_	_
44	free	free	ADJ	JJ	Degree=Pos	45	amod	_	_
45	object	object	NOUN	NN	Number=Sing	42	pobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Using a general characterization of the latter, we show that an algebra over a rig or ring $ R $ is coexponentiable if and only if it is finitely generated and projective as an $ R $ - module.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	advcl	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	general	general	ADJ	JJ	Degree=Pos	4	amod	_	_
4	characterization	characterization	NOUN	NN	Number=Sing	1	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	latter	latter	ADJ	JJ	Degree=Pos	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
9	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
10	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	that	that	SCONJ	IN	_	20	mark	_	_
12	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	algebra	algebra	NOUN	NN	Number=Sing	20	nsubj	_	_
14	over	over	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	rig	rig	NOUN	NN	Number=Sing	14	pobj	_	_
17	or	or	CCONJ	CC	ConjType=Cmp	13	cc	_	_
18	ring	ring	VERB	VB	VerbForm=Inf	13	conj	_	_
19	$ R $	$ r $	SYM	$	_	18	dobj	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	ccomp	_	_
21	coexponentiable	coexponentiable	ADJ	JJ	Degree=Pos	20	acomp	_	_
22	if	if	SCONJ	IN	_	20	prep	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	only	only	ADV	RB	_	29	advmod	_	_
25	if	if	SCONJ	IN	_	29	mark	_	_
26	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	29	nsubjpass	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	auxpass	_	_
28	finitely	finitely	ADV	RB	_	29	advmod	_	_
29	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	advcl	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
31	projective	projective	ADJ	JJ	Degree=Pos	29	conj	_	_
32	as	as	ADP	IN	_	31	prep	_	_
33	an	an	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
34	$ R $	$ r $	SYM	$	_	36	compound	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	36	punct	_	_
36	module	module	NOUN	NN	Number=Sing	32	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 3
# text = Omitting the finiteness condition, the same result (and proof) is obtained for algebras over a quantale.
1	Omitting	omit	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	advcl	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	finiteness	finiteness	NOUN	NN	Number=Sing	4	compound	_	_
4	condition	condition	NOUN	NN	Number=Sing	1	dobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	same	same	ADJ	JJ	Degree=Pos	8	amod	_	_
8	result	result	NOUN	NN	Number=Sing	14	nsubjpass	_	_
9	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	8	punct	_	SpaceAfter=No
10	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
11	proof	proof	NOUN	NN	Number=Sing	8	conj	_	SpaceAfter=No
12	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	8	punct	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
15	for	for	ADP	IN	_	14	prep	_	_
16	algebras	algebra	NOUN	NNS	Number=Plur	15	pobj	_	_
17	over	over	ADP	IN	_	14	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	quantale	quantale	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# doc_id = 616
# sent_id = 1
# text = The key notion to understand the left determined Olschok model category of star - shaped Cattani - Sassone transition systems is past - similarity.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	key	key	ADJ	JJ	Degree=Pos	3	amod	_	_
3	notion	notion	NOUN	NN	Number=Sing	21	nsubj	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	understand	understand	VERB	VB	VerbForm=Inf	3	acl	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
7	left	left	ADJ	JJ	Degree=Pos	8	advmod	_	_
8	determined	determine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
9	Olschok	Olschok	PROPN	NNP	Number=Sing	10	compound	_	_
10	model	model	NOUN	NN	Number=Sing	11	compound	_	_
11	category	category	NOUN	NN	Number=Sing	5	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	star	star	NOUN	NN	Number=Sing	15	npadvmod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	shaped	shape	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	amod	_	_
16	Cattani	Cattani	PROPN	NNP	Number=Sing	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	Sassone	Sassone	PROPN	NNP	Number=Sing	20	compound	_	_
19	transition	transition	NOUN	NN	Number=Sing	20	compound	_	_
20	systems	system	NOUN	NNS	Number=Plur	12	pobj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
22	past	past	NOUN	NN	Number=Sing	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	similarity	similarity	NOUN	NN	Number=Sing	21	attr	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# sent_id = 2
# text = Two states are past - similar if they have homotopic pasts.
1	Two	two	NUM	CD	NumType=Card	2	nummod	_	_
2	states	state	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	past	past	NOUN	NN	Number=Sing	6	advmod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	similar	similar	ADJ	JJ	Degree=Pos	3	acomp	_	_
7	if	if	SCONJ	IN	_	9	mark	_	_
8	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	9	nsubj	_	_
9	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	advcl	_	_
10	homotopic	homotopic	NOUN	NN	Number=Sing	11	compound	_	_
11	pasts	past	NOUN	NNS	Number=Plur	9	dobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = An object is fibrant if and only if the set of transitions is closed under past - similarity.
1	An	an	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	object	object	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	fibrant	fibrant	ADJ	JJ	Degree=Pos	3	acomp	_	_
5	if	if	SCONJ	IN	_	14	mark	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	only	only	ADV	RB	_	14	advmod	_	_
8	if	if	SCONJ	IN	_	14	mark	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	set	set	NOUN	NN	Number=Sing	13	nsubj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	transitions	transition	NOUN	NNS	Number=Plur	11	pobj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	advcl	_	_
15	under	under	ADP	IN	_	14	prep	_	_
16	past	past	ADJ	JJ	Degree=Pos	18	amod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	similarity	similarity	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = A map is a weak equivalence if and only if it induces an isomorphism after the identification of all past - similar states.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	map	map	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	weak	weak	ADJ	JJ	Degree=Pos	6	amod	_	_
6	equivalence	equivalence	NOUN	NN	Number=Sing	3	attr	_	_
7	if	if	SCONJ	IN	_	6	prep	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	only	only	ADV	RB	_	12	advmod	_	_
10	if	if	SCONJ	IN	_	12	mark	_	_
11	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	12	nsubj	_	_
12	induces	induce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	conj	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	isomorphism	isomorphism	NOUN	NN	Number=Sing	12	dobj	_	_
15	after	after	ADP	IN	_	12	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	identification	identification	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	all	all	DET	DT	_	23	det	_	_
20	past	past	ADJ	JJ	Degree=Pos	22	advmod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	similar	similar	ADJ	JJ	Degree=Pos	23	amod	_	_
23	states	state	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = The last part of this paper is a discussion about the link between causality and homotopy.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	last	last	ADJ	JJ	Degree=Pos	3	amod	_	_
3	part	part	NOUN	NN	Number=Sing	7	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	paper	paper	NOUN	NN	Number=Sing	4	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	discussion	discussion	NOUN	NN	Number=Sing	7	attr	_	_
10	about	about	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	link	link	NOUN	NN	Number=Sing	10	pobj	_	_
13	between	between	ADP	IN	_	12	prep	_	_
14	causality	causality	NOUN	NN	Number=Sing	13	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	homotopy	homotopy	NOUN	NN	Number=Sing	14	conj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 617
# sent_id = 1
# text = As we all know, the complete lattice $ I_D(S) $ of all $ D $ - ideals of a meet - semilattice $ S $ is precisely the injective hull of $ S $ in the category of meet - semilattices.
1	As	as	SCONJ	IN	_	4	mark	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
3	all	all	PRON	DT	_	2	appos	_	_
4	know	know	VERB	VBP	Tense=Pres|VerbForm=Fin	21	advcl	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	complete	complete	ADJ	JJ	Degree=Pos	8	amod	_	_
8	lattice	lattice	NOUN	NN	Number=Sing	21	nsubj	_	_
9	$ I_D(S) $	$ i_d(s) $	SYM	$	_	21	nsubj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	all	all	DET	DT	_	14	det	_	_
12	$ D $	$ d $	SYM	$	_	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	ideals	ideal	NOUN	NNS	Number=Plur	10	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
17	meet	meet	NOUN	NN	Number=Sing	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	semilattice	semilattice	NOUN	NN	Number=Sing	20	compound	_	_
20	$ S $	$ s $	SYM	$	_	15	pobj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
22	precisely	precisely	ADV	RB	_	25	advmod	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	injective	injective	ADJ	JJ	Degree=Pos	25	amod	_	_
25	hull	hull	NOUN	NN	Number=Sing	21	attr	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	$ S $	$ s $	SYM	$	_	26	pobj	_	_
28	in	in	ADP	IN	_	25	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	category	category	NOUN	NN	Number=Sing	28	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	meet	meet	NOUN	NN	Number=Sing	34	compound	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	semilattices	semilattice	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper, we consider $ sm $ - ideals of posemigroups which can be regarded as a generalization of $ D $ - ideals of meet - semilattices.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	$ sm $	$ sm $	SYM	$	_	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	ideals	ideal	NOUN	NNS	Number=Plur	6	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	posemigroups	posemigroup	NOUN	NNS	Number=Plur	10	pobj	_	_
12	which	which	PRON	WDT	_	15	nsubjpass	_	_
13	can	can	AUX	MD	VerbForm=Fin	15	aux	_	_
14	be	be	AUX	VB	VerbForm=Inf	15	auxpass	_	_
15	regarded	regard	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	relcl	_	_
16	as	as	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	generalization	generalization	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	$ D $	$ d $	SYM	$	_	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	ideals	ideal	NOUN	NNS	Number=Plur	19	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	meet	meet	NOUN	NN	Number=Sing	26	compound	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	semilattices	semilattice	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = Unfortunately, the quantale $ R(S) $ of all $ sm $ - ideals of a posemigroup $ S $ is in general not an injective hull of $ S $ .
1	Unfortunately	unfortunately	ADV	RB	_	15	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	quantale	quantale	NOUN	NN	Number=Sing	15	nsubj	_	_
5	$ R(S) $	$ r(s) $	SYM	$	_	4	appos	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	all	all	DET	DT	_	10	det	_	_
8	$ sm $	$ sm $	SYM	$	_	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	ideals	ideal	NOUN	NNS	Number=Plur	6	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	posemigroup	posemigroup	NOUN	NN	Number=Sing	11	pobj	_	_
14	$ S $	$ s $	SYM	$	_	4	appos	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	general	general	ADJ	JJ	Degree=Pos	16	amod	_	_
18	not	not	PART	RB	Polarity=Neg	21	neg	_	_
19	an	an	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	injective	injective	ADJ	JJ	Degree=Pos	21	amod	_	_
21	hull	hull	NOUN	NN	Number=Sing	15	attr	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	$ S $	$ s $	SYM	$	_	22	pobj	_	_
24	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 4
# text = However, $ R(S) $ can be seen as a new type of quantale completions of $ S $ .
1	However	however	ADV	RB	_	6	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
3	$ R(S) $	$ r(s) $	SYM	$	_	6	nsubjpass	_	_
4	can	can	AUX	MD	VerbForm=Fin	6	aux	_	_
5	be	be	AUX	VB	VerbForm=Inf	6	auxpass	_	_
6	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	as	as	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	new	new	ADJ	JJ	Degree=Pos	10	amod	_	_
10	type	type	NOUN	NN	Number=Sing	7	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	quantale	quantale	ADJ	JJ	Degree=Pos	13	compound	_	_
13	completions	completion	NOUN	NNS	Number=Plur	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	$ S $	$ s $	SYM	$	_	14	pobj	_	_
16	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = Further, we can see that $ R(S) $ is also a free object over $ S $ in the category $ PoSgr_v $ of posemigroups with $ sm $ - distributive join homomorphisms.
1	Further	far	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
4	can	can	AUX	MD	VerbForm=Fin	5	aux	_	_
5	see	see	VERB	VB	VerbForm=Inf	0	ROOT	_	_
6	that	that	SCONJ	IN	_	8	mark	_	_
7	$ R(S) $	$ r(s) $	SYM	$	_	8	nsubj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
9	also	also	ADV	RB	_	8	advmod	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	free	free	ADJ	JJ	Degree=Pos	12	amod	_	_
12	object	object	NOUN	NN	Number=Sing	8	attr	_	_
13	over	over	ADP	IN	_	12	prep	_	_
14	$ S $	$ s $	SYM	$	_	13	pobj	_	_
15	in	in	ADP	IN	_	12	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
18	$ PoSgr_v $	$ posgr_v $	SYM	$	_	17	appos	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	posemigroups	posemigroup	NOUN	NNS	Number=Plur	19	pobj	_	_
21	with	with	ADP	IN	_	12	prep	_	_
22	$ sm $	$ sm $	SYM	$	_	24	advmod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	distributive	distributive	ADJ	JJ	Degree=Pos	26	amod	_	_
25	join	join	NOUN	NN	Number=Sing	26	compound	_	_
26	homomorphisms	homomorphism	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 618
# sent_id = 1
# text = We provide an explicit model for the free 2 - category containing n composable adjunction morphisms, comparable to the Schanuel and Street model for the free adjunction.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	explicit	explicit	ADJ	JJ	Degree=Pos	5	amod	_	_
5	model	model	NOUN	NN	Number=Sing	2	dobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
8	free	free	ADJ	JJ	Degree=Pos	11	amod	_	_
9	2	2	NUM	CD	NumType=Card	11	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
12	containing	contain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	acl	_	_
13	n	n	CCONJ	CC	ConjType=Cmp	14	advmod	_	_
14	composable	composable	ADJ	JJ	Degree=Pos	16	amod	_	_
15	adjunction	adjunction	NOUN	NN	Number=Sing	16	compound	_	_
16	morphisms	morphism	NOUN	NNS	Number=Plur	12	dobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	comparable	comparable	ADJ	JJ	Degree=Pos	16	amod	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
21	Schanuel	Schanuel	PROPN	NNP	Number=Sing	24	nmod	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	Street	Street	PROPN	NNP	Number=Sing	21	conj	_	_
24	model	model	NOUN	NN	Number=Sing	19	pobj	_	_
25	for	for	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	free	free	ADJ	JJ	Degree=Pos	28	amod	_	_
28	adjunction	adjunction	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We can extract from it an explicit model for the free 2 - category containing n composable lax monad morphisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	can	can	AUX	MD	VerbForm=Fin	3	aux	_	_
3	extract	extract	VERB	VB	VerbForm=Inf	0	ROOT	_	_
4	from	from	ADP	IN	_	3	prep	_	_
5	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	4	pobj	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	explicit	explicit	ADJ	JJ	Degree=Pos	8	amod	_	_
8	model	model	NOUN	NN	Number=Sing	3	dobj	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
11	free	free	ADJ	JJ	Degree=Pos	14	amod	_	_
12	2	2	NUM	CD	NumType=Card	14	nummod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
15	containing	contain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	acl	_	_
16	n	n	ADV	RB	_	17	advmod	_	_
17	composable	composable	ADJ	JJ	Degree=Pos	20	amod	_	_
18	lax	lax	ADJ	JJ	Degree=Pos	19	amod	_	_
19	monad	monad	NOUN	NNS	Number=Plur	20	compound	_	_
20	morphisms	morphism	NOUN	NNS	Number=Plur	15	dobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = A careful proof is given, which goes through presentations of the hom - categories of our model.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	careful	careful	ADJ	JJ	Degree=Pos	3	amod	_	_
3	proof	proof	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	which	which	PRON	WDT	_	8	nsubj	_	_
8	goes	go	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	relcl	_	_
9	through	through	ADP	IN	_	8	prep	_	_
10	presentations	presentation	NOUN	NNS	Number=Plur	9	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
13	hom	hom	NOUN	NN	Number=Sing	15	amod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	18	poss	_	_
18	model	model	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = We use one of these hom - categories as an indexing category to construct an extended Artin - Mazur codiagonal, whose underlying bisimplicial set has the classical Artin - Mazur codiagonal as its first column.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	one	one	NUM	CD	NumType=Card	2	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	these	these	DET	DT	Number=Plur|PronType=Dem	8	det	_	_
6	hom	hom	NOUN	NN	Number=Sing	8	amod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	_
9	as	as	ADP	IN	_	2	prep	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	indexing	indexing	NOUN	NN	Number=Sing	12	compound	_	_
12	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	construct	construct	VERB	VB	VerbForm=Inf	2	xcomp	_	_
15	an	an	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
16	extended	extended	ADJ	JJ	Degree=Pos	20	amod	_	_
17	Artin	Artin	PROPN	NNP	Number=Sing	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	Mazur	Mazur	PROPN	NNP	Number=Sing	20	compound	_	_
20	codiagonal	codiagonal	NOUN	NN	Number=Sing	14	dobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	whose	whose	DET	WP$	Poss=Yes	25	poss	_	_
23	underlying	underlie	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	25	amod	_	_
24	bisimplicial	bisimplicial	ADJ	JJ	Degree=Pos	25	amod	_	_
25	set	set	NOUN	NN	Number=Sing	26	nsubj	_	_
26	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	relcl	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
28	classical	classical	ADJ	JJ	Degree=Pos	32	amod	_	_
29	Artin	Artin	PROPN	NNP	Number=Sing	31	compound	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	Mazur	Mazur	PROPN	NNP	Number=Sing	32	compound	_	_
32	codiagonal	codiagonal	ADJ	JJ	Degree=Pos	26	dobj	_	_
33	as	as	ADP	IN	_	32	prep	_	_
34	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	36	poss	_	_
35	first	first	ADJ	JJ	Degree=Pos	36	amod	_	_
36	column	column	NOUN	NN	Number=Sing	33	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 619
# sent_id = 1
# text = For each holomorphic vector bundle we construct a holomorphic bundle 2 - gerbe that geometrically represents its second Beilinson - Chern class.
1	For	for	ADP	IN	_	7	prep	_	_
2	each	each	DET	DT	_	5	det	_	_
3	holomorphic	holomorphic	ADJ	JJ	Degree=Pos	5	compound	_	_
4	vector	vector	NOUN	NN	Number=Sing	5	compound	_	_
5	bundle	bundle	NOUN	NN	Number=Sing	1	pobj	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	holomorphic	holomorphic	ADJ	JJ	Degree=Pos	10	amod	_	_
10	bundle	bundle	NOUN	NN	Number=Sing	7	dobj	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	gerbe	gerbe	NOUN	NN	Number=Sing	10	appos	_	_
14	that	that	PRON	WDT	PronType=Rel	16	nsubj	_	_
15	geometrically	geometrically	ADV	RB	_	16	advmod	_	_
16	represents	represent	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	relcl	_	_
17	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	22	poss	_	_
18	second	second	ADJ	JJ	Degree=Pos	22	amod	_	_
19	Beilinson	Beilinson	PROPN	NNP	Number=Sing	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	Chern	Chern	PROPN	NNP	Number=Sing	22	compound	_	_
22	class	class	NOUN	NN	Number=Sing	16	dobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 2
# text = Applied to the cotangent bundle, this may be regarded as a higher analogue of the canonical line bundle in complex geometry.
1	Applied	apply	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	advcl	_	_
2	to	to	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	cotangent	cotangent	NOUN	NN	Number=Sing	5	compound	_	_
5	bundle	bundle	NOUN	NN	Number=Sing	2	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
7	this	this	PRON	DT	Number=Sing|PronType=Dem	10	nsubjpass	_	_
8	may	may	AUX	MD	VerbForm=Fin	10	aux	_	_
9	be	be	AUX	VB	VerbForm=Inf	10	auxpass	_	_
10	regarded	regard	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	as	as	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	higher	high	ADJ	JJR	Degree=Cmp	14	amod	_	_
14	analogue	analogue	NOUN	NN	Number=Sing	11	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
17	canonical	canonical	ADJ	JJ	Degree=Pos	18	amod	_	_
18	line	line	NOUN	NN	Number=Sing	19	compound	_	_
19	bundle	bundle	NOUN	NN	Number=Sing	15	pobj	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	complex	complex	ADJ	JJ	Degree=Pos	22	amod	_	_
22	geometry	geometry	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 3
# text = Moreover, we exhibit the precise relationship between holomorphic and smooth gerbes.
1	Moreover	moreover	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	exhibit	exhibit	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	precise	precise	ADJ	JJ	Degree=Pos	7	amod	_	_
7	relationship	relationship	NOUN	NN	Number=Sing	4	dobj	_	_
8	between	between	ADP	IN	_	7	prep	_	_
9	holomorphic	holomorphic	PROPN	NNP	Number=Sing	12	nmod	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	smooth	smooth	ADJ	JJ	Degree=Pos	9	conj	_	_
12	gerbes	gerbes	PROPN	NNP	Number=Sing	8	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = For example, we introduce an Atiyah class for gerbes and prove a Koszul - Malgrange type theorem.
1	For	for	ADP	IN	_	5	prep	_	_
2	example	example	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	Atiyah	Atiyah	PROPN	NNP	Number=Sing	8	compound	_	_
8	class	class	NOUN	NN	Number=Sing	5	dobj	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	gerbes	gerbes	PROPN	NNP	Number=Sing	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
12	prove	prove	VERB	VB	VerbForm=Inf	5	conj	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
14	Koszul	Koszul	PROPN	NNP	Number=Sing	16	compound	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	Malgrange	Malgrange	PROPN	NNP	Number=Sing	17	compound	_	_
17	type	type	NOUN	NN	Number=Sing	18	compound	_	_
18	theorem	theorem	ADJ	JJ	Degree=Pos	12	oprd	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 620
# sent_id = 1
# text = If $ C $ is a category with pullbacks then there is a bicategory with the same objects as $ C $ , spans as morphisms, and maps of spans as 2 - morphisms, as shown by Benabou.
1	If	if	SCONJ	IN	_	3	mark	_	_
2	$ C $	$ c $	SYM	$	_	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	advcl	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	3	attr	_	_
6	with	with	ADP	IN	_	5	prep	_	_
7	pullbacks	pullback	NOUN	NNS	Number=Plur	6	pobj	_	_
8	then	then	ADV	RB	PronType=Dem	10	advmod	_	_
9	there	there	PRON	EX	_	10	expl	_	_
10	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	bicategory	bicategory	NOUN	NN	Number=Sing	10	attr	_	_
13	with	with	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	same	same	ADJ	JJ	Degree=Pos	16	amod	_	_
16	objects	object	NOUN	NNS	Number=Plur	13	pobj	_	_
17	as	as	ADP	IN	_	16	prep	_	_
18	$ C $	$ c $	SYM	$	_	17	pobj	_	_
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	spans	span	NOUN	NNS	Number=Plur	18	conj	_	_
21	as	as	ADP	IN	_	20	prep	_	_
22	morphisms	morphism	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
25	maps	map	NOUN	NNS	Number=Plur	20	conj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	spans	span	NOUN	NNS	Number=Plur	26	pobj	_	_
28	as	as	ADP	IN	_	16	prep	_	_
29	2	2	NUM	CD	NumType=Card	31	nummod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	morphisms	morphism	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
33	as	as	SCONJ	IN	_	34	mark	_	_
34	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	advcl	_	_
35	by	by	ADP	IN	_	34	agent	_	_
36	Benabou	Benabou	PROPN	NNP	Number=Sing	35	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = Fong has developed a theory of `decorated cospans', which are cospans in $ C $ equipped with extra structure.
1	Fong	Fong	PROPN	NNP	Number=Sing	3	nsubj	_	_
2	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	aux	_	_
3	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	theory	theory	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	6	punct	_	SpaceAfter=No
8	decorated	decorate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	amod	_	_
9	cospans	cospan	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
10	'	'	PROPN	NNP	Number=Sing	6	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
12	which	which	PRON	WDT	_	13	nsubj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	relcl	_	_
14	cospans	cospan	NOUN	NNS	Number=Plur	13	attr	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	$ C $	$ c $	SYM	$	_	15	pobj	_	_
17	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	acl	_	_
18	with	with	ADP	IN	_	17	prep	_	_
19	extra	extra	ADJ	JJ	Degree=Pos	20	amod	_	_
20	structure	structure	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = This extra structure arises from a symmetric lax monoidal functor $ F : C - - > D $ ; we use this functor to `decorate' each cospan with apex $ N $ in $ C $ with an element of $ F(N) $ .
1	This	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
2	extra	extra	ADJ	JJ	Degree=Pos	3	amod	_	_
3	structure	structure	NOUN	NN	Number=Sing	4	nsubj	_	_
4	arises	arise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	ccomp	_	_
5	from	from	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
7	symmetric	symmetric	ADJ	JJ	Degree=Pos	10	amod	_	_
8	lax	lax	ADJ	JJ	Degree=Pos	10	amod	_	_
9	monoidal	monoidal	NOUN	NN	Number=Sing	10	compound	_	_
10	functor	functor	NOUN	NN	Number=Sing	5	pobj	_	_
11	$ F : C - - > D $	$ f : c - - > d $	SYM	$	_	4	advmod	_	_
12	;	;	PUNCT	:	_	14	punct	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	this	this	DET	DT	Number=Sing|PronType=Dem	16	det	_	_
16	functor	functor	NOUN	NN	Number=Sing	14	dobj	_	_
17	to	to	PART	TO	_	19	aux	_	_
18	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	19	punct	_	SpaceAfter=No
19	decorate	decorate	VERB	VB	VerbForm=Inf	14	xcomp	_	SpaceAfter=No
20	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	19	punct	_	_
21	each	each	DET	DT	_	22	det	_	_
22	cospan	cospan	NOUN	NN	Number=Sing	19	dobj	_	_
23	with	with	ADP	IN	_	19	prep	_	_
24	apex	apex	PROPN	NNP	Number=Sing	23	pobj	_	_
25	$ N $	$ n $	SYM	$	_	24	appos	_	_
26	in	in	ADP	IN	_	19	prep	_	_
27	$ C $	$ c $	SYM	$	_	26	pobj	_	_
28	with	with	ADP	IN	_	19	prep	_	_
29	an	an	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
30	element	element	NOUN	NN	Number=Sing	28	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	$ F(N) $	$ f(n) $	SYM	$	_	31	pobj	_	_
33	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 4
# text = Using a result of Shulman, we show that when $ C $ has finite colimits, decorated cospans are morphisms in a symmetric monoidal bicategory.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	advcl	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	result	result	NOUN	NN	Number=Sing	1	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	Shulman	Shulman	PROPN	NNP	Number=Sing	4	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
7	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	8	nsubj	_	_
8	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	that	that	SCONJ	IN	_	18	mark	_	_
10	when	when	SCONJ	WRB	_	12	advmod	_	_
11	$ C $	$ c $	SYM	$	_	12	nsubj	_	_
12	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	advcl	_	_
13	finite	finite	ADJ	JJ	Degree=Pos	14	amod	_	_
14	colimits	colimit	NOUN	NNS	Number=Plur	12	dobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
16	decorated	decorate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	cospans	cospan	NOUN	NNS	Number=Plur	18	nsubj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	ccomp	_	_
19	morphisms	morphism	NOUN	NNS	Number=Plur	18	attr	_	_
20	in	in	ADP	IN	_	18	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
22	symmetric	symmetric	ADJ	JJ	Degree=Pos	24	amod	_	_
23	monoidal	monoidal	ADJ	JJ	Degree=Pos	24	amod	_	_
24	bicategory	bicategory	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 5
# text = We illustrate our construction with examples from electrical engineering and the theory of chemical reaction networks.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	illustrate	illustrate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	4	poss	_	_
4	construction	construction	NOUN	NN	Number=Sing	2	dobj	_	_
5	with	with	ADP	IN	_	2	prep	_	_
6	examples	example	NOUN	NNS	Number=Plur	5	pobj	_	_
7	from	from	ADP	IN	_	6	prep	_	_
8	electrical	electrical	ADJ	JJ	Degree=Pos	9	amod	_	_
9	engineering	engineering	NOUN	NN	Number=Sing	7	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	theory	theory	NOUN	NN	Number=Sing	9	conj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	chemical	chemical	ADJ	JJ	Degree=Pos	15	amod	_	_
15	reaction	reaction	NOUN	NN	Number=Sing	16	compound	_	_
16	networks	network	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 621
# sent_id = 1
# text = We associate to a bimonoidal functor, that is, a bifunctor which is monoidal in each variable, a nonabelian version of a biextension.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	associate	associate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	bimonoidal	bimonoidal	NOUN	NN	Number=Sing	6	compound	_	_
6	functor	functor	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	that	that	ADV	RB	_	9	advmod	_	_
9	is	is	ADV	RB	_	6	relcl	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	bifunctor	bifunctor	NOUN	NN	Number=Sing	6	appos	_	_
13	which	which	PRON	WDT	_	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	relcl	_	_
15	monoidal	monoidal	ADJ	JJ	Degree=Pos	14	acomp	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	each	each	DET	DT	_	18	det	_	_
18	variable	variable	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	nonabelian	nonabelian	ADJ	JJ	Degree=Pos	22	amod	_	_
22	version	version	NOUN	NN	Number=Sing	6	appos	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
25	biextension	biextension	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that such a biextension satisfies additional triviality conditions which make it a bilinear analog of the kind of spans known as butterflies and, conversely, these data determine a bimonoidal functor.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	31	mark	_	_
4	such	such	DET	PDT	_	7	predet	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	biextension	biextension	NOUN	NN	Number=Sing	7	compound	_	_
7	satisfies	satisfie	NOUN	NNS	Number=Plur	31	nsubj	_	_
8	additional	additional	ADJ	JJ	Degree=Pos	10	amod	_	_
9	triviality	triviality	NOUN	NN	Number=Sing	10	compound	_	_
10	conditions	condition	NOUN	NNS	Number=Plur	7	appos	_	_
11	which	which	PRON	WDT	_	12	nsubj	_	_
12	make	make	VERB	VBP	Tense=Pres|VerbForm=Fin	10	relcl	_	_
13	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	16	nsubj	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	bilinear	bilinear	ADJ	JJ	Degree=Pos	16	amod	_	_
16	analog	analog	NOUN	NN	Number=Sing	12	ccomp	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	kind	kind	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	spans	span	NOUN	NNS	Number=Plur	20	pobj	_	_
22	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	acl	_	_
23	as	as	ADP	IN	_	22	prep	_	_
24	butterflies	butterfly	NOUN	NNS	Number=Plur	23	pobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
27	conversely	conversely	ADV	RB	_	31	advmod	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
29	these	these	DET	DT	Number=Plur|PronType=Dem	30	det	_	_
30	data	datum	NOUN	NNS	Number=Plur	31	nsubj	_	_
31	determine	determine	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
33	bimonoidal	bimonoidal	NOUN	NN	Number=Sing	34	compound	_	_
34	functor	functor	NOUN	NN	Number=Sing	31	dobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We extend this result to $ n $ - variables, and prove that, in a manner analogous to that of butterflies, these multi - extensions can be composed.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	extend	extend	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	result	result	NOUN	NN	Number=Sing	2	dobj	_	_
5	to	to	ADP	IN	_	2	prep	_	_
6	$ n $	$ n $	SYM	$	_	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	variables	variable	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
11	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
12	that	that	SCONJ	IN	_	29	mark	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
14	in	in	ADP	IN	_	29	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	manner	manner	NOUN	NN	Number=Sing	14	pobj	_	_
17	analogous	analogous	ADJ	JJ	Degree=Pos	16	amod	_	_
18	to	to	ADP	IN	_	17	prep	_	_
19	that	that	PRON	DT	Number=Sing|PronType=Dem	18	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	butterflies	butterfly	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
23	these	these	DET	DT	Number=Plur|PronType=Dem	24	det	_	_
24	multi	multi	NOUN	NN	Number=Sing	26	compound	_	_
25	-	-	NOUN	NNS	Number=Plur	26	punct	_	_
26	extensions	extension	NOUN	NNS	Number=Plur	29	nsubjpass	_	_
27	can	can	AUX	MD	VerbForm=Fin	29	aux	_	_
28	be	be	AUX	VB	VerbForm=Inf	29	auxpass	_	_
29	composed	compose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	ccomp	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = This is phrased in terms of a multilinear functor calculus in a bicategory.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	phrased	phrase	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	in	in	ADP	IN	_	3	prep	_	_
5	terms	term	NOUN	NNS	Number=Plur	4	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	multilinear	multilinear	ADJ	JJ	Degree=Pos	10	amod	_	_
9	functor	functor	NOUN	NN	Number=Sing	10	compound	_	_
10	calculus	calculus	NOUN	NN	Number=Sing	6	pobj	_	_
11	in	in	ADP	IN	_	3	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	bicategory	bicategory	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = As an application, we study a bimonoidal category or stack, treating the multiplicative structure as a bimonoidal functor with respect to the additive one.
1	As	as	ADP	IN	_	6	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	bimonoidal	bimonoidal	NOUN	NN	Number=Sing	9	compound	_	_
9	category	category	NOUN	NN	Number=Sing	6	dobj	_	_
10	or	or	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	stack	stack	VERB	VB	VerbForm=Inf	9	conj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
13	treating	treat	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	advcl	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	multiplicative	multiplicative	ADJ	JJ	Degree=Pos	16	amod	_	_
16	structure	structure	NOUN	NN	Number=Sing	13	dobj	_	_
17	as	as	ADP	IN	_	13	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	bimonoidal	bimonoidal	NOUN	NN	Number=Sing	20	compound	_	_
20	functor	functor	NOUN	NN	Number=Sing	17	pobj	_	_
21	with	with	ADP	IN	_	20	prep	_	_
22	respect	respect	NOUN	NN	Number=Sing	21	pobj	_	_
23	to	to	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	additive	additive	ADJ	JJ	Degree=Pos	26	amod	_	_
26	one	one	NUM	CD	NumType=Card	23	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 6
# text = In the context of the multilinear functor calculus, we view the bimonoidal structure as an instance of the general notion of pseudo - monoid.
1	In	in	ADP	IN	_	11	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	context	context	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
6	multilinear	multilinear	NOUN	NN	Number=Sing	8	compound	_	_
7	functor	functor	PROPN	NNP	Number=Sing	8	compound	_	_
8	calculus	calculus	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
10	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	11	nsubj	_	_
11	view	view	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	bimonoidal	bimonoidal	NOUN	NN	Number=Sing	14	compound	_	_
14	structure	structure	NOUN	NN	Number=Sing	11	dobj	_	_
15	as	as	ADP	IN	_	11	prep	_	_
16	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	instance	instance	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	general	general	ADJ	JJ	Degree=Pos	21	amod	_	_
21	notion	notion	NOUN	NN	Number=Sing	18	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	pseudo	pseudo	NOUN	NN	Number=Sing	25	compound	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	monoid	monoid	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 7
# text = We show that when the structure is ring - like, that is the pseudo - monoid is a stack whose fibers are categorical rings, we can recover the classification by the third Mac~Lane cohomology of a ring with values in a bimodule.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	13	mark	_	_
4	when	when	SCONJ	WRB	_	7	advmod	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	structure	structure	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	advcl	_	_
8	ring	ring	NOUN	NN	Number=Sing	10	npadvmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	like	like	INTJ	UH	_	7	acomp	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
12	that	that	PRON	DT	Number=Sing|PronType=Dem	13	nsubj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	advcl	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	pseudo	pseudo	NOUN	NN	Number=Sing	17	compound	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	monoid	monoid	NOUN	NN	Number=Sing	18	nsubj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	stack	stack	NOUN	NN	Number=Sing	18	attr	_	_
21	whose	whose	DET	WP$	Poss=Yes	22	poss	_	_
22	fibers	fiber	NOUN	NNS	Number=Plur	23	nsubj	_	_
23	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	20	relcl	_	_
24	categorical	categorical	ADJ	JJ	Degree=Pos	25	amod	_	_
25	rings	ring	NOUN	NNS	Number=Plur	23	attr	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
27	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	29	nsubj	_	_
28	can	can	AUX	MD	VerbForm=Fin	29	aux	_	_
29	recover	recover	VERB	VB	VerbForm=Inf	2	ccomp	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	classification	classification	NOUN	NN	Number=Sing	29	dobj	_	_
32	by	by	ADP	IN	_	29	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
34	third	third	ADJ	JJ	Degree=Pos	35	amod	_	_
35	Mac	Mac	PROPN	NNP	Number=Sing	32	pobj	_	SpaceAfter=No
36	~	~	PUNCT	:	_	35	punct	_	SpaceAfter=No
37	Lane	Lane	PROPN	NNP	Number=Sing	38	compound	_	_
38	cohomology	cohomology	NOUN	NN	Number=Sing	35	appos	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
41	ring	ring	NOUN	NN	Number=Sing	39	pobj	_	_
42	with	with	ADP	IN	_	41	prep	_	_
43	values	value	NOUN	NNS	Number=Plur	42	pobj	_	_
44	in	in	ADP	IN	_	43	prep	_	_
45	a	a	DET	DT	Definite=Ind|PronType=Art	46	det	_	_
46	bimodule	bimodule	NOUN	NN	Number=Sing	44	pobj	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 622
# sent_id = 1
# text = Starting from the observation that through groupoids we can express in a unified way the notions of fundamental system of entourages of a uniform structure on a space $ X $ , respectively the system of neighborhoods of the unity of a topological group that determines its topology, we introduce in this paper a notion of $ G $ - uniformity for a groupoid $ G $ .
1	Starting	start	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	49	advcl	_	_
2	from	from	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	observation	observation	NOUN	NN	Number=Sing	2	pobj	_	_
5	that	that	SCONJ	IN	_	10	mark	_	_
6	through	through	ADP	IN	_	10	prep	_	_
7	groupoids	groupoid	NOUN	NNS	Number=Plur	6	pobj	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
9	can	can	AUX	MD	VerbForm=Fin	10	aux	_	_
10	express	express	VERB	VB	VerbForm=Inf	4	acl	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	unified	unified	ADJ	JJ	Degree=Pos	14	amod	_	_
14	way	way	NOUN	NN	Number=Sing	11	pobj	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	notions	notion	NOUN	NNS	Number=Plur	10	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	fundamental	fundamental	ADJ	JJ	Degree=Pos	19	amod	_	_
19	system	system	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	entourages	entourage	NOUN	NNS	Number=Plur	20	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	uniform	uniform	ADJ	JJ	Degree=Pos	25	amod	_	_
25	structure	structure	NOUN	NN	Number=Sing	22	pobj	_	_
26	on	on	ADP	IN	_	16	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	space	space	NOUN	NN	Number=Sing	26	pobj	_	_
29	$ X $	$ x $	SYM	$	_	28	appos	_	_
30	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
31	respectively	respectively	ADV	RB	_	33	advmod	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
33	system	system	NOUN	NN	Number=Sing	16	appos	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	neighborhoods	neighborhood	NOUN	NNS	Number=Plur	34	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	unity	unity	NOUN	NN	Number=Sing	36	pobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	a	a	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
41	topological	topological	ADJ	JJ	Degree=Pos	42	amod	_	_
42	group	group	NOUN	NN	Number=Sing	39	pobj	_	_
43	that	that	PRON	WDT	PronType=Rel	44	nsubj	_	_
44	determines	determine	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	42	relcl	_	_
45	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	46	poss	_	_
46	topology	topology	NOUN	NN	Number=Sing	44	dobj	_	SpaceAfter=No
47	,	,	PUNCT	,	PunctType=Comm	49	punct	_	_
48	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	49	nsubj	_	_
49	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
50	in	in	ADP	IN	_	49	prep	_	_
51	this	this	DET	DT	Number=Sing|PronType=Dem	52	det	_	_
52	paper	paper	NOUN	NN	Number=Sing	50	pobj	_	_
53	a	a	DET	DT	Definite=Ind|PronType=Art	54	det	_	_
54	notion	notion	NOUN	NN	Number=Sing	49	dobj	_	_
55	of	of	ADP	IN	_	54	prep	_	_
56	$ G $	$ g $	SYM	$	_	58	compound	_	_
57	-	-	PUNCT	HYPH	PunctType=Dash	58	punct	_	_
58	uniformity	uniformity	NOUN	NN	Number=Sing	55	pobj	_	_
59	for	for	ADP	IN	_	54	prep	_	_
60	a	a	DET	DT	Definite=Ind|PronType=Art	61	det	_	_
61	groupoid	groupoid	NOUN	NN	Number=Sing	62	compound	_	_
62	$ G $	$ g $	SYM	$	_	59	pobj	_	_
63	.	.	PUNCT	.	PunctType=Peri	49	punct	_	SpaceAfter=No

# sent_id = 2
# text = The topology induced by a $ G $ - uniformity turns $ G $ into a topological locally transitive groupoid.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	topology	topology	NOUN	NN	Number=Sing	9	nsubj	_	_
3	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acl	_	_
4	by	by	ADP	IN	_	3	agent	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
6	$ G $	$ g $	SYM	$	_	8	compound	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	uniformity	uniformity	NOUN	NN	Number=Sing	4	pobj	_	_
9	turns	turn	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	$ G $	$ g $	SYM	$	_	9	dobj	_	_
11	into	into	ADP	IN	_	9	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
13	topological	topological	ADJ	JJ	Degree=Pos	16	amod	_	_
14	locally	locally	ADV	RB	_	15	advmod	_	_
15	transitive	transitive	ADJ	JJ	Degree=Pos	16	amod	_	_
16	groupoid	groupoid	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also prove a Urysohn type lemma for groupoids and obtain metrization theorems for groupoids unifying in two ways the Alexandroff - Urysohn Theorem and Birkhoff - Kakutani Theorem.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	Urysohn	Urysohn	PROPN	NNP	Number=Sing	7	compound	_	_
6	type	type	NOUN	NN	Number=Sing	7	compound	_	_
7	lemma	lemma	NOUN	NN	Number=Sing	3	dobj	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	groupoids	groupoid	NOUN	NNS	Number=Plur	8	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
11	obtain	obtain	VERB	VB	VerbForm=Inf	3	conj	_	_
12	metrization	metrization	NOUN	NN	Number=Sing	13	compound	_	_
13	theorems	theorem	NOUN	NNS	Number=Plur	11	dobj	_	_
14	for	for	ADP	IN	_	13	prep	_	_
15	groupoids	groupoid	NOUN	NNS	Number=Plur	14	pobj	_	_
16	unifying	unify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	acl	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	two	two	NUM	CD	NumType=Card	19	nummod	_	_
19	ways	way	NOUN	NNS	Number=Plur	17	pobj	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
21	Alexandroff	Alexandroff	PROPN	NNP	Number=Sing	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	Urysohn	Urysohn	PROPN	NNP	Number=Sing	24	compound	_	_
24	Theorem	Theorem	PROPN	NNP	Number=Sing	11	dobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	Birkhoff	Birkhoff	PROPN	NNP	Number=Sing	28	compound	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	Kakutani	Kakutani	PROPN	NNP	Number=Sing	29	compound	_	_
29	Theorem	Theorem	PROPN	NNP	Number=Sing	24	conj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 623
# sent_id = 1
# text = Connections are an important tool of differential geometry.
1	Connections	connection	NOUN	NNS	Number=Plur	2	nsubj	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	important	important	ADJ	JJ	Degree=Pos	5	amod	_	_
5	tool	tool	NOUN	NN	Number=Sing	2	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	differential	differential	ADJ	JJ	Degree=Pos	8	amod	_	_
8	geometry	geometry	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This paper investigates their definition and structure in the abstract setting of tangent categories.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	investigates	investigate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	5	poss	_	_
5	definition	definition	NOUN	NN	Number=Sing	3	dobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	structure	structure	NOUN	NN	Number=Sing	5	conj	_	_
8	in	in	ADP	IN	_	3	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	abstract	abstract	ADJ	JJ	Degree=Pos	11	amod	_	_
11	setting	setting	NOUN	NN	Number=Sing	8	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	tangent	tangent	ADJ	JJ	Degree=Pos	14	amod	_	_
14	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = At this level of abstraction we derive several classically important results about connections, including the Bianchi identities, identities for curvature and torsion, almost complex structure, and parallel transport.
1	At	at	ADP	IN	_	7	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	level	level	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	abstraction	abstraction	NOUN	NN	Number=Sing	4	pobj	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	derive	derive	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	several	several	ADJ	JJ	Degree=Pos	11	amod	_	_
9	classically	classically	ADV	RB	_	10	advmod	_	_
10	important	important	ADJ	JJ	Degree=Pos	11	amod	_	_
11	results	result	NOUN	NNS	Number=Plur	7	dobj	_	_
12	about	about	ADP	IN	_	11	prep	_	_
13	connections	connection	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	Bianchi	Bianchi	PROPN	NNP	Number=Sing	18	compound	_	_
18	identities	identity	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
20	identities	identity	NOUN	NNS	Number=Plur	7	dobj	_	_
21	for	for	ADP	IN	_	20	prep	_	_
22	curvature	curvature	NOUN	NN	Number=Sing	21	pobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	torsion	torsion	NOUN	NN	Number=Sing	22	conj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
26	almost	almost	ADV	RB	_	27	advmod	_	_
27	complex	complex	ADJ	JJ	Degree=Pos	28	amod	_	_
28	structure	structure	NOUN	NN	Number=Sing	20	conj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
31	parallel	parallel	ADJ	JJ	Degree=Pos	32	amod	_	_
32	transport	transport	NOUN	NN	Number=Sing	28	conj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 624
# sent_id = 1
# text = In this paper we give an isomorphic description of the category of non - Archimedian approach spaces as a category of lax algebras for the ultrafilter monad and an appropriate quantale.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	8	amod	_	_
8	description	description	NOUN	NN	Number=Sing	5	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	non	non	ADJ	JJ	Degree=Pos	15	amod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	Archimedian	archimedian	ADJ	JJ	Degree=Pos	17	amod	_	_
16	approach	approach	NOUN	NN	Number=Sing	17	compound	_	_
17	spaces	space	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	pobj	_	_
18	as	as	ADP	IN	_	5	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	lax	lax	ADJ	JJ	Degree=Pos	23	amod	_	_
23	algebras	algebra	NOUN	NNS	Number=Plur	21	pobj	_	_
24	for	for	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	ultrafilter	ultrafilter	NOUN	NN	Number=Sing	27	compound	_	_
27	monad	monad	NOUN	NNS	Number=Plur	24	pobj	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
29	an	an	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	appropriate	appropriate	ADJ	JJ	Degree=Pos	31	amod	_	_
31	quantale	quantale	NOUN	NN	Number=Sing	27	conj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = Non - Archimedean approach spaces are characterised as those approach spaces having a tower consisting of topologies.
1	Non	non	ADJ	JJ	Degree=Pos	3	amod	_	_
2	-	-	PUNCT	HYPH	PunctType=Dash	3	punct	_	_
3	Archimedean	archimedean	ADJ	JJ	Degree=Pos	5	amod	_	_
4	approach	approach	NOUN	NN	Number=Sing	5	compound	_	_
5	spaces	space	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	characterised	characterise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	as	as	ADP	IN	_	7	prep	_	_
9	those	those	DET	DT	Number=Plur|PronType=Dem	11	det	_	_
10	approach	approach	NOUN	NN	Number=Sing	11	compound	_	_
11	spaces	space	NOUN	NNS	Number=Plur	8	pobj	_	_
12	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	acl	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	tower	tower	NOUN	NN	Number=Sing	12	dobj	_	_
15	consisting	consist	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	acl	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	topologies	topology	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = We study topological properties $ p $ , for $ p $ compactness and Hausdorff separation along with low - separation properties, regularity, normality and extremal disconnectedness and link these properties to the condition that all or some of the level topologies in the tower have $ p $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	topological	topological	ADJ	JJ	Degree=Pos	4	amod	_	_
4	properties	property	NOUN	NNS	Number=Plur	2	dobj	_	_
5	$ p $	$ p $	SYM	$	_	2	dobj	_	_
6	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
7	for	for	ADP	IN	_	2	prep	_	_
8	$ p $	$ p $	SYM	$	_	12	nmod	_	_
9	compactness	compactness	ADJ	JJ	Degree=Pos	8	nmod	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	9	conj	_	_
12	separation	separation	NOUN	NN	Number=Sing	7	pobj	_	_
13	along	along	ADP	IN	_	2	prep	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	low	low	ADJ	JJ	Degree=Pos	17	amod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	separation	separation	NOUN	NN	Number=Sing	18	compound	_	_
18	properties	property	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	regularity	regularity	NOUN	NN	Number=Sing	18	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	normality	normality	NOUN	NN	Number=Sing	20	conj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	extremal	extremal	ADJ	JJ	Degree=Pos	25	amod	_	_
25	disconnectedness	disconnectedness	NOUN	NN	Number=Sing	22	conj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
27	link	link	VERB	VB	VerbForm=Inf	2	conj	_	_
28	these	these	DET	DT	Number=Plur|PronType=Dem	29	det	_	_
29	properties	property	NOUN	NNS	Number=Plur	27	dobj	_	_
30	to	to	ADP	IN	_	27	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	condition	condition	NOUN	NN	Number=Sing	30	pobj	_	_
33	that	that	SCONJ	IN	_	44	mark	_	_
34	all	all	PRON	DT	_	44	nsubj	_	_
35	or	or	CCONJ	CC	ConjType=Cmp	34	cc	_	_
36	some	some	PRON	DT	_	34	conj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
39	level	level	NOUN	NN	Number=Sing	40	compound	_	_
40	topologies	topology	NOUN	NNS	Number=Plur	37	pobj	_	_
41	in	in	ADP	IN	_	40	prep	_	_
42	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
43	tower	tower	NOUN	NN	Number=Sing	41	pobj	_	_
44	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	32	acl	_	_
45	$ p $	$ p $	SYM	$	_	44	dobj	_	_
46	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = A compactification technique is developed based on Shanin's method.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	compactification	compactification	NOUN	NN	Number=Sing	3	compound	_	_
3	technique	technique	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	prep	_	_
7	on	on	ADP	IN	_	6	prep	_	_
8	Shanin	Shanin	PROPN	NNP	Number=Sing	10	poss	_	SpaceAfter=No
9	's	's	PART	POS	_	8	case	_	_
10	method	method	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 625
# sent_id = 1
# text = We prove a fundamental lemma of homological algebra and show how it sets a framework for many different lifting (or comparison) theorems of homological algebra and algebraic topology.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	fundamental	fundamental	ADJ	JJ	Degree=Pos	5	amod	_	_
5	lemma	lemma	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	homological	homological	ADJ	JJ	Degree=Pos	8	amod	_	_
8	algebra	algebra	NOUN	NN	Number=Sing	6	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
10	show	show	VERB	VB	VerbForm=Inf	2	conj	_	_
11	how	how	SCONJ	WRB	_	13	advmod	_	_
12	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	13	nsubj	_	_
13	sets	set	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	ccomp	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	framework	framework	NOUN	NN	Number=Sing	13	dobj	_	_
16	for	for	ADP	IN	_	15	prep	_	_
17	many	many	ADJ	JJ	Degree=Pos	19	amod	_	_
18	different	different	ADJ	JJ	Degree=Pos	19	amod	_	_
19	lifting	lifting	NOUN	NN	Number=Sing	16	pobj	_	_
20	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	19	punct	_	SpaceAfter=No
21	or	or	CCONJ	CC	ConjType=Cmp	19	cc	_	_
22	comparison	comparison	NOUN	NN	Number=Sing	19	conj	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	24	punct	_	_
24	theorems	theorem	NOUN	NNS	Number=Plur	2	conj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	homological	homological	ADJ	JJ	Degree=Pos	27	amod	_	_
27	algebra	algebra	NOUN	NN	Number=Sing	25	pobj	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
29	algebraic	algebraic	ADJ	JJ	Degree=Pos	30	amod	_	_
30	topology	topology	NOUN	NN	Number=Sing	27	conj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Among these are different versions of the acyclic models method.
1	Among	among	ADP	IN	_	3	prep	_	_
2	these	these	PRON	DT	Number=Plur|PronType=Dem	1	pobj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	different	different	ADJ	JJ	Degree=Pos	5	amod	_	_
5	versions	version	NOUN	NNS	Number=Plur	3	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	acyclic	acyclic	ADJ	JJ	Degree=Pos	9	compound	_	_
9	models	model	NOUN	NNS	Number=Plur	6	pobj	_	_
10	method	method	ADJ	JJ	Degree=Pos	3	advcl	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 626
# sent_id = 1
# text = We present an axiomatic theory, based on the notions of metric space and space with a (first order) neighbour relation.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	axiomatic	axiomatic	ADJ	JJ	Degree=Pos	5	amod	_	_
5	theory	theory	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	prep	_	_
8	on	on	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	notions	notion	NOUN	NNS	Number=Plur	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	metric	metric	ADJ	JJ	Degree=Pos	13	amod	_	_
13	space	space	NOUN	NN	Number=Sing	11	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	space	space	NOUN	NN	Number=Sing	13	conj	_	_
16	with	with	ADP	IN	_	10	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
18	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	20	punct	_	SpaceAfter=No
19	first	first	ADJ	JJ	Degree=Pos	20	amod	_	_
20	order	order	NOUN	NN	Number=Sing	23	nmod	_	SpaceAfter=No
21	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	20	punct	_	_
22	neighbour	neighbour	ADJ	JJ	Degree=Pos	23	amod	_	_
23	relation	relation	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The axiomatics implies a synthetic proof of Huygens' principle of wave fronts, as envelopes of a family of spheres.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	axiomatics	axiomatic	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	implies	imply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	synthetic	synthetic	ADJ	JJ	Degree=Pos	6	amod	_	_
6	proof	proof	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	Huygens	Huygens	PROPN	NNP	Number=Sing	10	poss	_	SpaceAfter=No
9	'	'	PART	POS	_	8	case	_	_
10	principle	principle	NOUN	NN	Number=Sing	7	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	wave	wave	NOUN	NN	Number=Sing	13	compound	_	_
13	fronts	front	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
15	as	as	ADP	IN	_	3	prep	_	_
16	envelopes	envelope	NOUN	NNS	Number=Plur	15	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	family	family	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	spheres	sphere	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = A model of the axiomatics is presented in terms of synthetic differential geometry.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	model	model	NOUN	NN	Number=Sing	7	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	axiomatics	axiomatic	NOUN	NNS	Number=Plur	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	terms	term	NOUN	NNS	Number=Plur	8	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	synthetic	synthetic	ADJ	JJ	Degree=Pos	13	amod	_	_
12	differential	differential	ADJ	JJ	Degree=Pos	13	amod	_	_
13	geometry	geometry	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 627
# sent_id = 1
# text = We define a Levi category to be a weakly orthogonal category equipped with a suitable length functor and prove two main theorems about them.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	Levi	Levi	PROPN	NNP	Number=Sing	5	compound	_	_
5	category	category	NOUN	NN	Number=Sing	2	dobj	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	be	be	AUX	VB	VerbForm=Inf	2	xcomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	weakly	weakly	ADJ	JJ	Degree=Pos	11	amod	_	_
10	orthogonal	orthogonal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	category	category	NOUN	NN	Number=Sing	7	attr	_	_
12	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acl	_	_
13	with	with	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	suitable	suitable	ADJ	JJ	Degree=Pos	17	amod	_	_
16	length	length	NOUN	NN	Number=Sing	17	compound	_	_
17	functor	functor	NOUN	NN	Number=Sing	13	pobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
19	prove	prove	VERB	VB	VerbForm=Inf	12	conj	_	_
20	two	two	NUM	CD	NumType=Card	22	nummod	_	_
21	main	main	ADJ	JJ	Degree=Pos	22	amod	_	_
22	theorems	theorem	NOUN	NNS	Number=Plur	19	dobj	_	_
23	about	about	ADP	IN	_	22	prep	_	_
24	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	23	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = First, skeletal cancellative Levi categories are precisely the categorical versions of graphs of groups with a given orientation.
1	First	first	ADV	RB	_	7	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
3	skeletal	skeletal	ADJ	JJ	Degree=Pos	6	amod	_	_
4	cancellative	cancellative	ADJ	JJ	Degree=Pos	6	amod	_	_
5	Levi	Levi	PROPN	NNP	Number=Sing	6	compound	_	_
6	categories	category	NOUN	NNS	Number=Plur	7	nsubj	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	precisely	precisely	ADV	RB	_	7	advmod	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	categorical	categorical	ADJ	JJ	Degree=Pos	11	amod	_	_
11	versions	version	NOUN	NNS	Number=Plur	7	attr	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	graphs	graph	NOUN	NNS	Number=Plur	12	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	groups	group	NOUN	NNS	Number=Plur	14	pobj	_	_
16	with	with	ADP	IN	_	11	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
19	orientation	orientation	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = Second, the universal groupoid of a skeletal cancellative Levi category is the fundamental groupoid of the corresponding graph of groups.
1	Second	second	ADV	RB	_	12	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	universal	universal	ADJ	JJ	Degree=Pos	5	amod	_	_
5	groupoid	groupoid	NOUN	NN	Number=Sing	12	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	skeletal	skeletal	ADJ	JJ	Degree=Pos	11	amod	_	_
9	cancellative	cancellative	ADJ	JJ	Degree=Pos	11	amod	_	_
10	Levi	Levi	PROPN	NNP	Number=Sing	11	compound	_	_
11	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	fundamental	fundamental	ADJ	JJ	Degree=Pos	15	amod	_	_
15	groupoid	groupoid	NOUN	NN	Number=Sing	12	attr	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	corresponding	corresponding	ADJ	JJ	Degree=Pos	19	amod	_	_
19	graph	graph	NOUN	NN	Number=Sing	16	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	groups	group	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 4
# text = These two results can be viewed as a co - ordinate - free refinement of a classical theorem of Philip Higgins.
1	These	these	DET	DT	Number=Plur|PronType=Dem	3	det	_	_
2	two	two	NUM	CD	NumType=Card	3	nummod	_	_
3	results	result	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
4	can	can	AUX	MD	VerbForm=Fin	6	aux	_	_
5	be	be	AUX	VB	VerbForm=Inf	6	auxpass	_	_
6	viewed	view	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	as	as	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
9	co	co	NOUN	NN	Number=Sing	13	npadvmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
11	ordinate	ordinate	NOUN	NN	Number=Sing	13	amod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	free	free	ADJ	JJ	Degree=Pos	14	amod	_	_
14	refinement	refinement	NOUN	NN	Number=Sing	7	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	classical	classical	ADJ	JJ	Degree=Pos	18	amod	_	_
18	theorem	theorem	NOUN	NN	Number=Sing	15	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	Philip	Philip	PROPN	NNP	Number=Sing	21	compound	_	_
21	Higgins	Higgins	PROPN	NNP	Number=Sing	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 628
# sent_id = 1
# text = We show that a fully faithful and covering regular functor between regular categories induces a fully faithful (and covering) functor between their respective effectivizations.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	14	mark	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
5	fully	fully	ADV	RB	_	6	advmod	_	_
6	faithful	faithful	ADJ	JJ	Degree=Pos	14	amod	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	covering	cover	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	conj	_	_
9	regular	regular	ADJ	JJ	Degree=Pos	10	amod	_	_
10	functor	functor	NOUN	NN	Number=Sing	8	dobj	_	_
11	between	between	ADP	IN	_	10	prep	_	_
12	regular	regular	ADJ	JJ	Degree=Pos	13	amod	_	_
13	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
14	induces	induce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
16	fully	fully	ADV	RB	_	17	advmod	_	_
17	faithful	faithful	ADJ	JJ	Degree=Pos	22	amod	_	_
18	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	17	punct	_	SpaceAfter=No
19	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
20	covering	cover	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	conj	_	SpaceAfter=No
21	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	22	punct	_	_
22	functor	functor	NOUN	NN	Number=Sing	14	dobj	_	_
23	between	between	ADP	IN	_	22	prep	_	_
24	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	26	poss	_	_
25	respective	respective	ADJ	JJ	Degree=Pos	26	amod	_	_
26	effectivizations	effectivization	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Such a functor between effective categories is known to be an equivalence.
1	Such	such	DET	PDT	_	3	predet	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	functor	functor	NOUN	NN	Number=Sing	8	nsubjpass	_	_
4	between	between	ADP	IN	_	3	prep	_	_
5	effective	effective	ADJ	JJ	Degree=Pos	6	amod	_	_
6	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	be	be	AUX	VB	VerbForm=Inf	8	xcomp	_	_
11	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	equivalence	equivalence	NOUN	NN	Number=Sing	10	attr	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 3
# text = We exploit this result in order to give a constructive proof of conceptual completeness for regular logic.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	exploit	exploit	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	result	result	NOUN	NN	Number=Sing	2	dobj	_	_
5	in	in	ADP	IN	_	2	prep	_	_
6	order	order	NOUN	NN	Number=Sing	5	pobj	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	give	give	VERB	VB	VerbForm=Inf	6	acl	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	constructive	constructive	ADJ	JJ	Degree=Pos	11	amod	_	_
11	proof	proof	NOUN	NN	Number=Sing	8	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	conceptual	conceptual	ADJ	JJ	Degree=Pos	14	amod	_	_
14	completeness	completeness	NOUN	NN	Number=Sing	12	pobj	_	_
15	for	for	ADP	IN	_	14	prep	_	_
16	regular	regular	ADJ	JJ	Degree=Pos	17	amod	_	_
17	logic	logic	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We also use it in analyzing what it means for a morphism between effective categories to be a quotient in the 2 - category of effective categories and regular functors between them.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	dobj	_	_
5	in	in	ADP	IN	_	3	prep	_	_
6	analyzing	analyze	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	what	what	PRON	WP	_	9	dobj	_	_
8	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	9	nsubj	_	_
9	means	mean	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
10	for	for	SCONJ	IN	_	17	mark	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	morphism	morphism	NOUN	NN	Number=Sing	17	nsubj	_	_
13	between	between	ADP	IN	_	12	prep	_	_
14	effective	effective	ADJ	JJ	Degree=Pos	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	_
16	to	to	PART	TO	_	17	aux	_	_
17	be	be	AUX	VB	VerbForm=Inf	9	advcl	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	quotient	quotient	NOUN	NN	Number=Sing	17	attr	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
22	2	2	NUM	CD	NumType=Card	24	nummod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	category	category	NOUN	NN	Number=Sing	20	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	effective	effective	ADJ	JJ	Degree=Pos	27	amod	_	_
27	categories	category	NOUN	NNS	Number=Plur	25	pobj	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
29	regular	regular	ADJ	JJ	Degree=Pos	30	amod	_	_
30	functors	functor	NOUN	NNS	Number=Plur	27	conj	_	_
31	between	between	ADP	IN	_	27	prep	_	_
32	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	31	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 629
# sent_id = 1
# text = For a small quantaloid $ Q $ we consider four fundamental 2 - monads $ T $ on $ Q $ - Cat, given by the presheaf 2 - monad $ P $ and the copresheaf 2 - monad $ P^{dagger} $ , as well as by their two composite 2 - monads, and establish that they all laxly distribute over $ P $ .
1	For	for	ADP	IN	_	7	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	small	small	ADJ	JJ	Degree=Pos	4	amod	_	_
4	quantaloid	quantaloid	NOUN	NN	Number=Sing	1	pobj	_	_
5	$ Q $	$ q $	SYM	$	_	4	nmod	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	four	four	NUM	CD	NumType=Card	12	nummod	_	_
9	fundamental	fundamental	ADJ	JJ	Degree=Pos	12	amod	_	_
10	2	2	NUM	CD	NumType=Card	12	nummod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	monads	monad	NOUN	NNS	Number=Plur	7	dobj	_	_
13	$ T $	$ t $	SYM	$	_	12	appos	_	_
14	on	on	ADP	IN	_	12	prep	_	_
15	$ Q $	$ q $	SYM	$	_	17	compound	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	Cat	cat	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
19	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	prep	_	_
20	by	by	ADP	IN	_	19	agent	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	presheaf	presheaf	ADJ	JJ	Degree=Pos	20	pobj	_	_
23	2	2	NUM	CD	NumType=Card	25	nummod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	monad	monad	NOUN	NNS	Number=Plur	26	compound	_	_
26	$ P $	$ p $	SYM	$	_	19	pobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
29	copresheaf	copresheaf	ADJ	JJ	Degree=Pos	33	amod	_	_
30	2	2	NUM	CD	NumType=Card	32	nummod	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	monad	monad	NOUN	NNS	Number=Plur	33	compound	_	_
33	$ P^{dagger} $	$ p^{dagger} $	SYM	$	_	19	conj	_	_
34	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
35	as	as	ADV	RB	_	37	advmod	_	_
36	well	well	ADV	RB	Degree=Pos	37	advmod	_	_
37	as	as	ADP	IN	_	19	cc	_	_
38	by	by	ADP	IN	_	19	agent	_	_
39	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	44	poss	_	_
40	two	two	NUM	CD	NumType=Card	44	nummod	_	_
41	composite	composite	ADJ	JJ	Degree=Pos	44	amod	_	_
42	2	2	NUM	CD	NumType=Card	44	nummod	_	_
43	-	-	PUNCT	HYPH	PunctType=Dash	44	punct	_	_
44	monads	monad	NOUN	NNS	Number=Plur	38	pobj	_	SpaceAfter=No
45	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
46	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
47	establish	establish	VERB	VB	VerbForm=Inf	7	conj	_	_
48	that	that	SCONJ	IN	_	52	mark	_	_
49	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	52	nsubj	_	_
50	all	all	DET	DT	_	51	det	_	_
51	laxly	laxly	ADJ	JJ	Degree=Pos	49	appos	_	_
52	distribute	distribute	VERB	VBP	Tense=Pres|VerbForm=Fin	47	ccomp	_	_
53	over	over	ADP	IN	_	52	prt	_	_
54	$ P $	$ p $	SYM	$	_	52	dep	_	_
55	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 2
# text = These four 2 - monads therefore admit lax extensions to the category $ Q $ - Dist of $ Q $ - categories and their distributors.
1	These	these	DET	DT	Number=Plur|PronType=Dem	5	det	_	_
2	four	four	NUM	CD	NumType=Card	5	nummod	_	_
3	2	2	NUM	CD	NumType=Card	5	nummod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	monads	monad	NOUN	NNS	Number=Plur	7	nsubj	_	_
6	therefore	therefore	ADV	RB	_	7	advmod	_	_
7	admit	admit	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	lax	lax	ADJ	JJ	Degree=Pos	9	amod	_	_
9	extensions	extension	NOUN	NNS	Number=Plur	7	dobj	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
13	$ Q $	$ q $	SYM	$	_	12	nmod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	Dist	dist	NOUN	NN	Number=Sing	12	appos	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	$ Q $	$ q $	SYM	$	_	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	22	poss	_	_
22	distributors	distributor	NOUN	NNS	Number=Plur	19	conj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = We characterize the corresponding $ (T, Q) $ - categories in each of the four cases, leading us to both known and novel categorical structures.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
4	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	amod	_	_
5	$ (T, Q) $	$ (t, q) $	SYM	$	_	7	compound	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	categories	category	NOUN	NNS	Number=Plur	2	dobj	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	each	each	PRON	DT	_	8	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	four	four	NUM	CD	NumType=Card	13	nummod	_	_
13	cases	case	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
15	leading	lead	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
16	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	15	dobj	_	_
17	to	to	ADP	IN	_	15	prep	_	_
18	both	both	PRON	DT	_	19	preconj	_	_
19	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	amod	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	novel	novel	ADJ	JJ	Degree=Pos	19	conj	_	_
22	categorical	categorical	ADJ	JJ	Degree=Pos	23	amod	_	_
23	structures	structure	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 630
# sent_id = 1
# text = We give several new ways of constructing spectral spaces starting with objects in abelian categories satisfying certain conditions which apply, in particular, to Grothendieck categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	several	several	ADJ	JJ	Degree=Pos	5	amod	_	_
4	new	new	ADJ	JJ	Degree=Pos	5	amod	_	_
5	ways	way	NOUN	NNS	Number=Plur	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	constructing	construct	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	pcomp	_	_
8	spectral	spectral	ADJ	JJ	Degree=Pos	9	amod	_	_
9	spaces	space	NOUN	NNS	Number=Plur	7	dobj	_	_
10	starting	start	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
11	with	with	ADP	IN	_	10	prep	_	_
12	objects	object	NOUN	NNS	Number=Plur	11	pobj	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	abelian	abelian	ADJ	JJ	Degree=Pos	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	_
16	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	acl	_	_
17	certain	certain	ADJ	JJ	Degree=Pos	18	amod	_	_
18	conditions	condition	NOUN	NNS	Number=Plur	16	dobj	_	_
19	which	which	PRON	WDT	_	20	nsubj	_	_
20	apply	apply	VERB	VBP	Tense=Pres|VerbForm=Fin	18	relcl	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	in	in	ADP	IN	_	20	prep	_	_
23	particular	particular	ADJ	JJ	Degree=Pos	22	amod	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
25	to	to	ADP	IN	_	20	prep	_	_
26	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	27	compound	_	_
27	categories	category	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = For this, we consider the spaces of invariants of closure operators acting on subobjects of a given object.
1	For	for	ADP	IN	_	5	prep	_	_
2	this	this	PRON	DT	Number=Sing|PronType=Dem	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	spaces	space	NOUN	NNS	Number=Plur	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	invariants	invariant	NOUN	NNS	Number=Plur	8	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	closure	closure	NOUN	NN	Number=Sing	12	compound	_	_
12	operators	operator	NOUN	NNS	Number=Plur	10	pobj	_	_
13	acting	act	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	acl	_	_
14	on	on	ADP	IN	_	13	prep	_	_
15	subobjects	subobject	NOUN	NNS	Number=Plur	14	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
19	object	object	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = The key to our results is a newly discovered criterion of Finocchiaro that uses ultrafilters to identify spectral spaces along with subbases of quasi - compact open sets.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	key	key	NOUN	NN	Number=Sing	6	nsubj	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	5	poss	_	_
5	results	result	NOUN	NNS	Number=Plur	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	newly	newly	ADV	RB	_	9	advmod	_	_
9	discovered	discover	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	criterion	criterion	NOUN	NN	Number=Sing	6	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	Finocchiaro	Finocchiaro	PROPN	NNP	Number=Sing	11	pobj	_	_
13	that	that	PRON	WDT	PronType=Rel	14	nsubj	_	_
14	uses	use	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	relcl	_	_
15	ultrafilters	ultrafilter	NOUN	NNS	Number=Plur	14	dobj	_	_
16	to	to	PART	TO	_	17	aux	_	_
17	identify	identify	VERB	VB	VerbForm=Inf	14	xcomp	_	_
18	spectral	spectral	ADJ	JJ	Degree=Pos	19	amod	_	_
19	spaces	space	NOUN	NNS	Number=Plur	17	dobj	_	_
20	along	along	ADP	IN	_	17	prep	_	_
21	with	with	ADP	IN	_	20	prep	_	_
22	subbases	subbase	NOUN	NNS	Number=Plur	21	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	quasi	quasi	ADJ	JJ	Degree=Pos	28	amod	_	_
25	-	-	ADJ	JJ	Degree=Pos	28	amod	_	_
26	compact	compact	ADJ	JJ	Degree=Pos	28	amod	_	_
27	open	open	ADJ	JJ	Degree=Pos	28	amod	_	_
28	sets	set	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 631
# sent_id = 1
# text = Finitary monads on a locally finitely presentable category $ A $ are well - known to possess a presentation by signatures and equations.
1	Finitary	finitary	NOUN	NN	Number=Sing	2	nsubj	_	_
2	monads	monad	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	nsubj	_	_
3	on	on	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
5	locally	locally	ADV	RB	_	6	advmod	_	_
6	finitely	finitely	ADV	RB	_	7	advmod	_	_
7	presentable	presentable	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	3	pobj	_	_
9	$ A $	$ a $	SYM	$	_	2	dobj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	well	well	ADV	RB	Degree=Pos	13	advmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acomp	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	possess	possess	VERB	VB	VerbForm=Inf	10	xcomp	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	presentation	presentation	NOUN	NN	Number=Sing	15	dobj	_	_
18	by	by	ADP	IN	_	17	prep	_	_
19	signatures	signature	NOUN	NNS	Number=Plur	18	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	equations	equation	NOUN	NNS	Number=Plur	19	conj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = Here we prove that, analogously, bases on $ A $ , that is, finitary functors from $ A $ to the category of finitary monads on $ A $ , possess a presentation by parametrized signatures and equations.
1	Here	here	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	8	mark	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
6	analogously	analogously	ADV	RB	_	8	advmod	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
8	bases	basis	NOUN	NNS	Number=Plur	3	ccomp	_	_
9	on	on	ADP	IN	_	8	prep	_	_
10	$ A $	$ a $	SYM	$	_	9	pobj	_	_
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	that	that	ADV	RB	_	13	advmod	_	_
13	is	is	ADV	RB	_	16	advmod	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
15	finitary	finitary	ADJ	JJ	Degree=Pos	16	amod	_	_
16	functors	functor	NOUN	NNS	Number=Plur	8	dobj	_	_
17	from	from	ADP	IN	_	16	prep	_	_
18	$ A $	$ a $	SYM	$	_	17	pobj	_	_
19	to	to	ADP	IN	_	17	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	category	category	NOUN	NN	Number=Sing	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	finitary	finitary	ADJ	JJ	Degree=Pos	24	amod	_	_
24	monads	monad	NOUN	NNS	Number=Plur	22	pobj	_	_
25	on	on	ADP	IN	_	24	prep	_	_
26	$ A $	$ a $	SYM	$	_	25	pobj	_	_
27	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
28	possess	possess	VERB	VB	VerbForm=Inf	3	ccomp	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
30	presentation	presentation	NOUN	NN	Number=Sing	28	dobj	_	_
31	by	by	ADP	IN	_	30	prep	_	_
32	parametrized	parametrized	ADJ	JJ	Degree=Pos	33	amod	_	_
33	signatures	signature	NOUN	NNS	Number=Plur	31	pobj	_	_
34	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
35	equations	equation	NOUN	NNS	Number=Plur	33	conj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 632
# sent_id = 1
# text = We explicitly show that symmetric Frobenius structures on a finite - dimensional, semi - simple algebra stand in bijection to homotopy fixed points of the trivial $ SO(2) $ - action on the bicategory of finite - dimensional, semi - simple algebras, bimodules and intertwiners.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	explicitly	explicitly	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	7	mark	_	_
5	symmetric	symmetric	ADJ	JJ	Degree=Pos	7	amod	_	_
6	Frobenius	Frobenius	PROPN	NNP	Number=Sing	7	compound	_	_
7	structures	structure	NOUN	NNS	Number=Plur	3	ccomp	_	_
8	on	on	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
10	finite	finite	ADJ	JJ	Degree=Pos	12	npadvmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	dimensional	dimensional	ADJ	JJ	Degree=Pos	17	amod	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
14	semi	semi	ADJ	JJ	Degree=Pos	17	amod	_	_
15	-	-	ADJ	JJ	Degree=Pos	16	punct	_	_
16	simple	simple	ADJ	JJ	Degree=Pos	17	amod	_	_
17	algebra	algebra	NOUN	NN	Number=Sing	18	compound	_	_
18	stand	stand	VERB	VBP	Tense=Pres|VerbForm=Fin	8	pobj	_	_
19	in	in	ADP	IN	_	18	prep	_	_
20	bijection	bijection	NOUN	NN	Number=Sing	19	pobj	_	_
21	to	to	PART	TO	_	22	aux	_	_
22	homotopy	homotopy	VERB	VB	VerbForm=Inf	18	advcl	_	_
23	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
24	points	point	NOUN	NNS	Number=Plur	22	dobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
27	trivial	trivial	ADJ	JJ	Degree=Pos	30	amod	_	_
28	$ SO(2) $	$ so(2) $	SYM	$	_	30	compound	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	action	action	NOUN	NN	Number=Sing	25	pobj	_	_
31	on	on	ADP	IN	_	30	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
33	bicategory	bicategory	NOUN	NN	Number=Sing	31	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	finite	finite	PROPN	NNP	Number=Sing	37	npadvmod	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	dimensional	dimensional	ADJ	JJ	Degree=Pos	42	amod	_	SpaceAfter=No
38	,	,	PUNCT	,	PunctType=Comm	42	punct	_	_
39	semi	semi	ADJ	JJ	Degree=Pos	42	amod	_	_
40	-	-	ADJ	JJ	Degree=Pos	41	punct	_	_
41	simple	simple	ADJ	JJ	Degree=Pos	42	amod	_	_
42	algebras	algebra	NOUN	NNS	Number=Plur	34	pobj	_	SpaceAfter=No
43	,	,	PUNCT	,	PunctType=Comm	42	punct	_	_
44	bimodules	bimodule	NOUN	NNS	Number=Plur	42	conj	_	_
45	and	and	CCONJ	CC	ConjType=Cmp	44	cc	_	_
46	intertwiners	intertwiner	NOUN	NNS	Number=Plur	44	conj	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = The results are motivated by the 2 - dimensional Cobordism Hypothesis for oriented manifolds, and can hence be interpreted in the realm of Topological Quantum Field Theory.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	results	result	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	by	by	ADP	IN	_	4	agent	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
7	2	2	NUM	CD	NumType=Card	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	dimensional	dimensional	ADJ	JJ	Degree=Pos	11	amod	_	_
10	Cobordism	Cobordism	PROPN	NNP	Number=Sing	11	compound	_	_
11	Hypothesis	Hypothesis	PROPN	NNP	Number=Sing	5	pobj	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	oriented	oriented	ADJ	JJ	Degree=Pos	14	amod	_	_
14	manifolds	manifold	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
17	can	can	AUX	MD	VerbForm=Fin	20	aux	_	_
18	hence	hence	ADV	RB	_	20	advmod	_	_
19	be	be	AUX	VB	VerbForm=Inf	20	auxpass	_	_
20	interpreted	interpret	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	conj	_	_
21	in	in	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	realm	realm	NOUN	NN	Number=Sing	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	Topological	Topological	PROPN	NNP	Number=Sing	27	compound	_	_
26	Quantum	Quantum	PROPN	NNP	Number=Sing	27	compound	_	_
27	Field	Field	PROPN	NNP	Number=Sing	28	compound	_	_
28	Theory	Theory	PROPN	NNP	Number=Sing	24	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 633
# sent_id = 1
# text = Databases have been studied category - theoretically for decades.
1	Databases	database	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
2	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	aux	_	_
3	been	be	AUX	VBN	Tense=Past|VerbForm=Part	4	auxpass	_	_
4	studied	study	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	category	category	NOUN	NN	Number=Sing	4	npadvmod	_	_
6	-	-	PUNCT	:	_	4	punct	_	_
7	theoretically	theoretically	ADV	RB	_	8	advmod	_	_
8	for	for	ADP	IN	_	4	prep	_	_
9	decades	decade	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = While mathematically elegant, previous categorical models have typically struggled withrepresenting concrete data such as integers or strings.
1	While	while	SCONJ	IN	_	10	mark	_	_
2	mathematically	mathematically	ADV	RB	_	3	advmod	_	_
3	elegant	elegant	ADJ	JJ	Degree=Pos	7	amod	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
5	previous	previous	ADJ	JJ	Degree=Pos	7	amod	_	_
6	categorical	categorical	ADJ	JJ	Degree=Pos	7	amod	_	_
7	models	model	NOUN	NNS	Number=Plur	10	nsubj	_	_
8	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	10	aux	_	_
9	typically	typically	ADV	RB	_	10	advmod	_	_
10	struggled	struggle	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	withrepresenting	withrepresente	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	xcomp	_	_
12	concrete	concrete	ADJ	JJ	Degree=Pos	13	amod	_	_
13	data	datum	NOUN	NNS	Number=Plur	11	dobj	_	_
14	such	such	ADJ	JJ	Degree=Pos	15	amod	_	_
15	as	as	ADP	IN	_	13	prep	_	_
16	integers	integer	NOUN	NNS	Number=Plur	15	pobj	_	_
17	or	or	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	strings	string	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 3
# text = In the present work, we propose an extension of the earlier set - valued functor model, making use of multi - sorted algebraic theories (also known as Lawvere theories) to incorporate concrete data in a principled way.
1	In	in	ADP	IN	_	7	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	present	present	ADJ	JJ	Degree=Pos	4	amod	_	_
4	work	work	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	propose	propose	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	extension	extension	NOUN	NN	Number=Sing	7	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
12	earlier	early	ADV	RBR	Degree=Cmp	17	amod	_	_
13	set	set	NOUN	NN	Number=Sing	15	npadvmod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
16	functor	functor	NOUN	NN	Number=Sing	17	compound	_	_
17	model	model	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
19	making	make	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	advcl	_	_
20	use	use	NOUN	NN	Number=Sing	19	dobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	multi	multi	ADJ	JJ	Degree=Pos	24	advmod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	sorted	sorted	ADJ	JJ	Degree=Pos	26	amod	_	_
25	algebraic	algebraic	ADJ	JJ	Degree=Pos	26	amod	_	_
26	theories	theory	NOUN	NNS	Number=Plur	21	pobj	_	_
27	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	26	punct	_	SpaceAfter=No
28	also	also	ADV	RB	_	29	advmod	_	_
29	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	acl	_	_
30	as	as	ADP	IN	_	29	prep	_	_
31	Lawvere	Lawvere	PROPN	NNP	Number=Sing	32	compound	_	_
32	theories	theory	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
33	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	26	punct	_	_
34	to	to	PART	TO	_	35	aux	_	_
35	incorporate	incorporate	VERB	VB	VerbForm=Inf	19	advcl	_	_
36	concrete	concrete	ADJ	JJ	Degree=Pos	37	amod	_	_
37	data	datum	NOUN	NNS	Number=Plur	35	dobj	_	_
38	in	in	ADP	IN	_	35	prep	_	_
39	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
40	principled	principled	ADJ	JJ	Degree=Pos	41	amod	_	_
41	way	way	NOUN	NN	Number=Sing	38	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = This approach easily handles missing information (null values), and also allows constraints and queries to make use of operations on data, such as multiplication or comparison of numbers, helping to bridge the gap between traditional databases and programming languages.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	approach	approach	NOUN	NN	Number=Sing	4	nsubj	_	_
3	easily	easily	ADV	RB	_	4	advmod	_	_
4	handles	handle	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	missing	miss	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	xcomp	_	_
6	information	information	NOUN	NN	Number=Sing	5	dobj	_	_
7	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	6	punct	_	SpaceAfter=No
8	null	null	ADJ	JJ	Degree=Pos	9	amod	_	_
9	values	value	NOUN	NNS	Number=Plur	6	appos	_	SpaceAfter=No
10	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	6	punct	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
13	also	also	ADV	RB	_	14	advmod	_	_
14	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	conj	_	_
15	constraints	constraint	NOUN	NNS	Number=Plur	19	nsubj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	queries	query	NOUN	NNS	Number=Plur	15	conj	_	_
18	to	to	PART	TO	_	19	aux	_	_
19	make	make	VERB	VB	VerbForm=Inf	14	ccomp	_	_
20	use	use	NOUN	NN	Number=Sing	19	dobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	operations	operation	NOUN	NNS	Number=Plur	21	pobj	_	_
23	on	on	ADP	IN	_	19	prep	_	_
24	data	datum	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	such	such	ADJ	JJ	Degree=Pos	27	amod	_	_
27	as	as	ADP	IN	_	24	prep	_	_
28	multiplication	multiplication	NOUN	NN	Number=Sing	27	pobj	_	_
29	or	or	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	comparison	comparison	NOUN	NN	Number=Sing	28	conj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	numbers	number	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
34	helping	help	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	advcl	_	_
35	to	to	PART	TO	_	36	aux	_	_
36	bridge	bridge	VERB	VB	VerbForm=Inf	34	xcomp	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	gap	gap	NOUN	NN	Number=Sing	36	dobj	_	_
39	between	between	ADP	IN	_	38	prep	_	_
40	traditional	traditional	ADJ	JJ	Degree=Pos	41	amod	_	_
41	databases	database	NOUN	NNS	Number=Plur	39	pobj	_	_
42	and	and	CCONJ	CC	ConjType=Cmp	41	cc	_	_
43	programming	programming	NOUN	NN	Number=Sing	44	compound	_	_
44	languages	language	NOUN	NNS	Number=Plur	41	conj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = We also show how all of the components of our model—including schemas, instances, change - of - schema functors, and queries fit into a single double categorical structure called a proarrow equipment (also known as framed bicategory).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	how	how	SCONJ	WRB	_	5	advmod	_	_
5	all	all	PRON	DT	_	3	ccomp	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	components	component	NOUN	NNS	Number=Plur	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	11	poss	_	_
11	model	model	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	—	—	PUNCT	:	_	11	punct	_	SpaceAfter=No
13	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	prep	_	_
14	schemas	schema	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	instances	instance	NOUN	NNS	Number=Plur	14	conj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	change	change	NOUN	NN	Number=Sing	23	nmod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
20	of	of	ADP	IN	_	18	prep	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
22	schema	schema	PROPN	NNP	Number=Sing	20	pobj	_	_
23	functors	functor	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
26	queries	query	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
27	fit	fit	ADJ	JJ	Degree=Pos	26	acomp	_	_
28	into	into	ADP	IN	_	27	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
30	single	single	ADJ	JJ	Degree=Pos	33	amod	_	_
31	double	double	ADJ	JJ	Degree=Pos	33	amod	_	_
32	categorical	categorical	ADJ	JJ	Degree=Pos	33	amod	_	_
33	structure	structure	NOUN	NN	Number=Sing	28	pobj	_	_
34	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	33	acl	_	_
35	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
36	proarrow	proarrow	NOUN	NN	Number=Sing	37	compound	_	_
37	equipment	equipment	NOUN	NN	Number=Sing	34	oprd	_	_
38	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	26	punct	_	SpaceAfter=No
39	also	also	ADV	RB	_	40	advmod	_	_
40	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	acl	_	_
41	as	as	ADP	IN	_	40	prep	_	_
42	framed	framed	ADJ	JJ	Degree=Pos	43	amod	_	_
43	bicategory	bicategory	NOUN	NN	Number=Sing	41	pobj	_	SpaceAfter=No
44	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	26	punct	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 634
# sent_id = 1
# text = The author and Tomer Schlank studied a much weaker homotopical structure than a model category, which we called a "weak cofibration category".
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	author	author	NOUN	NN	Number=Sing	6	nsubj	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	Tomer	Tomer	PROPN	NNP	Number=Sing	5	compound	_	_
5	Schlank	Schlank	PROPN	NNP	Number=Sing	2	conj	_	_
6	studied	study	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	much	much	ADV	RB	_	9	advmod	_	_
9	weaker	weak	ADJ	JJR	Degree=Cmp	11	amod	_	_
10	homotopical	homotopical	ADJ	JJ	Degree=Pos	11	amod	_	_
11	structure	structure	NOUN	NN	Number=Sing	6	dobj	_	_
12	than	than	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	model	model	NOUN	NN	Number=Sing	15	compound	_	_
15	category	category	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	which	which	PRON	WDT	_	19	dobj	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	15	relcl	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
21	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	24	punct	_	SpaceAfter=No
22	weak	weak	ADJ	JJ	Degree=Pos	24	amod	_	_
23	cofibration	cofibration	NOUN	NN	Number=Sing	24	compound	_	_
24	category	category	NOUN	NN	Number=Sing	19	oprd	_	SpaceAfter=No
25	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	6	punct	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = We showed that a small weak cofibration category induces in a natural way a model category structure on its ind - category, provided the ind - category satisfies a certain two out of three property.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	showed	show	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	9	mark	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
5	small	small	ADJ	JJ	Degree=Pos	8	amod	_	_
6	weak	weak	ADJ	JJ	Degree=Pos	8	amod	_	_
7	cofibration	cofibration	NOUN	NN	Number=Sing	8	compound	_	_
8	category	category	NOUN	NN	Number=Sing	9	nsubj	_	_
9	induces	induce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	natural	natural	ADJ	JJ	Degree=Pos	13	amod	_	_
13	way	way	NOUN	NN	Number=Sing	10	pobj	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	model	model	NOUN	NN	Number=Sing	17	compound	_	_
16	category	category	NOUN	NN	Number=Sing	17	compound	_	_
17	structure	structure	NOUN	NN	Number=Sing	9	dobj	_	_
18	on	on	ADP	IN	_	17	prep	_	_
19	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	22	poss	_	_
20	ind	ind	ADJ	JJ	Degree=Pos	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	category	category	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
24	provided	provide	VERB	VBD	Tense=Past|VerbForm=Fin	2	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
26	ind	ind	ADJ	JJ	Degree=Pos	28	compound	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	category	category	NOUN	NN	Number=Sing	29	compound	_	_
29	satisfies	satisfie	NOUN	NNS	Number=Plur	24	dative	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
31	certain	certain	ADJ	JJ	Degree=Pos	32	amod	_	_
32	two	two	NUM	CD	NumType=Card	36	nummod	_	_
33	out	out	ADP	IN	_	35	quantmod	_	_
34	of	of	ADP	IN	_	35	quantmod	_	_
35	three	three	NUM	CD	NumType=Card	36	nummod	_	_
36	property	property	NOUN	NN	Number=Sing	29	dobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = The main purpose of this paper is to give sufficient intrinsic conditions on a weak cofibration category for this two out of three property to hold.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	purpose	purpose	NOUN	NN	Number=Sing	7	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	paper	paper	NOUN	NN	Number=Sing	4	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	give	give	VERB	VB	VerbForm=Inf	7	xcomp	_	_
10	sufficient	sufficient	ADJ	JJ	Degree=Pos	12	amod	_	_
11	intrinsic	intrinsic	ADJ	JJ	Degree=Pos	12	amod	_	_
12	conditions	condition	NOUN	NNS	Number=Plur	9	dobj	_	_
13	on	on	ADP	IN	_	9	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	weak	weak	ADJ	JJ	Degree=Pos	17	amod	_	_
16	cofibration	cofibration	NOUN	NN	Number=Sing	17	compound	_	_
17	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
18	for	for	ADP	IN	_	17	prep	_	_
19	this	this	DET	DT	Number=Sing|PronType=Dem	24	det	_	_
20	two	two	NUM	CD	NumType=Card	24	nummod	_	_
21	out	out	ADP	IN	_	23	quantmod	_	_
22	of	of	ADP	IN	_	23	quantmod	_	_
23	three	three	NUM	CD	NumType=Card	24	nummod	_	_
24	property	property	NOUN	NN	Number=Sing	18	pobj	_	_
25	to	to	PART	TO	_	26	aux	_	_
26	hold	hold	VERB	VB	VerbForm=Inf	24	relcl	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = We consider an application to the category of compact metrizable spaces, and thus obtain a model structure on its ind - category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	application	application	NOUN	NN	Number=Sing	2	dobj	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	compact	compact	ADJ	JJ	Degree=Pos	11	amod	_	_
10	metrizable	metrizable	ADJ	JJ	Degree=Pos	11	amod	_	_
11	spaces	space	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
14	thus	thus	ADV	RB	_	15	advmod	_	_
15	obtain	obtain	VERB	VB	VerbForm=Inf	2	conj	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	model	model	NOUN	NN	Number=Sing	18	compound	_	_
18	structure	structure	NOUN	NN	Number=Sing	15	dobj	_	_
19	on	on	ADP	IN	_	15	prep	_	_
20	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	23	poss	_	_
21	ind	ind	NOUN	NN	Number=Sing	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	category	category	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = This model structure is defined on a category that is closely related to a category of topological spaces and has many convenient formal properties.
1	This	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
2	model	model	NOUN	NN	Number=Sing	3	compound	_	_
3	structure	structure	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	on	on	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
9	that	that	PRON	WDT	PronType=Rel	12	nsubjpass	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
11	closely	closely	ADV	RB	_	12	advmod	_	_
12	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	relcl	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	topological	topological	ADJ	JJ	Degree=Pos	18	amod	_	_
18	spaces	space	NOUN	NNS	Number=Plur	16	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
20	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	conj	_	_
21	many	many	ADJ	JJ	Degree=Pos	24	amod	_	_
22	convenient	convenient	ADJ	JJ	Degree=Pos	24	amod	_	_
23	formal	formal	ADJ	JJ	Degree=Pos	24	amod	_	_
24	properties	property	NOUN	NNS	Number=Plur	20	dobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 6
# text = A more general application of these results, to the (opposite) category of separable $ C^* $ - algebras, appears in a paper by the author, Michael Joachim and Snigdhayan Mahanta.
1	A	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
2	more	more	ADV	RBR	Degree=Cmp	3	advmod	_	_
3	general	general	ADJ	JJ	Degree=Pos	4	amod	_	_
4	application	application	NOUN	NN	Number=Sing	21	nsubj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	these	these	DET	DT	Number=Plur|PronType=Dem	7	det	_	_
7	results	result	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
9	to	to	ADP	IN	_	4	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
11	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
12	opposite	opposite	ADJ	JJ	Degree=Pos	14	amod	_	SpaceAfter=No
13	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	14	punct	_	_
14	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	separable	separable	ADJ	JJ	Degree=Pos	19	amod	_	_
17	$ C^* $	$ c^* $	SYM	$	_	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	algebras	algebra	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
21	appears	appear	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
22	in	in	ADP	IN	_	21	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	paper	paper	NOUN	NN	Number=Sing	22	pobj	_	_
25	by	by	ADP	IN	_	21	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	author	author	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
29	Michael	Michael	PROPN	NNP	Number=Sing	30	compound	_	_
30	Joachim	Joachim	PROPN	NNP	Number=Sing	4	appos	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
32	Snigdhayan	Snigdhayan	PROPN	NNP	Number=Sing	33	compound	_	_
33	Mahanta	Mahanta	PROPN	NNP	Number=Sing	30	conj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# doc_id = 635
# sent_id = 1
# text = We will construct a Quillen model structure out of the multiplier ideal sheaves on a smooth quasi - projective variety using earlier works of Isaksen and Barnea and Schlank.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	will	will	AUX	MD	VerbForm=Fin	3	aux	_	_
3	construct	construct	VERB	VB	VerbForm=Inf	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	Quillen	quillen	ADJ	JJ	Degree=Pos	7	amod	_	_
6	model	model	NOUN	NN	Number=Sing	7	compound	_	_
7	structure	structure	NOUN	NN	Number=Sing	3	dobj	_	_
8	out	out	ADP	IN	_	3	prep	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
11	multiplier	multipli	ADJ	JJR	Degree=Cmp	13	amod	_	_
12	ideal	ideal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	sheaves	sheaf	NOUN	NNS	Number=Plur	9	pobj	_	_
14	on	on	ADP	IN	_	3	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
16	smooth	smooth	ADJ	JJ	Degree=Pos	20	amod	_	_
17	quasi	quasi	ADJ	JJ	Degree=Pos	20	amod	_	_
18	-	-	ADJ	JJ	Degree=Pos	20	amod	_	_
19	projective	projective	ADJ	JJ	Degree=Pos	20	amod	_	_
20	variety	variety	NOUN	NN	Number=Sing	14	pobj	_	_
21	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	acl	_	_
22	earlier	early	ADJ	JJR	Degree=Cmp	23	amod	_	_
23	works	work	NOUN	NNS	Number=Plur	21	dobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	Isaksen	Isaksen	PROPN	NNP	Number=Sing	24	pobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	Barnea	Barnea	PROPN	NNP	Number=Sing	25	conj	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
29	Schlank	Schlank	PROPN	NNP	Number=Sing	27	conj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = We also show that fibrant objects of this model category are made of kawamata log terminal pairs in birational geometry.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	12	mark	_	_
5	fibrant	fibrant	ADJ	JJ	Degree=Pos	6	amod	_	_
6	objects	object	NOUN	NNS	Number=Plur	12	nsubjpass	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	this	this	DET	DT	Number=Sing|PronType=Dem	10	det	_	_
9	model	model	NOUN	NN	Number=Sing	10	compound	_	_
10	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	made	make	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	ccomp	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	kawamata	kawamata	PROPN	NNP	Number=Sing	15	compound	_	_
15	log	log	NOUN	NN	Number=Sing	17	nmod	_	_
16	terminal	terminal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	pairs	pair	NOUN	NNS	Number=Plur	13	pobj	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	birational	birational	ADJ	JJ	Degree=Pos	20	amod	_	_
20	geometry	geometry	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 636
# sent_id = 1
# text = Picard - Vessiot rings are present in many settings like differential Galois theory, difference Galois theory and Galois theory of Artinian simple module algebras.
1	Picard	Picard	PROPN	NNP	Number=Sing	3	compound	_	_
2	-	-	PUNCT	HYPH	PunctType=Dash	3	punct	_	_
3	Vessiot	Vessiot	PROPN	NNP	Number=Sing	4	compound	_	_
4	rings	ring	NOUN	NNS	Number=Plur	5	nsubj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	present	present	ADJ	JJ	Degree=Pos	5	acomp	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	many	many	ADJ	JJ	Degree=Pos	9	amod	_	_
9	settings	setting	NOUN	NNS	Number=Plur	7	pobj	_	_
10	like	like	ADP	IN	_	9	prep	_	_
11	differential	differential	ADJ	JJ	Degree=Pos	13	amod	_	_
12	Galois	Galois	PROPN	NNP	Number=Sing	13	compound	_	_
13	theory	theory	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
15	difference	difference	NOUN	NN	Number=Sing	17	compound	_	_
16	Galois	Galois	PROPN	NNP	Number=Sing	17	compound	_	_
17	theory	theory	NOUN	NN	Number=Sing	5	dep	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	Galois	Galois	PROPN	NNP	Number=Sing	20	compound	_	_
20	theory	theory	NOUN	NN	Number=Sing	17	conj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	Artinian	artinian	ADJ	JJ	Degree=Pos	25	amod	_	_
23	simple	simple	ADJ	JJ	Degree=Pos	25	amod	_	_
24	module	module	NOUN	NN	Number=Sing	25	compound	_	_
25	algebras	algebra	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this article we set up an abstract framework in which we can prove theorems on existence and uniqueness of Picard - Vessiot rings, as well as on Galois groups corresponding to the Picard - Vessiot rings.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	article	article	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	set	set	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	up	up	ADP	RP	_	5	prt	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	abstract	abstract	ADJ	JJ	Degree=Pos	9	amod	_	_
9	framework	framework	NOUN	NN	Number=Sing	5	dobj	_	_
10	in	in	ADP	IN	_	14	prep	_	_
11	which	which	PRON	WDT	_	10	pobj	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
13	can	can	AUX	MD	VerbForm=Fin	14	aux	_	_
14	prove	prove	VERB	VB	VerbForm=Inf	9	relcl	_	_
15	theorems	theorem	NOUN	NNS	Number=Plur	14	dobj	_	_
16	on	on	ADP	IN	_	14	prep	_	_
17	existence	existence	NOUN	NN	Number=Sing	16	pobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	uniqueness	uniqueness	NOUN	NN	Number=Sing	17	conj	_	_
20	of	of	ADP	IN	_	17	prep	_	_
21	Picard	Picard	PROPN	NNP	Number=Sing	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	Vessiot	Vessiot	PROPN	NNP	Number=Sing	24	compound	_	_
24	rings	ring	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
26	as	as	ADV	RB	_	28	advmod	_	_
27	well	well	ADV	RB	Degree=Pos	28	advmod	_	_
28	as	as	ADP	IN	_	14	cc	_	_
29	on	on	ADP	IN	_	28	prep	_	_
30	Galois	Galois	PROPN	NNP	Number=Sing	31	compound	_	_
31	groups	group	NOUN	NNS	Number=Plur	29	pobj	_	_
32	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	31	acl	_	_
33	to	to	ADP	IN	_	32	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
35	Picard	Picard	PROPN	NNP	Number=Sing	37	compound	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	Vessiot	Vessiot	PROPN	NNP	Number=Sing	38	compound	_	_
38	rings	ring	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = As the present approach restricts to the categorical properties which all the categories of differential modules (respectively, difference modules, et cetera) share, it gives unified proofs for all these Galois theories (and maybe more general ones).
1	As	as	SCONJ	IN	_	5	mark	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
3	present	present	ADJ	JJ	Degree=Pos	5	amod	_	_
4	approach	approach	NOUN	NN	Number=Sing	5	compound	_	_
5	restricts	restrict	NOUN	NNS	Number=Plur	29	advcl	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	categorical	categorical	ADJ	JJ	Degree=Pos	9	amod	_	_
9	properties	property	NOUN	NNS	Number=Plur	6	pobj	_	_
10	which	which	PRON	WDT	_	26	dobj	_	_
11	all	all	DET	PDT	_	13	predet	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	categories	category	NOUN	NNS	Number=Plur	26	nmod	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	differential	differential	ADJ	JJ	Degree=Pos	16	amod	_	_
16	modules	module	NOUN	NNS	Number=Plur	14	pobj	_	_
17	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	16	punct	_	SpaceAfter=No
18	respectively	respectively	ADV	RB	_	21	advmod	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
20	difference	difference	NOUN	NN	Number=Sing	21	compound	_	_
21	modules	module	NOUN	NNS	Number=Plur	13	conj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	et	et	NOUN	NN	Number=Sing	24	nmod	_	_
24	cetera	cetera	PROPN	NNP	Number=Sing	26	nmod	_	SpaceAfter=No
25	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	26	punct	_	_
26	share	share	NOUN	NN	Number=Sing	9	relcl	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
28	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	29	nsubj	_	_
29	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
30	unified	unified	ADJ	JJ	Degree=Pos	31	amod	_	_
31	proofs	proof	NOUN	NNS	Number=Plur	29	dobj	_	_
32	for	for	ADP	IN	_	31	prep	_	_
33	all	all	DET	PDT	_	36	predet	_	_
34	these	these	DET	DT	Number=Plur|PronType=Dem	36	det	_	_
35	Galois	Galois	PROPN	NNP	Number=Sing	36	compound	_	_
36	theories	theory	NOUN	NNS	Number=Plur	32	pobj	_	_
37	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	36	punct	_	SpaceAfter=No
38	and	and	CCONJ	CC	ConjType=Cmp	36	cc	_	_
39	maybe	maybe	ADV	RB	_	40	advmod	_	_
40	more	more	ADV	RBR	Degree=Cmp	42	amod	_	_
41	general	general	ADJ	JJ	Degree=Pos	42	amod	_	_
42	ones	one	NOUN	NNS	Number=Plur	36	conj	_	SpaceAfter=No
43	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	36	punct	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	29	punct	_	SpaceAfter=No

# doc_id = 637
# sent_id = 1
# text = On a category $ mathscr{C} $ with a designated (well - behaved) class $ mathcal{M} $ of monomorphisms, a closure operator in the sense of Dikranjan and Giuli is a pointed endofunctor of $ mathcal{M} $ , seen as a full subcategory of the arrow - category $ mathscr{C}^mathbf{2} $ whose objects are morphisms from the class $ mathcal{M} $ , which ``commutes'' with the codomain functor $ mathsf{cod}colon mathcal{M}to mathscr{C} $ .
1	On	on	ADP	IN	_	28	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	category	category	NOUN	NN	Number=Sing	1	pobj	_	_
4	$ mathscr{C} $	$ mathscr{c} $	SYM	$	_	1	pobj	_	_
5	with	with	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
7	designated	designate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
8	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	13	punct	_	SpaceAfter=No
9	well	well	ADV	RB	Degree=Pos	11	advmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	behaved	behave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	SpaceAfter=No
12	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	13	punct	_	_
13	class	class	NOUN	NN	Number=Sing	14	compound	_	_
14	$ mathcal{M} $	$ mathcal{m} $	SYM	$	_	5	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	closure	closure	NOUN	NN	Number=Sing	20	compound	_	_
20	operator	operator	NOUN	NN	Number=Sing	28	nsubj	_	_
21	in	in	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	sense	sense	NOUN	NN	Number=Sing	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	Dikranjan	Dikranjan	PROPN	NNP	Number=Sing	24	pobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	Giuli	Giuli	PROPN	NNP	Number=Sing	25	conj	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	pointed	pointed	ADJ	JJ	Degree=Pos	31	amod	_	_
31	endofunctor	endofunctor	NOUN	NN	Number=Sing	28	attr	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	$ mathcal{M} $	$ mathcal{m} $	SYM	$	_	32	pobj	_	_
34	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
35	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	acl	_	_
36	as	as	ADP	IN	_	35	prep	_	_
37	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
38	full	full	ADJ	JJ	Degree=Pos	39	amod	_	_
39	subcategory	subcategory	NOUN	NN	Number=Sing	36	pobj	_	_
40	of	of	ADP	IN	_	39	prep	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	45	det	_	_
42	arrow	arrow	NOUN	NN	Number=Sing	44	compound	_	_
43	-	-	PUNCT	HYPH	PunctType=Dash	44	punct	_	_
44	category	category	NOUN	NN	Number=Sing	45	compound	_	_
45	$ mathscr{C}^mathbf{2} $	$ mathscr{c}^mathbf{2} $	SYM	$	_	40	pobj	_	_
46	whose	whose	DET	WP$	Poss=Yes	47	poss	_	_
47	objects	object	NOUN	NNS	Number=Plur	48	nsubj	_	_
48	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	45	relcl	_	_
49	morphisms	morphism	NOUN	NNS	Number=Plur	48	attr	_	_
50	from	from	ADP	IN	_	49	prep	_	_
51	the	the	DET	DT	Definite=Def|PronType=Art	52	det	_	_
52	class	class	NOUN	NN	Number=Sing	53	nmod	_	_
53	$ mathcal{M} $	$ mathcal{m} $	SYM	$	_	50	pobj	_	_
54	,	,	PUNCT	,	PunctType=Comm	53	punct	_	_
55	which	which	DET	WDT	_	58	det	_	_
56	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	58	punct	_	SpaceAfter=No
57	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	58	punct	_	SpaceAfter=No
58	commutes	commute	NOUN	NNS	Number=Plur	31	relcl	_	SpaceAfter=No
59	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	58	punct	_	_
60	with	with	ADP	IN	_	58	prep	_	_
61	the	the	DET	DT	Definite=Def|PronType=Art	63	det	_	_
62	codomain	codomain	ADJ	JJ	Degree=Pos	63	amod	_	_
63	functor	functor	NOUN	NN	Number=Sing	60	pobj	_	_
64	$ mathsf{cod}colon mathcal{M}to mathscr{C} $	$ mathsf{cod}colon mathcal{m}to mathscr{c} $	SYM	$	_	63	appos	_	_
65	.	.	PUNCT	.	PunctType=Peri	28	punct	_	SpaceAfter=No

# sent_id = 2
# text = In other words, a closure operator consists of a functor $ Ccolon mathcal{M}tomathcal{M} $ and a natural transformation $ ccolon 1_mathcal{M}to C $ such that $ mathsf{cod} cdot C=C $ and $ mathsf{cod}cdot c=1_mathsf{cod} $ .
1	In	in	ADP	IN	_	8	prep	_	_
2	other	other	ADJ	JJ	Degree=Pos	3	amod	_	_
3	words	word	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	closure	closure	NOUN	NN	Number=Sing	7	compound	_	_
7	operator	operator	NOUN	NN	Number=Sing	8	nsubj	_	_
8	consists	consist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	functor	functor	NOUN	NN	Number=Sing	12	compound	_	_
12	$ Ccolon mathcal{M}tomathcal{M} $	$ ccolon mathcal{m}tomathcal{m} $	SYM	$	_	9	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	natural	natural	ADJ	JJ	Degree=Pos	16	amod	_	_
16	transformation	transformation	NOUN	NN	Number=Sing	12	conj	_	_
17	$ ccolon 1_mathcal{M}to C $	$ ccolon 1_mathcal{m}to c $	SYM	$	_	18	nmod	_	_
18	such	such	ADJ	JJ	Degree=Pos	22	dobj	_	_
19	that	that	SCONJ	IN	_	22	det	_	_
20	$ mathsf{cod} cdot C=C $	$ mathsf{cod} cdot c=c $	SYM	$	_	22	nmod	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	$ mathsf{cod}cdot c=1_mathsf{cod} $	$ mathsf{cod}cdot c=1_mathsf{cod} $	SYM	$	_	7	appos	_	_
23	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this paper we adapt this notion to the domain functor $ mathsf{dom}colon mathcal{E}tomathscr{C} $ , where $ mathcal{E} $ is a class of epimorphisms in $ mathscr{C} $ , and show that such closure operators can be used to classify $ mathcal{E} $ - epireflective subcategories of $ mathscr{C} $ , provided $ mathcal{E} $ is closed under composition and contains isomorphisms.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	adapt	adapt	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
7	notion	notion	NOUN	NN	Number=Sing	5	dobj	_	_
8	to	to	ADP	IN	_	5	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	domain	domain	NOUN	NN	Number=Sing	11	compound	_	_
11	functor	functor	NOUN	NN	Number=Sing	8	pobj	_	_
12	$ mathsf{dom}colon mathcal{E}tomathscr{C} $	$ mathsf{dom}colon mathcal{e}tomathscr{c} $	SYM	$	_	11	appos	_	_
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	where	where	SCONJ	WRB	_	16	advmod	_	_
15	$ mathcal{E} $	$ mathcal{e} $	SYM	$	_	16	nsubj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	relcl	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	class	class	NOUN	NN	Number=Sing	16	attr	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	19	pobj	_	_
21	in	in	ADP	IN	_	18	prep	_	_
22	$ mathscr{C} $	$ mathscr{c} $	SYM	$	_	21	pobj	_	_
23	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
25	show	show	VERB	VB	VerbForm=Inf	5	conj	_	_
26	that	that	SCONJ	IN	_	32	mark	_	_
27	such	such	ADJ	JJ	Degree=Pos	28	amod	_	_
28	closure	closure	NOUN	NN	Number=Sing	29	compound	_	_
29	operators	operator	NOUN	NNS	Number=Plur	32	nsubjpass	_	_
30	can	can	AUX	MD	VerbForm=Fin	32	aux	_	_
31	be	be	AUX	VB	VerbForm=Inf	32	auxpass	_	_
32	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	ccomp	_	_
33	to	to	PART	TO	_	34	aux	_	_
34	classify	classify	VERB	VB	VerbForm=Inf	32	xcomp	_	_
35	$ mathcal{E} $	$ mathcal{e} $	SYM	$	_	37	quantmod	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	epireflective	epireflective	ADJ	JJ	Degree=Pos	38	amod	_	_
38	subcategories	subcategorie	NOUN	NNS	Number=Plur	34	dobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	$ mathscr{C} $	$ mathscr{c} $	SYM	$	_	39	pobj	_	_
41	,	,	PUNCT	,	PunctType=Comm	34	punct	_	_
42	provided	provide	VERB	VBD	Tense=Past|VerbForm=Fin	25	conj	_	_
43	$ mathcal{E} $	$ mathcal{e} $	SYM	$	_	42	dobj	_	_
44	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	45	auxpass	_	_
45	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	ccomp	_	_
46	under	under	ADP	IN	_	45	prep	_	_
47	composition	composition	NOUN	NN	Number=Sing	46	pobj	_	_
48	and	and	CCONJ	CC	ConjType=Cmp	45	cc	_	_
49	contains	contain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	45	conj	_	_
50	isomorphisms	isomorphism	NOUN	NNS	Number=Plur	49	dobj	_	SpaceAfter=No
51	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 638
# sent_id = 1
# text = Guided by the microcosm principle of Baez - Dolan and by the algebraic definitions of operads of Kelly and Fiore, we introduce two ``monoid - like'' definitions of cyclic operads, one for the original, ``exchangable - output'' characterisation of Getzler - Kapranov, and the other for the alternative ``entries - only'' characterisation, both within the category of Joyal's species of structures.
1	Guided	guide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	advcl	_	_
2	by	by	ADP	IN	_	1	agent	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	microcosm	microcosm	PROPN	NNP	Number=Sing	5	amod	_	_
5	principle	principle	NOUN	NN	Number=Sing	2	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Baez	Baez	PROPN	NNP	Number=Sing	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	Dolan	Dolan	PROPN	NNP	Number=Sing	6	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
11	by	by	ADP	IN	_	2	conj	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	algebraic	algebraic	ADJ	JJ	Degree=Pos	14	amod	_	_
14	definitions	definition	NOUN	NNS	Number=Plur	11	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	operads	operad	NOUN	NNS	Number=Plur	15	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	Kelly	Kelly	PROPN	NNP	Number=Sing	17	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	Fiore	Fiore	PROPN	NNP	Number=Sing	18	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
22	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	23	nsubj	_	_
23	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
24	two	two	NUM	CD	NumType=Card	31	nummod	_	_
25	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	31	punct	_	SpaceAfter=No
26	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	31	punct	_	SpaceAfter=No
27	monoid	monoid	NOUN	NN	Number=Sing	29	npadvmod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	like	like	ADJ	JJ	Degree=Pos	31	amod	_	SpaceAfter=No
30	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	31	punct	_	_
31	definitions	definition	NOUN	NNS	Number=Plur	23	dobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	cyclic	cyclic	ADJ	JJ	Degree=Pos	34	amod	_	_
34	operads	operad	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
35	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
36	one	one	NUM	CD	NumType=Card	31	appos	_	_
37	for	for	ADP	IN	_	36	prep	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	47	det	_	_
39	original	original	ADJ	JJ	Degree=Pos	47	amod	_	SpaceAfter=No
40	,	,	PUNCT	,	PunctType=Comm	47	punct	_	_
41	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	47	punct	_	SpaceAfter=No
42	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	47	punct	_	SpaceAfter=No
43	exchangable	exchangable	ADJ	JJ	Degree=Pos	45	amod	_	_
44	-	-	PUNCT	HYPH	PunctType=Dash	45	punct	_	_
45	output	output	NOUN	NN	Number=Sing	47	nmod	_	SpaceAfter=No
46	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	47	punct	_	_
47	characterisation	characterisation	NOUN	NN	Number=Sing	37	pobj	_	_
48	of	of	ADP	IN	_	47	prep	_	_
49	Getzler	Getzler	PROPN	NNP	Number=Sing	51	compound	_	_
50	-	-	PUNCT	HYPH	PunctType=Dash	51	punct	_	_
51	Kapranov	Kapranov	PROPN	NNP	Number=Sing	48	pobj	_	SpaceAfter=No
52	,	,	PUNCT	,	PunctType=Comm	51	punct	_	_
53	and	and	CCONJ	CC	ConjType=Cmp	36	cc	_	_
54	the	the	DET	DT	Definite=Def|PronType=Art	55	det	_	_
55	other	other	ADJ	JJ	Degree=Pos	36	conj	_	_
56	for	for	ADP	IN	_	55	prep	_	_
57	the	the	DET	DT	Definite=Def|PronType=Art	65	det	_	_
58	alternative	alternative	ADJ	JJ	Degree=Pos	65	amod	_	_
59	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	61	punct	_	SpaceAfter=No
60	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	61	punct	_	SpaceAfter=No
61	entries	entry	NOUN	NNS	Number=Plur	65	nmod	_	_
62	-	-	PUNCT	:	_	61	punct	_	_
63	only	only	ADV	RB	_	61	advmod	_	SpaceAfter=No
64	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	65	punct	_	_
65	characterisation	characterisation	NOUN	NN	Number=Sing	56	pobj	_	SpaceAfter=No
66	,	,	PUNCT	,	PunctType=Comm	55	punct	_	_
67	both	both	PRON	DT	_	68	preconj	_	_
68	within	within	ADP	IN	_	55	prep	_	_
69	the	the	DET	DT	Definite=Def|PronType=Art	70	det	_	_
70	category	category	NOUN	NN	Number=Sing	68	pobj	_	_
71	of	of	ADP	IN	_	70	prep	_	_
72	Joyal	Joyal	PROPN	NNP	Number=Sing	74	poss	_	SpaceAfter=No
73	's	's	PART	POS	_	72	case	_	_
74	species	specie	NOUN	NNS	Number=Plur	71	pobj	_	_
75	of	of	ADP	IN	_	74	prep	_	_
76	structures	structure	NOUN	NNS	Number=Plur	75	pobj	_	SpaceAfter=No
77	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# sent_id = 2
# text = Relying on a result of Lamarche on descent for species, we use these "monoid - like" definitions to prove the equivalence between the ``exchangable - output'' and ``entries - only'' points of view on cyclic operads.
1	Relying	rely	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	advcl	_	_
2	on	on	ADP	IN	_	1	prep	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	result	result	NOUN	NN	Number=Sing	2	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	Lamarche	Lamarche	PROPN	NNP	Number=Sing	5	pobj	_	_
7	on	on	ADP	IN	_	1	prep	_	_
8	descent	descent	NOUN	NN	Number=Sing	7	pobj	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	species	specie	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	these	these	DET	DT	Number=Plur|PronType=Dem	20	det	_	_
15	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	20	punct	_	SpaceAfter=No
16	monoid	monoid	NOUN	NN	Number=Sing	18	npadvmod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	like	like	ADJ	JJ	Degree=Pos	20	amod	_	SpaceAfter=No
19	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	20	punct	_	_
20	definitions	definition	NOUN	NNS	Number=Plur	13	dobj	_	_
21	to	to	PART	TO	_	22	aux	_	_
22	prove	prove	VERB	VB	VerbForm=Inf	13	xcomp	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	equivalence	equivalence	NOUN	NN	Number=Sing	22	dobj	_	_
25	between	between	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
27	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	31	punct	_	SpaceAfter=No
28	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	31	punct	_	SpaceAfter=No
29	exchangable	exchangable	ADJ	JJ	Degree=Pos	31	amod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	output	output	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
32	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	31	punct	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
34	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	36	punct	_	SpaceAfter=No
35	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	36	punct	_	SpaceAfter=No
36	entries	entry	NOUN	NNS	Number=Plur	40	nmod	_	_
37	-	-	PUNCT	:	_	36	punct	_	_
38	only	only	ADV	RB	_	36	advmod	_	SpaceAfter=No
39	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	40	punct	_	_
40	points	point	NOUN	NNS	Number=Plur	31	conj	_	_
41	of	of	ADP	IN	_	40	prep	_	_
42	view	view	NOUN	NN	Number=Sing	41	pobj	_	_
43	on	on	ADP	IN	_	42	prep	_	_
44	cyclic	cyclic	ADJ	JJ	Degree=Pos	45	amod	_	_
45	operads	operad	NOUN	NNS	Number=Plur	43	pobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# doc_id = 639
# sent_id = 1
# text = At the heart of differential geometry is the construction of the tangent bundle of a manifold.
1	At	at	ADP	IN	_	7	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	heart	heart	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	differential	differential	ADJ	JJ	Degree=Pos	6	amod	_	_
6	geometry	geometry	NOUN	NN	Number=Sing	4	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	construction	construction	NOUN	NN	Number=Sing	7	nsubj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	tangent	tangent	ADJ	JJ	Degree=Pos	13	compound	_	_
13	bundle	bundle	NOUN	NN	Number=Sing	10	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	manifold	manifold	ADJ	JJ	Degree=Pos	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 2
# text = There are various abstractions of this construction, and of particular interest here is that of Tangent Structures.
1	There	there	PRON	EX	_	2	expl	_	_
2	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	various	various	ADJ	JJ	Degree=Pos	4	amod	_	_
4	abstractions	abstraction	NOUN	NNS	Number=Plur	2	attr	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
7	construction	construction	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
10	of	of	ADP	IN	_	4	prep	_	_
11	particular	particular	ADJ	JJ	Degree=Pos	12	amod	_	_
12	interest	interest	NOUN	NN	Number=Sing	10	pobj	_	_
13	here	here	ADV	RB	PronType=Dem	12	advmod	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
15	that	that	PRON	DT	Number=Sing|PronType=Dem	14	nsubj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	Tangent	Tangent	PROPN	NNP	Number=Sing	18	compound	_	_
18	Structures	Structures	PROPN	NNPS	Number=Plur	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Tangent Structure is defined via giving an underlying category $ M $ and a tangent functor $ T $ along with a list of natural transformations satisfying a set of axioms, then detailing the behaviour of $ T $ in the category $ End(M) $ .
1	Tangent	Tangent	PROPN	NNP	Number=Sing	2	compound	_	_
2	Structure	Structure	PROPN	NNP	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	via	via	ADP	IN	_	4	prep	_	_
6	giving	give	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	underlying	underlying	ADJ	JJ	Degree=Pos	9	amod	_	_
9	category	category	NOUN	NN	Number=Sing	6	dobj	_	_
10	$ M $	$ m $	SYM	$	_	9	nummod	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	tangent	tangent	NOUN	NN	Number=Sing	14	compound	_	_
14	functor	functor	NOUN	NN	Number=Sing	6	dobj	_	_
15	$ T $	$ t $	SYM	$	_	14	dobj	_	_
16	along	along	ADP	IN	_	6	prep	_	_
17	with	with	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	list	list	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	natural	natural	ADJ	JJ	Degree=Pos	22	amod	_	_
22	transformations	transformation	NOUN	NNS	Number=Plur	20	pobj	_	_
23	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	advcl	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
25	set	set	NOUN	NN	Number=Sing	23	dobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	axioms	axiom	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
29	then	then	ADV	RB	PronType=Dem	30	advmod	_	_
30	detailing	detail	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	advcl	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	behaviour	behaviour	NOUN	NN	Number=Sing	30	dobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	$ T $	$ t $	SYM	$	_	33	pobj	_	_
35	in	in	ADP	IN	_	32	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	category	category	NOUN	NN	Number=Sing	35	pobj	_	_
38	$ End(M) $	$ end(m) $	SYM	$	_	30	dobj	_	_
39	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = However, this axiomatic definition at first seems somewhat disjoint from other approaches in differential geometry.
1	However	however	ADV	RB	_	8	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
4	axiomatic	axiomatic	ADJ	JJ	Degree=Pos	5	amod	_	_
5	definition	definition	NOUN	NN	Number=Sing	8	nsubj	_	_
6	at	at	ADP	IN	_	5	prep	_	_
7	first	first	ADV	RB	_	6	pobj	_	_
8	seems	seem	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	somewhat	somewhat	ADV	RB	_	10	advmod	_	_
10	disjoint	disjoint	NOUN	NN	Number=Sing	8	oprd	_	_
11	from	from	ADP	IN	_	10	prep	_	_
12	other	other	ADJ	JJ	Degree=Pos	13	amod	_	_
13	approaches	approach	NOUN	NNS	Number=Plur	11	pobj	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	differential	differential	ADJ	JJ	Degree=Pos	16	amod	_	_
16	geometry	geometry	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 5
# text = The aim of this paper is to present a perspective that addresses this issue.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	aim	aim	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	paper	paper	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	present	present	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	perspective	perspective	NOUN	NN	Number=Sing	8	dobj	_	_
11	that	that	PRON	WDT	PronType=Rel	12	nsubj	_	_
12	addresses	address	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	relcl	_	_
13	this	this	DET	DT	Number=Sing|PronType=Dem	14	det	_	_
14	issue	issue	NOUN	NN	Number=Sing	12	dobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 6
# text = More specifically, this paper highlights a very explicit relationship between the axiomatic definition of Tangent Structure and the Weil algebras (which have a well established place in differential geometry).
1	More	more	ADV	RBR	Degree=Cmp	2	advmod	_	_
2	specifically	specifically	ADV	RB	_	6	advmod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	paper	paper	NOUN	NN	Number=Sing	6	nsubj	_	_
6	highlights	highlight	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	very	very	ADV	RB	_	9	advmod	_	_
9	explicit	explicit	ADJ	JJ	Degree=Pos	10	amod	_	_
10	relationship	relationship	NOUN	NN	Number=Sing	6	dobj	_	_
11	between	between	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	axiomatic	axiomatic	ADJ	JJ	Degree=Pos	14	amod	_	_
14	definition	definition	NOUN	NN	Number=Sing	11	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	Tangent	Tangent	PROPN	NNP	Number=Sing	17	compound	_	_
17	Structure	Structure	PROPN	NNP	Number=Sing	15	pobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	Weil	Weil	PROPN	NNP	Number=Sing	21	compound	_	_
21	algebras	algebra	NOUN	NNS	Number=Plur	17	conj	_	_
22	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	21	punct	_	SpaceAfter=No
23	which	which	PRON	WDT	_	24	nsubj	_	_
24	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	10	relcl	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
26	well	well	ADV	RB	Degree=Pos	27	advmod	_	_
27	established	establish	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	amod	_	_
28	place	place	NOUN	NN	Number=Sing	24	dobj	_	_
29	in	in	ADP	IN	_	28	prep	_	_
30	differential	differential	ADJ	JJ	Degree=Pos	31	amod	_	_
31	geometry	geometry	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
32	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	6	punct	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 640
# sent_id = 1
# text = Just as binary relations between sets may be understood as jointly monic spans, so too may equivalence relations on the disjoint union of sets be understood as jointly epic cospans.
1	Just	just	ADV	RB	_	9	advmod	_	_
2	as	as	SCONJ	IN	_	9	mark	_	_
3	binary	binary	ADJ	JJ	Degree=Pos	4	amod	_	_
4	relations	relation	NOUN	NNS	Number=Plur	9	nsubjpass	_	_
5	between	between	ADP	IN	_	4	prep	_	_
6	sets	set	NOUN	NNS	Number=Plur	5	pobj	_	_
7	may	may	AUX	MD	VerbForm=Fin	9	aux	_	_
8	be	be	AUX	VB	VerbForm=Inf	9	auxpass	_	_
9	understood	understand	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	advcl	_	_
10	as	as	ADP	IN	_	9	prep	_	_
11	jointly	jointly	ADV	RB	_	13	advmod	_	_
12	monic	monic	ADJ	JJ	Degree=Pos	13	amod	_	_
13	spans	span	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
15	so	so	ADV	RB	_	16	advmod	_	_
16	too	too	ADV	RB	_	18	advmod	_	_
17	may	may	AUX	MD	VerbForm=Fin	18	aux	_	_
18	equivalence	equivalence	VERB	VB	VerbForm=Inf	0	ROOT	_	_
19	relations	relation	NOUN	NNS	Number=Plur	27	nsubjpass	_	_
20	on	on	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	disjoint	disjoint	NOUN	NN	Number=Sing	23	compound	_	_
23	union	union	NOUN	NN	Number=Sing	20	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	sets	set	NOUN	NNS	Number=Plur	24	pobj	_	_
26	be	be	AUX	VB	VerbForm=Inf	27	auxpass	_	_
27	understood	understand	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	ccomp	_	_
28	as	as	ADP	IN	_	27	prep	_	_
29	jointly	jointly	ADV	RB	_	30	advmod	_	_
30	epic	epic	ADJ	JJ	Degree=Pos	31	amod	_	_
31	cospans	cospan	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	27	punct	_	SpaceAfter=No

# sent_id = 2
# text = With the ensuing notion of composition inherited from the pushout of cospans, we call these equivalence relations corelations.
1	With	with	ADP	IN	_	15	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	ensuing	ensue	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	amod	_	_
4	notion	notion	NOUN	NN	Number=Sing	1	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	composition	composition	NOUN	NN	Number=Sing	5	pobj	_	_
7	inherited	inherit	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	acl	_	_
8	from	from	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	pushout	pushout	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	cospans	cospan	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
14	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	15	nsubj	_	_
15	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	these	these	DET	DT	Number=Plur|PronType=Dem	19	det	_	_
17	equivalence	equivalence	NOUN	NN	Number=Sing	18	compound	_	_
18	relations	relation	NOUN	NNS	Number=Plur	19	compound	_	_
19	corelations	corelation	NOUN	NNS	Number=Plur	15	dobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 3
# text = We define the category of corelations between finite sets and prove that it is equivalent to the prop for extraspecial commutative Frobenius monoids.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	category	category	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	corelations	corelation	NOUN	NNS	Number=Plur	5	pobj	_	_
7	between	between	ADP	IN	_	6	prep	_	_
8	finite	finite	ADJ	JJ	Degree=Pos	9	compound	_	_
9	sets	set	NOUN	NNS	Number=Plur	7	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
11	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
12	that	that	SCONJ	IN	_	14	mark	_	_
13	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	ccomp	_	_
15	equivalent	equivalent	ADJ	JJ	Degree=Pos	14	acomp	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	prop	prop	NOUN	NN	Number=Sing	16	pobj	_	_
19	for	for	ADP	IN	_	14	prep	_	_
20	extraspecial	extraspecial	ADJ	JJ	Degree=Pos	23	amod	_	_
21	commutative	commutative	ADJ	JJ	Degree=Pos	23	amod	_	_
22	Frobenius	Frobenius	PROPN	NNP	Number=Sing	23	compound	_	_
23	monoids	monoid	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = Dually, we show that the category of relations is equivalent to the prop for special commutative bimonoids.
1	Dually	Dually	PROPN	NNP	Number=Sing	4	npadvmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	10	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	category	category	NOUN	NN	Number=Sing	10	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	relations	relation	NOUN	NNS	Number=Plur	8	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
11	equivalent	equivalent	ADJ	JJ	Degree=Pos	10	acomp	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	prop	prop	NOUN	NN	Number=Sing	12	pobj	_	_
15	for	for	ADP	IN	_	10	prep	_	_
16	special	special	ADJ	JJ	Degree=Pos	18	amod	_	_
17	commutative	commutative	ADJ	JJ	Degree=Pos	18	amod	_	_
18	bimonoids	bimonoids	PROPN	NNP	Number=Sing	15	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = Throughout, we emphasise how corelations model interconnection.
1	Throughout	throughout	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	emphasise	emphasise	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	how	how	SCONJ	WRB	_	8	advmod	_	_
6	corelations	corelation	NOUN	NNS	Number=Plur	8	compound	_	_
7	model	model	NOUN	NN	Number=Sing	8	compound	_	_
8	interconnection	interconnection	NOUN	NN	Number=Sing	4	dobj	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 641
# sent_id = 1
# text = Given an order - enriched category, it is known that all its KZ - monadic subcategories can be described by Kan - injectivity with respect to a collection of morphisms.
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
3	order	order	NOUN	NN	Number=Sing	5	npadvmod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
8	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	10	nsubjpass	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
11	that	that	SCONJ	IN	_	20	mark	_	_
12	all	all	DET	PDT	_	17	predet	_	_
13	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	17	poss	_	_
14	KZ	KZ	PROPN	NNP	Number=Sing	16	npadvmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	monadic	monadic	ADJ	JJ	Degree=Pos	17	amod	_	_
17	subcategories	subcategorie	NOUN	NNS	Number=Plur	20	nsubjpass	_	_
18	can	can	AUX	MD	VerbForm=Fin	20	aux	_	_
19	be	be	AUX	VB	VerbForm=Inf	20	auxpass	_	_
20	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	ccomp	_	_
21	by	by	ADP	IN	_	20	agent	_	_
22	Kan	Kan	PROPN	NNP	Number=Sing	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	injectivity	injectivity	NOUN	NN	Number=Sing	21	pobj	_	_
25	with	with	ADP	IN	_	20	prep	_	_
26	respect	respect	NOUN	NN	Number=Sing	25	pobj	_	_
27	to	to	ADP	IN	_	26	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
29	collection	collection	NOUN	NN	Number=Sing	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	morphisms	morphism	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 2
# text = We prove the analogous result for Kan - injectivity with respect to a collection $ H $ of commutative squares.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	analogous	analogous	ADJ	JJ	Degree=Pos	5	amod	_	_
5	result	result	NOUN	NN	Number=Sing	2	dobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	Kan	Kan	PROPN	NNP	Number=Sing	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	injectivity	injectivity	NOUN	NN	Number=Sing	6	pobj	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	respect	respect	NOUN	NN	Number=Sing	10	pobj	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	collection	collection	NOUN	NN	Number=Sing	12	pobj	_	_
15	$ H $	$ h $	SYM	$	_	14	appos	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	commutative	commutative	ADJ	JJ	Degree=Pos	18	amod	_	_
18	squares	square	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = A square is called a Kan - injective consequence of $ H $ if by adding it to $ H $ Kan - injectivity is not changed.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	square	square	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
6	Kan	Kan	PROPN	NNP	Number=Sing	8	npadvmod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	injective	injective	ADJ	JJ	Degree=Pos	9	amod	_	_
9	consequence	consequence	NOUN	NN	Number=Sing	4	oprd	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	$ H $	$ h $	SYM	$	_	10	pobj	_	_
12	if	if	SCONJ	IN	_	4	dep	_	_
13	by	by	ADP	IN	_	4	prep	_	_
14	adding	add	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	pcomp	_	_
15	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	14	dobj	_	_
16	to	to	ADP	IN	_	14	prep	_	_
17	$ H $	$ h $	SYM	$	_	20	nmod	_	_
18	Kan	Kan	PROPN	NNP	Number=Sing	20	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	injectivity	injectivity	NOUN	NN	Number=Sing	16	pobj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	auxpass	_	_
22	not	not	PART	RB	Polarity=Neg	23	neg	_	_
23	changed	change	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	conj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = We present a sound logic for Kan - injectivity consequences and prove that in ``reasonable" categories (such as $ Pos $ or $ Top_0 $ ) it is also complete for every set $ H $ of squares.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	sound	sound	ADJ	JJ	Degree=Pos	5	amod	_	_
5	logic	logic	NOUN	NN	Number=Sing	2	dobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	Kan	Kan	PROPN	NNP	Number=Sing	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	injectivity	injectivity	NOUN	NN	Number=Sing	10	compound	_	_
10	consequences	consequence	NOUN	NNS	Number=Plur	6	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
12	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
13	that	that	SCONJ	IN	_	28	mark	_	_
14	in	in	ADP	IN	_	28	prep	_	_
15	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	19	punct	_	SpaceAfter=No
16	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	19	punct	_	SpaceAfter=No
17	reasonable	reasonable	ADJ	JJ	Degree=Pos	19	amod	_	SpaceAfter=No
18	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	19	punct	_	_
19	categories	category	NOUN	NNS	Number=Plur	14	pobj	_	_
20	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	19	punct	_	SpaceAfter=No
21	such	such	ADJ	JJ	Degree=Pos	22	amod	_	_
22	as	as	ADP	IN	_	19	prep	_	_
23	$ Pos $	$ pos $	SYM	$	_	22	nmod	_	_
24	or	or	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	$ Top_0 $	$ top_0 $	SYM	$	_	22	pobj	_	_
26	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	19	punct	_	_
27	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	28	nsubj	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	ccomp	_	_
29	also	also	ADV	RB	_	28	advmod	_	_
30	complete	complete	ADJ	JJ	Degree=Pos	28	acomp	_	_
31	for	for	ADP	IN	_	30	prep	_	_
32	every	every	DET	DT	_	33	det	_	_
33	set	set	NOUN	NN	Number=Sing	31	pobj	_	_
34	$ H $	$ h $	SYM	$	_	33	appos	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	squares	square	NOUN	NNS	Number=Plur	35	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 642
# sent_id = 1
# text = One way to define Witt vectors starts with a truncation set $ S subset N $ .
1	One	one	NUM	CD	NumType=Card	2	nummod	_	_
2	way	way	NOUN	NN	Number=Sing	7	nsubj	_	_
3	to	to	PART	TO	_	4	aux	_	_
4	define	define	VERB	VB	VerbForm=Inf	2	relcl	_	_
5	Witt	Witt	PROPN	NNP	Number=Sing	6	compound	_	_
6	vectors	vector	NOUN	NNS	Number=Plur	4	dobj	_	_
7	starts	start	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	with	with	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	truncation	truncation	NOUN	NN	Number=Sing	8	pobj	_	_
11	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acl	_	_
12	$ S subset N $	$ s subset n $	SYM	$	_	11	dep	_	_
13	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 2
# text = We generalize Witt vectors to truncation posets, and show how three types of maps of truncation posets can be used to encode the following six structure maps on Witt vectors: addition, multiplication, restriction, Frobenius, Verschiebung and norm.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	Witt	Witt	PROPN	NNP	Number=Sing	4	compound	_	_
4	vectors	vector	NOUN	NNS	Number=Plur	2	dobj	_	_
5	to	to	PART	TO	_	2	prep	_	_
6	truncation	truncation	NOUN	NN	Number=Sing	7	compound	_	_
7	posets	poset	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
10	show	show	VERB	VB	VerbForm=Inf	2	conj	_	_
11	how	how	SCONJ	WRB	_	21	advmod	_	_
12	three	three	NUM	CD	NumType=Card	13	nummod	_	_
13	types	type	NOUN	NNS	Number=Plur	21	nsubjpass	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	maps	map	NOUN	NNS	Number=Plur	14	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	truncation	truncation	NOUN	NN	Number=Sing	18	compound	_	_
18	posets	poset	NOUN	NNS	Number=Plur	16	pobj	_	_
19	can	can	AUX	MD	VerbForm=Fin	21	aux	_	_
20	be	be	AUX	VB	VerbForm=Inf	21	auxpass	_	_
21	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	ccomp	_	_
22	to	to	PART	TO	_	23	aux	_	_
23	encode	encode	VERB	VB	VerbForm=Inf	21	xcomp	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
25	following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	28	amod	_	_
26	six	six	NUM	CD	NumType=Card	28	nummod	_	_
27	structure	structure	NOUN	NN	Number=Sing	28	compound	_	_
28	maps	map	NOUN	NNS	Number=Plur	23	dobj	_	_
29	on	on	ADP	IN	_	28	prep	_	_
30	Witt	Witt	PROPN	NNP	Number=Sing	31	compound	_	_
31	vectors	vector	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
32	:	:	PUNCT	:	_	28	punct	_	_
33	addition	addition	NOUN	NN	Number=Sing	28	appos	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
35	multiplication	multiplication	NOUN	NN	Number=Sing	33	conj	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
37	restriction	restriction	NOUN	NN	Number=Sing	35	conj	_	SpaceAfter=No
38	,	,	PUNCT	,	PunctType=Comm	37	punct	_	_
39	Frobenius	Frobenius	PROPN	NNP	Number=Sing	37	conj	_	SpaceAfter=No
40	,	,	PUNCT	,	PunctType=Comm	39	punct	_	_
41	Verschiebung	Verschiebung	PROPN	NNP	Number=Sing	39	conj	_	_
42	and	and	CCONJ	CC	ConjType=Cmp	41	cc	_	_
43	norm	norm	NOUN	NN	Number=Sing	41	conj	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 643
# sent_id = 1
# text = In this note, we prove the existence of $ E_leq $ - injective hulls in the category $ PoSgr_leq $ of posemigroups and their submultiplicative order - preserving maps; here $ E_leq $ denotes the class of those morphisms $ h : A to B $ for which $ h(a_1)...h(a_n)leq h(a) $ always implies $ a_1...a_nleq a $ .
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	note	note	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	30	ccomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	existence	existence	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	$ E_leq $	$ e_leq $	SYM	$	_	12	quantmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	injective	injective	ADJ	JJ	Degree=Pos	13	amod	_	_
13	hulls	hull	NOUN	NNS	Number=Plur	9	pobj	_	_
14	in	in	ADP	IN	_	8	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	category	category	NOUN	NN	Number=Sing	14	pobj	_	_
17	$ PoSgr_leq $	$ posgr_leq $	SYM	$	_	16	appos	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	posemigroups	posemigroup	NOUN	NNS	Number=Plur	18	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
21	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	26	poss	_	_
22	submultiplicative	submultiplicative	ADJ	JJ	Degree=Pos	26	amod	_	_
23	order	order	NOUN	NN	Number=Sing	25	npadvmod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	26	amod	_	_
26	maps	map	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
27	;	;	PUNCT	:	_	30	punct	_	_
28	here	here	ADV	RB	PronType=Dem	30	advmod	_	_
29	$ E_leq $	$ e_leq $	SYM	$	_	30	nsubj	_	_
30	denotes	denote	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	class	class	NOUN	NN	Number=Sing	30	dobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	those	those	DET	DT	Number=Plur|PronType=Dem	35	det	_	_
35	morphisms	morphism	NOUN	NNS	Number=Plur	33	pobj	_	_
36	$ h : A to B $	$ h : a to b $	SYM	$	_	32	appos	_	_
37	for	for	ADP	IN	_	41	prep	_	_
38	which	which	PRON	WDT	_	37	pobj	_	_
39	$ h(a_1)...h(a_n)leq h(a) $	$ h(a_1)...h(a_n)leq h(a) $	SYM	$	_	41	nsubj	_	_
40	always	always	ADV	RB	_	41	advmod	_	_
41	implies	imply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	36	relcl	_	_
42	$ a_1...a_nleq a $	$ a_1...a_nleq a $	SYM	$	_	41	dobj	_	_
43	.	.	PUNCT	.	PunctType=Peri	30	punct	_	SpaceAfter=No

# sent_id = 2
# text = The result of this note subsumes the results given by Lambek and by Zhang and Laan.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	result	result	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	note	note	NOUN	NN	Number=Sing	3	pobj	_	_
6	subsumes	subsume	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	results	result	NOUN	NNS	Number=Plur	6	dobj	_	_
9	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	by	by	ADP	IN	_	9	agent	_	_
11	Lambek	Lambek	PROPN	NNP	Number=Sing	10	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
13	by	by	ADP	IN	_	10	conj	_	_
14	Zhang	Zhang	PROPN	NNP	Number=Sing	13	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	Laan	Laan	PROPN	NNP	Number=Sing	14	conj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 644
# sent_id = 1
# text = Normal monomorphisms in the sense of Bourn describe the equivalence classes of an internal equivalence relation.
1	Normal	normal	ADJ	JJ	Degree=Pos	2	amod	_	_
2	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	8	nsubj	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	sense	sense	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Bourn	Bourn	PROPN	NNP	Number=Sing	6	pobj	_	_
8	describe	describe	VERB	VB	VerbForm=Inf	0	ROOT	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	equivalence	equivalence	NOUN	NN	Number=Sing	11	compound	_	_
11	classes	class	NOUN	NNS	Number=Plur	8	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
14	internal	internal	ADJ	JJ	Degree=Pos	15	amod	_	_
15	equivalence	equivalence	NOUN	NN	Number=Sing	16	compound	_	_
16	relation	relation	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = Although the definition is given in the fairly general setting of a category with finite limits, later investigations on this subject often focus on protomodular settings, where normality becomes a property.
1	Although	although	SCONJ	IN	_	5	mark	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	definition	definition	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	advcl	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	fairly	fairly	ADV	RB	_	9	advmod	_	_
9	general	general	ADJ	JJ	Degree=Pos	10	amod	_	_
10	setting	setting	NOUN	NN	Number=Sing	6	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	finite	finite	ADJ	JJ	Degree=Pos	16	compound	_	_
16	limits	limit	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
18	later	later	ADJ	JJ	Degree=Pos	19	amod	_	_
19	investigations	investigation	NOUN	NNS	Number=Plur	24	nsubj	_	_
20	on	on	ADP	IN	_	19	prep	_	_
21	this	this	DET	DT	Number=Sing|PronType=Dem	22	det	_	_
22	subject	subject	NOUN	NN	Number=Sing	20	pobj	_	_
23	often	often	ADV	RB	_	24	advmod	_	_
24	focus	focus	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
25	on	on	ADP	IN	_	24	prep	_	_
26	protomodular	protomodular	ADJ	JJ	Degree=Pos	27	amod	_	_
27	settings	setting	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
29	where	where	SCONJ	WRB	_	31	advmod	_	_
30	normality	normality	NOUN	NN	Number=Sing	31	nsubj	_	_
31	becomes	become	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	relcl	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
33	property	property	NOUN	NN	Number=Sing	31	attr	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# sent_id = 3
# text = This paper clarifies the connections between internal equivalence relations and Bourn - normal monomorphisms in regular Maltsev categories with pushouts of split monomorphisms along arbitrary morphisms, whereas a full description is achieved for quasi - pointed regular Maltsev categories with pushouts of split monomorphisms along arbitrary morphisms.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	clarifies	clarify	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	connections	connection	NOUN	NNS	Number=Plur	3	dobj	_	_
6	between	between	ADP	IN	_	5	prep	_	_
7	internal	internal	ADJ	JJ	Degree=Pos	9	amod	_	_
8	equivalence	equivalence	NOUN	NN	Number=Sing	9	compound	_	_
9	relations	relation	NOUN	NNS	Number=Plur	6	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	Bourn	Bourn	PROPN	NNP	Number=Sing	13	npadvmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	normal	normal	ADJ	JJ	Degree=Pos	14	amod	_	_
14	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	9	conj	_	_
15	in	in	ADP	IN	_	9	prep	_	_
16	regular	regular	ADJ	JJ	Degree=Pos	18	amod	_	_
17	Maltsev	Maltsev	PROPN	NNP	Number=Sing	18	compound	_	_
18	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	_
19	with	with	ADP	IN	_	5	prep	_	_
20	pushouts	pushout	NOUN	NNS	Number=Plur	19	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	split	split	NOUN	NN	Number=Sing	23	compound	_	_
23	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	21	pobj	_	_
24	along	along	ADP	IN	_	20	prep	_	_
25	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	26	amod	_	_
26	morphisms	morphism	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
28	whereas	whereas	SCONJ	IN	_	33	mark	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	full	full	ADJ	JJ	Degree=Pos	31	amod	_	_
31	description	description	NOUN	NN	Number=Sing	33	nsubjpass	_	_
32	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	33	auxpass	_	_
33	achieved	achieve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	advcl	_	_
34	for	for	ADP	IN	_	33	prep	_	_
35	quasi	quasi	ADJ	JJ	Degree=Pos	37	advmod	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	pointed	point	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	40	amod	_	_
38	regular	regular	ADJ	JJ	Degree=Pos	40	amod	_	_
39	Maltsev	Maltsev	PROPN	NNP	Number=Sing	40	compound	_	_
40	categories	category	NOUN	NNS	Number=Plur	34	pobj	_	_
41	with	with	ADP	IN	_	40	prep	_	_
42	pushouts	pushout	NOUN	NNS	Number=Plur	41	pobj	_	_
43	of	of	ADP	IN	_	42	prep	_	_
44	split	split	NOUN	NN	Number=Sing	45	compound	_	_
45	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	43	pobj	_	_
46	along	along	ADP	IN	_	42	prep	_	_
47	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	48	amod	_	_
48	morphisms	morphism	NOUN	NNS	Number=Plur	46	pobj	_	SpaceAfter=No
49	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 645
# sent_id = 1
# text = We study the existence and left properness of transferred model structures for ``monoid - like'' objects in monoidal model categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	existence	existence	NOUN	NN	Number=Sing	2	dobj	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
6	left	leave	VERB	VBD	Tense=Past|VerbForm=Fin	2	conj	_	_
7	properness	properness	NOUN	NN	Number=Sing	6	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	transferred	transfer	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
10	model	model	NOUN	NN	Number=Sing	11	compound	_	_
11	structures	structure	NOUN	NNS	Number=Plur	8	pobj	_	_
12	for	for	ADP	IN	_	6	prep	_	_
13	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	19	punct	_	SpaceAfter=No
14	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	19	punct	_	SpaceAfter=No
15	monoid	monoid	NOUN	NN	Number=Sing	17	npadvmod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	like	like	ADJ	JJ	Degree=Pos	19	amod	_	SpaceAfter=No
18	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	19	punct	_	_
19	objects	object	NOUN	NNS	Number=Plur	12	pobj	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	monoidal	monoidal	ADJ	JJ	Degree=Pos	23	amod	_	_
22	model	model	NOUN	NN	Number=Sing	23	compound	_	_
23	categories	category	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = These include genuine monoids, but also all kinds of operads as for instance symmetric, cyclic, modular, higher operads, properads and PROP's.
1	These	these	PRON	DT	Number=Plur|PronType=Dem	2	nsubj	_	_
2	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	genuine	genuine	ADJ	JJ	Degree=Pos	4	amod	_	_
4	monoids	monoid	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
6	but	but	CCONJ	CC	ConjType=Cmp	2	cc	_	_
7	also	also	ADV	RB	_	6	advmod	_	_
8	all	all	DET	DT	_	9	det	_	_
9	kinds	kind	NOUN	NNS	Number=Plur	2	conj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	operads	operad	NOUN	NNS	Number=Plur	10	pobj	_	_
12	as	as	ADP	IN	_	9	prep	_	_
13	for	for	ADP	IN	_	12	prep	_	_
14	instance	instance	NOUN	NN	Number=Sing	22	nmod	_	_
15	symmetric	symmetric	ADJ	JJ	Degree=Pos	22	amod	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	cyclic	cyclic	PROPN	NNP	Number=Sing	15	conj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	modular	modular	ADJ	JJ	Degree=Pos	22	amod	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
21	higher	high	ADJ	JJR	Degree=Cmp	22	amod	_	_
22	operads	operad	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	properads	properad	NOUN	NNS	Number=Plur	22	conj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	PROP	PROP	PROPN	NNP	Number=Sing	24	conj	_	SpaceAfter=No
27	's	's	PART	POS	_	26	case	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = All these structures can be realised as algebras over polynomial monads.
1	All	all	DET	PDT	_	3	predet	_	_
2	these	these	DET	DT	Number=Plur|PronType=Dem	3	det	_	_
3	structures	structure	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
4	can	can	AUX	MD	VerbForm=Fin	6	aux	_	_
5	be	be	AUX	VB	VerbForm=Inf	6	auxpass	_	_
6	realised	realise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	as	as	ADP	IN	_	6	prep	_	_
8	algebras	algebra	NOUN	NNS	Number=Plur	7	pobj	_	_
9	over	over	ADP	IN	_	6	prep	_	_
10	polynomial	polynomial	ADJ	JJ	Degree=Pos	11	amod	_	_
11	monads	monad	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = We give a general condition for a polynomial monad which ensures the existence and (relative) left properness of a transferred model structure for its algebras.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	general	general	ADJ	JJ	Degree=Pos	5	amod	_	_
5	condition	condition	NOUN	NN	Number=Sing	2	dobj	_	_
6	for	for	ADP	IN	_	2	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	polynomial	polynomial	ADJ	JJ	Degree=Pos	9	amod	_	_
9	monad	monad	NOUN	NNS	Number=Plur	6	pobj	_	_
10	which	which	PRON	WDT	_	11	nsubj	_	_
11	ensures	ensure	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	relcl	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	existence	existence	NOUN	NN	Number=Sing	11	dobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
15	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	16	punct	_	SpaceAfter=No
16	relative	relative	NOUN	NN	Number=Sing	11	conj	_	SpaceAfter=No
17	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	16	punct	_	_
18	left	leave	VERB	VBD	Tense=Past|VerbForm=Fin	2	conj	_	_
19	properness	properness	NOUN	NN	Number=Sing	18	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
22	transferred	transfer	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
23	model	model	NOUN	NN	Number=Sing	24	compound	_	_
24	structure	structure	NOUN	NN	Number=Sing	20	pobj	_	_
25	for	for	ADP	IN	_	24	prep	_	_
26	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	27	poss	_	_
27	algebras	algebra	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = This condition is of a combinatorial nature and singles out a special class of polynomial monads which we call tame polynomial.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	condition	condition	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	7	amod	_	_
7	nature	nature	NOUN	NN	Number=Sing	4	pobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
9	singles	single	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
10	out	out	ADP	RP	_	9	prt	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	special	special	ADJ	JJ	Degree=Pos	13	amod	_	_
13	class	class	NOUN	NN	Number=Sing	9	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	polynomial	polynomial	ADJ	JJ	Degree=Pos	16	amod	_	_
16	monads	monad	NOUN	NNS	Number=Plur	14	pobj	_	_
17	which	which	PRON	WDT	_	19	dobj	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	13	relcl	_	_
20	tame	tame	ADJ	JJ	Degree=Pos	21	amod	_	_
21	polynomial	polynomial	NOUN	NN	Number=Sing	19	oprd	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = Many important monads are shown to be tame polynomial.
1	Many	many	ADJ	JJ	Degree=Pos	3	amod	_	_
2	important	important	ADJ	JJ	Degree=Pos	3	amod	_	_
3	monads	monad	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	be	be	AUX	VB	VerbForm=Inf	5	xcomp	_	_
8	tame	tame	ADJ	JJ	Degree=Pos	9	amod	_	_
9	polynomial	polynomial	NOUN	NN	Number=Sing	7	attr	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 646
# sent_id = 1
# text = We define the notion of a $ (P, tilde{P}) $ - structure on a universe $ p $ in a locally cartesian closed category category with a binary product structure and construct a $ (Pi, lambda) $ - structure on the $ C $ - systems $ CC(C, p) $ from a $ (P, tilde{P}) $ - structure on $ p $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	$ (P, tilde{P}) $	$ (p, tilde{p}) $	SYM	$	_	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	structure	structure	NOUN	NN	Number=Sing	5	pobj	_	_
10	on	on	ADP	IN	_	2	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	universe	universe	NOUN	NN	Number=Sing	10	pobj	_	_
13	$ p $	$ p $	SYM	$	_	12	appos	_	_
14	in	in	ADP	IN	_	2	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
16	locally	locally	ADV	RB	_	17	advmod	_	_
17	cartesian	cartesian	ADJ	JJ	Degree=Pos	20	amod	_	_
18	closed	closed	ADJ	JJ	Degree=Pos	20	amod	_	_
19	category	category	NOUN	NN	Number=Sing	20	compound	_	_
20	category	category	NOUN	NN	Number=Sing	14	pobj	_	_
21	with	with	ADP	IN	_	20	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
23	binary	binary	ADJ	JJ	Degree=Pos	25	amod	_	_
24	product	product	NOUN	NN	Number=Sing	25	compound	_	_
25	structure	structure	NOUN	NN	Number=Sing	21	pobj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
27	construct	construct	VERB	VB	VerbForm=Inf	2	conj	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
29	$ (Pi, lambda) $	$ (pi, lambda) $	NUM	CD	NumType=Card	31	compound	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	structure	structure	NOUN	NN	Number=Sing	27	dobj	_	_
32	on	on	ADP	IN	_	27	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
34	$ C $	$ c $	SYM	$	_	36	compound	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	36	punct	_	_
36	systems	system	NOUN	NNS	Number=Plur	32	pobj	_	_
37	$ CC(C, p) $	$ cc(c, p) $	SYM	$	_	27	dep	_	_
38	from	from	ADP	IN	_	27	prep	_	_
39	a	a	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
40	$ (P, tilde{P}) $	$ (p, tilde{p}) $	SYM	$	_	42	compound	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	structure	structure	NOUN	NN	Number=Sing	38	pobj	_	_
43	on	on	ADP	IN	_	42	prep	_	_
44	$ p $	$ p $	SYM	$	_	43	pobj	_	_
45	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We then define homomorphisms of $ C $ - systems with $ (Pi, lambda) $ - structures and functors of universe categories with $ (P, tilde{P}) $ - structures and show that our construction is functorial relative to these definitions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	homomorphisms	homomorphism	NOUN	NNS	Number=Plur	3	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	$ C $	$ c $	SYM	$	_	8	compound	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	systems	system	NOUN	NNS	Number=Plur	5	pobj	_	_
9	with	with	ADP	IN	_	3	prep	_	_
10	$ (Pi, lambda) $	$ (pi, lambda) $	SYM	$	_	12	compound	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	structures	structure	NOUN	NNS	Number=Plur	9	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	functors	functor	NOUN	NNS	Number=Plur	12	conj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	universe	universe	ADJ	JJ	Degree=Pos	17	amod	_	_
17	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	_
18	with	with	ADP	IN	_	17	prep	_	_
19	$ (P, tilde{P}) $	$ (p, tilde{p}) $	SYM	$	_	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	structures	structure	NOUN	NNS	Number=Plur	18	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
23	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	3	conj	_	_
24	that	that	SCONJ	IN	_	27	mark	_	_
25	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	26	poss	_	_
26	construction	construction	NOUN	NN	Number=Sing	27	nsubj	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	ccomp	_	_
28	functorial	functorial	ADJ	JJ	Degree=Pos	29	amod	_	_
29	relative	relative	ADJ	JJ	Degree=Pos	27	acomp	_	_
30	to	to	ADP	IN	_	29	prep	_	_
31	these	these	DET	DT	Number=Plur|PronType=Dem	32	det	_	_
32	definitions	definition	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 647
# sent_id = 1
# text = The main result of this paper may be stated as a construction of "almost representations" $ mu_n $ and $ tilde{mu}_n $ for the presheaves $ Ob_n $ and $ tilde{Ob}_n $ on the $ C $ - systems defined by locally cartesian closed universe categories with binary product structures and the study of the behavior of these "almost representations" with respect to the universe category functors.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	result	result	NOUN	NN	Number=Sing	9	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	paper	paper	NOUN	NN	Number=Sing	4	pobj	_	_
7	may	may	AUX	MD	VerbForm=Fin	9	aux	_	_
8	be	be	AUX	VB	VerbForm=Inf	9	auxpass	_	_
9	stated	state	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
10	as	as	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	construction	construction	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	16	punct	_	SpaceAfter=No
15	almost	almost	ADV	RB	_	16	advmod	_	_
16	representations	representation	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	pobj	_	SpaceAfter=No
17	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	16	punct	_	_
18	$ mu_n $	$ mu_n $	SYM	$	_	16	appos	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	$ tilde{mu}_n $	$ tilde{mu}_n $	SYM	$	_	18	conj	_	_
21	for	for	ADP	IN	_	16	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	presheaves	presheave	NOUN	NNS	Number=Plur	21	pobj	_	_
24	$ Ob_n $	$ ob_n $	SYM	$	_	23	appos	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	$ tilde{Ob}_n $	$ tilde{ob}_n $	SYM	$	_	24	conj	_	_
27	on	on	ADP	IN	_	16	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
29	$ C $	$ c $	SYM	$	_	31	compound	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	systems	system	NOUN	NNS	Number=Plur	27	pobj	_	_
32	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	acl	_	_
33	by	by	ADP	IN	_	32	agent	_	_
34	locally	locally	ADV	RB	_	35	advmod	_	_
35	cartesian	cartesian	ADJ	JJ	Degree=Pos	38	amod	_	_
36	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	38	amod	_	_
37	universe	universe	ADJ	JJ	Degree=Pos	38	amod	_	_
38	categories	category	NOUN	NNS	Number=Plur	33	pobj	_	_
39	with	with	ADP	IN	_	38	prep	_	_
40	binary	binary	ADJ	JJ	Degree=Pos	42	amod	_	_
41	product	product	NOUN	NN	Number=Sing	42	compound	_	_
42	structures	structure	NOUN	NNS	Number=Plur	39	pobj	_	_
43	and	and	CCONJ	CC	ConjType=Cmp	42	cc	_	_
44	the	the	DET	DT	Definite=Def|PronType=Art	45	det	_	_
45	study	study	NOUN	NN	Number=Sing	42	conj	_	_
46	of	of	ADP	IN	_	45	prep	_	_
47	the	the	DET	DT	Definite=Def|PronType=Art	48	det	_	_
48	behavior	behavior	NOUN	NN	Number=Sing	46	pobj	_	_
49	of	of	ADP	IN	_	48	prep	_	_
50	these	these	DET	DT	Number=Plur|PronType=Dem	53	det	_	_
51	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	53	punct	_	SpaceAfter=No
52	almost	almost	ADV	RB	_	53	advmod	_	_
53	representations	representation	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	49	pobj	_	SpaceAfter=No
54	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	53	punct	_	_
55	with	with	ADP	IN	_	53	prep	_	_
56	respect	respect	NOUN	NN	Number=Sing	55	pobj	_	_
57	to	to	ADP	IN	_	56	prep	_	_
58	the	the	DET	DT	Definite=Def|PronType=Art	61	det	_	_
59	universe	universe	ADJ	JJ	Degree=Pos	61	compound	_	_
60	category	category	NOUN	NN	Number=Sing	61	compound	_	_
61	functors	functor	NOUN	NNS	Number=Plur	57	pobj	_	SpaceAfter=No
62	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 2
# text = In addition, we study a number of constructions on presheaves on $ C $ - systems and on universe categories that are used in the proofs of our main results, but are expected to have other applications as well.
1	In	in	ADP	IN	_	5	prep	_	_
2	addition	addition	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	number	number	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	constructions	construction	NOUN	NNS	Number=Plur	8	pobj	_	_
10	on	on	ADP	IN	_	5	prep	_	_
11	presheaves	presheave	NOUN	NNS	Number=Plur	10	pobj	_	_
12	on	on	ADP	IN	_	11	prep	_	_
13	$ C $	$ c $	SYM	$	_	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	systems	system	NOUN	NNS	Number=Plur	12	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
17	on	on	ADP	IN	_	5	prep	_	_
18	universe	universe	ADJ	JJ	Degree=Pos	19	amod	_	_
19	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	_
20	that	that	PRON	WDT	PronType=Rel	22	nsubjpass	_	_
21	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	22	auxpass	_	_
22	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	relcl	_	_
23	in	in	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	proofs	proof	NOUN	NNS	Number=Plur	23	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	29	poss	_	_
28	main	main	ADJ	JJ	Degree=Pos	29	amod	_	_
29	results	result	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
31	but	but	CCONJ	CC	ConjType=Cmp	5	cc	_	_
32	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	33	auxpass	_	_
33	expected	expect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	conj	_	_
34	to	to	PART	TO	_	35	aux	_	_
35	have	have	VERB	VB	VerbForm=Inf	33	xcomp	_	_
36	other	other	ADJ	JJ	Degree=Pos	37	amod	_	_
37	applications	application	NOUN	NNS	Number=Plur	35	dobj	_	_
38	as	as	ADV	RB	_	39	advmod	_	_
39	well	well	ADV	RB	Degree=Pos	35	advmod	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 648
# sent_id = 1
# text = We introduce a functor called the simplicial nerve of an $ A_infty $ - category defined on the category of $ A_infty $ - categories with values in simplicial sets.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	functor	functor	NOUN	NN	Number=Sing	2	dobj	_	_
5	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	4	acl	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	simplicial	simplicial	ADJ	JJ	Degree=Pos	8	amod	_	_
8	nerve	nerve	NOUN	NN	Number=Sing	5	oprd	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	$ A_infty $	$ a_infty $	SYM	$	_	13	amod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
14	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	acl	_	_
15	on	on	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	$ A_infty $	$ a_infty $	SYM	$	_	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	categories	category	NOUN	NNS	Number=Plur	18	pobj	_	_
22	with	with	ADP	IN	_	17	prep	_	_
23	values	value	NOUN	NNS	Number=Plur	22	pobj	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	simplicial	simplicial	ADJ	JJ	Degree=Pos	26	amod	_	_
26	sets	set	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that the nerve of an $ A_infty $ - category is an $ (infty, 1) $ - category in the sense of Lurie.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	11	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	nerve	nerve	NOUN	NN	Number=Sing	11	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	$ A_infty $	$ a_infty $	SYM	$	_	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
12	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	$ (infty, 1) $	$ (infty, 1) $	SYM	$	_	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	category	category	NOUN	NN	Number=Sing	11	attr	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	sense	sense	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	Lurie	Lurie	PROPN	NNP	Number=Sing	19	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = This construction generalizes the nerve construction for differential graded categories given by Lurie.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	construction	construction	NOUN	NN	Number=Sing	3	nsubj	_	_
3	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	nerve	nerve	NOUN	NN	Number=Sing	6	compound	_	_
6	construction	construction	NOUN	NN	Number=Sing	3	dobj	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	differential	differential	ADJ	JJ	Degree=Pos	10	amod	_	_
9	graded	grade	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
11	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acl	_	_
12	by	by	ADP	IN	_	11	agent	_	_
13	Lurie	Lurie	PROPN	NNP	Number=Sing	12	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = We prove that if a differential graded category is pretriangulated in the sense of Bondal and Kapranov then its nerve is a stable $ (infty, 1) $ - category in the sense of Lurie.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	21	mark	_	_
4	if	if	SCONJ	IN	_	10	mark	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
6	differential	differential	ADJ	JJ	Degree=Pos	7	advmod	_	_
7	graded	grade	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	10	nsubjpass	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	pretriangulated	pretriangulate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	advcl	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	sense	sense	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	Bondal	Bondal	PROPN	NNP	Number=Sing	14	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	Kapranov	Kapranov	PROPN	NNP	Number=Sing	15	conj	_	_
18	then	then	ADV	RB	PronType=Dem	21	advmod	_	_
19	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	20	poss	_	_
20	nerve	nerve	NOUN	NN	Number=Sing	21	nsubj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
23	stable	stable	ADJ	JJ	Degree=Pos	26	amod	_	_
24	$ (infty, 1) $	$ (infty, 1) $	SYM	$	_	26	compound	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	category	category	NOUN	NN	Number=Sing	21	attr	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
29	sense	sense	NOUN	NN	Number=Sing	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	Lurie	Lurie	PROPN	NNP	Number=Sing	30	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 649
# sent_id = 1
# text = We consider Toeplitz and Cuntz - Krieger $ C^* $ - algebras associated with finitely aligned left cancellative small categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	Toeplitz	Toeplitz	PROPN	NNP	Number=Sing	2	dobj	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	Cuntz	Cuntz	PROPN	NNP	Number=Sing	7	compound	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	Krieger	Krieger	PROPN	NNP	Number=Sing	3	conj	_	_
8	$ C^* $	$ c^* $	SYM	$	_	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	algebras	algebra	NOUN	NNS	Number=Plur	3	conj	_	_
11	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acl	_	_
12	with	with	ADP	IN	_	11	prep	_	_
13	finitely	finitely	ADV	RB	_	14	advmod	_	_
14	aligned	align	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
15	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
16	cancellative	cancellative	ADJ	JJ	Degree=Pos	18	amod	_	_
17	small	small	ADJ	JJ	Degree=Pos	18	amod	_	_
18	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We pay special attention to the case where such a category arises as the Zappa - Szep product of a category and a group linked by a one - cocycle.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	pay	pay	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	special	special	ADJ	JJ	Degree=Pos	4	amod	_	_
4	attention	attention	NOUN	NN	Number=Sing	2	dobj	_	_
5	to	to	ADP	IN	_	2	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	case	case	NOUN	NN	Number=Sing	5	pobj	_	_
8	where	where	SCONJ	WRB	_	12	advmod	_	_
9	such	such	DET	PDT	_	11	predet	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	category	category	NOUN	NN	Number=Sing	12	nsubj	_	_
12	arises	arise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	relcl	_	_
13	as	as	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
15	Zappa	Zappa	PROPN	NNP	Number=Sing	17	compound	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	Szep	Szep	PROPN	NNP	Number=Sing	18	compound	_	_
18	product	product	NOUN	NN	Number=Sing	13	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	category	category	NOUN	NN	Number=Sing	19	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	group	group	NOUN	NN	Number=Sing	18	conj	_	_
25	linked	link	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	acl	_	_
26	by	by	ADP	IN	_	25	agent	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
28	one	one	NUM	CD	NumType=Card	30	nummod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	cocycle	cocycle	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = As our main application, we obtain a new approach to Exel - Pardo algebras in the case of row - finite graphs.
1	As	as	ADP	IN	_	7	prep	_	_
2	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	4	poss	_	_
3	main	main	ADJ	JJ	Degree=Pos	4	amod	_	_
4	application	application	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	new	new	ADJ	JJ	Degree=Pos	10	amod	_	_
10	approach	approach	NOUN	NN	Number=Sing	7	dobj	_	_
11	to	to	ADP	IN	_	10	prep	_	_
12	Exel	Exel	PROPN	NNP	Number=Sing	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	Pardo	Pardo	PROPN	NNP	Number=Sing	15	compound	_	_
15	algebras	algebra	NOUN	NNS	Number=Plur	11	pobj	_	_
16	in	in	ADP	IN	_	7	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	case	case	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	row	row	NOUN	NN	Number=Sing	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	finite	finite	ADJ	JJ	Degree=Pos	23	amod	_	_
23	graphs	graph	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = We also present some other ways of constructing $ C^* $ - algebras from left cancellative small categories and discuss their relationship.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	some	some	DET	DT	_	6	det	_	_
5	other	other	ADJ	JJ	Degree=Pos	6	amod	_	_
6	ways	way	NOUN	NNS	Number=Plur	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	constructing	construct	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	pcomp	_	_
9	$ C^* $	$ c^* $	SYM	$	_	11	compound	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	algebras	algebra	NOUN	NNS	Number=Plur	8	dobj	_	_
12	from	from	ADP	IN	_	11	prep	_	_
13	left	left	ADJ	JJ	Degree=Pos	16	amod	_	_
14	cancellative	cancellative	ADJ	JJ	Degree=Pos	16	amod	_	_
15	small	small	ADJ	JJ	Degree=Pos	16	amod	_	_
16	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
18	discuss	discuss	VERB	VB	VerbForm=Inf	8	conj	_	_
19	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	20	poss	_	_
20	relationship	relationship	NOUN	NN	Number=Sing	18	dobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 650
# sent_id = 1
# text = Coarse - graining is a standard method of extracting a simpler Markov process from a more complicated one by identifying states.
1	Coarse	coarse	ADV	RB	_	3	amod	_	_
2	-	-	PUNCT	HYPH	PunctType=Dash	3	punct	_	_
3	graining	graining	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	standard	standard	ADJ	JJ	Degree=Pos	7	amod	_	_
7	method	method	NOUN	NN	Number=Sing	4	attr	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	extracting	extract	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	pcomp	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	simpler	simple	ADJ	JJR	Degree=Cmp	13	amod	_	_
12	Markov	Markov	PROPN	NNP	Number=Sing	13	compound	_	_
13	process	process	NOUN	NN	Number=Sing	9	dobj	_	_
14	from	from	ADP	IN	_	9	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
16	more	more	ADV	RBR	Degree=Cmp	17	advmod	_	_
17	complicated	complicated	ADJ	JJ	Degree=Pos	18	amod	_	_
18	one	one	NUM	CD	NumType=Card	14	pobj	_	_
19	by	by	ADP	IN	_	9	prep	_	_
20	identifying	identify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	pcomp	_	_
21	states	state	NOUN	NNS	Number=Plur	20	dobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = Here we extend coarse - graining to `open' Markov processes: that is, those where probability can flow in or out of certain states called `inputs' and `outputs'.
1	Here	here	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	extend	extend	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	coarse	coarse	ADV	RB	_	6	advmod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	graining	grain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	amod	_	_
7	to	to	PART	TO	_	9	aux	_	_
8	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	9	punct	_	SpaceAfter=No
9	open	open	VERB	VB	VerbForm=Inf	12	amod	_	SpaceAfter=No
10	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	12	punct	_	_
11	Markov	Markov	PROPN	NNP	Number=Sing	12	compound	_	_
12	processes	process	NOUN	NNS	Number=Plur	3	dobj	_	SpaceAfter=No
13	:	:	PUNCT	:	_	12	punct	_	_
14	that	that	PRON	DT	Number=Sing|PronType=Dem	15	advmod	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	advmod	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	those	those	PRON	DT	Number=Plur|PronType=Dem	15	attr	_	_
18	where	where	SCONJ	WRB	_	21	advmod	_	_
19	probability	probability	NOUN	NN	Number=Sing	21	nsubj	_	_
20	can	can	AUX	MD	VerbForm=Fin	21	aux	_	_
21	flow	flow	VERB	VB	VerbForm=Inf	17	relcl	_	_
22	in	in	ADP	IN	_	21	prep	_	_
23	or	or	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	out	out	ADP	IN	_	22	conj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	certain	certain	ADJ	JJ	Degree=Pos	27	amod	_	_
27	states	state	NOUN	NNS	Number=Plur	25	pobj	_	_
28	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	acl	_	_
29	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	30	punct	_	SpaceAfter=No
30	inputs	input	NOUN	NNS	Number=Plur	28	oprd	_	SpaceAfter=No
31	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	30	punct	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
33	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	34	punct	_	SpaceAfter=No
34	outputs	output	NOUN	NNS	Number=Plur	30	conj	_	SpaceAfter=No
35	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	15	punct	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 3
# text = One can build up an ordinary Markov process from smaller open pieces in two basic ways: composition, where we identify the outputs of one open Markov process with the inputs of another, and tensoring, where we set two open Markov processes side by side.
1	One	one	PRON	PRP	PronType=Prs	3	nsubj	_	_
2	can	can	AUX	MD	VerbForm=Fin	3	aux	_	_
3	build	build	VERB	VB	VerbForm=Inf	0	ROOT	_	_
4	up	up	ADP	RP	_	3	prt	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
6	ordinary	ordinary	ADJ	JJ	Degree=Pos	8	amod	_	_
7	Markov	Markov	PROPN	NNP	Number=Sing	8	compound	_	_
8	process	process	NOUN	NN	Number=Sing	3	dobj	_	_
9	from	from	ADP	IN	_	3	prep	_	_
10	smaller	small	ADJ	JJR	Degree=Cmp	12	amod	_	_
11	open	open	ADJ	JJ	Degree=Pos	12	amod	_	_
12	pieces	piece	NOUN	NNS	Number=Plur	9	pobj	_	_
13	in	in	ADP	IN	_	3	prep	_	_
14	two	two	NUM	CD	NumType=Card	16	nummod	_	_
15	basic	basic	ADJ	JJ	Degree=Pos	16	amod	_	_
16	ways	way	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
17	:	:	PUNCT	:	_	16	punct	_	_
18	composition	composition	NOUN	NN	Number=Sing	16	appos	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	where	where	SCONJ	WRB	_	22	advmod	_	_
21	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	22	nsubj	_	_
22	identify	identify	VERB	VBP	Tense=Pres|VerbForm=Fin	18	relcl	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	outputs	output	NOUN	NNS	Number=Plur	22	dobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	one	one	NUM	CD	NumType=Card	29	nummod	_	_
27	open	open	ADJ	JJ	Degree=Pos	29	amod	_	_
28	Markov	Markov	PROPN	NNP	Number=Sing	29	compound	_	_
29	process	process	NOUN	NN	Number=Sing	25	pobj	_	_
30	with	with	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	inputs	input	NOUN	NNS	Number=Plur	30	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	another	another	PRON	DT	_	33	pobj	_	SpaceAfter=No
35	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
37	tensoring	tensoring	NOUN	NN	Number=Sing	18	conj	_	SpaceAfter=No
38	,	,	PUNCT	,	PunctType=Comm	37	punct	_	_
39	where	where	SCONJ	WRB	_	41	advmod	_	_
40	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	41	nsubj	_	_
41	set	set	VERB	VBD	Tense=Past|VerbForm=Fin	18	relcl	_	_
42	two	two	NUM	CD	NumType=Card	45	nummod	_	_
43	open	open	ADJ	JJ	Degree=Pos	45	amod	_	_
44	Markov	Markov	PROPN	NNP	Number=Sing	45	compound	_	_
45	processes	process	NOUN	NNS	Number=Plur	41	dobj	_	_
46	side	side	NOUN	NN	Number=Sing	41	dobj	_	_
47	by	by	ADP	IN	_	41	prep	_	_
48	side	side	NOUN	NN	Number=Sing	47	pobj	_	SpaceAfter=No
49	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = In previous work, Fong, Pollard and the first author showed that these constructions make open Markov processes into the morphisms of a symmetric monoidal category.
1	In	in	ADP	IN	_	12	prep	_	_
2	previous	previous	ADJ	JJ	Degree=Pos	3	amod	_	_
3	work	work	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
5	Fong	Fong	PROPN	NNP	Number=Sing	12	nsubj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	Pollard	Pollard	PROPN	NNP	Number=Sing	5	conj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	first	first	ADJ	JJ	Degree=Pos	11	amod	_	_
11	author	author	NOUN	NN	Number=Sing	7	conj	_	_
12	showed	show	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
13	that	that	SCONJ	IN	_	16	mark	_	_
14	these	these	DET	DT	Number=Plur|PronType=Dem	15	det	_	_
15	constructions	construction	NOUN	NNS	Number=Plur	16	nsubj	_	_
16	make	make	VERB	VBP	Tense=Pres|VerbForm=Fin	12	ccomp	_	_
17	open	open	ADJ	JJ	Degree=Pos	19	amod	_	_
18	Markov	Markov	PROPN	NNP	Number=Sing	19	compound	_	_
19	processes	process	NOUN	NNS	Number=Plur	16	dobj	_	_
20	into	into	ADP	IN	_	16	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	morphisms	morphism	NOUN	NNS	Number=Plur	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
25	symmetric	symmetric	ADJ	JJ	Degree=Pos	27	amod	_	_
26	monoidal	monoidal	ADJ	JJ	Degree=Pos	27	amod	_	_
27	category	category	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 5
# text = Here we go further by constructing a symmetric monoidal double category where the 2 - morphisms include ways of coarse - graining open Markov processes.
1	Here	here	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	go	go	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	further	far	ADV	RB	_	3	advmod	_	_
5	by	by	ADP	IN	_	3	prep	_	_
6	constructing	construct	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	symmetric	symmetric	ADJ	JJ	Degree=Pos	9	amod	_	_
9	monoidal	monoidal	ADJ	JJ	Degree=Pos	11	amod	_	_
10	double	double	ADJ	JJ	Degree=Pos	11	amod	_	_
11	category	category	NOUN	NN	Number=Sing	6	dobj	_	_
12	where	where	SCONJ	WRB	_	17	advmod	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
14	2	2	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	morphisms	morphism	NOUN	NNS	Number=Plur	17	nsubj	_	_
17	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	11	relcl	_	_
18	ways	way	NOUN	NNS	Number=Plur	17	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	coarse	coarse	ADV	RB	_	22	advmod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	graining	grain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	25	amod	_	_
23	open	open	ADJ	JJ	Degree=Pos	25	amod	_	_
24	Markov	Markov	PROPN	NNP	Number=Sing	25	compound	_	_
25	processes	process	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = We also extend the already known `black - boxing' functor from the category of open Markov processes to our double category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	extend	extend	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
5	already	already	ADV	RB	_	6	advmod	_	_
6	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
7	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	10	punct	_	SpaceAfter=No
8	black	black	ADJ	JJ	Degree=Pos	10	amod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	boxing	box	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	poss	_	SpaceAfter=No
11	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	12	punct	_	_
12	functor	functor	NOUN	NN	Number=Sing	3	dobj	_	_
13	from	from	ADP	IN	_	3	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	open	open	ADJ	JJ	Degree=Pos	19	amod	_	_
18	Markov	Markov	PROPN	NNP	Number=Sing	19	compound	_	_
19	processes	process	NOUN	NNS	Number=Plur	16	pobj	_	_
20	to	to	ADP	IN	_	3	prep	_	_
21	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	23	poss	_	_
22	double	double	ADJ	JJ	Degree=Pos	23	amod	_	_
23	category	category	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = Black - boxing sends any open Markov process to the linear relation between input and output data that holds in steady states, including nonequilibrium steady states where there is a nonzero flow of probability through the process.
1	Black	black	ADJ	JJ	Degree=Pos	3	compound	_	_
2	-	-	PUNCT	HYPH	PunctType=Dash	3	punct	_	_
3	boxing	boxing	NOUN	NN	Number=Sing	4	nsubj	_	_
4	sends	send	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	any	any	DET	DT	_	8	det	_	_
6	open	open	ADJ	JJ	Degree=Pos	8	amod	_	_
7	Markov	Markov	PROPN	NNP	Number=Sing	8	compound	_	_
8	process	process	NOUN	NN	Number=Sing	4	dobj	_	_
9	to	to	ADP	IN	_	4	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	linear	linear	PROPN	NNP	Number=Sing	12	compound	_	_
12	relation	relation	NOUN	NN	Number=Sing	9	pobj	_	_
13	between	between	ADP	IN	_	12	prep	_	_
14	input	input	NOUN	NN	Number=Sing	13	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	output	output	NOUN	NN	Number=Sing	14	conj	_	_
17	data	datum	NOUN	NNS	Number=Plur	14	conj	_	_
18	that	that	PRON	WDT	PronType=Rel	19	nsubj	_	_
19	holds	hold	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	steady	steady	ADJ	JJ	Degree=Pos	22	amod	_	_
22	states	state	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	prep	_	_
25	nonequilibrium	nonequilibrium	NOUN	NN	Number=Sing	27	nmod	_	_
26	steady	steady	ADJ	JJ	Degree=Pos	27	amod	_	_
27	states	state	NOUN	NNS	Number=Plur	24	pobj	_	_
28	where	where	SCONJ	WRB	_	30	advmod	_	_
29	there	there	PRON	EX	_	30	expl	_	_
30	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	relcl	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
32	nonzero	nonzero	NOUN	NN	Number=Sing	33	compound	_	_
33	flow	flow	NOUN	NN	Number=Sing	30	attr	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	probability	probability	NOUN	NN	Number=Sing	34	pobj	_	_
36	through	through	ADP	IN	_	33	prep	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	process	process	NOUN	NN	Number=Sing	36	pobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 8
# text = To extend black - boxing to a functor between double categories, we need to prove that black - boxing is compatible with coarse - graining.
1	To	to	PART	TO	_	2	aux	_	_
2	extend	extend	VERB	VB	VerbForm=Inf	14	advcl	_	_
3	black	black	ADJ	JJ	Degree=Pos	5	amod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	boxing	boxing	NOUN	NN	Number=Sing	2	dobj	_	_
6	to	to	ADP	IN	_	2	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	functor	functor	NOUN	NN	Number=Sing	6	pobj	_	_
9	between	between	ADP	IN	_	8	prep	_	_
10	double	double	ADJ	JJ	Degree=Pos	11	amod	_	_
11	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	need	need	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	prove	prove	VERB	VB	VerbForm=Inf	14	xcomp	_	_
17	that	that	SCONJ	IN	_	21	mark	_	_
18	black	black	NOUN	NN	Number=Sing	20	amod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	boxing	boxing	NOUN	NN	Number=Sing	21	nsubj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	ccomp	_	_
22	compatible	compatible	ADJ	JJ	Degree=Pos	21	acomp	_	_
23	with	with	ADP	IN	_	22	prep	_	_
24	coarse	coarse	ADV	RB	_	26	advmod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	graining	graining	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# doc_id = 651
# sent_id = 1
# text = It has been shown by Funk, Hofstra and Steinberg that any Grothendieck topos $ T $ is endowed with a canonical group object, called its isotropy group, which acts functorially on every object of the topos.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	4	nsubjpass	_	_
2	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	aux	_	_
3	been	be	AUX	VBN	Tense=Past|VerbForm=Part	4	auxpass	_	_
4	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	by	by	ADP	IN	_	4	agent	_	_
6	Funk	Funk	PROPN	NNP	Number=Sing	5	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	Hofstra	Hofstra	PROPN	NNP	Number=Sing	6	conj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	Steinberg	Steinberg	PROPN	NNP	Number=Sing	8	conj	_	_
11	that	that	SCONJ	IN	_	17	mark	_	_
12	any	any	DET	DT	_	13	det	_	_
13	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	17	nsubjpass	_	_
14	topos	topos	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	13	nmod	_	_
15	$ T $	$ t $	SYM	$	_	14	dobj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	auxpass	_	_
17	endowed	endow	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	relcl	_	_
18	with	with	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
20	canonical	canonical	ADJ	JJ	Degree=Pos	22	amod	_	_
21	group	group	NOUN	NN	Number=Sing	22	compound	_	_
22	object	object	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
24	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	4	conj	_	_
25	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	27	poss	_	_
26	isotropy	isotropy	ADJ	JJ	Degree=Pos	27	amod	_	_
27	group	group	NOUN	NN	Number=Sing	24	dobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
29	which	which	PRON	WDT	_	30	nsubj	_	_
30	acts	act	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	relcl	_	_
31	functorially	functorially	ADV	RB	_	30	advmod	_	_
32	on	on	ADP	IN	_	30	prep	_	_
33	every	every	DET	DT	_	34	det	_	_
34	object	object	NOUN	NN	Number=Sing	32	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	topos	topos	NOUN	NN	Number=Sing	35	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that this group is in fact the group of points of a localic group object, called the localic isotropy group, which also acts on every object, and in fact also on every internal locale and on every $ T $ - topos.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	6	mark	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	group	group	NOUN	NN	Number=Sing	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	fact	fact	NOUN	NN	Number=Sing	7	pobj	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	group	group	NOUN	NN	Number=Sing	19	nsubj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	points	point	NOUN	NNS	Number=Plur	11	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
15	localic	localic	ADJ	JJ	Degree=Pos	17	amod	_	_
16	group	group	NOUN	NN	Number=Sing	17	compound	_	_
17	object	object	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
19	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	6	ccomp	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
21	localic	localic	ADJ	JJ	Degree=Pos	23	amod	_	_
22	isotropy	isotropy	PROPN	NNP	Number=Sing	23	compound	_	_
23	group	group	NOUN	NN	Number=Sing	19	oprd	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
25	which	which	PRON	WDT	_	27	nsubj	_	_
26	also	also	ADV	RB	_	27	advmod	_	_
27	acts	act	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	relcl	_	_
28	on	on	ADP	IN	_	27	prep	_	_
29	every	every	DET	DT	_	30	det	_	_
30	object	object	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
33	in	in	ADP	IN	_	36	prep	_	_
34	fact	fact	NOUN	NN	Number=Sing	33	pobj	_	_
35	also	also	ADV	RB	_	36	advmod	_	_
36	on	on	ADP	IN	_	19	prep	_	_
37	every	every	DET	DT	_	39	det	_	_
38	internal	internal	ADJ	JJ	Degree=Pos	39	amod	_	_
39	locale	locale	NOUN	NN	Number=Sing	36	pobj	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	36	cc	_	_
41	on	on	ADP	IN	_	36	conj	_	_
42	every	every	DET	DT	_	45	det	_	_
43	$ T $	$ t $	SYM	$	_	45	compound	_	_
44	-	-	PUNCT	HYPH	PunctType=Dash	45	punct	_	_
45	topos	topos	NOUN	NN	Number=Sing	41	pobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = This new localic isotropy group has better functoriality and stability property than the original version and sheds some light on the phenomenon of higher isotropy observed for the ordinary isotropy group.
1	This	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
2	new	new	ADJ	JJ	Degree=Pos	5	amod	_	_
3	localic	localic	ADJ	JJ	Degree=Pos	5	amod	_	_
4	isotropy	isotropy	PROPN	NNP	Number=Sing	5	compound	_	_
5	group	group	PROPN	NNP	Number=Sing	6	nsubj	_	_
6	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	better	well	ADJ	JJR	Degree=Cmp	8	amod	_	_
8	functoriality	functoriality	NOUN	NN	Number=Sing	6	dobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	stability	stability	NOUN	NN	Number=Sing	11	compound	_	_
11	property	property	NOUN	NN	Number=Sing	8	conj	_	_
12	than	than	ADP	IN	_	8	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	original	original	ADJ	JJ	Degree=Pos	15	amod	_	_
15	version	version	NOUN	NN	Number=Sing	12	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
17	sheds	shed	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	conj	_	_
18	some	some	DET	DT	_	19	det	_	_
19	light	light	NOUN	NN	Number=Sing	17	dobj	_	_
20	on	on	ADP	IN	_	17	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	phenomenon	phenomenon	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	higher	high	ADJ	JJR	Degree=Cmp	25	amod	_	_
25	isotropy	isotropy	NOUN	NN	Number=Sing	23	pobj	_	_
26	observed	observe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	acl	_	_
27	for	for	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
29	ordinary	ordinary	ADJ	JJ	Degree=Pos	31	amod	_	_
30	isotropy	isotropy	ADJ	JJ	Degree=Pos	31	compound	_	_
31	group	group	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = We prove in particular using a localic version of the isotropy quotient that any geometric morphism can be factored uniquely as a connected atomic geometric morphism followed by a so called ``essentially anisotropic'' geometric morphism, and that connected atomic morphisms are exactly the quotients by open isotropy actions, hence providing a form of Galois theory for general (unpointed) connected atomic geometric morphisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	particular	particular	ADJ	JJ	Degree=Pos	3	amod	_	_
5	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	localic	localic	ADJ	JJ	Degree=Pos	8	amod	_	_
8	version	version	NOUN	NN	Number=Sing	5	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	isotropy	isotropy	NOUN	NN	Number=Sing	12	amod	_	_
12	quotient	quotient	NOUN	NN	Number=Sing	9	pobj	_	_
13	that	that	SCONJ	IN	_	19	mark	_	_
14	any	any	DET	DT	_	16	det	_	_
15	geometric	geometric	ADJ	JJ	Degree=Pos	16	amod	_	_
16	morphism	morphism	NOUN	NN	Number=Sing	19	nsubjpass	_	_
17	can	can	AUX	MD	VerbForm=Fin	19	aux	_	_
18	be	be	AUX	VB	VerbForm=Inf	19	auxpass	_	_
19	factored	factor	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
20	uniquely	uniquely	ADV	RB	_	19	advmod	_	_
21	as	as	ADP	IN	_	19	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
23	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
24	atomic	atomic	ADJ	JJ	Degree=Pos	26	amod	_	_
25	geometric	geometric	ADJ	JJ	Degree=Pos	26	amod	_	_
26	morphism	morphism	NOUN	NN	Number=Sing	21	pobj	_	_
27	followed	follow	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	acl	_	_
28	by	by	ADP	IN	_	27	agent	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
30	so	so	ADV	RB	_	31	advmod	_	_
31	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	35	amod	_	_
32	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	35	punct	_	SpaceAfter=No
33	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	35	punct	_	SpaceAfter=No
34	essentially	essentially	ADV	RB	_	35	advmod	_	_
35	anisotropic	anisotropic	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
36	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	35	punct	_	_
37	geometric	geometric	ADJ	JJ	Degree=Pos	38	amod	_	_
38	morphism	morphism	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
41	that	that	SCONJ	IN	_	45	mark	_	_
42	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	44	amod	_	_
43	atomic	atomic	ADJ	JJ	Degree=Pos	44	amod	_	_
44	morphisms	morphism	NOUN	NNS	Number=Plur	45	nsubj	_	_
45	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	19	conj	_	_
46	exactly	exactly	ADV	RB	_	48	advmod	_	_
47	the	the	DET	DT	Definite=Def|PronType=Art	48	det	_	_
48	quotients	quotient	NOUN	NNS	Number=Plur	45	attr	_	_
49	by	by	ADP	IN	_	48	prep	_	_
50	open	open	ADJ	JJ	Degree=Pos	52	amod	_	_
51	isotropy	isotropy	PROPN	NNP	Number=Sing	52	compound	_	_
52	actions	action	NOUN	NNS	Number=Plur	49	pobj	_	SpaceAfter=No
53	,	,	PUNCT	,	PunctType=Comm	45	punct	_	_
54	hence	hence	ADV	RB	_	55	advmod	_	_
55	providing	provide	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	45	advcl	_	_
56	a	a	DET	DT	Definite=Ind|PronType=Art	57	det	_	_
57	form	form	NOUN	NN	Number=Sing	55	dobj	_	_
58	of	of	ADP	IN	_	57	prep	_	_
59	Galois	Galois	PROPN	NNP	Number=Sing	60	compound	_	_
60	theory	theory	NOUN	NN	Number=Sing	58	pobj	_	_
61	for	for	ADP	IN	_	60	prep	_	_
62	general	general	ADJ	JJ	Degree=Pos	69	amod	_	_
63	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	69	punct	_	SpaceAfter=No
64	unpointed	unpointed	ADJ	JJ	Degree=Pos	69	amod	_	SpaceAfter=No
65	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	69	punct	_	_
66	connected	connect	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	69	amod	_	_
67	atomic	atomic	ADJ	JJ	Degree=Pos	69	amod	_	_
68	geometric	geometric	ADJ	JJ	Degree=Pos	69	amod	_	_
69	morphisms	morphism	NOUN	NNS	Number=Plur	61	pobj	_	SpaceAfter=No
70	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 652
# sent_id = 1
# text = The present article is the first of a series whose goal is to define a logical formalism in which it is possible to reason about genetics.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	present	present	ADJ	JJ	Degree=Pos	3	amod	_	_
3	article	article	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	first	first	ADJ	JJ	Degree=Pos	4	attr	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	series	series	NOUN	NN	Number=Sing	7	pobj	_	_
10	whose	whose	DET	WP$	Poss=Yes	11	poss	_	_
11	goal	goal	NOUN	NN	Number=Sing	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	relcl	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	define	define	VERB	VB	VerbForm=Inf	12	xcomp	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	logical	logical	ADJ	JJ	Degree=Pos	17	amod	_	_
17	formalism	formalism	NOUN	NN	Number=Sing	14	dobj	_	_
18	in	in	ADP	IN	_	21	prep	_	_
19	which	which	PRON	WDT	_	18	pobj	_	_
20	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	21	nsubj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
22	possible	possible	ADJ	JJ	Degree=Pos	21	acomp	_	_
23	to	to	PART	TO	_	24	aux	_	_
24	reason	reason	VERB	VB	VerbForm=Inf	21	xcomp	_	_
25	about	about	ADP	IN	_	24	prep	_	_
26	genetics	genetic	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper, we introduce the main concepts of our language whose domain of discourse consists of a class of limit - sketches and their associated models.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	main	main	ADJ	JJ	Degree=Pos	9	amod	_	_
9	concepts	concept	NOUN	NNS	Number=Plur	6	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	12	poss	_	_
12	language	language	NOUN	NN	Number=Sing	10	pobj	_	_
13	whose	whose	DET	WP$	Poss=Yes	14	poss	_	_
14	domain	domain	NOUN	NN	Number=Sing	17	nsubj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	discourse	discourse	NOUN	NN	Number=Sing	15	pobj	_	_
17	consists	consist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	relcl	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	class	class	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	limit	limit	NOUN	NN	Number=Sing	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	sketches	sketch	NOUN	NNS	Number=Plur	21	pobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	28	poss	_	_
27	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	amod	_	_
28	models	model	NOUN	NNS	Number=Plur	24	conj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = While our program will aim to show that different phenomena of genetics can be modeled by changing the category in which the models take their values, in this paper, we study models in the category of sets to capture mutation mechanisms such as insertions, deletions, substitutions, duplications and inversions.
1	While	while	SCONJ	IN	_	5	mark	_	_
2	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	3	poss	_	_
3	program	program	NOUN	NN	Number=Sing	5	nsubj	_	_
4	will	will	AUX	MD	VerbForm=Fin	5	aux	_	_
5	aim	aim	VERB	VB	VerbForm=Inf	33	advcl	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	show	show	VERB	VB	VerbForm=Inf	5	xcomp	_	_
8	that	that	SCONJ	IN	_	15	mark	_	_
9	different	different	ADJ	JJ	Degree=Pos	10	amod	_	_
10	phenomena	phenomenon	NOUN	NNS	Number=Plur	15	nsubjpass	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	genetics	genetic	NOUN	NNS	Number=Plur	11	pobj	_	_
13	can	can	AUX	MD	VerbForm=Fin	15	aux	_	_
14	be	be	AUX	VB	VerbForm=Inf	15	auxpass	_	_
15	modeled	model	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	ccomp	_	_
16	by	by	ADP	IN	_	15	prep	_	_
17	changing	change	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	pcomp	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	category	category	NOUN	NN	Number=Sing	17	dobj	_	_
20	in	in	ADP	IN	_	24	prep	_	_
21	which	which	PRON	WDT	_	20	pobj	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	models	model	NOUN	NNS	Number=Plur	24	nsubj	_	_
24	take	take	VERB	VBP	Tense=Pres|VerbForm=Fin	19	relcl	_	_
25	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	26	poss	_	_
26	values	value	NOUN	NNS	Number=Plur	24	dobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
28	in	in	ADP	IN	_	17	prep	_	_
29	this	this	DET	DT	Number=Sing|PronType=Dem	30	det	_	_
30	paper	paper	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
32	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	33	nsubj	_	_
33	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
34	models	model	NOUN	NNS	Number=Plur	33	dobj	_	_
35	in	in	ADP	IN	_	33	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
37	category	category	NOUN	NN	Number=Sing	35	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	sets	set	NOUN	NNS	Number=Plur	38	pobj	_	_
40	to	to	PART	TO	_	41	aux	_	_
41	capture	capture	VERB	VB	VerbForm=Inf	33	advcl	_	_
42	mutation	mutation	NOUN	NN	Number=Sing	43	compound	_	_
43	mechanisms	mechanism	NOUN	NNS	Number=Plur	41	dobj	_	_
44	such	such	ADJ	JJ	Degree=Pos	45	amod	_	_
45	as	as	ADP	IN	_	43	prep	_	_
46	insertions	insertion	NOUN	NNS	Number=Plur	45	pobj	_	SpaceAfter=No
47	,	,	PUNCT	,	PunctType=Comm	46	punct	_	_
48	deletions	deletion	NOUN	NNS	Number=Plur	46	conj	_	SpaceAfter=No
49	,	,	PUNCT	,	PunctType=Comm	48	punct	_	_
50	substitutions	substitution	NOUN	NNS	Number=Plur	48	conj	_	SpaceAfter=No
51	,	,	PUNCT	,	PunctType=Comm	50	punct	_	_
52	duplications	duplication	NOUN	NNS	Number=Plur	50	conj	_	_
53	and	and	CCONJ	CC	ConjType=Cmp	52	cc	_	_
54	inversions	inversion	NOUN	NNS	Number=Plur	52	conj	_	SpaceAfter=No
55	.	.	PUNCT	.	PunctType=Peri	33	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show how the proposed formalism can be used for constructing multiple sequence alignments with an emphasis on mutation mechanisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	how	how	SCONJ	WRB	_	9	advmod	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	proposed	propose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	amod	_	_
6	formalism	formalism	NOUN	NN	Number=Sing	9	nsubjpass	_	_
7	can	can	AUX	MD	VerbForm=Fin	9	aux	_	_
8	be	be	AUX	VB	VerbForm=Inf	9	auxpass	_	_
9	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
10	for	for	ADP	IN	_	9	prep	_	_
11	constructing	construct	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	pcomp	_	_
12	multiple	multiple	ADJ	JJ	Degree=Pos	14	amod	_	_
13	sequence	sequence	NOUN	NN	Number=Sing	14	compound	_	_
14	alignments	alignment	NOUN	NNS	Number=Plur	11	dobj	_	_
15	with	with	ADP	IN	_	11	prep	_	_
16	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	emphasis	emphasis	NOUN	NN	Number=Sing	15	pobj	_	_
18	on	on	ADP	IN	_	17	prep	_	_
19	mutation	mutation	NOUN	NN	Number=Sing	20	compound	_	_
20	mechanisms	mechanism	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 653
# sent_id = 1
# text = We show that a Hopf monad on a $ * $ - autonomous category lifts $ * $ - autonomous structure to the category of algebras precisely when there is an algebra structure on the dualizing object.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	6	mark	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	Hopf	Hopf	PROPN	NNP	Number=Sing	6	compound	_	_
6	monad	monad	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
7	on	on	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
9	$ * $	$ * $	SYM	$	_	11	advmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	autonomous	autonomous	ADJ	JJ	Degree=Pos	12	amod	_	_
12	category	category	NOUN	NN	Number=Sing	13	compound	_	_
13	lifts	lift	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	pobj	_	_
14	$ * $	$ * $	SYM	$	_	16	advmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	autonomous	autonomous	ADJ	JJ	Degree=Pos	17	amod	_	_
17	structure	structure	NOUN	NN	Number=Sing	13	dobj	_	_
18	to	to	ADP	IN	_	13	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	algebras	algebra	NOUN	NNS	Number=Plur	21	pobj	_	_
23	precisely	precisely	ADV	RB	_	24	advmod	_	_
24	when	when	SCONJ	WRB	_	26	advmod	_	_
25	there	there	PRON	EX	_	26	expl	_	_
26	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	advcl	_	_
27	an	an	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	algebra	algebra	NOUN	NN	Number=Sing	29	compound	_	_
29	structure	structure	NOUN	NN	Number=Sing	26	attr	_	_
30	on	on	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	dualizing	dualize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	33	amod	_	_
33	object	object	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Our proof is based on Pastro's characterization of $ * $ - autonomous (co)monads as linearly distributive (co)monads with negation.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	proof	proof	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	on	on	ADP	IN	_	4	prep	_	_
6	Pastro	Pastro	PROPN	NNP	Number=Sing	8	poss	_	SpaceAfter=No
7	's	's	PART	POS	_	6	case	_	_
8	characterization	characterization	NOUN	NN	Number=Sing	5	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	$ * $	$ * $	SYM	$	_	12	advmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	autonomous	autonomous	ADJ	JJ	Degree=Pos	14	amod	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
14	co)monads	co)monad	NOUN	NNS	Number=Plur	9	pobj	_	_
15	as	as	ADP	IN	_	14	prep	_	_
16	linearly	linearly	ADV	RB	_	17	advmod	_	_
17	distributive	distributive	ADJ	JJ	Degree=Pos	15	amod	_	_
18	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	19	punct	_	SpaceAfter=No
19	co)monads	co)monad	NOUN	NNS	Number=Plur	8	appos	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	negation	negation	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 654
# sent_id = 1
# text = We study the structure of the category of polynomials in a locally cartesian closed category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	structure	structure	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	polynomials	polynomial	NOUN	NNS	Number=Plur	8	pobj	_	_
10	in	in	ADP	IN	_	2	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
12	locally	locally	ADV	RB	_	13	advmod	_	_
13	cartesian	cartesian	ADJ	JJ	Degree=Pos	15	amod	_	_
14	closed	closed	ADJ	JJ	Degree=Pos	15	amod	_	_
15	category	category	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Formalizing the conceptual view that polynomials are constructed from sums and products, we characterize this category in terms of the composite of the pseudomonads which freely add fibred sums and products to fibrations.
1	Formalizing	formalizing	ADJ	JJ	Degree=Pos	15	advcl	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	conceptual	conceptual	ADJ	JJ	Degree=Pos	4	amod	_	_
4	view	view	NOUN	NN	Number=Sing	1	dobj	_	_
5	that	that	SCONJ	IN	_	8	mark	_	_
6	polynomials	polynomial	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	acl	_	_
9	from	from	ADP	IN	_	8	prep	_	_
10	sums	sum	NOUN	NNS	Number=Plur	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	products	product	NOUN	NNS	Number=Plur	10	conj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
14	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	15	nsubj	_	_
15	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	this	this	DET	DT	Number=Sing|PronType=Dem	17	det	_	_
17	category	category	NOUN	NN	Number=Sing	15	dobj	_	_
18	in	in	ADP	IN	_	15	prep	_	_
19	terms	term	NOUN	NNS	Number=Plur	18	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	composite	composite	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	pseudomonads	pseudomonad	NOUN	NNS	Number=Plur	23	pobj	_	_
26	which	which	PRON	WDT	_	28	nsubj	_	_
27	freely	freely	ADV	RB	_	28	advmod	_	_
28	add	add	VERB	VBP	Tense=Pres|VerbForm=Fin	25	relcl	_	_
29	fibred	fibred	ADJ	JJ	Degree=Pos	30	amod	_	_
30	sums	sum	NOUN	NNS	Number=Plur	28	dobj	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
32	products	product	NOUN	NNS	Number=Plur	30	conj	_	_
33	to	to	ADP	IN	_	28	prep	_	_
34	fibrations	fibration	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 3
# text = The composite pseudomonad structure corresponds to a pseudo - distributive law between these two pseudomonads, which exists if and only if the base category is locally cartesian closed.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	composite	composite	ADJ	JJ	Degree=Pos	3	amod	_	_
3	pseudomonad	pseudomonad	NOUN	NNS	Number=Plur	4	compound	_	_
4	structure	structure	NOUN	NN	Number=Sing	5	nsubj	_	_
5	corresponds	correspond	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	pseudo	pseudo	NOUN	NN	Number=Sing	10	npadvmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	distributive	distributive	ADJ	JJ	Degree=Pos	11	amod	_	_
11	law	law	NOUN	NN	Number=Sing	6	pobj	_	_
12	between	between	ADP	IN	_	11	prep	_	_
13	these	these	DET	DT	Number=Plur|PronType=Dem	15	det	_	_
14	two	two	NUM	CD	NumType=Card	15	nummod	_	_
15	pseudomonads	pseudomonad	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	which	which	PRON	WDT	_	18	nsubj	_	_
18	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	relcl	_	_
19	if	if	SCONJ	IN	_	18	prep	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	only	only	ADV	RB	_	26	advmod	_	_
22	if	if	SCONJ	IN	_	26	mark	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	base	base	NOUN	NN	Number=Sing	25	compound	_	_
25	category	category	NOUN	NN	Number=Sing	26	nsubj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	advcl	_	_
27	locally	locally	ADV	RB	_	28	advmod	_	_
28	cartesian	cartesian	ADJ	JJ	Degree=Pos	29	amod	_	_
29	closed	closed	ADJ	JJ	Degree=Pos	26	acomp	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 655
# sent_id = 1
# text = The Faa di Bruno construction, introduced by Cockett and Seely, constructs a comonad Faa whose coalgebras are precisely Cartesian differential categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
2	Faa	Faa	PROPN	NNP	Number=Sing	4	compound	_	_
3	di	di	PROPN	NNP	Number=Sing	4	compound	_	_
4	Bruno	Bruno	PROPN	NNP	Number=Sing	5	compound	_	_
5	construction	construction	NOUN	NN	Number=Sing	13	nsubj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	acl	_	_
8	by	by	ADP	IN	_	7	agent	_	_
9	Cockett	Cockett	PROPN	NNP	Number=Sing	8	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	Seely	Seely	PROPN	NNP	Number=Sing	9	conj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
13	constructs	construct	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	comonad	comonad	NOUN	NNS	Number=Plur	13	dobj	_	_
16	Faa	Faa	PROPN	NNP	Number=Sing	13	npadvmod	_	_
17	whose	whose	DET	WP$	Poss=Yes	18	poss	_	_
18	coalgebras	coalgebra	NOUN	NNS	Number=Plur	19	nsubj	_	_
19	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	16	relcl	_	_
20	precisely	precisely	ADV	RB	_	21	advmod	_	_
21	Cartesian	cartesian	ADJ	JJ	Degree=Pos	23	amod	_	_
22	differential	differential	ADJ	JJ	Degree=Pos	23	amod	_	_
23	categories	category	NOUN	NNS	Number=Plur	19	attr	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 2
# text = In other words, for a Cartesian left additive category $ X $ , $ Faa(X) $ is the cofree Cartesian differential category over X. Composition in these cofree Cartesian differential categories is based on the Faa di Bruno formula, and corresponds to composition of differential forms.
1	In	in	ADP	IN	_	8	prep	_	_
2	other	other	ADJ	JJ	Degree=Pos	3	amod	_	_
3	words	word	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
5	for	for	SCONJ	IN	_	8	mark	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	Cartesian	Cartesian	PROPN	NNP	Number=Sing	8	nsubj	_	_
8	left	leave	VERB	VBD	Tense=Past|VerbForm=Fin	14	advcl	_	_
9	additive	additive	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	8	dobj	_	_
11	$ X $	$ x $	SYM	$	_	8	oprd	_	_
12	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
13	$ Faa(X) $	$ faa(x) $	SYM	$	_	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
16	cofree	cofree	ADJ	JJ	Degree=Pos	19	amod	_	_
17	Cartesian	cartesian	ADJ	JJ	Degree=Pos	19	amod	_	_
18	differential	differential	ADJ	JJ	Degree=Pos	19	amod	_	_
19	category	category	NOUN	NN	Number=Sing	30	nsubjpass	_	_
20	over	over	ADP	IN	_	19	prep	_	_
21	X.	X.	PROPN	NNP	Number=Sing	22	compound	_	_
22	Composition	Composition	PROPN	NNP	Number=Sing	20	pobj	_	_
23	in	in	ADP	IN	_	19	prep	_	_
24	these	these	DET	DT	Number=Plur|PronType=Dem	28	det	_	_
25	cofree	cofree	ADJ	JJ	Degree=Pos	28	amod	_	_
26	Cartesian	cartesian	ADJ	JJ	Degree=Pos	28	amod	_	_
27	differential	differential	ADJ	JJ	Degree=Pos	28	amod	_	_
28	categories	category	NOUN	NNS	Number=Plur	23	pobj	_	_
29	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	auxpass	_	_
30	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	prep	_	_
31	on	on	ADP	IN	_	30	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
33	Faa	Faa	PROPN	NNP	Number=Sing	35	compound	_	_
34	di	di	PROPN	NNP	Number=Sing	35	compound	_	_
35	Bruno	Bruno	PROPN	NNP	Number=Sing	36	compound	_	_
36	formula	formula	NOUN	NN	Number=Sing	31	pobj	_	SpaceAfter=No
37	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
38	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
39	corresponds	correspond	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	conj	_	_
40	to	to	ADP	IN	_	39	prep	_	_
41	composition	composition	NOUN	NN	Number=Sing	40	pobj	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	differential	differential	ADJ	JJ	Degree=Pos	44	amod	_	_
44	forms	form	NOUN	NNS	Number=Plur	42	pobj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 3
# text = This composition, however, is somewhat complex and difficult to work with.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	composition	composition	NOUN	NN	Number=Sing	6	nsubj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
4	however	however	ADV	RB	_	6	advmod	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	somewhat	somewhat	ADV	RB	_	8	advmod	_	_
8	complex	complex	ADJ	JJ	Degree=Pos	6	acomp	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	difficult	difficult	ADJ	JJ	Degree=Pos	8	conj	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	work	work	VERB	VB	VerbForm=Inf	6	xcomp	_	_
13	with	with	ADP	IN	_	12	prep	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = In this paper we provide an alternative construction of cofree Cartesian differential categories inspired by tangent categories.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	alternative	alternative	ADJ	JJ	Degree=Pos	8	amod	_	_
8	construction	construction	NOUN	NN	Number=Sing	5	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	cofree	cofree	ADJ	JJ	Degree=Pos	13	amod	_	_
11	Cartesian	cartesian	ADJ	JJ	Degree=Pos	13	amod	_	_
12	differential	differential	ADJ	JJ	Degree=Pos	13	amod	_	_
13	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	_
14	inspired	inspire	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	acl	_	_
15	by	by	ADP	IN	_	14	agent	_	_
16	tangent	tangent	ADJ	JJ	Degree=Pos	17	amod	_	_
17	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = In particular, composition defined here is based on the fact that the chain rule for Cartesian differential categories can be expressed using the tangent functor, which simplifies the formulation of the higher order chain rule.
1	In	in	ADP	IN	_	8	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
4	composition	composition	NOUN	NN	Number=Sing	8	nsubjpass	_	_
5	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	acl	_	_
6	here	here	ADV	RB	PronType=Dem	5	advmod	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	on	on	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	fact	fact	NOUN	NN	Number=Sing	9	pobj	_	_
12	that	that	SCONJ	IN	_	22	mark	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	chain	chain	NOUN	NN	Number=Sing	15	compound	_	_
15	rule	rule	NOUN	NN	Number=Sing	22	nsubjpass	_	_
16	for	for	ADP	IN	_	15	prep	_	_
17	Cartesian	cartesian	ADJ	JJ	Degree=Pos	19	amod	_	_
18	differential	differential	ADJ	JJ	Degree=Pos	19	amod	_	_
19	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	_
20	can	can	AUX	MD	VerbForm=Fin	22	aux	_	_
21	be	be	AUX	VB	VerbForm=Inf	22	auxpass	_	_
22	expressed	express	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acl	_	_
23	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	xcomp	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	tangent	tangent	NOUN	NN	Number=Sing	26	compound	_	_
26	functor	functor	NOUN	NN	Number=Sing	23	dobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
28	which	which	PRON	WDT	_	29	nsubj	_	_
29	simplifies	simplify	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	relcl	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	formulation	formulation	NOUN	NN	Number=Sing	29	dobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
34	higher	high	ADJ	JJR	Degree=Cmp	35	amod	_	_
35	order	order	NOUN	NN	Number=Sing	36	compound	_	_
36	chain	chain	NOUN	NN	Number=Sing	37	compound	_	_
37	rule	rule	NOUN	NN	Number=Sing	32	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 656
# sent_id = 1
# text = In this paper, we introduce the concept of a topological space in the topos $ M - Set $ of $ M $ - sets, for a monoid $ M $ .
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	concept	concept	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	topological	topological	ADJ	JJ	Degree=Pos	12	amod	_	_
12	space	space	NOUN	NN	Number=Sing	9	pobj	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	topos	topos	NOUN	NN	Number=Sing	13	pobj	_	_
16	$ M - Set $	$ m - set $	SYM	$	_	15	appos	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	$ M $	$ m $	SYM	$	_	20	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	sets	set	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
22	for	for	ADP	IN	_	6	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	monoid	monoid	NOUN	NN	Number=Sing	22	pobj	_	_
25	$ M $	$ m $	SYM	$	_	22	pobj	_	_
26	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = We do this by replacing the notion of open "subset" by open "subobject" in the definition of a topology.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	do	do	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	this	this	PRON	DT	Number=Sing|PronType=Dem	2	dobj	_	_
4	by	by	ADP	IN	_	2	prep	_	_
5	replacing	replace	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	pcomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	notion	notion	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	open	open	ADJ	JJ	Degree=Pos	11	amod	_	_
10	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	11	punct	_	SpaceAfter=No
11	subset	subset	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
12	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	11	punct	_	_
13	by	by	ADP	IN	_	7	prep	_	_
14	open	open	ADJ	JJ	Degree=Pos	16	amod	_	_
15	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	16	punct	_	SpaceAfter=No
16	subobject	subobject	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
17	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	16	punct	_	_
18	in	in	ADP	IN	_	16	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	definition	definition	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
23	topology	topology	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We prove that the resulting category has an open subobject classifier, which is the counterpart of the Sierpinski space in this topos.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	7	nsubj	_	_
7	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	open	open	ADJ	JJ	Degree=Pos	11	amod	_	_
10	subobject	subobject	NOUN	NN	Number=Sing	11	compound	_	_
11	classifier	classifier	NOUN	NN	Number=Sing	7	dobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	which	which	PRON	WDT	_	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	relcl	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	counterpart	counterpart	NOUN	NN	Number=Sing	14	attr	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	Sierpinski	Sierpinski	PROPN	NNP	Number=Sing	20	compound	_	_
20	space	space	NOUN	NN	Number=Sing	17	pobj	_	_
21	in	in	ADP	IN	_	16	prep	_	_
22	this	this	DET	DT	Number=Sing|PronType=Dem	23	det	_	_
23	topos	topos	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We also study the relation between the given notion of topology and the notion of a poset in this universe.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	relation	relation	NOUN	NN	Number=Sing	3	dobj	_	_
6	between	between	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	amod	_	_
9	notion	notion	NOUN	NN	Number=Sing	6	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	topology	topology	NOUN	NN	Number=Sing	10	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	notion	notion	NOUN	NN	Number=Sing	9	conj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	poset	poset	NOUN	NN	Number=Sing	15	pobj	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	this	this	DET	DT	Number=Sing|PronType=Dem	20	det	_	_
20	universe	universe	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = In fact, the counterpart of the specialization pre - order is given for topological spaces in $ M - Set $ , and it is shown that, similar to the classic case, for a special kind of topological spaces in $ M - Set $ , namely $ T_0 $ ones, it is a partial order.
1	In	in	ADP	IN	_	13	prep	_	_
2	fact	fact	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	counterpart	counterpart	NOUN	NN	Number=Sing	13	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	specialization	specialization	NOUN	NN	Number=Sing	6	pobj	_	_
9	pre	pre	NOUN	NN	Number=Sing	5	nmod	_	_
10	-	-	PUNCT	:	_	13	punct	_	_
11	order	order	NOUN	NN	Number=Sing	13	nsubjpass	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
14	for	for	ADP	IN	_	13	prep	_	_
15	topological	topological	ADJ	JJ	Degree=Pos	16	amod	_	_
16	spaces	space	NOUN	NNS	Number=Plur	14	pobj	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	$ M - Set $	$ m - set $	SYM	$	_	17	pobj	_	_
19	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
21	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	23	nsubjpass	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	auxpass	_	_
23	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	conj	_	_
24	that	that	SCONJ	IN	_	47	mark	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	47	punct	_	_
26	similar	similar	ADJ	JJ	Degree=Pos	47	advcl	_	_
27	to	to	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
29	classic	classic	ADJ	JJ	Degree=Pos	30	amod	_	_
30	case	case	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	47	punct	_	_
32	for	for	ADP	IN	_	47	prep	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
34	special	special	ADJ	JJ	Degree=Pos	35	amod	_	_
35	kind	kind	NOUN	NN	Number=Sing	32	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	topological	topological	ADJ	JJ	Degree=Pos	38	amod	_	_
38	spaces	space	NOUN	NNS	Number=Plur	36	pobj	_	_
39	in	in	ADP	IN	_	38	prep	_	_
40	$ M - Set $	$ m - set $	SYM	$	_	39	pobj	_	_
41	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
42	namely	namely	ADV	RB	_	43	advmod	_	_
43	$ T_0 $	$ t_0 $	SYM	$	_	44	nummod	_	_
44	ones	one	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
45	,	,	PUNCT	,	PunctType=Comm	47	punct	_	_
46	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	47	nsubj	_	_
47	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	ccomp	_	_
48	a	a	DET	DT	Definite=Ind|PronType=Art	50	det	_	_
49	partial	partial	ADJ	JJ	Degree=Pos	50	amod	_	_
50	order	order	NOUN	NN	Number=Sing	47	attr	_	SpaceAfter=No
51	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# sent_id = 6
# text = Furthermore, we obtain the universal $ T_0 $ space, and give the adjunction between topological spaces and $ T_0 $ posets, in $ M - Set $ .
1	Furthermore	furthermore	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
6	universal	universal	ADJ	JJ	Degree=Pos	8	amod	_	_
7	$ T_0 $	$ t_0 $	SYM	$	_	8	nmod	_	_
8	space	space	NOUN	NN	Number=Sing	4	dobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
11	give	give	VERB	VB	VerbForm=Inf	4	conj	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	adjunction	adjunction	NOUN	NN	Number=Sing	11	dobj	_	_
14	between	between	ADP	IN	_	13	prep	_	_
15	topological	topological	ADJ	JJ	Degree=Pos	16	amod	_	_
16	spaces	space	NOUN	NNS	Number=Plur	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	$ T_0 $	$ t_0 $	SYM	$	_	19	nmod	_	_
19	posets	poset	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
21	in	in	ADP	IN	_	11	prep	_	_
22	$ M - Set $	$ m - set $	SYM	$	_	21	pobj	_	_
23	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 657
# sent_id = 1
# text = In this paper, we prove that there is a canonical homotopy $ (n+1) $ - algebra structure on the shifted operadic deformation complex $ Def(e_ntomathcal{P})[ - n] $ for any operad $ mathcal{P} $ and a map of operads $ fcolon e_ntomathcal{P} $ .
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	9	mark	_	_
8	there	there	PRON	EX	_	9	expl	_	_
9	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	canonical	canonical	ADJ	JJ	Degree=Pos	12	amod	_	_
12	homotopy	homotopy	NOUN	NN	Number=Sing	9	attr	_	_
13	$ (n+1) $	$ (n+1) $	PROPN	NNP	Number=Sing	15	nummod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	algebra	algebra	NOUN	NN	Number=Sing	16	compound	_	_
16	structure	structure	NOUN	NN	Number=Sing	12	appos	_	_
17	on	on	ADP	IN	_	12	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
19	shifted	shifted	ADJ	JJ	Degree=Pos	22	amod	_	_
20	operadic	operadic	ADJ	JJ	Degree=Pos	22	amod	_	_
21	deformation	deformation	NOUN	NN	Number=Sing	22	compound	_	_
22	complex	complex	NOUN	NN	Number=Sing	17	pobj	_	_
23	$ Def(e_ntomathcal{P})[ - n] $	$ def(e_ntomathcal{p})[ - n] $	SYM	$	_	12	appos	_	_
24	for	for	ADP	IN	_	12	prep	_	_
25	any	any	DET	DT	_	27	det	_	_
26	operad	operad	ADJ	JJ	Degree=Pos	27	amod	_	_
27	$ mathcal{P} $	$ mathcal{p} $	SYM	$	_	24	pobj	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
30	map	map	NOUN	NN	Number=Sing	27	conj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	operads	operad	NOUN	NNS	Number=Plur	31	pobj	_	_
33	$ fcolon e_ntomathcal{P} $	$ fcolon e_ntomathcal{p} $	SYM	$	_	12	appos	_	_
34	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = This result generalizes a result of Tamarkin, who considered the case $ mathcal{P}=End_Op(X) $ .
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	result	result	NOUN	NN	Number=Sing	3	nsubj	_	_
3	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	result	result	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Tamarkin	Tamarkin	PROPN	NNP	Number=Sing	6	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	who	who	PRON	WP	_	10	nsubj	_	_
10	considered	consider	VERB	VBD	Tense=Past|VerbForm=Fin	7	relcl	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	case	case	NOUN	NN	Number=Sing	13	nsubj	_	_
13	$ mathcal{P}=End_Op(X) $	$ mathcal{p}=end_op(x) $	SYM	$	_	10	ccomp	_	_
14	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Another more computational proof of the same result was recently sketched by Calaque and Willwacher.
1	Another	another	DET	DT	_	4	det	_	_
2	more	more	ADV	RBR	Degree=Cmp	3	advmod	_	_
3	computational	computational	ADJ	JJ	Degree=Pos	4	amod	_	_
4	proof	proof	NOUN	NN	Number=Sing	11	nsubjpass	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	same	same	ADJ	JJ	Degree=Pos	8	amod	_	_
8	result	result	NOUN	NN	Number=Sing	5	pobj	_	_
9	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	11	auxpass	_	_
10	recently	recently	ADV	RB	_	11	advmod	_	_
11	sketched	sketch	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
12	by	by	ADP	IN	_	11	agent	_	_
13	Calaque	Calaque	PROPN	NNP	Number=Sing	12	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	Willwacher	Willwacher	PROPN	NNP	Number=Sing	13	conj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 4
# text = Our method combines the one of Tamarkin, with the categorical algebra on the category of symmetric sequences, introduced by Rezk and further developed by Kapranov - Manin and Fresse.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	method	method	NOUN	NN	Number=Sing	3	nsubj	_	_
3	combines	combine	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	one	one	NUM	CD	NumType=Card	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Tamarkin	Tamarkin	PROPN	NNP	Number=Sing	6	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
9	with	with	ADP	IN	_	3	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	categorical	categorical	ADJ	JJ	Degree=Pos	12	amod	_	_
12	algebra	algebra	NOUN	NNS	Number=Plur	9	pobj	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	symmetric	symmetric	ADJ	JJ	Degree=Pos	18	amod	_	_
18	sequences	sequence	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
20	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
21	by	by	ADP	IN	_	20	agent	_	_
22	Rezk	Rezk	PROPN	NNP	Number=Sing	21	pobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
24	further	far	ADV	RB	_	25	advmod	_	_
25	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	conj	_	_
26	by	by	ADP	IN	_	25	agent	_	_
27	Kapranov	Kapranov	PROPN	NNP	Number=Sing	29	compound	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	Manin	Manin	PROPN	NNP	Number=Sing	26	pobj	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
31	Fresse	Fresse	PROPN	NNP	Number=Sing	29	conj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = We define suitable deformation functors on $ n $ - coalgebras, which are considered as the "non - commutative" base of deformation, prove their representability, and translate properties of the functors to the corresponding properties of the representing objects.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	suitable	suitable	ADJ	JJ	Degree=Pos	5	amod	_	_
4	deformation	deformation	NOUN	NN	Number=Sing	5	compound	_	_
5	functors	functor	NOUN	NNS	Number=Plur	2	dobj	_	_
6	on	on	ADP	IN	_	5	prep	_	_
7	$ n $	$ n $	SYM	$	_	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	coalgebras	coalgebras	PROPN	NNP	Number=Sing	6	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	which	which	PRON	WDT	_	13	nsubjpass	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	auxpass	_	_
13	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	relcl	_	_
14	as	as	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
16	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	21	punct	_	SpaceAfter=No
17	non	non	ADJ	JJ	Degree=Pos	19	amod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	commutative	commutative	ADJ	JJ	Degree=Pos	21	amod	_	SpaceAfter=No
20	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	21	punct	_	_
21	base	base	NOUN	NN	Number=Sing	14	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	deformation	deformation	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
25	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
26	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	27	poss	_	_
27	representability	representability	NOUN	NN	Number=Sing	25	dobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
30	translate	translate	VERB	VB	VerbForm=Inf	25	conj	_	_
31	properties	property	NOUN	NNS	Number=Plur	30	dobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
34	functors	functor	NOUN	NNS	Number=Plur	32	pobj	_	_
35	to	to	ADP	IN	_	30	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
37	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	38	amod	_	_
38	properties	property	NOUN	NNS	Number=Plur	35	pobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	the	the	DET	DT	Definite=Def|PronType=Art	42	det	_	_
41	representing	represent	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	42	amod	_	_
42	objects	object	NOUN	NNS	Number=Plur	39	pobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = A new point, which makes the method more powerful, is to consider the argument of our deformation theory as an object of the category of symmetric sequences of dg vector spaces, not as just a single dg vector space .
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	new	new	ADJ	JJ	Degree=Pos	3	amod	_	_
3	point	point	NOUN	NN	Number=Sing	12	nsubj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
5	which	which	PRON	WDT	_	6	nsubj	_	_
6	makes	make	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	relcl	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	method	method	NOUN	NN	Number=Sing	10	nsubj	_	_
9	more	more	ADV	RBR	Degree=Cmp	10	advmod	_	_
10	powerful	powerful	ADJ	JJ	Degree=Pos	6	ccomp	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	consider	consider	VERB	VB	VerbForm=Inf	12	xcomp	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	argument	argument	NOUN	NN	Number=Sing	14	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	20	poss	_	_
19	deformation	deformation	NOUN	NN	Number=Sing	20	compound	_	_
20	theory	theory	NOUN	NN	Number=Sing	17	pobj	_	_
21	as	as	ADP	IN	_	14	prep	_	_
22	an	an	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
23	object	object	NOUN	NN	Number=Sing	21	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	category	category	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	symmetric	symmetric	ADJ	JJ	Degree=Pos	29	amod	_	_
29	sequences	sequence	NOUN	NNS	Number=Plur	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	dg	dg	PROPN	NNP	Number=Sing	32	compound	_	_
32	vector	vector	NOUN	NN	Number=Sing	33	compound	_	_
33	spaces	space	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
35	not	not	PART	RB	Polarity=Neg	36	neg	_	_
36	as	as	ADP	IN	_	14	prep	_	_
37	just	just	ADV	RB	_	42	advmod	_	_
38	a	a	DET	DT	Definite=Ind|PronType=Art	42	det	_	_
39	single	single	ADJ	JJ	Degree=Pos	42	amod	_	_
40	dg	dg	PROPN	NNP	Number=Sing	42	compound	_	_
41	vector	vector	NOUN	NN	Number=Sing	42	compound	_	_
42	space	space	NOUN	NN	Number=Sing	36	pobj	_	_
43	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# doc_id = 658
# sent_id = 1
# text = Quantum categories have been recently studied because of their relation to bialgebroids, small categories, and skew monoidales.
1	Quantum	quantum	NOUN	NN	Number=Sing	2	compound	_	_
2	categories	category	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
3	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	aux	_	_
4	been	be	AUX	VBN	Tense=Past|VerbForm=Part	6	auxpass	_	_
5	recently	recently	ADV	RB	_	6	advmod	_	_
6	studied	study	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	because	because	SCONJ	IN	_	6	prep	_	_
8	of	of	ADP	IN	_	7	pcomp	_	_
9	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	10	poss	_	_
10	relation	relation	NOUN	NN	Number=Sing	7	pobj	_	_
11	to	to	ADP	IN	_	10	prep	_	_
12	bialgebroids	bialgebroid	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	small	small	ADJ	JJ	Degree=Pos	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	12	conj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
18	skew	skew	NOUN	NN	Number=Sing	19	compound	_	_
19	monoidales	monoidale	NOUN	NNS	Number=Plur	15	conj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = This is the first of a series of papers based on the author's PhD thesis in which we examine the theory of quantum categories developed by Day, Lack, and Street.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	first	first	ADJ	JJ	Degree=Pos	2	attr	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	series	series	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	papers	paper	NOUN	NNS	Number=Plur	8	pobj	_	_
10	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	acl	_	_
11	on	on	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	author	author	NOUN	NN	Number=Sing	16	poss	_	SpaceAfter=No
14	's	's	PART	POS	_	13	case	_	_
15	PhD	phd	NOUN	NN	Number=Sing	16	compound	_	_
16	thesis	thesis	NOUN	NN	Number=Sing	11	pobj	_	_
17	in	in	ADP	IN	_	20	prep	_	_
18	which	which	PRON	WDT	_	17	pobj	_	_
19	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	20	nsubj	_	_
20	examine	examine	VERB	VBP	Tense=Pres|VerbForm=Fin	9	relcl	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	theory	theory	NOUN	NN	Number=Sing	20	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	quantum	quantum	ADJ	JJ	Degree=Pos	25	amod	_	_
25	categories	category	NOUN	NNS	Number=Plur	23	pobj	_	_
26	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	acl	_	_
27	by	by	ADP	IN	_	26	agent	_	_
28	Day	Day	PROPN	NNP	Number=Sing	27	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
30	Lack	Lack	PROPN	NNP	Number=Sing	28	conj	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
33	Street	Street	PROPN	NNP	Number=Sing	30	conj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = A quantum category is an opmonoidal monad on the monoidale associated to a biduality $ Rdashv R^{o} $ , or enveloping monoidale, in a monoidal bicategory of modules $ Mod(V}) $ for a monoidal category $ V $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	quantum	quantum	ADJ	JJ	Degree=Pos	3	amod	_	_
3	category	category	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	opmonoidal	opmonoidal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	monad	monad	NOUN	NNS	Number=Plur	4	attr	_	_
8	on	on	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	monoidale	monoidale	NOUN	NN	Number=Sing	8	pobj	_	_
11	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acl	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	biduality	biduality	NOUN	NN	Number=Sing	12	pobj	_	_
15	$ Rdashv R^{o} $	$ rdashv r^{o} $	SYM	$	_	14	appos	_	_
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	or	or	CCONJ	CC	ConjType=Cmp	15	cc	_	_
18	enveloping	envelop	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	conj	_	_
19	monoidale	monoidale	NOUN	NN	Number=Sing	18	dobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
21	in	in	ADP	IN	_	7	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
23	monoidal	monoidal	ADJ	JJ	Degree=Pos	24	amod	_	_
24	bicategory	bicategory	NOUN	NN	Number=Sing	21	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	modules	module	NOUN	NNS	Number=Plur	25	pobj	_	_
27	$ Mod(V}) $	$ mod(v}) $	SYM	$	_	4	dep	_	_
28	for	for	ADP	IN	_	27	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	monoidal	monoidal	ADJ	JJ	Degree=Pos	31	amod	_	_
31	category	category	NOUN	NN	Number=Sing	28	pobj	_	_
32	$ V $	$ v $	SYM	$	_	4	dep	_	_
33	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = Lack and Street proved that quantum categories are in equivalence with right skew monoidales whose unit has a right adjoint in $ Mod(V) $ .
1	Lack	lack	NOUN	NN	Number=Sing	4	nsubj	_	_
2	and	and	CCONJ	CC	ConjType=Cmp	1	cc	_	_
3	Street	Street	PROPN	NNP	Number=Sing	1	conj	_	_
4	proved	prove	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	8	mark	_	_
6	quantum	quantum	ADJ	JJ	Degree=Pos	7	compound	_	_
7	categories	category	NOUN	NNS	Number=Plur	8	nsubj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	equivalence	equivalence	NOUN	NN	Number=Sing	9	pobj	_	_
11	with	with	ADP	IN	_	10	prep	_	_
12	right	right	ADJ	JJ	Degree=Pos	14	amod	_	_
13	skew	skew	NOUN	NN	Number=Sing	14	compound	_	_
14	monoidales	monoidale	NOUN	NNS	Number=Plur	11	pobj	_	_
15	whose	whose	DET	WP$	Poss=Yes	16	poss	_	_
16	unit	unit	NOUN	NN	Number=Sing	17	nsubj	_	_
17	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	right	right	ADJ	JJ	Degree=Pos	20	amod	_	_
20	adjoint	adjoint	NOUN	NN	Number=Sing	17	dobj	_	_
21	in	in	ADP	IN	_	20	prep	_	_
22	$ Mod(V) $	$ mod(v) $	SYM	$	_	21	pobj	_	_
23	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = Our first important result is similar to that of Lack and Street.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	4	poss	_	_
2	first	first	ADJ	JJ	Degree=Pos	4	amod	_	_
3	important	important	ADJ	JJ	Degree=Pos	4	amod	_	_
4	result	result	NOUN	NN	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	similar	similar	ADJ	JJ	Degree=Pos	5	acomp	_	_
7	to	to	ADP	IN	_	6	prep	_	_
8	that	that	PRON	DT	Number=Sing|PronType=Dem	7	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Lack	Lack	PROPN	NNP	Number=Sing	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	Street	Street	PROPN	NNP	Number=Sing	10	conj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 6
# text = It is a characterisation of opmonoidal arrows on enveloping monoidales in terms of a new structure named oplax action.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	characterisation	characterisation	NOUN	NN	Number=Sing	2	attr	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	opmonoidal	opmonoidal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	arrows	arrow	NOUN	NNS	Number=Plur	5	pobj	_	_
8	on	on	ADP	IN	_	4	prep	_	_
9	enveloping	envelop	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	pcomp	_	_
10	monoidales	monoidale	NOUN	NNS	Number=Plur	9	dobj	_	_
11	in	in	ADP	IN	_	4	prep	_	_
12	terms	term	NOUN	NNS	Number=Plur	11	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	new	new	ADJ	JJ	Degree=Pos	16	amod	_	_
16	structure	structure	NOUN	NN	Number=Sing	13	pobj	_	_
17	named	name	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	acl	_	_
18	oplax	oplax	PROPN	NNP	Number=Sing	19	compound	_	_
19	action	action	NOUN	NN	Number=Sing	17	oprd	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = We then provide three different notions of comodule for an opmonoidal arrow, and using a similar technique we prove that they are equivalent.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	three	three	NUM	CD	NumType=Card	6	nummod	_	_
5	different	different	ADJ	JJ	Degree=Pos	6	amod	_	_
6	notions	notion	NOUN	NNS	Number=Plur	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	comodule	comodule	NOUN	NN	Number=Sing	7	pobj	_	_
9	for	for	ADP	IN	_	3	prep	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	opmonoidal	opmonoidal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	arrow	arrow	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
15	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	conj	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	similar	similar	ADJ	JJ	Degree=Pos	18	amod	_	_
18	technique	technique	NOUN	NN	Number=Sing	15	dobj	_	_
19	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	20	nsubj	_	_
20	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	18	relcl	_	_
21	that	that	SCONJ	IN	_	23	mark	_	_
22	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	23	nsubj	_	_
23	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	20	ccomp	_	_
24	equivalent	equivalent	ADJ	JJ	Degree=Pos	23	acomp	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 8
# text = Finally, when the opmonoidal arrow is an opmonoidal monad, we are able to provide the category of comodules for a quantum category with a monoidal structure such that the forgetful functor is monoidal.
1	Finally	finally	ADV	RB	_	13	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
3	when	when	SCONJ	WRB	_	7	advmod	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	opmonoidal	opmonoidal	ADJ	JJ	Degree=Pos	6	amod	_	_
6	arrow	arrow	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	advcl	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	opmonoidal	opmonoidal	ADJ	JJ	Degree=Pos	10	amod	_	_
10	monad	monad	NOUN	NNS	Number=Plur	7	attr	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	able	able	ADJ	JJ	Degree=Pos	13	acomp	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	provide	provide	VERB	VB	VerbForm=Inf	14	xcomp	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	category	category	NOUN	NN	Number=Sing	16	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	comodules	comodule	NOUN	NNS	Number=Plur	19	pobj	_	_
21	for	for	ADP	IN	_	16	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
23	quantum	quantum	ADJ	JJ	Degree=Pos	24	amod	_	_
24	category	category	NOUN	NN	Number=Sing	21	pobj	_	_
25	with	with	ADP	IN	_	24	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
27	monoidal	monoidal	ADJ	JJ	Degree=Pos	28	amod	_	_
28	structure	structure	NOUN	NN	Number=Sing	25	pobj	_	_
29	such	such	ADJ	JJ	Degree=Pos	34	mark	_	_
30	that	that	SCONJ	IN	_	34	mark	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	forgetful	forgetful	ADJ	JJ	Degree=Pos	33	amod	_	_
33	functor	functor	NOUN	NN	Number=Sing	34	nsubj	_	_
34	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	advcl	_	_
35	monoidal	monoidal	ADJ	JJ	Degree=Pos	34	acomp	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# doc_id = 659
# sent_id = 1
# text = We study deformation of tube algebra under twisting of graded monoidal categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	deformation	deformation	NOUN	NN	Number=Sing	2	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	tube	tube	NOUN	NN	Number=Sing	6	compound	_	_
6	algebra	algebra	NOUN	NNS	Number=Plur	4	pobj	_	_
7	under	under	ADP	IN	_	2	prep	_	_
8	twisting	twisting	NOUN	NN	Number=Sing	7	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	graded	grade	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
11	monoidal	monoidal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = When a tensor category $ C $ is graded over a group $ Gammaa $ , a torus - valued 3 - cocycle on $ Gamma $ can be used to deform the associator of $ C $ .
1	When	when	SCONJ	WRB	_	7	advmod	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	tensor	tensor	NOUN	NN	Number=Sing	4	compound	_	_
4	category	category	NOUN	NN	Number=Sing	7	nsubjpass	_	_
5	$ C $	$ c $	SYM	$	_	4	appos	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	graded	grade	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	advcl	_	_
8	over	over	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	group	group	NOUN	NN	Number=Sing	8	pobj	_	_
11	$ Gammaa $	$ gammaa $	SYM	$	_	10	appos	_	_
12	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
14	torus	torus	NOUN	NN	Number=Sing	16	npadvmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
17	3	3	NUM	CD	NumType=Card	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	cocycle	cocycle	NOUN	NN	Number=Sing	24	nsubjpass	_	_
20	on	on	ADP	IN	_	19	prep	_	_
21	$ Gamma $	$ gamma $	SYM	$	_	20	pobj	_	_
22	can	can	AUX	MD	VerbForm=Fin	24	aux	_	_
23	be	be	AUX	VB	VerbForm=Inf	24	auxpass	_	_
24	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
25	to	to	PART	TO	_	26	aux	_	_
26	deform	deform	VERB	VB	VerbForm=Inf	24	xcomp	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	associator	associator	NOUN	NN	Number=Sing	26	dobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	$ C $	$ c $	SYM	$	_	29	pobj	_	_
31	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that it induces a 2 - cocycle on the groupoid of the adjoint action of $ Gammaa $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	5	nsubj	_	_
5	induces	induce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	2	2	NUM	CD	NumType=Card	9	nummod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	cocycle	cocycle	NOUN	NN	Number=Sing	5	dobj	_	_
10	on	on	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	groupoid	groupoid	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	adjoint	adjoint	NOUN	NN	Number=Sing	16	compound	_	_
16	action	action	NOUN	NN	Number=Sing	13	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	$ Gammaa $	$ gammaa $	SYM	$	_	17	pobj	_	_
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = Combined with the natural Fell bundle structure of tube algebra over this groupoid, we show that the tube algebra of the twisted category is a 2 - cocycle twisting of the original one.
1	Combined	combine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	advcl	_	_
2	with	with	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
4	natural	natural	ADJ	JJ	Degree=Pos	7	amod	_	_
5	Fell	Fell	PROPN	NNP	Number=Sing	6	compound	_	_
6	bundle	bundle	NOUN	NN	Number=Sing	7	compound	_	_
7	structure	structure	NOUN	NN	Number=Sing	2	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	tube	tube	NOUN	NN	Number=Sing	10	compound	_	_
10	algebra	algebra	NOUN	NNS	Number=Plur	8	pobj	_	_
11	over	over	ADP	IN	_	7	prep	_	_
12	this	this	DET	DT	Number=Sing|PronType=Dem	13	det	_	_
13	groupoid	groupoid	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
15	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	16	nsubj	_	_
16	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
17	that	that	SCONJ	IN	_	25	mark	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	tube	tube	NOUN	NN	Number=Sing	20	compound	_	_
20	algebra	algebra	NOUN	NN	Number=Sing	25	nsubj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	twisted	twisted	ADJ	JJ	Degree=Pos	24	amod	_	_
24	category	category	NOUN	NN	Number=Sing	21	pobj	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	ccomp	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
27	2	2	NUM	CD	NumType=Card	29	nummod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	cocycle	cocycle	NOUN	NN	Number=Sing	30	compound	_	_
30	twisting	twisting	NOUN	NN	Number=Sing	25	attr	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
33	original	original	ADJ	JJ	Degree=Pos	34	amod	_	_
34	one	one	NOUN	NN	Number=Sing	31	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# doc_id = 660
# sent_id = 1
# text = In this paper we consider a crossed product of two crossed modules of Hopf monoids in a strict symmetric monoidal category $ {mathcal C} $ and give necessary and sufficient conditions to get a new crossed module of Hopf monoids in $ {mathcal C} $ .
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	crossed	crossed	ADJ	JJ	Degree=Pos	8	amod	_	_
8	product	product	NOUN	NN	Number=Sing	5	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	two	two	NUM	CD	NumType=Card	12	nummod	_	_
11	crossed	crossed	ADJ	JJ	Degree=Pos	12	amod	_	_
12	modules	module	NOUN	NNS	Number=Plur	9	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	Hopf	hopf	NOUN	NN	Number=Sing	15	compound	_	_
15	monoids	monoid	NOUN	NNS	Number=Plur	13	pobj	_	_
16	in	in	ADP	IN	_	5	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
18	strict	strict	ADJ	JJ	Degree=Pos	21	amod	_	_
19	symmetric	symmetric	ADJ	JJ	Degree=Pos	21	amod	_	_
20	monoidal	monoidal	ADJ	JJ	Degree=Pos	21	amod	_	_
21	category	category	NOUN	NN	Number=Sing	16	pobj	_	_
22	$ {mathcal C} $	$ {mathcal c} $	SYM	$	_	5	dobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
24	give	give	VERB	VB	VerbForm=Inf	5	conj	_	_
25	necessary	necessary	ADJ	JJ	Degree=Pos	28	amod	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	sufficient	sufficient	ADJ	JJ	Degree=Pos	25	conj	_	_
28	conditions	condition	NOUN	NNS	Number=Plur	24	dobj	_	_
29	to	to	PART	TO	_	30	aux	_	_
30	get	get	VERB	VB	VerbForm=Inf	24	advcl	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
32	new	new	ADJ	JJ	Degree=Pos	34	amod	_	_
33	crossed	crossed	ADJ	JJ	Degree=Pos	34	amod	_	_
34	module	module	NOUN	NN	Number=Sing	30	dobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	Hopf	Hopf	PROPN	NNP	Number=Sing	37	compound	_	_
37	monoids	monoid	NOUN	NNS	Number=Plur	35	pobj	_	_
38	in	in	ADP	IN	_	37	prep	_	_
39	$ {mathcal C} $	$ {mathcal c} $	SYM	$	_	38	pobj	_	_
40	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = Moreover we introduce the notion of projection of crossed modules of Hopf monoids and show that with additional hypotheses, any of these projections defines a new crossed module of Hopf monoids and allows us to construct an example of this kind of crossed product.
1	Moreover	moreover	ADV	RB	_	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	notion	notion	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	projection	projection	NOUN	NN	Number=Sing	6	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	crossed	crossed	ADJ	JJ	Degree=Pos	10	amod	_	_
10	modules	module	NOUN	NNS	Number=Plur	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	Hopf	hopf	NOUN	NN	Number=Sing	13	compound	_	_
13	monoids	monoid	NOUN	NNS	Number=Plur	11	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
15	show	show	VERB	VB	VerbForm=Inf	3	conj	_	_
16	that	that	SCONJ	IN	_	25	mark	_	_
17	with	with	ADP	IN	_	25	prep	_	_
18	additional	additional	ADJ	JJ	Degree=Pos	19	amod	_	_
19	hypotheses	hypothesis	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
21	any	any	PRON	DT	_	25	nsubj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	these	these	DET	DT	Number=Plur|PronType=Dem	24	det	_	_
24	projections	projection	NOUN	NNS	Number=Plur	22	pobj	_	_
25	defines	define	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	ccomp	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
27	new	new	ADJ	JJ	Degree=Pos	29	amod	_	_
28	crossed	crossed	ADJ	JJ	Degree=Pos	29	amod	_	_
29	module	module	NOUN	NN	Number=Sing	25	dobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	Hopf	hopf	NOUN	NN	Number=Sing	32	compound	_	_
32	monoids	monoid	NOUN	NNS	Number=Plur	30	pobj	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
34	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	conj	_	_
35	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	37	nsubj	_	_
36	to	to	PART	TO	_	37	aux	_	_
37	construct	construct	VERB	VB	VerbForm=Inf	34	ccomp	_	_
38	an	an	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
39	example	example	NOUN	NN	Number=Sing	37	dobj	_	_
40	of	of	ADP	IN	_	39	prep	_	_
41	this	this	DET	DT	Number=Sing|PronType=Dem	42	det	_	_
42	kind	kind	NOUN	NN	Number=Sing	40	pobj	_	_
43	of	of	ADP	IN	_	42	prep	_	_
44	crossed	crossed	ADJ	JJ	Degree=Pos	45	amod	_	_
45	product	product	NOUN	NN	Number=Sing	43	pobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Finally, we develop the explicit computations of a crossed product associated to a projection of crossed modules in groups.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	explicit	explicit	ADJ	JJ	Degree=Pos	7	amod	_	_
7	computations	computation	NOUN	NNS	Number=Plur	4	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
11	product	product	NOUN	NN	Number=Sing	8	pobj	_	_
12	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acl	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	projection	projection	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
18	modules	module	NOUN	NNS	Number=Plur	16	pobj	_	_
19	in	in	ADP	IN	_	18	prep	_	_
20	groups	group	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 661
# sent_id = 1
# text = Tangent categories provide an axiomatic approach to key structural aspects of differential geometry that exist not only in the classical category of smooth manifolds but also in algebraic geometry, homological algebra, computer science, and combinatorics.
1	Tangent	tangent	ADJ	JJ	Degree=Pos	2	compound	_	_
2	categories	category	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	axiomatic	axiomatic	ADJ	JJ	Degree=Pos	6	amod	_	_
6	approach	approach	NOUN	NN	Number=Sing	3	dobj	_	_
7	to	to	ADP	IN	_	6	prep	_	_
8	key	key	ADJ	JJ	Degree=Pos	10	amod	_	_
9	structural	structural	ADJ	JJ	Degree=Pos	10	amod	_	_
10	aspects	aspect	NOUN	NNS	Number=Plur	7	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	differential	differential	ADJ	JJ	Degree=Pos	13	amod	_	_
13	geometry	geometry	NOUN	NN	Number=Sing	11	pobj	_	_
14	that	that	PRON	WDT	PronType=Rel	15	nsubj	_	_
15	exist	exist	VERB	VBP	Tense=Pres|VerbForm=Fin	10	relcl	_	_
16	not	not	PART	RB	Polarity=Neg	18	preconj	_	_
17	only	only	ADV	RB	_	16	advmod	_	_
18	in	in	ADP	IN	_	15	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	classical	classical	ADJ	JJ	Degree=Pos	21	amod	_	_
21	category	category	NOUN	NN	Number=Sing	18	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	smooth	smooth	ADJ	JJ	Degree=Pos	24	amod	_	_
24	manifolds	manifold	NOUN	NNS	Number=Plur	22	pobj	_	_
25	but	but	CCONJ	CC	ConjType=Cmp	18	cc	_	_
26	also	also	ADV	RB	_	25	advmod	_	_
27	in	in	ADP	IN	_	18	conj	_	_
28	algebraic	algebraic	ADJ	JJ	Degree=Pos	29	amod	_	_
29	geometry	geometry	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
31	homological	homological	ADJ	JJ	Degree=Pos	32	amod	_	_
32	algebra	algebra	NOUN	NN	Number=Sing	29	conj	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
34	computer	computer	NOUN	NN	Number=Sing	35	compound	_	_
35	science	science	NOUN	NN	Number=Sing	32	conj	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
37	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
38	combinatorics	combinatoric	NOUN	NNS	Number=Plur	35	conj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = Generalizing the notion of (linear) connection on a smooth vector bundle, Cockett and Cruttwell have defined a notion of connection on a differential bundle in an arbitrary tangent category.
1	Generalizing	generalize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	advcl	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	notion	notion	NOUN	NN	Number=Sing	1	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	8	punct	_	SpaceAfter=No
6	linear	linear	ADJ	JJ	Degree=Pos	8	nmod	_	SpaceAfter=No
7	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	8	punct	_	_
8	connection	connection	NOUN	NN	Number=Sing	4	pobj	_	_
9	on	on	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	smooth	smooth	ADJ	JJ	Degree=Pos	13	amod	_	_
12	vector	vector	NOUN	NN	Number=Sing	13	compound	_	_
13	bundle	bundle	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
15	Cockett	Cockett	PROPN	NNP	Number=Sing	19	nsubj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	Cruttwell	Cruttwell	PROPN	NNP	Number=Sing	15	conj	_	_
18	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	19	aux	_	_
19	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	notion	notion	NOUN	NN	Number=Sing	19	dobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	connection	connection	NOUN	NN	Number=Sing	22	pobj	_	_
24	on	on	ADP	IN	_	23	prep	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
26	differential	differential	ADJ	JJ	Degree=Pos	27	amod	_	_
27	bundle	bundle	NOUN	NN	Number=Sing	24	pobj	_	_
28	in	in	ADP	IN	_	27	prep	_	_
29	an	an	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
30	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	32	amod	_	_
31	tangent	tangent	NOUN	NN	Number=Sing	32	compound	_	_
32	category	category	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 3
# text = Herein, we establish equivalent formulations of this notion of connection that reduce the amount of specified structure required.
1	Herein	Herein	PROPN	NNP	Number=Sing	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	establish	establish	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	equivalent	equivalent	ADJ	JJ	Degree=Pos	6	amod	_	_
6	formulations	formulation	NOUN	NNS	Number=Plur	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	this	this	DET	DT	Number=Sing|PronType=Dem	9	det	_	_
9	notion	notion	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	connection	connection	NOUN	NN	Number=Sing	10	pobj	_	_
12	that	that	PRON	WDT	PronType=Rel	13	nsubj	_	_
13	reduce	reduce	VERB	VBP	Tense=Pres|VerbForm=Fin	11	relcl	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	amount	amount	NOUN	NN	Number=Sing	13	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	specified	specify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	amod	_	_
18	structure	structure	NOUN	NN	Number=Sing	16	pobj	_	_
19	required	require	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	acl	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = Further, one of our equivalent formulations substantially reduces the number of axioms imposed, and others provide useful abstract conceptualizations of connections.
1	Further	far	ADV	RB	_	9	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
3	one	one	NUM	CD	NumType=Card	9	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	7	poss	_	_
6	equivalent	equivalent	ADJ	JJ	Degree=Pos	7	amod	_	_
7	formulations	formulation	NOUN	NNS	Number=Plur	4	pobj	_	_
8	substantially	substantially	ADV	RB	_	9	advmod	_	_
9	reduces	reduce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	number	number	NOUN	NN	Number=Sing	9	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	axioms	axiom	NOUN	NNS	Number=Plur	12	pobj	_	_
14	imposed	impose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	acl	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
17	others	other	NOUN	NNS	Number=Plur	18	nsubj	_	_
18	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	9	conj	_	_
19	useful	useful	ADJ	JJ	Degree=Pos	21	amod	_	_
20	abstract	abstract	ADJ	JJ	Degree=Pos	21	amod	_	_
21	conceptualizations	conceptualization	NOUN	NNS	Number=Plur	18	dobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	connections	connection	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# sent_id = 5
# text = In particular, we show that a connection on a differential bundle $ E $ over $ M $ is equivalently given by a single morphism $ K $ that induces a suitable decomposition of $ TE $ as a biproduct.
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	18	mark	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	connection	connection	NOUN	NN	Number=Sing	18	nsubjpass	_	_
9	on	on	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	differential	differential	ADJ	JJ	Degree=Pos	12	amod	_	_
12	bundle	bundle	NOUN	NN	Number=Sing	9	pobj	_	_
13	$ E $	$ e $	SYM	$	_	15	nmod	_	_
14	over	over	ADP	IN	_	15	advmod	_	_
15	$ M $	$ m $	SYM	$	_	8	appos	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	auxpass	_	_
17	equivalently	equivalently	ADV	RB	_	18	advmod	_	_
18	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	ccomp	_	_
19	by	by	ADP	IN	_	18	agent	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	single	single	ADJ	JJ	Degree=Pos	22	amod	_	_
22	morphism	morphism	NOUN	NN	Number=Sing	19	pobj	_	_
23	$ K $	$ k $	SYM	$	_	22	appos	_	_
24	that	that	PRON	WDT	PronType=Rel	25	nsubj	_	_
25	induces	induce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	relcl	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
27	suitable	suitable	ADJ	JJ	Degree=Pos	28	amod	_	_
28	decomposition	decomposition	NOUN	NN	Number=Sing	25	dobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	$ TE $	$ te $	SYM	$	_	29	pobj	_	_
31	as	as	ADP	IN	_	25	prep	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
33	biproduct	biproduct	NOUN	NN	Number=Sing	31	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 6
# text = We also show that a connection is equivalently given by a vertical connection $ K $ for which a certain associated diagram is a limit diagram.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	9	mark	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	connection	connection	NOUN	NN	Number=Sing	9	nsubjpass	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
8	equivalently	equivalently	ADV	RB	_	9	advmod	_	_
9	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	ccomp	_	_
10	by	by	ADP	IN	_	9	agent	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	vertical	vertical	ADJ	JJ	Degree=Pos	13	amod	_	_
13	connection	connection	NOUN	NN	Number=Sing	10	pobj	_	_
14	$ K $	$ k $	SYM	$	_	13	appos	_	_
15	for	for	ADP	IN	_	21	prep	_	_
16	which	which	PRON	WDT	_	15	pobj	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
18	certain	certain	ADJ	JJ	Degree=Pos	20	amod	_	_
19	associated	associated	ADJ	JJ	Degree=Pos	20	amod	_	_
20	diagram	diagram	NOUN	NN	Number=Sing	21	nsubj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	relcl	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
23	limit	limit	NOUN	NN	Number=Sing	24	compound	_	_
24	diagram	diagram	NOUN	NN	Number=Sing	21	attr	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 662
# sent_id = 1
# text = The Ehresmann - Schein - Nambooripad Theorem asserts an equivalence between the category of inverse semigroups and the category of inductive groupoids.
1	The	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
2	Ehresmann	Ehresmann	PROPN	NNP	Number=Sing	4	compound	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	Schein	Schein	PROPN	NNP	Number=Sing	6	compound	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
6	Nambooripad	Nambooripad	PROPN	NNP	Number=Sing	7	compound	_	_
7	Theorem	Theorem	PROPN	NNP	Number=Sing	8	nsubj	_	_
8	asserts	assert	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	equivalence	equivalence	NOUN	NN	Number=Sing	8	dobj	_	_
11	between	between	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	inverse	inverse	ADJ	JJ	Degree=Pos	16	amod	_	_
16	semigroups	semigroup	NOUN	NNS	Number=Plur	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	category	category	NOUN	NN	Number=Sing	13	conj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	inductive	inductive	ADJ	JJ	Degree=Pos	22	amod	_	_
22	groupoids	groupoid	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper, we consider the category of inverse categories and functors—a natural generalization of inverse semigroups and semigroup homomorphisms—and extend the ESN Theorem to an equivalence between this category and the category of locally complete inductive groupoids and locally inductive functors.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	inverse	inverse	ADJ	JJ	Degree=Pos	11	amod	_	_
11	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	functors	functor	NOUN	NNS	Number=Plur	11	conj	_	SpaceAfter=No
14	—	—	PUNCT	:	_	8	punct	_	SpaceAfter=No
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	natural	natural	ADJ	JJ	Degree=Pos	17	amod	_	_
17	generalization	generalization	NOUN	NN	Number=Sing	8	appos	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	inverse	inverse	ADJ	JJ	Degree=Pos	20	amod	_	_
20	semigroups	semigroup	NOUN	NNS	Number=Plur	18	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	semigroup	semigroup	NOUN	NN	Number=Sing	23	compound	_	_
23	homomorphisms	homomorphism	NOUN	NNS	Number=Plur	20	conj	_	SpaceAfter=No
24	—	—	PUNCT	:	_	8	punct	_	SpaceAfter=No
25	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
26	extend	extend	VERB	VB	VerbForm=Inf	6	conj	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	ESN	ESN	PROPN	NNP	Number=Sing	29	compound	_	_
29	Theorem	Theorem	PROPN	NNP	Number=Sing	26	dobj	_	_
30	to	to	ADP	IN	_	26	prep	_	_
31	an	an	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
32	equivalence	equivalence	NOUN	NN	Number=Sing	30	pobj	_	_
33	between	between	ADP	IN	_	32	prep	_	_
34	this	this	DET	DT	Number=Sing|PronType=Dem	35	det	_	_
35	category	category	NOUN	NN	Number=Sing	33	pobj	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	category	category	NOUN	NN	Number=Sing	35	conj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	locally	locally	ADV	RB	_	41	advmod	_	_
41	complete	complete	ADJ	JJ	Degree=Pos	43	amod	_	_
42	inductive	inductive	ADJ	JJ	Degree=Pos	43	amod	_	_
43	groupoids	groupoid	NOUN	NNS	Number=Plur	39	pobj	_	_
44	and	and	CCONJ	CC	ConjType=Cmp	43	cc	_	_
45	locally	locally	ADV	RB	_	46	advmod	_	_
46	inductive	inductive	ADJ	JJ	Degree=Pos	47	amod	_	_
47	functors	functor	NOUN	NNS	Number=Plur	43	conj	_	SpaceAfter=No
48	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = From the proof of this extension, we also generalize the ESN Theorem to an equivalence between the category of inverse semicategories and the category of locally inductive groupoids and to an equivalence between the category of inverse categories with oplax functors and the category of locally complete inductive groupoids and ordered functors.
1	From	from	ADP	IN	_	10	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	proof	proof	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	extension	extension	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
9	also	also	ADV	RB	_	10	advmod	_	_
10	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	ESN	ESN	PROPN	NNP	Number=Sing	13	compound	_	_
13	Theorem	Theorem	PROPN	NNP	Number=Sing	10	dobj	_	_
14	to	to	ADP	IN	_	10	prep	_	_
15	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	equivalence	equivalence	NOUN	NN	Number=Sing	14	pobj	_	_
17	between	between	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	category	category	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	inverse	inverse	ADJ	JJ	Degree=Pos	22	amod	_	_
22	semicategories	semicategorie	NOUN	NNS	Number=Plur	20	pobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	category	category	NOUN	NN	Number=Sing	19	conj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	locally	locally	ADV	RB	_	28	advmod	_	_
28	inductive	inductive	ADJ	JJ	Degree=Pos	29	amod	_	_
29	groupoids	groupoid	NOUN	NNS	Number=Plur	26	pobj	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
31	to	to	ADP	IN	_	26	conj	_	_
32	an	an	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
33	equivalence	equivalence	NOUN	NN	Number=Sing	31	pobj	_	_
34	between	between	ADP	IN	_	33	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	category	category	NOUN	NN	Number=Sing	34	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	inverse	inverse	ADJ	JJ	Degree=Pos	39	amod	_	_
39	categories	category	NOUN	NNS	Number=Plur	37	pobj	_	_
40	with	with	ADP	IN	_	39	prep	_	_
41	oplax	oplax	PROPN	NNP	Number=Sing	42	compound	_	_
42	functors	functor	NOUN	NNS	Number=Plur	40	pobj	_	_
43	and	and	CCONJ	CC	ConjType=Cmp	42	cc	_	_
44	the	the	DET	DT	Definite=Def|PronType=Art	45	det	_	_
45	category	category	NOUN	NN	Number=Sing	42	conj	_	_
46	of	of	ADP	IN	_	45	prep	_	_
47	locally	locally	ADV	RB	_	48	advmod	_	_
48	complete	complete	ADJ	JJ	Degree=Pos	50	amod	_	_
49	inductive	inductive	ADJ	JJ	Degree=Pos	50	amod	_	_
50	groupoids	groupoid	NOUN	NNS	Number=Plur	46	pobj	_	_
51	and	and	CCONJ	CC	ConjType=Cmp	36	cc	_	_
52	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	advcl	_	_
53	functors	functor	NOUN	NNS	Number=Plur	52	dobj	_	SpaceAfter=No
54	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# doc_id = 663
# sent_id = 1
# text = Let $ H $ be a quasi - Hopf algebra.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ H $	$ h $	SYM	$	_	1	ccomp	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
5	quasi	quasi	ADJ	JJ	Degree=Pos	8	amod	_	_
6	-	-	ADJ	JJ	Degree=Pos	8	punct	_	_
7	Hopf	hopf	ADJ	JJ	Degree=Pos	8	amod	_	_
8	algebra	algebra	NOUN	NN	Number=Sing	3	attr	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that any $ H $ - bimodule coalgebra $ C $ for which there exists an $ H $ - bimodule coalgebra morphism $ n : C - > H $ is isomorphic to what we will call a smash product coalgebra.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	21	mark	_	_
4	any	any	DET	DT	_	8	det	_	_
5	$ H $	$ h $	SYM	$	_	7	amod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	bimodule	bimodule	NOUN	NN	Number=Sing	8	compound	_	_
8	coalgebra	coalgebra	NOUN	NNS	Number=Plur	21	nsubj	_	_
9	$ C $	$ c $	SYM	$	_	8	appos	_	_
10	for	for	ADP	IN	_	13	prep	_	_
11	which	which	PRON	WDT	_	10	pobj	_	_
12	there	there	PRON	EX	_	13	expl	_	_
13	exists	exist	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	relcl	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
15	$ H $	$ h $	SYM	$	_	17	advmod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	bimodule	bimodule	NOUN	NN	Number=Sing	19	compound	_	_
18	coalgebra	coalgebra	PROPN	NNP	Number=Sing	19	compound	_	_
19	morphism	morphism	PROPN	NNP	Number=Sing	13	dobj	_	_
20	$ n : C - > H $	$ n : c - > h $	SYM	$	_	13	npadvmod	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
22	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	21	acomp	_	_
23	to	to	ADP	IN	_	22	prep	_	_
24	what	what	PRON	WP	_	27	dobj	_	_
25	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	27	nsubj	_	_
26	will	will	AUX	MD	VerbForm=Fin	27	aux	_	_
27	call	call	VERB	VB	VerbForm=Inf	23	pcomp	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
29	smash	smash	NOUN	NN	Number=Sing	30	compound	_	_
30	product	product	NOUN	NN	Number=Sing	31	compound	_	_
31	coalgebra	coalgebra	NOUN	NNS	Number=Plur	27	oprd	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = To this end, we use an explicit monoidal equivalence between the category of two - sided two - cosided Hopf modules over $ H $ and the category of left Yetter - Drinfeld modules over $ H $ .
1	To	to	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	end	end	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	explicit	explicit	ADJ	JJ	Degree=Pos	10	amod	_	_
9	monoidal	monoidal	ADJ	JJ	Degree=Pos	10	amod	_	_
10	equivalence	equivalence	NOUN	NN	Number=Sing	6	dobj	_	_
11	between	between	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	two	two	NUM	CD	NumType=Card	14	pobj	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	sided	sided	ADJ	JJ	Degree=Pos	22	amod	_	_
18	two	two	NUM	CD	NumType=Card	20	advmod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	cosided	coside	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	amod	_	_
21	Hopf	Hopf	PROPN	NNP	Number=Sing	22	compound	_	_
22	modules	module	NOUN	NNS	Number=Plur	6	dobj	_	_
23	over	over	ADP	IN	_	22	prep	_	_
24	$ H $	$ h $	SYM	$	_	23	pobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	category	category	NOUN	NN	Number=Sing	22	conj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	amod	_	_
30	Yetter	Yetter	PROPN	NNP	Number=Sing	32	compound	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	Drinfeld	Drinfeld	PROPN	NNP	Number=Sing	33	compound	_	_
33	modules	module	NOUN	NNS	Number=Plur	28	pobj	_	_
34	over	over	ADP	IN	_	33	prep	_	_
35	$ H $	$ h $	SYM	$	_	34	pobj	_	_
36	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = This categorical method allows also to reobtain the structure theorem for a quasi - Hopf (bi)comodule algebra given by Panaite and Van Oystaeyen, and by Dello et al.
1	This	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
2	categorical	categorical	ADJ	JJ	Degree=Pos	3	amod	_	_
3	method	method	NOUN	NN	Number=Sing	4	nsubj	_	_
4	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	also	also	ADV	RB	_	4	advmod	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	reobtain	reobtain	VERB	VB	VerbForm=Inf	4	xcomp	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	structure	structure	NOUN	NN	Number=Sing	10	nsubj	_	_
10	theorem	theorem	VERB	VBD	Tense=Past|VerbForm=Fin	7	ccomp	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
13	quasi	quasi	ADJ	JJ	Degree=Pos	18	compound	_	_
14	-	-	PUNCT	:	_	18	punct	_	_
15	Hopf	hopf	NOUN	NN	Number=Sing	18	nmod	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	18	punct	_	SpaceAfter=No
17	bi)comodule	bi)comodule	NOUN	NN	Number=Sing	18	compound	_	_
18	algebra	algebra	NOUN	NN	Number=Sing	11	pobj	_	_
19	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	acl	_	_
20	by	by	ADP	IN	_	19	agent	_	_
21	Panaite	Panaite	PROPN	NNP	Number=Sing	24	nmod	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	Van	Van	PROPN	NNP	Number=Sing	24	compound	_	_
24	Oystaeyen	Oystaeyen	PROPN	NNP	Number=Sing	20	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
27	by	by	ADP	IN	_	11	conj	_	_
28	Dello	Dello	PROPN	NNP	Number=Sing	27	pobj	_	_
29	et	et	NOUN	NN	Number=Sing	27	pobj	_	_
30	al	al	PROPN	NNP	Number=Sing	27	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 664
# sent_id = 1
# text = Passive linear networks are used in a wide variety of engineering applications, but the best studied are electrical circuits made of resistors, inductors and capacitors.
1	Passive	passive	ADJ	JJ	Degree=Pos	3	amod	_	_
2	linear	linear	ADJ	JJ	Degree=Pos	3	compound	_	_
3	networks	network	NOUN	NNS	Number=Plur	5	nsubjpass	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	wide	wide	ADJ	JJ	Degree=Pos	9	amod	_	_
9	variety	variety	NOUN	NN	Number=Sing	6	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	engineering	engineering	NOUN	NN	Number=Sing	12	compound	_	_
12	applications	application	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
14	but	but	CCONJ	CC	ConjType=Cmp	5	cc	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	best	good	ADJ	JJS	Degree=Sup	17	amod	_	_
17	studied	study	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	nsubj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	conj	_	_
19	electrical	electrical	ADJ	JJ	Degree=Pos	20	amod	_	_
20	circuits	circuit	NOUN	NNS	Number=Plur	18	attr	_	_
21	made	make	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	acl	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	resistors	resistor	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
25	inductors	inductor	NOUN	NNS	Number=Plur	23	conj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	capacitors	capacitor	NOUN	NNS	Number=Plur	25	conj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# sent_id = 2
# text = We describe a category where a morphism is a circuit of this sort with marked input and output terminals.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	category	category	NOUN	NN	Number=Sing	2	dobj	_	_
5	where	where	SCONJ	WRB	_	8	advmod	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	morphism	morphism	NOUN	NN	Number=Sing	8	nsubj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	relcl	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	circuit	circuit	NOUN	NN	Number=Sing	8	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	this	this	DET	DT	Number=Sing|PronType=Dem	13	det	_	_
13	sort	sort	NOUN	NN	Number=Sing	11	pobj	_	_
14	with	with	ADP	IN	_	10	prep	_	_
15	marked	marked	ADJ	JJ	Degree=Pos	16	amod	_	_
16	input	input	NOUN	NN	Number=Sing	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	output	output	NOUN	NN	Number=Sing	19	compound	_	_
19	terminals	terminal	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this category, composition describes the process of attaching the outputs of one circuit to the inputs of another.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	category	category	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	composition	composition	NOUN	NN	Number=Sing	6	nsubj	_	_
6	describes	describe	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	process	process	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	attaching	attach	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	pcomp	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	outputs	output	NOUN	NNS	Number=Plur	10	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	one	one	NUM	CD	NumType=Card	15	nummod	_	_
15	circuit	circuit	NOUN	NN	Number=Sing	13	pobj	_	_
16	to	to	ADP	IN	_	10	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	inputs	input	NOUN	NNS	Number=Plur	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	another	another	PRON	DT	_	19	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = We construct a functor, dubbed the `black box functor', that takes a circuit, forgets its internal structure, and remembers only its external behavior.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	functor	functor	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
6	dubbed	dub	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	acl	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
8	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	11	punct	_	SpaceAfter=No
9	black	black	PROPN	NNP	Number=Sing	10	amod	_	_
10	box	box	PROPN	NNP	Number=Sing	11	compound	_	_
11	functor	functor	NOUN	NN	Number=Sing	6	oprd	_	SpaceAfter=No
12	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	4	punct	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
14	that	that	PRON	WDT	PronType=Rel	15	nsubj	_	_
15	takes	take	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	relcl	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	circuit	circuit	NOUN	NN	Number=Sing	15	dobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
19	forgets	forget	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
20	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	22	poss	_	_
21	internal	internal	ADJ	JJ	Degree=Pos	22	amod	_	_
22	structure	structure	NOUN	NN	Number=Sing	19	dobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
25	remembers	remember	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	conj	_	_
26	only	only	ADV	RB	_	29	advmod	_	_
27	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	29	poss	_	_
28	external	external	ADJ	JJ	Degree=Pos	29	amod	_	_
29	behavior	behavior	NOUN	NN	Number=Sing	25	dobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = Two circuits have the same external behavior if and only if they impose same relation between currents and potentials at their terminals.
1	Two	two	NUM	CD	NumType=Card	2	nummod	_	_
2	circuits	circuit	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	same	same	ADJ	JJ	Degree=Pos	7	amod	_	_
6	external	external	ADJ	JJ	Degree=Pos	7	amod	_	_
7	behavior	behavior	NOUN	NN	Number=Sing	3	dobj	_	_
8	if	if	SCONJ	IN	_	3	punct	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	only	only	ADV	RB	_	13	advmod	_	_
11	if	if	SCONJ	IN	_	13	mark	_	_
12	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	13	nsubj	_	_
13	impose	impose	VERB	VBP	Tense=Pres|VerbForm=Fin	3	advcl	_	_
14	same	same	ADJ	JJ	Degree=Pos	15	amod	_	_
15	relation	relation	NOUN	NN	Number=Sing	13	dobj	_	_
16	between	between	ADP	IN	_	15	prep	_	_
17	currents	current	NOUN	NNS	Number=Plur	16	pobj	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	potentials	potential	NOUN	NNS	Number=Plur	17	conj	_	_
20	at	at	ADP	IN	_	13	prep	_	_
21	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	22	poss	_	_
22	terminals	terminal	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = The space of these currents and potentials naturally has the structure of a symplectic vector space, and the relation imposed by a circuit is a Lagrangian linear relation.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	space	space	NOUN	NN	Number=Sing	9	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	these	these	DET	DT	Number=Plur|PronType=Dem	5	det	_	_
5	currents	current	NOUN	NNS	Number=Plur	3	pobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	potentials	potential	NOUN	NNS	Number=Plur	5	conj	_	_
8	naturally	naturally	ADV	RB	_	9	advmod	_	_
9	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	structure	structure	NOUN	NN	Number=Sing	9	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
14	symplectic	symplectic	ADJ	JJ	Degree=Pos	16	amod	_	_
15	vector	vector	NOUN	NN	Number=Sing	16	compound	_	_
16	space	space	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	relation	relation	NOUN	NN	Number=Sing	25	nsubj	_	_
21	imposed	impose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	acl	_	_
22	by	by	ADP	IN	_	21	agent	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	circuit	circuit	NOUN	NN	Number=Sing	22	pobj	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	conj	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
27	Lagrangian	lagrangian	ADJ	JJ	Degree=Pos	29	amod	_	_
28	linear	linear	ADJ	JJ	Degree=Pos	29	compound	_	_
29	relation	relation	NOUN	NN	Number=Sing	25	attr	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	25	punct	_	SpaceAfter=No

# sent_id = 7
# text = Thus, the black box functor goes from our category of circuits to a category with Lagrangian linear relations as morphisms.
1	Thus	thus	ADV	RB	_	7	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
4	black	black	ADJ	JJ	Degree=Pos	5	amod	_	_
5	box	box	NOUN	NN	Number=Sing	6	compound	_	_
6	functor	functor	NOUN	NN	Number=Sing	7	nsubj	_	_
7	goes	go	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	from	from	ADP	IN	_	7	prep	_	_
9	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	10	poss	_	_
10	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	circuits	circuit	NOUN	NNS	Number=Plur	11	pobj	_	_
13	to	to	ADP	IN	_	7	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
16	with	with	ADP	IN	_	15	prep	_	_
17	Lagrangian	lagrangian	ADJ	JJ	Degree=Pos	19	amod	_	_
18	linear	linear	ADJ	JJ	Degree=Pos	19	compound	_	_
19	relations	relation	NOUN	NNS	Number=Plur	16	pobj	_	_
20	as	as	ADP	IN	_	19	prep	_	_
21	morphisms	morphism	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 8
# text = We prove that this functor is symmetric monoidal and indeed a hypergraph functor.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	6	mark	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	functor	functor	NOUN	NN	Number=Sing	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
7	symmetric	symmetric	ADJ	JJ	Degree=Pos	8	amod	_	_
8	monoidal	monoidal	NOUN	NN	Number=Sing	6	attr	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	indeed	indeed	ADV	RB	_	13	advmod	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	hypergraph	hypergraph	NOUN	NN	Number=Sing	13	compound	_	_
13	functor	functor	NOUN	NN	Number=Sing	8	conj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 9
# text = We assume the reader is familiar with category theory, but not with circuit theory or symplectic linear algebra.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	assume	assume	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	reader	reader	NOUN	NN	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	familiar	familiar	ADJ	JJ	Degree=Pos	5	acomp	_	_
7	with	with	ADP	IN	_	6	prep	_	_
8	category	category	NOUN	NN	Number=Sing	9	compound	_	_
9	theory	theory	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
11	but	but	CCONJ	CC	ConjType=Cmp	5	cc	_	_
12	not	not	PART	RB	Polarity=Neg	13	neg	_	_
13	with	with	ADP	IN	_	5	conj	_	_
14	circuit	circuit	NOUN	NN	Number=Sing	15	compound	_	_
15	theory	theory	NOUN	NN	Number=Sing	13	pobj	_	_
16	or	or	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	symplectic	symplectic	ADJ	JJ	Degree=Pos	19	amod	_	_
18	linear	linear	ADJ	JJ	Degree=Pos	19	compound	_	_
19	algebra	algebra	PROPN	NNP	Number=Sing	15	conj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 665
# sent_id = 1
# text = Long before the invention of Feynman diagrams, engineers were using similar diagrams to reason about electrical circuits and more general networks containing mechanical, hydraulic, thermodynamic and chemical components.
1	Long	long	ADV	RB	_	2	advmod	_	_
2	before	before	ADP	IN	_	11	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	invention	invention	NOUN	NN	Number=Sing	2	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	Feynman	Feynman	PROPN	NNP	Number=Sing	7	compound	_	_
7	diagrams	diagram	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
9	engineers	engineer	NOUN	NNS	Number=Plur	11	nsubj	_	_
10	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	11	aux	_	_
11	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	0	ROOT	_	_
12	similar	similar	ADJ	JJ	Degree=Pos	13	amod	_	_
13	diagrams	diagram	NOUN	NNS	Number=Plur	11	dobj	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	reason	reason	VERB	VB	VerbForm=Inf	11	xcomp	_	_
16	about	about	ADP	IN	_	15	prep	_	_
17	electrical	electrical	ADJ	JJ	Degree=Pos	18	amod	_	_
18	circuits	circuit	NOUN	NNS	Number=Plur	16	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	more	more	ADJ	JJR	Degree=Cmp	21	advmod	_	_
21	general	general	ADJ	JJ	Degree=Pos	22	amod	_	_
22	networks	network	NOUN	NNS	Number=Plur	18	conj	_	_
23	containing	contain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	acl	_	_
24	mechanical	mechanical	ADJ	JJ	Degree=Pos	31	amod	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	hydraulic	hydraulic	ADJ	JJ	Degree=Pos	24	conj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
28	thermodynamic	thermodynamic	ADJ	JJ	Degree=Pos	26	conj	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	chemical	chemical	ADJ	JJ	Degree=Pos	28	conj	_	_
31	components	component	NOUN	NNS	Number=Plur	23	dobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 2
# text = We can formalize this reasoning using props: that is, strict symmetric monoidal categories where the objects are natural numbers, with the tensor product of objects given by addition.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	can	can	AUX	MD	VerbForm=Fin	3	aux	_	_
3	formalize	formalize	VERB	VB	VerbForm=Inf	10	ccomp	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	reasoning	reasoning	NOUN	NN	Number=Sing	3	dobj	_	_
6	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	advcl	_	_
7	props	prop	NOUN	NNS	Number=Plur	6	dobj	_	SpaceAfter=No
8	:	:	PUNCT	:	_	10	punct	_	_
9	that	that	PRON	DT	Number=Sing|PronType=Dem	10	advmod	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
12	strict	strict	ADJ	JJ	Degree=Pos	15	amod	_	_
13	symmetric	symmetric	ADJ	JJ	Degree=Pos	15	amod	_	_
14	monoidal	monoidal	ADJ	JJ	Degree=Pos	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	10	attr	_	_
16	where	where	SCONJ	WRB	_	19	advmod	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	objects	object	NOUN	NNS	Number=Plur	19	nsubj	_	_
19	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	relcl	_	_
20	natural	natural	ADJ	JJ	Degree=Pos	21	amod	_	_
21	numbers	number	NOUN	NNS	Number=Plur	19	attr	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
23	with	with	ADP	IN	_	15	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	tensor	tensor	NOUN	NN	Number=Sing	26	compound	_	_
26	product	product	NOUN	NN	Number=Sing	23	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	objects	object	NOUN	NNS	Number=Plur	27	pobj	_	_
29	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	acl	_	_
30	by	by	ADP	IN	_	29	agent	_	_
31	addition	addition	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this approach, each kind of network corresponds to a prop, and each network of this kind is a morphism in that prop.
1	In	in	ADP	IN	_	9	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	approach	approach	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
5	each	each	DET	DT	_	6	det	_	_
6	kind	kind	NOUN	NN	Number=Sing	9	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	network	network	NOUN	NN	Number=Sing	9	compound	_	_
9	corresponds	correspond	NOUN	NNS	Number=Plur	0	ROOT	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	prop	prop	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
15	each	each	DET	DT	_	16	det	_	_
16	network	network	NOUN	NN	Number=Sing	20	nsubj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	this	this	DET	DT	Number=Sing|PronType=Dem	19	det	_	_
19	kind	kind	NOUN	NN	Number=Sing	17	pobj	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	conj	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	morphism	morphism	NOUN	NN	Number=Sing	20	attr	_	_
23	in	in	ADP	IN	_	22	prep	_	_
24	that	that	DET	DT	Number=Sing|PronType=Dem	25	det	_	_
25	prop	prop	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 4
# text = A network with $ m $ inputs and $ n $ outputs is a morphism from $ m $ to $ n $ , putting networks together in series is composition, and setting them side by side is tensoring.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	network	network	NOUN	NN	Number=Sing	9	nsubj	_	_
3	with	with	ADP	IN	_	2	prep	_	_
4	$ m $	$ m $	SYM	$	_	5	nmod	_	_
5	inputs	input	NOUN	NNS	Number=Plur	3	pobj	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	$ n $	$ n $	SYM	$	_	8	nmod	_	_
8	outputs	output	NOUN	NNS	Number=Plur	5	conj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	ccomp	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	morphism	morphism	NOUN	NN	Number=Sing	9	attr	_	_
12	from	from	ADP	IN	_	11	prep	_	_
13	$ m $	$ m $	SYM	$	_	12	pobj	_	_
14	to	to	PART	TO	_	12	prep	_	_
15	$ n $	$ n $	SYM	$	_	14	pobj	_	_
16	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
17	putting	put	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	csubj	_	_
18	networks	network	NOUN	NNS	Number=Plur	17	dobj	_	_
19	together	together	ADV	RB	_	17	advmod	_	_
20	in	in	ADP	IN	_	17	prep	_	_
21	series	series	NOUN	NN	Number=Sing	20	pobj	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
23	composition	composition	NOUN	NN	Number=Sing	22	attr	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
26	setting	set	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	32	csubj	_	_
27	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	26	dobj	_	_
28	side	side	NOUN	NN	Number=Sing	26	dobj	_	_
29	by	by	ADP	IN	_	26	prep	_	_
30	side	side	NOUN	NN	Number=Sing	29	pobj	_	_
31	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	32	aux	_	_
32	tensoring	tensore	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	conj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	32	punct	_	SpaceAfter=No

# sent_id = 5
# text = Here we work out the details of this approach for various kinds of electrical circuits, starting with circuits made solely of ideal perfectly conductive wires, then circuits with passive linear components, and then circuits that also have voltage and current sources.
1	Here	here	ADV	RB	PronType=Dem	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	work	work	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	out	out	ADP	RP	_	3	prt	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	details	detail	NOUN	NNS	Number=Plur	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	this	this	DET	DT	Number=Sing|PronType=Dem	9	det	_	_
9	approach	approach	NOUN	NN	Number=Sing	7	pobj	_	_
10	for	for	ADP	IN	_	9	prep	_	_
11	various	various	ADJ	JJ	Degree=Pos	12	amod	_	_
12	kinds	kind	NOUN	NNS	Number=Plur	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	electrical	electrical	ADJ	JJ	Degree=Pos	15	amod	_	_
15	circuits	circuit	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
17	starting	start	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	advcl	_	_
18	with	with	ADP	IN	_	17	prep	_	_
19	circuits	circuit	NOUN	NNS	Number=Plur	18	pobj	_	_
20	made	make	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	acl	_	_
21	solely	solely	ADV	RB	_	22	advmod	_	_
22	of	of	ADP	IN	_	20	prep	_	_
23	ideal	ideal	ADJ	JJ	Degree=Pos	26	amod	_	_
24	perfectly	perfectly	ADV	RB	_	25	advmod	_	_
25	conductive	conductive	ADJ	JJ	Degree=Pos	26	amod	_	_
26	wires	wire	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
28	then	then	ADV	RB	PronType=Dem	29	advmod	_	_
29	circuits	circuit	NOUN	NNS	Number=Plur	3	dep	_	_
30	with	with	ADP	IN	_	29	prep	_	_
31	passive	passive	ADJ	JJ	Degree=Pos	33	amod	_	_
32	linear	linear	ADJ	JJ	Degree=Pos	33	amod	_	_
33	components	component	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
36	then	then	ADV	RB	PronType=Dem	37	advmod	_	_
37	circuits	circuit	NOUN	NNS	Number=Plur	29	conj	_	_
38	that	that	PRON	WDT	PronType=Rel	40	nsubj	_	_
39	also	also	ADV	RB	_	40	advmod	_	_
40	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	37	relcl	_	_
41	voltage	voltage	NOUN	NN	Number=Sing	40	dobj	_	_
42	and	and	CCONJ	CC	ConjType=Cmp	41	cc	_	_
43	current	current	ADJ	JJ	Degree=Pos	44	amod	_	_
44	sources	source	NOUN	NNS	Number=Plur	41	conj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = Each kind of circuit corresponds to a mathematically natural prop.
1	Each	each	DET	DT	_	2	det	_	_
2	kind	kind	NOUN	NN	Number=Sing	0	ROOT	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	circuit	circuit	NOUN	NN	Number=Sing	5	compound	_	_
5	corresponds	correspond	NOUN	NNS	Number=Plur	3	pobj	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	mathematically	mathematically	ADV	RB	_	9	advmod	_	_
9	natural	natural	ADJ	JJ	Degree=Pos	10	amod	_	_
10	prop	prop	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = We describe the `behavior' of these circuits using morphisms between props.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	5	punct	_	SpaceAfter=No
5	behavior	behavior	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
6	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	5	punct	_	_
7	of	of	ADP	IN	_	5	prep	_	_
8	these	these	DET	DT	Number=Plur|PronType=Dem	9	det	_	_
9	circuits	circuit	NOUN	NNS	Number=Plur	7	pobj	_	_
10	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	acl	_	_
11	morphisms	morphism	NOUN	NNS	Number=Plur	10	dobj	_	_
12	between	between	ADP	IN	_	10	prep	_	_
13	props	prop	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 8
# text = In particular, we give a new construction of the black - boxing functor of Fong and the first author; unlike the original construction, this new one easily generalizes to circuits with nonlinear components.
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	31	ccomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	new	new	ADJ	JJ	Degree=Pos	8	amod	_	_
8	construction	construction	NOUN	NN	Number=Sing	5	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
11	black	black	ADJ	JJ	Degree=Pos	13	amod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	boxing	boxing	NOUN	NN	Number=Sing	14	amod	_	_
14	functor	functor	NOUN	NN	Number=Sing	9	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	Fong	Fong	PROPN	NNP	Number=Sing	15	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
19	first	first	ADJ	JJ	Degree=Pos	20	amod	_	_
20	author	author	NOUN	NN	Number=Sing	8	conj	_	SpaceAfter=No
21	;	;	PUNCT	:	_	31	punct	_	_
22	unlike	unlike	ADP	IN	_	31	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	original	original	ADJ	JJ	Degree=Pos	25	amod	_	_
25	construction	construction	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
27	this	this	DET	DT	Number=Sing|PronType=Dem	29	det	_	_
28	new	new	ADJ	JJ	Degree=Pos	29	amod	_	_
29	one	one	NUM	CD	NumType=Card	31	nsubj	_	_
30	easily	easily	ADV	RB	_	31	advmod	_	_
31	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
32	to	to	ADP	IN	_	31	prep	_	_
33	circuits	circuit	NOUN	NNS	Number=Plur	32	pobj	_	_
34	with	with	ADP	IN	_	33	prep	_	_
35	nonlinear	nonlinear	ADJ	JJ	Degree=Pos	36	amod	_	_
36	components	component	NOUN	NNS	Number=Plur	34	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	31	punct	_	SpaceAfter=No

# sent_id = 9
# text = We also use a morphism of props to clarify the relation between circuit diagrams and the signal - flow diagrams in control theory.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	morphism	morphism	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	props	prop	NOUN	NNS	Number=Plur	6	pobj	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	clarify	clarify	VERB	VB	VerbForm=Inf	3	xcomp	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	relation	relation	NOUN	NN	Number=Sing	9	dobj	_	_
12	between	between	ADP	IN	_	11	prep	_	_
13	circuit	circuit	NOUN	NN	Number=Sing	14	compound	_	_
14	diagrams	diagram	NOUN	NNS	Number=Plur	12	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
17	signal	signal	NOUN	NN	Number=Sing	19	amod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	flow	flow	NOUN	NN	Number=Sing	20	compound	_	_
20	diagrams	diagram	NOUN	NNS	Number=Plur	14	conj	_	_
21	in	in	ADP	IN	_	20	prep	_	_
22	control	control	NOUN	NN	Number=Sing	23	compound	_	_
23	theory	theory	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 10
# text = Technically, the key tools are the Rosebrugh - Sabadini - Walters result relating circuits to special commutative Frobenius monoids, the monadic adjunction between props and signatures, and a result saying which symmetric monoidal categories are equivalent to props.
1	Technically	technically	ADV	RB	_	6	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	key	key	ADJ	JJ	Degree=Pos	5	amod	_	_
5	tools	tool	NOUN	NNS	Number=Plur	6	nsubj	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
8	Rosebrugh	Rosebrugh	PROPN	NNP	Number=Sing	12	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
10	Sabadini	Sabadini	PROPN	NNP	Number=Sing	12	compound	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	Walters	Walters	PROPN	NNP	Number=Sing	13	nsubj	_	_
13	result	result	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	relating	relate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	xcomp	_	_
15	circuits	circuit	NOUN	NNS	Number=Plur	14	dobj	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	special	special	ADJ	JJ	Degree=Pos	20	amod	_	_
18	commutative	commutative	ADJ	JJ	Degree=Pos	20	amod	_	_
19	Frobenius	Frobenius	PROPN	NNP	Number=Sing	20	compound	_	_
20	monoids	monoid	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	monadic	monadic	ADJ	JJ	Degree=Pos	24	amod	_	_
24	adjunction	adjunction	NOUN	NN	Number=Sing	20	appos	_	_
25	between	between	ADP	IN	_	24	prep	_	_
26	props	prop	NOUN	NNS	Number=Plur	25	pobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	signatures	signature	NOUN	NNS	Number=Plur	26	conj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
32	result	result	NOUN	NN	Number=Sing	24	conj	_	_
33	saying	say	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	32	acl	_	_
34	which	which	PRON	WDT	_	38	mark	_	_
35	symmetric	symmetric	ADJ	JJ	Degree=Pos	37	amod	_	_
36	monoidal	monoidal	ADJ	JJ	Degree=Pos	37	amod	_	_
37	categories	category	NOUN	NNS	Number=Plur	38	nsubj	_	_
38	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	33	ccomp	_	_
39	equivalent	equivalent	ADJ	JJ	Degree=Pos	38	acomp	_	_
40	to	to	ADP	IN	_	39	prep	_	_
41	props	prop	NOUN	NNS	Number=Plur	40	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# doc_id = 666
# sent_id = 1
# text = Good atlases are defined for effective orbifolds, and a spark complex is constructed on each good atlas.
1	Good	good	ADJ	JJ	Degree=Pos	2	amod	_	_
2	atlases	atlas	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	effective	effective	ADJ	JJ	Degree=Pos	7	amod	_	_
7	orbifolds	orbifold	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	spark	spark	NOUN	NN	Number=Sing	12	compound	_	_
12	complex	complex	NOUN	NN	Number=Sing	14	nsubjpass	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	conj	_	_
15	on	on	ADP	IN	_	14	prep	_	_
16	each	each	DET	DT	_	18	det	_	_
17	good	good	ADJ	JJ	Degree=Pos	18	amod	_	_
18	atlas	atlas	PROPN	NNP	Number=Sing	15	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 2
# text = It is proved that this process is 2 - functorial with compatible systems playing as morphisms between good atlases, and that the spark character 2 - functor factors through this 2 - functor.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	that	that	SCONJ	IN	_	7	mark	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	process	process	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
8	2	2	NUM	CD	NumType=Card	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	functorial	functorial	NOUN	NN	Number=Sing	7	acomp	_	_
11	with	with	ADP	IN	_	10	prep	_	_
12	compatible	compatible	ADJ	JJ	Degree=Pos	13	amod	_	_
13	systems	system	NOUN	NNS	Number=Plur	11	pobj	_	_
14	playing	play	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	acl	_	_
15	as	as	ADP	IN	_	14	prep	_	_
16	morphisms	morphism	NOUN	NNS	Number=Plur	15	pobj	_	_
17	between	between	ADP	IN	_	16	prep	_	_
18	good	good	ADJ	JJ	Degree=Pos	19	amod	_	_
19	atlases	atlas	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
22	that	that	SCONJ	IN	_	25	mark	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	spark	spark	NOUN	NN	Number=Sing	25	compound	_	_
25	character	character	NOUN	NN	Number=Sing	7	conj	_	_
26	2	2	NUM	CD	NumType=Card	28	nummod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	functor	functor	NOUN	NN	Number=Sing	29	compound	_	_
29	factors	factor	NOUN	NNS	Number=Plur	25	appos	_	_
30	through	through	ADP	IN	_	25	prep	_	_
31	this	this	DET	DT	Number=Sing|PronType=Dem	34	det	_	_
32	2	2	NUM	CD	NumType=Card	34	nummod	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	functor	functor	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 667
# sent_id = 1
# text = Following the pattern of the Frobenius structure usually assigned to the 1 - dimensional sphere, we investigate the Frobenius structures of spheres in all other dimensions.
1	Following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	18	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	pattern	pattern	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	Frobenius	Frobenius	PROPN	NNP	Number=Sing	7	compound	_	_
7	structure	structure	NOUN	NN	Number=Sing	4	pobj	_	_
8	usually	usually	ADV	RB	_	9	advmod	_	_
9	assigned	assign	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	acl	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
12	1	1	NUM	CD	NumType=Card	14	advmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	dimensional	dimensional	ADJ	JJ	Degree=Pos	15	amod	_	_
15	sphere	sphere	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
17	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	18	nsubj	_	_
18	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	Frobenius	Frobenius	PROPN	NNP	Number=Sing	21	compound	_	_
21	structures	structure	NOUN	NNS	Number=Plur	18	dobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	spheres	sphere	NOUN	NNS	Number=Plur	22	pobj	_	_
24	in	in	ADP	IN	_	21	prep	_	_
25	all	all	DET	DT	_	27	det	_	_
26	other	other	ADJ	JJ	Degree=Pos	27	amod	_	_
27	dimensions	dimension	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# sent_id = 2
# text = Starting from dimension $ d=1 $ , all the spheres are commutative Frobenius objects in categories whose arrows are $ (d+1) $ - dimensional cobordisms.
1	Starting	start	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	advcl	_	_
2	from	from	ADP	IN	_	1	prep	_	_
3	dimension	dimension	NOUN	NN	Number=Sing	2	pobj	_	_
4	$ d=1 $	$ d=1 $	SYM	$	_	1	dobj	_	_
5	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
6	all	all	DET	PDT	_	8	predet	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	spheres	sphere	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	commutative	commutative	ADJ	JJ	Degree=Pos	12	amod	_	_
11	Frobenius	Frobenius	PROPN	NNP	Number=Sing	12	compound	_	_
12	objects	object	NOUN	NNS	Number=Plur	9	attr	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	_
15	whose	whose	DET	WP$	Poss=Yes	16	poss	_	_
16	arrows	arrow	NOUN	NNS	Number=Plur	17	nsubj	_	_
17	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	relcl	_	_
18	$ (d+1) $	$ (d+1) $	SYM	$	_	20	advmod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	dimensional	dimensional	ADJ	JJ	Degree=Pos	21	amod	_	_
21	cobordisms	cobordism	NOUN	NNS	Number=Plur	17	attr	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 3
# text = With respect to the language of Frobenius objects, there is no distinction between these spheres—they are all free of additional equations formulated in this language.
1	With	with	ADP	IN	_	11	prep	_	_
2	respect	respect	NOUN	NN	Number=Sing	1	pobj	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	language	language	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Frobenius	Frobenius	PROPN	NNP	Number=Sing	8	compound	_	_
8	objects	object	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
10	there	there	PRON	EX	_	11	expl	_	_
11	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	ccomp	_	_
12	no	no	DET	DT	_	13	det	_	_
13	distinction	distinction	NOUN	NN	Number=Sing	11	attr	_	_
14	between	between	ADP	IN	_	13	prep	_	_
15	these	these	DET	DT	Number=Plur|PronType=Dem	16	det	_	_
16	spheres	sphere	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	—	—	PUNCT	:	_	19	punct	_	SpaceAfter=No
18	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	19	nsubj	_	_
19	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	all	all	ADV	RB	_	19	advmod	_	_
21	free	free	ADJ	JJ	Degree=Pos	19	acomp	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	additional	additional	ADJ	JJ	Degree=Pos	24	amod	_	_
24	equations	equation	NOUN	NNS	Number=Plur	22	pobj	_	_
25	formulated	formulate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	acl	_	_
26	in	in	ADP	IN	_	25	prep	_	_
27	this	this	DET	DT	Number=Sing|PronType=Dem	28	det	_	_
28	language	language	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 4
# text = The corresponding structure makes out of the 0 - dimensional sphere not a commutative but a symmetric Frobenius object.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	amod	_	_
3	structure	structure	NOUN	NN	Number=Sing	4	nsubj	_	_
4	makes	make	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	out	out	ADP	IN	_	4	prep	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
8	0	0	NUM	CD	NumType=Card	10	advmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	dimensional	dimensional	ADJ	JJ	Degree=Pos	11	amod	_	_
11	sphere	sphere	NOUN	NN	Number=Sing	6	pobj	_	_
12	not	not	PART	RB	Polarity=Neg	14	neg	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	commutative	commutative	NOUN	NN	Number=Sing	11	appos	_	_
15	but	but	CCONJ	CC	ConjType=Cmp	4	cc	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
17	symmetric	symmetric	ADJ	JJ	Degree=Pos	19	amod	_	_
18	Frobenius	Frobenius	PROPN	NNP	Number=Sing	19	compound	_	_
19	object	object	NOUN	NN	Number=Sing	4	conj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = This sphere is mapped to a matrix Frobenius algebra by a 1 - dimensional topological quantum field theory, which corresponds to the representation of a class of diagrammatic algebras given by Richard Brauer.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	sphere	sphere	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	mapped	map	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	matrix	matrix	NOUN	NN	Number=Sing	5	pobj	_	_
8	Frobenius	Frobenius	PROPN	NNP	Number=Sing	9	compound	_	_
9	algebra	algebra	NOUN	NN	Number=Sing	7	appos	_	_
10	by	by	ADP	IN	_	4	agent	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
12	1	1	NUM	CD	NumType=Card	14	advmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	dimensional	dimensional	ADJ	JJ	Degree=Pos	18	amod	_	_
15	topological	topological	ADJ	JJ	Degree=Pos	18	amod	_	_
16	quantum	quantum	NOUN	NN	Number=Sing	17	compound	_	_
17	field	field	NOUN	NN	Number=Sing	18	compound	_	_
18	theory	theory	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	which	which	PRON	WDT	_	21	nsubj	_	_
21	corresponds	correspond	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	relcl	_	_
22	to	to	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	representation	representation	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	class	class	NOUN	NN	Number=Sing	25	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	diagrammatic	diagrammatic	ADJ	JJ	Degree=Pos	30	amod	_	_
30	algebras	algebra	NOUN	NNS	Number=Plur	28	pobj	_	_
31	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	acl	_	_
32	by	by	ADP	IN	_	31	agent	_	_
33	Richard	Richard	PROPN	NNP	Number=Sing	34	compound	_	_
34	Brauer	Brauer	PROPN	NNP	Number=Sing	32	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 668
# sent_id = 1
# text = Let $ C $ be a category with finite colimits, and let $ (E, M) $ be a factorisation system on $ C $ with $ M $ stable under pushout.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ C $	$ c $	SYM	$	_	3	nsubj	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	3	attr	_	_
6	with	with	ADP	IN	_	5	prep	_	_
7	finite	finite	ADJ	JJ	Degree=Pos	8	amod	_	_
8	colimits	colimit	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
11	let	let	VERB	VB	VerbForm=Inf	3	conj	_	_
12	$ (E, M) $	$ (e, m) $	SYM	$	_	13	nsubj	_	_
13	be	be	AUX	VB	VerbForm=Inf	11	ccomp	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	factorisation	factorisation	NOUN	NN	Number=Sing	16	compound	_	_
16	system	system	NOUN	NN	Number=Sing	13	attr	_	_
17	on	on	ADP	IN	_	16	prep	_	_
18	$ C $	$ c $	SYM	$	_	17	pobj	_	_
19	with	with	ADP	IN	_	13	prep	_	_
20	$ M $	$ m $	SYM	$	_	19	pobj	_	_
21	stable	stable	ADJ	JJ	Degree=Pos	13	acomp	_	_
22	under	under	ADP	IN	_	13	prep	_	_
23	pushout	pushout	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = Writing $ C;M^{op} $ for the symmetric monoidal category with morphisms cospans of the form $ stackrel{c}to stackrel{m}leftarrow $ , where $ c in C $ and $ m in M $ , we give a method for constructing a category from a symmetric lax monoidal functor $ F : (C; mc M^{op}, +) to (Set, times) $ .
1	Writing	write	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	advcl	_	_
2	$ C;M^{op} $	$ c;m^{op} $	SYM	$	_	1	dobj	_	_
3	for	for	ADP	IN	_	1	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	symmetric	symmetric	ADJ	JJ	Degree=Pos	7	amod	_	_
6	monoidal	monoidal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	category	category	NOUN	NN	Number=Sing	3	pobj	_	_
8	with	with	ADP	IN	_	7	prep	_	_
9	morphisms	morphism	NOUN	NNS	Number=Plur	10	compound	_	_
10	cospans	cospan	NOUN	NNS	Number=Plur	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	form	form	NOUN	NN	Number=Sing	11	pobj	_	_
14	$ stackrel{c}to stackrel{m}leftarrow $	$ stackrel{c}to stackrel{m}leftarrow $	SYM	$	_	1	dep	_	_
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	where	where	SCONJ	WRB	_	17	advmod	_	_
17	$ c in C $	$ c in c $	SYM	$	_	14	relcl	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	$ m in M $	$ m in m $	SYM	$	_	17	conj	_	_
20	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
21	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	22	nsubj	_	_
22	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	method	method	NOUN	NN	Number=Sing	22	dobj	_	_
25	for	for	ADP	IN	_	24	prep	_	_
26	constructing	construct	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	25	pcomp	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	category	category	NOUN	NN	Number=Sing	26	dobj	_	_
29	from	from	ADP	IN	_	26	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
31	symmetric	symmetric	ADJ	JJ	Degree=Pos	34	amod	_	_
32	lax	lax	ADJ	JJ	Degree=Pos	34	amod	_	_
33	monoidal	monoidal	NOUN	NN	Number=Sing	34	compound	_	_
34	functor	functor	NOUN	NN	Number=Sing	29	pobj	_	_
35	$ F : (C; mc M^{op}, +) to (Set, times) $	$ f : (c; mc m^{op}, +) to (set, times) $	SYM	$	_	22	dative	_	_
36	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# sent_id = 3
# text = A morphism in this category, termed a decorated corelation, comprises (i) a cospan $ X to N leftarrow Y $ in $ C $ such that the canonical copairing $ X+Y to N $ lies in $ E $ , together with (ii) an element of $ FN $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	morphism	morphism	NOUN	NN	Number=Sing	7	nsubj	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
7	termed	term	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	decorated	decorate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	corelation	corelation	NOUN	NN	Number=Sing	7	dobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
12	comprises	comprise	NOUN	NNS	Number=Plur	7	dep	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
14	i	i	NOUN	NN	Number=Sing	12	appos	_	SpaceAfter=No
15	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	14	punct	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	cospan	cospan	NOUN	NN	Number=Sing	14	appos	_	_
18	$ X to N leftarrow Y $	$ x to n leftarrow y $	SYM	$	_	12	dep	_	_
19	in	in	ADP	IN	_	12	prep	_	_
20	$ C $	$ c $	SYM	$	_	21	nmod	_	_
21	such	such	ADJ	JJ	Degree=Pos	19	pobj	_	_
22	that	that	SCONJ	IN	_	27	mark	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	canonical	canonical	NOUN	NN	Number=Sing	27	nsubj	_	_
25	copairing	copaire	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	24	acl	_	_
26	$ X+Y to N $	$ x+y to n $	SYM	$	_	27	poss	_	_
27	lies	lie	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	ccomp	_	_
28	in	in	ADP	IN	_	27	prep	_	_
29	$ E $	$ e $	SYM	$	_	28	pobj	_	_
30	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
31	together	together	ADV	RB	_	32	advmod	_	_
32	with	with	ADP	IN	_	27	prep	_	_
33	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	34	punct	_	SpaceAfter=No
34	ii	ii	PROPN	NNP	Number=Sing	32	pobj	_	SpaceAfter=No
35	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	32	punct	_	_
36	an	an	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
37	element	element	NOUN	NN	Number=Sing	32	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	$ FN $	$ fn $	SYM	$	_	38	pobj	_	_
40	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = Functors between decorated corelation categories can be constructed from natural transformations between the decorating functors $ F $ .
1	Functors	functor	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
2	between	between	ADP	IN	_	1	prep	_	_
3	decorated	decorate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	amod	_	_
4	corelation	corelation	NOUN	NN	Number=Sing	5	compound	_	_
5	categories	category	NOUN	NNS	Number=Plur	2	pobj	_	_
6	can	can	AUX	MD	VerbForm=Fin	8	aux	_	_
7	be	be	AUX	VB	VerbForm=Inf	8	auxpass	_	_
8	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	from	from	ADP	IN	_	8	prep	_	_
10	natural	natural	ADJ	JJ	Degree=Pos	11	amod	_	_
11	transformations	transformation	NOUN	NNS	Number=Plur	9	pobj	_	_
12	between	between	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	decorating	decorate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	amod	_	_
15	functors	functor	NOUN	NNS	Number=Plur	12	pobj	_	_
16	$ F $	$ f $	SYM	$	_	8	dep	_	_
17	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 5
# text = This provides a general method for constructing hypergraph categories—symmetric monoidal categories in which each object is a special commutative Frobenius monoid in a coherent way—and their functors.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	general	general	ADJ	JJ	Degree=Pos	5	amod	_	_
5	method	method	NOUN	NN	Number=Sing	2	dobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	constructing	construct	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	pcomp	_	_
8	hypergraph	hypergraph	ADJ	JJ	Degree=Pos	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	7	dobj	_	SpaceAfter=No
10	—	—	PUNCT	:	_	2	punct	_	SpaceAfter=No
11	symmetric	symmetric	ADJ	JJ	Degree=Pos	13	amod	_	_
12	monoidal	monoidal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	categories	category	NOUN	NNS	Number=Plur	1	appos	_	_
14	in	in	ADP	IN	_	18	prep	_	_
15	which	which	PRON	WDT	_	14	pobj	_	_
16	each	each	DET	DT	_	17	det	_	_
17	object	object	NOUN	NN	Number=Sing	18	nsubj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	relcl	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
20	special	special	ADJ	JJ	Degree=Pos	23	amod	_	_
21	commutative	commutative	ADJ	JJ	Degree=Pos	23	amod	_	_
22	Frobenius	Frobenius	PROPN	NNP	Number=Sing	23	compound	_	_
23	monoid	monoid	NOUN	NN	Number=Sing	18	attr	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
26	coherent	coherent	ADJ	JJ	Degree=Pos	27	amod	_	_
27	way	way	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
28	—	—	PUNCT	:	_	13	punct	_	SpaceAfter=No
29	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
30	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	31	poss	_	_
31	functors	functor	NOUN	NNS	Number=Plur	13	conj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = Such categories are useful for modelling network languages, for example circuit diagrams, and such functors are useful for modelling their semantics.
1	Such	such	ADJ	JJ	Degree=Pos	2	amod	_	_
2	categories	category	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	useful	useful	ADJ	JJ	Degree=Pos	3	acomp	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	modelling	model	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	pcomp	_	_
7	network	network	NOUN	NN	Number=Sing	8	compound	_	_
8	languages	language	NOUN	NNS	Number=Plur	6	dobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
10	for	for	ADP	IN	_	3	prep	_	_
11	example	example	NOUN	NN	Number=Sing	13	compound	_	_
12	circuit	circuit	NOUN	NN	Number=Sing	13	compound	_	_
13	diagrams	diagram	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
16	such	such	ADJ	JJ	Degree=Pos	17	amod	_	_
17	functors	functor	NOUN	NNS	Number=Plur	18	nsubj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	conj	_	_
19	useful	useful	ADJ	JJ	Degree=Pos	18	acomp	_	_
20	for	for	ADP	IN	_	19	prep	_	_
21	modelling	model	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	20	pcomp	_	_
22	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	23	poss	_	_
23	semantics	semantic	NOUN	NNS	Number=Plur	21	dobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# doc_id = 669
# sent_id = 1
# text = We associate to a 2 - vector bundle over an essentially finite groupoid a 2 - vector space of parallel sections, or, in representation theoretic terms, of higher invariants, which can be described as homotopy fixed points.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	associate	associate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
5	2	2	NUM	CD	NumType=Card	7	nummod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	vector	vector	NOUN	NN	Number=Sing	8	compound	_	_
8	bundle	bundle	NOUN	NN	Number=Sing	3	pobj	_	_
9	over	over	ADP	IN	_	8	prep	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	essentially	essentially	ADV	RB	_	12	advmod	_	_
12	finite	finite	ADJ	JJ	Degree=Pos	13	amod	_	_
13	groupoid	groupoid	NOUN	NN	Number=Sing	9	pobj	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
15	2	2	NUM	CD	NumType=Card	17	nummod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	vector	vector	NOUN	NN	Number=Sing	18	compound	_	_
18	space	space	NOUN	NN	Number=Sing	13	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	parallel	parallel	ADJ	JJ	Degree=Pos	21	amod	_	_
21	sections	section	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
23	or	or	CCONJ	CC	ConjType=Cmp	2	cc	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
25	in	in	ADP	IN	_	2	prep	_	_
26	representation	representation	NOUN	NN	Number=Sing	28	nmod	_	_
27	theoretic	theoretic	ADJ	JJ	Degree=Pos	28	amod	_	_
28	terms	term	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
30	of	of	ADP	IN	_	28	prep	_	_
31	higher	high	ADJ	JJR	Degree=Cmp	32	amod	_	_
32	invariants	invariant	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
34	which	which	PRON	WDT	_	37	nsubjpass	_	_
35	can	can	AUX	MD	VerbForm=Fin	37	aux	_	_
36	be	be	AUX	VB	VerbForm=Inf	37	auxpass	_	_
37	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	relcl	_	_
38	as	as	ADP	IN	_	37	prep	_	_
39	homotopy	homotopy	NOUN	NN	Number=Sing	41	nmod	_	_
40	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	41	amod	_	_
41	points	point	NOUN	NNS	Number=Plur	38	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Our main result is the extension of this assignment to a symmetric monoidal 2 - functor $ Par : 2VecBunGrpd to 2Vect $ .
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	3	poss	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	result	result	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	extension	extension	NOUN	NN	Number=Sing	4	attr	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	this	this	DET	DT	Number=Sing|PronType=Dem	9	det	_	_
9	assignment	assignment	NOUN	NN	Number=Sing	7	pobj	_	_
10	to	to	ADP	IN	_	6	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	symmetric	symmetric	ADJ	JJ	Degree=Pos	13	amod	_	_
13	monoidal	monoidal	NOUN	NN	Number=Sing	10	pobj	_	_
14	2	2	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	functor	functor	NOUN	NN	Number=Sing	4	dep	_	_
17	$ Par : 2VecBunGrpd to 2Vect $	$ par : 2vecbungrpd to 2vect $	SYM	$	_	16	appos	_	_
18	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = It is defined on the symmetric monoidal bicategory $ 2VecBunGrpd $ whose morphisms arise from spans of groupoids in such a way that the functor $ Par $ provides pull - push maps between 2 - vector spaces of parallel sections of 2 - vector bundles.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	on	on	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
6	symmetric	symmetric	ADJ	JJ	Degree=Pos	8	amod	_	_
7	monoidal	monoidal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	bicategory	bicategory	NOUN	NN	Number=Sing	4	pobj	_	_
9	$ 2VecBunGrpd $	$ 2vecbungrpd $	SYM	$	_	8	appos	_	_
10	whose	whose	DET	WP$	Poss=Yes	11	poss	_	_
11	morphisms	morphism	NOUN	NNS	Number=Plur	12	nsubj	_	_
12	arise	arise	VERB	VBP	Tense=Pres|VerbForm=Fin	9	relcl	_	_
13	from	from	ADP	IN	_	12	prep	_	_
14	spans	span	NOUN	NNS	Number=Plur	13	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	groupoids	groupoid	NOUN	NNS	Number=Plur	15	pobj	_	_
17	in	in	ADP	IN	_	12	prep	_	_
18	such	such	DET	PDT	_	20	predet	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	way	way	NOUN	NN	Number=Sing	17	pobj	_	_
21	that	that	PRON	WDT	PronType=Rel	25	advmod	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	functor	functor	NOUN	NN	Number=Sing	25	nsubj	_	_
24	$ Par $	$ par $	SYM	$	_	23	appos	_	_
25	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	relcl	_	_
26	pull	pull	VERB	VB	VerbForm=Inf	28	compound	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	push	push	NOUN	NN	Number=Sing	29	compound	_	_
29	maps	map	NOUN	NNS	Number=Plur	25	dobj	_	_
30	between	between	ADP	IN	_	25	prep	_	_
31	2	2	NUM	CD	NumType=Card	33	nummod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	vector	vector	NOUN	NN	Number=Sing	34	compound	_	_
34	spaces	space	NOUN	NNS	Number=Plur	30	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	parallel	parallel	ADJ	JJ	Degree=Pos	37	amod	_	_
37	sections	section	NOUN	NNS	Number=Plur	35	pobj	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	2	2	NUM	CD	NumType=Card	41	nummod	_	_
40	-	-	PUNCT	HYPH	PunctType=Dash	41	punct	_	_
41	vector	vector	NOUN	NN	Number=Sing	42	compound	_	_
42	bundles	bundle	NOUN	NNS	Number=Plur	38	pobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = The direct motivation for our construction comes from the orbifoldization of extended equivariant topological field theories.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	direct	direct	ADJ	JJ	Degree=Pos	3	amod	_	_
3	motivation	motivation	NOUN	NN	Number=Sing	7	nsubj	_	_
4	for	for	ADP	IN	_	3	prep	_	_
5	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	6	poss	_	_
6	construction	construction	NOUN	NN	Number=Sing	4	pobj	_	_
7	comes	come	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	from	from	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	orbifoldization	orbifoldization	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	extended	extended	ADJ	JJ	Degree=Pos	16	amod	_	_
13	equivariant	equivariant	ADJ	JJ	Degree=Pos	16	amod	_	_
14	topological	topological	ADJ	JJ	Degree=Pos	15	amod	_	_
15	field	field	NOUN	NN	Number=Sing	16	compound	_	_
16	theories	theory	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 670
# sent_id = 1
# text = The interleaving distance was originally defined in the field of Topological Data Analysis (TDA) by Chazal as a metric on the class of persistence modules parametrized over the real line.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	interleaving	interleave	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	amod	_	_
3	distance	distance	NOUN	NN	Number=Sing	6	nsubjpass	_	_
4	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	6	auxpass	_	_
5	originally	originally	ADV	RB	_	6	advmod	_	_
6	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	field	field	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	Topological	Topological	PROPN	NNP	Number=Sing	13	compound	_	_
12	Data	Data	PROPN	NNP	Number=Sing	13	compound	_	_
13	Analysis	Analysis	PROPN	NNP	Number=Sing	10	pobj	_	_
14	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	13	punct	_	SpaceAfter=No
15	TDA	TDA	PROPN	NNP	Number=Sing	13	appos	_	SpaceAfter=No
16	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	13	punct	_	_
17	by	by	ADP	IN	_	6	agent	_	_
18	Chazal	Chazal	PROPN	NNP	Number=Sing	17	pobj	_	_
19	as	as	ADP	IN	_	6	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	metric	metric	NOUN	NN	Number=Sing	19	pobj	_	_
22	on	on	ADP	IN	_	21	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	class	class	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	persistence	persistence	NOUN	NN	Number=Sing	27	compound	_	_
27	modules	module	NOUN	NNS	Number=Plur	25	pobj	_	_
28	parametrized	parametrize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	acl	_	_
29	over	over	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	real	real	ADJ	JJ	Degree=Pos	32	amod	_	_
32	line	line	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = Bubenik et
1	Bubenik	Bubenik	PROPN	NNP	Number=Sing	0	ROOT	_	_
2	et	et	NOUN	NN	Number=Sing	1	intj	_	SpaceAfter=No

# sent_id = 3
# text = al.
1	al	al	PROPN	NNP	Number=Sing	0	ROOT	_	SpaceAfter=No
2	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 4
# text = subsequently extended the definition to categories of functors on a poset, the objects in these categories being regarded as `generalized persistence modules'.
1	subsequently	subsequently	ADV	RB	_	2	advmod	_	_
2	extended	extend	VERB	VBD	Tense=Past|VerbForm=Fin	19	advcl	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	definition	definition	NOUN	NN	Number=Sing	2	dobj	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	functors	functor	NOUN	NNS	Number=Plur	7	pobj	_	_
9	on	on	ADP	IN	_	6	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	poset	poset	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	objects	object	NOUN	NNS	Number=Plur	19	nsubjpass	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	these	these	DET	DT	Number=Plur|PronType=Dem	17	det	_	_
17	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	_
18	being	be	AUX	VBG	VerbForm=Ger	19	auxpass	_	_
19	regarded	regard	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
20	as	as	ADP	IN	_	19	prep	_	_
21	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	24	punct	_	SpaceAfter=No
22	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
23	persistence	persistence	NOUN	NN	Number=Sing	24	compound	_	_
24	modules	module	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
25	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	19	punct	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 5
# text = These metrics typically depend on the choice of a lax semigroup of endomorphisms of the poset.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	metrics	metric	NOUN	NNS	Number=Plur	4	nsubj	_	_
3	typically	typically	ADV	RB	_	4	advmod	_	_
4	depend	depend	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	on	on	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	choice	choice	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	lax	lax	ADJ	JJ	Degree=Pos	11	amod	_	_
11	semigroup	semigroup	NOUN	NN	Number=Sing	8	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	endomorphisms	endomorphism	NOUN	NNS	Number=Plur	12	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	poset	poset	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 6
# text = The purpose of the present paper is to develop a more general framework for the notion of interleaving distance using the theory of `actegories'.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	purpose	purpose	NOUN	NN	Number=Sing	7	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	present	present	ADJ	JJ	Degree=Pos	6	amod	_	_
6	paper	paper	NOUN	NN	Number=Sing	3	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	develop	develop	VERB	VB	VerbForm=Inf	7	xcomp	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	more	more	ADV	RBR	Degree=Cmp	12	advmod	_	_
12	general	general	ADJ	JJ	Degree=Pos	13	amod	_	_
13	framework	framework	NOUN	NN	Number=Sing	9	dobj	_	_
14	for	for	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	notion	notion	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	interleaving	interleave	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	amod	_	_
19	distance	distance	NOUN	NN	Number=Sing	17	pobj	_	_
20	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	acl	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	theory	theory	NOUN	NN	Number=Sing	20	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	23	punct	_	SpaceAfter=No
25	actegories	actegorie	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	23	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 7
# text = Specifically, we extend the notion of interleaving distance to arbitrary categories equipped with a flow, that is, a lax monoidal action by the monoid $ [0, infty) $ .
1	Specifically	specifically	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	extend	extend	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	notion	notion	NOUN	NN	Number=Sing	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	interleaving	interleave	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	amod	_	_
9	distance	distance	NOUN	NN	Number=Sing	7	pobj	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	12	amod	_	_
12	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
13	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	flow	flow	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
18	that	that	ADV	RB	_	19	advmod	_	_
19	is	is	ADV	RB	_	24	advmod	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
22	lax	lax	ADJ	JJ	Degree=Pos	24	amod	_	_
23	monoidal	monoidal	ADJ	JJ	Degree=Pos	24	amod	_	_
24	action	action	NOUN	NN	Number=Sing	4	dobj	_	_
25	by	by	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	monoid	monoid	NOUN	NN	Number=Sing	25	pobj	_	_
28	$ [0, infty) $	$ [0, infty) $	SYM	$	_	4	dep	_	_
29	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 8
# text = In this way, the class of objects in such a category acquires the structure of a Lawvere metric space.
1	In	in	ADP	IN	_	13	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	way	way	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	class	class	NOUN	NN	Number=Sing	13	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	objects	object	NOUN	NNS	Number=Plur	7	pobj	_	_
9	in	in	ADP	IN	_	6	prep	_	_
10	such	such	DET	PDT	_	12	predet	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
13	acquires	acquire	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	structure	structure	NOUN	NN	Number=Sing	13	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
18	Lawvere	lawvere	ADV	RB	_	19	advmod	_	_
19	metric	metric	ADJ	JJ	Degree=Pos	20	amod	_	_
20	space	space	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 9
# text = Functors that are colax $ [0, infty) $ - equivariant yield maps that are 1 - Lipschitz.
1	Functors	functor	NOUN	NNS	Number=Plur	0	ROOT	_	_
2	that	that	PRON	WDT	PronType=Rel	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	colax	colax	ADJ	JJ	Degree=Pos	1	relcl	_	_
5	$ [0, infty) $	$ [0, infty) $	SYM	$	_	7	advmod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	equivariant	equivariant	ADJ	JJ	Degree=Pos	9	amod	_	_
8	yield	yield	NOUN	NN	Number=Sing	9	compound	_	_
9	maps	map	NOUN	NNS	Number=Plur	4	dobj	_	_
10	that	that	PRON	WDT	PronType=Rel	11	nsubj	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	relcl	_	_
12	1	1	NUM	CD	NumType=Card	14	nummod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	Lipschitz	Lipschitz	PROPN	NNP	Number=Sing	11	attr	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 10
# text = This leads to concise proofs of various known stability results from TDA, by considering appropriate colax $ [0, infty) $ - equivariant functors.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	leads	lead	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	concise	concise	ADJ	JJ	Degree=Pos	5	amod	_	_
5	proofs	proof	NOUN	NNS	Number=Plur	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	various	various	ADJ	JJ	Degree=Pos	10	amod	_	_
8	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
9	stability	stability	NOUN	NN	Number=Sing	10	compound	_	_
10	results	result	NOUN	NNS	Number=Plur	6	pobj	_	_
11	from	from	ADP	IN	_	5	prep	_	_
12	TDA	TDA	PROPN	NNP	Number=Sing	11	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
14	by	by	ADP	IN	_	2	prep	_	_
15	considering	consider	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	pcomp	_	_
16	appropriate	appropriate	ADJ	JJ	Degree=Pos	17	amod	_	_
17	colax	colax	PROPN	NNP	Number=Sing	15	dobj	_	_
18	$ [0, infty) $	$ [0, infty) $	SYM	$	_	20	quantmod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	equivariant	equivariant	ADJ	JJ	Degree=Pos	21	amod	_	_
21	functors	functor	NOUN	NNS	Number=Plur	17	appos	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 11
# text = Along the way, we show that several common metrics, including the Hausdorff distance and the $ L^infty $ - norm, can be realized as interleaving distances in this general perspective.
1	Along	along	ADP	IN	_	6	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	way	way	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	24	mark	_	_
8	several	several	ADJ	JJ	Degree=Pos	10	amod	_	_
9	common	common	ADJ	JJ	Degree=Pos	10	amod	_	_
10	metrics	metric	NOUN	NNS	Number=Plur	24	nsubjpass	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	15	compound	_	_
15	distance	distance	NOUN	NN	Number=Sing	12	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
18	$ L^infty $	$ l^infty $	SYM	$	_	20	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	norm	norm	NOUN	NN	Number=Sing	15	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
22	can	can	AUX	MD	VerbForm=Fin	24	aux	_	_
23	be	be	AUX	VB	VerbForm=Inf	24	auxpass	_	_
24	realized	realize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	ccomp	_	_
25	as	as	ADP	IN	_	24	prep	_	_
26	interleaving	interleave	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	27	amod	_	_
27	distances	distance	NOUN	NNS	Number=Plur	25	pobj	_	_
28	in	in	ADP	IN	_	27	prep	_	_
29	this	this	DET	DT	Number=Sing|PronType=Dem	31	det	_	_
30	general	general	ADJ	JJ	Degree=Pos	31	amod	_	_
31	perspective	perspective	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 671
# sent_id = 1
# text = We introduce and compare several new exactness conditions involving what we call split cubes.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	compare	compare	VERB	VB	VerbForm=Inf	2	conj	_	_
5	several	several	ADJ	JJ	Degree=Pos	8	amod	_	_
6	new	new	ADJ	JJ	Degree=Pos	8	amod	_	_
7	exactness	exactness	NOUN	NN	Number=Sing	8	compound	_	_
8	conditions	condition	NOUN	NNS	Number=Plur	4	dobj	_	_
9	involving	involve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	acl	_	_
10	what	what	PRON	WP	_	12	dobj	_	_
11	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	12	nsubj	_	_
12	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	9	ccomp	_	_
13	split	split	ADJ	JJ	Degree=Pos	14	amod	_	_
14	cubes	cube	NOUN	NNS	Number=Plur	12	oprd	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = These conditions are motivated by their special cases, some which become familiar, in the pointed context, once we reformulate them with split cubes replaced with split extensions.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	conditions	condition	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	ccomp	_	_
5	by	by	ADP	IN	_	4	agent	_	_
6	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	8	poss	_	_
7	special	special	ADJ	JJ	Degree=Pos	8	amod	_	_
8	cases	case	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
10	some	some	PRON	DT	_	22	nsubj	_	_
11	which	which	PRON	WDT	_	12	nsubj	_	_
12	become	become	VERB	VBP	Tense=Pres|VerbForm=Fin	10	relcl	_	_
13	familiar	familiar	ADJ	JJ	Degree=Pos	12	acomp	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
15	in	in	ADP	IN	_	10	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	pointed	pointed	ADJ	JJ	Degree=Pos	18	amod	_	_
18	context	context	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
20	once	once	SCONJ	IN	_	22	mark	_	_
21	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	22	nsubj	_	_
22	reformulate	reformulate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
23	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	22	dobj	_	_
24	with	with	ADP	IN	_	22	prep	_	_
25	split	split	ADJ	JJ	Degree=Pos	26	amod	_	_
26	cubes	cube	NOUN	NNS	Number=Plur	24	pobj	_	_
27	replaced	replace	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	acl	_	_
28	with	with	ADP	IN	_	27	prep	_	_
29	split	split	ADJ	JJ	Degree=Pos	30	amod	_	_
30	extensions	extension	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# doc_id = 672
# sent_id = 1
# text = This paper is about an invariant of small categories called isotropy.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	about	about	ADP	IN	_	3	prep	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	invariant	invariant	NOUN	NN	Number=Sing	4	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	small	small	ADJ	JJ	Degree=Pos	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
10	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	9	acl	_	_
11	isotropy	isotropy	NOUN	NN	Number=Sing	10	oprd	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = Every small category $ C $ has associated with it a presheaf of groups on $ C $ , called its isotropy group, which in a sense solves the problem of making the assignment $ C | - > Aut(C) $ functorial.
1	Every	every	DET	DT	_	3	det	_	_
2	small	small	ADJ	JJ	Degree=Pos	3	amod	_	_
3	category	category	NOUN	NN	Number=Sing	6	nsubj	_	_
4	$ C $	$ c $	SYM	$	_	3	appos	_	_
5	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	aux	_	_
6	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	with	with	ADP	IN	_	6	prep	_	_
8	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	7	pobj	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	presheaf	presheaf	NOUN	NN	Number=Sing	6	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	groups	group	NOUN	NNS	Number=Plur	11	pobj	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	$ C $	$ c $	SYM	$	_	13	pobj	_	_
15	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
16	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	6	dep	_	_
17	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	19	poss	_	_
18	isotropy	isotropy	ADJ	JJ	Degree=Pos	19	amod	_	_
19	group	group	NOUN	NN	Number=Sing	16	oprd	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	which	which	PRON	WDT	_	25	nsubj	_	_
22	in	in	ADP	IN	_	25	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	sense	sense	NOUN	NN	Number=Sing	22	pobj	_	_
25	solves	solve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	relcl	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	problem	problem	NOUN	NN	Number=Sing	25	dobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	making	make	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	28	pcomp	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	assignment	assignment	NOUN	NN	Number=Sing	33	nsubj	_	_
32	$ C | - > Aut(C) $	$ c | - > aut(c) $	SYM	$	_	33	nmod	_	_
33	functorial	functorial	NOUN	NN	Number=Sing	29	ccomp	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = Consequently, every category has a canonical congruence that annihilates the isotropy; however, it turns out that the resulting quotient may itself have non - trivial isotropy.
1	Consequently	consequently	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	every	every	DET	DT	_	4	det	_	_
4	category	category	NOUN	NN	Number=Sing	5	nsubj	_	_
5	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	ccomp	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	canonical	canonical	ADJ	JJ	Degree=Pos	8	amod	_	_
8	congruence	congruence	NOUN	NN	Number=Sing	5	dobj	_	_
9	that	that	PRON	WDT	PronType=Rel	10	nsubj	_	_
10	annihilates	annihilate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	relcl	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	isotropy	isotropy	NOUN	NN	Number=Sing	10	dobj	_	SpaceAfter=No
13	;	;	PUNCT	:	_	17	punct	_	_
14	however	however	ADV	RB	_	17	advmod	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
16	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	17	nsubj	_	_
17	turns	turn	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
18	out	out	ADP	RP	_	17	prt	_	_
19	that	that	SCONJ	IN	_	25	mark	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	amod	_	_
22	quotient	quotient	NOUN	NN	Number=Sing	25	nsubj	_	_
23	may	may	AUX	MD	VerbForm=Fin	25	aux	_	_
24	itself	itself	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs|Reflex=Yes	25	nsubj	_	_
25	have	have	VERB	VB	VerbForm=Inf	17	ccomp	_	_
26	non	non	ADJ	JJ	Degree=Pos	29	amod	_	_
27	-	-	ADJ	JJ	Degree=Pos	29	amod	_	_
28	trivial	trivial	ADJ	JJ	Degree=Pos	29	amod	_	_
29	isotropy	isotropy	NOUN	NN	Number=Sing	25	dobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 4
# text = This phenomenon, which we term higher order isotropy, is the subject of our investigation.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	phenomenon	phenomenon	NOUN	NN	Number=Sing	11	nsubj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
4	which	which	PRON	WDT	_	6	dobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	term	term	VERB	VBP	Tense=Pres|VerbForm=Fin	2	relcl	_	_
7	higher	high	ADJ	JJR	Degree=Cmp	9	amod	_	_
8	order	order	NOUN	NN	Number=Sing	9	compound	_	_
9	isotropy	isotropy	NOUN	NN	Number=Sing	6	dobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	subject	subject	NOUN	NN	Number=Sing	11	attr	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	16	poss	_	_
16	investigation	investigation	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 5
# text = We show that with each category $ C $ we may associate a sequence of groups called its higher isotropy groups, and that these give rise to a sequence of quotients of $ C $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	10	mark	_	_
4	with	with	ADP	IN	_	10	prep	_	_
5	each	each	DET	DT	_	6	det	_	_
6	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
7	$ C $	$ c $	SYM	$	_	6	appos	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
9	may	may	AUX	MD	VerbForm=Fin	10	aux	_	_
10	associate	associate	VERB	VB	VerbForm=Inf	2	ccomp	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	sequence	sequence	NOUN	NN	Number=Sing	10	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	groups	group	NOUN	NNS	Number=Plur	13	pobj	_	_
15	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	14	acl	_	_
16	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	19	poss	_	_
17	higher	high	ADJ	JJR	Degree=Cmp	19	amod	_	_
18	isotropy	isotropy	ADJ	JJ	Degree=Pos	19	amod	_	_
19	groups	group	NOUN	NNS	Number=Plur	15	dobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
22	that	that	SCONJ	IN	_	24	mark	_	_
23	these	these	PRON	DT	Number=Plur|PronType=Dem	24	nsubj	_	_
24	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	10	conj	_	_
25	rise	rise	NOUN	NN	Number=Sing	24	dobj	_	_
26	to	to	ADP	IN	_	25	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	sequence	sequence	NOUN	NN	Number=Sing	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	quotients	quotient	NOUN	NNS	Number=Plur	29	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	$ C $	$ c $	SYM	$	_	31	pobj	_	_
33	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = This sequence leads us to an ordinal invariant for small categories, which we call isotropy rank: the isotropy rank of a small category is the ordinal at which the sequence of quotients stabilizes.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	sequence	sequence	NOUN	NN	Number=Sing	3	nsubj	_	_
3	leads	lead	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	ccomp	_	_
4	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	3	dobj	_	_
5	to	to	ADP	IN	_	3	prep	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	ordinal	ordinal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	invariant	invariant	NOUN	NN	Number=Sing	5	pobj	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	small	small	ADJ	JJ	Degree=Pos	11	amod	_	_
11	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	which	which	PRON	WDT	_	15	nsubj	_	_
14	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	15	nsubj	_	_
15	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	11	relcl	_	_
16	isotropy	isotropy	PROPN	NNP	Number=Sing	17	amod	_	_
17	rank	rank	PROPN	NNP	Number=Sing	15	oprd	_	SpaceAfter=No
18	:	:	PUNCT	:	_	26	punct	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	isotropy	isotropy	ADJ	JJ	Degree=Pos	21	amod	_	_
21	rank	rank	NOUN	NN	Number=Sing	26	nsubj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	small	small	ADJ	JJ	Degree=Pos	25	amod	_	_
25	category	category	NOUN	NN	Number=Sing	22	pobj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	ordinal	ordinal	ADJ	JJ	Degree=Pos	26	attr	_	_
29	at	at	ADP	IN	_	35	prep	_	_
30	which	which	PRON	WDT	_	29	pobj	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	sequence	sequence	NOUN	NN	Number=Sing	35	nsubj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	quotients	quotient	NOUN	NNS	Number=Plur	33	pobj	_	_
35	stabilizes	stabilize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	28	relcl	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	26	punct	_	SpaceAfter=No

# sent_id = 7
# text = Our main results state that each small category has a well - defined isotropy rank, and moreover, that for each small ordinal one may construct a small category with precisely that rank.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	3	poss	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	results	result	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	state	state	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	9	mark	_	_
6	each	each	DET	DT	_	8	det	_	_
7	small	small	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	9	nsubj	_	_
9	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
11	well	well	ADV	RB	Degree=Pos	13	advmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
14	isotropy	isotropy	ADJ	JJ	Degree=Pos	15	amod	_	_
15	rank	rank	NOUN	NN	Number=Sing	9	dobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
18	moreover	moreover	ADV	RB	_	27	advmod	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
20	that	that	SCONJ	IN	_	27	mark	_	_
21	for	for	ADP	IN	_	27	prep	_	_
22	each	each	DET	DT	_	25	det	_	_
23	small	small	ADJ	JJ	Degree=Pos	25	amod	_	_
24	ordinal	ordinal	ADJ	JJ	Degree=Pos	25	amod	_	_
25	one	one	NOUN	NN	Number=Sing	27	nsubj	_	_
26	may	may	AUX	MD	VerbForm=Fin	27	aux	_	_
27	construct	construct	VERB	VB	VerbForm=Inf	4	conj	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
29	small	small	ADJ	JJ	Degree=Pos	30	amod	_	_
30	category	category	NOUN	NN	Number=Sing	27	dobj	_	_
31	with	with	ADP	IN	_	27	prep	_	_
32	precisely	precisely	ADV	RB	_	34	advmod	_	_
33	that	that	DET	DT	Number=Sing|PronType=Dem	34	det	_	_
34	rank	rank	NOUN	NN	Number=Sing	31	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	27	punct	_	SpaceAfter=No

# sent_id = 8
# text = It happens that isotropy rank of a small category is an instance of the same concept for Grothendieck toposes, for which corresponding statements hold.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	happens	happen	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	PRON	WDT	PronType=Rel	4	nsubj	_	_
4	isotropy	isotropy	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
5	rank	rank	NOUN	NN	Number=Sing	4	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	small	small	ADJ	JJ	Degree=Pos	9	amod	_	_
9	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
11	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	instance	instance	NOUN	NN	Number=Sing	10	attr	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	same	same	ADJ	JJ	Degree=Pos	16	amod	_	_
16	concept	concept	NOUN	NN	Number=Sing	13	pobj	_	_
17	for	for	ADP	IN	_	16	prep	_	_
18	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	19	compound	_	_
19	toposes	topos	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	for	for	ADP	IN	_	25	prep	_	_
22	which	which	PRON	WDT	_	21	pobj	_	_
23	corresponding	corresponding	ADJ	JJ	Degree=Pos	24	amod	_	_
24	statements	statement	NOUN	NNS	Number=Plur	25	nsubj	_	_
25	hold	hold	VERB	VBP	Tense=Pres|VerbForm=Fin	19	relcl	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 9
# text = Most of the technical work in the paper is concerned with the development of tools that allow us to compute (higher) isotropy groups of categories in terms of those of certain suitable subcategories.
1	Most	Most	ADJ	JJS	Degree=Sup	10	nsubjpass	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	technical	technical	ADJ	JJ	Degree=Pos	5	amod	_	_
5	work	work	NOUN	NN	Number=Sing	2	pobj	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	paper	paper	NOUN	NN	Number=Sing	6	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	concerned	concern	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	ccomp	_	_
11	with	with	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	development	development	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	tools	tool	NOUN	NNS	Number=Plur	14	pobj	_	_
16	that	that	PRON	WDT	PronType=Rel	17	nsubj	_	_
17	allow	allow	VERB	VBP	Tense=Pres|VerbForm=Fin	15	relcl	_	_
18	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	20	nsubj	_	_
19	to	to	PART	TO	_	20	aux	_	_
20	compute	compute	VERB	VB	VerbForm=Inf	17	ccomp	_	_
21	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
22	higher	high	ADJ	JJR	Degree=Cmp	24	amod	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	24	punct	_	_
24	isotropy	isotropy	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
25	groups	group	NOUN	NNS	Number=Plur	24	dobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	categories	category	NOUN	NNS	Number=Plur	26	pobj	_	_
28	in	in	ADP	IN	_	24	prep	_	_
29	terms	term	NOUN	NNS	Number=Plur	28	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	those	those	PRON	DT	Number=Plur|PronType=Dem	30	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	certain	certain	ADJ	JJ	Degree=Pos	35	amod	_	_
34	suitable	suitable	ADJ	JJ	Degree=Pos	35	amod	_	_
35	subcategories	subcategorie	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# doc_id = 673
# sent_id = 1
# text = In this paper we prove a stability result for inner fibrations in terms of the wide, or fat join operation on simplicial sets.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	stability	stability	NOUN	NN	Number=Sing	8	compound	_	_
8	result	result	NOUN	NN	Number=Sing	5	dobj	_	_
9	for	for	ADP	IN	_	8	prep	_	_
10	inner	inner	ADJ	JJ	Degree=Pos	11	amod	_	_
11	fibrations	fibration	NOUN	NNS	Number=Plur	9	pobj	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	terms	term	NOUN	NNS	Number=Plur	12	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
16	wide	wide	ADJ	JJ	Degree=Pos	21	amod	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	or	or	CCONJ	CC	ConjType=Cmp	16	cc	_	_
19	fat	fat	ADJ	JJ	Degree=Pos	16	conj	_	_
20	join	join	VERB	VBP	Tense=Pres|VerbForm=Fin	16	conj	_	_
21	operation	operation	NOUN	NN	Number=Sing	14	pobj	_	_
22	on	on	ADP	IN	_	21	prep	_	_
23	simplicial	simplicial	ADJ	JJ	Degree=Pos	24	amod	_	_
24	sets	set	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = We also prove some additional results on inner anodyne morphisms that may be of independent interest.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	some	some	DET	DT	_	6	det	_	_
5	additional	additional	ADJ	JJ	Degree=Pos	6	amod	_	_
6	results	result	NOUN	NNS	Number=Plur	3	dobj	_	_
7	on	on	ADP	IN	_	6	prep	_	_
8	inner	inner	ADJ	JJ	Degree=Pos	9	amod	_	_
9	anodyne	anodyne	NOUN	NN	Number=Sing	10	compound	_	_
10	morphisms	morphism	NOUN	NNS	Number=Plur	7	pobj	_	_
11	that	that	PRON	WDT	PronType=Rel	13	nsubj	_	_
12	may	may	AUX	MD	VerbForm=Fin	13	aux	_	_
13	be	be	AUX	VB	VerbForm=Inf	6	relcl	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	independent	independent	ADJ	JJ	Degree=Pos	16	amod	_	_
16	interest	interest	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 674
# sent_id = 1
# text = It is well known that a relation $ phi $ between sets is regular if, and only if, $ Kphi $ is completely distributive, where $ Kphi $ is the complete lattice consisting of fixed points of the Kan adjunction induced by $ phi $ .
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	well	well	ADV	RB	Degree=Pos	4	advmod	_	_
4	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	acomp	_	_
5	that	that	SCONJ	IN	_	11	mark	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	relation	relation	NOUN	NN	Number=Sing	11	nsubj	_	_
8	$ phi $	$ phi $	SYM	$	_	7	appos	_	_
9	between	between	ADP	IN	_	7	prep	_	_
10	sets	set	NOUN	NNS	Number=Plur	9	pobj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
12	regular	regular	ADJ	JJ	Degree=Pos	11	acomp	_	_
13	if	if	SCONJ	IN	_	11	prep	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
16	only	only	ADV	RB	_	20	advmod	_	_
17	if	if	SCONJ	IN	_	20	mark	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
19	$ Kphi $	$ kphi $	SYM	$	_	20	nsubj	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	advcl	_	_
21	completely	completely	ADV	RB	_	22	advmod	_	_
22	distributive	distributive	ADJ	JJ	Degree=Pos	20	acomp	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
24	where	where	SCONJ	WRB	_	26	advmod	_	_
25	$ Kphi $	$ kphi $	SYM	$	_	26	nsubj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	complete	complete	ADJ	JJ	Degree=Pos	29	amod	_	_
29	lattice	lattice	NOUN	NN	Number=Sing	26	attr	_	_
30	consisting	consist	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	29	acl	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	amod	_	_
33	points	point	NOUN	NNS	Number=Plur	31	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
36	Kan	Kan	PROPN	NNP	Number=Sing	37	compound	_	_
37	adjunction	adjunction	NOUN	NN	Number=Sing	34	pobj	_	_
38	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	37	acl	_	_
39	by	by	ADP	IN	_	38	agent	_	_
40	$ phi $	$ phi $	SYM	$	_	39	pobj	_	_
41	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = For a small quantaloid Q, we investigate the $ Q $ - enriched version of this classical result, that is, the regularity of $ Q $ - distributors versus the constructive complete distributivity of $ Q $ - categories, and prove that ``the dual of $ Kphi $ is constructive completely distributive implies $ phi $ is regular implies $ Kphi $ is constructive completely distributive for any $ Q $ - distributor $ phi $ .
1	For	for	ADP	IN	_	8	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
3	small	small	ADJ	JJ	Degree=Pos	5	amod	_	_
4	quantaloid	quantaloid	NOUN	NN	Number=Sing	5	compound	_	_
5	Q	Q	PROPN	NNP	Number=Sing	1	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
7	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	8	nsubj	_	_
8	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
10	$ Q $	$ q $	SYM	$	_	12	advmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
13	version	version	NOUN	NN	Number=Sing	8	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	this	this	DET	DT	Number=Sing|PronType=Dem	17	det	_	_
16	classical	classical	ADJ	JJ	Degree=Pos	17	amod	_	_
17	result	result	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
19	that	that	ADV	RB	_	20	advmod	_	_
20	is	is	ADV	RB	_	23	advmod	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	regularity	regularity	NOUN	NN	Number=Sing	8	dobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	$ Q $	$ q $	SYM	$	_	27	compound	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	distributors	distributor	NOUN	NNS	Number=Plur	24	pobj	_	_
28	versus	versus	ADP	IN	_	27	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
30	constructive	constructive	ADJ	JJ	Degree=Pos	32	amod	_	_
31	complete	complete	ADJ	JJ	Degree=Pos	32	amod	_	_
32	distributivity	distributivity	NOUN	NN	Number=Sing	28	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	$ Q $	$ q $	SYM	$	_	36	nmod	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	36	punct	_	_
36	categories	category	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
37	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
38	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
39	prove	prove	VERB	VB	VerbForm=Inf	8	conj	_	_
40	that	that	SCONJ	IN	_	47	mark	_	_
41	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	47	punct	_	SpaceAfter=No
42	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	47	punct	_	SpaceAfter=No
43	the	the	DET	DT	Definite=Def|PronType=Art	44	det	_	_
44	dual	dual	ADJ	JJ	Degree=Pos	47	nsubj	_	_
45	of	of	ADP	IN	_	44	prep	_	_
46	$ Kphi $	$ kphi $	SYM	$	_	45	pobj	_	_
47	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	39	ccomp	_	_
48	constructive	constructive	ADJ	JJ	Degree=Pos	47	acomp	_	_
49	completely	completely	ADV	RB	_	50	advmod	_	_
50	distributive	distributive	ADJ	JJ	Degree=Pos	48	amod	_	_
51	implies	imply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	39	conj	_	_
52	$ phi $	$ phi $	SYM	$	_	53	nsubj	_	_
53	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	51	ccomp	_	_
54	regular	regular	ADJ	JJ	Degree=Pos	53	acomp	_	_
55	implies	imply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	conj	_	_
56	$ Kphi $	$ kphi $	SYM	$	_	57	nsubj	_	_
57	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	55	ccomp	_	_
58	constructive	constructive	ADJ	JJ	Degree=Pos	57	acomp	_	_
59	completely	completely	ADV	RB	_	60	advmod	_	_
60	distributive	distributive	ADJ	JJ	Degree=Pos	57	acomp	_	_
61	for	for	ADP	IN	_	60	prep	_	_
62	any	any	DET	DT	_	65	det	_	_
63	$ Q $	$ q $	SYM	$	_	65	compound	_	_
64	-	-	PUNCT	HYPH	PunctType=Dash	65	punct	_	_
65	distributor	distributor	NOUN	NN	Number=Sing	61	pobj	_	_
66	$ phi $	$ phi $	SYM	$	_	65	appos	_	_
67	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 3
# text = Although the converse implications do not hold in general, in the case that $ Q $ is a commutative integral quantale, we show that these three statements are equivalent for any $ phi $ if, and only if, $ Q $ is a Girard quantale.
1	Although	although	SCONJ	IN	_	7	mark	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	converse	converse	NOUN	NN	Number=Sing	4	compound	_	_
4	implications	implication	NOUN	NNS	Number=Plur	7	nsubj	_	_
5	do	do	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	aux	_	_
6	not	not	PART	RB	Polarity=Neg	7	neg	_	_
7	hold	hold	VERB	VB	VerbForm=Inf	23	advcl	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	general	general	ADJ	JJ	Degree=Pos	8	amod	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
11	in	in	ADP	IN	_	23	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	case	case	NOUN	NN	Number=Sing	11	pobj	_	_
14	that	that	SCONJ	IN	_	16	mark	_	_
15	$ Q $	$ q $	SYM	$	_	16	nsubj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	acl	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
18	commutative	commutative	ADJ	JJ	Degree=Pos	20	amod	_	_
19	integral	integral	ADJ	JJ	Degree=Pos	20	amod	_	_
20	quantale	quantale	NOUN	NN	Number=Sing	16	attr	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
22	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	23	nsubj	_	_
23	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
24	that	that	SCONJ	IN	_	28	mark	_	_
25	these	these	DET	DT	Number=Plur|PronType=Dem	27	det	_	_
26	three	three	NUM	CD	NumType=Card	27	nummod	_	_
27	statements	statement	NOUN	NNS	Number=Plur	28	nsubj	_	_
28	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	23	ccomp	_	_
29	equivalent	equivalent	ADJ	JJ	Degree=Pos	28	acomp	_	_
30	for	for	ADP	IN	_	29	prep	_	_
31	any	any	DET	DT	_	32	det	_	_
32	$ phi $	$ phi $	SYM	$	_	33	nmod	_	_
33	if	if	SCONJ	IN	_	28	dep	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
36	only	only	ADV	RB	_	40	advmod	_	_
37	if	if	SCONJ	IN	_	40	mark	_	SpaceAfter=No
38	,	,	PUNCT	,	PunctType=Comm	40	punct	_	_
39	$ Q $	$ q $	SYM	$	_	40	nsubj	_	_
40	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	28	conj	_	_
41	a	a	DET	DT	Definite=Ind|PronType=Art	43	det	_	_
42	Girard	Girard	PROPN	NNP	Number=Sing	43	amod	_	_
43	quantale	quantale	NOUN	NN	Number=Sing	40	attr	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# doc_id = 675
# sent_id = 1
# text = We give a direct proof that between two toposes, $ F $ and $ E $ , bounded over a base topos $ S $ , adjunctions $ L - | R: Loc_F - > Loc_E $ over $ Loc_S $ are Frobenius if and only if $ R $ commutes with the double power locale monad and finite coproducts.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	direct	direct	ADJ	JJ	Degree=Pos	5	amod	_	_
5	proof	proof	NOUN	NN	Number=Sing	2	dobj	_	_
6	that	that	SCONJ	IN	_	26	mark	_	_
7	between	between	ADP	IN	_	26	prep	_	_
8	two	two	NUM	CD	NumType=Card	9	nummod	_	_
9	toposes	topos	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	$ F $	$ f $	SYM	$	_	9	appos	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	$ E $	$ e $	SYM	$	_	9	appos	_	_
14	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
15	bounded	bound	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	acl	_	_
16	over	over	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	base	base	NOUN	NN	Number=Sing	19	compound	_	_
19	topos	topos	NOUN	NN	Number=Sing	16	pobj	_	_
20	$ S $	$ s $	SYM	$	_	19	appos	_	_
21	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
22	adjunctions	adjunction	NOUN	NNS	Number=Plur	7	pobj	_	_
23	$ L - | R: Loc_F - > Loc_E $	$ l - | r: loc_f - > loc_e $	SYM	$	_	25	quantmod	_	_
24	over	over	ADP	IN	_	25	advmod	_	_
25	$ Loc_S $	$ loc_s $	SYM	$	_	7	pobj	_	_
26	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	acl	_	_
27	Frobenius	Frobenius	PROPN	NNP	Number=Sing	26	attr	_	_
28	if	if	SCONJ	IN	_	26	prep	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	only	only	ADV	RB	_	31	advmod	_	_
31	if	if	SCONJ	IN	_	32	cc	_	_
32	$ R $	$ r $	SYM	$	_	33	poss	_	_
33	commutes	commute	NOUN	NNS	Number=Plur	28	conj	_	_
34	with	with	ADP	IN	_	33	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
36	double	double	ADJ	JJ	Degree=Pos	39	amod	_	_
37	power	power	NOUN	NN	Number=Sing	38	compound	_	_
38	locale	locale	NOUN	NN	Number=Sing	39	compound	_	_
39	monad	monad	NOUN	NNS	Number=Plur	34	pobj	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	39	cc	_	_
41	finite	finite	ADJ	JJ	Degree=Pos	42	amod	_	_
42	coproducts	coproduct	NOUN	NNS	Number=Plur	39	conj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The proof uses only certain categorical properties of the category of locales, Loc.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	proof	proof	NOUN	NN	Number=Sing	3	nsubj	_	_
3	uses	use	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	only	only	ADV	RB	_	7	advmod	_	_
5	certain	certain	ADJ	JJ	Degree=Pos	7	amod	_	_
6	categorical	categorical	ADJ	JJ	Degree=Pos	7	amod	_	_
7	properties	property	NOUN	NNS	Number=Plur	3	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	locales	locale	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
14	Loc	Loc	PROPN	NNP	Number=Sing	7	appos	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = This implies that between categories axiomatized to behave like categories of locales, it does not make a difference whether maps are defined as structure preserving adjunctions (that is, those that commute with the double power monads) or Frobenius adjunctions.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	implies	imply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	17	mark	_	_
4	between	between	ADP	IN	_	17	prep	_	_
5	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	_
6	axiomatized	axiomatize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	acl	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	behave	behave	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	like	like	ADP	IN	_	8	prep	_	_
10	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	locales	locale	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
14	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	17	nsubj	_	_
15	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	aux	_	_
16	not	not	PART	RB	Polarity=Neg	17	neg	_	_
17	make	make	VERB	VB	VerbForm=Inf	2	ccomp	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	difference	difference	NOUN	NN	Number=Sing	17	dobj	_	_
20	whether	whether	SCONJ	IN	_	23	mark	_	_
21	maps	map	NOUN	NNS	Number=Plur	23	nsubjpass	_	_
22	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	23	auxpass	_	_
23	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	acl	_	_
24	as	as	ADP	IN	_	23	prep	_	_
25	structure	structure	NOUN	NN	Number=Sing	26	npadvmod	_	_
26	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	27	amod	_	_
27	adjunctions	adjunction	NOUN	NNS	Number=Plur	24	pobj	_	_
28	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	27	punct	_	SpaceAfter=No
29	that	that	ADV	RB	_	30	nsubj	_	_
30	is	is	ADV	RB	_	27	parataxis	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	30	punct	_	_
32	those	those	PRON	DT	Number=Plur|PronType=Dem	30	attr	_	_
33	that	that	PRON	WDT	PronType=Rel	34	nsubj	_	_
34	commute	commute	VERB	VBP	Tense=Pres|VerbForm=Fin	32	relcl	_	_
35	with	with	ADP	IN	_	34	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
37	double	double	ADJ	JJ	Degree=Pos	39	amod	_	_
38	power	power	NOUN	NN	Number=Sing	39	compound	_	_
39	monads	monad	NOUN	NNS	Number=Plur	35	pobj	_	SpaceAfter=No
40	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	39	punct	_	_
41	or	or	CCONJ	CC	ConjType=Cmp	39	cc	_	_
42	Frobenius	Frobenius	PROPN	NNP	Number=Sing	43	compound	_	_
43	adjunctions	adjunction	NOUN	NNS	Number=Plur	39	conj	_	SpaceAfter=No
44	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 676
# sent_id = 1
# text = The formation of the "strict" span category $ Span(C) $ of a category $ C $ with pullbacks is a standard organizational tool of category theory.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	formation	formation	NOUN	NN	Number=Sing	17	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
5	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	9	punct	_	SpaceAfter=No
6	strict	strict	ADJ	JJ	Degree=Pos	9	amod	_	SpaceAfter=No
7	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	9	punct	_	_
8	span	span	NOUN	NN	Number=Sing	9	compound	_	_
9	category	category	NOUN	NN	Number=Sing	3	pobj	_	_
10	$ Span(C) $	$ span(c) $	SYM	$	_	9	appos	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
14	$ C $	$ c $	SYM	$	_	9	punct	_	_
15	with	with	ADP	IN	_	2	prep	_	_
16	pullbacks	pullback	NOUN	NNS	Number=Plur	15	pobj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
19	standard	standard	ADJ	JJ	Degree=Pos	21	amod	_	_
20	organizational	organizational	ADJ	JJ	Degree=Pos	21	amod	_	_
21	tool	tool	NOUN	NN	Number=Sing	17	attr	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	category	category	NOUN	NN	Number=Sing	24	compound	_	_
24	theory	theory	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 2
# text = Unfortunately, limits or colimits in $ Span(C) $ are not easily computed in terms of constructions in $ C $ .
1	Unfortunately	unfortunately	ADV	RB	_	11	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
3	limits	limit	NOUN	NNS	Number=Plur	11	nsubjpass	_	_
4	or	or	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	colimits	colimit	NOUN	NNS	Number=Plur	3	conj	_	_
6	in	in	ADP	IN	_	3	prep	_	_
7	$ Span(C) $	$ span(c) $	SYM	$	_	6	pobj	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
9	not	not	PART	RB	Polarity=Neg	11	neg	_	_
10	easily	easily	ADV	RB	_	11	advmod	_	_
11	computed	compute	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	terms	term	NOUN	NNS	Number=Plur	12	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	constructions	construction	NOUN	NNS	Number=Plur	14	pobj	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	$ C $	$ c $	SYM	$	_	16	pobj	_	_
18	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 3
# text = This paper shows how to form the pullback in $ Span(C) $ for many, but not all, pairs of spans, given the existence of some specific so - called lax pullback complements in $ C $ of the "left legs" of at least one of the two given spans.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	shows	show	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	how	how	SCONJ	WRB	_	6	advmod	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	form	form	VERB	VB	VerbForm=Inf	3	xcomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	pullback	pullback	NOUN	NN	Number=Sing	6	dobj	_	_
9	in	in	ADP	IN	_	6	prep	_	_
10	$ Span(C) $	$ span(c) $	SYM	$	_	9	pobj	_	_
11	for	for	ADP	IN	_	6	prep	_	_
12	many	many	ADJ	JJ	Degree=Pos	11	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	but	but	CCONJ	CC	ConjType=Cmp	11	cc	_	_
15	not	not	PART	RB	Polarity=Neg	16	neg	_	_
16	all	all	DET	DT	_	18	det	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
18	pairs	pair	NOUN	NNS	Number=Plur	3	conj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	spans	span	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
22	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	prep	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	existence	existence	NOUN	NN	Number=Sing	22	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	some	some	DET	DT	_	33	det	_	_
27	specific	specific	ADJ	JJ	Degree=Pos	33	amod	_	_
28	so	so	ADV	RB	_	30	advmod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	amod	_	_
31	lax	lax	ADJ	JJ	Degree=Pos	33	amod	_	_
32	pullback	pullback	NOUN	NN	Number=Sing	33	compound	_	_
33	complements	complement	NOUN	NNS	Number=Plur	25	pobj	_	_
34	in	in	ADP	IN	_	24	prep	_	_
35	$ C $	$ c $	SYM	$	_	34	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
38	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	40	punct	_	SpaceAfter=No
39	left	left	ADJ	JJ	Degree=Pos	40	amod	_	_
40	legs	leg	NOUN	NNS	Number=Plur	36	pobj	_	SpaceAfter=No
41	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	40	punct	_	_
42	of	of	ADP	IN	_	40	prep	_	_
43	at	at	ADV	RB	_	44	advmod	_	_
44	least	least	ADJ	JJS	Degree=Sup	45	advmod	_	_
45	one	one	NUM	CD	NumType=Card	42	pobj	_	_
46	of	of	ADP	IN	_	45	prep	_	_
47	the	the	DET	DT	Definite=Def|PronType=Art	50	det	_	_
48	two	two	NUM	CD	NumType=Card	50	nummod	_	_
49	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	50	amod	_	_
50	spans	span	NOUN	NNS	Number=Plur	46	pobj	_	SpaceAfter=No
51	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = For some types of spans we require the ambient category to be adhesive to be able to form at least a weak pullback in $ Span(C) $ .
1	For	for	ADP	IN	_	7	prep	_	_
2	some	some	DET	DT	_	3	det	_	_
3	types	type	NOUN	NNS	Number=Plur	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	spans	span	NOUN	NNS	Number=Plur	4	pobj	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	require	require	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	ambient	ambient	ADJ	JJ	Degree=Pos	10	amod	_	_
10	category	category	NOUN	NN	Number=Sing	7	dobj	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	be	be	AUX	VB	VerbForm=Inf	7	xcomp	_	_
13	adhesive	adhesive	ADJ	JJ	Degree=Pos	12	acomp	_	_
14	to	to	PART	TO	_	15	aux	_	_
15	be	be	AUX	VB	VerbForm=Inf	13	xcomp	_	_
16	able	able	ADJ	JJ	Degree=Pos	15	acomp	_	_
17	to	to	PART	TO	_	18	aux	_	_
18	form	form	VERB	VB	VerbForm=Inf	16	xcomp	_	_
19	at	at	ADV	RB	_	20	advmod	_	_
20	least	least	ADJ	JJS	Degree=Sup	23	advmod	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	weak	weak	ADJ	JJ	Degree=Pos	23	amod	_	_
23	pullback	pullback	NOUN	NN	Number=Sing	18	dobj	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	$ Span(C) $	$ span(c) $	SYM	$	_	24	pobj	_	_
26	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 5
# text = The existence of all lax pullback complements in $ C $ along a given morphism is equivalent to the exponentiability of that morphism.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	existence	existence	NOUN	NN	Number=Sing	14	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	all	all	DET	DT	_	7	det	_	_
5	lax	lax	ADJ	JJ	Degree=Pos	7	amod	_	_
6	pullback	pullback	NOUN	NN	Number=Sing	7	compound	_	_
7	complements	complement	NOUN	NNS	Number=Plur	3	pobj	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	$ C $	$ c $	SYM	$	_	8	pobj	_	_
10	along	along	ADP	IN	_	2	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
13	morphism	morphism	NOUN	NN	Number=Sing	10	pobj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	equivalent	equivalent	ADJ	JJ	Degree=Pos	14	acomp	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	exponentiability	exponentiability	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	that	that	DET	DT	Number=Sing|PronType=Dem	21	det	_	_
21	morphism	morphism	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 6
# text = Since exponentiability is a rather restrictive property of a morphism, the paper first develops a comprehensive framework of rules for individual lax pullback complement diagrams, which resembles the set of pasting and cancellation rules for pullback diagrams, including their behaviour under pullback.
1	Since	since	SCONJ	IN	_	3	mark	_	_
2	exponentiability	exponentiability	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	advcl	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
5	rather	rather	ADV	RB	_	6	advmod	_	_
6	restrictive	restrictive	ADJ	JJ	Degree=Pos	7	amod	_	_
7	property	property	NOUN	NN	Number=Sing	3	attr	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	morphism	morphism	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	paper	paper	NOUN	NN	Number=Sing	15	nsubj	_	_
14	first	first	ADV	RB	_	15	advmod	_	_
15	develops	develop	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	comprehensive	comprehensive	ADJ	JJ	Degree=Pos	18	amod	_	_
18	framework	framework	NOUN	NN	Number=Sing	15	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	rules	rule	NOUN	NNS	Number=Plur	19	pobj	_	_
21	for	for	ADP	IN	_	20	prep	_	_
22	individual	individual	ADJ	JJ	Degree=Pos	26	amod	_	_
23	lax	lax	ADJ	JJ	Degree=Pos	22	nmod	_	_
24	pullback	pullback	NOUN	NN	Number=Sing	25	compound	_	_
25	complement	complement	NOUN	NN	Number=Sing	26	compound	_	_
26	diagrams	diagram	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
28	which	which	PRON	WDT	_	29	nsubj	_	_
29	resembles	resemble	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	26	relcl	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	set	set	NOUN	NN	Number=Sing	29	dobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	pasting	pasting	NOUN	NN	Number=Sing	36	nmod	_	_
34	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
35	cancellation	cancellation	NOUN	NN	Number=Sing	33	conj	_	_
36	rules	rule	NOUN	NNS	Number=Plur	32	pobj	_	_
37	for	for	ADP	IN	_	36	prep	_	_
38	pullback	pullback	NOUN	NN	Number=Sing	39	compound	_	_
39	diagrams	diagram	NOUN	NNS	Number=Plur	37	pobj	_	SpaceAfter=No
40	,	,	PUNCT	,	PunctType=Comm	39	punct	_	_
41	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	39	prep	_	_
42	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	43	poss	_	_
43	behaviour	behaviour	NOUN	NN	Number=Sing	41	pobj	_	_
44	under	under	ADP	IN	_	43	prep	_	_
45	pullback	pullback	NOUN	NN	Number=Sing	44	pobj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 7
# text = We also present examples of lax pullback complements along non - exponentiable morphisms, obtained via lifting along a fibration.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	present	present	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	examples	example	NOUN	NNS	Number=Plur	3	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	lax	lax	ADJ	JJ	Degree=Pos	8	amod	_	_
7	pullback	pullback	NOUN	NN	Number=Sing	8	compound	_	_
8	complements	complement	NOUN	NNS	Number=Plur	5	pobj	_	_
9	along	along	ADP	IN	_	8	prep	_	_
10	non	non	ADJ	JJ	Degree=Pos	13	amod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	13	amod	_	_
12	exponentiable	exponentiable	ADJ	JJ	Degree=Pos	13	amod	_	_
13	morphisms	morphism	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
15	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	acl	_	_
16	via	via	ADP	IN	_	15	prep	_	_
17	lifting	lift	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	pobj	_	_
18	along	along	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	fibration	fibration	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 677
# sent_id = 1
# text = There are two main constructions in classical descent theory: the category of algebras and the descent category, which are known to be examples of weighted bilimits.
1	There	there	PRON	EX	_	2	expl	_	_
2	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	two	two	NUM	CD	NumType=Card	5	nummod	_	_
4	main	main	ADJ	JJ	Degree=Pos	5	amod	_	_
5	constructions	construction	NOUN	NNS	Number=Plur	2	attr	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	classical	classical	ADJ	JJ	Degree=Pos	8	amod	_	_
8	descent	descent	NOUN	NN	Number=Sing	9	compound	_	_
9	theory	theory	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
10	:	:	PUNCT	:	_	5	punct	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	category	category	NOUN	NN	Number=Sing	5	appos	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	algebras	algebra	NOUN	NNS	Number=Plur	13	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	descent	descent	NOUN	NN	Number=Sing	18	compound	_	_
18	category	category	NOUN	NN	Number=Sing	12	conj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	which	which	PRON	WDT	_	22	nsubjpass	_	_
21	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	22	auxpass	_	_
22	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	relcl	_	_
23	to	to	PART	TO	_	24	aux	_	_
24	be	be	AUX	VB	VerbForm=Inf	22	xcomp	_	_
25	examples	example	NOUN	NNS	Number=Plur	24	attr	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	weighted	weighted	ADJ	JJ	Degree=Pos	28	amod	_	_
28	bilimits	bilimit	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We give a formal approach to descent theory, employing formal consequences of commuting properties of bilimits to prove classical and new theorems in the context of Janelidze - Tholen ``Facets of Descent II'', such as Benabou - Roubaud Theorems, a Galois Theorem, embedding results and formal ways of getting effective descent morphisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	formal	formal	ADJ	JJ	Degree=Pos	5	amod	_	_
5	approach	approach	NOUN	NN	Number=Sing	2	dobj	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	descent	descent	VERB	VB	VerbForm=Inf	5	relcl	_	_
8	theory	theory	NOUN	NN	Number=Sing	7	dobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
10	employing	employ	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
11	formal	formal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	consequences	consequence	NOUN	NNS	Number=Plur	10	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	commuting	commute	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	pcomp	_	_
15	properties	property	NOUN	NNS	Number=Plur	14	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	bilimits	bilimit	NOUN	NNS	Number=Plur	16	pobj	_	_
18	to	to	PART	TO	_	19	aux	_	_
19	prove	prove	VERB	VB	VerbForm=Inf	12	relcl	_	_
20	classical	classical	ADJ	JJ	Degree=Pos	23	amod	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	new	new	ADJ	JJ	Degree=Pos	20	conj	_	_
23	theorems	theorem	NOUN	NNS	Number=Plur	19	dobj	_	_
24	in	in	ADP	IN	_	19	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	context	context	NOUN	NN	Number=Sing	24	pobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	Janelidze	Janelidze	PROPN	NNP	Number=Sing	30	compound	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	Tholen	Tholen	PROPN	NNP	Number=Sing	33	nmod	_	_
31	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	33	punct	_	SpaceAfter=No
32	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	33	punct	_	SpaceAfter=No
33	Facets	facet	NOUN	NNS	Number=Plur	50	nsubj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	Descent	Descent	PROPN	NNP	Number=Sing	36	compound	_	_
36	II	II	PROPN	NNP	Number=Sing	34	pobj	_	SpaceAfter=No
37	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	33	punct	_	SpaceAfter=No
38	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
39	such	such	ADJ	JJ	Degree=Pos	40	amod	_	_
40	as	as	ADP	IN	_	33	prep	_	_
41	Benabou	Benabou	PROPN	NNP	Number=Sing	43	compound	_	_
42	-	-	PUNCT	HYPH	PunctType=Dash	43	punct	_	_
43	Roubaud	Roubaud	PROPN	NNP	Number=Sing	44	compound	_	_
44	Theorems	Theorems	PROPN	NNP	Number=Sing	40	pobj	_	SpaceAfter=No
45	,	,	PUNCT	,	PunctType=Comm	44	punct	_	_
46	a	a	DET	DT	Definite=Ind|PronType=Art	48	det	_	_
47	Galois	Galois	PROPN	NNP	Number=Sing	48	compound	_	_
48	Theorem	Theorem	PROPN	NNP	Number=Sing	44	appos	_	SpaceAfter=No
49	,	,	PUNCT	,	PunctType=Comm	44	punct	_	_
50	embedding	embed	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	conj	_	_
51	results	result	NOUN	NNS	Number=Plur	50	dobj	_	_
52	and	and	CCONJ	CC	ConjType=Cmp	51	cc	_	_
53	formal	formal	ADJ	JJ	Degree=Pos	54	amod	_	_
54	ways	way	NOUN	NNS	Number=Plur	51	conj	_	_
55	of	of	ADP	IN	_	54	prep	_	_
56	getting	get	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	55	pcomp	_	_
57	effective	effective	ADJ	JJ	Degree=Pos	59	amod	_	_
58	descent	descent	NOUN	NN	Number=Sing	59	compound	_	_
59	morphisms	morphism	NOUN	NNS	Number=Plur	56	dobj	_	SpaceAfter=No
60	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = In order to do this, we develop the formal part of the theory on commuting bilimits via pseudomonad theory, studying idempotent pseudomonads and proving a 2 - dimensional version of the adjoint triangle theorem.
1	In	in	ADP	IN	_	8	prep	_	_
2	order	order	NOUN	NN	Number=Sing	1	pobj	_	_
3	to	to	PART	TO	_	4	aux	_	_
4	do	do	AUX	VB	VerbForm=Inf	2	acl	_	_
5	this	this	PRON	DT	Number=Sing|PronType=Dem	4	dobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
7	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	8	nsubj	_	_
8	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	formal	formal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	part	part	NOUN	NN	Number=Sing	8	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	theory	theory	NOUN	NN	Number=Sing	12	pobj	_	_
15	on	on	ADP	IN	_	14	prep	_	_
16	commuting	commute	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	pcomp	_	_
17	bilimits	bilimit	NOUN	NNS	Number=Plur	16	dobj	_	_
18	via	via	ADP	IN	_	16	prep	_	_
19	pseudomonad	pseudomonad	NOUN	NNS	Number=Plur	20	compound	_	_
20	theory	theory	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
22	studying	study	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	advcl	_	_
23	idempotent	idempotent	ADJ	JJ	Degree=Pos	24	amod	_	_
24	pseudomonads	pseudomonad	NOUN	NNS	Number=Plur	22	dobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
26	proving	prove	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	conj	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
28	2	2	NUM	CD	NumType=Card	30	advmod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	dimensional	dimensional	ADJ	JJ	Degree=Pos	31	amod	_	_
31	version	version	NOUN	NN	Number=Sing	26	dobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
34	adjoint	adjoint	NOUN	NN	Number=Sing	35	compound	_	_
35	triangle	triangle	NOUN	NN	Number=Sing	32	pobj	_	_
36	theorem	theorem	ADJ	JJ	Degree=Pos	26	oprd	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 4
# text = Also, we work out the concept of pointwise pseudo - Kan extension, used as a framework to talk about bilimits, commutativity and the descent object.
1	Also	also	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	work	work	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	out	out	ADP	RP	_	4	prt	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	concept	concept	NOUN	NN	Number=Sing	4	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	pointwise	pointwise	ADJ	JJ	Degree=Pos	10	amod	_	_
10	pseudo	pseudo	NOUN	NN	Number=Sing	12	compound	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	Kan	Kan	PROPN	NNP	Number=Sing	13	compound	_	_
13	extension	extension	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
15	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	acl	_	_
16	as	as	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	framework	framework	NOUN	NN	Number=Sing	16	pobj	_	_
19	to	to	PART	TO	_	20	aux	_	_
20	talk	talk	VERB	VB	VerbForm=Inf	15	xcomp	_	_
21	about	about	ADP	IN	_	20	prep	_	_
22	bilimits	bilimit	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	commutativity	commutativity	NOUN	NN	Number=Sing	22	conj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	descent	descent	NOUN	NN	Number=Sing	28	compound	_	_
28	object	object	NOUN	NN	Number=Sing	24	conj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = As a subproduct, this formal approach can be an alternative perspective/guiding template for the development of higher descent theory.
1	As	as	ADP	IN	_	9	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	subproduct	subproduct	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	7	det	_	_
6	formal	formal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	approach	approach	NOUN	NN	Number=Sing	9	nsubj	_	_
8	can	can	AUX	MD	VerbForm=Fin	9	aux	_	_
9	be	be	AUX	VB	VerbForm=Inf	0	ROOT	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
11	alternative	alternative	ADJ	JJ	Degree=Pos	15	amod	_	_
12	perspective	perspective	NOUN	NN	Number=Sing	15	nmod	_	SpaceAfter=No
13	/	/	SYM	SYM	_	14	punct	_	SpaceAfter=No
14	guiding	guide	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	amod	_	_
15	template	template	NOUN	NN	Number=Sing	9	attr	_	_
16	for	for	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	development	development	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	higher	high	ADJ	JJR	Degree=Cmp	22	amod	_	_
21	descent	descent	NOUN	NN	Number=Sing	22	compound	_	_
22	theory	theory	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 678
# sent_id = 1
# text = Stable derivators provide an enhancement of triangulated categories as is indicated by the existence of canonical triangulations.
1	Stable	stable	ADJ	JJ	Degree=Pos	2	amod	_	_
2	derivators	derivator	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	enhancement	enhancement	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	triangulated	triangulate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
9	as	as	SCONJ	IN	_	11	mark	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	indicated	indicate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	advcl	_	_
12	by	by	ADP	IN	_	11	agent	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	existence	existence	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	canonical	canonical	ADJ	JJ	Degree=Pos	17	amod	_	_
17	triangulations	triangulation	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper we show that exact morphisms of stable derivators induce exact functors of canonical triangulations, and similarly for arbitrary natural transformations.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	12	mark	_	_
7	exact	exact	ADJ	JJ	Degree=Pos	8	amod	_	_
8	morphisms	morphism	NOUN	NNS	Number=Plur	12	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	stable	stable	ADJ	JJ	Degree=Pos	11	amod	_	_
11	derivators	derivator	NOUN	NNS	Number=Plur	9	pobj	_	_
12	induce	induce	VERB	VBP	Tense=Pres|VerbForm=Fin	5	ccomp	_	_
13	exact	exact	ADJ	JJ	Degree=Pos	14	amod	_	_
14	functors	functor	NOUN	NNS	Number=Plur	12	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	canonical	canonical	ADJ	JJ	Degree=Pos	17	amod	_	_
17	triangulations	triangulation	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
20	similarly	similarly	ADV	RB	_	21	advmod	_	_
21	for	for	ADP	IN	_	5	prep	_	_
22	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	24	amod	_	_
23	natural	natural	ADJ	JJ	Degree=Pos	24	amod	_	_
24	transformations	transformation	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = This 2 - categorical refinement also provides a uniqueness statement concerning canonical triangulations.
1	This	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
2	2	2	NUM	CD	NumType=Card	4	nummod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	categorical	categorical	ADJ	JJ	Degree=Pos	5	amod	_	_
5	refinement	refinement	NOUN	NN	Number=Sing	7	nsubj	_	_
6	also	also	ADV	RB	_	7	advmod	_	_
7	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	uniqueness	uniqueness	ADJ	JJ	Degree=Pos	10	amod	_	_
10	statement	statement	NOUN	NN	Number=Sing	7	dobj	_	_
11	concerning	concern	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	acl	_	_
12	canonical	canonical	ADJ	JJ	Degree=Pos	13	amod	_	_
13	triangulations	triangulation	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = These results rely on a more careful study of morphisms of derivators and this study is of independent interest.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	results	result	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	rely	rely	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	on	on	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
6	more	more	ADV	RBR	Degree=Cmp	7	advmod	_	_
7	careful	careful	ADJ	JJ	Degree=Pos	8	amod	_	_
8	study	study	NOUN	NN	Number=Sing	4	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	morphisms	morphism	NOUN	NNS	Number=Plur	9	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	derivators	derivator	NOUN	NNS	Number=Plur	11	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
14	this	this	DET	DT	Number=Sing|PronType=Dem	15	det	_	_
15	study	study	NOUN	NN	Number=Sing	16	nsubj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	independent	independent	ADJ	JJ	Degree=Pos	19	amod	_	_
19	interest	interest	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 5
# text = We analyze the interaction of morphisms of derivators with limits, colimits, and Kan extensions, including a discussion of invariance and closure properties of the class of Kan extensions preserved by a fixed morphism.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	analyze	analyze	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	interaction	interaction	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	morphisms	morphism	NOUN	NNS	Number=Plur	5	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	derivators	derivator	NOUN	NNS	Number=Plur	7	pobj	_	_
9	with	with	ADP	IN	_	4	prep	_	_
10	limits	limit	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	colimits	colimit	NOUN	NNS	Number=Plur	10	conj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
15	Kan	Kan	PROPN	NNP	Number=Sing	16	compound	_	_
16	extensions	extension	NOUN	NNS	Number=Plur	12	conj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	discussion	discussion	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	invariance	invariance	NOUN	NN	Number=Sing	25	nmod	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	closure	closure	NOUN	NN	Number=Sing	22	conj	_	_
25	properties	property	NOUN	NNS	Number=Plur	21	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	class	class	NOUN	NN	Number=Sing	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	Kan	Kan	PROPN	NNP	Number=Sing	31	compound	_	_
31	extensions	extension	NOUN	NNS	Number=Plur	29	pobj	_	_
32	preserved	preserve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	acl	_	_
33	by	by	ADP	IN	_	32	agent	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
35	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	36	amod	_	_
36	morphism	morphism	NOUN	NN	Number=Sing	33	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 679
# sent_id = 1
# text = This paper generalizes the normally ordered tensor product from Tate vector spaces to Tate objects over arbitrary exact categories.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
5	normally	normally	ADV	RB	_	6	advmod	_	_
6	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
7	tensor	tensor	NOUN	NN	Number=Sing	8	compound	_	_
8	product	product	NOUN	NN	Number=Sing	3	dobj	_	_
9	from	from	ADP	IN	_	3	prep	_	_
10	Tate	Tate	PROPN	NNP	Number=Sing	12	compound	_	_
11	vector	vector	NOUN	NN	Number=Sing	12	compound	_	_
12	spaces	space	NOUN	NNS	Number=Plur	9	pobj	_	_
13	to	to	ADP	IN	_	3	prep	_	_
14	Tate	Tate	PROPN	NNP	Number=Sing	15	compound	_	_
15	objects	object	NOUN	NNS	Number=Plur	13	pobj	_	_
16	over	over	ADP	IN	_	15	prep	_	_
17	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	19	amod	_	_
18	exact	exact	ADJ	JJ	Degree=Pos	19	amod	_	_
19	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show how to lift bi - right exact monoidal structures, duality functors, and construct external Homs.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	how	how	SCONJ	WRB	_	5	advmod	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	lift	lift	VERB	VB	VerbForm=Inf	2	xcomp	_	_
6	bi	bi	ADJ	JJ	Degree=Pos	8	amod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	right	right	ADJ	JJ	Degree=Pos	11	amod	_	_
9	exact	exact	ADJ	JJ	Degree=Pos	11	amod	_	_
10	monoidal	monoidal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	structures	structure	NOUN	NNS	Number=Plur	5	dobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	duality	duality	NOUN	NN	Number=Sing	14	compound	_	_
14	functors	functor	NOUN	NNS	Number=Plur	11	conj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
17	construct	construct	VERB	VB	VerbForm=Inf	2	conj	_	_
18	external	external	ADJ	JJ	Degree=Pos	19	amod	_	_
19	Homs	hom	NOUN	NNS	Number=Plur	17	dobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We list some applications: (i) Adeles of a flag can be written as ordered tensor products; (ii) Intersection numbers can be interpreted via these tensor products; (iii) Pontryagin duality uniquely extends to $ n $ - Tate objects in locally compact abelian groups.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	list	list	VERB	VBP	Tense=Pres|VerbForm=Fin	40	ccomp	_	_
3	some	some	DET	DT	_	4	det	_	_
4	applications	application	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
5	:	:	PUNCT	:	_	4	punct	_	_
6	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	9	punct	_	SpaceAfter=No
7	i	i	NOUN	NN	Number=Sing	9	nmod	_	SpaceAfter=No
8	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	9	punct	_	_
9	Adeles	Adeles	PROPN	NNPS	Number=Plur	15	nsubjpass	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	flag	flag	NOUN	NN	Number=Sing	10	pobj	_	_
13	can	can	AUX	MD	VerbForm=Fin	15	aux	_	_
14	be	be	AUX	VB	VerbForm=Inf	15	auxpass	_	_
15	written	write	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	acl	_	_
16	as	as	SCONJ	IN	_	17	mark	_	_
17	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
18	tensor	tensor	NOUN	NN	Number=Sing	19	compound	_	_
19	products	product	NOUN	NNS	Number=Plur	15	dobj	_	SpaceAfter=No
20	;	;	PUNCT	:	_	4	punct	_	_
21	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	28	punct	_	SpaceAfter=No
22	ii	ii	PROPN	NNP	Number=Sing	25	nmod	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	25	punct	_	_
24	Intersection	intersection	NOUN	NN	Number=Sing	25	compound	_	_
25	numbers	number	NOUN	NNS	Number=Plur	28	nsubjpass	_	_
26	can	can	AUX	MD	VerbForm=Fin	28	aux	_	_
27	be	be	AUX	VB	VerbForm=Inf	28	auxpass	_	_
28	interpreted	interpret	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	acl	_	_
29	via	via	ADP	IN	_	28	prep	_	_
30	these	these	DET	DT	Number=Plur|PronType=Dem	32	det	_	_
31	tensor	tensor	NOUN	NN	Number=Sing	32	compound	_	_
32	products	product	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
33	;	;	PUNCT	:	_	40	punct	_	_
34	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	40	punct	_	SpaceAfter=No
35	iii	iii	X	LS	NumType=Ord	38	nmod	_	SpaceAfter=No
36	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	38	punct	_	_
37	Pontryagin	Pontryagin	PROPN	NNP	Number=Sing	38	compound	_	_
38	duality	duality	NOUN	NN	Number=Sing	40	nsubj	_	_
39	uniquely	uniquely	ADV	RB	_	40	advmod	_	_
40	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
41	to	to	ADP	IN	_	40	prep	_	_
42	$ n $	$ n $	SYM	$	_	44	quantmod	_	_
43	-	-	PUNCT	HYPH	PunctType=Dash	44	punct	_	_
44	Tate	tate	ADJ	JJ	Degree=Pos	45	compound	_	_
45	objects	object	NOUN	NNS	Number=Plur	41	pobj	_	_
46	in	in	ADP	IN	_	45	prep	_	_
47	locally	locally	ADV	RB	_	50	amod	_	_
48	compact	compact	ADJ	JJ	Degree=Pos	50	amod	_	_
49	abelian	abelian	ADJ	JJ	Degree=Pos	50	compound	_	_
50	groups	group	NOUN	NNS	Number=Plur	46	pobj	_	SpaceAfter=No
51	.	.	PUNCT	.	PunctType=Peri	40	punct	_	SpaceAfter=No

# doc_id = 680
# sent_id = 1
# text = This paper provides three characterizations of final functors between internal groupoids in an exact category (in the sense of Barr).
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	three	three	NUM	CD	NumType=Card	5	nummod	_	_
5	characterizations	characterization	NOUN	NNS	Number=Plur	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	final	final	ADJ	JJ	Degree=Pos	8	amod	_	_
8	functors	functor	NOUN	NNS	Number=Plur	6	pobj	_	_
9	between	between	ADP	IN	_	8	prep	_	_
10	internal	internal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	groupoids	groupoid	NOUN	NNS	Number=Plur	9	pobj	_	_
12	in	in	ADP	IN	_	3	prep	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	exact	exact	ADJ	JJ	Degree=Pos	15	amod	_	_
15	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	15	punct	_	SpaceAfter=No
17	in	in	ADP	IN	_	3	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	sense	sense	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	Barr	Barr	PROPN	NNP	Number=Sing	20	pobj	_	SpaceAfter=No
22	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	3	punct	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = In particular, it is proved that a functor between internal groupoids is final if and only if it is internally full and essentially surjective.
1	In	in	ADP	IN	_	6	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
4	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	6	nsubjpass	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	proved	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	that	that	SCONJ	IN	_	13	mark	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	functor	functor	NOUN	NN	Number=Sing	13	nsubj	_	_
10	between	between	ADP	IN	_	9	prep	_	_
11	internal	internal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	groupoids	groupoid	NOUN	NNS	Number=Plur	10	pobj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
14	final	final	ADJ	JJ	Degree=Pos	13	acomp	_	_
15	if	if	SCONJ	IN	_	20	mark	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
17	only	only	ADV	RB	_	20	advmod	_	_
18	if	if	SCONJ	IN	_	20	mark	_	_
19	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	20	nsubj	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	advcl	_	_
21	internally	internally	ADV	RB	_	22	advmod	_	_
22	full	full	ADJ	JJ	Degree=Pos	20	acomp	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	essentially	essentially	ADV	RB	_	25	advmod	_	_
25	surjective	surjective	ADJ	JJ	Degree=Pos	22	conj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 681
# sent_id = 1
# text = We introduce a new class of categories generalizing locally presentable ones.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	new	new	ADJ	JJ	Degree=Pos	5	amod	_	_
5	class	class	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
8	generalizing	generalize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	acl	_	_
9	locally	locally	ADV	RB	_	11	advmod	_	_
10	presentable	presentable	ADJ	JJ	Degree=Pos	11	amod	_	_
11	ones	one	NOUN	NNS	Number=Plur	8	dobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = The distinction does not manifest in the abelian case and, assuming Vopenka's principle, the same happens in the regular case.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	distinction	distinction	NOUN	NN	Number=Sing	5	nsubj	_	_
3	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	aux	_	_
4	not	not	PART	RB	Polarity=Neg	5	neg	_	_
5	manifest	manifest	VERB	VB	VerbForm=Inf	19	ccomp	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	abelian	abelian	PROPN	NNP	Number=Sing	9	compound	_	_
9	case	case	NOUN	NN	Number=Sing	6	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
12	assuming	assume	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	5	advcl	_	_
13	Vopenka	Vopenka	PROPN	NNP	Number=Sing	15	poss	_	SpaceAfter=No
14	's	's	PART	POS	_	13	case	_	_
15	principle	principle	NOUN	NN	Number=Sing	12	dobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	same	same	ADJ	JJ	Degree=Pos	19	nsubj	_	_
19	happens	happen	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	in	in	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	regular	regular	ADJ	JJ	Degree=Pos	23	amod	_	_
23	case	case	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 3
# text = The category of complete partial orders is the natural example of a nearly locally finitely presentable category which is not locally presentable.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	7	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	complete	complete	ADJ	JJ	Degree=Pos	6	amod	_	_
5	partial	partial	ADJ	JJ	Degree=Pos	6	amod	_	_
6	orders	order	NOUN	NNS	Number=Plur	3	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	natural	natural	ADJ	JJ	Degree=Pos	10	amod	_	_
10	example	example	NOUN	NN	Number=Sing	7	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
13	nearly	nearly	ADV	RB	_	14	advmod	_	_
14	locally	locally	ADV	RB	_	15	advmod	_	_
15	finitely	finitely	ADV	RB	_	17	amod	_	_
16	presentable	presentable	ADJ	JJ	Degree=Pos	17	amod	_	_
17	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
18	which	which	PRON	WDT	_	19	nsubj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
20	not	not	PART	RB	Polarity=Neg	19	neg	_	_
21	locally	locally	ADV	RB	_	22	advmod	_	_
22	presentable	presentable	ADJ	JJ	Degree=Pos	19	acomp	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# doc_id = 682
# sent_id = 1
# text = Brauer - Clifford groups are equivariant Brauer groups for which a Hopf algebra acts or coacts nontrivially on the base ring.
1	Brauer	Brauer	PROPN	NNP	Number=Sing	3	compound	_	_
2	-	-	PUNCT	HYPH	PunctType=Dash	3	punct	_	_
3	Clifford	Clifford	PROPN	NNP	Number=Sing	4	compound	_	_
4	groups	group	NOUN	NNS	Number=Plur	5	nsubj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	equivariant	equivariant	ADJ	JJ	Degree=Pos	8	amod	_	_
7	Brauer	Brauer	PROPN	NNP	Number=Sing	8	compound	_	_
8	groups	group	NOUN	NNS	Number=Plur	5	attr	_	_
9	for	for	ADP	IN	_	14	prep	_	_
10	which	which	PRON	WDT	_	9	pobj	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	Hopf	Hopf	PROPN	NNP	Number=Sing	13	compound	_	_
13	algebra	algebra	NOUN	NN	Number=Sing	14	nsubj	_	_
14	acts	act	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	relcl	_	_
15	or	or	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	coacts	coact	NOUN	NNS	Number=Plur	14	conj	_	_
17	nontrivially	nontrivially	ADV	RB	_	16	advmod	_	_
18	on	on	ADP	IN	_	16	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	base	base	NOUN	NN	Number=Sing	21	compound	_	_
21	ring	ring	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = Brauer - Clifford groups have been established previously in the category of modules for a skew group ring $ SG $ , the category of modules for the smash product $ SH $ over a cocommutative Hopf algebra $ H $ , and its dual category of $ (S, H) $ - Hopf modules over a commutative Hopf algebra $ H $ .
1	Brauer	Brauer	PROPN	NNP	Number=Sing	3	compound	_	_
2	-	-	PUNCT	HYPH	PunctType=Dash	3	punct	_	_
3	Clifford	Clifford	PROPN	NNP	Number=Sing	4	compound	_	_
4	groups	group	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
5	have	have	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	aux	_	_
6	been	be	AUX	VBN	Tense=Past|VerbForm=Part	7	auxpass	_	_
7	established	establish	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	previously	previously	ADV	RB	_	7	advmod	_	_
9	in	in	ADP	IN	_	7	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	modules	module	NOUN	NNS	Number=Plur	12	pobj	_	_
14	for	for	ADP	IN	_	7	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	skew	skew	NOUN	NN	Number=Sing	17	compound	_	_
17	group	group	NOUN	NN	Number=Sing	18	compound	_	_
18	ring	ring	NOUN	NN	Number=Sing	14	pobj	_	_
19	$ SG $	$ sg $	SYM	$	_	7	dep	_	_
20	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	category	category	NOUN	NN	Number=Sing	4	appos	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	modules	module	NOUN	NNS	Number=Plur	23	pobj	_	_
25	for	for	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	smash	smash	NOUN	NN	Number=Sing	28	compound	_	_
28	product	product	NOUN	NN	Number=Sing	25	pobj	_	_
29	$ SH $	$ sh $	SYM	$	_	22	dep	_	_
30	over	over	ADP	IN	_	22	prep	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
32	cocommutative	cocommutative	ADJ	JJ	Degree=Pos	34	amod	_	_
33	Hopf	hopf	NOUN	NN	Number=Sing	34	compound	_	_
34	algebra	algebra	NOUN	NN	Number=Sing	30	pobj	_	_
35	$ H $	$ h $	SYM	$	_	34	appos	_	_
36	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
37	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
38	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	40	poss	_	_
39	dual	dual	ADJ	JJ	Degree=Pos	40	amod	_	_
40	category	category	NOUN	NN	Number=Sing	22	conj	_	_
41	of	of	ADP	IN	_	40	prep	_	_
42	$ (S, H) $	$ (s, h) $	SYM	$	_	44	compound	_	_
43	-	-	PUNCT	HYPH	PunctType=Dash	44	punct	_	_
44	Hopf	hopf	NOUN	NN	Number=Sing	45	compound	_	_
45	modules	module	NOUN	NNS	Number=Plur	41	pobj	_	_
46	over	over	ADP	IN	_	45	prep	_	_
47	a	a	DET	DT	Definite=Ind|PronType=Art	50	det	_	_
48	commutative	commutative	ADJ	JJ	Degree=Pos	50	amod	_	_
49	Hopf	Hopf	PROPN	NNP	Number=Sing	50	compound	_	_
50	algebra	algebra	NOUN	NN	Number=Sing	46	pobj	_	_
51	$ H $	$ h $	SYM	$	_	50	appos	_	_
52	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this article the authors introduce a Brauer - Clifford group for the category of dyslectic Hopf Yetter - Drinfel'd $ (S, H) $ - modules for an $ H $ - commutative base ring $ S $ and quantum group $ H $ .
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	article	article	NOUN	NN	Number=Sing	1	pobj	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	authors	author	NOUN	NNS	Number=Plur	6	nsubj	_	_
6	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	Brauer	Brauer	PROPN	NNP	Number=Sing	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	Clifford	Clifford	PROPN	NNP	Number=Sing	11	compound	_	_
11	group	group	NOUN	NN	Number=Sing	6	dobj	_	_
12	for	for	ADP	IN	_	6	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	dyslectic	dyslectic	ADJ	JJ	Degree=Pos	23	amod	_	_
17	Hopf	Hopf	PROPN	NNP	Number=Sing	20	nmod	_	_
18	Yetter	Yetter	PROPN	NNP	Number=Sing	20	nmod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	Drinfel'd	drinfel'd	X	ADD	_	23	nmod	_	_
21	$ (S, H) $	$ (s, h) $	SYM	$	_	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	modules	module	NOUN	NNS	Number=Plur	15	pobj	_	_
24	for	for	ADP	IN	_	6	prep	_	_
25	an	an	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
26	$ H $	$ h $	SYM	$	_	28	advmod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	commutative	commutative	ADJ	JJ	Degree=Pos	29	amod	_	_
29	base	base	NOUN	NN	Number=Sing	30	compound	_	_
30	ring	ring	NOUN	NN	Number=Sing	24	pobj	_	_
31	$ S $	$ s $	SYM	$	_	30	dep	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
33	quantum	quantum	NOUN	NN	Number=Sing	34	compound	_	_
34	group	group	NOUN	NN	Number=Sing	30	conj	_	_
35	$ H $	$ h $	SYM	$	_	6	dobj	_	_
36	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = This is the first such example in a category of modules for a quantum group, and it gives a new example of an equivariant Brauer group in a braided monoidal category.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
4	first	first	ADJ	JJ	Degree=Pos	6	amod	_	_
5	such	such	ADJ	JJ	Degree=Pos	6	amod	_	_
6	example	example	NOUN	NN	Number=Sing	2	attr	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	modules	module	NOUN	NNS	Number=Plur	10	pobj	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	quantum	quantum	NOUN	NN	Number=Sing	15	compound	_	_
15	group	group	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
18	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	19	nsubj	_	_
19	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	conj	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	new	new	ADJ	JJ	Degree=Pos	22	amod	_	_
22	example	example	NOUN	NN	Number=Sing	19	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	an	an	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
25	equivariant	equivariant	ADJ	JJ	Degree=Pos	27	amod	_	_
26	Brauer	Brauer	PROPN	NNP	Number=Sing	27	compound	_	_
27	group	group	NOUN	NN	Number=Sing	23	pobj	_	_
28	in	in	ADP	IN	_	27	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
30	braided	braid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	amod	_	_
31	monoidal	monoidal	ADJ	JJ	Degree=Pos	32	amod	_	_
32	category	category	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# doc_id = 683
# sent_id = 1
# text = It is known since the late 1960's that the dual of the category of compact Hausdorff spaces and continuous maps is a variety—not finitary, but bounded by $ aleph_1 $ .
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	since	since	SCONJ	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	late	late	ADJ	JJ	Degree=Pos	7	amod	_	_
7	1960	1960	NUM	CD	NumType=Card	4	pobj	_	SpaceAfter=No
8	's	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	case	_	_
9	that	that	SCONJ	IN	_	22	mark	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	dual	dual	ADJ	JJ	Degree=Pos	22	nsubj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	compact	compact	ADJ	JJ	Degree=Pos	18	amod	_	_
17	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	18	compound	_	_
18	spaces	space	NOUN	NNS	Number=Plur	15	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	continuous	continuous	ADJ	JJ	Degree=Pos	21	amod	_	_
21	maps	map	NOUN	NNS	Number=Plur	18	conj	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	variety	variety	NOUN	NN	Number=Sing	22	attr	_	SpaceAfter=No
25	—	—	PUNCT	:	_	24	punct	_	SpaceAfter=No
26	not	not	PART	RB	Polarity=Neg	27	neg	_	_
27	finitary	finitary	ADJ	JJ	Degree=Pos	24	appos	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
29	but	but	CCONJ	CC	ConjType=Cmp	22	cc	_	_
30	bounded	bound	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	conj	_	_
31	by	by	ADP	IN	_	30	agent	_	_
32	$ aleph_1 $	$ aleph_1 $	SYM	$	_	31	pobj	_	_
33	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this note we show that the dual of the category of partially ordered compact spaces and monotone continuous maps is an $ aleph_1 $ - ary quasivariety, and describe partially its algebraic theory.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	note	note	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	21	mark	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	dual	dual	ADJ	JJ	Degree=Pos	21	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	partially	partially	ADV	RB	_	14	advmod	_	_
14	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
15	compact	compact	ADJ	JJ	Degree=Pos	16	amod	_	_
16	spaces	space	NOUN	NNS	Number=Plur	12	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	monotone	monotone	ADJ	JJ	Degree=Pos	20	amod	_	_
19	continuous	continuous	ADJ	JJ	Degree=Pos	20	amod	_	_
20	maps	map	NOUN	NNS	Number=Plur	16	conj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
22	an	an	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
23	$ aleph_1 $	$ aleph_1 $	SYM	$	_	25	quantmod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	ary	ary	PROPN	NNP	Number=Sing	26	compound	_	_
26	quasivariety	quasivariety	NOUN	NN	Number=Sing	21	attr	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
29	describe	describe	VERB	VB	VerbForm=Inf	21	conj	_	_
30	partially	partially	ADV	RB	_	29	advmod	_	_
31	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	33	poss	_	_
32	algebraic	algebraic	ADJ	JJ	Degree=Pos	33	amod	_	_
33	theory	theory	NOUN	NN	Number=Sing	29	dobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = Based on this description, we extend these results to categories of Vietoris coalgebras and homomorphisms on ordered compact spaces.
1	Based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	prep	_	_
2	on	on	ADP	IN	_	1	prep	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	description	description	NOUN	NN	Number=Sing	2	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	extend	extend	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	these	these	DET	DT	Number=Plur|PronType=Dem	9	det	_	_
9	results	result	NOUN	NNS	Number=Plur	7	dobj	_	_
10	to	to	ADP	IN	_	7	prep	_	_
11	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	Vietoris	Vietoris	PROPN	NNP	Number=Sing	14	compound	_	_
14	coalgebras	coalgebra	NOUN	NNS	Number=Plur	12	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	homomorphisms	homomorphism	NOUN	NNS	Number=Plur	14	conj	_	_
17	on	on	ADP	IN	_	7	prep	_	_
18	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	amod	_	_
19	compact	compact	ADJ	JJ	Degree=Pos	20	amod	_	_
20	spaces	space	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = We also characterise the $ aleph_1 $ - copresentable partially ordered compact spaces.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	characterise	characterise	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
5	$ aleph_1 $	$ aleph_1 $	SYM	$	_	7	advmod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	copresentable	copresentable	ADJ	JJ	Degree=Pos	11	amod	_	_
8	partially	partially	ADV	RB	_	9	advmod	_	_
9	ordered	order	VERB	VBD	Tense=Past|VerbForm=Fin	11	amod	_	_
10	compact	compact	ADJ	JJ	Degree=Pos	11	amod	_	_
11	spaces	space	NOUN	NNS	Number=Plur	3	dobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 684
# sent_id = 1
# text = Given a 2 - category $ A $ , a 2 - functor $ F : A to Cat $ and a distinguished 1 - subcategory $ Sigma subset A $ containing all the objects, a $ sigma $ - cone for $ F $ (with respect to $ Sigma $ ) is a lax cone such that the structural 2 - cells corresponding to the arrows of $ Sigma $ are invertible.
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	37	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
3	2	2	NUM	CD	NumType=Card	5	nummod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	category	category	NOUN	NN	Number=Sing	6	compound	_	_
6	$ A $	$ a $	SYM	$	_	1	pobj	_	_
7	,	,	PUNCT	,	PunctType=Comm	1	punct	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
9	2	2	NUM	CD	NumType=Card	11	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	functor	functor	NOUN	NN	Number=Sing	12	compound	_	_
12	$ F : A to Cat $	$ f : a to cat $	SYM	$	_	1	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
15	distinguished	distinguished	ADJ	JJ	Degree=Pos	19	amod	_	_
16	1	1	NUM	CD	NumType=Card	18	nummod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	subcategory	subcategory	NOUN	NN	Number=Sing	19	compound	_	_
19	$ Sigma subset A $	$ sigma subset a $	SYM	$	_	12	conj	_	_
20	containing	contain	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	12	acl	_	_
21	all	all	DET	PDT	_	23	predet	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	objects	object	NOUN	NNS	Number=Plur	20	dobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	37	punct	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
26	$ sigma $	$ sigma $	SYM	$	_	28	compound	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	cone	cone	NOUN	NN	Number=Sing	37	nsubj	_	_
29	for	for	ADP	IN	_	28	prep	_	_
30	$ F $	$ f $	SYM	$	_	29	pobj	_	_
31	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	28	punct	_	SpaceAfter=No
32	with	with	ADP	IN	_	28	prep	_	_
33	respect	respect	NOUN	NN	Number=Sing	32	pobj	_	_
34	to	to	ADP	IN	_	33	prep	_	_
35	$ Sigma $	$ sigma $	SYM	$	_	34	pobj	_	_
36	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	28	punct	_	_
37	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
38	a	a	DET	DT	Definite=Ind|PronType=Art	40	det	_	_
39	lax	lax	ADJ	JJ	Degree=Pos	40	amod	_	_
40	cone	cone	NOUN	NN	Number=Sing	37	attr	_	_
41	such	such	ADJ	JJ	Degree=Pos	40	nmod	_	_
42	that	that	SCONJ	IN	_	54	mark	_	_
43	the	the	DET	DT	Definite=Def|PronType=Art	47	det	_	_
44	structural	structural	ADJ	JJ	Degree=Pos	47	amod	_	_
45	2	2	NUM	CD	NumType=Card	47	nummod	_	_
46	-	-	PUNCT	HYPH	PunctType=Dash	47	punct	_	_
47	cells	cell	NOUN	NNS	Number=Plur	54	nsubj	_	_
48	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	47	acl	_	_
49	to	to	ADP	IN	_	48	prep	_	_
50	the	the	DET	DT	Definite=Def|PronType=Art	51	det	_	_
51	arrows	arrow	NOUN	NNS	Number=Plur	49	pobj	_	_
52	of	of	ADP	IN	_	51	prep	_	_
53	$ Sigma $	$ sigma $	SYM	$	_	52	pobj	_	_
54	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	37	ccomp	_	_
55	invertible	invertible	ADJ	JJ	Degree=Pos	54	acomp	_	SpaceAfter=No
56	.	.	PUNCT	.	PunctType=Peri	37	punct	_	SpaceAfter=No

# sent_id = 2
# text = The conical $ sigma $ - limit} is the universal (up to isomorphism) $ sigma $ - cone.
1	The	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
2	conical	conical	ADJ	JJ	Degree=Pos	5	amod	_	_
3	$ sigma $	$ sigma $	SYM	$	_	5	compound	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	limit	limit	NOUN	NN	Number=Sing	7	nsubj	_	SpaceAfter=No
6	}	}	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	7	punct	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	universal	universal	ADJ	JJ	Degree=Pos	7	attr	_	_
10	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	9	punct	_	SpaceAfter=No
11	up	up	ADP	IN	_	9	prep	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	isomorphism	isomorphism	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
14	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	9	punct	_	_
15	$ sigma $	$ sigma $	SYM	$	_	17	compound	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	cone	cone	NOUN	NN	Number=Sing	7	acomp	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = The notion of $ sigma $ - limit generalizes the well known notions of pseudo and lax limit.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	notion	notion	NOUN	NN	Number=Sing	7	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	$ sigma $	$ sigma $	SYM	$	_	6	compound	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	limit	limit	NOUN	NN	Number=Sing	3	pobj	_	_
7	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
9	well	well	ADV	RB	Degree=Pos	10	advmod	_	_
10	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
11	notions	notion	NOUN	NNS	Number=Plur	7	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	pseudo	pseudo	NOUN	NN	Number=Sing	12	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	lax	lax	ADJ	JJ	Degree=Pos	16	amod	_	_
16	limit	limit	NOUN	NN	Number=Sing	13	conj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = We consider the fundamental notion of $ sigma $ - filtered pair $ (A, Sigma) $ which generalizes the notion of 2 - filtered 2 - category.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	fundamental	fundamental	ADJ	JJ	Degree=Pos	5	amod	_	_
5	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	$ sigma $	$ sigma $	SYM	$	_	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	filtered	filter	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	pair	pair	NOUN	NN	Number=Sing	11	compound	_	_
11	$ (A, Sigma) $	$ (a, sigma) $	SYM	$	_	6	pobj	_	_
12	which	which	PRON	WDT	_	13	nsubj	_	_
13	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	relcl	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	notion	notion	NOUN	NN	Number=Sing	13	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	2	2	NUM	CD	NumType=Card	19	npadvmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	filtered	filter	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	amod	_	_
20	2	2	NUM	CD	NumType=Card	22	nummod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	category	category	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = We give an explicit construction of $ sigma $ - filtered $ sigma $ - colimits of categories, a construction which allows computations with these colimits.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	explicit	explicit	ADJ	JJ	Degree=Pos	5	amod	_	_
5	construction	construction	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	$ sigma $	$ sigma $	SYM	$	_	9	dep	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	filtered	filter	VERB	VBD	Tense=Past|VerbForm=Fin	6	pobj	_	_
10	$ sigma $	$ sigma $	SYM	$	_	12	nmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	colimits	colimit	NOUN	NNS	Number=Plur	9	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	construction	construction	NOUN	NN	Number=Sing	12	appos	_	_
18	which	which	PRON	WDT	_	19	nsubj	_	_
19	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
20	computations	computation	NOUN	NNS	Number=Plur	19	dobj	_	_
21	with	with	ADP	IN	_	20	prep	_	_
22	these	these	DET	DT	Number=Plur|PronType=Dem	23	det	_	_
23	colimits	colimit	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = We then state and prove a basic exactness property of the 2 - category of categories, namely, that $ sigma $ - filtered $ sigma $ - colimits commute with finite weighted pseudo (or bi) limits.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	state	state	NOUN	NN	Number=Sing	0	ROOT	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	prove	prove	VERB	VB	VerbForm=Inf	3	conj	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	basic	basic	ADJ	JJ	Degree=Pos	9	amod	_	_
8	exactness	exactness	NOUN	NN	Number=Sing	9	amod	_	_
9	property	property	NOUN	NN	Number=Sing	5	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
12	2	2	NUM	CD	NumType=Card	14	nummod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
18	namely	namely	ADV	RB	_	5	advmod	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
20	that	that	SCONJ	IN	_	23	mark	_	_
21	$ sigma $	$ sigma $	SYM	$	_	23	dep	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	filtered	filter	VERB	VBD	Tense=Past|VerbForm=Fin	3	conj	_	_
24	$ sigma $	$ sigma $	SYM	$	_	26	compound	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	colimits	colimit	NOUN	NNS	Number=Plur	27	compound	_	_
27	commute	commute	NOUN	NN	Number=Sing	23	dobj	_	_
28	with	with	ADP	IN	_	27	prep	_	_
29	finite	finite	PROPN	NNP	Number=Sing	28	pobj	_	_
30	weighted	weight	VERB	VBD	Tense=Past|VerbForm=Fin	31	amod	_	_
31	pseudo	pseudo	NOUN	NN	Number=Sing	36	nmod	_	_
32	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	31	punct	_	SpaceAfter=No
33	or	or	CCONJ	CC	ConjType=Cmp	31	cc	_	_
34	bi	bi	NOUN	NN	Number=Sing	31	conj	_	SpaceAfter=No
35	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	31	punct	_	_
36	limits	limit	NOUN	NNS	Number=Plur	3	conj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 7
# text = An important corollary of this result is that a $ sigma $ - filtered $ sigma $ - colimit of exact category valued 2 - functors is exact.
1	An	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	important	important	ADJ	JJ	Degree=Pos	3	amod	_	_
3	corollary	corollary	NOUN	NN	Number=Sing	7	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	result	result	NOUN	NN	Number=Sing	4	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	that	that	SCONJ	IN	_	23	mark	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
10	$ sigma $	$ sigma $	SYM	$	_	12	dep	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	filtered	filter	VERB	VBD	Tense=Past|VerbForm=Fin	15	amod	_	_
13	$ sigma $	$ sigma $	SYM	$	_	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	colimit	colimit	NOUN	NN	Number=Sing	23	nsubj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	exact	exact	ADJ	JJ	Degree=Pos	18	amod	_	_
18	category	category	NOUN	NN	Number=Sing	16	pobj	_	_
19	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	acl	_	_
20	2	2	NUM	CD	NumType=Card	22	nummod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	functors	functor	NOUN	NNS	Number=Plur	19	dobj	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	ccomp	_	_
24	exact	exact	ADJ	JJ	Degree=Pos	23	acomp	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 8
# text = This corollary is essential in the 2 - dimensional theory of flat and pro - representable 2 - functors, that we develop elsewhere.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	corollary	corollary	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	essential	essential	ADJ	JJ	Degree=Pos	3	acomp	_	_
5	in	in	ADP	IN	_	3	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
7	2	2	NUM	CD	NumType=Card	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	dimensional	dimensional	ADJ	JJ	Degree=Pos	10	amod	_	_
10	theory	theory	NOUN	NN	Number=Sing	5	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	flat	flat	ADJ	JJ	Degree=Pos	16	amod	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	pro	pro	ADJ	JJ	Degree=Pos	12	conj	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	representable	representable	ADJ	JJ	Degree=Pos	19	amod	_	_
17	2	2	NUM	CD	NumType=Card	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	functors	functor	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
21	that	that	SCONJ	IN	_	23	mark	_	_
22	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	23	nsubj	_	_
23	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	3	ccomp	_	_
24	elsewhere	elsewhere	ADV	RB	_	23	advmod	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 685
# sent_id = 1
# text = We show that the regular patterns of Getzler form a 2 - category biequivalent to the 2 - category of substitudes of Day and Street, and that the Feynman categories of Kaufmann and Ward form a 2 - category biequivalent to the 2 - category of coloured operads (with invertible 2 - cells).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	9	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	regular	regular	ADJ	JJ	Degree=Pos	6	amod	_	_
6	patterns	pattern	NOUN	NNS	Number=Plur	9	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	Getzler	Getzler	PROPN	NNP	Number=Sing	7	pobj	_	_
9	form	form	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	category	category	NOUN	NN	Number=Sing	14	compound	_	_
14	biequivalent	biequivalent	NOUN	NN	Number=Sing	9	dobj	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
17	2	2	NUM	CD	NumType=Card	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	substitudes	substitude	NOUN	NNS	Number=Plur	20	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	Day	Day	PROPN	NNP	Number=Sing	22	pobj	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	Street	Street	PROPN	NNP	Number=Sing	23	conj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
28	that	that	SCONJ	IN	_	36	mark	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
30	Feynman	Feynman	PROPN	NNP	Number=Sing	31	compound	_	_
31	categories	category	NOUN	NNS	Number=Plur	36	nsubj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	Kaufmann	Kaufmann	PROPN	NNP	Number=Sing	32	pobj	_	_
34	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
35	Ward	Ward	PROPN	NNP	Number=Sing	33	conj	_	_
36	form	form	VERB	VB	VerbForm=Inf	9	conj	_	_
37	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
38	2	2	NUM	CD	NumType=Card	40	nummod	_	_
39	-	-	PUNCT	HYPH	PunctType=Dash	40	punct	_	_
40	category	category	NOUN	NN	Number=Sing	41	compound	_	_
41	biequivalent	biequivalent	NOUN	NN	Number=Sing	36	dobj	_	_
42	to	to	ADP	IN	_	41	prep	_	_
43	the	the	DET	DT	Definite=Def|PronType=Art	46	det	_	_
44	2	2	NUM	CD	NumType=Card	46	nummod	_	_
45	-	-	PUNCT	HYPH	PunctType=Dash	46	punct	_	_
46	category	category	NOUN	NN	Number=Sing	42	pobj	_	_
47	of	of	ADP	IN	_	46	prep	_	_
48	coloured	coloured	ADJ	JJ	Degree=Pos	49	amod	_	_
49	operads	operad	NOUN	NNS	Number=Plur	47	pobj	_	_
50	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	46	punct	_	SpaceAfter=No
51	with	with	ADP	IN	_	36	prep	_	_
52	invertible	invertible	ADJ	JJ	Degree=Pos	55	amod	_	_
53	2	2	NUM	CD	NumType=Card	55	nummod	_	_
54	-	-	PUNCT	HYPH	PunctType=Dash	55	punct	_	_
55	cells	cell	NOUN	NNS	Number=Plur	51	pobj	_	SpaceAfter=No
56	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	36	punct	_	SpaceAfter=No
57	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = These biequivalences induce equivalences between the corresponding categories of algebras.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	biequivalences	biequivalence	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	induce	induce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	equivalences	equivalence	NOUN	NNS	Number=Plur	3	dobj	_	_
5	between	between	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	algebras	algebra	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = There are three main ingredients in establishing these biequivalences.
1	There	there	PRON	EX	_	2	expl	_	_
2	are	be	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	three	three	NUM	CD	NumType=Card	5	nummod	_	_
4	main	main	ADJ	JJ	Degree=Pos	5	amod	_	_
5	ingredients	ingredient	NOUN	NNS	Number=Plur	2	attr	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	establishing	establish	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	pcomp	_	_
8	these	these	DET	DT	Number=Plur|PronType=Dem	9	det	_	_
9	biequivalences	biequivalence	NOUN	NNS	Number=Plur	7	dobj	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = The first is a strictification theorem (exploiting Power's General Coherence Result) which allows to reduce to the case where the structure maps are identity - on - objects functors and strict monoidal.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	first	first	ADJ	JJ	Degree=Pos	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	strictification	strictification	NOUN	NN	Number=Sing	6	npadvmod	_	_
6	theorem	theorem	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	attr	_	_
7	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	6	punct	_	SpaceAfter=No
8	exploiting	exploit	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	acl	_	_
9	Power	Power	PROPN	NNP	Number=Sing	13	poss	_	SpaceAfter=No
10	's	's	PART	POS	_	9	case	_	_
11	General	General	PROPN	NNP	Number=Sing	12	compound	_	_
12	Coherence	Coherence	PROPN	NNP	Number=Sing	13	compound	_	_
13	Result	Result	PROPN	NNP	Number=Sing	8	dobj	_	SpaceAfter=No
14	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	13	punct	_	_
15	which	which	PRON	WDT	_	16	nsubj	_	_
16	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	relcl	_	_
17	to	to	PART	TO	_	18	aux	_	_
18	reduce	reduce	VERB	VB	VerbForm=Inf	16	xcomp	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	case	case	NOUN	NN	Number=Sing	19	pobj	_	_
22	where	where	SCONJ	WRB	_	26	advmod	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	structure	structure	NOUN	NN	Number=Sing	25	compound	_	_
25	maps	map	NOUN	NNS	Number=Plur	26	nsubj	_	_
26	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	21	relcl	_	_
27	identity	identity	NOUN	NN	Number=Sing	32	nmod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
29	on	on	ADP	IN	_	27	prep	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
31	objects	object	NOUN	NNS	Number=Plur	29	pobj	_	_
32	functors	functor	NOUN	NNS	Number=Plur	26	attr	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
34	strict	strict	ADJ	JJ	Degree=Pos	35	amod	_	_
35	monoidal	monoidal	NOUN	NN	Number=Sing	32	conj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = Second, we subsume the Getzler and Kaufmann - Ward hereditary axioms into the notion of Guitart exactness, a general condition ensuring compatibility between certain left Kan extensions and a given monad, in this case the free - symmetric - monoidal - category monad.
1	Second	second	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	subsume	subsume	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	Getzler	Getzler	PROPN	NNP	Number=Sing	4	dobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	Kaufmann	Kaufmann	PROPN	NNP	Number=Sing	10	compound	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	Ward	Ward	PROPN	NNP	Number=Sing	6	conj	_	_
11	hereditary	hereditary	ADJ	JJ	Degree=Pos	12	amod	_	_
12	axioms	axiom	NOUN	NNS	Number=Plur	4	dobj	_	_
13	into	into	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	notion	notion	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	Guitart	Guitart	PROPN	NNP	Number=Sing	18	compound	_	_
18	exactness	exactness	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	general	general	ADJ	JJ	Degree=Pos	22	amod	_	_
22	condition	condition	NOUN	NN	Number=Sing	12	appos	_	_
23	ensuring	ensure	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	acl	_	_
24	compatibility	compatibility	NOUN	NN	Number=Sing	23	dobj	_	_
25	between	between	ADP	IN	_	24	prep	_	_
26	certain	certain	ADJ	JJ	Degree=Pos	29	amod	_	_
27	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	amod	_	_
28	Kan	Kan	PROPN	NNP	Number=Sing	29	compound	_	_
29	extensions	extension	NOUN	NNS	Number=Plur	25	pobj	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	29	cc	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
32	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	amod	_	_
33	monad	monad	NOUN	NNS	Number=Plur	29	conj	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
35	in	in	ADP	IN	_	46	prep	_	_
36	this	this	DET	DT	Number=Sing|PronType=Dem	37	det	_	_
37	case	case	NOUN	NN	Number=Sing	35	pobj	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	46	det	_	_
39	free	free	ADJ	JJ	Degree=Pos	43	amod	_	_
40	-	-	PUNCT	HYPH	PunctType=Dash	43	punct	_	_
41	symmetric	symmetric	ADJ	JJ	Degree=Pos	43	amod	_	_
42	-	-	PUNCT	HYPH	PunctType=Dash	43	punct	_	_
43	monoidal	monoidal	ADJ	JJ	Degree=Pos	45	amod	_	_
44	-	-	PUNCT	HYPH	PunctType=Dash	45	punct	_	_
45	category	category	NOUN	NN	Number=Sing	46	compound	_	_
46	monad	monad	NOUN	NNS	Number=Plur	4	dobj	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 6
# text = Finally we set up a biadjunction between substitudes and what we call pinned symmetric monoidal categories, from which the results follow as a consequence of the fact that the hereditary map is precisely the counit of this biadjunction.
1	Finally	finally	ADV	RB	_	3	advmod	_	_
2	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
3	set	set	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	up	up	ADP	RP	_	3	prt	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	biadjunction	biadjunction	NOUN	NN	Number=Sing	3	dobj	_	_
7	between	between	ADP	IN	_	6	prep	_	_
8	substitudes	substitude	NOUN	NNS	Number=Plur	7	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	what	what	PRON	WP	_	12	dobj	_	_
11	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	12	nsubj	_	_
12	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	3	ccomp	_	_
13	pinned	pin	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	conj	_	_
14	symmetric	symmetric	ADJ	JJ	Degree=Pos	16	amod	_	_
15	monoidal	monoidal	ADJ	JJ	Degree=Pos	16	amod	_	_
16	categories	category	NOUN	NNS	Number=Plur	13	dobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	from	from	ADP	IN	_	22	prep	_	_
19	which	which	PRON	WDT	_	18	pobj	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	results	result	NOUN	NNS	Number=Plur	22	nsubj	_	_
22	follow	follow	VERB	VBP	Tense=Pres|VerbForm=Fin	16	relcl	_	_
23	as	as	ADP	IN	_	22	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
25	consequence	consequence	NOUN	NN	Number=Sing	23	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	fact	fact	NOUN	NN	Number=Sing	26	pobj	_	_
29	that	that	SCONJ	IN	_	33	mark	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	hereditary	hereditary	ADJ	JJ	Degree=Pos	32	amod	_	_
32	map	map	NOUN	NN	Number=Sing	33	nsubj	_	_
33	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	28	acl	_	_
34	precisely	precisely	ADV	RB	_	36	advmod	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	counit	counit	NOUN	NN	Number=Sing	33	attr	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	this	this	DET	DT	Number=Sing|PronType=Dem	39	det	_	_
39	biadjunction	biadjunction	NOUN	NN	Number=Sing	37	pobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 686
# sent_id = 1
# text = We study spans of cospans in a category $ C $ and explain how to horizontally and vertically compose these.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	spans	span	NOUN	NNS	Number=Plur	2	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	cospans	cospan	NOUN	NNS	Number=Plur	4	pobj	_	_
6	in	in	ADP	IN	_	2	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
9	$ C $	$ c $	SYM	$	_	2	dep	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
11	explain	explain	VERB	VB	VerbForm=Inf	2	conj	_	_
12	how	how	SCONJ	WRB	_	17	advmod	_	_
13	to	to	PART	TO	_	17	aux	_	_
14	horizontally	horizontally	ADV	RB	_	17	advmod	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	vertically	vertically	ADV	RB	_	17	advmod	_	_
17	compose	compose	VERB	VB	VerbForm=Inf	11	xcomp	_	_
18	these	these	PRON	DT	Number=Plur|PronType=Dem	17	dobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = When $ C $ is a topos and the legs of the spans are monic, these two forms of composition satisfy the interchange law.
1	When	when	SCONJ	WRB	_	3	advmod	_	_
2	$ C $	$ c $	SYM	$	_	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	advcl	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	topos	topos	NOUN	NN	Number=Sing	3	attr	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	legs	leg	NOUN	NNS	Number=Plur	5	conj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	spans	span	NOUN	NNS	Number=Plur	9	pobj	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	20	ccomp	_	_
13	monic	monic	ADJ	JJ	Degree=Pos	12	acomp	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
15	these	these	DET	DT	Number=Plur|PronType=Dem	17	det	_	_
16	two	two	NUM	CD	NumType=Card	17	nummod	_	_
17	forms	form	NOUN	NNS	Number=Plur	20	nsubj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	composition	composition	NOUN	NN	Number=Sing	18	pobj	_	_
20	satisfy	satisfy	VERB	VB	VerbForm=Inf	0	ROOT	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	interchange	interchange	ADJ	JJ	Degree=Pos	23	compound	_	_
23	law	law	NOUN	NN	Number=Sing	20	dobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this case there is a bicategory of objects, cospans, and `monic - legged' spans of cospans in $ C $ .
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	case	case	NOUN	NN	Number=Sing	1	pobj	_	_
4	there	there	PRON	EX	_	5	expl	_	_
5	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	bicategory	bicategory	NOUN	NN	Number=Sing	5	attr	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	objects	object	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	cospans	cospan	NOUN	NNS	Number=Plur	9	conj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
14	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	19	punct	_	SpaceAfter=No
15	monic	monic	ADJ	JJ	Degree=Pos	17	amod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	legged	legged	ADJ	JJ	Degree=Pos	19	amod	_	SpaceAfter=No
18	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	19	punct	_	_
19	spans	span	NOUN	NNS	Number=Plur	11	conj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	cospans	cospan	NOUN	NNS	Number=Plur	20	pobj	_	_
22	in	in	ADP	IN	_	7	prep	_	_
23	$ C $	$ c $	SYM	$	_	22	pobj	_	_
24	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = One motivation for this construction is an application to graph rewriting.
1	One	one	NUM	CD	NumType=Card	2	nummod	_	_
2	motivation	motivation	NOUN	NN	Number=Sing	6	nsubj	_	_
3	for	for	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	construction	construction	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	application	application	NOUN	NN	Number=Sing	6	attr	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	graph	graph	VERB	VB	VerbForm=Inf	8	acl	_	_
11	rewriting	rewrite	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	dobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 687
# sent_id = 1
# text = We define strict and weak duality involutions on 2 - categories, and prove a coherence theorem that every bicategory with a weak duality involution is biequivalent to a 2 - category with a strict duality involution.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	strict	strict	ADJ	JJ	Degree=Pos	7	amod	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	weak	weak	ADJ	JJ	Degree=Pos	3	conj	_	_
6	duality	duality	NOUN	NN	Number=Sing	7	compound	_	_
7	involutions	involution	NOUN	NNS	Number=Plur	2	dobj	_	_
8	on	on	ADP	IN	_	7	prep	_	_
9	2	2	NUM	CD	NumType=Card	11	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
14	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	coherence	coherence	NOUN	NN	Number=Sing	17	nsubj	_	_
17	theorem	theorem	ADJ	JJ	Degree=Pos	14	ccomp	_	_
18	that	that	SCONJ	IN	_	26	mark	_	_
19	every	every	DET	DT	_	20	det	_	_
20	bicategory	bicategory	NOUN	NN	Number=Sing	26	nsubj	_	_
21	with	with	ADP	IN	_	20	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
23	weak	weak	ADJ	JJ	Degree=Pos	25	amod	_	_
24	duality	duality	NOUN	NN	Number=Sing	25	compound	_	_
25	involution	involution	NOUN	NN	Number=Sing	21	pobj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	ccomp	_	_
27	biequivalent	biequivalent	NOUN	NN	Number=Sing	26	acomp	_	_
28	to	to	ADP	IN	_	27	prep	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
30	2	2	NUM	CD	NumType=Card	32	nummod	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	category	category	NOUN	NN	Number=Sing	28	pobj	_	_
33	with	with	ADP	IN	_	27	prep	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
35	strict	strict	ADJ	JJ	Degree=Pos	37	amod	_	_
36	duality	duality	NOUN	NN	Number=Sing	37	compound	_	_
37	involution	involution	NOUN	NN	Number=Sing	33	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = For this purpose we introduce "2 - categories with contravariance", a sort of enhanced 2 - category with a basic notion of "contravariant morphism", which can be regarded either as generalized multicategories or as enriched categories.
1	For	for	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	purpose	purpose	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	9	punct	_	SpaceAfter=No
7	2	2	NUM	CD	NumType=Card	9	nummod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	categories	category	NOUN	NNS	Number=Plur	5	dobj	_	_
10	with	with	ADP	IN	_	5	prep	_	_
11	contravariance	contravariance	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
12	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	5	punct	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	sort	sort	NOUN	NN	Number=Sing	5	dobj	_	_
16	of	of	ADV	RB	_	17	advmod	_	_
17	enhanced	enhance	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	amod	_	_
18	2	2	NUM	CD	NumType=Card	20	nummod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	category	category	NOUN	NN	Number=Sing	15	appos	_	_
21	with	with	ADP	IN	_	15	prep	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
23	basic	basic	ADJ	JJ	Degree=Pos	24	amod	_	_
24	notion	notion	NOUN	NN	Number=Sing	21	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	25	punct	_	SpaceAfter=No
27	contravariant	contravariant	ADJ	JJ	Degree=Pos	28	amod	_	_
28	morphism	morphism	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
29	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	28	punct	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
31	which	which	PRON	WDT	_	34	nsubjpass	_	_
32	can	can	AUX	MD	VerbForm=Fin	34	aux	_	_
33	be	be	AUX	VB	VerbForm=Inf	34	auxpass	_	_
34	regarded	regard	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	relcl	_	_
35	either	either	CCONJ	CC	ConjType=Cmp	36	preconj	_	_
36	as	as	ADP	IN	_	34	prep	_	_
37	generalized	generalize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	38	amod	_	_
38	multicategories	multicategorie	NOUN	NNS	Number=Plur	36	pobj	_	_
39	or	or	CCONJ	CC	ConjType=Cmp	38	cc	_	_
40	as	as	ADP	IN	_	38	conj	_	_
41	enriched	enriched	ADJ	JJ	Degree=Pos	42	amod	_	_
42	categories	category	NOUN	NNS	Number=Plur	40	pobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = This enables a universal characterization of duality involutions using absolute weighted colimits, leading to a conceptual proof of the coherence theorem.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	enables	enable	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	universal	universal	ADJ	JJ	Degree=Pos	5	amod	_	_
5	characterization	characterization	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	duality	duality	NOUN	NN	Number=Sing	8	compound	_	_
8	involutions	involution	NOUN	NNS	Number=Plur	6	pobj	_	_
9	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	acl	_	_
10	absolute	absolute	ADJ	JJ	Degree=Pos	12	amod	_	_
11	weighted	weighted	ADJ	JJ	Degree=Pos	12	amod	_	_
12	colimits	colimit	NOUN	NNS	Number=Plur	9	dobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
14	leading	lead	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	conceptual	conceptual	ADJ	JJ	Degree=Pos	18	amod	_	_
18	proof	proof	NOUN	NN	Number=Sing	15	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	coherence	coherence	NOUN	NN	Number=Sing	19	pobj	_	_
22	theorem	theorem	ADJ	JJ	Degree=Pos	2	ccomp	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 688
# sent_id = 1
# text = In this technical note, we proffer a very explicit construction of the dual cocartesian fibration of a cartesian fibration, and we show they are classified by the same functor to the $ infty $ - category of $ infty $ - categories.
1	In	in	ADP	IN	_	7	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
3	technical	technical	ADJ	JJ	Degree=Pos	4	amod	_	_
4	note	note	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	proffer	proffer	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	very	very	ADV	RB	_	10	advmod	_	_
10	explicit	explicit	ADJ	JJ	Degree=Pos	11	amod	_	_
11	construction	construction	NOUN	NN	Number=Sing	7	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
14	dual	dual	ADJ	JJ	Degree=Pos	15	amod	_	_
15	cocartesian	cocartesian	NOUN	NN	Number=Sing	16	compound	_	_
16	fibration	fibration	NOUN	NN	Number=Sing	12	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	cartesian	cartesian	ADJ	JJ	Degree=Pos	20	amod	_	_
20	fibration	fibration	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
23	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	24	nsubj	_	_
24	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	7	conj	_	_
25	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	27	nsubjpass	_	_
26	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	27	auxpass	_	_
27	classified	classify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	ccomp	_	_
28	by	by	ADP	IN	_	27	agent	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
30	same	same	ADJ	JJ	Degree=Pos	31	amod	_	_
31	functor	functor	NOUN	NN	Number=Sing	28	pobj	_	_
32	to	to	ADP	IN	_	27	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
34	$ infty $	$ infty $	SYM	$	_	36	nmod	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	36	punct	_	_
36	category	category	NOUN	NN	Number=Sing	32	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	$ infty $	$ infty $	SYM	$	_	40	compound	_	_
39	-	-	PUNCT	HYPH	PunctType=Dash	40	punct	_	_
40	categories	category	NOUN	NNS	Number=Plur	37	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# doc_id = 689
# sent_id = 1
# text = In this paper, we study properties of maps between fibrant objects in model categories.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	properties	property	NOUN	NNS	Number=Plur	6	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	maps	map	NOUN	NNS	Number=Plur	8	pobj	_	_
10	between	between	ADP	IN	_	9	prep	_	_
11	fibrant	fibrant	ADJ	JJ	Degree=Pos	12	amod	_	_
12	objects	object	NOUN	NNS	Number=Plur	10	pobj	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	model	model	NOUN	NN	Number=Sing	15	compound	_	_
15	categories	category	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = We give a characterization of weak equivalences between fibrant objects.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	characterization	characterization	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	weak	weak	ADJ	JJ	Degree=Pos	7	amod	_	_
7	equivalences	equivalence	NOUN	NNS	Number=Plur	5	pobj	_	_
8	between	between	ADP	IN	_	4	prep	_	_
9	fibrant	fibrant	ADJ	JJ	Degree=Pos	10	amod	_	_
10	objects	object	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = If every object of a model category is fibrant, then we give a simple description of a set of generating cofibrations.
1	If	if	SCONJ	IN	_	8	mark	_	_
2	every	every	DET	DT	_	3	det	_	_
3	object	object	NOUN	NN	Number=Sing	8	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	model	model	NOUN	NN	Number=Sing	7	compound	_	_
7	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	advcl	_	_
9	fibrant	fibrant	ADJ	JJ	Degree=Pos	8	acomp	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
11	then	then	ADV	RB	PronType=Dem	13	advmod	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	simple	simple	ADJ	JJ	Degree=Pos	16	amod	_	_
16	description	description	NOUN	NN	Number=Sing	13	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	set	set	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	generating	generating	NOUN	NN	Number=Sing	22	compound	_	_
22	cofibrations	cofibration	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show that to construct such a model structure it is enough to check some relatively simple conditions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	PRON	DT	Number=Sing|PronType=Dem	5	mark	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	construct	construct	VERB	VB	VerbForm=Inf	2	ccomp	_	_
6	such	such	DET	PDT	_	9	predet	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	model	model	NOUN	NN	Number=Sing	9	compound	_	_
9	structure	structure	NOUN	NN	Number=Sing	5	dobj	_	_
10	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	11	nsubj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	relcl	_	_
12	enough	enough	ADJ	JJ	Degree=Pos	11	acomp	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	check	check	VERB	VB	VerbForm=Inf	12	xcomp	_	_
15	some	some	DET	DT	_	18	det	_	_
16	relatively	relatively	ADV	RB	_	17	advmod	_	_
17	simple	simple	ADJ	JJ	Degree=Pos	18	amod	_	_
18	conditions	condition	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 690
# sent_id = 1
# text = We extend to the category of crossed modules of Leibniz algebras the notion of biderivation via the action of a Leibniz algebra.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	extend	extend	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	crossed	crossed	ADJ	JJ	Degree=Pos	8	amod	_	_
8	modules	module	NOUN	NNS	Number=Plur	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Leibniz	Leibniz	PROPN	NNP	Number=Sing	9	pobj	_	_
11	algebras	algebra	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	advcl	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	notion	notion	NOUN	NN	Number=Sing	11	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	biderivation	biderivation	NOUN	NN	Number=Sing	14	pobj	_	_
16	via	via	ADP	IN	_	11	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	action	action	NOUN	NN	Number=Sing	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	Leibniz	Leibniz	PROPN	NNP	Number=Sing	22	compound	_	_
22	algebra	algebra	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This results into a pair of Leibniz algebras which allow us to construct an object which is the actor under certain circumstances.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	results	result	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	into	into	ADP	IN	_	2	prep	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	pair	pair	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Leibniz	Leibniz	PROPN	NNP	Number=Sing	8	compound	_	_
8	algebras	algebra	NOUN	NNS	Number=Plur	6	pobj	_	_
9	which	which	PRON	WDT	_	10	nsubj	_	_
10	allow	allow	VERB	VBP	Tense=Pres|VerbForm=Fin	5	relcl	_	_
11	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
12	to	to	PART	TO	_	13	aux	_	_
13	construct	construct	VERB	VB	VerbForm=Inf	10	ccomp	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	object	object	NOUN	NN	Number=Sing	13	dobj	_	_
16	which	which	PRON	WDT	_	17	nsubj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	relcl	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	actor	actor	NOUN	NN	Number=Sing	17	attr	_	_
20	under	under	ADP	IN	_	19	prep	_	_
21	certain	certain	ADJ	JJ	Degree=Pos	22	amod	_	_
22	circumstances	circumstance	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Additionally, we give a description of an action in the category of crossed modules of Leibniz algebras in terms of equations.
1	Additionally	additionally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	description	description	NOUN	NN	Number=Sing	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	action	action	NOUN	NN	Number=Sing	7	pobj	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	crossed	crossed	ADJ	JJ	Degree=Pos	15	amod	_	_
15	modules	module	NOUN	NNS	Number=Plur	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	Leibniz	Leibniz	PROPN	NNP	Number=Sing	18	compound	_	_
18	algebras	algebra	NOUN	NNS	Number=Plur	16	pobj	_	_
19	in	in	ADP	IN	_	4	prep	_	_
20	terms	term	NOUN	NNS	Number=Plur	19	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	equations	equation	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = Finally, we check that, under the aforementioned conditions, the kernel of the canonical map from a crossed module to its actor coincides with the center and we introduce the notions of crossed module of inner and outer biderivations.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	check	check	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	31	mark	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
7	under	under	ADP	IN	_	31	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	aforementioned	aforementioned	ADJ	JJ	Degree=Pos	10	amod	_	_
10	conditions	condition	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	kernel	kernel	NOUN	NN	Number=Sing	31	nsubj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	canonical	canonical	ADJ	JJ	Degree=Pos	17	amod	_	_
17	map	map	NOUN	NN	Number=Sing	14	pobj	_	_
18	from	from	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	crossed	crossed	ADJ	JJ	Degree=Pos	21	amod	_	_
21	module	module	NOUN	NN	Number=Sing	18	pobj	_	_
22	to	to	ADP	IN	_	21	prep	_	_
23	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	25	poss	_	_
24	actor	actor	NOUN	NN	Number=Sing	25	compound	_	_
25	coincides	coincide	NOUN	NNS	Number=Plur	22	pobj	_	_
26	with	with	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	center	center	NOUN	NN	Number=Sing	26	pobj	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
30	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	31	nsubj	_	_
31	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	4	ccomp	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
33	notions	notion	NOUN	NNS	Number=Plur	31	dobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	36	amod	_	_
36	module	module	NOUN	NN	Number=Sing	34	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	inner	inner	ADJ	JJ	Degree=Pos	41	amod	_	_
39	and	and	CCONJ	CC	ConjType=Cmp	38	cc	_	_
40	outer	outer	ADJ	JJ	Degree=Pos	38	conj	_	_
41	biderivations	biderivation	NOUN	NNS	Number=Plur	37	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 691
# sent_id = 1
# text = For a topos $ T $ , there is a bicategory $ MonicSp(Csp(T)) $ whose objects are those of $ T $ , morphisms are cospans in $ T $ , and 2 - morphisms are isomorphism classes of monic spans of cospans in $ T $ .
1	For	for	ADP	IN	_	7	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	topos	topos	NOUN	NN	Number=Sing	1	pobj	_	_
4	$ T $	$ t $	SYM	$	_	3	appos	_	_
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	there	there	PRON	EX	_	7	expl	_	_
7	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	ccomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	bicategory	bicategory	NOUN	NN	Number=Sing	7	attr	_	_
10	$ MonicSp(Csp(T)) $	$ monicsp(csp(t)) $	SYM	$	_	13	attr	_	_
11	whose	whose	DET	WP$	Poss=Yes	12	poss	_	_
12	objects	object	NOUN	NNS	Number=Plur	13	nsubj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	19	advcl	_	_
14	those	those	PRON	DT	Number=Plur|PronType=Dem	13	attr	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	$ T $	$ t $	SYM	$	_	15	pobj	_	_
17	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
18	morphisms	morphism	NOUN	NNS	Number=Plur	19	nsubj	_	_
19	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	cospans	cospan	NOUN	NNS	Number=Plur	19	attr	_	_
21	in	in	ADP	IN	_	20	prep	_	_
22	$ T $	$ t $	SYM	$	_	21	pobj	_	_
23	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
25	2	2	NUM	CD	NumType=Card	27	nummod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	morphisms	morphism	NOUN	NNS	Number=Plur	28	nsubj	_	_
28	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	19	conj	_	_
29	isomorphism	isomorphism	NOUN	NN	Number=Sing	30	compound	_	_
30	classes	class	NOUN	NNS	Number=Plur	28	attr	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	monic	monic	ADJ	JJ	Degree=Pos	33	amod	_	_
33	spans	span	NOUN	NNS	Number=Plur	31	pobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	cospans	cospan	NOUN	NNS	Number=Plur	34	pobj	_	_
36	in	in	ADP	IN	_	30	prep	_	_
37	$ T $	$ t $	SYM	$	_	36	pobj	_	_
38	.	.	PUNCT	.	PunctType=Peri	28	punct	_	SpaceAfter=No

# sent_id = 2
# text = Using a result of Shulman, we prove that $ MonicSp(Csp(T)) $ is symmetric monoidal, and moreover, that it is compact closed in the sense of Stay.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	advcl	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	result	result	NOUN	NN	Number=Sing	1	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	Shulman	Shulman	PROPN	NNP	Number=Sing	4	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
7	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	8	nsubj	_	_
8	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	that	that	SCONJ	IN	_	11	mark	_	_
10	$ MonicSp(Csp(T)) $	$ monicsp(csp(t)) $	SYM	$	_	11	nsubj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	ccomp	_	_
12	symmetric	symmetric	ADJ	JJ	Degree=Pos	13	amod	_	_
13	monoidal	monoidal	NOUN	NN	Number=Sing	11	attr	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
16	moreover	moreover	ADV	RB	_	11	advmod	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	that	that	SCONJ	IN	_	20	mark	_	_
19	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	20	nsubj	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	ccomp	_	_
21	compact	compact	ADJ	JJ	Degree=Pos	20	acomp	_	_
22	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	acomp	_	_
23	in	in	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	sense	sense	NOUN	NN	Number=Sing	23	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	Stay	Stay	PROPN	NNP	Number=Sing	26	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 3
# text = We provide an application which illustrates how to encode double pushout rewrite rules as 2 - morphisms inside a compact closed sub - bicategory of $ MonicSp(Csp(Graph)) $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	an	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	application	application	NOUN	NN	Number=Sing	2	dobj	_	_
5	which	which	PRON	WDT	_	6	nsubj	_	_
6	illustrates	illustrate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	relcl	_	_
7	how	how	SCONJ	WRB	_	9	advmod	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	encode	encode	VERB	VB	VerbForm=Inf	6	xcomp	_	_
10	double	double	ADJ	JJ	Degree=Pos	13	amod	_	_
11	pushout	pushout	NOUN	NN	Number=Sing	13	compound	_	_
12	rewrite	rewrite	NOUN	NN	Number=Sing	13	compound	_	_
13	rules	rule	NOUN	NNS	Number=Plur	9	dobj	_	_
14	as	as	ADP	IN	_	9	prep	_	_
15	2	2	NUM	CD	NumType=Card	17	nummod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	morphisms	morphism	NOUN	NNS	Number=Plur	14	pobj	_	_
18	inside	inside	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
20	compact	compact	ADJ	JJ	Degree=Pos	24	amod	_	_
21	closed	closed	ADJ	JJ	Degree=Pos	24	amod	_	_
22	sub	sub	NOUN	NN	Number=Sing	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	bicategory	bicategory	NOUN	NN	Number=Sing	18	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	$ MonicSp(Csp(Graph)) $	$ monicsp(csp(graph)) $	SYM	$	_	2	dobj	_	_
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 692
# sent_id = 1
# text = Given a set $ Sigma $ of morphisms in a category $ C $ , we construct a functor $ F $ which sends elements of $ Sigma $ to split monomorphisms.
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	set	set	NOUN	NN	Number=Sing	1	pobj	_	_
4	$ Sigma $	$ sigma $	SYM	$	_	3	prep	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	morphisms	morphism	NOUN	NNS	Number=Plur	5	pobj	_	_
7	in	in	ADP	IN	_	3	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
10	$ C $	$ c $	SYM	$	_	9	nummod	_	_
11	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	functor	functor	NOUN	NN	Number=Sing	13	dobj	_	_
16	$ F $	$ f $	SYM	$	_	15	punct	_	_
17	which	which	PRON	WDT	_	18	nsubj	_	_
18	sends	send	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	15	relcl	_	_
19	elements	element	NOUN	NNS	Number=Plur	18	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	$ Sigma $	$ sigma $	SYM	$	_	20	pobj	_	_
22	to	to	PART	TO	_	23	aux	_	_
23	split	split	VERB	VB	VerbForm=Inf	18	advcl	_	_
24	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	23	dobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 2
# text = Moreover, we prove that $ F $ is weakly universal with that property when considered in the world of locally posetal 2 - categories.
1	Moreover	moreover	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	7	mark	_	_
6	$ F $	$ f $	SYM	$	_	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
8	weakly	weakly	ADV	RB	_	9	advmod	_	_
9	universal	universal	ADJ	JJ	Degree=Pos	7	acomp	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	that	that	DET	DT	Number=Sing|PronType=Dem	12	det	_	_
12	property	property	NOUN	NN	Number=Sing	10	pobj	_	_
13	when	when	SCONJ	WRB	_	14	advmod	_	_
14	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	advcl	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	world	world	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	locally	locally	ADV	RB	_	20	advmod	_	_
20	posetal	posetal	ADJ	JJ	Degree=Pos	23	amod	_	_
21	2	2	NUM	CD	NumType=Card	23	nummod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	categories	category	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = Besides, we also use locally posetal 2 - categories in order to construct weak left adjoints to those functors for which any object in the codomain admits a weak reflection.
1	Besides	besides	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
4	also	also	ADV	RB	_	5	advmod	_	_
5	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	locally	locally	ADV	RB	_	7	advmod	_	_
7	posetal	posetal	ADJ	JJ	Degree=Pos	10	amod	_	_
8	2	2	NUM	CD	NumType=Card	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	categories	category	NOUN	NNS	Number=Plur	5	dobj	_	_
11	in	in	ADP	IN	_	5	prep	_	_
12	order	order	NOUN	NN	Number=Sing	11	pobj	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	construct	construct	VERB	VB	VerbForm=Inf	12	acl	_	_
15	weak	weak	ADJ	JJ	Degree=Pos	17	amod	_	_
16	left	left	ADJ	JJ	Degree=Pos	17	amod	_	_
17	adjoints	adjoint	NOUN	NNS	Number=Plur	14	dobj	_	_
18	to	to	ADP	IN	_	14	prep	_	_
19	those	those	DET	DT	Number=Plur|PronType=Dem	20	det	_	_
20	functors	functor	NOUN	NNS	Number=Plur	18	pobj	_	_
21	for	for	ADP	IN	_	28	prep	_	_
22	which	which	PRON	WDT	_	21	pobj	_	_
23	any	any	DET	DT	_	24	det	_	_
24	object	object	NOUN	NN	Number=Sing	28	nsubj	_	_
25	in	in	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	codomain	codomain	NOUN	NN	Number=Sing	25	pobj	_	_
28	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	relcl	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	weak	weak	ADJ	JJ	Degree=Pos	31	amod	_	_
31	reflection	reflection	NOUN	NN	Number=Sing	28	dobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = We then apply these two results in order to restate the Injective Subcategory Problem for $ Sigma $ into the existence of some kind of weak right adjoint for $ F $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	apply	apply	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	these	these	DET	DT	Number=Plur|PronType=Dem	6	det	_	_
5	two	two	NUM	CD	NumType=Card	6	nummod	_	_
6	results	result	NOUN	NNS	Number=Plur	3	dobj	_	_
7	in	in	ADP	IN	_	3	prep	_	_
8	order	order	NOUN	NN	Number=Sing	7	pobj	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	restate	restate	VERB	VB	VerbForm=Inf	8	acl	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
12	Injective	Injective	PROPN	NNP	Number=Sing	14	compound	_	_
13	Subcategory	Subcategory	PROPN	NNP	Number=Sing	14	compound	_	_
14	Problem	Problem	PROPN	NNP	Number=Sing	10	dobj	_	_
15	for	for	ADP	IN	_	10	prep	_	_
16	$ Sigma $	$ sigma $	SYM	$	_	15	pobj	_	_
17	into	into	ADP	IN	_	10	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	existence	existence	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	some	some	DET	DT	_	22	det	_	_
22	kind	kind	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	weak	weak	ADJ	JJ	Degree=Pos	26	amod	_	_
25	right	right	ADJ	JJ	Degree=Pos	26	amod	_	_
26	adjoint	adjoint	NOUN	NN	Number=Sing	23	pobj	_	_
27	for	for	ADP	IN	_	26	prep	_	_
28	$ F $	$ f $	SYM	$	_	27	pobj	_	_
29	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 693
# sent_id = 1
# text = From the interpretation of Linear Logic multiplicative disjunction as the epsilon product defined by Laurent Schwartz, we construct several models of Differential Linear Logic based on the usual mathematical notions of smooth maps.
1	From	from	ADP	IN	_	19	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	interpretation	interpretation	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	Linear	Linear	PROPN	NNP	Number=Sing	6	compound	_	_
6	Logic	Logic	PROPN	NNP	Number=Sing	8	nmod	_	_
7	multiplicative	multiplicative	ADJ	JJ	Degree=Pos	8	amod	_	_
8	disjunction	disjunction	NOUN	NN	Number=Sing	4	pobj	_	_
9	as	as	ADP	IN	_	3	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	epsilon	epsilon	NOUN	NN	Number=Sing	12	compound	_	_
12	product	product	NOUN	NN	Number=Sing	9	pobj	_	_
13	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
14	by	by	ADP	IN	_	13	agent	_	_
15	Laurent	Laurent	PROPN	NNP	Number=Sing	16	compound	_	_
16	Schwartz	Schwartz	PROPN	NNP	Number=Sing	14	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	several	several	ADJ	JJ	Degree=Pos	21	amod	_	_
21	models	model	NOUN	NNS	Number=Plur	19	dobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	Differential	Differential	PROPN	NNP	Number=Sing	24	compound	_	_
24	Linear	Linear	PROPN	NNP	Number=Sing	25	compound	_	_
25	Logic	Logic	PROPN	NNP	Number=Sing	22	pobj	_	_
26	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	prep	_	_
27	on	on	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
29	usual	usual	ADJ	JJ	Degree=Pos	31	amod	_	_
30	mathematical	mathematical	ADJ	JJ	Degree=Pos	31	amod	_	_
31	notions	notion	NOUN	NNS	Number=Plur	27	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	smooth	smooth	ADJ	JJ	Degree=Pos	34	amod	_	_
34	maps	map	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 2
# text = This improves on previous results by Blute, Ehrhard and Tasson based on convenient smoothness where only intuitionist models were built.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	improves	improve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	on	on	ADP	IN	_	2	prep	_	_
4	previous	previous	ADJ	JJ	Degree=Pos	5	amod	_	_
5	results	result	NOUN	NNS	Number=Plur	3	pobj	_	_
6	by	by	ADP	IN	_	5	prep	_	_
7	Blute	Blute	PROPN	NNP	Number=Sing	6	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	Ehrhard	Ehrhard	PROPN	NNP	Number=Sing	7	conj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	Tasson	Tasson	PROPN	NNP	Number=Sing	9	conj	_	_
12	based	base	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	prep	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	convenient	convenient	ADJ	JJ	Degree=Pos	15	amod	_	_
15	smoothness	smoothness	NOUN	NN	Number=Sing	13	pobj	_	_
16	where	where	SCONJ	WRB	_	21	advmod	_	_
17	only	only	ADV	RB	_	19	advmod	_	_
18	intuitionist	intuitionist	ADJ	JJ	Degree=Pos	19	amod	_	_
19	models	model	NOUN	NNS	Number=Plur	21	nsubjpass	_	_
20	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	21	auxpass	_	_
21	built	build	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	relcl	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We isolate a completeness condition, called $ k $ - quasi - completeness, and an associated notion which is stable under duality called $ k $ - reflexivity, allowing for a star - autonomous category of $ k $ - reflexive spaces in which the dual of the tensor product is the reflexive version of the epsilon - product.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	isolate	isolate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	completeness	completeness	NOUN	NN	Number=Sing	5	compound	_	_
5	condition	condition	NOUN	NN	Number=Sing	2	dobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
7	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	2	conj	_	_
8	$ k $	$ k $	SYM	$	_	10	quantmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	quasi	quasi	NOUN	NN	Number=Sing	7	oprd	_	_
11	-	-	NOUN	NN	Number=Sing	10	punct	_	_
12	completeness	completeness	NOUN	NN	Number=Sing	10	conj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
15	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	associated	associated	ADJ	JJ	Degree=Pos	17	amod	_	_
17	notion	notion	NOUN	NN	Number=Sing	2	conj	_	_
18	which	which	PRON	WDT	_	19	nsubj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
20	stable	stable	ADJ	JJ	Degree=Pos	19	acomp	_	_
21	under	under	ADP	IN	_	20	prep	_	_
22	duality	duality	NOUN	NN	Number=Sing	21	pobj	_	_
23	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
24	$ k $	$ k $	SYM	$	_	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	reflexivity	reflexivity	NOUN	NN	Number=Sing	23	oprd	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
28	allowing	allow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	23	advcl	_	_
29	for	for	ADP	IN	_	28	prep	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
31	star	star	NOUN	NN	Number=Sing	33	npadvmod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	autonomous	autonomous	ADJ	JJ	Degree=Pos	34	amod	_	_
34	category	category	NOUN	NN	Number=Sing	29	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	$ k $	$ k $	SYM	$	_	38	advmod	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	38	punct	_	_
38	reflexive	reflexive	ADJ	JJ	Degree=Pos	39	amod	_	_
39	spaces	space	NOUN	NNS	Number=Plur	35	pobj	_	_
40	in	in	ADP	IN	_	48	prep	_	_
41	which	which	PRON	WDT	_	40	pobj	_	_
42	the	the	DET	DT	Definite=Def|PronType=Art	43	det	_	_
43	dual	dual	ADJ	JJ	Degree=Pos	48	nsubj	_	_
44	of	of	ADP	IN	_	43	prep	_	_
45	the	the	DET	DT	Definite=Def|PronType=Art	47	det	_	_
46	tensor	tensor	NOUN	NN	Number=Sing	47	compound	_	_
47	product	product	NOUN	NN	Number=Sing	44	pobj	_	_
48	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	39	relcl	_	_
49	the	the	DET	DT	Definite=Def|PronType=Art	51	det	_	_
50	reflexive	reflexive	ADJ	JJ	Degree=Pos	51	amod	_	_
51	version	version	NOUN	NN	Number=Sing	48	attr	_	_
52	of	of	ADP	IN	_	51	prep	_	_
53	the	the	DET	DT	Definite=Def|PronType=Art	56	det	_	_
54	epsilon	epsilon	NOUN	NN	Number=Sing	56	compound	_	_
55	-	-	PUNCT	HYPH	PunctType=Dash	56	punct	_	_
56	product	product	NOUN	NN	Number=Sing	52	pobj	_	SpaceAfter=No
57	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We adapt Meise's definition of smooth maps into a first model of Differential Linear Logic, made of $ k $ - reflexive spaces.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	adapt	adapt	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	Meise	Meise	PROPN	NNP	Number=Sing	5	poss	_	SpaceAfter=No
4	's	's	PART	POS	_	3	case	_	_
5	definition	definition	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	smooth	smooth	ADJ	JJ	Degree=Pos	8	amod	_	_
8	maps	map	NOUN	NNS	Number=Plur	6	pobj	_	_
9	into	into	ADP	IN	_	2	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	first	first	ADJ	JJ	Degree=Pos	12	amod	_	_
12	model	model	NOUN	NN	Number=Sing	9	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	Differential	Differential	PROPN	NNP	Number=Sing	16	compound	_	_
15	Linear	Linear	PROPN	NNP	Number=Sing	16	compound	_	_
16	Logic	Logic	PROPN	NNP	Number=Sing	13	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
18	made	make	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	$ k $	$ k $	SYM	$	_	22	advmod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	reflexive	reflexive	ADJ	JJ	Degree=Pos	23	amod	_	_
23	spaces	space	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = We also build two new models of Linear Logic with conveniently smooth maps, on categories made respectively of Mackey - complete Schwartz spaces and Mackey - complete Nuclear Spaces (with extra reflexivity conditions).
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	build	build	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	two	two	NUM	CD	NumType=Card	6	nummod	_	_
5	new	new	ADJ	JJ	Degree=Pos	6	amod	_	_
6	models	model	NOUN	NNS	Number=Plur	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	Linear	Linear	PROPN	NNP	Number=Sing	9	compound	_	_
9	Logic	Logic	PROPN	NNP	Number=Sing	7	pobj	_	_
10	with	with	ADP	IN	_	3	prep	_	_
11	conveniently	conveniently	ADV	RB	_	12	advmod	_	_
12	smooth	smooth	ADJ	JJ	Degree=Pos	13	amod	_	_
13	maps	map	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
15	on	on	ADP	IN	_	3	prep	_	_
16	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	_
17	made	make	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	acl	_	_
18	respectively	respectively	ADV	RB	_	17	advmod	_	_
19	of	of	ADP	IN	_	17	prep	_	_
20	Mackey	Mackey	PROPN	NNP	Number=Sing	22	npadvmod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	complete	complete	ADJ	JJ	Degree=Pos	24	amod	_	_
23	Schwartz	Schwartz	PROPN	NNP	Number=Sing	24	compound	_	_
24	spaces	space	NOUN	NNS	Number=Plur	19	pobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	Mackey	Mackey	PROPN	NNP	Number=Sing	28	npadvmod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	complete	complete	ADJ	JJ	Degree=Pos	30	amod	_	_
29	Nuclear	Nuclear	PROPN	NNP	Number=Sing	30	compound	_	_
30	Spaces	Spaces	PROPN	NNPS	Number=Plur	24	conj	_	_
31	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	30	punct	_	SpaceAfter=No
32	with	with	ADP	IN	_	30	prep	_	_
33	extra	extra	ADJ	JJ	Degree=Pos	35	amod	_	_
34	reflexivity	reflexivity	NOUN	NN	Number=Sing	35	compound	_	_
35	conditions	condition	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
36	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	3	punct	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = Varying slightly the notion of smoothness, one also recovers models of DiLL on the same star - autonomous categories.
1	Varying	vary	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	advcl	_	_
2	slightly	slightly	ADV	RB	_	1	advmod	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	1	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	smoothness	smoothness	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
8	one	one	PRON	PRP	PronType=Prs	10	nsubj	_	_
9	also	also	ADV	RB	_	10	advmod	_	_
10	recovers	recover	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	models	model	NOUN	NNS	Number=Plur	10	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	DiLL	DiLL	PROPN	NNP	Number=Sing	12	pobj	_	_
14	on	on	ADP	IN	_	10	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
16	same	same	ADJ	JJ	Degree=Pos	20	amod	_	_
17	star	star	NOUN	NN	Number=Sing	19	npadvmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	autonomous	autonomous	ADJ	JJ	Degree=Pos	20	amod	_	_
20	categories	category	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 7
# text = Throughout the article, we work within the setting of Dialogue categories where the tensor product is exactly the epsilon - product (without reflexivization).
1	Throughout	throughout	ADP	IN	_	6	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	article	article	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	work	work	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	within	within	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	setting	setting	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	Dialogue	Dialogue	PROPN	NNP	Number=Sing	12	compound	_	_
12	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
13	where	where	SCONJ	WRB	_	17	advmod	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	tensor	tensor	NOUN	NN	Number=Sing	16	compound	_	_
16	product	product	NOUN	NN	Number=Sing	17	nsubj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	advcl	_	_
18	exactly	exactly	ADV	RB	_	17	advmod	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
20	epsilon	epsilon	NOUN	NN	Number=Sing	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	product	product	NOUN	NN	Number=Sing	17	attr	_	_
23	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	22	punct	_	SpaceAfter=No
24	without	without	ADP	IN	_	22	prep	_	_
25	reflexivization	reflexivization	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
26	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	22	punct	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 694
# sent_id = 1
# text = In a recent paper, Hofmann, Neves and Nora proved that the dual of the category of compact ordered spaces and monotone continuous maps is a quasi - variety—not finitary, but bounded by $ aleph_1 $ .
1	In	in	ADP	IN	_	11	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	recent	recent	ADJ	JJ	Degree=Pos	4	amod	_	_
4	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
6	Hofmann	Hofmann	PROPN	NNP	Number=Sing	4	appos	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	Neves	Neves	PROPN	NNPS	Number=Plur	6	conj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	Nora	Nora	PROPN	NNP	Number=Sing	8	conj	_	_
11	proved	prove	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
12	that	that	SCONJ	IN	_	26	mark	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	dual	dual	ADJ	JJ	Degree=Pos	26	nsubj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	compact	compact	ADJ	JJ	Degree=Pos	20	amod	_	_
20	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	amod	_	_
21	spaces	space	NOUN	NNS	Number=Plur	18	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
23	monotone	monotone	ADJ	JJ	Degree=Pos	25	amod	_	_
24	continuous	continuous	ADJ	JJ	Degree=Pos	25	amod	_	_
25	maps	map	NOUN	NNS	Number=Plur	14	conj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	ccomp	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
28	quasi	quasi	ADJ	JJ	Degree=Pos	30	compound	_	_
29	-	-	NOUN	NN	Number=Sing	30	punct	_	_
30	variety	variety	NOUN	NN	Number=Sing	26	attr	_	SpaceAfter=No
31	—	—	PUNCT	:	_	30	punct	_	SpaceAfter=No
32	not	not	PART	RB	Polarity=Neg	33	neg	_	_
33	finitary	finitary	ADJ	JJ	Degree=Pos	30	appos	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
35	but	but	CCONJ	CC	ConjType=Cmp	26	cc	_	_
36	bounded	bound	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	conj	_	_
37	by	by	ADP	IN	_	36	prep	_	_
38	$ aleph_1 $	$ aleph_1 $	SYM	$	_	37	pobj	_	_
39	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 2
# text = An open question was: is it also a variety?
1	An	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	open	open	ADJ	JJ	Degree=Pos	3	amod	_	_
3	question	question	NOUN	NN	Number=Sing	4	nsubj	_	_
4	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	6	ccomp	_	SpaceAfter=No
5	:	:	PUNCT	:	_	4	punct	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	6	nsubj	_	_
8	also	also	ADV	RB	_	6	advmod	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	variety	variety	NOUN	NN	Number=Sing	6	attr	_	SpaceAfter=No
11	?	?	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that the answer is affirmative.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	6	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	answer	answer	NOUN	NN	Number=Sing	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
7	affirmative	affirmative	ADJ	JJ	Degree=Pos	6	acomp	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We describe the variety by means of a set of finitary operations, together with an operation of countably infinite arity, and equational axioms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	variety	variety	NOUN	NN	Number=Sing	2	dobj	_	_
5	by	by	ADP	IN	_	2	prep	_	_
6	means	mean	NOUN	NNS	Number=Plur	5	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	set	set	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	finitary	finitary	ADJ	JJ	Degree=Pos	12	amod	_	_
12	operations	operation	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
14	together	together	ADV	RB	_	15	advmod	_	_
15	with	with	ADP	IN	_	2	prep	_	_
16	an	an	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	operation	operation	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	countably	countably	ADV	RB	_	20	advmod	_	_
20	infinite	infinite	ADJ	JJ	Degree=Pos	21	amod	_	_
21	arity	arity	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
24	equational	equational	ADJ	JJ	Degree=Pos	25	amod	_	_
25	axioms	axiom	NOUN	NNS	Number=Plur	21	conj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = The dual equivalence is induced by the dualizing object $ [0, 1] $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	dual	dual	ADJ	JJ	Degree=Pos	3	amod	_	_
3	equivalence	equivalence	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	by	by	ADP	IN	_	5	agent	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	dualizing	dualize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	amod	_	_
9	object	object	NOUN	NN	Number=Sing	6	pobj	_	_
10	$ [0, 1] $	$ [0, 1] $	SYM	$	_	9	appos	_	_
11	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 695
# sent_id = 1
# text = In this paper, we investigate the property P that binary products commute with arbitrary coequalizers in pointed categories.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	property	property	NOUN	NN	Number=Sing	9	compound	_	_
9	P	p	NOUN	NN	Number=Sing	6	dobj	_	_
10	that	that	SCONJ	IN	_	13	dobj	_	_
11	binary	binary	ADJ	JJ	Degree=Pos	12	amod	_	_
12	products	product	NOUN	NNS	Number=Plur	13	compound	_	_
13	commute	commute	NOUN	NN	Number=Sing	6	ccomp	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	16	amod	_	_
16	coequalizers	coequalizer	NOUN	NNS	Number=Plur	14	pobj	_	_
17	in	in	ADP	IN	_	13	prep	_	_
18	pointed	pointed	ADJ	JJ	Degree=Pos	19	amod	_	_
19	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = Examples of such categories include any regular unital or (pointed) majority category with coequalizers, as well as any pointed factor permutable category with coequalizers.
1	Examples	example	NOUN	NNS	Number=Plur	5	nsubj	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	such	such	ADJ	JJ	Degree=Pos	4	amod	_	_
4	categories	category	NOUN	NNS	Number=Plur	2	pobj	_	_
5	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	any	any	DET	DT	_	8	det	_	_
7	regular	regular	ADJ	JJ	Degree=Pos	8	amod	_	_
8	unital	unital	NOUN	NN	Number=Sing	5	dobj	_	_
9	or	or	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	11	punct	_	SpaceAfter=No
11	pointed	point	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	SpaceAfter=No
12	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	11	punct	_	_
13	majority	majority	NOUN	NN	Number=Sing	14	compound	_	_
14	category	category	NOUN	NN	Number=Sing	8	conj	_	_
15	with	with	ADP	IN	_	14	prep	_	_
16	coequalizers	coequalizer	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
18	as	as	ADV	RB	_	20	advmod	_	_
19	well	well	ADV	RB	Degree=Pos	20	advmod	_	_
20	as	as	ADP	IN	_	14	cc	_	_
21	any	any	DET	DT	_	23	det	_	_
22	pointed	pointed	ADJ	JJ	Degree=Pos	23	amod	_	_
23	factor	factor	NOUN	NN	Number=Sing	25	nmod	_	_
24	permutable	permutable	ADJ	JJ	Degree=Pos	25	amod	_	_
25	category	category	NOUN	NN	Number=Sing	14	conj	_	_
26	with	with	ADP	IN	_	14	prep	_	_
27	coequalizers	coequalizer	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = We establish a Maltsev term condition characterizing pointed varieties of universal algebras satisfying P.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	establish	establish	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
4	Maltsev	Maltsev	PROPN	NNP	Number=Sing	6	compound	_	_
5	term	term	NOUN	NN	Number=Sing	6	compound	_	_
6	condition	condition	NOUN	NN	Number=Sing	2	dobj	_	_
7	characterizing	characterize	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	acl	_	_
8	pointed	point	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	amod	_	_
9	varieties	variety	NOUN	NNS	Number=Plur	7	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	universal	universal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	algebras	algebra	NOUN	NNS	Number=Plur	10	pobj	_	_
13	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	acl	_	_
14	P.	P.	PROPN	NNP	Number=Sing	13	dobj	_	SpaceAfter=No

# sent_id = 4
# text = We then consider categories satisfying P locally, that is, those categories for which every fibre of the fibration of points satisfies P. Examples include any regular Maltsev or majority category with coequalizers, as well as any regular Gumm category with coequalizers.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	categories	category	NOUN	NNS	Number=Plur	5	nsubj	_	_
5	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	ccomp	_	_
6	P	p	NOUN	NN	Number=Sing	5	dobj	_	_
7	locally	locally	ADV	RB	_	5	advmod	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
9	that	that	ADV	RB	_	10	advmod	_	_
10	is	is	ADV	RB	_	13	advmod	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
12	those	those	DET	DT	Number=Plur|PronType=Dem	13	det	_	_
13	categories	category	NOUN	NNS	Number=Plur	5	dobj	_	_
14	for	for	ADP	IN	_	26	prep	_	_
15	which	which	PRON	WDT	_	14	pobj	_	_
16	every	every	DET	DT	_	17	det	_	_
17	fibre	fibre	NOUN	NN	Number=Sing	26	nsubj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	fibration	fibration	NOUN	NN	Number=Sing	18	pobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	points	point	NOUN	NNS	Number=Plur	23	compound	_	_
23	satisfies	satisfie	NOUN	NNS	Number=Plur	21	pobj	_	_
24	P.	P.	PROPN	NNP	Number=Sing	25	compound	_	_
25	Examples	Examples	PROPN	NNP	Number=Sing	17	appos	_	_
26	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	13	relcl	_	_
27	any	any	DET	DT	_	32	det	_	_
28	regular	regular	ADJ	JJ	Degree=Pos	32	amod	_	_
29	Maltsev	Maltsev	PROPN	NNP	Number=Sing	32	nmod	_	_
30	or	or	CCONJ	CC	ConjType=Cmp	29	cc	_	_
31	majority	majority	NOUN	NN	Number=Sing	29	conj	_	_
32	category	category	NOUN	NN	Number=Sing	26	dobj	_	_
33	with	with	ADP	IN	_	32	prep	_	_
34	coequalizers	coequalizer	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
35	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
36	as	as	ADV	RB	_	38	advmod	_	_
37	well	well	ADV	RB	Degree=Pos	38	advmod	_	_
38	as	as	ADP	IN	_	32	cc	_	_
39	any	any	DET	DT	_	42	det	_	_
40	regular	regular	ADJ	JJ	Degree=Pos	42	amod	_	_
41	Gumm	Gumm	PROPN	NNP	Number=Sing	42	compound	_	_
42	category	category	NOUN	NN	Number=Sing	32	conj	_	_
43	with	with	ADP	IN	_	42	prep	_	_
44	coequalizers	coequalizer	NOUN	NNS	Number=Plur	43	pobj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = Varieties satisfying P locally are also characterized by a Maltsev term condition, which turns out to be equivalent to a variant of Gumm's shifting lemma.
1	Varieties	variety	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
2	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	1	acl	_	_
3	P	p	NOUN	NN	Number=Sing	2	dobj	_	_
4	locally	locally	ADV	RB	_	7	advmod	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
6	also	also	ADV	RB	_	7	advmod	_	_
7	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	by	by	ADP	IN	_	7	agent	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
10	Maltsev	Maltsev	PROPN	NNP	Number=Sing	12	compound	_	_
11	term	term	NOUN	NN	Number=Sing	12	compound	_	_
12	condition	condition	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	which	which	PRON	WDT	_	15	nsubj	_	_
15	turns	turn	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	relcl	_	_
16	out	out	ADP	RP	_	15	prt	_	_
17	to	to	PART	TO	_	18	aux	_	_
18	be	be	AUX	VB	VerbForm=Inf	15	xcomp	_	_
19	equivalent	equivalent	ADJ	JJ	Degree=Pos	18	acomp	_	_
20	to	to	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	variant	variant	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	Gumm	Gumm	PROPN	NNP	Number=Sing	27	poss	_	SpaceAfter=No
25	's	's	PART	POS	_	24	case	_	_
26	shifting	shift	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	27	amod	_	_
27	lemma	lemma	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 6
# text = Furthermore, we show that the varieties satisfying P locally are precisely the varieties with normal local projections in the sense of Janelidze.
1	Furthermore	furthermore	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	11	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	varieties	variety	NOUN	NNS	Number=Plur	11	nsubj	_	_
8	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	acl	_	_
9	P	p	NOUN	NN	Number=Sing	8	dobj	_	_
10	locally	locally	ADV	RB	_	11	advmod	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
12	precisely	precisely	ADV	RB	_	14	advmod	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	varieties	variety	NOUN	NNS	Number=Plur	11	attr	_	_
15	with	with	ADP	IN	_	14	prep	_	_
16	normal	normal	ADJ	JJ	Degree=Pos	18	amod	_	_
17	local	local	ADJ	JJ	Degree=Pos	18	amod	_	_
18	projections	projection	NOUN	NNS	Number=Plur	15	pobj	_	_
19	in	in	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	sense	sense	NOUN	NN	Number=Sing	19	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	Janelidze	Janelidze	PROPN	NNP	Number=Sing	22	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 696
# sent_id = 1
# text = Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones.
1	Universal	universal	ADJ	JJ	Degree=Pos	2	amod	_	_
2	algebra	algebra	NOUN	NN	Number=Sing	4	nsubj	_	_
3	uniformly	uniformly	ADV	RB	_	4	advmod	_	_
4	captures	capture	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	various	various	ADJ	JJ	Degree=Pos	7	amod	_	_
6	algebraic	algebraic	ADJ	JJ	Degree=Pos	7	amod	_	_
7	structures	structure	NOUN	NNS	Number=Plur	4	dobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
9	by	by	ADP	IN	_	4	prep	_	_
10	expressing	express	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	pcomp	_	_
11	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	10	dobj	_	_
12	as	as	ADP	IN	_	10	prep	_	_
13	equational	equational	ADJ	JJ	Degree=Pos	14	amod	_	_
14	theories	theory	NOUN	NNS	Number=Plur	12	pobj	_	_
15	or	or	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	abstract	abstract	ADJ	JJ	Degree=Pos	17	amod	_	_
17	clones	clone	NOUN	NNS	Number=Plur	14	conj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of universal algebra, such as theories of symmetric operads, non - symmetric operads, generalised operads, PROPs, PROs, and monads.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	ubiquity	ubiquity	NOUN	NN	Number=Sing	12	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	algebraic	algebraic	ADJ	JJ	Degree=Pos	5	amod	_	_
5	structures	structure	NOUN	NNS	Number=Plur	3	pobj	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	mathematics	mathematic	NOUN	NNS	Number=Plur	6	pobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	fields	field	NOUN	NNS	Number=Plur	7	conj	_	_
11	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	aux	_	_
12	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
13	rise	rise	NOUN	NN	Number=Sing	12	dobj	_	_
14	to	to	ADP	IN	_	12	prep	_	_
15	several	several	ADJ	JJ	Degree=Pos	16	amod	_	_
16	variants	variant	NOUN	NNS	Number=Plur	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	universal	universal	ADJ	JJ	Degree=Pos	19	amod	_	_
19	algebra	algebra	PROPN	NNP	Number=Sing	17	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	such	such	ADJ	JJ	Degree=Pos	22	amod	_	_
22	as	as	ADP	IN	_	19	prep	_	_
23	theories	theory	NOUN	NNS	Number=Plur	22	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	symmetric	symmetric	ADJ	JJ	Degree=Pos	26	amod	_	_
26	operads	operad	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
28	non	non	ADJ	JJ	Degree=Pos	31	amod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	31	amod	_	_
30	symmetric	symmetric	ADJ	JJ	Degree=Pos	31	amod	_	_
31	operads	operad	NOUN	NNS	Number=Plur	26	conj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
33	generalised	generalise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	34	amod	_	_
34	operads	operad	NOUN	NNS	Number=Plur	31	conj	_	SpaceAfter=No
35	,	,	PUNCT	,	PunctType=Comm	34	punct	_	_
36	PROPs	prop	NOUN	NNS	Number=Plur	34	conj	_	SpaceAfter=No
37	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
38	PROs	pro	NOUN	NNS	Number=Plur	36	conj	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	38	punct	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	38	cc	_	_
41	monads	monad	NOUN	NNS	Number=Plur	38	conj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 3
# text = These variants of universal algebra are called notions of algebraic theory.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	variants	variant	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	universal	universal	ADJ	JJ	Degree=Pos	5	amod	_	_
5	algebra	algebra	NOUN	NNS	Number=Plur	3	pobj	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	notions	notion	NOUN	NNS	Number=Plur	7	oprd	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	algebraic	algebraic	ADJ	JJ	Degree=Pos	11	amod	_	_
11	theory	theory	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = In this paper, we develop a unified framework for them.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	unified	unified	ADJ	JJ	Degree=Pos	9	amod	_	_
9	framework	framework	NOUN	NN	Number=Sing	6	dobj	_	_
10	for	for	ADP	IN	_	9	prep	_	_
11	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	10	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = The key observation is that each notion of algebraic theory can be identified with a monoidal category, in such a way that algebraic theories correspond to monoid objects therein.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	key	key	ADJ	JJ	Degree=Pos	3	amod	_	_
3	observation	observation	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	13	mark	_	_
6	each	each	DET	DT	_	7	det	_	_
7	notion	notion	NOUN	NN	Number=Sing	13	nsubjpass	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	algebraic	algebraic	ADJ	JJ	Degree=Pos	10	amod	_	_
10	theory	theory	NOUN	NN	Number=Sing	8	pobj	_	_
11	can	can	AUX	MD	VerbForm=Fin	13	aux	_	_
12	be	be	AUX	VB	VerbForm=Inf	13	auxpass	_	_
13	identified	identify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	ccomp	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	monoidal	monoidal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	category	category	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
19	in	in	ADP	IN	_	13	prep	_	_
20	such	such	DET	PDT	_	22	predet	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	way	way	NOUN	NN	Number=Sing	19	pobj	_	_
23	that	that	PRON	WDT	PronType=Rel	26	advmod	_	_
24	algebraic	algebraic	ADJ	JJ	Degree=Pos	25	amod	_	_
25	theories	theory	NOUN	NNS	Number=Plur	26	nsubj	_	_
26	correspond	correspond	VERB	VBP	Tense=Pres|VerbForm=Fin	22	relcl	_	_
27	to	to	ADP	IN	_	26	prep	_	_
28	monoid	monoid	NOUN	NN	Number=Sing	29	compound	_	_
29	objects	object	NOUN	NNS	Number=Plur	27	pobj	_	_
30	therein	therein	ADV	RB	_	29	advmod	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 6
# text = To incorporate semantics, we introduce a categorical structure called metamodel, which formalises a definition of models of algebraic theories.
1	To	to	PART	TO	_	2	aux	_	_
2	incorporate	incorporate	VERB	VB	VerbForm=Inf	6	advcl	_	_
3	semantics	semantic	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	categorical	categorical	ADJ	JJ	Degree=Pos	9	amod	_	_
9	structure	structure	NOUN	NN	Number=Sing	6	dobj	_	_
10	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	acl	_	_
11	metamodel	metamodel	NOUN	NN	Number=Sing	10	oprd	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	which	which	PRON	WDT	_	14	nsubj	_	_
14	formalises	formalise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	relcl	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	definition	definition	NOUN	NN	Number=Sing	14	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	models	model	NOUN	NNS	Number=Plur	17	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	algebraic	algebraic	ADJ	JJ	Degree=Pos	21	amod	_	_
21	theories	theory	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 7
# text = We also define morphisms between notions of algebraic theory, which are a monoidal version of profunctors.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	morphisms	morphism	NOUN	NNS	Number=Plur	3	dobj	_	_
5	between	between	ADP	IN	_	4	prep	_	_
6	notions	notion	NOUN	NNS	Number=Plur	5	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	algebraic	algebraic	ADJ	JJ	Degree=Pos	9	amod	_	_
9	theory	theory	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	which	which	PRON	WDT	_	12	nsubj	_	_
12	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	relcl	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	monoidal	monoidal	ADJ	JJ	Degree=Pos	15	amod	_	_
15	version	version	NOUN	NN	Number=Sing	12	attr	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	profunctors	profunctor	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 8
# text = Every strong monoidal functor gives rise to an adjoint pair of such morphisms, and provides a uniform method to establish isomorphisms between categories of models in different notions of algebraic theory.
1	Every	every	DET	DT	_	4	det	_	_
2	strong	strong	ADJ	JJ	Degree=Pos	4	amod	_	_
3	monoidal	monoidal	ADJ	JJ	Degree=Pos	4	amod	_	_
4	functor	functor	NOUN	NN	Number=Sing	5	nsubj	_	_
5	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	rise	rise	NOUN	NN	Number=Sing	5	dobj	_	_
7	to	to	ADP	IN	_	6	prep	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	adjoint	adjoint	NOUN	NN	Number=Sing	10	compound	_	_
10	pair	pair	NOUN	NN	Number=Sing	7	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	such	such	ADJ	JJ	Degree=Pos	13	amod	_	_
13	morphisms	morphism	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
16	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	conj	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	uniform	uniform	ADJ	JJ	Degree=Pos	19	amod	_	_
19	method	method	NOUN	NN	Number=Sing	16	dobj	_	_
20	to	to	PART	TO	_	21	aux	_	_
21	establish	establish	VERB	VB	VerbForm=Inf	16	advcl	_	_
22	isomorphisms	isomorphism	NOUN	NNS	Number=Plur	21	dobj	_	_
23	between	between	ADP	IN	_	22	prep	_	_
24	categories	category	NOUN	NNS	Number=Plur	23	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	models	model	NOUN	NNS	Number=Plur	25	pobj	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	different	different	ADJ	JJ	Degree=Pos	29	amod	_	_
29	notions	notion	NOUN	NNS	Number=Plur	27	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	algebraic	algebraic	ADJ	JJ	Degree=Pos	32	amod	_	_
32	theory	theory	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 9
# text = A general structure - semantics adjointness result and a double categorical universal property of categories of models are also shown.
1	A	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
2	general	general	ADJ	JJ	Degree=Pos	7	amod	_	_
3	structure	structure	NOUN	NN	Number=Sing	5	compound	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	semantics	semantic	NOUN	NNS	Number=Plur	6	compound	_	_
6	adjointness	adjointness	PROPN	NNP	Number=Sing	7	compound	_	_
7	result	result	PROPN	NNP	Number=Sing	20	nsubjpass	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
10	double	double	ADJ	JJ	Degree=Pos	13	amod	_	_
11	categorical	categorical	ADJ	JJ	Degree=Pos	13	amod	_	_
12	universal	universal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	property	property	NOUN	NN	Number=Sing	7	conj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	categories	category	NOUN	NNS	Number=Plur	14	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	models	model	NOUN	NNS	Number=Plur	16	pobj	_	_
18	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	20	auxpass	_	_
19	also	also	ADV	RB	_	20	advmod	_	_
20	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# doc_id = 697
# sent_id = 1
# text = This is the first part of a two paper series studying free globularly generated double categories.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	first	first	ADJ	JJ	Degree=Pos	5	amod	_	_
5	part	part	NOUN	NN	Number=Sing	2	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
8	two	two	NUM	CD	NumType=Card	10	nummod	_	_
9	paper	paper	NOUN	NN	Number=Sing	10	compound	_	_
10	series	series	NOUN	NN	Number=Sing	6	pobj	_	_
11	studying	study	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	acl	_	_
12	free	free	ADJ	JJ	Degree=Pos	16	amod	_	_
13	globularly	globularly	ADV	RB	_	14	advmod	_	_
14	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
15	double	double	ADJ	JJ	Degree=Pos	16	amod	_	_
16	categories	category	NOUN	NNS	Number=Plur	11	dobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this first installment we introduce the free globularly generated double category construction.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
3	first	first	ADJ	JJ	Degree=Pos	4	amod	_	_
4	installment	installment	NOUN	NN	Number=Sing	1	pobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
8	free	free	ADJ	JJ	Degree=Pos	13	amod	_	_
9	globularly	globularly	ADV	RB	_	10	advmod	_	_
10	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
11	double	double	ADJ	JJ	Degree=Pos	13	amod	_	_
12	category	category	NOUN	NN	Number=Sing	13	compound	_	_
13	construction	construction	NOUN	NN	Number=Sing	6	dobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = The free globularly generated double category construction canonically associates to every bicategory together with a possible category of vertical morphisms, a double category fixing this set of initial data in a free and minimal way.
1	The	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
2	free	free	ADJ	JJ	Degree=Pos	7	amod	_	_
3	globularly	globularly	ADV	RB	_	4	advmod	_	_
4	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
5	double	double	ADJ	JJ	Degree=Pos	7	amod	_	_
6	category	category	NOUN	NN	Number=Sing	7	compound	_	_
7	construction	construction	NOUN	NN	Number=Sing	9	nsubj	_	_
8	canonically	canonically	ADV	RB	_	9	advmod	_	_
9	associates	associate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	to	to	ADP	IN	_	9	prep	_	_
11	every	every	DET	DT	_	12	det	_	_
12	bicategory	bicategory	NOUN	NN	Number=Sing	10	pobj	_	_
13	together	together	ADV	RB	_	14	advmod	_	_
14	with	with	ADP	IN	_	9	prep	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	possible	possible	ADJ	JJ	Degree=Pos	17	amod	_	_
17	category	category	NOUN	NN	Number=Sing	14	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	vertical	vertical	ADJ	JJ	Degree=Pos	20	amod	_	_
20	morphisms	morphism	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
23	double	double	ADJ	JJ	Degree=Pos	24	amod	_	_
24	category	category	NOUN	NN	Number=Sing	9	appos	_	_
25	fixing	fix	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	24	acl	_	_
26	this	this	DET	DT	Number=Sing|PronType=Dem	27	det	_	_
27	set	set	NOUN	NN	Number=Sing	25	dobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	initial	initial	ADJ	JJ	Degree=Pos	30	amod	_	_
30	data	datum	NOUN	NNS	Number=Plur	28	pobj	_	_
31	in	in	ADP	IN	_	25	prep	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
33	free	free	ADJ	JJ	Degree=Pos	36	amod	_	_
34	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
35	minimal	minimal	ADJ	JJ	Degree=Pos	33	conj	_	_
36	way	way	NOUN	NN	Number=Sing	31	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 4
# text = We use the free globularly generated double category to study length, free products, and problems of internalization.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
4	free	free	ADJ	JJ	Degree=Pos	8	amod	_	_
5	globularly	globularly	ADV	RB	_	6	advmod	_	_
6	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
7	double	double	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	2	dobj	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	study	study	VERB	VB	VerbForm=Inf	2	xcomp	_	_
11	length	length	NOUN	NN	Number=Sing	10	dobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	free	free	ADJ	JJ	Degree=Pos	14	amod	_	_
14	products	product	NOUN	NNS	Number=Plur	11	conj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
17	problems	problem	NOUN	NNS	Number=Plur	14	conj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	internalization	internalization	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = We use the free globularly generated double category construction to provide formal functorial extensions of the Haagerup standard form construction and the Connes fusion operation to inclusions of factors of not - necessarily finite Jones index.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
4	free	free	ADJ	JJ	Degree=Pos	9	amod	_	_
5	globularly	globularly	ADV	RB	_	6	advmod	_	_
6	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	amod	_	_
7	double	double	ADJ	JJ	Degree=Pos	9	amod	_	_
8	category	category	NOUN	NN	Number=Sing	9	compound	_	_
9	construction	construction	NOUN	NN	Number=Sing	2	dobj	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	provide	provide	VERB	VB	VerbForm=Inf	2	xcomp	_	_
12	formal	formal	ADJ	JJ	Degree=Pos	14	amod	_	_
13	functorial	functorial	ADJ	JJ	Degree=Pos	14	amod	_	_
14	extensions	extension	NOUN	NNS	Number=Plur	11	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	Haagerup	Haagerup	PROPN	NNP	Number=Sing	18	compound	_	_
18	standard	standard	NOUN	NN	Number=Sing	20	amod	_	_
19	form	form	NOUN	NN	Number=Sing	20	compound	_	_
20	construction	construction	NOUN	NN	Number=Sing	15	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
23	Connes	Connes	PROPN	NNP	Number=Sing	24	compound	_	_
24	fusion	fusion	NOUN	NN	Number=Sing	25	compound	_	_
25	operation	operation	NOUN	NN	Number=Sing	20	conj	_	_
26	to	to	ADP	IN	_	11	prep	_	_
27	inclusions	inclusion	NOUN	NNS	Number=Plur	26	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	factors	factor	NOUN	NNS	Number=Plur	28	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	not	not	PART	RB	Polarity=Neg	33	neg	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	necessarily	necessarily	ADV	RB	_	34	advmod	_	_
34	finite	finite	PROPN	NNP	Number=Sing	36	amod	_	_
35	Jones	Jones	PROPN	NNP	Number=Sing	36	compound	_	_
36	index	index	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 698
# sent_id = 1
# text = By the Three Graces we refer, following Loday, to the algebraic operads $ Ass $ , $ Com $ , and $ Lie $ , each generated by a single binary operation; algebras over these operads are respectively associative, commutative associative, and Lie.
1	By	by	ADP	IN	_	34	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	Three	Three	PROPN	NNP	Number=Sing	4	compound	_	_
4	Graces	Graces	PROPN	NNPS	Number=Plur	1	pobj	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	refer	refer	VERB	VBP	Tense=Pres|VerbForm=Fin	4	relcl	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	prep	_	_
9	Loday	Loday	PROPN	NNP	Number=Sing	8	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
11	to	to	ADP	IN	_	1	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	algebraic	algebraic	ADJ	JJ	Degree=Pos	14	amod	_	_
14	operads	operad	NOUN	NNS	Number=Plur	11	pobj	_	_
15	$ Ass $	$ ass $	SYM	$	_	14	appos	_	_
16	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
17	$ Com $	$ com $	SYM	$	_	14	appos	_	_
18	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
20	$ Lie $	$ lie $	SYM	$	_	1	pcomp	_	_
21	,	,	PUNCT	,	PunctType=Comm	34	punct	_	_
22	each	each	PRON	DT	_	34	dep	_	_
23	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	acl	_	_
24	by	by	ADP	IN	_	23	agent	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
26	single	single	ADJ	JJ	Degree=Pos	28	amod	_	_
27	binary	binary	ADJ	JJ	Degree=Pos	28	amod	_	_
28	operation	operation	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
29	;	;	PUNCT	:	_	34	punct	_	_
30	algebras	algebra	NOUN	NNS	Number=Plur	34	nsubj	_	_
31	over	over	ADP	IN	_	30	prep	_	_
32	these	these	DET	DT	Number=Plur|PronType=Dem	33	det	_	_
33	operads	operad	NOUN	NNS	Number=Plur	31	pobj	_	_
34	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
35	respectively	respectively	ADV	RB	_	36	advmod	_	_
36	associative	associative	ADJ	JJ	Degree=Pos	34	acomp	_	SpaceAfter=No
37	,	,	PUNCT	,	PunctType=Comm	34	punct	_	_
38	commutative	commutative	ADJ	JJ	Degree=Pos	39	amod	_	_
39	associative	associative	NOUN	NN	Number=Sing	34	conj	_	SpaceAfter=No
40	,	,	PUNCT	,	PunctType=Comm	39	punct	_	_
41	and	and	CCONJ	CC	ConjType=Cmp	39	cc	_	_
42	Lie	Lie	PROPN	NNP	Number=Sing	39	conj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	34	punct	_	SpaceAfter=No

# sent_id = 2
# text = We classify all distributive laws (in the categorical sense of Beck) between these three operads.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	classify	classify	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	all	all	DET	DT	_	5	det	_	_
4	distributive	distributive	ADJ	JJ	Degree=Pos	5	amod	_	_
5	laws	law	NOUN	NNS	Number=Plur	2	dobj	_	_
6	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	5	punct	_	SpaceAfter=No
7	in	in	ADP	IN	_	5	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	categorical	categorical	ADJ	JJ	Degree=Pos	10	amod	_	_
10	sense	sense	NOUN	NN	Number=Sing	7	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	Beck	Beck	PROPN	NNP	Number=Sing	11	pobj	_	SpaceAfter=No
13	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	7	punct	_	_
14	between	between	ADP	IN	_	5	prep	_	_
15	these	these	DET	DT	Number=Plur|PronType=Dem	17	det	_	_
16	three	three	NUM	CD	NumType=Card	17	nummod	_	_
17	operads	operad	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Some of our results depend on the computer algebra system Maple, especially its packages LinearAlgebra and Groebner.
1	Some	some	PRON	DT	_	5	nsubj	_	_
2	of	of	ADP	IN	_	1	prep	_	_
3	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	4	poss	_	_
4	results	result	NOUN	NNS	Number=Plur	2	pobj	_	_
5	depend	depend	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	on	on	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
8	computer	computer	NOUN	NN	Number=Sing	9	compound	_	_
9	algebra	algebra	NOUN	NN	Number=Sing	10	compound	_	_
10	system	system	NOUN	NN	Number=Sing	11	compound	_	_
11	Maple	Maple	PROPN	NNP	Number=Sing	6	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	especially	especially	ADV	RB	_	15	advmod	_	_
14	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	15	poss	_	_
15	packages	package	NOUN	NNS	Number=Plur	11	appos	_	_
16	LinearAlgebra	LinearAlgebra	PROPN	NNP	Number=Sing	15	appos	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	Groebner	Groebner	PROPN	NNP	Number=Sing	16	conj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 699
# sent_id = 1
# text = The Noether Isomorphism Theorems and the Zassenhaus Lemma from group theory have a non - pointed version in a suitable categorical context first considered by Tholen in his PhD thesis.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	Noether	Noether	PROPN	NNP	Number=Sing	4	compound	_	_
3	Isomorphism	Isomorphism	PROPN	NNP	Number=Sing	4	compound	_	_
4	Theorems	Theorems	PROPN	NNP	Number=Sing	12	nsubj	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	Zassenhaus	Zassenhaus	PROPN	NNP	Number=Sing	8	compound	_	_
8	Lemma	Lemma	PROPN	NNP	Number=Sing	4	conj	_	_
9	from	from	ADP	IN	_	8	prep	_	_
10	group	group	NOUN	NN	Number=Sing	11	compound	_	_
11	theory	theory	NOUN	NN	Number=Sing	9	pobj	_	_
12	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
14	non	non	ADV	RB	_	16	advmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	pointed	point	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	version	version	NOUN	NN	Number=Sing	12	dobj	_	_
18	in	in	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
20	suitable	suitable	ADJ	JJ	Degree=Pos	22	amod	_	_
21	categorical	categorical	ADJ	JJ	Degree=Pos	22	amod	_	_
22	context	context	NOUN	NN	Number=Sing	18	pobj	_	_
23	first	first	ADV	RB	_	24	advmod	_	_
24	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	acl	_	_
25	by	by	ADP	IN	_	24	agent	_	_
26	Tholen	Tholen	PROPN	NNP	Number=Sing	25	pobj	_	_
27	in	in	ADP	IN	_	24	prep	_	_
28	his	his	PRON	PRP$	Gender=Masc|Number=Sing|Person=3|Poss=Yes|PronType=Prs	30	poss	_	_
29	PhD	phd	NOUN	NN	Number=Sing	30	compound	_	_
30	thesis	thesis	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 2
# text = This article leads to a unification of these results with the ones in the pointed categorical context previously considered by Wyler, by working in the framework of star - regular categories introduced by Gran, Janelidze and Ursini.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	article	article	NOUN	NN	Number=Sing	3	nsubj	_	_
3	leads	lead	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	to	to	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	unification	unification	NOUN	NN	Number=Sing	4	pobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	these	these	DET	DT	Number=Plur|PronType=Dem	9	det	_	_
9	results	result	NOUN	NNS	Number=Plur	7	pobj	_	_
10	with	with	ADP	IN	_	6	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	ones	one	NOUN	NNS	Number=Plur	10	pobj	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
15	pointed	pointed	ADJ	JJ	Degree=Pos	17	amod	_	_
16	categorical	categorical	ADJ	JJ	Degree=Pos	17	amod	_	_
17	context	context	NOUN	NN	Number=Sing	13	pobj	_	_
18	previously	previously	ADV	RB	_	19	advmod	_	_
19	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
20	by	by	ADP	IN	_	19	agent	_	_
21	Wyler	Wyler	PROPN	NNP	Number=Sing	20	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
23	by	by	ADP	IN	_	3	prep	_	_
24	working	work	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	23	pcomp	_	_
25	in	in	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	framework	framework	NOUN	NN	Number=Sing	25	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	star	star	NOUN	NN	Number=Sing	31	compound	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	regular	regular	ADJ	JJ	Degree=Pos	32	amod	_	_
32	categories	category	NOUN	NNS	Number=Plur	28	pobj	_	_
33	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	acl	_	_
34	by	by	ADP	IN	_	33	agent	_	_
35	Gran	Gran	PROPN	NNP	Number=Sing	34	pobj	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
37	Janelidze	Janelidze	PROPN	NNP	Number=Sing	35	conj	_	_
38	and	and	CCONJ	CC	ConjType=Cmp	37	cc	_	_
39	Ursini	Ursini	PROPN	NNP	Number=Sing	37	conj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Some concrete examples of categories where these results hold are examined in detail.
1	Some	some	DET	DT	_	3	det	_	_
2	concrete	concrete	ADJ	JJ	Degree=Pos	3	amod	_	_
3	examples	example	NOUN	NNS	Number=Plur	11	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	_
6	where	where	SCONJ	WRB	_	9	advmod	_	_
7	these	these	DET	DT	Number=Plur|PronType=Dem	8	det	_	_
8	results	result	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	hold	hold	VERB	VBP	Tense=Pres|VerbForm=Fin	3	relcl	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	examined	examine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	detail	detail	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# doc_id = 700
# sent_id = 1
# text = For finitary regular monads $ T $ on locally finitely presentable categories we characterize the finitely presentable objects in the category of $ T $ - algebras in the style known from general algebra: they are precisely the algebras presentable by finitely many generators and finitely many relations.
1	For	for	ADP	IN	_	33	prep	_	_
2	finitary	finitary	ADJ	JJ	Degree=Pos	4	amod	_	_
3	regular	regular	ADJ	JJ	Degree=Pos	4	amod	_	_
4	monads	monad	NOUN	NNS	Number=Plur	1	pobj	_	_
5	$ T $	$ t $	SYM	$	_	1	dep	_	_
6	on	on	ADP	IN	_	1	prep	_	_
7	locally	locally	ADV	RB	_	8	advmod	_	_
8	finitely	finitely	ADV	RB	_	10	amod	_	_
9	presentable	presentable	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	_
11	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	12	nsubj	_	_
12	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	10	relcl	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
14	finitely	finitely	ADV	RB	_	15	advmod	_	_
15	presentable	presentable	ADJ	JJ	Degree=Pos	16	amod	_	_
16	objects	object	NOUN	NNS	Number=Plur	12	dobj	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	category	category	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	$ T $	$ t $	SYM	$	_	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	algebras	algebra	NOUN	NNS	Number=Plur	20	pobj	_	_
24	in	in	ADP	IN	_	19	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	style	style	NOUN	NN	Number=Sing	24	pobj	_	_
27	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	acl	_	_
28	from	from	ADP	IN	_	27	prep	_	_
29	general	general	ADJ	JJ	Degree=Pos	30	amod	_	_
30	algebra	algebra	PROPN	NNP	Number=Sing	28	pobj	_	SpaceAfter=No
31	:	:	PUNCT	:	_	33	punct	_	_
32	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	33	nsubj	_	_
33	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
34	precisely	precisely	ADV	RB	_	33	advmod	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	algebras	algebras	PROPN	NNPS	Number=Plur	33	attr	_	_
37	presentable	presentable	ADJ	JJ	Degree=Pos	36	amod	_	_
38	by	by	ADP	IN	_	37	prep	_	_
39	finitely	finitely	ADV	RB	_	40	advmod	_	_
40	many	many	ADJ	JJ	Degree=Pos	41	amod	_	_
41	generators	generator	NOUN	NNS	Number=Plur	38	pobj	_	_
42	and	and	CCONJ	CC	ConjType=Cmp	41	cc	_	_
43	finitely	finitely	ADV	RB	_	44	advmod	_	_
44	many	many	ADJ	JJ	Degree=Pos	45	amod	_	_
45	relations	relation	NOUN	NNS	Number=Plur	41	conj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	33	punct	_	SpaceAfter=No

# doc_id = 701
# sent_id = 1
# text = By theorems of Carlson and Renaudin, the theory of $ (∞, 1) $ - categories embeds in that of prederivators.
1	By	by	ADP	IN	_	14	prep	_	_
2	theorems	theorem	NOUN	NNS	Number=Plur	1	pobj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	Carlson	Carlson	PROPN	NNP	Number=Sing	3	pobj	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
6	Renaudin	Renaudin	PROPN	NNP	Number=Sing	4	conj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	theory	theory	NOUN	NN	Number=Sing	14	nsubj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	$ (∞, 1) $	$ (∞, 1) $	SYM	$	_	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	categories	category	NOUN	NNS	Number=Plur	14	nsubj	_	_
14	embeds	embed	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	that	that	PRON	DT	Number=Sing|PronType=Dem	15	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	prederivators	prederivator	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 2
# text = The purpose of this paper is to give a two - fold answer to the inverse problem: understanding which prederivators model $ (∞, 1) $ - categories, either strictly or in a homotopical sense.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	purpose	purpose	NOUN	NN	Number=Sing	6	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	paper	paper	NOUN	NN	Number=Sing	3	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	give	give	VERB	VB	VerbForm=Inf	6	xcomp	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
10	two	two	NUM	CD	NumType=Card	12	nummod	_	_
11	-	-	ADJ	JJ	Degree=Pos	12	punct	_	_
12	fold	fold	ADJ	JJ	Degree=Pos	13	amod	_	_
13	answer	answer	NOUN	NN	Number=Sing	8	dobj	_	_
14	to	to	ADP	IN	_	8	dative	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	inverse	inverse	ADJ	JJ	Degree=Pos	17	amod	_	_
17	problem	problem	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
18	:	:	PUNCT	:	_	17	punct	_	_
19	understanding	understanding	NOUN	NN	Number=Sing	17	appos	_	_
20	which	which	PRON	WDT	_	21	nsubj	_	_
21	prederivators	prederivator	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	relcl	_	_
22	model	model	NOUN	NN	Number=Sing	21	dobj	_	_
23	$ (∞, 1) $	$ (∞, 1) $	PROPN	NNP	Number=Sing	25	nmod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	categories	category	NOUN	NNS	Number=Plur	22	dobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
27	either	either	CCONJ	CC	ConjType=Cmp	28	preconj	_	_
28	strictly	strictly	ADV	RB	_	21	advmod	_	_
29	or	or	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	in	in	ADP	IN	_	28	conj	_	_
31	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
32	homotopical	homotopical	ADJ	JJ	Degree=Pos	33	amod	_	_
33	sense	sense	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = First, we characterize which prederivators arise on the nose as prederivators associated to quasicategories.
1	First	first	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	characterize	characterize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	which	which	PRON	WDT	_	7	dobj	_	_
6	prederivators	prederivator	NOUN	NNS	Number=Plur	7	nsubj	_	_
7	arise	arise	VERB	VBP	Tense=Pres|VerbForm=Fin	4	ccomp	_	_
8	on	on	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	nose	nose	NOUN	NN	Number=Sing	8	pobj	_	_
11	as	as	ADP	IN	_	7	prep	_	_
12	prederivators	prederivator	NOUN	NNS	Number=Plur	11	pobj	_	_
13	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	acl	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	quasicategories	quasicategorie	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = Next, we put a model structure on the category of prederivators and strict natural transformations, and prove a Quillen equivalence with the Joyal model structure for quasicategories.
1	Next	next	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	put	put	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	model	model	NOUN	NN	Number=Sing	7	compound	_	_
7	structure	structure	NOUN	NN	Number=Sing	4	dobj	_	_
8	on	on	ADP	IN	_	4	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	prederivators	prederivator	NOUN	NNS	Number=Plur	11	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
14	strict	strict	ADJ	JJ	Degree=Pos	16	amod	_	_
15	natural	natural	ADJ	JJ	Degree=Pos	16	amod	_	_
16	transformations	transformation	NOUN	NNS	Number=Plur	10	conj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
19	prove	prove	VERB	VB	VerbForm=Inf	4	conj	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	Quillen	quillen	ADJ	JJ	Degree=Pos	22	amod	_	_
22	equivalence	equivalence	NOUN	NN	Number=Sing	19	dobj	_	_
23	with	with	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
25	Joyal	joyal	ADJ	JJ	Degree=Pos	27	amod	_	_
26	model	model	NOUN	NN	Number=Sing	27	compound	_	_
27	structure	structure	NOUN	NN	Number=Sing	23	pobj	_	_
28	for	for	ADP	IN	_	27	prep	_	_
29	quasicategories	quasicategorie	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 702
# sent_id = 1
# text = The category of 1 - cat groups, which is equivalent to the category of crossed modules, has internal object actions which are representable (by internal automorphism groups).
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	category	category	NOUN	NN	Number=Sing	19	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	1	1	NUM	CD	NumType=Card	6	nummod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	cat	cat	NOUN	NN	Number=Sing	7	compound	_	_
7	groups	group	NOUN	NNS	Number=Plur	3	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	which	which	PRON	WDT	_	10	nsubj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	relcl	_	_
11	equivalent	equivalent	ADJ	JJ	Degree=Pos	10	acomp	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	crossed	crossed	ADJ	JJ	Degree=Pos	17	amod	_	_
17	modules	module	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
19	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	internal	internal	ADJ	JJ	Degree=Pos	22	amod	_	_
21	object	object	NOUN	NN	Number=Sing	22	compound	_	_
22	actions	action	NOUN	NNS	Number=Plur	19	dobj	_	_
23	which	which	PRON	WDT	_	24	nsubj	_	_
24	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	22	relcl	_	_
25	representable	representable	ADJ	JJ	Degree=Pos	24	acomp	_	_
26	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	25	punct	_	SpaceAfter=No
27	by	by	ADP	IN	_	25	prep	_	_
28	internal	internal	ADJ	JJ	Degree=Pos	30	amod	_	_
29	automorphism	automorphism	NOUN	NN	Number=Sing	30	compound	_	_
30	groups	group	NOUN	NNS	Number=Plur	27	pobj	_	SpaceAfter=No
31	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	22	punct	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 2
# text = Moreover, it is known that the crossed module, corresponding to the representing object $ [X] = Aut(X) $ associated with a 1 - cat group $ X $ , must be isomorphic to the Norrie actor of the crossed module corresponding to $ X $ .
1	Moreover	moreover	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	that	that	SCONJ	IN	_	17	mark	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	crossed	cross	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	amod	_	_
9	module	module	NOUN	NN	Number=Sing	17	nsubj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	amod	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	representing	represent	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	amod	_	_
15	object	object	NOUN	NN	Number=Sing	12	pobj	_	_
16	$ [X] = Aut(X) $	$ [x] = aut(x) $	SYM	$	_	17	nsubj	_	_
17	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	ccomp	_	_
18	with	with	ADP	IN	_	17	prep	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
20	1	1	NUM	CD	NumType=Card	22	nummod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	cat	cat	NOUN	NN	Number=Sing	23	compound	_	_
23	group	group	NOUN	NN	Number=Sing	18	pobj	_	_
24	$ X $	$ x $	SYM	$	_	23	appos	_	_
25	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
26	must	must	AUX	MD	VerbForm=Fin	27	aux	_	_
27	be	be	AUX	VB	VerbForm=Inf	5	conj	_	_
28	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	27	acomp	_	_
29	to	to	ADP	IN	_	28	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
31	Norrie	Norrie	PROPN	NNP	Number=Sing	32	amod	_	_
32	actor	actor	NOUN	NN	Number=Sing	29	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
35	crossed	crossed	ADJ	JJ	Degree=Pos	36	amod	_	_
36	module	module	NOUN	NN	Number=Sing	33	pobj	_	_
37	corresponding	corresponding	NOUN	NN	Number=Sing	36	amod	_	_
38	to	to	ADP	IN	_	37	prep	_	_
39	$ X $	$ x $	SYM	$	_	38	pobj	_	_
40	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = We recall the description of $ Aut(X) $ from the author's PhD thesis, and construct that isomorphism explicitly.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	recall	recall	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	description	description	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	$ Aut(X) $	$ aut(x) $	SYM	$	_	5	pobj	_	_
7	from	from	ADP	IN	_	2	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	author	author	NOUN	NN	Number=Sing	12	poss	_	SpaceAfter=No
10	's	's	PART	POS	_	9	case	_	_
11	PhD	phd	NOUN	NN	Number=Sing	12	compound	_	_
12	thesis	thesis	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
15	construct	construct	VERB	VB	VerbForm=Inf	2	conj	_	_
16	that	that	DET	DT	Number=Sing|PronType=Dem	17	det	_	_
17	isomorphism	isomorphism	NOUN	NN	Number=Sing	15	dobj	_	_
18	explicitly	explicitly	ADV	RB	_	15	advmod	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 703
# sent_id = 1
# text = A simple criterion for a functor to be finitary is presented: we call $ F $ finitely bounded if for all objects $ X $ every finitely generated subobject of $ FX $ factorizes through the $ F $ - image of a finitely generated subobject of $ X $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	simple	simple	ADJ	JJ	Degree=Pos	3	amod	_	_
3	criterion	criterion	NOUN	NN	Number=Sing	11	nsubjpass	_	_
4	for	for	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	functor	functor	NOUN	NN	Number=Sing	11	nsubjpass	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	be	be	AUX	VB	VerbForm=Inf	6	acl	_	_
9	finitary	finitary	ADJ	JJ	Degree=Pos	8	acomp	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	ccomp	_	SpaceAfter=No
12	:	:	PUNCT	:	_	14	punct	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	call	call	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	$ F $	$ f $	SYM	$	_	17	dep	_	_
16	finitely	finitely	ADV	RB	_	17	advmod	_	_
17	bounded	bound	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	advcl	_	_
18	if	if	SCONJ	IN	_	14	prep	_	_
19	for	for	ADP	IN	_	14	prep	_	_
20	all	all	DET	DT	_	21	det	_	_
21	objects	object	NOUN	NNS	Number=Plur	19	pobj	_	_
22	$ X $	$ x $	SYM	$	_	23	nmod	_	_
23	every	every	DET	DT	_	26	det	_	_
24	finitely	finitely	ADV	RB	_	25	advmod	_	_
25	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
26	subobject	subobject	NOUN	NN	Number=Sing	14	dobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	$ FX $	$ fx $	SYM	$	_	29	nsubj	_	_
29	factorizes	factorize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	pobj	_	_
30	through	through	ADP	IN	_	14	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
32	$ F $	$ f $	SYM	$	_	34	compound	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	image	image	NOUN	NN	Number=Sing	30	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	a	a	DET	DT	Definite=Ind|PronType=Art	39	det	_	_
37	finitely	finitely	ADV	RB	_	38	advmod	_	_
38	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	39	amod	_	_
39	subobject	subobject	NOUN	NN	Number=Sing	35	pobj	_	_
40	of	of	ADP	IN	_	39	prep	_	_
41	$ X $	$ x $	SYM	$	_	40	pobj	_	_
42	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 2
# text = This is equivalent to $ F $ being finitary for all functors between `reasonable' locally finitely presentable categories, provided that $ F $ preserves monomorphisms.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	equivalent	equivalent	ADJ	JJ	Degree=Pos	2	acomp	_	_
4	to	to	ADP	IN	_	3	prep	_	_
5	$ F $	$ f $	SYM	$	_	4	pobj	_	_
6	being	be	AUX	VBG	VerbForm=Ger	2	advcl	_	_
7	finitary	finitary	ADJ	JJ	Degree=Pos	6	acomp	_	_
8	for	for	ADP	IN	_	6	prep	_	_
9	all	all	DET	DT	_	10	det	_	_
10	functors	functor	NOUN	NNS	Number=Plur	8	pobj	_	_
11	between	between	ADP	IN	_	10	prep	_	_
12	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	11	punct	_	SpaceAfter=No
13	reasonable	reasonable	ADJ	JJ	Degree=Pos	18	amod	_	SpaceAfter=No
14	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	13	punct	_	_
15	locally	locally	ADV	RB	_	16	advmod	_	_
16	finitely	finitely	ADV	RB	_	17	advmod	_	_
17	presentable	presentable	ADJ	JJ	Degree=Pos	18	amod	_	_
18	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
20	provided	provide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	prep	_	_
21	that	that	SCONJ	IN	_	23	mark	_	_
22	$ F $	$ f $	SYM	$	_	23	nsubj	_	_
23	preserves	preserve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	pcomp	_	_
24	monomorphisms	monomorphism	NOUN	NNS	Number=Plur	23	dobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also discuss the question when that last assumption can be dropped.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	discuss	discuss	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	question	question	NOUN	NN	Number=Sing	3	dobj	_	_
6	when	when	SCONJ	WRB	_	12	advmod	_	_
7	that	that	DET	DT	Number=Sing|PronType=Dem	9	det	_	_
8	last	last	ADJ	JJ	Degree=Pos	9	amod	_	_
9	assumption	assumption	NOUN	NN	Number=Sing	12	nsubjpass	_	_
10	can	can	AUX	MD	VerbForm=Fin	12	aux	_	_
11	be	be	AUX	VB	VerbForm=Inf	12	auxpass	_	_
12	dropped	drop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	advcl	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = The answer is affirmative for functors between categories such as $ Set $ , $ K - Vec $ (vector spaces), boolean algebras, and actions of any finite group either on $ Set $ or on $ K - Vec $ for fields $ K $ of characteristic 0.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	answer	answer	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	affirmative	affirmative	ADJ	JJ	Degree=Pos	3	acomp	_	_
5	for	for	ADP	IN	_	4	prep	_	_
6	functors	functor	NOUN	NNS	Number=Plur	5	pobj	_	_
7	between	between	ADP	IN	_	6	prep	_	_
8	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
9	such	such	ADJ	JJ	Degree=Pos	10	amod	_	_
10	as	as	ADP	IN	_	8	prep	_	_
11	$ Set $	$ set $	SYM	$	_	10	pobj	_	_
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	$ K - Vec $	$ k - vec $	SYM	$	_	11	conj	_	_
14	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	13	punct	_	SpaceAfter=No
15	vector	vector	NOUN	NN	Number=Sing	16	compound	_	_
16	spaces	space	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
17	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	16	punct	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
19	boolean	boolean	PROPN	NNP	Number=Sing	20	compound	_	_
20	algebras	algebras	PROPN	NNP	Number=Sing	16	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
23	actions	action	NOUN	NNS	Number=Plur	20	conj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	any	any	DET	DT	_	27	det	_	_
26	finite	finite	PROPN	NNP	Number=Sing	27	compound	_	_
27	group	group	NOUN	NN	Number=Sing	24	pobj	_	_
28	either	either	CCONJ	CC	ConjType=Cmp	29	preconj	_	_
29	on	on	ADP	IN	_	23	prep	_	_
30	$ Set $	$ set $	SYM	$	_	29	pobj	_	_
31	or	or	CCONJ	CC	ConjType=Cmp	30	cc	_	_
32	on	on	ADP	IN	_	30	conj	_	_
33	$ K - Vec $	$ k - vec $	SYM	$	_	32	pobj	_	_
34	for	for	ADP	IN	_	23	prep	_	_
35	fields	field	NOUN	NNS	Number=Plur	34	pobj	_	_
36	$ K $	$ k $	SYM	$	_	6	appos	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	characteristic	characteristic	ADJ	JJ	Degree=Pos	37	pobj	_	_
39	0	0	NUM	CD	NumType=Card	37	pobj	_	SpaceAfter=No
40	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = All this generalizes to locally $ lambda $ - presentable categories, $ lambda $ - accessible functors and $ lambda $ - presentable algebras.
1	All	all	DET	PDT	_	2	predet	_	_
2	this	this	PRON	DT	Number=Sing|PronType=Dem	3	nsubj	_	_
3	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	to	to	ADP	IN	_	3	prep	_	_
5	locally	locally	ADV	RB	_	9	advmod	_	_
6	$ lambda $	$ lambda $	SYM	$	_	8	advmod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	presentable	presentable	ADJ	JJ	Degree=Pos	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	$ lambda $	$ lambda $	SYM	$	_	13	advmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	accessible	accessible	ADJ	JJ	Degree=Pos	14	amod	_	_
14	functors	functor	NOUN	NNS	Number=Plur	9	conj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	$ lambda $	$ lambda $	SYM	$	_	18	advmod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	presentable	presentable	ADJ	JJ	Degree=Pos	19	amod	_	_
19	algebras	algebra	NOUN	NNS	Number=Plur	14	conj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = As an application we obtain an easy proof that the Hausdorff functor on the category of complete metric spaces is $ aleph_1 $ - accessible.
1	As	as	ADP	IN	_	5	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	easy	easy	ADJ	JJ	Degree=Pos	8	amod	_	_
8	proof	proof	NOUN	NN	Number=Sing	5	dobj	_	_
9	that	that	SCONJ	IN	_	20	mark	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	Hausdorff	Hausdorff	PROPN	NNP	Number=Sing	12	compound	_	_
12	functor	functor	NOUN	NN	Number=Sing	20	nsubj	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	complete	complete	ADJ	JJ	Degree=Pos	19	amod	_	_
18	metric	metric	ADJ	JJ	Degree=Pos	19	amod	_	_
19	spaces	space	NOUN	NNS	Number=Plur	16	pobj	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	acl	_	_
21	$ aleph_1 $	$ aleph_1 $	SYM	$	_	23	advmod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	accessible	accessible	ADJ	JJ	Degree=Pos	20	acomp	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 704
# sent_id = 1
# text = Higher categorical structures are often defined by induction on dimension, which a priori produces only finite - dimensional structures.
1	Higher	high	ADJ	JJR	Degree=Cmp	3	amod	_	_
2	categorical	categorical	ADJ	JJ	Degree=Pos	3	amod	_	_
3	structures	structure	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
5	often	often	ADV	RB	_	6	advmod	_	_
6	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	by	by	ADP	IN	_	6	agent	_	_
8	induction	induction	NOUN	NN	Number=Sing	7	pobj	_	_
9	on	on	ADP	IN	_	8	prep	_	_
10	dimension	dimension	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	which	which	PRON	WDT	_	15	nsubj	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	priori	priori	X	FW	Foreign=Yes	15	nsubj	_	_
15	produces	produce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	10	relcl	_	_
16	only	only	ADV	RB	_	20	amod	_	_
17	finite	finite	ADJ	JJ	Degree=Pos	19	npadvmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	dimensional	dimensional	ADJ	JJ	Degree=Pos	20	amod	_	_
20	structures	structure	NOUN	NNS	Number=Plur	15	dobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper we show how to extend such definitions to infinite dimensions using the theory of terminal coalgebras, and we apply this method to Trimble's notion of weak $ n $ - category.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	how	how	SCONJ	WRB	_	8	advmod	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	extend	extend	VERB	VB	VerbForm=Inf	5	xcomp	_	_
9	such	such	ADJ	JJ	Degree=Pos	10	amod	_	_
10	definitions	definition	NOUN	NNS	Number=Plur	8	dobj	_	_
11	to	to	PART	TO	_	8	prep	_	_
12	infinite	infinite	VERB	VB	VerbForm=Inf	13	amod	_	_
13	dimensions	dimension	NOUN	NNS	Number=Plur	11	pobj	_	_
14	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	advcl	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	theory	theory	NOUN	NN	Number=Sing	14	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	terminal	terminal	ADJ	JJ	Degree=Pos	19	amod	_	_
19	coalgebras	coalgebra	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
22	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	23	nsubj	_	_
23	apply	apply	VERB	VBP	Tense=Pres|VerbForm=Fin	5	conj	_	_
24	this	this	DET	DT	Number=Sing|PronType=Dem	25	det	_	_
25	method	method	NOUN	NN	Number=Sing	23	dobj	_	_
26	to	to	ADP	IN	_	23	prep	_	_
27	Trimble	Trimble	PROPN	NNP	Number=Sing	29	poss	_	SpaceAfter=No
28	's	's	PART	POS	_	27	case	_	_
29	notion	notion	NOUN	NN	Number=Sing	26	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	weak	weak	ADJ	JJ	Degree=Pos	34	amod	_	_
32	$ n $	$ n $	SYM	$	_	34	nummod	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	category	category	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# sent_id = 3
# text = Trimble's definition makes explicit the relationship between $ n $ - categories and topological spaces; our extended theory produces a definition of Trimble $ infty $ - category and a fundamental $ infty $ - groupoid construction.
1	Trimble	trimble	ADJ	JJ	Degree=Pos	3	poss	_	SpaceAfter=No
2	's	's	PART	POS	_	1	case	_	_
3	definition	definition	NOUN	NN	Number=Sing	4	nsubj	_	_
4	makes	make	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	ccomp	_	_
5	explicit	explicit	ADJ	JJ	Degree=Pos	4	ccomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	relationship	relationship	NOUN	NN	Number=Sing	5	dobj	_	_
8	between	between	ADP	IN	_	7	prep	_	_
9	$ n $	$ n $	SYM	$	_	11	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	topological	topological	ADJ	JJ	Degree=Pos	14	amod	_	_
14	spaces	space	NOUN	NNS	Number=Plur	11	conj	_	SpaceAfter=No
15	;	;	PUNCT	:	_	19	punct	_	_
16	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	18	poss	_	_
17	extended	extended	ADJ	JJ	Degree=Pos	18	amod	_	_
18	theory	theory	NOUN	NN	Number=Sing	19	nsubj	_	_
19	produces	produce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	definition	definition	NOUN	NN	Number=Sing	19	dobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	Trimble	Trimble	PROPN	NNP	Number=Sing	26	amod	_	_
24	$ infty $	$ infty $	SYM	$	_	26	compound	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	category	category	NOUN	NN	Number=Sing	22	pobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
29	fundamental	fundamental	ADJ	JJ	Degree=Pos	33	amod	_	_
30	$ infty $	$ infty $	SYM	$	_	32	nmod	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	32	punct	_	_
32	groupoid	groupoid	NOUN	NN	Number=Sing	33	compound	_	_
33	construction	construction	NOUN	NN	Number=Sing	21	conj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 4
# text = Furthermore, terminal coalgebras are often constructed as limits of a certain type.
1	Furthermore	furthermore	ADV	RB	_	7	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
3	terminal	terminal	ADJ	JJ	Degree=Pos	4	amod	_	_
4	coalgebras	coalgebra	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
6	often	often	ADV	RB	_	7	advmod	_	_
7	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	as	as	ADP	IN	_	7	prep	_	_
9	limits	limit	NOUN	NNS	Number=Plur	8	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	certain	certain	ADJ	JJ	Degree=Pos	13	amod	_	_
13	type	type	NOUN	NN	Number=Sing	10	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 5
# text = We prove that the theory of Batanin - Leinster weak $ infty $ - categories arises as just such a limit, justifying our approach to Trimble $ infty $ - categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	14	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	theory	theory	NOUN	NN	Number=Sing	14	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	Batanin	Batanin	PROPN	NNP	Number=Sing	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	Leinster	leinster	NOUN	NN	Number=Sing	6	pobj	_	_
10	weak	weak	ADJ	JJ	Degree=Pos	13	amod	_	_
11	$ infty $	$ infty $	SYM	$	_	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	categories	category	NOUN	NNS	Number=Plur	9	appos	_	_
14	arises	arise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
15	as	as	ADP	IN	_	14	prep	_	_
16	just	just	ADV	RB	_	19	advmod	_	_
17	such	such	DET	PDT	_	19	predet	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	limit	limit	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
21	justifying	justify	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	advcl	_	_
22	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	23	poss	_	_
23	approach	approach	NOUN	NN	Number=Sing	21	dobj	_	_
24	to	to	ADP	IN	_	23	prep	_	_
25	Trimble	Trimble	PROPN	NNP	Number=Sing	28	amod	_	_
26	$ infty $	$ infty $	SYM	$	_	28	compound	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	categories	category	NOUN	NNS	Number=Plur	24	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = In fact we work at the level of monads for $ infty $ - categories, rather than $ infty $ - categories themselves; this requires more sophisticated technology but also provides a more complete theory of the structures in question.
1	In	in	ADP	IN	_	4	prep	_	_
2	fact	fact	NOUN	NN	Number=Sing	1	pobj	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	work	work	VERB	VBP	Tense=Pres|VerbForm=Fin	23	ccomp	_	_
5	at	at	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	level	level	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	monads	monad	NOUN	NNS	Number=Plur	8	pobj	_	_
10	for	for	ADP	IN	_	7	prep	_	_
11	$ infty $	$ infty $	SYM	$	_	13	nmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	rather	rather	ADV	RB	_	16	advmod	_	_
16	than	than	ADP	IN	_	13	cc	_	_
17	$ infty $	$ infty $	SYM	$	_	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	categories	category	NOUN	NNS	Number=Plur	13	conj	_	_
20	themselves	themselves	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs|Reflex=Yes	19	appos	_	SpaceAfter=No
21	;	;	PUNCT	:	_	23	punct	_	_
22	this	this	PRON	DT	Number=Sing|PronType=Dem	23	nsubj	_	_
23	requires	require	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
24	more	more	ADV	RBR	Degree=Cmp	25	advmod	_	_
25	sophisticated	sophisticated	ADJ	JJ	Degree=Pos	26	amod	_	_
26	technology	technology	NOUN	NN	Number=Sing	23	dobj	_	_
27	but	but	CCONJ	CC	ConjType=Cmp	23	cc	_	_
28	also	also	ADV	RB	_	27	advmod	_	_
29	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	conj	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
31	more	more	ADV	RBR	Degree=Cmp	32	advmod	_	_
32	complete	complete	ADJ	JJ	Degree=Pos	33	amod	_	_
33	theory	theory	NOUN	NN	Number=Sing	29	dobj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	structures	structure	NOUN	NNS	Number=Plur	34	pobj	_	_
37	in	in	ADP	IN	_	29	prep	_	_
38	question	question	NOUN	NN	Number=Sing	37	pobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# doc_id = 705
# sent_id = 1
# text = This paper studies the homotopy theory of parametrized spectrum objects in a model category from a global point of view.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	studies	study	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	homotopy	homotopy	NOUN	NN	Number=Sing	6	compound	_	_
6	theory	theory	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	parametrized	parametrized	ADJ	JJ	Degree=Pos	10	amod	_	_
9	spectrum	spectrum	NOUN	NN	Number=Sing	10	compound	_	_
10	objects	object	NOUN	NNS	Number=Plur	7	pobj	_	_
11	in	in	ADP	IN	_	3	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	model	model	NOUN	NN	Number=Sing	14	compound	_	_
14	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
15	from	from	ADP	IN	_	3	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	global	global	ADJ	JJ	Degree=Pos	18	amod	_	_
18	point	point	NOUN	NN	Number=Sing	15	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	view	view	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = More precisely, for a model category $ M $ satisfying suitable conditions, we construct a map of model categories $ TM to M $ , called the tangent bundle, whose fiber over an object in $ M $ is a model category for spectra in its over - category.
1	More	more	ADV	RBR	Degree=Cmp	2	advmod	_	_
2	precisely	precisely	ADV	RB	_	14	advmod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
4	for	for	ADP	IN	_	14	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	model	model	NOUN	NN	Number=Sing	7	compound	_	_
7	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
8	$ M $	$ m $	SYM	$	_	7	appos	_	_
9	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	pcomp	_	_
10	suitable	suitable	ADJ	JJ	Degree=Pos	11	amod	_	_
11	conditions	condition	NOUN	NNS	Number=Plur	9	dobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	map	map	NOUN	NN	Number=Sing	14	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	model	model	NOUN	NN	Number=Sing	19	compound	_	_
19	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	_
20	$ TM to M $	$ tm to m $	SYM	$	_	16	appos	_	_
21	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
22	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	16	acl	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	tangent	tangent	NOUN	NN	Number=Sing	25	compound	_	_
25	bundle	bundle	NOUN	NN	Number=Sing	22	oprd	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
27	whose	whose	DET	WP$	Poss=Yes	28	poss	_	_
28	fiber	fiber	NOUN	NN	Number=Sing	34	nsubj	_	_
29	over	over	ADP	IN	_	28	prep	_	_
30	an	an	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
31	object	object	NOUN	NN	Number=Sing	29	pobj	_	_
32	in	in	ADP	IN	_	31	prep	_	_
33	$ M $	$ m $	SYM	$	_	32	pobj	_	_
34	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	relcl	_	_
35	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
36	model	model	NOUN	NN	Number=Sing	37	compound	_	_
37	category	category	NOUN	NN	Number=Sing	34	attr	_	_
38	for	for	ADP	IN	_	37	prep	_	_
39	spectra	spectra	PROPN	NNP	Number=Sing	38	pobj	_	_
40	in	in	ADP	IN	_	34	prep	_	_
41	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	44	poss	_	_
42	over	over	ADP	IN	_	44	nmod	_	_
43	-	-	PUNCT	HYPH	PunctType=Dash	44	punct	_	_
44	category	category	NOUN	NN	Number=Sing	40	pobj	_	SpaceAfter=No
45	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 3
# text = We show that the tangent bundle is a relative model category and presents the $ infty $ - categorical tangent bundle, as constructed by Lurie.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	tangent	tangent	NOUN	NN	Number=Sing	6	compound	_	_
6	bundle	bundle	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	relative	relative	ADJ	JJ	Degree=Pos	10	amod	_	_
10	model	model	NOUN	NN	Number=Sing	11	compound	_	_
11	category	category	NOUN	NN	Number=Sing	7	attr	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
13	presents	present	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	conj	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
15	$ infty $	$ infty $	SYM	$	_	17	advmod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	categorical	categorical	ADJ	JJ	Degree=Pos	19	amod	_	_
18	tangent	tangent	NOUN	NN	Number=Sing	19	compound	_	_
19	bundle	bundle	NOUN	NN	Number=Sing	13	dobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
21	as	as	SCONJ	IN	_	22	mark	_	_
22	constructed	construct	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	advcl	_	_
23	by	by	ADP	IN	_	22	agent	_	_
24	Lurie	Lurie	PROPN	NNP	Number=Sing	23	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = Moreover, the tangent bundle $ TM $ inherits an enriched model structure from $ M $ .
1	Moreover	moreover	ADV	RB	_	5	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	tangent	tangent	NOUN	NN	Number=Sing	5	nsubj	_	_
5	bundle	bundle	VERB	VB	VerbForm=Inf	0	ROOT	_	_
6	$ TM $	$ tm $	SYM	$	_	7	nsubj	_	_
7	inherits	inherit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	enriched	enriched	ADJ	JJ	Degree=Pos	11	amod	_	_
10	model	model	NOUN	NN	Number=Sing	11	compound	_	_
11	structure	structure	NOUN	NN	Number=Sing	7	dobj	_	_
12	from	from	ADP	IN	_	7	prep	_	_
13	$ M $	$ m $	SYM	$	_	12	pobj	_	_
14	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = This additional structure is used in subsequent work to identify the tangent bundles of algebras over an operad and of enriched categories, but may be of independent interest.
1	This	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
2	additional	additional	ADJ	JJ	Degree=Pos	3	amod	_	_
3	structure	structure	NOUN	NN	Number=Sing	5	nsubjpass	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	auxpass	_	_
5	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	subsequent	subsequent	ADJ	JJ	Degree=Pos	8	amod	_	_
8	work	work	NOUN	NN	Number=Sing	6	pobj	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	identify	identify	VERB	VB	VerbForm=Inf	5	xcomp	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	tangent	tangent	ADJ	JJ	Degree=Pos	13	compound	_	_
13	bundles	bundle	NOUN	NNS	Number=Plur	10	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	algebras	algebra	NOUN	NNS	Number=Plur	14	pobj	_	_
16	over	over	ADP	IN	_	10	prep	_	_
17	an	an	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	operad	operad	NOUN	NN	Number=Sing	16	pobj	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	of	of	ADP	IN	_	18	prep	_	_
21	enriched	enriched	ADJ	JJ	Degree=Pos	22	amod	_	_
22	categories	category	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
24	but	but	CCONJ	CC	ConjType=Cmp	5	cc	_	_
25	may	may	AUX	MD	VerbForm=Fin	26	aux	_	_
26	be	be	AUX	VB	VerbForm=Inf	5	conj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	independent	independent	ADJ	JJ	Degree=Pos	29	amod	_	_
29	interest	interest	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 706
# sent_id = 1
# text = An extensive category can be defined as a category $ C $ with finite coproducts such that for each pair $ X $ , $ Y $ of objects in $ C $ , the canonical functor $ + : C/X times C/Y to C/(X + Y) $ is an equivalence.
1	An	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	extensive	extensive	ADJ	JJ	Degree=Pos	3	amod	_	_
3	category	category	NOUN	NN	Number=Sing	6	nsubjpass	_	_
4	can	can	AUX	MD	VerbForm=Fin	6	aux	_	_
5	be	be	AUX	VB	VerbForm=Inf	6	auxpass	_	_
6	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	as	as	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
10	$ C $	$ c $	SYM	$	_	9	appos	_	_
11	with	with	ADP	IN	_	6	prep	_	_
12	finite	finite	ADJ	JJ	Degree=Pos	13	amod	_	_
13	coproducts	coproduct	NOUN	NNS	Number=Plur	11	pobj	_	_
14	such	such	ADJ	JJ	Degree=Pos	15	amod	_	_
15	that	that	SCONJ	IN	_	31	mark	_	_
16	for	for	ADP	IN	_	31	prep	_	_
17	each	each	DET	DT	_	18	det	_	_
18	pair	pair	NOUN	NN	Number=Sing	16	pobj	_	_
19	$ X $	$ x $	SYM	$	_	16	pobj	_	_
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	$ Y $	$ y $	SYM	$	_	16	dep	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	objects	object	NOUN	NNS	Number=Plur	22	pobj	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	$ C $	$ c $	SYM	$	_	24	pobj	_	_
26	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
28	canonical	canonical	ADJ	JJ	Degree=Pos	29	amod	_	_
29	functor	functor	NOUN	NN	Number=Sing	31	nsubj	_	_
30	$ + : C/X times C/Y to C/(X + Y) $	$ + : c/x times c/y to c/(x + y) $	SYM	$	_	29	appos	_	_
31	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	advcl	_	_
32	an	an	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
33	equivalence	equivalence	NOUN	NN	Number=Sing	31	attr	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = We say that a category $ C $ with finite products is left coextensive if the dual canonical functor $ times : X/C times Y/C to (X times Y)/C $ is fully faithful.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	say	say	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	11	mark	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	11	nsubjpass	_	_
6	$ C $	$ c $	SYM	$	_	5	appos	_	_
7	with	with	ADP	IN	_	5	prep	_	_
8	finite	finite	ADJ	JJ	Degree=Pos	9	amod	_	_
9	products	product	NOUN	NNS	Number=Plur	7	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
12	coextensive	coextensive	ADJ	JJ	Degree=Pos	11	oprd	_	_
13	if	if	SCONJ	IN	_	19	mark	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
15	dual	dual	ADJ	JJ	Degree=Pos	17	amod	_	_
16	canonical	canonical	NOUN	NN	Number=Sing	17	compound	_	_
17	functor	functor	NOUN	NN	Number=Sing	19	nsubj	_	_
18	$ times : X/C times Y/C to (X times Y)/C $	$ times : x/c times y/c to (x times y)/c $	SYM	$	_	17	appos	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	advcl	_	_
20	fully	fully	ADV	RB	_	21	advmod	_	_
21	faithful	faithful	ADJ	JJ	Degree=Pos	19	acomp	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We then give a syntactical characterization of left coextensive varieties of universal algebras.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	syntactical	syntactical	ADJ	JJ	Degree=Pos	6	amod	_	_
6	characterization	characterization	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	left	left	ADJ	JJ	Degree=Pos	10	amod	_	_
9	coextensive	coextensive	ADJ	JJ	Degree=Pos	10	amod	_	_
10	varieties	variety	NOUN	NNS	Number=Plur	7	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	universal	universal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	algebras	algebra	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 707
# sent_id = 1
# text = We say a set - valued functor on a category is nearly representable if it is a quotient of a representable functor by a group of automorphisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	say	say	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
4	set	set	NOUN	NN	Number=Sing	6	npadvmod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	amod	_	_
7	functor	functor	NOUN	NN	Number=Sing	11	nsubj	_	_
8	on	on	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
12	nearly	nearly	ADV	RB	_	13	advmod	_	_
13	representable	representable	ADJ	JJ	Degree=Pos	11	acomp	_	_
14	if	if	SCONJ	IN	_	16	mark	_	_
15	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	16	nsubj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	advcl	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	quotient	quotient	NOUN	NN	Number=Sing	16	attr	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	representable	representable	ADJ	JJ	Degree=Pos	22	amod	_	_
22	functor	functor	NOUN	NN	Number=Sing	19	pobj	_	_
23	by	by	ADP	IN	_	16	prep	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
25	group	group	NOUN	NN	Number=Sing	23	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	automorphisms	automorphism	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = A distributor is a set - valued functor in two arguments, contravariant in one argument and covariant in the other.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	distributor	distributor	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
5	set	set	NOUN	NN	Number=Sing	7	npadvmod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
8	functor	functor	NOUN	NN	Number=Sing	3	attr	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	two	two	NUM	CD	NumType=Card	11	nummod	_	_
11	arguments	argument	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	contravariant	contravariant	ADJ	JJ	Degree=Pos	11	amod	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	one	one	NUM	CD	NumType=Card	16	nummod	_	_
16	argument	argument	NOUN	NN	Number=Sing	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	covariant	covariant	NOUN	NN	Number=Sing	16	conj	_	_
19	in	in	ADP	IN	_	16	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	other	other	ADJ	JJ	Degree=Pos	19	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = We say a distributor is slicewise nearly representable if it is nearly representable in either of the arguments whenever the other argument is fixed.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	say	say	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	distributor	distributor	NOUN	NN	Number=Sing	5	nsubj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	slicewise	slicewise	ADJ	JJR	Degree=Cmp	5	acomp	_	_
7	nearly	nearly	ADV	RB	_	8	advmod	_	_
8	representable	representable	ADJ	JJ	Degree=Pos	5	acomp	_	_
9	if	if	SCONJ	IN	_	11	mark	_	_
10	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	11	nsubj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	advcl	_	_
12	nearly	nearly	ADV	RB	_	13	advmod	_	_
13	representable	representable	ADJ	JJ	Degree=Pos	11	acomp	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	either	either	PRON	DT	_	14	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	arguments	argument	NOUN	NNS	Number=Plur	16	pobj	_	_
19	whenever	whenever	SCONJ	WRB	_	24	advmod	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	other	other	ADJ	JJ	Degree=Pos	22	amod	_	_
22	argument	argument	NOUN	NN	Number=Sing	24	nsubjpass	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	auxpass	_	_
24	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	advcl	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We consider such a distributor a weak analogue of adjunction.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	such	such	DET	PDT	_	5	predet	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	distributor	distributor	NOUN	NN	Number=Sing	8	nsubj	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	weak	weak	ADJ	JJ	Degree=Pos	8	amod	_	_
8	analogue	analogue	NOUN	NN	Number=Sing	2	ccomp	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	adjunction	adjunction	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = Under a finiteness assumption on the domain categories, we show that every slicewise nearly representable functor is a composite of two distributors, each of which may be considered as a weak analogue of (co - )reflective adjunction.
1	Under	under	ADP	IN	_	11	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	finiteness	finiteness	ADJ	JJ	Degree=Pos	4	amod	_	_
4	assumption	assumption	NOUN	NN	Number=Sing	1	pobj	_	_
5	on	on	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	domain	domain	NOUN	NN	Number=Sing	8	compound	_	_
8	categories	category	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
10	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	11	nsubj	_	_
11	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	that	that	SCONJ	IN	_	18	mark	_	_
13	every	every	DET	DT	_	17	det	_	_
14	slicewise	slicewise	ADJ	JJ	Degree=Pos	17	amod	_	_
15	nearly	nearly	ADV	RB	_	16	advmod	_	_
16	representable	representable	ADJ	JJ	Degree=Pos	17	amod	_	_
17	functor	functor	NOUN	NN	Number=Sing	18	nsubj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	ccomp	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	composite	composite	NOUN	NN	Number=Sing	18	attr	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	two	two	NUM	CD	NumType=Card	23	nummod	_	_
23	distributors	distributor	NOUN	NNS	Number=Plur	21	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
25	each	each	PRON	DT	_	30	nsubjpass	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	which	which	PRON	WDT	_	26	pobj	_	_
28	may	may	AUX	MD	VerbForm=Fin	30	aux	_	_
29	be	be	AUX	VB	VerbForm=Inf	30	auxpass	_	_
30	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	relcl	_	_
31	as	as	ADP	IN	_	30	prep	_	_
32	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
33	weak	weak	ADJ	JJ	Degree=Pos	34	amod	_	_
34	analogue	analogue	NOUN	NN	Number=Sing	31	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	35	punct	_	SpaceAfter=No
37	co	co	VERB	VB	VerbForm=Inf	41	nmod	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
39	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	37	punct	_	SpaceAfter=No
40	reflective	reflective	ADJ	JJ	Degree=Pos	41	amod	_	_
41	adjunction	adjunction	NOUN	NN	Number=Sing	35	pobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# doc_id = 708
# sent_id = 1
# text = Noetherian forms provide an abstract self - dual context in which one can establish homomorphism theorems (Noether isomorphism theorems and homological diagram lemmas) for groups, rings, modules and other group - like structures.
1	Noetherian	noetherian	ADJ	JJ	Degree=Pos	2	amod	_	_
2	forms	form	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
5	abstract	abstract	ADJ	JJ	Degree=Pos	9	amod	_	_
6	self	self	NOUN	NN	Number=Sing	8	npadvmod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	dual	dual	ADJ	JJ	Degree=Pos	9	amod	_	_
9	context	context	NOUN	NN	Number=Sing	3	dobj	_	_
10	in	in	ADP	IN	_	14	prep	_	_
11	which	which	PRON	WDT	_	10	pobj	_	_
12	one	one	PRON	PRP	PronType=Prs	14	nsubj	_	_
13	can	can	AUX	MD	VerbForm=Fin	14	aux	_	_
14	establish	establish	VERB	VB	VerbForm=Inf	9	relcl	_	_
15	homomorphism	homomorphism	NOUN	NN	Number=Sing	16	compound	_	_
16	theorems	theorem	NOUN	NNS	Number=Plur	14	dobj	_	_
17	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	20	punct	_	SpaceAfter=No
18	Noether	Noether	PROPN	NNP	Number=Sing	20	advmod	_	_
19	isomorphism	isomorphism	NOUN	NN	Number=Sing	20	compound	_	_
20	theorems	theorem	NOUN	NNS	Number=Plur	9	appos	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	homological	homological	ADJ	JJ	Degree=Pos	23	amod	_	_
23	diagram	diagram	NOUN	NN	Number=Sing	24	compound	_	_
24	lemmas	lemma	NOUN	NNS	Number=Plur	20	conj	_	SpaceAfter=No
25	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	24	punct	_	_
26	for	for	ADP	IN	_	20	prep	_	_
27	groups	group	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
29	rings	ring	NOUN	NNS	Number=Plur	27	conj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	29	punct	_	_
31	modules	module	NOUN	NNS	Number=Plur	29	conj	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	other	other	ADJ	JJ	Degree=Pos	37	amod	_	_
34	group	group	NOUN	NN	Number=Sing	36	npadvmod	_	_
35	-	-	PUNCT	HYPH	PunctType=Dash	36	punct	_	_
36	like	like	ADJ	JJ	Degree=Pos	37	amod	_	_
37	structures	structure	NOUN	NNS	Number=Plur	31	conj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = In fact, any semi - abelian category in the sense of Janelidze, Marki and Tholen, as well as any exact category in the sense of Grandis (and hence, in particular, any abelian category), can be seen as an example of a noetherian form.
1	In	in	ADP	IN	_	44	prep	_	_
2	fact	fact	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	44	punct	_	_
4	any	any	DET	DT	_	8	det	_	_
5	semi	semi	ADJ	JJ	Degree=Pos	8	amod	_	_
6	-	-	ADJ	JJ	Degree=Pos	8	amod	_	_
7	abelian	abelian	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	44	nsubjpass	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	sense	sense	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	Janelidze	Janelidze	PROPN	NNP	Number=Sing	12	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	Marki	Marki	PROPN	NNP	Number=Sing	13	conj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	Tholen	Tholen	PROPN	NNP	Number=Sing	15	conj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
19	as	as	ADV	RB	_	21	advmod	_	_
20	well	well	ADV	RB	Degree=Pos	21	advmod	_	_
21	as	as	ADP	IN	_	13	cc	_	_
22	any	any	DET	DT	_	24	det	_	_
23	exact	exact	ADJ	JJ	Degree=Pos	24	amod	_	_
24	category	category	NOUN	NN	Number=Sing	13	conj	_	_
25	in	in	ADP	IN	_	8	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	sense	sense	NOUN	NN	Number=Sing	25	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	Grandis	Grandis	PROPN	NNP	Number=Sing	28	pobj	_	_
30	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	29	punct	_	SpaceAfter=No
31	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
32	hence	hence	ADV	RB	_	25	conj	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
34	in	in	ADP	IN	_	39	prep	_	_
35	particular	particular	ADJ	JJ	Degree=Pos	34	amod	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	39	punct	_	_
37	any	any	DET	DT	_	39	det	_	_
38	abelian	abelian	ADJ	JJ	Degree=Pos	39	compound	_	_
39	category	category	NOUN	NN	Number=Sing	8	appos	_	SpaceAfter=No
40	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	39	punct	_	SpaceAfter=No
41	,	,	PUNCT	,	PunctType=Comm	44	punct	_	_
42	can	can	AUX	MD	VerbForm=Fin	44	aux	_	_
43	be	be	AUX	VB	VerbForm=Inf	44	auxpass	_	_
44	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
45	as	as	ADP	IN	_	44	prep	_	_
46	an	an	DET	DT	Definite=Ind|PronType=Art	47	det	_	_
47	example	example	NOUN	NN	Number=Sing	45	pobj	_	_
48	of	of	ADP	IN	_	47	prep	_	_
49	a	a	DET	DT	Definite=Ind|PronType=Art	51	det	_	_
50	noetherian	noetherian	ADJ	JJ	Degree=Pos	51	amod	_	_
51	form	form	NOUN	NN	Number=Sing	48	pobj	_	SpaceAfter=No
52	.	.	PUNCT	.	PunctType=Peri	44	punct	_	SpaceAfter=No

# sent_id = 3
# text = In this paper we generalize the notion of a biproduct of objects in an abelian category to a noetherian form and apply it do develop commutator theory in noetherian forms.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	generalize	generalize	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	notion	notion	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	biproduct	biproduct	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	objects	object	NOUN	NNS	Number=Plur	11	pobj	_	_
13	in	in	ADP	IN	_	10	prep	_	_
14	an	an	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	abelian	abelian	ADJ	JJ	Degree=Pos	16	amod	_	_
16	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
17	to	to	ADP	IN	_	10	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
19	noetherian	noetherian	ADJ	JJ	Degree=Pos	20	amod	_	_
20	form	form	NOUN	NN	Number=Sing	17	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
22	apply	apply	VERB	VB	VerbForm=Inf	5	conj	_	_
23	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	25	nsubj	_	_
24	do	do	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	25	aux	_	_
25	develop	develop	VERB	VB	VerbForm=Inf	22	ccomp	_	_
26	commutator	commutator	NOUN	NN	Number=Sing	27	compound	_	_
27	theory	theory	NOUN	NN	Number=Sing	25	dobj	_	_
28	in	in	ADP	IN	_	25	prep	_	_
29	noetherian	noetherian	ADJ	JJ	Degree=Pos	30	amod	_	_
30	forms	form	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = In the case of semi - abelian categories, biproducts give usual products of objects and our commutators coincide with the so - called Huq commutators (which in the case of groups are the usual commutators of subgroups).
1	In	in	ADP	IN	_	11	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	case	case	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	semi	semi	ADJ	JJ	Degree=Pos	8	amod	_	_
6	-	-	ADJ	JJ	Degree=Pos	8	amod	_	_
7	abelian	abelian	ADJ	JJ	Degree=Pos	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
10	biproducts	biproduct	NOUN	NNS	Number=Plur	11	nsubj	_	_
11	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	usual	usual	ADJ	JJ	Degree=Pos	13	amod	_	_
13	products	product	NOUN	NNS	Number=Plur	11	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	objects	object	NOUN	NNS	Number=Plur	14	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
17	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	18	poss	_	_
18	commutators	commutator	NOUN	NNS	Number=Plur	13	conj	_	_
19	coincide	coincide	VERB	VBP	Tense=Pres|VerbForm=Fin	11	dobj	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
22	so	so	ADV	RB	_	24	advmod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
25	Huq	Huq	PROPN	NNP	Number=Sing	26	compound	_	_
26	commutators	commutator	NOUN	NNS	Number=Plur	20	pobj	_	_
27	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	26	punct	_	SpaceAfter=No
28	which	which	PRON	WDT	_	34	nsubj	_	_
29	in	in	ADP	IN	_	34	prep	_	_
30	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
31	case	case	NOUN	NN	Number=Sing	29	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	groups	group	NOUN	NNS	Number=Plur	32	pobj	_	_
34	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	26	relcl	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
36	usual	usual	ADJ	JJ	Degree=Pos	37	amod	_	_
37	commutators	commutator	NOUN	NNS	Number=Plur	34	attr	_	_
38	of	of	ADP	IN	_	37	prep	_	_
39	subgroups	subgroup	NOUN	NNS	Number=Plur	38	pobj	_	SpaceAfter=No
40	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	26	punct	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 5
# text = This paper thus shows that the structure of a noetherian form allows for a self - dual approach to products and commutators in semi - abelian categories, similarly as has been known for homomorphism theorems.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	4	nsubj	_	_
3	thus	thus	ADV	RB	_	4	advmod	_	_
4	shows	show	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	12	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	structure	structure	NOUN	NN	Number=Sing	12	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	noetherian	noetherian	ADJ	JJ	Degree=Pos	11	amod	_	_
11	form	form	NOUN	NN	Number=Sing	8	pobj	_	_
12	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
13	for	for	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
15	self	self	NOUN	NN	Number=Sing	17	npadvmod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	dual	dual	ADJ	JJ	Degree=Pos	18	amod	_	_
18	approach	approach	NOUN	NN	Number=Sing	13	pobj	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	products	product	NOUN	NNS	Number=Plur	19	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	commutators	commutator	NOUN	NNS	Number=Plur	20	conj	_	_
23	in	in	ADP	IN	_	20	prep	_	_
24	semi	semi	ADJ	JJ	Degree=Pos	27	amod	_	_
25	-	-	ADJ	JJ	Degree=Pos	27	amod	_	_
26	abelian	abelian	ADJ	JJ	Degree=Pos	27	amod	_	_
27	categories	category	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
29	similarly	similarly	ADV	RB	_	33	advmod	_	_
30	as	as	SCONJ	IN	_	33	mark	_	_
31	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	33	aux	_	_
32	been	be	AUX	VBN	Tense=Past|VerbForm=Part	33	auxpass	_	_
33	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	advcl	_	_
34	for	for	ADP	IN	_	33	prep	_	_
35	homomorphism	homomorphism	NOUN	NN	Number=Sing	36	compound	_	_
36	theorems	theorem	NOUN	NNS	Number=Plur	34	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 709
# sent_id = 1
# text = Poly - bicategories generalise planar polycategories in the same way as bicategories generalise monoidal categories.
1	Poly	poly	ADJ	JJ	Degree=Pos	3	amod	_	_
2	-	-	PUNCT	HYPH	PunctType=Dash	3	punct	_	_
3	bicategories	bicategorie	NOUN	NNS	Number=Plur	6	compound	_	_
4	generalise	generalise	NOUN	NN	Number=Sing	6	compound	_	_
5	planar	planar	ADJ	JJ	Degree=Pos	6	amod	_	_
6	polycategories	polycategorie	NOUN	NNS	Number=Plur	0	ROOT	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
9	same	same	ADJ	JJ	Degree=Pos	10	amod	_	_
10	way	way	NOUN	NN	Number=Sing	7	pobj	_	_
11	as	as	SCONJ	IN	_	13	mark	_	_
12	bicategories	bicategorie	NOUN	NNS	Number=Plur	13	nsubj	_	_
13	generalise	generalise	VERB	VBP	Tense=Pres|VerbForm=Fin	6	advcl	_	_
14	monoidal	monoidal	ADJ	JJ	Degree=Pos	15	amod	_	_
15	categories	category	NOUN	NNS	Number=Plur	13	dobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = In a poly - bicategory, the existence of enough 2 - cells satisfying certain universal properties (representability) induces coherent algebraic structure on the 2 - graph of single - input, single - output 2 - cells.
1	In	in	ADP	IN	_	21	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
3	poly	poly	ADJ	JJ	Degree=Pos	5	amod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	bicategory	bicategory	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	existence	existence	NOUN	NN	Number=Sing	21	nsubj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	enough	enough	ADJ	JJ	Degree=Pos	13	amod	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	cells	cell	NOUN	NNS	Number=Plur	9	pobj	_	_
14	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	acl	_	_
15	certain	certain	ADJ	JJ	Degree=Pos	17	amod	_	_
16	universal	universal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	properties	property	NOUN	NNS	Number=Plur	14	dobj	_	_
18	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	17	punct	_	SpaceAfter=No
19	representability	representability	NOUN	NN	Number=Sing	17	appos	_	SpaceAfter=No
20	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	17	punct	_	_
21	induces	induce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
22	coherent	coherent	ADJ	JJ	Degree=Pos	24	amod	_	_
23	algebraic	algebraic	ADJ	JJ	Degree=Pos	24	amod	_	_
24	structure	structure	NOUN	NN	Number=Sing	21	dobj	_	_
25	on	on	ADP	IN	_	21	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
27	2	2	NUM	CD	NumType=Card	29	nummod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	graph	graph	NOUN	NN	Number=Sing	25	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	single	single	ADJ	JJ	Degree=Pos	33	amod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	input	input	ADJ	JJ	Degree=Pos	40	nmod	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	40	punct	_	_
35	single	single	ADJ	JJ	Degree=Pos	37	amod	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	output	output	NOUN	NN	Number=Sing	40	nmod	_	_
38	2	2	NUM	CD	NumType=Card	40	nummod	_	_
39	-	-	PUNCT	HYPH	PunctType=Dash	40	punct	_	_
40	cells	cell	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# sent_id = 3
# text = A special case of this theory was used by Hermida to produce a proof of strictification for bicategories.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	special	special	ADJ	JJ	Degree=Pos	3	amod	_	_
3	case	case	NOUN	NN	Number=Sing	8	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	theory	theory	NOUN	NN	Number=Sing	4	pobj	_	_
7	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	8	auxpass	_	_
8	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	by	by	ADP	IN	_	8	agent	_	_
10	Hermida	Hermida	PROPN	NNP	Number=Sing	9	pobj	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	produce	produce	VERB	VB	VerbForm=Inf	8	xcomp	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	proof	proof	NOUN	NN	Number=Sing	12	dobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	strictification	strictification	NOUN	NN	Number=Sing	15	pobj	_	_
17	for	for	ADP	IN	_	16	prep	_	_
18	bicategories	bicategorie	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 4
# text = No full strictification is possible for higher - dimensional categories, seemingly due to problems with 2 - cells that have degenerate boundaries; it was conjectured by Simpson that semi - strictification excluding units may be possible.
1	No	no	DET	DT	_	3	det	_	_
2	full	full	ADJ	JJ	Degree=Pos	3	amod	_	_
3	strictification	strictification	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	ccomp	_	_
5	possible	possible	ADJ	JJ	Degree=Pos	4	acomp	_	_
6	for	for	ADP	IN	_	4	prep	_	_
7	higher	high	ADJ	JJR	Degree=Cmp	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	dimensional	dimensional	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	seemingly	seemingly	ADV	RB	_	13	advmod	_	_
13	due	due	ADJ	JJ	Degree=Pos	10	amod	_	_
14	to	to	ADP	IN	_	13	prep	_	_
15	problems	problem	NOUN	NNS	Number=Plur	14	pobj	_	_
16	with	with	ADP	IN	_	15	prep	_	_
17	2	2	NUM	CD	NumType=Card	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	cells	cell	NOUN	NNS	Number=Plur	16	pobj	_	_
20	that	that	PRON	WDT	PronType=Rel	21	nsubj	_	_
21	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	19	relcl	_	_
22	degenerate	degenerate	ADJ	JJ	Degree=Pos	23	amod	_	_
23	boundaries	boundary	NOUN	NNS	Number=Plur	21	dobj	_	SpaceAfter=No
24	;	;	PUNCT	:	_	27	punct	_	_
25	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	27	nsubjpass	_	_
26	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	27	auxpass	_	_
27	conjectured	conjecture	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
28	by	by	ADP	IN	_	27	agent	_	_
29	Simpson	Simpson	PROPN	NNP	Number=Sing	28	pobj	_	_
30	that	that	SCONJ	IN	_	37	mark	_	_
31	semi	semi	ADJ	JJ	Degree=Pos	33	amod	_	_
32	-	-	ADJ	JJ	Degree=Pos	33	punct	_	_
33	strictification	strictification	NOUN	NN	Number=Sing	37	nsubj	_	_
34	excluding	exclude	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	33	prep	_	_
35	units	unit	NOUN	NNS	Number=Plur	34	pobj	_	_
36	may	may	AUX	MD	VerbForm=Fin	37	aux	_	_
37	be	be	AUX	VB	VerbForm=Inf	27	ccomp	_	_
38	possible	possible	ADJ	JJ	Degree=Pos	37	acomp	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	27	punct	_	SpaceAfter=No

# sent_id = 5
# text = We study poly - bicategories where 2 - cells with degenerate boundaries are barred, and show that we can recover the structure of a bicategory through a different construction of weak units.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	poly	poly	ADJ	JJ	Degree=Pos	5	amod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	bicategories	bicategorie	NOUN	NNS	Number=Plur	2	dobj	_	_
6	where	where	SCONJ	WRB	_	14	advmod	_	_
7	2	2	NUM	CD	NumType=Card	9	nummod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	cells	cell	NOUN	NNS	Number=Plur	14	nsubjpass	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	degenerate	degenerate	ADJ	JJ	Degree=Pos	12	amod	_	_
12	boundaries	boundary	NOUN	NNS	Number=Plur	10	pobj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	barred	bar	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	relcl	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
17	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	2	conj	_	_
18	that	that	SCONJ	IN	_	21	mark	_	_
19	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	21	nsubj	_	_
20	can	can	AUX	MD	VerbForm=Fin	21	aux	_	_
21	recover	recover	VERB	VB	VerbForm=Inf	17	ccomp	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
23	structure	structure	NOUN	NN	Number=Sing	21	dobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
26	bicategory	bicategory	NOUN	NN	Number=Sing	24	pobj	_	_
27	through	through	ADP	IN	_	21	prep	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
29	different	different	ADJ	JJ	Degree=Pos	30	amod	_	_
30	construction	construction	NOUN	NN	Number=Sing	27	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	weak	weak	ADJ	JJ	Degree=Pos	33	amod	_	_
33	units	unit	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = We prove that the existence of these units is equivalent to the existence of 1 - cells satisfying lower - dimensional universal properties, and study the relation between preservation of units and universal cells.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	9	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	existence	existence	NOUN	NN	Number=Sing	9	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	these	these	DET	DT	Number=Plur|PronType=Dem	8	det	_	_
8	units	unit	NOUN	NNS	Number=Plur	6	pobj	_	_
9	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
10	equivalent	equivalent	ADJ	JJ	Degree=Pos	9	acomp	_	_
11	to	to	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	existence	existence	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	1	1	NUM	CD	NumType=Card	17	nummod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	cells	cell	NOUN	NNS	Number=Plur	14	pobj	_	_
18	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	acl	_	_
19	lower	low	ADJ	JJR	Degree=Cmp	21	advmod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	dimensional	dimensional	ADJ	JJ	Degree=Pos	23	amod	_	_
22	universal	universal	ADJ	JJ	Degree=Pos	23	amod	_	_
23	properties	property	NOUN	NNS	Number=Plur	18	dobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
26	study	study	VERB	VB	VerbForm=Inf	9	conj	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	relation	relation	NOUN	NN	Number=Sing	26	dobj	_	_
29	between	between	ADP	IN	_	28	prep	_	_
30	preservation	preservation	NOUN	NN	Number=Sing	29	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	units	unit	NOUN	NNS	Number=Plur	31	pobj	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
34	universal	universal	ADJ	JJ	Degree=Pos	35	amod	_	_
35	cells	cell	NOUN	NNS	Number=Plur	32	conj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = Then, we introduce merge - bicategories, a variant of poly - bicategories with more composition operations, which admits a natural monoidal closed structure, giving access to higher morphisms.
1	Then	then	ADV	RB	PronType=Dem	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	merge	merge	NOUN	NN	Number=Sing	7	compound	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	bicategories	bicategorie	NOUN	NNS	Number=Plur	4	dobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	variant	variant	NOUN	NN	Number=Sing	4	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	poly	poly	ADJ	JJ	Degree=Pos	14	amod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	bicategories	bicategorie	NOUN	NNS	Number=Plur	11	pobj	_	_
15	with	with	ADP	IN	_	10	prep	_	_
16	more	more	ADJ	JJR	Degree=Cmp	18	amod	_	_
17	composition	composition	NOUN	NN	Number=Sing	18	compound	_	_
18	operations	operation	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	which	which	PRON	WDT	_	21	nsubj	_	_
21	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	relcl	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
23	natural	natural	ADJ	JJ	Degree=Pos	24	amod	_	_
24	monoidal	monoidal	NOUN	NN	Number=Sing	26	amod	_	_
25	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
26	structure	structure	NOUN	NN	Number=Sing	21	dobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
28	giving	give	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	advcl	_	_
29	access	access	NOUN	NN	Number=Sing	28	dobj	_	_
30	to	to	ADP	IN	_	29	prep	_	_
31	higher	high	ADJ	JJR	Degree=Cmp	32	amod	_	_
32	morphisms	morphism	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 8
# text = We derive equivalences between morphisms, transformations, and modifications of representable merge - bicategories and the corresponding notions for bicategories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	derive	derive	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	equivalences	equivalence	NOUN	NNS	Number=Plur	2	dobj	_	_
4	between	between	ADP	IN	_	3	prep	_	_
5	morphisms	morphism	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
7	transformations	transformation	NOUN	NNS	Number=Plur	5	conj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
10	modifications	modification	NOUN	NNS	Number=Plur	7	conj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	representable	representable	ADJ	JJ	Degree=Pos	15	amod	_	_
13	merge	merge	NOUN	NN	Number=Sing	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	bicategories	bicategorie	NOUN	NNS	Number=Plur	11	pobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	amod	_	_
19	notions	notion	NOUN	NNS	Number=Plur	5	conj	_	_
20	for	for	ADP	IN	_	19	prep	_	_
21	bicategories	bicategorie	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 9
# text = Finally, we prove a semi - strictification theorem for representable merge - bicategories with a choice of composites and units.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
6	semi	semi	ADJ	JJ	Degree=Pos	9	amod	_	_
7	-	-	ADJ	JJ	Degree=Pos	9	amod	_	_
8	strictification	strictification	NOUN	NN	Number=Sing	9	compound	_	_
9	theorem	theorem	NOUN	NN	Number=Sing	4	dobj	_	_
10	for	for	ADP	IN	_	9	prep	_	_
11	representable	representable	ADJ	JJ	Degree=Pos	14	amod	_	_
12	merge	merge	NOUN	NN	Number=Sing	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	bicategories	bicategorie	NOUN	NNS	Number=Plur	10	pobj	_	_
15	with	with	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	choice	choice	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	composites	composite	NOUN	NNS	Number=Plur	18	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	units	unit	NOUN	NNS	Number=Plur	19	conj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 710
# sent_id = 1
# text = We construct model category structures on various types of (marked) $ * $ - categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	model	model	NOUN	NN	Number=Sing	5	compound	_	_
4	category	category	NOUN	NN	Number=Sing	5	compound	_	_
5	structures	structure	NOUN	NNS	Number=Plur	2	dobj	_	_
6	on	on	ADP	IN	_	5	prep	_	_
7	various	various	ADJ	JJ	Degree=Pos	8	amod	_	_
8	types	type	NOUN	NNS	Number=Plur	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	9	punct	_	SpaceAfter=No
11	marked	marked	ADJ	JJ	Degree=Pos	15	amod	_	SpaceAfter=No
12	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	11	punct	_	_
13	$ * $	$ * $	SYM	$	_	15	nummod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	categories	category	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = These structures are used to present the infinity categories of (marked) $ * $ - categories obtained by inverting (marked) unitary equivalences.
1	These	these	DET	DT	Number=Plur|PronType=Dem	2	det	_	_
2	structures	structure	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	to	to	PART	TO	_	6	aux	_	_
6	present	present	VERB	VB	VerbForm=Inf	4	xcomp	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	infinity	infinity	NOUN	NN	Number=Sing	9	compound	_	_
9	categories	category	NOUN	NNS	Number=Plur	6	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	10	punct	_	SpaceAfter=No
12	marked	marked	ADJ	JJ	Degree=Pos	16	amod	_	SpaceAfter=No
13	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	16	punct	_	_
14	$ * $	$ * $	SYM	$	_	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
17	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	acl	_	_
18	by	by	ADP	IN	_	17	agent	_	_
19	inverting	inverting	NOUN	NN	Number=Sing	24	nmod	_	_
20	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
21	marked	marked	ADJ	JJ	Degree=Pos	24	amod	_	SpaceAfter=No
22	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	24	punct	_	_
23	unitary	unitary	ADJ	JJ	Degree=Pos	24	amod	_	_
24	equivalences	equivalence	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = We use this presentation to explicitly calculate the $ infty $ - categorical $ G $ - fixed points and $ G $ - orbits for $ G $ - equivariant (marked) $ * $ - categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	4	det	_	_
4	presentation	presentation	NOUN	NN	Number=Sing	2	dobj	_	_
5	to	to	PART	TO	_	7	aux	_	_
6	explicitly	explicitly	ADV	RB	_	7	advmod	_	_
7	calculate	calculate	VERB	VB	VerbForm=Inf	2	xcomp	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
9	$ infty $	$ infty $	SYM	$	_	11	advmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	categorical	categorical	ADJ	JJ	Degree=Pos	15	amod	_	_
12	$ G $	$ g $	SYM	$	_	14	advmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
15	points	point	NOUN	NNS	Number=Plur	7	dobj	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	$ G $	$ g $	SYM	$	_	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	orbits	orbit	NOUN	NNS	Number=Plur	15	conj	_	_
20	for	for	ADP	IN	_	19	prep	_	_
21	$ G $	$ g $	SYM	$	_	23	quantmod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	equivariant	equivariant	ADJ	JJ	Degree=Pos	29	amod	_	_
24	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	29	punct	_	SpaceAfter=No
25	marked	marked	ADJ	JJ	Degree=Pos	29	amod	_	SpaceAfter=No
26	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	29	punct	_	_
27	$ * $	$ * $	SYM	$	_	29	nummod	_	_
28	-	-	PUNCT	HYPH	PunctType=Dash	29	punct	_	_
29	categories	category	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 711
# sent_id = 1
# text = We construct a generalization of the operadic nerve, providing a translation between the equivariant simplicially enriched operadic world to the parametrized $ infty $ - categorical perspective.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	generalization	generalization	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	operadic	operadic	ADJ	JJ	Degree=Pos	8	amod	_	_
8	nerve	nerve	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
10	providing	provide	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	translation	translation	NOUN	NN	Number=Sing	10	dobj	_	_
13	between	between	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
15	equivariant	equivariant	ADJ	JJ	Degree=Pos	19	amod	_	_
16	simplicially	simplicially	ADV	RB	_	17	advmod	_	_
17	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
18	operadic	operadic	ADJ	JJ	Degree=Pos	19	amod	_	_
19	world	world	NOUN	NN	Number=Sing	13	pobj	_	_
20	to	to	ADP	IN	_	10	dative	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
22	parametrized	parametrized	ADJ	JJ	Degree=Pos	26	amod	_	_
23	$ infty $	$ infty $	SYM	$	_	25	advmod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	categorical	categorical	ADJ	JJ	Degree=Pos	26	amod	_	_
26	perspective	perspective	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This naturally factors through genuine equivariant operads, a model for ``equivariant operads with norms up to homotopy''.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	3	nsubj	_	_
2	naturally	naturally	ADV	RB	_	3	advmod	_	_
3	factors	factor	NOUN	NNS	Number=Plur	0	ROOT	_	_
4	through	through	ADP	IN	_	3	prep	_	_
5	genuine	genuine	ADJ	JJ	Degree=Pos	7	amod	_	_
6	equivariant	equivariant	ADJ	JJ	Degree=Pos	7	amod	_	_
7	operads	operad	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	model	model	NOUN	NN	Number=Sing	7	appos	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	15	punct	_	SpaceAfter=No
13	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	15	punct	_	SpaceAfter=No
14	equivariant	equivariant	ADJ	JJ	Degree=Pos	15	amod	_	_
15	operads	operad	NOUN	NNS	Number=Plur	11	pobj	_	_
16	with	with	ADP	IN	_	15	prep	_	_
17	norms	norm	NOUN	NNS	Number=Plur	16	pobj	_	_
18	up	up	ADP	IN	_	3	prep	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	homotopy	homotopy	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
21	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	3	punct	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = We introduce the notion of an op - fibration of genuine equivariant operads, extending Grothendieck op - fibrations, and characterize fibrant operads as the image of genuine equivariant symmetric monoidal categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
7	op	op	NOUN	NN	Number=Sing	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	fibration	fibration	NOUN	NN	Number=Sing	5	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	genuine	genuine	ADJ	JJ	Degree=Pos	13	amod	_	_
12	equivariant	equivariant	ADJ	JJ	Degree=Pos	13	amod	_	_
13	operads	operad	NOUN	NNS	Number=Plur	10	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
15	extending	extend	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
16	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	19	compound	_	_
17	op	op	NOUN	NN	Number=Sing	19	compound	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	fibrations	fibration	NOUN	NNS	Number=Plur	15	dobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
22	characterize	characterize	VERB	VB	VerbForm=Inf	2	conj	_	_
23	fibrant	fibrant	ADJ	JJ	Degree=Pos	24	amod	_	_
24	operads	operad	NOUN	NNS	Number=Plur	22	dobj	_	_
25	as	as	ADP	IN	_	22	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	image	image	NOUN	NN	Number=Sing	25	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	genuine	genuine	ADJ	JJ	Degree=Pos	33	amod	_	_
30	equivariant	equivariant	ADJ	JJ	Degree=Pos	33	amod	_	_
31	symmetric	symmetric	ADJ	JJ	Degree=Pos	33	amod	_	_
32	monoidal	monoidal	ADJ	JJ	Degree=Pos	33	amod	_	_
33	categories	category	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = Moreover, we show that under the operadic nerve, this image is sent to $ G $ - symmetric monoidal $ G $ - $ infty $ - categories.
1	Moreover	moreover	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	14	mark	_	_
6	under	under	ADP	IN	_	14	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	operadic	operadic	ADJ	JJ	Degree=Pos	9	amod	_	_
9	nerve	nerve	NOUN	NN	Number=Sing	6	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
11	this	this	DET	DT	Number=Sing|PronType=Dem	12	det	_	_
12	image	image	NOUN	NN	Number=Sing	14	nsubjpass	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	auxpass	_	_
14	sent	send	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	ccomp	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	$ G $	$ g $	SYM	$	_	18	quantmod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	symmetric	symmetric	ADJ	JJ	Degree=Pos	19	amod	_	_
19	monoidal	monoidal	NOUN	NN	Number=Sing	15	pobj	_	_
20	$ G $	$ g $	SYM	$	_	24	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
22	$ infty $	$ infty $	SYM	$	_	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	categories	category	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = Finally, we produce a functor comparing the notion of algebra over an operad in each of these two contexts.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	produce	produce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	functor	functor	NOUN	NN	Number=Sing	4	dobj	_	_
7	comparing	compare	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	acl	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	notion	notion	NOUN	NN	Number=Sing	7	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	algebra	algebra	NOUN	NN	Number=Sing	10	pobj	_	_
12	over	over	ADP	IN	_	7	prep	_	_
13	an	an	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	operad	operad	NOUN	NN	Number=Sing	12	pobj	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	each	each	PRON	DT	_	15	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	these	these	DET	DT	Number=Plur|PronType=Dem	20	det	_	_
19	two	two	NUM	CD	NumType=Card	20	nummod	_	_
20	contexts	context	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 712
# sent_id = 1
# text = Let $ E $ be a topos.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ E $	$ e $	SYM	$	_	3	nsubj	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	topos	topos	NOUN	NN	Number=Sing	3	attr	_	SpaceAfter=No
6	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = If $ l $ is a level of $ E $ with monic skeleta then it makes sense to consider the objects in $ E $ that have $ l $ - skeletal boundaries.
1	If	if	SCONJ	IN	_	3	mark	_	_
2	$ l $	$ l $	SYM	$	_	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	advcl	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	level	level	NOUN	NN	Number=Sing	3	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	$ E $	$ e $	SYM	$	_	6	pobj	_	_
8	with	with	ADP	IN	_	5	prep	_	_
9	monic	monic	ADJ	JJ	Degree=Pos	10	amod	_	_
10	skeleta	skeleta	NOUN	NN	Number=Sing	8	pobj	_	_
11	then	then	ADV	RB	PronType=Dem	13	advmod	_	_
12	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	13	nsubj	_	_
13	makes	make	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
14	sense	sense	NOUN	NN	Number=Sing	13	dobj	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	consider	consider	VERB	VB	VerbForm=Inf	13	xcomp	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	objects	object	NOUN	NNS	Number=Plur	16	dobj	_	_
19	in	in	ADP	IN	_	18	prep	_	_
20	$ E $	$ e $	SYM	$	_	19	pobj	_	_
21	that	that	PRON	WDT	PronType=Rel	22	nsubj	_	_
22	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	18	relcl	_	_
23	$ l $	$ l $	SYM	$	_	25	quantmod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	skeletal	skeletal	ADJ	JJ	Degree=Pos	26	amod	_	_
26	boundaries	boundary	NOUN	NNS	Number=Plur	22	dobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	13	punct	_	SpaceAfter=No

# sent_id = 3
# text = In particular, if $ p : E to S $ is a pre - cohesive geometric morphism then its centre (that may be called level 0) has monic skeleta.
1	In	in	ADP	IN	_	6	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
4	if	if	SCONJ	IN	_	6	mark	_	_
5	$ p : E to S $	$ p : e to s $	SYM	$	_	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
8	pre	pre	ADJ	JJ	Degree=Pos	10	advmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	cohesive	cohesive	ADJ	JJ	Degree=Pos	12	amod	_	_
11	geometric	geometric	ADJ	JJ	Degree=Pos	12	amod	_	_
12	morphism	morphism	NOUN	NN	Number=Sing	6	attr	_	_
13	then	then	ADV	RB	PronType=Dem	15	advmod	_	_
14	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	15	poss	_	_
15	centre	centre	NOUN	NN	Number=Sing	24	nsubj	_	_
16	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	20	punct	_	SpaceAfter=No
17	that	that	PRON	WDT	PronType=Rel	20	nsubjpass	_	_
18	may	may	AUX	MD	VerbForm=Fin	20	aux	_	_
19	be	be	AUX	VB	VerbForm=Inf	20	auxpass	_	_
20	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	parataxis	_	_
21	level	level	NOUN	NN	Number=Sing	20	oprd	_	_
22	0	0	NUM	CD	NumType=Card	20	oprd	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	15	punct	_	_
24	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	relcl	_	_
25	monic	monic	ADJ	JJ	Degree=Pos	26	amod	_	_
26	skeleta	skeleta	NOUN	NN	Number=Sing	24	dobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = Let level 1 be the Aufhebung of level 0.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	level	level	NOUN	NN	Number=Sing	4	nsubj	_	_
3	1	1	NUM	CD	NumType=Card	2	nummod	_	_
4	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	Aufhebung	Aufhebung	PROPN	NNP	Number=Sing	4	attr	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	level	level	NOUN	NN	Number=Sing	7	pobj	_	_
9	0	0	NUM	CD	NumType=Card	8	nummod	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 5
# text = We show that if level 1 has monic skeleta then the quotients of 0 - separated objects with 0 - skeletal boundaries are 1 - skeletal.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	23	mark	_	_
4	if	if	SCONJ	IN	_	7	mark	_	_
5	level	level	NOUN	NN	Number=Sing	7	nsubj	_	_
6	1	1	NUM	CD	NumType=Card	5	nummod	_	_
7	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	advcl	_	_
8	monic	monic	ADJ	JJ	Degree=Pos	9	amod	_	_
9	skeleta	skeleta	NOUN	NN	Number=Sing	7	dobj	_	_
10	then	then	ADV	RB	PronType=Dem	23	advmod	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	quotients	quotient	NOUN	NNS	Number=Plur	23	nsubj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	0	0	NUM	CD	NumType=Card	17	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	separated	separate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	amod	_	_
17	objects	object	NOUN	NNS	Number=Plur	13	pobj	_	_
18	with	with	ADP	IN	_	17	prep	_	_
19	0	0	NUM	CD	NumType=Card	22	nummod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	skeletal	skeletal	ADJ	JJ	Degree=Pos	22	amod	_	_
22	boundaries	boundary	NOUN	NNS	Number=Plur	18	pobj	_	_
23	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
24	1	1	NUM	CD	NumType=Card	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	skeletal	skeletal	ADJ	JJ	Degree=Pos	23	acomp	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = We also prove that in several examples (such as the classifier of non - trivial Boolean algebras, simplicial sets and the classifier of strictly bipointed objects) every 1 - skeletal object is of that form.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	35	mark	_	_
5	in	in	ADP	IN	_	35	prep	_	_
6	several	several	ADJ	JJ	Degree=Pos	7	amod	_	_
7	examples	example	NOUN	NNS	Number=Plur	5	pobj	_	_
8	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	7	punct	_	SpaceAfter=No
9	such	such	ADJ	JJ	Degree=Pos	10	amod	_	_
10	as	as	ADP	IN	_	7	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	classifier	classifier	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	non	non	ADJ	JJ	Degree=Pos	16	amod	_	_
15	-	-	ADJ	JJ	Degree=Pos	16	punct	_	_
16	trivial	trivial	ADJ	JJ	Degree=Pos	18	amod	_	_
17	Boolean	boolean	ADJ	JJ	Degree=Pos	18	amod	_	_
18	algebras	algebra	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	simplicial	simplicial	ADJ	JJ	Degree=Pos	21	amod	_	_
21	sets	set	NOUN	NNS	Number=Plur	18	conj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	classifier	classifier	NOUN	NN	Number=Sing	21	conj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	strictly	strictly	ADV	RB	_	27	advmod	_	_
27	bipointed	bipointe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	amod	_	_
28	objects	object	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
29	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	35	punct	_	_
30	every	every	DET	DT	_	34	det	_	_
31	1	1	NUM	CD	NumType=Card	33	nummod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	skeletal	skeletal	ADJ	JJ	Degree=Pos	34	amod	_	_
34	object	object	NOUN	NN	Number=Sing	35	nsubj	_	_
35	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	that	that	DET	DT	Number=Sing|PronType=Dem	38	det	_	_
38	form	form	NOUN	NN	Number=Sing	36	pobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 713
# sent_id = 1
# text = In this work we define a 2 - dimensional analogue of extranatural transformation and use these to characterise codescent objects.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	work	work	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
7	2	2	NUM	CD	NumType=Card	9	advmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	dimensional	dimensional	ADJ	JJ	Degree=Pos	10	amod	_	_
10	analogue	analogue	NOUN	NN	Number=Sing	5	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	extranatural	extranatural	ADJ	JJ	Degree=Pos	13	amod	_	_
13	transformation	transformation	NOUN	NN	Number=Sing	11	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
15	use	use	VERB	VB	VerbForm=Inf	5	conj	_	_
16	these	these	PRON	DT	Number=Plur|PronType=Dem	15	dobj	_	_
17	to	to	PART	TO	_	18	aux	_	_
18	characterise	characterise	VERB	VB	VerbForm=Inf	15	xcomp	_	_
19	codescent	codescent	NOUN	NN	Number=Sing	20	compound	_	_
20	objects	object	NOUN	NNS	Number=Plur	18	dobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = They will be seen as universal objects amongst pseudo - extranatural transformations in a similar manner in which coends are universal objects amongst extranatural transformations.
1	They	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	4	nsubjpass	_	_
2	will	will	AUX	MD	VerbForm=Fin	4	aux	_	_
3	be	be	AUX	VB	VerbForm=Inf	4	auxpass	_	_
4	seen	see	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	as	as	ADP	IN	_	4	prep	_	_
6	universal	universal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	objects	object	NOUN	NNS	Number=Plur	5	pobj	_	_
8	amongst	amongst	ADP	IN	_	7	prep	_	_
9	pseudo	pseudo	NOUN	NN	Number=Sing	11	npadvmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	extranatural	extranatural	ADJ	JJ	Degree=Pos	12	amod	_	_
12	transformations	transformation	NOUN	NNS	Number=Plur	8	pobj	_	_
13	in	in	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	similar	similar	ADJ	JJ	Degree=Pos	16	amod	_	_
16	manner	manner	NOUN	NN	Number=Sing	13	pobj	_	_
17	in	in	ADP	IN	_	20	prep	_	_
18	which	which	PRON	WDT	_	17	pobj	_	_
19	coends	coend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	nsubj	_	_
20	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	16	relcl	_	_
21	universal	universal	ADJ	JJ	Degree=Pos	22	amod	_	_
22	objects	object	NOUN	NNS	Number=Plur	20	attr	_	_
23	amongst	amongst	ADP	IN	_	22	prep	_	_
24	extranatural	extranatural	ADJ	JJ	Degree=Pos	25	amod	_	_
25	transformations	transformation	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 3
# text = Some composition lemmas concerning these transformations are introduced and a Fubini theorem for codescent objects is proven using the universal characterisation description.
1	Some	some	DET	DT	_	3	det	_	_
2	composition	composition	NOUN	NN	Number=Sing	3	compound	_	_
3	lemmas	lemma	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
4	concerning	concern	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	prep	_	_
5	these	these	DET	DT	Number=Plur|PronType=Dem	6	det	_	_
6	transformations	transformation	NOUN	NNS	Number=Plur	4	pobj	_	_
7	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	Fubini	Fubini	PROPN	NNP	Number=Sing	12	compound	_	_
12	theorem	theorem	ADJ	JJ	Degree=Pos	17	nsubjpass	_	_
13	for	for	ADP	IN	_	12	prep	_	_
14	codescent	codescent	NOUN	NN	Number=Sing	15	compound	_	_
15	objects	object	NOUN	NNS	Number=Plur	13	pobj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	auxpass	_	_
17	proven	prove	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	conj	_	_
18	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	xcomp	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
20	universal	universal	ADJ	JJ	Degree=Pos	22	amod	_	_
21	characterisation	characterisation	NOUN	NN	Number=Sing	22	compound	_	_
22	description	description	NOUN	NN	Number=Sing	18	dobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# doc_id = 714
# sent_id = 1
# text = Given 2 - categories $ C $ and $ D $ , let Lax $ (C, D) $ denote the 2 - category of lax functors, lax natural transformations and modifications, and $ [C, D]_lnt $ its full sub - 2 - category of (strict) 2 - functors.
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	prep	_	_
2	2	2	NUM	CD	NumType=Card	4	nummod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	categories	category	NOUN	NNS	Number=Plur	1	pobj	_	_
5	$ C $	$ c $	SYM	$	_	4	appos	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
7	$ D $	$ d $	SYM	$	_	1	advmod	_	_
8	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
9	let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
10	Lax	Lax	PROPN	NNP	Number=Sing	12	nsubj	_	_
11	$ (C, D) $	$ (c, d) $	SYM	$	_	12	nsubj	_	_
12	denote	denote	VERB	VBD	Tense=Past|VerbForm=Fin	9	ccomp	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
14	2	2	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	category	category	NOUN	NN	Number=Sing	12	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	lax	lax	ADJ	JJ	Degree=Pos	19	amod	_	_
19	functors	functor	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
21	lax	lax	ADJ	JJ	Degree=Pos	23	amod	_	_
22	natural	natural	ADJ	JJ	Degree=Pos	23	amod	_	_
23	transformations	transformation	NOUN	NNS	Number=Plur	16	conj	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	modifications	modification	NOUN	NNS	Number=Plur	23	conj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
28	$ [C, D]_lnt $	$ [c, d]_lnt $	SYM	$	_	35	poss	_	_
29	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	35	poss	_	_
30	full	full	ADJ	JJ	Degree=Pos	35	amod	_	_
31	sub	sub	NOUN	NN	Number=Sing	35	nmod	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
33	2	2	NUM	CD	NumType=Card	35	nummod	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	category	category	NOUN	NN	Number=Sing	12	conj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	42	punct	_	SpaceAfter=No
38	strict	strict	ADJ	JJ	Degree=Pos	42	amod	_	SpaceAfter=No
39	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	42	punct	_	_
40	2	2	NUM	CD	NumType=Card	42	nummod	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	functors	functor	NOUN	NNS	Number=Plur	36	pobj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 2
# text = We give two isomorphic constructions of a 2 - category $ C boxtimes D $ satisfying Lax $ (C, Lax(D, E)) cong [C boxtimes D, E}_lnt $ , hence generalising the case of the free distributive law $ 1 boxtimes 1 $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	two	two	NUM	CD	NumType=Card	5	nummod	_	_
4	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	5	amod	_	_
5	constructions	construction	NOUN	NNS	Number=Plur	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	2	2	NUM	CD	NumType=Card	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	category	category	NOUN	NN	Number=Sing	11	compound	_	_
11	$ C boxtimes D $	$ c boxtimes d $	SYM	$	_	6	pobj	_	_
12	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
13	Lax	Lax	PROPN	NNP	Number=Sing	14	compound	_	_
14	$ (C, Lax(D, E)) cong [C boxtimes D, E}_lnt $	$ (c, lax(d, e)) cong [c boxtimes d, e}_lnt $	SYM	$	_	12	dobj	_	_
15	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
16	hence	hence	ADV	RB	_	17	advmod	_	_
17	generalising	generalise	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	advcl	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	case	case	NOUN	NN	Number=Sing	17	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
22	free	free	ADJ	JJ	Degree=Pos	23	amod	_	_
23	distributive	distributive	ADJ	JJ	Degree=Pos	24	amod	_	_
24	law	law	NOUN	NN	Number=Sing	20	pobj	_	_
25	$ 1 boxtimes 1 $	$ 1 boxtimes 1 $	SYM	$	_	24	appos	_	_
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also discuss dual constructions.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	discuss	discuss	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	dual	dual	ADJ	JJ	Degree=Pos	5	amod	_	_
5	constructions	construction	NOUN	NNS	Number=Plur	3	dobj	_	SpaceAfter=No
6	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 715
# sent_id = 1
# text = A Lie 2 - group $ G $ is a category internal to the category of Lie groups.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	Lie	lie	NOUN	NN	Number=Sing	7	nsubj	_	_
3	2	2	NUM	CD	NumType=Card	5	nummod	_	_
4	-	-	PUNCT	HYPH	PunctType=Dash	5	punct	_	_
5	group	group	NOUN	NN	Number=Sing	2	npadvmod	_	_
6	$ G $	$ g $	SYM	$	_	2	appos	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	category	category	NOUN	NN	Number=Sing	7	attr	_	_
10	internal	internal	ADJ	JJ	Degree=Pos	9	amod	_	_
11	to	to	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	Lie	lie	NOUN	NN	Number=Sing	16	compound	_	_
16	groups	group	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 2
# text = Consequently it is a monoidal category and a Lie groupoid.
1	Consequently	consequently	ADV	RB	_	3	advmod	_	_
2	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	monoidal	monoidal	ADJ	JJ	Degree=Pos	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	3	attr	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	Lie	lie	NOUN	NN	Number=Sing	10	compound	_	_
10	groupoid	groupoid	NOUN	NN	Number=Sing	6	conj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = The Lie groupoid structure on $ G $ gives rise to the Lie 2 - algebra $ X(G) $ of multiplicative vector fields.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	Lie	lie	NOUN	NN	Number=Sing	4	compound	_	_
3	groupoid	groupoid	NOUN	NN	Number=Sing	4	compound	_	_
4	structure	structure	NOUN	NN	Number=Sing	7	nsubj	_	_
5	on	on	ADP	IN	_	4	prep	_	_
6	$ G $	$ g $	SYM	$	_	5	pobj	_	_
7	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	rise	rise	VERB	VB	VerbForm=Inf	7	dobj	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	Lie	lie	NOUN	NN	Number=Sing	9	pobj	_	_
12	2	2	NUM	CD	NumType=Card	14	nummod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	algebra	algebra	PROPN	NNP	Number=Sing	15	nmod	_	_
15	$ X(G) $	$ x(g) $	SYM	$	_	7	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	multiplicative	multiplicative	ADJ	JJ	Degree=Pos	19	amod	_	_
18	vector	vector	NOUN	NN	Number=Sing	19	compound	_	_
19	fields	field	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = The monoidal structure on $ G $ gives rise to a left action of the 2 - group $ G $ on the Lie groupoid $ G $ , hence to an action of $ G $ on the Lie 2 - algebra $ X(G) $ .
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	monoidal	monoidal	ADJ	JJ	Degree=Pos	3	amod	_	_
3	structure	structure	NOUN	NN	Number=Sing	6	nsubj	_	_
4	on	on	ADP	IN	_	3	prep	_	_
5	$ G $	$ g $	SYM	$	_	4	pobj	_	_
6	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	rise	rise	VERB	VB	VerbForm=Inf	6	dobj	_	_
8	to	to	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	left	left	ADJ	JJ	Degree=Pos	11	amod	_	_
11	action	action	NOUN	NN	Number=Sing	8	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
14	2	2	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	group	group	NOUN	NN	Number=Sing	12	pobj	_	_
17	$ G $	$ g $	SYM	$	_	16	appos	_	_
18	on	on	ADP	IN	_	7	prep	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	Lie	lie	NOUN	NN	Number=Sing	18	pobj	_	_
21	groupoid	groupoid	VERB	VB	VerbForm=Inf	6	dobj	_	_
22	$ G $	$ g $	SYM	$	_	21	dobj	_	_
23	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
24	hence	hence	ADV	RB	_	25	advmod	_	_
25	to	to	ADP	IN	_	6	prep	_	_
26	an	an	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	action	action	NOUN	NN	Number=Sing	25	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	$ G $	$ g $	SYM	$	_	28	pobj	_	_
30	on	on	ADP	IN	_	27	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	Lie	lie	NOUN	NN	Number=Sing	36	nmod	_	_
33	2	2	NUM	CD	NumType=Card	35	nummod	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	algebra	algebra	PROPN	NNP	Number=Sing	36	nmod	_	_
36	$ X(G) $	$ x(g) $	SYM	$	_	30	pobj	_	_
37	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = As a result we get the Lie 2 - algebra $ X(G)^G $ of left - invariant multiplicative vector fields.
1	As	as	ADP	IN	_	5	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	result	result	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	get	get	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	Lie	lie	NOUN	NN	Number=Sing	5	dobj	_	_
8	2	2	NUM	CD	NumType=Card	10	nummod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	algebra	algebra	NOUN	NN	Number=Sing	5	npadvmod	_	_
11	$ X(G)^G $	$ x(g)^g $	SYM	$	_	10	appos	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	left	left	ADJ	JJ	Degree=Pos	15	amod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	invariant	invariant	ADJ	JJ	Degree=Pos	18	amod	_	_
16	multiplicative	multiplicative	ADJ	JJ	Degree=Pos	17	amod	_	_
17	vector	vector	NOUN	NN	Number=Sing	18	compound	_	_
18	fields	field	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 6
# text = On the other hand there is a well - known construction that associates a Lie 2 - algebra $ g $ to a Lie 2 - group $ G $ : apply the functor $ Lie : LieGp - > LieAlg $ to the structure maps of the category $ G $ .
1	On	on	ADP	IN	_	6	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	other	other	ADJ	JJ	Degree=Pos	4	amod	_	_
4	hand	hand	NOUN	NN	Number=Sing	1	pobj	_	_
5	there	there	PRON	EX	_	6	expl	_	_
6	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	well	well	ADV	RB	Degree=Pos	10	advmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	amod	_	_
11	construction	construction	NOUN	NN	Number=Sing	6	attr	_	_
12	that	that	PRON	WDT	PronType=Rel	13	nsubj	_	_
13	associates	associate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	relcl	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	Lie	lie	NOUN	NN	Number=Sing	13	dobj	_	_
16	2	2	NUM	CD	NumType=Card	18	nummod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	algebra	algebra	NOUN	NN	Number=Sing	19	nmod	_	_
19	$ g $	$ g $	SYM	$	_	15	nummod	_	_
20	to	to	ADP	IN	_	13	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	Lie	lie	NOUN	NN	Number=Sing	20	pobj	_	_
23	2	2	NUM	CD	NumType=Card	25	nummod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	group	group	NOUN	NN	Number=Sing	20	pobj	_	_
26	$ G $	$ g $	SYM	$	_	25	appos	_	_
27	:	:	PUNCT	:	_	6	punct	_	_
28	apply	apply	VERB	VB	VerbForm=Inf	6	conj	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	functor	functor	NOUN	NN	Number=Sing	28	dobj	_	_
31	$ Lie : LieGp - > LieAlg $	$ lie : liegp - > liealg $	SYM	$	_	28	dep	_	_
32	to	to	ADP	IN	_	28	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
34	structure	structure	NOUN	NN	Number=Sing	35	compound	_	_
35	maps	map	NOUN	NNS	Number=Plur	32	pobj	_	_
36	of	of	ADP	IN	_	35	prep	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	category	category	NOUN	NN	Number=Sing	36	pobj	_	_
39	$ G $	$ g $	SYM	$	_	28	dep	_	_
40	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 7
# text = We show that the Lie 2 - algebra $ g $ is isomorphic to the Lie 2 - algebra $ X(G)^G $ of left invariant multiplicative vector fields.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	10	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
5	Lie	Lie	PROPN	NNP	Number=Sing	9	nmod	_	_
6	2	2	NUM	CD	NumType=Card	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	algebra	algebra	NOUN	NN	Number=Sing	9	nmod	_	_
9	$ g $	$ g $	SYM	$	_	10	nsubj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
11	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	10	acomp	_	_
12	to	to	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	Lie	lie	NOUN	NN	Number=Sing	12	pobj	_	_
15	2	2	NUM	CD	NumType=Card	17	nummod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	algebra	algebra	NOUN	NN	Number=Sing	10	npadvmod	_	_
18	$ X(G)^G $	$ x(g)^g $	SYM	$	_	17	appos	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	left	left	ADJ	JJ	Degree=Pos	24	amod	_	_
21	invariant	invariant	ADJ	JJ	Degree=Pos	24	amod	_	_
22	multiplicative	multiplicative	ADJ	JJ	Degree=Pos	23	amod	_	_
23	vector	vector	NOUN	NN	Number=Sing	24	compound	_	_
24	fields	field	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 716
# sent_id = 1
# text = This paper studies a category $ X $ with an endofunctor $ T : X to X $ .
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	studies	study	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	3	dobj	_	_
6	$ X $	$ x $	SYM	$	_	5	appos	_	_
7	with	with	ADP	IN	_	3	prep	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	endofunctor	endofunctor	NOUN	NN	Number=Sing	7	pobj	_	_
10	$ T : X to X $	$ t : x to x $	SYM	$	_	9	appos	_	_
11	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = A $ T $ - algebra is given by a morphism $ Tx to x in X $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
2	$ T $	$ t $	SYM	$	_	4	compound	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	algebra	algebra	PROPN	NNP	Number=Sing	6	nsubjpass	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	by	by	ADP	IN	_	6	agent	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	morphism	morphism	NOUN	NN	Number=Sing	7	pobj	_	_
10	$ Tx to x in X $	$ tx to x in x $	SYM	$	_	9	appos	_	_
11	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = We examine the related questions of when $ T $ freely generates a triple (or monad) on $ X $ ; when an object $ x $ in $ X $ freely generates a $ T $ - algebra; and when the category of $ T $ - algebras has coequalizers and other colimits.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	examine	examine	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	related	related	ADJ	JJ	Degree=Pos	5	amod	_	_
5	questions	question	NOUN	NNS	Number=Plur	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	when	when	SCONJ	WRB	_	10	advmod	_	_
8	$ T $	$ t $	SYM	$	_	10	nsubj	_	_
9	freely	freely	ADV	RB	_	10	advmod	_	_
10	generates	generate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	pcomp	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
12	triple	triple	ADJ	JJ	Degree=Pos	15	amod	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
14	or	or	CCONJ	CC	ConjType=Cmp	12	cc	_	_
15	monad	monad	NOUN	NNS	Number=Plur	10	dobj	_	SpaceAfter=No
16	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	10	punct	_	_
17	on	on	ADP	IN	_	10	prep	_	_
18	$ X $	$ x $	SYM	$	_	17	pobj	_	_
19	;	;	PUNCT	:	_	5	punct	_	_
20	when	when	SCONJ	WRB	_	27	advmod	_	_
21	an	an	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
22	object	object	NOUN	NN	Number=Sing	27	nsubj	_	_
23	$ x $	$ x $	SYM	$	_	22	prep	_	_
24	in	in	ADP	IN	_	22	prep	_	_
25	$ X $	$ x $	SYM	$	_	27	nsubj	_	_
26	freely	freely	ADV	RB	_	27	advmod	_	_
27	generates	generate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	advcl	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
29	$ T $	$ t $	SYM	$	_	31	nmod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	algebra	algebra	NOUN	NN	Number=Sing	27	dobj	_	SpaceAfter=No
32	;	;	PUNCT	:	_	27	punct	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
34	when	when	SCONJ	WRB	_	41	advmod	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	category	category	NOUN	NN	Number=Sing	41	nsubj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	$ T $	$ t $	SYM	$	_	40	compound	_	_
39	-	-	PUNCT	HYPH	PunctType=Dash	40	punct	_	_
40	algebras	algebras	PROPN	NNP	Number=Sing	37	pobj	_	_
41	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	conj	_	_
42	coequalizers	coequalizer	NOUN	NNS	Number=Plur	41	dobj	_	_
43	and	and	CCONJ	CC	ConjType=Cmp	42	cc	_	_
44	other	other	ADJ	JJ	Degree=Pos	45	amod	_	_
45	colimits	colimit	NOUN	NNS	Number=Plur	42	conj	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = The paper defines a category of `` $ T $ - horns'' which effectively contains $ X $ as well as all $ T $ - algebras.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	defines	define	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	3	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	6	punct	_	SpaceAfter=No
8	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	6	punct	_	_
9	$ T $	$ t $	SYM	$	_	11	compound	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	horns	horn	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
12	''	''	PUNCT	''	PunctSide=Fin|PunctType=Quot	5	punct	_	_
13	which	which	PRON	WDT	_	15	nsubj	_	_
14	effectively	effectively	ADV	RB	_	15	advmod	_	_
15	contains	contain	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	relcl	_	_
16	$ X $	$ x $	SYM	$	_	15	dobj	_	_
17	as	as	ADV	RB	_	19	advmod	_	_
18	well	well	ADV	RB	Degree=Pos	19	advmod	_	_
19	as	as	ADP	IN	_	16	cc	_	_
20	all	all	DET	DT	_	23	det	_	_
21	$ T $	$ t $	SYM	$	_	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	algebras	algebra	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = It is assume that $ Xs $ is cocomplete and has a factorization system $ (E, M) $ satisfying reasonable properties.
1	It	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	3	nsubjpass	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	aux	_	_
3	assume	assume	VERB	VB	VerbForm=Inf	0	ROOT	_	_
4	that	that	SCONJ	IN	_	6	mark	_	_
5	$ Xs $	$ xs $	SYM	$	_	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
7	cocomplete	cocomplete	ADJ	JJ	Degree=Pos	6	acomp	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
9	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	conj	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	factorization	factorization	NOUN	NN	Number=Sing	12	compound	_	_
12	system	system	NOUN	NN	Number=Sing	9	dobj	_	_
13	$ (E, M) $	$ (e, m) $	SYM	$	_	14	nsubj	_	_
14	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	advcl	_	_
15	reasonable	reasonable	ADJ	JJ	Degree=Pos	16	amod	_	_
16	properties	property	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = An ordinal - indexed sequence of $ T $ - horns is then defined which provides successive approximations to a free $ T $ - algebra generated by an object $ x $ in $ X $ , as well as approximations to coequalizers and other colimits for the category of $ T $ - algebras.
1	An	an	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
2	ordinal	ordinal	ADJ	JJ	Degree=Pos	4	advmod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	amod	_	_
5	sequence	sequence	NOUN	NN	Number=Sing	12	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	$ T $	$ t $	SYM	$	_	9	compound	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	horns	horn	NOUN	NNS	Number=Plur	6	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
11	then	then	ADV	RB	PronType=Dem	12	advmod	_	_
12	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
13	which	which	PRON	WDT	_	14	nsubj	_	_
14	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	ccomp	_	_
15	successive	successive	ADJ	JJ	Degree=Pos	16	amod	_	_
16	approximations	approximation	NOUN	NNS	Number=Plur	14	dobj	_	_
17	to	to	ADP	IN	_	14	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
19	free	free	ADJ	JJ	Degree=Pos	22	amod	_	_
20	$ T $	$ t $	SYM	$	_	22	compound	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	algebra	algebra	NOUN	NN	Number=Sing	17	pobj	_	_
23	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	22	acl	_	_
24	by	by	ADP	IN	_	23	agent	_	_
25	an	an	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
26	object	object	NOUN	NN	Number=Sing	24	pobj	_	_
27	$ x $	$ x $	SYM	$	_	26	prep	_	_
28	in	in	ADP	IN	_	26	prep	_	_
29	$ X $	$ x $	SYM	$	_	28	pobj	_	_
30	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
31	as	as	ADV	RB	_	33	advmod	_	_
32	well	well	ADV	RB	Degree=Pos	33	advmod	_	_
33	as	as	ADP	IN	_	26	cc	_	_
34	approximations	approximation	NOUN	NNS	Number=Plur	26	conj	_	_
35	to	to	ADP	IN	_	34	prep	_	_
36	coequalizers	coequalizer	NOUN	NNS	Number=Plur	35	pobj	_	_
37	and	and	CCONJ	CC	ConjType=Cmp	36	cc	_	_
38	other	other	ADJ	JJ	Degree=Pos	39	amod	_	_
39	colimits	colimit	NOUN	NNS	Number=Plur	36	conj	_	_
40	for	for	ADP	IN	_	34	prep	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	42	det	_	_
42	category	category	NOUN	NN	Number=Sing	40	pobj	_	_
43	of	of	ADP	IN	_	42	prep	_	_
44	$ T $	$ t $	SYM	$	_	43	pobj	_	_
45	-	-	PUNCT	HYPH	PunctType=Dash	46	punct	_	_
46	algebras	algebra	NOUN	NNS	Number=Plur	43	pobj	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 7
# text = Using the notions of an $ M $ - cone and a separated $ T $ - horn it is shown that if $ X $ is $ M $ - well - powered, then the ordinal sequence stabilizes at the desired free algebra or coequalizer or other colimit whenever they exist.
1	Using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	advcl	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	notions	notion	NOUN	NNS	Number=Plur	1	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
6	$ M $	$ m $	SYM	$	_	8	compound	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	cone	cone	NOUN	NN	Number=Sing	4	pobj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
11	separated	separate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	amod	_	_
12	$ T $	$ t $	SYM	$	_	14	nmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	horn	horn	NOUN	NN	Number=Sing	1	conj	_	_
15	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	17	nsubjpass	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	auxpass	_	_
17	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
18	that	that	SCONJ	IN	_	32	mark	_	_
19	if	if	SCONJ	IN	_	21	mark	_	_
20	$ X $	$ x $	SYM	$	_	21	nsubj	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	32	advcl	_	_
22	$ M $	$ m $	SYM	$	_	26	advmod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
24	well	well	ADV	RB	Degree=Pos	26	advmod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	powered	power	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	acomp	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
28	then	then	ADV	RB	PronType=Dem	32	advmod	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
30	ordinal	ordinal	ADJ	JJ	Degree=Pos	31	amod	_	_
31	sequence	sequence	NOUN	NN	Number=Sing	32	nsubj	_	_
32	stabilizes	stabilize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	ccomp	_	_
33	at	at	ADP	IN	_	32	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
35	desired	desire	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	37	amod	_	_
36	free	free	ADJ	JJ	Degree=Pos	37	amod	_	_
37	algebra	algebra	NOUN	NNS	Number=Plur	33	pobj	_	_
38	or	or	CCONJ	CC	ConjType=Cmp	37	cc	_	_
39	coequalizer	coequalizer	NOUN	NN	Number=Sing	37	conj	_	_
40	or	or	CCONJ	CC	ConjType=Cmp	39	cc	_	_
41	other	other	ADJ	JJ	Degree=Pos	42	amod	_	_
42	colimit	colimit	NOUN	NN	Number=Sing	39	conj	_	_
43	whenever	whenever	SCONJ	WRB	_	45	advmod	_	_
44	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	45	nsubj	_	_
45	exist	exist	VERB	VBP	Tense=Pres|VerbForm=Fin	32	advcl	_	SpaceAfter=No
46	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 8
# text = This paper is a successor to a paper written by the first author in 1970 that showed that $ T $ generates a free triple when every $ x $ in $ X $ generates a free $ T $ - algebra.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	successor	successor	NOUN	NN	Number=Sing	3	attr	_	_
6	to	to	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	paper	paper	NOUN	NN	Number=Sing	6	pobj	_	_
9	written	write	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
10	by	by	ADP	IN	_	9	agent	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	first	first	ADJ	JJ	Degree=Pos	13	amod	_	_
13	author	author	NOUN	NN	Number=Sing	10	pobj	_	_
14	in	in	ADP	IN	_	9	prep	_	_
15	1970	1970	NUM	CD	NumType=Card	14	pobj	_	_
16	that	that	PRON	WDT	PronType=Rel	17	nsubj	_	_
17	showed	show	VERB	VBD	Tense=Past|VerbForm=Fin	8	relcl	_	_
18	that	that	SCONJ	IN	_	20	mark	_	_
19	$ T $	$ t $	SYM	$	_	20	nsubj	_	_
20	generates	generate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	ccomp	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
22	free	free	ADJ	JJ	Degree=Pos	23	amod	_	_
23	triple	triple	NOUN	NN	Number=Sing	20	dobj	_	_
24	when	when	SCONJ	WRB	_	29	advmod	_	_
25	every	every	DET	DT	_	26	det	_	_
26	$ x $	$ x $	SYM	$	_	29	nsubj	_	_
27	in	in	ADP	IN	_	29	prep	_	_
28	$ X $	$ x $	SYM	$	_	27	pobj	_	_
29	generates	generate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	advcl	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	34	det	_	_
31	free	free	ADJ	JJ	Degree=Pos	34	amod	_	_
32	$ T $	$ t $	SYM	$	_	34	compound	_	_
33	-	-	PUNCT	HYPH	PunctType=Dash	34	punct	_	_
34	algebra	algebra	NOUN	NN	Number=Sing	29	dobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 9
# text = We also consider colimits in triple algebras and give some examples of functors $ T $ for which no $ x $ in $ T $ generates a free $ T $ - algebra.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	colimits	colimit	NOUN	NNS	Number=Plur	3	dobj	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	triple	triple	ADJ	JJ	Degree=Pos	7	amod	_	_
7	algebras	algebra	NOUN	NNS	Number=Plur	5	pobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
9	give	give	VERB	VB	VerbForm=Inf	3	conj	_	_
10	some	some	DET	DT	_	11	det	_	_
11	examples	example	NOUN	NNS	Number=Plur	9	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	functors	functor	NOUN	NNS	Number=Plur	12	pobj	_	_
14	$ T $	$ t $	SYM	$	_	9	dobj	_	_
15	for	for	ADP	IN	_	21	prep	_	_
16	which	which	PRON	WDT	_	15	pobj	_	_
17	no	no	PRON	DT	_	21	nsubj	_	_
18	$ x $	$ x $	SYM	$	_	17	nmod	_	_
19	in	in	ADP	IN	_	21	prep	_	_
20	$ T $	$ t $	SYM	$	_	19	pobj	_	_
21	generates	generate	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
23	free	free	ADJ	JJ	Degree=Pos	26	amod	_	_
24	$ T $	$ t $	SYM	$	_	26	compound	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	algebra	algebra	NOUN	NN	Number=Sing	21	dobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 717
# sent_id = 1
# text = We unify previous constructions from our work on concurrent game semantics into a single categorical framework.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	unify	unify	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	previous	previous	ADJ	JJ	Degree=Pos	4	amod	_	_
4	constructions	construction	NOUN	NNS	Number=Plur	2	dobj	_	_
5	from	from	ADP	IN	_	2	prep	_	_
6	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	7	poss	_	_
7	work	work	NOUN	NN	Number=Sing	5	pobj	_	_
8	on	on	ADP	IN	_	2	prep	_	_
9	concurrent	concurrent	ADJ	JJ	Degree=Pos	11	amod	_	_
10	game	game	NOUN	NN	Number=Sing	11	compound	_	_
11	semantics	semantic	NOUN	NNS	Number=Plur	8	pobj	_	_
12	into	into	ADP	IN	_	2	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
14	single	single	ADJ	JJ	Degree=Pos	16	amod	_	_
15	categorical	categorical	ADJ	JJ	Degree=Pos	16	amod	_	_
16	framework	framework	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = From an operational description of positions and moves in some game, called a signature, we produce a pseudo double category, in which objects are positions and vertical morphisms are plays.
1	From	from	ADP	IN	_	13	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	operational	operational	ADJ	JJ	Degree=Pos	4	amod	_	_
4	description	description	NOUN	NN	Number=Sing	1	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	positions	position	NOUN	NNS	Number=Plur	5	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	moves	move	NOUN	NNS	Number=Plur	6	conj	_	_
9	in	in	ADP	IN	_	4	prep	_	_
10	some	some	DET	DT	_	11	det	_	_
11	game	game	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
13	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	18	ccomp	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
15	signature	signature	NOUN	NN	Number=Sing	13	oprd	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
17	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	18	nsubj	_	_
18	produce	produce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
20	pseudo	pseudo	NOUN	NN	Number=Sing	22	nmod	_	_
21	double	double	ADJ	JJ	Degree=Pos	22	amod	_	_
22	category	category	NOUN	NN	Number=Sing	18	dobj	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
24	in	in	ADP	IN	_	27	prep	_	_
25	which	which	PRON	WDT	_	24	pobj	_	_
26	objects	object	NOUN	NNS	Number=Plur	27	nsubj	_	_
27	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	22	relcl	_	_
28	positions	position	NOUN	NNS	Number=Plur	27	attr	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
30	vertical	vertical	ADJ	JJ	Degree=Pos	31	amod	_	_
31	morphisms	morphism	NOUN	NNS	Number=Plur	28	conj	_	_
32	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	18	conj	_	_
33	plays	play	NOUN	NNS	Number=Plur	32	attr	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# sent_id = 3
# text = The considered games are multi - player, so it makes sense to consider embeddings of positions: these are the horizontal morphisms.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	considered	considered	ADJ	JJ	Degree=Pos	3	amod	_	_
3	games	game	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	11	ccomp	_	_
5	multi	multi	ADJ	JJ	Degree=Pos	7	amod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	player	player	NOUN	NN	Number=Sing	4	attr	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
9	so	so	CCONJ	CC	ConjType=Cmp	11	advmod	_	_
10	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	11	nsubj	_	_
11	makes	make	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	ccomp	_	_
12	sense	sense	NOUN	NN	Number=Sing	11	dobj	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	consider	consider	VERB	VB	VerbForm=Inf	11	xcomp	_	_
15	embeddings	embedding	NOUN	NNS	Number=Plur	14	dobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	positions	position	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
18	:	:	PUNCT	:	_	20	punct	_	_
19	these	these	PRON	DT	Number=Plur|PronType=Dem	20	nsubj	_	_
20	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	horizontal	horizontal	ADJ	JJ	Degree=Pos	23	amod	_	_
23	morphisms	morphism	NOUN	NNS	Number=Plur	20	attr	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	20	punct	_	SpaceAfter=No

# sent_id = 4
# text = Finally, cells may be thought of as embeddings of plays preserving initial and final positions.
1	Finally	finally	ADV	RB	_	6	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
3	cells	cell	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
4	may	may	AUX	MD	VerbForm=Fin	6	aux	_	_
5	be	be	AUX	VB	VerbForm=Inf	6	auxpass	_	_
6	thought	think	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	as	as	ADP	IN	_	6	prep	_	_
9	embeddings	embedding	NOUN	NNS	Number=Plur	12	nsubj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	plays	play	NOUN	NNS	Number=Plur	10	pobj	_	_
12	preserving	preserve	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	pcomp	_	_
13	initial	initial	ADJ	JJ	Degree=Pos	16	amod	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	final	final	ADJ	JJ	Degree=Pos	13	conj	_	_
16	positions	position	NOUN	NNS	Number=Plur	12	dobj	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 5
# text = In order to be suitable for game semantics, the obtained pseudo double category should enjoy a certain fibredness property.
1	In	in	ADP	IN	_	16	prep	_	_
2	order	order	NOUN	NN	Number=Sing	1	pobj	_	_
3	to	to	PART	TO	_	4	aux	_	_
4	be	be	AUX	VB	VerbForm=Inf	2	acl	_	_
5	suitable	suitable	ADJ	JJ	Degree=Pos	4	acomp	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	game	game	NOUN	NN	Number=Sing	8	compound	_	_
8	semantics	semantic	NOUN	NNS	Number=Plur	6	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	12	amod	_	_
12	pseudo	pseudo	NOUN	NN	Number=Sing	14	nmod	_	_
13	double	double	ADJ	JJ	Degree=Pos	14	amod	_	_
14	category	category	NOUN	NN	Number=Sing	16	nsubj	_	_
15	should	should	AUX	MD	VerbForm=Fin	16	aux	_	_
16	enjoy	enjoy	VERB	VB	VerbForm=Inf	0	ROOT	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
18	certain	certain	ADJ	JJ	Degree=Pos	20	amod	_	_
19	fibredness	fibredness	NOUN	NN	Number=Sing	20	compound	_	_
20	property	property	NOUN	NN	Number=Sing	16	dobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 6
# text = Under suitable hypotheses, we show that our construction actually produces such a fibred pseudo double category, from which we can define relevant categories of plays, and thus of strategies.
1	Under	under	ADP	IN	_	6	prep	_	_
2	suitable	suitable	ADJ	JJ	Degree=Pos	3	amod	_	_
3	hypotheses	hypothesis	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	11	mark	_	_
8	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	9	poss	_	_
9	construction	construction	NOUN	NN	Number=Sing	11	nsubj	_	_
10	actually	actually	ADV	RB	_	11	advmod	_	_
11	produces	produce	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
12	such	such	DET	PDT	_	17	predet	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
14	fibred	fibred	ADJ	JJ	Degree=Pos	15	amod	_	_
15	pseudo	pseudo	NOUN	NN	Number=Sing	17	nmod	_	_
16	double	double	ADJ	JJ	Degree=Pos	17	amod	_	_
17	category	category	NOUN	NN	Number=Sing	11	dobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	from	from	ADP	IN	_	23	prep	_	_
20	which	which	PRON	WDT	_	19	pobj	_	_
21	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	23	nsubj	_	_
22	can	can	AUX	MD	VerbForm=Fin	23	aux	_	_
23	define	define	VERB	VB	VerbForm=Inf	17	relcl	_	_
24	relevant	relevant	ADJ	JJ	Degree=Pos	25	amod	_	_
25	categories	category	NOUN	NNS	Number=Plur	23	dobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	plays	play	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
30	thus	thus	ADV	RB	_	31	advmod	_	_
31	of	of	ADP	IN	_	23	conj	_	_
32	strategies	strategy	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 7
# text = We give a first necessary and sufficient criterion for this to hold and then a sufficient criterion that can be checked more easily.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
4	first	first	ADJ	JJ	Degree=Pos	8	amod	_	_
5	necessary	necessary	ADJ	JJ	Degree=Pos	8	amod	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
7	sufficient	sufficient	ADJ	JJ	Degree=Pos	5	conj	_	_
8	criterion	criterion	NOUN	NN	Number=Sing	2	dobj	_	_
9	for	for	SCONJ	IN	_	12	mark	_	_
10	this	this	PRON	DT	Number=Sing|PronType=Dem	12	nsubj	_	_
11	to	to	PART	TO	_	12	aux	_	_
12	hold	hold	VERB	VB	VerbForm=Inf	8	advcl	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	then	then	ADV	RB	PronType=Dem	17	advmod	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
16	sufficient	sufficient	ADJ	JJ	Degree=Pos	17	amod	_	_
17	criterion	criterion	NOUN	NN	Number=Sing	8	conj	_	_
18	that	that	PRON	WDT	PronType=Rel	21	nsubjpass	_	_
19	can	can	AUX	MD	VerbForm=Fin	21	aux	_	_
20	be	be	AUX	VB	VerbForm=Inf	21	auxpass	_	_
21	checked	check	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	relcl	_	_
22	more	more	ADV	RBR	Degree=Cmp	23	advmod	_	_
23	easily	easily	ADV	RB	_	21	advmod	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 718
# sent_id = 1
# text = Having given a characterization of the categorical congruence modularity getting rid of the assumption that the ground category is regular, we give now a characterization of the categorical congruence distributivity.
1	Having	having	AUX	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	2	aux	_	_
2	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	23	advcl	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	characterization	characterization	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
7	categorical	categorical	ADJ	JJ	Degree=Pos	9	amod	_	_
8	congruence	congruence	NOUN	NN	Number=Sing	9	compound	_	_
9	modularity	modularity	NOUN	NN	Number=Sing	10	compound	_	_
10	getting	getting	AUX	NN	Number=Sing	11	auxpass	_	_
11	rid	rid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	pcomp	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	assumption	assumption	NOUN	NN	Number=Sing	12	pobj	_	_
15	that	that	SCONJ	IN	_	19	mark	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
17	ground	ground	NOUN	NN	Number=Sing	18	compound	_	_
18	category	category	NOUN	NN	Number=Sing	19	nsubj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	acl	_	_
20	regular	regular	ADJ	JJ	Degree=Pos	19	acomp	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
22	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	23	nsubj	_	_
23	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
24	now	now	ADV	RB	_	23	advmod	_	_
25	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
26	characterization	characterization	NOUN	NN	Number=Sing	23	dobj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
29	categorical	categorical	ADJ	JJ	Degree=Pos	31	amod	_	_
30	congruence	congruence	NOUN	NN	Number=Sing	31	compound	_	_
31	distributivity	distributivity	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	23	punct	_	SpaceAfter=No

# sent_id = 2
# text = We have a look as well at the case where the congruence distributivity is only involved, in some sense, for a subclass $ Gamma $ of equivalence relations.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	have	have	VERB	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	look	look	NOUN	NN	Number=Sing	2	dobj	_	_
5	as	as	ADV	RB	_	6	advmod	_	_
6	well	well	ADV	RB	Degree=Pos	4	advmod	_	_
7	at	at	ADP	IN	_	4	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	case	case	NOUN	NN	Number=Sing	7	pobj	_	_
10	where	where	SCONJ	WRB	_	14	advmod	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
12	congruence	congruence	NOUN	NN	Number=Sing	13	compound	_	_
13	distributivity	distributivity	NOUN	NN	Number=Sing	14	nsubj	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	relcl	_	_
15	only	only	ADV	RB	_	16	advmod	_	_
16	involved	involve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	acomp	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
18	in	in	ADP	IN	_	14	prep	_	_
19	some	some	DET	DT	_	20	det	_	_
20	sense	sense	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
22	for	for	ADP	IN	_	14	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	subclass	subclass	ADJ	JJ	Degree=Pos	25	amod	_	_
25	$ Gamma $	$ gamma $	SYM	$	_	22	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	equivalence	equivalence	NOUN	NN	Number=Sing	28	compound	_	_
28	relations	relation	NOUN	NNS	Number=Plur	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 719
# sent_id = 1
# text = We study properties of a category after quotienting out a suitable chosen group of isomorphisms on each object.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	properties	property	NOUN	NNS	Number=Plur	2	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	category	category	NOUN	NN	Number=Sing	4	pobj	_	_
7	after	after	ADP	IN	_	2	prep	_	_
8	quotienting	quotiente	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	pcomp	_	_
9	out	out	ADP	RP	_	8	prt	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	suitable	suitable	ADJ	JJ	Degree=Pos	13	amod	_	_
12	chosen	choose	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
13	group	group	NOUN	NN	Number=Sing	8	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	isomorphisms	isomorphism	NOUN	NNS	Number=Plur	14	pobj	_	_
16	on	on	ADP	IN	_	13	prep	_	_
17	each	each	DET	DT	_	18	det	_	_
18	object	object	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Coproducts in the original category are described in its quotient by our new weaker notion of a `phased coproduct'.
1	Coproducts	coproduct	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
2	in	in	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	original	original	ADJ	JJ	Degree=Pos	5	amod	_	_
5	category	category	NOUN	NN	Number=Sing	2	pobj	_	_
6	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
7	described	describe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	10	poss	_	_
10	quotient	quotient	NOUN	NN	Number=Sing	8	pobj	_	_
11	by	by	ADP	IN	_	7	agent	_	_
12	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	15	poss	_	_
13	new	new	ADJ	JJ	Degree=Pos	15	amod	_	_
14	weaker	weak	ADJ	JJR	Degree=Cmp	15	amod	_	_
15	notion	notion	NOUN	NN	Number=Sing	11	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
18	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	20	punct	_	SpaceAfter=No
19	phased	phase	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	amod	_	_
20	coproduct	coproduct	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
21	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	7	punct	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = We examine these and show that any suitable category with them arises as such a quotient of a category with coproducts.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	examine	examine	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	these	these	PRON	DT	Number=Plur|PronType=Dem	2	dobj	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
5	show	show	VERB	VB	VerbForm=Inf	2	conj	_	_
6	that	that	SCONJ	IN	_	12	mark	_	_
7	any	any	DET	DT	_	9	det	_	_
8	suitable	suitable	ADJ	JJ	Degree=Pos	9	amod	_	_
9	category	category	NOUN	NN	Number=Sing	12	nsubj	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	10	pobj	_	_
12	arises	arise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	ccomp	_	_
13	as	as	ADP	IN	_	12	prep	_	_
14	such	such	DET	PDT	_	16	predet	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	quotient	quotient	NOUN	NN	Number=Sing	13	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	category	category	NOUN	NN	Number=Sing	17	pobj	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	coproducts	coproduct	NOUN	NNS	Number=Plur	20	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = Motivation comes from projective geometry, and also quantum theory where they describe superpositions in the category of Hilbert spaces and continuous linear maps up to global phase.
1	Motivation	motivation	NOUN	NN	Number=Sing	2	nsubj	_	_
2	comes	come	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	from	from	ADP	IN	_	2	prep	_	_
4	projective	projective	ADJ	JJ	Degree=Pos	5	amod	_	_
5	geometry	geometry	NOUN	NN	Number=Sing	3	pobj	_	SpaceAfter=No
6	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
8	also	also	ADV	RB	_	10	advmod	_	_
9	quantum	quantum	ADJ	JJ	Degree=Pos	10	amod	_	_
10	theory	theory	NOUN	NN	Number=Sing	2	conj	_	_
11	where	where	SCONJ	WRB	_	13	advmod	_	_
12	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	13	nsubj	_	_
13	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	10	relcl	_	_
14	superpositions	superposition	NOUN	NNS	Number=Plur	13	dobj	_	_
15	in	in	ADP	IN	_	13	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	Hilbert	Hilbert	PROPN	NNP	Number=Sing	20	compound	_	_
20	spaces	space	NOUN	NNS	Number=Plur	18	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	continuous	continuous	ADJ	JJ	Degree=Pos	24	amod	_	_
23	linear	linear	PROPN	NNP	Number=Sing	24	compound	_	_
24	maps	map	NOUN	NNS	Number=Plur	20	conj	_	_
25	up	up	ADP	RP	_	13	prep	_	_
26	to	to	ADP	IN	_	13	prep	_	_
27	global	global	ADJ	JJ	Degree=Pos	28	amod	_	_
28	phase	phase	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = The quotients we consider also generalise those induced by categorical isotropy in the sense of Funk et al.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	quotients	quotient	NOUN	NNS	Number=Plur	0	ROOT	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	2	relcl	_	_
5	also	also	ADV	RB	_	6	advmod	_	_
6	generalise	generalise	VERB	VB	VerbForm=Inf	4	ccomp	_	_
7	those	those	PRON	DT	Number=Plur|PronType=Dem	6	dobj	_	_
8	induced	induce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	acl	_	_
9	by	by	ADP	IN	_	8	agent	_	_
10	categorical	categorical	ADJ	JJ	Degree=Pos	11	amod	_	_
11	isotropy	isotropy	NOUN	NN	Number=Sing	9	pobj	_	_
12	in	in	ADP	IN	_	8	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	sense	sense	NOUN	NN	Number=Sing	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	Funk	Funk	PROPN	NNP	Number=Sing	15	pobj	_	_
17	et	et	NOUN	NN	Number=Sing	2	appos	_	_
18	al	al	PROPN	NNP	Number=Sing	2	appos	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 720
# sent_id = 1
# text = We develop a notion of limit for dagger categories, that we show is suitable in the following ways: it subsumes special cases known from the literature; dagger limits are unique up to unitary isomorphism; a wide class of dagger limits can be built from a small selection of them; dagger limits of a fixed shape can be phrased as dagger adjoints to a diagonal functor; dagger limits can be built from ordinary limits in the presence of polar decomposition; dagger limits commute with dagger colimits in many cases.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	22	ccomp	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	limit	limit	NOUN	NN	Number=Sing	5	pobj	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	dagger	dagger	NOUN	NN	Number=Sing	9	compound	_	_
9	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
11	that	that	SCONJ	IN	_	14	nsubj	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	13	nsubj	_	_
13	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	2	advcl	_	_
14	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	ccomp	_	_
15	suitable	suitable	ADJ	JJ	Degree=Pos	14	acomp	_	_
16	in	in	ADP	IN	_	14	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	19	amod	_	_
19	ways	way	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
20	:	:	PUNCT	:	_	22	punct	_	_
21	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	22	nsubj	_	_
22	subsumes	subsume	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	32	ccomp	_	_
23	special	special	ADJ	JJ	Degree=Pos	24	amod	_	_
24	cases	case	NOUN	NNS	Number=Plur	22	dobj	_	_
25	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	acl	_	_
26	from	from	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	literature	literature	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
29	;	;	PUNCT	:	_	32	punct	_	_
30	dagger	dagger	NOUN	NN	Number=Sing	31	compound	_	_
31	limits	limit	NOUN	NNS	Number=Plur	32	nsubj	_	_
32	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	47	ccomp	_	_
33	unique	unique	ADJ	JJ	Degree=Pos	32	acomp	_	_
34	up	up	ADP	IN	_	33	prep	_	_
35	to	to	ADP	IN	_	34	prep	_	_
36	unitary	unitary	ADJ	JJ	Degree=Pos	37	amod	_	_
37	isomorphism	isomorphism	NOUN	NN	Number=Sing	35	pobj	_	SpaceAfter=No
38	;	;	PUNCT	:	_	47	punct	_	_
39	a	a	DET	DT	Definite=Ind|PronType=Art	41	det	_	_
40	wide	wide	ADJ	JJ	Degree=Pos	41	amod	_	_
41	class	class	NOUN	NN	Number=Sing	47	nsubjpass	_	_
42	of	of	ADP	IN	_	41	prep	_	_
43	dagger	dagger	NOUN	NN	Number=Sing	44	compound	_	_
44	limits	limit	NOUN	NNS	Number=Plur	42	pobj	_	_
45	can	can	AUX	MD	VerbForm=Fin	47	aux	_	_
46	be	be	AUX	VB	VerbForm=Inf	47	auxpass	_	_
47	built	build	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	63	ccomp	_	_
48	from	from	ADP	IN	_	47	prep	_	_
49	a	a	DET	DT	Definite=Ind|PronType=Art	51	det	_	_
50	small	small	ADJ	JJ	Degree=Pos	51	amod	_	_
51	selection	selection	NOUN	NN	Number=Sing	48	pobj	_	_
52	of	of	ADP	IN	_	51	prep	_	_
53	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	52	pobj	_	SpaceAfter=No
54	;	;	PUNCT	:	_	63	punct	_	_
55	dagger	dagger	NOUN	NN	Number=Sing	56	compound	_	_
56	limits	limit	NOUN	NNS	Number=Plur	63	nsubjpass	_	_
57	of	of	ADP	IN	_	56	prep	_	_
58	a	a	DET	DT	Definite=Ind|PronType=Art	60	det	_	_
59	fixed	fix	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	60	amod	_	_
60	shape	shape	NOUN	NN	Number=Sing	57	pobj	_	_
61	can	can	AUX	MD	VerbForm=Fin	63	aux	_	_
62	be	be	AUX	VB	VerbForm=Inf	63	auxpass	_	_
63	phrased	phrase	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	76	ccomp	_	_
64	as	as	ADP	IN	_	63	prep	_	_
65	dagger	dagg	ADJ	JJR	Degree=Cmp	66	compound	_	_
66	adjoints	adjoint	NOUN	NNS	Number=Plur	64	pobj	_	_
67	to	to	ADP	IN	_	63	prep	_	_
68	a	a	DET	DT	Definite=Ind|PronType=Art	70	det	_	_
69	diagonal	diagonal	ADJ	JJ	Degree=Pos	70	amod	_	_
70	functor	functor	NOUN	NN	Number=Sing	67	pobj	_	SpaceAfter=No
71	;	;	PUNCT	:	_	76	punct	_	_
72	dagger	dagger	NOUN	NN	Number=Sing	73	compound	_	_
73	limits	limit	NOUN	NNS	Number=Plur	76	nsubjpass	_	_
74	can	can	AUX	MD	VerbForm=Fin	76	aux	_	_
75	be	be	AUX	VB	VerbForm=Inf	76	auxpass	_	_
76	built	build	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	89	ccomp	_	_
77	from	from	ADP	IN	_	76	prep	_	_
78	ordinary	ordinary	ADJ	JJ	Degree=Pos	79	amod	_	_
79	limits	limit	NOUN	NNS	Number=Plur	77	pobj	_	_
80	in	in	ADP	IN	_	76	prep	_	_
81	the	the	DET	DT	Definite=Def|PronType=Art	82	det	_	_
82	presence	presence	NOUN	NN	Number=Sing	80	pobj	_	_
83	of	of	ADP	IN	_	82	prep	_	_
84	polar	polar	ADJ	JJ	Degree=Pos	85	amod	_	_
85	decomposition	decomposition	NOUN	NN	Number=Sing	83	pobj	_	SpaceAfter=No
86	;	;	PUNCT	:	_	89	punct	_	_
87	dagger	dagger	NOUN	NN	Number=Sing	88	compound	_	_
88	limits	limit	NOUN	NNS	Number=Plur	89	nsubj	_	_
89	commute	commute	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
90	with	with	ADP	IN	_	89	prep	_	_
91	dagger	dagger	NOUN	NN	Number=Sing	92	compound	_	_
92	colimits	colimit	NOUN	NNS	Number=Plur	90	pobj	_	_
93	in	in	ADP	IN	_	89	prep	_	_
94	many	many	ADJ	JJ	Degree=Pos	95	amod	_	_
95	cases	case	NOUN	NNS	Number=Plur	93	pobj	_	SpaceAfter=No
96	.	.	PUNCT	.	PunctType=Peri	89	punct	_	SpaceAfter=No

# doc_id = 721
# sent_id = 1
# text = If $ C $ is a monoidal category with reflexive coequalizers which are preserved by tensoring from both sides, then the category $ MonC $ of monoids over $ C $ has all coequalizers and these are regular epimorphisms in $ C $ .
1	If	if	SCONJ	IN	_	3	mark	_	_
2	$ C $	$ c $	SYM	$	_	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	27	advcl	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	monoidal	monoidal	ADJ	JJ	Degree=Pos	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	3	attr	_	_
7	with	with	ADP	IN	_	6	prep	_	_
8	reflexive	reflexive	ADJ	JJ	Degree=Pos	9	amod	_	_
9	coequalizers	coequalizer	NOUN	NNS	Number=Plur	7	pobj	_	_
10	which	which	PRON	WDT	_	12	nsubjpass	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	12	auxpass	_	_
12	preserved	preserve	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	relcl	_	_
13	by	by	ADP	IN	_	12	agent	_	_
14	tensoring	tensore	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	pcomp	_	_
15	from	from	ADP	IN	_	14	prep	_	_
16	both	both	DET	DT	_	17	det	_	_
17	sides	side	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
19	then	then	ADV	RB	PronType=Dem	27	advmod	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	category	category	NOUN	NN	Number=Sing	27	nsubj	_	_
22	$ MonC $	$ monc $	SYM	$	_	21	appos	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	monoids	monoid	NOUN	NNS	Number=Plur	23	pobj	_	_
25	over	over	ADP	IN	_	21	prep	_	_
26	$ C $	$ c $	SYM	$	_	25	pobj	_	_
27	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
28	all	all	DET	DT	_	29	det	_	_
29	coequalizers	coequalizer	NOUN	NNS	Number=Plur	27	dobj	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
31	these	these	PRON	DT	Number=Plur|PronType=Dem	32	nsubj	_	_
32	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	27	conj	_	_
33	regular	regular	ADJ	JJ	Degree=Pos	34	amod	_	_
34	epimorphisms	epimorphism	NOUN	NNS	Number=Plur	32	attr	_	_
35	in	in	ADP	IN	_	34	prep	_	_
36	$ C $	$ c $	SYM	$	_	35	pobj	_	_
37	.	.	PUNCT	.	PunctType=Peri	32	punct	_	SpaceAfter=No

# sent_id = 2
# text = This implies that $ MonC $ has all colimits which exist in $ C $ , provided that $ C $ in addition has (regular epi, jointly monomorphic) - factorizations of discrete cones and admits arbitrary free monoids.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	implies	imply	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	5	mark	_	_
4	$ MonC $	$ monc $	SYM	$	_	5	nsubj	_	_
5	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
6	all	all	DET	DT	_	7	det	_	_
7	colimits	colimit	NOUN	NNS	Number=Plur	5	dobj	_	_
8	which	which	PRON	WDT	_	9	nsubj	_	_
9	exist	exist	VERB	VBP	Tense=Pres|VerbForm=Fin	7	relcl	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	$ C $	$ c $	SYM	$	_	10	pobj	_	_
12	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
13	provided	provide	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	prep	_	_
14	that	that	SCONJ	IN	_	18	mark	_	_
15	$ C $	$ c $	SYM	$	_	18	nsubj	_	_
16	in	in	ADP	IN	_	18	prep	_	_
17	addition	addition	NOUN	NN	Number=Sing	16	pobj	_	_
18	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	pcomp	_	_
19	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	18	punct	_	SpaceAfter=No
20	regular	regular	ADJ	JJ	Degree=Pos	21	amod	_	_
21	epi	epi	NOUN	NN	Number=Sing	27	dep	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	jointly	jointly	ADV	RB	_	24	advmod	_	_
24	monomorphic	monomorphic	ADJ	JJ	Degree=Pos	21	amod	_	SpaceAfter=No
25	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	21	punct	_	_
26	-	-	PUNCT	:	_	27	punct	_	_
27	factorizations	factorization	NOUN	NNS	Number=Plur	18	dobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	discrete	discrete	ADJ	JJ	Degree=Pos	30	amod	_	_
30	cones	cone	NOUN	NNS	Number=Plur	28	pobj	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
32	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	18	conj	_	_
33	arbitrary	arbitrary	ADJ	JJ	Degree=Pos	35	amod	_	_
34	free	free	ADJ	JJ	Degree=Pos	35	amod	_	_
35	monoids	monoid	NOUN	NNS	Number=Plur	32	dobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = A further application is a lifting theorem for adjunctions with a monoidal right adjoint whose left adjoint is not necessarily strong to adjunctions between the respective categories of monoids.
1	A	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
2	further	further	ADJ	JJ	Degree=Pos	3	amod	_	_
3	application	application	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	lifting	lifting	NOUN	NN	Number=Sing	7	amod	_	_
7	theorem	theorem	NOUN	NN	Number=Sing	4	attr	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	adjunctions	adjunction	NOUN	NNS	Number=Plur	8	pobj	_	_
10	with	with	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
12	monoidal	monoidal	ADJ	JJ	Degree=Pos	14	amod	_	_
13	right	right	NOUN	NN	Number=Sing	14	amod	_	_
14	adjoint	adjoint	NOUN	NN	Number=Sing	10	pobj	_	_
15	whose	whose	DET	WP$	Poss=Yes	17	poss	_	_
16	left	left	ADJ	JJ	Degree=Pos	17	amod	_	_
17	adjoint	adjoint	NOUN	NN	Number=Sing	18	nsubj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	relcl	_	_
19	not	not	PART	RB	Polarity=Neg	18	neg	_	_
20	necessarily	necessarily	ADV	RB	_	18	advmod	_	_
21	strong	strong	ADJ	JJ	Degree=Pos	18	acomp	_	_
22	to	to	ADP	IN	_	21	prep	_	_
23	adjunctions	adjunction	NOUN	NNS	Number=Plur	22	pobj	_	_
24	between	between	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	respective	respective	ADJ	JJ	Degree=Pos	27	amod	_	_
27	categories	category	NOUN	NNS	Number=Plur	24	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	monoids	monoid	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 722
# sent_id = 1
# text = Van den Bergh has defined the blowup of a noncommutative surface at a point lying on a commutative divisor.
1	Van	van	NOUN	NN	Number=Sing	2	compound	_	_
2	den	den	NOUN	NN	Number=Sing	5	npadvmod	_	_
3	Bergh	Bergh	PROPN	NNP	Number=Sing	5	nsubj	_	_
4	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	aux	_	_
5	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	blowup	blowup	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	noncommutative	noncommutative	ADJ	JJ	Degree=Pos	11	amod	_	_
11	surface	surface	NOUN	NN	Number=Sing	8	pobj	_	_
12	at	at	ADP	IN	_	5	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	point	point	NOUN	NN	Number=Sing	12	pobj	_	_
15	lying	lie	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	acl	_	_
16	on	on	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
18	commutative	commutative	ADJ	JJ	Degree=Pos	19	amod	_	_
19	divisor	divisor	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = We study one aspect of the construction, with an eventual aim of defining more general kinds of noncommutative blowups.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	study	study	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	one	one	NUM	CD	NumType=Card	4	nummod	_	_
4	aspect	aspect	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	construction	construction	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
9	with	with	ADP	IN	_	2	prep	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
11	eventual	eventual	ADJ	JJ	Degree=Pos	12	amod	_	_
12	aim	aim	NOUN	NN	Number=Sing	9	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	defining	define	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	pcomp	_	_
15	more	more	ADJ	JJR	Degree=Cmp	17	amod	_	_
16	general	general	ADJ	JJ	Degree=Pos	17	amod	_	_
17	kinds	kind	NOUN	NNS	Number=Plur	14	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	noncommutative	noncommutative	ADJ	JJ	Degree=Pos	20	amod	_	_
20	blowups	blowup	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Our basic object of study is a quasi - scheme $ X $ (a Grothendieck category).
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	3	poss	_	_
2	basic	basic	ADJ	JJ	Degree=Pos	3	amod	_	_
3	object	object	NOUN	NN	Number=Sing	6	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	study	study	NOUN	NN	Number=Sing	4	pobj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	quasi	quasi	ADJ	JJ	Degree=Pos	11	amod	_	_
9	-	-	ADJ	JJ	Degree=Pos	11	punct	_	_
10	scheme	scheme	NOUN	NN	Number=Sing	11	amod	_	_
11	$ X $	$ x $	SYM	$	_	6	attr	_	_
12	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	11	punct	_	SpaceAfter=No
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	15	compound	_	_
15	category	category	NOUN	NN	Number=Sing	11	appos	_	SpaceAfter=No
16	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	11	punct	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = Given a closed subcategory $ Z $ , in order to define a blowup of $ X $ along $ Z $ one first needs to have a functor $ F_Z $ which is an analog of tensoring with the defining ideal of $ Z $ .
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
3	closed	closed	ADJ	JJ	Degree=Pos	4	amod	_	_
4	subcategory	subcategory	NOUN	NN	Number=Sing	1	pobj	_	_
5	$ Z $	$ z $	SYM	$	_	4	appos	_	_
6	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
7	in	in	ADP	IN	_	19	prep	_	_
8	order	order	NOUN	NN	Number=Sing	7	pobj	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	define	define	VERB	VB	VerbForm=Inf	8	acl	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
12	blowup	blowup	NOUN	NN	Number=Sing	10	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	$ X $	$ x $	SYM	$	_	13	pobj	_	_
15	along	along	ADP	IN	_	10	prep	_	_
16	$ Z $	$ z $	SYM	$	_	17	nmod	_	_
17	one	one	NUM	CD	NumType=Card	15	pobj	_	_
18	first	first	ADJ	JJ	Degree=Pos	19	amod	_	_
19	needs	need	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
20	to	to	PART	TO	_	21	aux	_	_
21	have	have	VERB	VB	VerbForm=Inf	19	xcomp	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
23	functor	functor	NOUN	NN	Number=Sing	21	dobj	_	_
24	$ F_Z $	$ f_z $	SYM	$	_	23	prep	_	_
25	which	which	PRON	WDT	_	26	nsubj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	23	relcl	_	_
27	an	an	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	analog	analog	NOUN	NN	Number=Sing	26	attr	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	tensoring	tensore	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	29	pcomp	_	_
31	with	with	ADP	IN	_	30	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
33	defining	define	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	34	amod	_	_
34	ideal	ideal	NOUN	NN	Number=Sing	31	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	$ Z $	$ z $	SYM	$	_	35	pobj	_	_
37	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 5
# text = Following Van den Bergh, a closed subcategory $ Z $ which has such a functor is called well - closed.
1	Following	follow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	prep	_	_
2	Van	Van	PROPN	NNP	Number=Sing	3	compound	_	_
3	den	den	NOUN	NN	Number=Sing	4	compound	_	_
4	Bergh	Bergh	PROPN	NNP	Number=Sing	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	closed	closed	ADJ	JJ	Degree=Pos	8	amod	_	_
8	subcategory	subcategory	NOUN	NN	Number=Sing	4	appos	_	_
9	$ Z $	$ z $	SYM	$	_	8	prep	_	_
10	which	which	PRON	WDT	_	11	nsubj	_	_
11	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	relcl	_	_
12	such	such	DET	PDT	_	14	predet	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	functor	functor	NOUN	NN	Number=Sing	16	nsubjpass	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	auxpass	_	_
16	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
17	well	well	ADV	RB	Degree=Pos	19	advmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	closed	closed	ADJ	JJ	Degree=Pos	16	oprd	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 6
# text = We show that well - closedness can be characterized by the existence of certain projective effacements for each object of $ X $ , and that the needed functor $ F_Z $ has an explicit description in terms of such effacements.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	9	mark	_	_
4	well	well	ADV	RB	Degree=Pos	6	amod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	closedness	closedness	NOUN	NN	Number=Sing	9	nsubjpass	_	_
7	can	can	AUX	MD	VerbForm=Fin	9	aux	_	_
8	be	be	AUX	VB	VerbForm=Inf	9	auxpass	_	_
9	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
10	by	by	ADP	IN	_	9	agent	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	existence	existence	NOUN	NN	Number=Sing	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	certain	certain	ADJ	JJ	Degree=Pos	16	amod	_	_
15	projective	projective	ADJ	JJ	Degree=Pos	16	amod	_	_
16	effacements	effacement	NOUN	NNS	Number=Plur	13	pobj	_	_
17	for	for	ADP	IN	_	16	prep	_	_
18	each	each	DET	DT	_	19	det	_	_
19	object	object	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	$ X $	$ x $	SYM	$	_	20	pobj	_	_
22	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
24	that	that	SCONJ	IN	_	29	mark	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
26	needed	need	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	amod	_	_
27	functor	functor	NOUN	NN	Number=Sing	29	nsubj	_	_
28	$ F_Z $	$ f_z $	SYM	$	_	27	appos	_	_
29	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	conj	_	_
30	an	an	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
31	explicit	explicit	ADJ	JJ	Degree=Pos	32	amod	_	_
32	description	description	NOUN	NN	Number=Sing	29	dobj	_	_
33	in	in	ADP	IN	_	32	prep	_	_
34	terms	term	NOUN	NNS	Number=Plur	33	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	such	such	ADJ	JJ	Degree=Pos	37	amod	_	_
37	effacements	effacement	NOUN	NNS	Number=Plur	35	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = As an application, we prove that closed points are well - closed in quite general quasi - schemes.
1	As	as	ADP	IN	_	6	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	that	that	SCONJ	IN	_	10	mark	_	_
8	closed	closed	ADJ	JJ	Degree=Pos	9	amod	_	_
9	points	point	NOUN	NNS	Number=Plur	10	nsubj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	ccomp	_	_
11	well	well	ADV	RB	Degree=Pos	13	advmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	closed	close	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	acomp	_	_
14	in	in	ADP	IN	_	13	prep	_	_
15	quite	quite	ADV	RB	_	16	advmod	_	_
16	general	general	ADJ	JJ	Degree=Pos	17	amod	_	_
17	quasi	quasi	NOUN	NNS	Number=Plur	14	pobj	_	_
18	-	-	NOUN	NNS	Number=Plur	14	pobj	_	_
19	schemes	scheme	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 723
# sent_id = 1
# text = We continue the program of structural differential geometry that .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	continue	continue	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	program	program	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	structural	structural	ADJ	JJ	Degree=Pos	8	amod	_	_
7	differential	differential	ADJ	JJ	Degree=Pos	8	amod	_	_
8	geometry	geometry	NOUN	NN	Number=Sing	5	pobj	_	_
9	that	that	PRON	WDT	PronType=Rel	2	dobj	_	_
10	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 724
# sent_id = 1
# text = We introduce a new condition on an abstract span of categories which we refer to as having right fibred right adjoints, RFRA for short.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	new	new	ADJ	JJ	Degree=Pos	5	amod	_	_
5	condition	condition	NOUN	NN	Number=Sing	2	dobj	_	_
6	on	on	ADP	IN	_	5	prep	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	abstract	abstract	ADJ	JJ	Degree=Pos	9	amod	_	_
9	span	span	NOUN	NN	Number=Sing	6	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
12	which	which	PRON	WDT	_	15	pobj	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	refer	refer	VERB	VBP	Tense=Pres|VerbForm=Fin	9	relcl	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	as	as	ADP	IN	_	14	prep	_	_
17	having	have	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	16	pcomp	_	_
18	right	right	ADV	RB	_	19	advmod	_	_
19	fibred	fibre	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	amod	_	_
20	right	right	ADJ	JJ	Degree=Pos	21	amod	_	_
21	adjoints	adjoint	NOUN	NNS	Number=Plur	17	dobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
23	RFRA	RFRA	PROPN	NNP	Number=Sing	2	npadvmod	_	_
24	for	for	ADP	IN	_	23	prep	_	_
25	short	short	ADJ	JJ	Degree=Pos	24	amod	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that: (i) the span of split extensions of a semi - abelian category $ C $ has RFRA if and only if $ C $ is action representable; (ii) the reversed span to the one considered in (i) has RFRA if and only if $ C $ is locally algebraically cartesian closed; (iii) the span of split extensions of the category of morphisms of $ C $ has RFRA if and only if $ C $ is action representable and has normalizers; (iv) the reversed span to the one considered in (iii) has RFRA if and only if $ C $ is locally algebraically cartesian closed.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	45	ccomp	_	_
3	that	that	SCONJ	IN	_	20	mark	_	SpaceAfter=No
4	:	:	PUNCT	:	_	20	punct	_	_
5	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	6	punct	_	SpaceAfter=No
6	i	i	NOUN	NN	Case=Nom|Number=Sing|Person=1|PronType=Prs	20	nsubj	_	SpaceAfter=No
7	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	6	punct	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	span	span	NOUN	NN	Number=Sing	20	nsubj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	split	split	ADJ	JJ	Degree=Pos	12	amod	_	_
12	extensions	extension	NOUN	NNS	Number=Plur	10	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
15	semi	semi	ADJ	JJ	Degree=Pos	18	amod	_	_
16	-	-	ADJ	JJ	Degree=Pos	18	amod	_	_
17	abelian	abelian	ADJ	JJ	Degree=Pos	18	amod	_	_
18	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
19	$ C $	$ c $	SYM	$	_	18	appos	_	_
20	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
21	RFRA	RFRA	PROPN	NNP	Number=Sing	20	dobj	_	_
22	if	if	SCONJ	IN	_	27	mark	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	27	cc	_	_
24	only	only	ADV	RB	_	27	advmod	_	_
25	if	if	SCONJ	IN	_	27	mark	_	_
26	$ C $	$ c $	SYM	$	_	27	nsubj	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	advcl	_	_
28	action	action	NOUN	NN	Number=Sing	27	attr	_	_
29	representable	representable	ADJ	JJ	Degree=Pos	28	amod	_	SpaceAfter=No
30	;	;	PUNCT	:	_	45	punct	_	_
31	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	32	punct	_	SpaceAfter=No
32	ii	ii	PROPN	NNP	Number=Sing	45	dep	_	SpaceAfter=No
33	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	32	punct	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
35	reversed	reversed	ADJ	JJ	Degree=Pos	36	amod	_	_
36	span	span	NOUN	NN	Number=Sing	45	nsubj	_	_
37	to	to	ADP	IN	_	36	prep	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
39	one	one	NOUN	NN	Number=Sing	37	pobj	_	_
40	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	39	acl	_	_
41	in	in	ADP	IN	_	40	prep	_	_
42	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	41	punct	_	SpaceAfter=No
43	i	i	NOUN	NN	Case=Acc|Number=Sing|Person=1|PronType=Prs	41	pobj	_	SpaceAfter=No
44	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	39	punct	_	_
45	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	101	ccomp	_	_
46	RFRA	RFRA	PROPN	NNP	Number=Sing	45	dobj	_	_
47	if	if	SCONJ	IN	_	73	mark	_	_
48	and	and	CCONJ	CC	ConjType=Cmp	73	cc	_	_
49	only	only	ADV	RB	_	52	advmod	_	_
50	if	if	SCONJ	IN	_	52	mark	_	_
51	$ C $	$ c $	SYM	$	_	52	nsubj	_	_
52	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	73	advcl	_	_
53	locally	locally	ADV	RB	_	52	advmod	_	_
54	algebraically	algebraically	ADV	RB	_	55	advmod	_	_
55	cartesian	cartesian	ADJ	JJ	Degree=Pos	56	amod	_	_
56	closed	closed	ADJ	JJ	Degree=Pos	52	acomp	_	SpaceAfter=No
57	;	;	PUNCT	:	_	73	punct	_	_
58	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	59	punct	_	SpaceAfter=No
59	iii	iii	NOUN	NN	Number=Sing	73	meta	_	SpaceAfter=No
60	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	59	punct	_	_
61	the	the	DET	DT	Definite=Def|PronType=Art	62	det	_	_
62	span	span	NOUN	NN	Number=Sing	73	nsubj	_	_
63	of	of	ADP	IN	_	62	prep	_	_
64	split	split	ADJ	JJ	Degree=Pos	65	amod	_	_
65	extensions	extension	NOUN	NNS	Number=Plur	63	pobj	_	_
66	of	of	ADP	IN	_	65	prep	_	_
67	the	the	DET	DT	Definite=Def|PronType=Art	68	det	_	_
68	category	category	NOUN	NN	Number=Sing	66	pobj	_	_
69	of	of	ADP	IN	_	68	prep	_	_
70	morphisms	morphism	NOUN	NNS	Number=Plur	69	pobj	_	_
71	of	of	ADP	IN	_	70	prep	_	_
72	$ C $	$ c $	SYM	$	_	71	pobj	_	_
73	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	45	advcl	_	_
74	RFRA	RFRA	PROPN	NNP	Number=Sing	73	dobj	_	_
75	if	if	SCONJ	IN	_	80	mark	_	_
76	and	and	CCONJ	CC	ConjType=Cmp	80	cc	_	_
77	only	only	ADV	RB	_	80	advmod	_	_
78	if	if	SCONJ	IN	_	80	mark	_	_
79	$ C $	$ c $	SYM	$	_	80	nsubj	_	_
80	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	73	advcl	_	_
81	action	action	NOUN	NN	Number=Sing	82	npadvmod	_	_
82	representable	representable	ADJ	JJ	Degree=Pos	80	acomp	_	_
83	and	and	CCONJ	CC	ConjType=Cmp	80	cc	_	_
84	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	80	conj	_	_
85	normalizers	normalizer	NOUN	NNS	Number=Plur	84	dobj	_	SpaceAfter=No
86	;	;	PUNCT	:	_	101	punct	_	_
87	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	88	punct	_	SpaceAfter=No
88	iv	iv	PROPN	NNP	Number=Sing	101	meta	_	SpaceAfter=No
89	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	88	punct	_	_
90	the	the	DET	DT	Definite=Def|PronType=Art	92	det	_	_
91	reversed	reversed	ADJ	JJ	Degree=Pos	92	amod	_	_
92	span	span	NOUN	NN	Number=Sing	101	nsubj	_	_
93	to	to	ADP	IN	_	92	prep	_	_
94	the	the	DET	DT	Definite=Def|PronType=Art	95	det	_	_
95	one	one	NOUN	NN	Number=Sing	93	pobj	_	_
96	considered	consider	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	95	acl	_	_
97	in	in	ADP	IN	_	96	prep	_	_
98	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	97	punct	_	SpaceAfter=No
99	iii	iii	NOUN	NN	Number=Sing	97	pobj	_	SpaceAfter=No
100	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	95	punct	_	_
101	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
102	RFRA	RFRA	PROPN	NNP	Number=Sing	101	dobj	_	_
103	if	if	SCONJ	IN	_	108	mark	_	_
104	and	and	CCONJ	CC	ConjType=Cmp	108	cc	_	_
105	only	only	ADV	RB	_	108	advmod	_	_
106	if	if	SCONJ	IN	_	108	mark	_	_
107	$ C $	$ c $	SYM	$	_	108	nsubj	_	_
108	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	101	advcl	_	_
109	locally	locally	ADV	RB	_	108	advmod	_	_
110	algebraically	algebraically	ADV	RB	_	111	advmod	_	_
111	cartesian	cartesian	ADJ	JJ	Degree=Pos	112	amod	_	_
112	closed	closed	ADJ	JJ	Degree=Pos	108	acomp	_	SpaceAfter=No
113	.	.	PUNCT	.	PunctType=Peri	101	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also examine our condition for the span of monoid actions (of monoids in a monoidal category $ C $ on objects in a given category on which $ C $ acts), and for various other spans.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	examine	examine	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	5	poss	_	_
5	condition	condition	NOUN	NN	Number=Sing	3	dobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	span	span	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	monoid	monoid	NOUN	NN	Number=Sing	11	compound	_	_
11	actions	action	NOUN	NNS	Number=Plur	9	pobj	_	_
12	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	11	punct	_	SpaceAfter=No
13	of	of	ADP	IN	_	11	prep	_	_
14	monoids	monoid	NOUN	NNS	Number=Plur	13	pobj	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	monoidal	monoidal	ADJ	JJ	Degree=Pos	18	amod	_	_
18	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
19	$ C $	$ c $	SYM	$	_	3	dep	_	_
20	on	on	ADP	IN	_	3	prep	_	_
21	objects	object	NOUN	NNS	Number=Plur	20	pobj	_	_
22	in	in	ADP	IN	_	21	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
24	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	amod	_	_
25	category	category	NOUN	NN	Number=Sing	22	pobj	_	_
26	on	on	ADP	IN	_	29	prep	_	_
27	which	which	PRON	WDT	_	26	pobj	_	_
28	$ C $	$ c $	SYM	$	_	29	nmod	_	_
29	acts	act	NOUN	NNS	Number=Plur	25	relcl	_	SpaceAfter=No
30	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	3	punct	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
33	for	for	ADP	IN	_	3	prep	_	_
34	various	various	ADJ	JJ	Degree=Pos	36	amod	_	_
35	other	other	ADJ	JJ	Degree=Pos	36	amod	_	_
36	spans	span	NOUN	NNS	Number=Plur	33	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 725
# sent_id = 1
# text = We relate the relative nerve $ N_f(D) $ of a diagram of simplicial sets $ f : D to sSet $ with the Grothendieck construction $ Gr F $ of a simplicial functor $ F : D to sCat $ in the case where $ f = N F $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	relate	relate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	relative	relative	ADJ	JJ	Degree=Pos	5	amod	_	_
5	nerve	nerve	NOUN	NN	Number=Sing	2	dobj	_	_
6	$ N_f(D) $	$ n_f(d) $	SYM	$	_	5	appos	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
9	diagram	diagram	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	simplicial	simplicial	ADJ	JJ	Degree=Pos	12	amod	_	_
12	sets	set	NOUN	NNS	Number=Plur	10	pobj	_	_
13	$ f : D to sSet $	$ f : d to sset $	SYM	$	_	6	appos	_	_
14	with	with	ADP	IN	_	5	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	17	compound	_	_
17	construction	construction	NOUN	NN	Number=Sing	14	pobj	_	_
18	$ Gr F $	$ gr f $	SYM	$	_	2	dep	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
21	simplicial	simplicial	ADJ	JJ	Degree=Pos	22	amod	_	_
22	functor	functor	NOUN	NN	Number=Sing	19	pobj	_	_
23	$ F : D to sCat $	$ f : d to scat $	SYM	$	_	22	appos	_	_
24	in	in	ADP	IN	_	22	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	case	case	NOUN	NN	Number=Sing	24	pobj	_	_
27	where	where	SCONJ	WRB	_	28	advmod	_	_
28	$ f = N F $	$ f = n f $	SYM	$	_	2	advcl	_	_
29	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We further show that any strict monoidal simplicial category $ C $ gives rise to a functor $ C^bullet : Delta^op to sCat $ , and that the relative nerve of $ N C^bullet $ is the operadic nerve $ N^otimes(C) $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	further	far	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	11	mark	_	_
5	any	any	DET	DT	_	9	det	_	_
6	strict	strict	ADJ	JJ	Degree=Pos	9	amod	_	_
7	monoidal	monoidal	ADJ	JJ	Degree=Pos	9	amod	_	_
8	simplicial	simplicial	NOUN	NN	Number=Sing	9	amod	_	_
9	category	category	NOUN	NN	Number=Sing	11	nsubj	_	_
10	$ C $	$ c $	SYM	$	_	9	appos	_	_
11	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
12	rise	rise	VERB	VB	VerbForm=Inf	11	dobj	_	_
13	to	to	ADP	IN	_	12	prep	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	functor	functor	NOUN	NN	Number=Sing	16	compound	_	_
16	$ C^bullet : Delta^op to sCat $	$ c^bullet : delta^op to scat $	SYM	$	_	13	pobj	_	_
17	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
19	that	that	SCONJ	IN	_	25	mark	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
21	relative	relative	ADJ	JJ	Degree=Pos	22	amod	_	_
22	nerve	nerve	NOUN	NN	Number=Sing	25	nsubj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	$ N C^bullet $	$ n c^bullet $	SYM	$	_	23	pobj	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	conj	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	operadic	operadic	NOUN	NN	Number=Sing	28	compound	_	_
28	nerve	nerve	NOUN	NN	Number=Sing	25	attr	_	_
29	$ N^otimes(C) $	$ n^otimes(c) $	SYM	$	_	25	attr	_	_
30	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Finally, we show that all the above constructions commute with appropriately defined opposite functors.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	that	that	SCONJ	IN	_	10	mark	_	_
6	all	all	DET	PDT	_	9	predet	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	above	above	ADJ	JJ	Degree=Pos	9	amod	_	_
9	constructions	construction	NOUN	NNS	Number=Plur	10	nsubj	_	_
10	commute	commute	VERB	VBP	Tense=Pres|VerbForm=Fin	4	ccomp	_	_
11	with	with	ADP	IN	_	10	prep	_	_
12	appropriately	appropriately	ADV	RB	_	13	advmod	_	_
13	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
14	opposite	opposite	ADJ	JJ	Degree=Pos	15	amod	_	_
15	functors	functor	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 726
# sent_id = 1
# text = Certain aspects of Street's formal theory of monads in 2 - categories are extended to multimonoidal monads in symmetric strict monoidal 2 - categories.
1	Certain	certain	ADJ	JJ	Degree=Pos	2	amod	_	_
2	aspects	aspect	NOUN	NNS	Number=Plur	15	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	Street	Street	PROPN	NNP	Number=Sing	7	poss	_	SpaceAfter=No
5	's	's	PART	POS	_	4	case	_	_
6	formal	formal	ADJ	JJ	Degree=Pos	7	amod	_	_
7	theory	theory	NOUN	NN	Number=Sing	3	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	monads	monad	NOUN	NNS	Number=Plur	8	pobj	_	_
10	in	in	ADP	IN	_	2	prep	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	categories	category	NOUN	NNS	Number=Plur	10	pobj	_	_
14	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	auxpass	_	_
15	extended	extend	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
16	to	to	ADP	IN	_	15	prep	_	_
17	multimonoidal	multimonoidal	ADJ	JJ	Degree=Pos	18	amod	_	_
18	monads	monad	NOUN	NNS	Number=Plur	16	pobj	_	_
19	in	in	ADP	IN	_	15	prep	_	_
20	symmetric	symmetric	ADJ	JJ	Degree=Pos	25	amod	_	_
21	strict	strict	ADJ	JJ	Degree=Pos	25	amod	_	_
22	monoidal	monoidal	ADJ	JJ	Degree=Pos	25	amod	_	_
23	2	2	NUM	CD	NumType=Card	25	nummod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	categories	category	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 2
# text = Namely, any symmetric strict monoidal 2 - category $ M $ admits a symmetric strict monoidal 2 - category of pseudomonoids, monoidal 1 - cells and monoidal 2 - cells in $ M $ .
1	Namely	namely	ADV	RB	_	11	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
3	any	any	DET	DT	_	9	det	_	_
4	symmetric	symmetric	ADJ	JJ	Degree=Pos	6	amod	_	_
5	strict	strict	ADJ	JJ	Degree=Pos	6	amod	_	_
6	monoidal	monoidal	ADJ	JJ	Degree=Pos	9	amod	_	_
7	2	2	NUM	CD	NumType=Card	9	nummod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	category	category	NOUN	NN	Number=Sing	11	nsubj	_	_
10	$ M $	$ m $	SYM	$	_	11	nsubj	_	_
11	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
13	symmetric	symmetric	ADJ	JJ	Degree=Pos	18	amod	_	_
14	strict	strict	ADJ	JJ	Degree=Pos	18	amod	_	_
15	monoidal	monoidal	ADJ	JJ	Degree=Pos	18	amod	_	_
16	2	2	NUM	CD	NumType=Card	18	nummod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	category	category	NOUN	NN	Number=Sing	11	dobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	pseudomonoids	pseudomonoid	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
22	monoidal	monoidal	ADJ	JJ	Degree=Pos	25	amod	_	_
23	1	1	NUM	CD	NumType=Card	25	nummod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	cells	cell	NOUN	NNS	Number=Plur	18	conj	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
27	monoidal	monoidal	ADJ	JJ	Degree=Pos	30	amod	_	_
28	2	2	NUM	CD	NumType=Card	30	nummod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	cells	cell	NOUN	NNS	Number=Plur	25	conj	_	_
31	in	in	ADP	IN	_	25	prep	_	_
32	$ M $	$ m $	SYM	$	_	31	pobj	_	_
33	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 3
# text = Dually, there is a symmetric strict monoidal 2 - category of pseudomonoids, opmonoidal 1 - cells and opmonoidal 2 - cells in $ M $ .
1	Dually	Dually	PROPN	NNP	Number=Sing	4	npadvmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	there	there	PRON	EX	_	4	expl	_	_
4	is	be	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
6	symmetric	symmetric	ADJ	JJ	Degree=Pos	11	amod	_	_
7	strict	strict	ADJ	JJ	Degree=Pos	11	amod	_	_
8	monoidal	monoidal	ADJ	JJ	Degree=Pos	11	amod	_	_
9	2	2	NUM	CD	NumType=Card	11	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	category	category	NOUN	NN	Number=Sing	4	attr	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	pseudomonoids	pseudomonoid	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
15	opmonoidal	opmonoidal	ADJ	JJ	Degree=Pos	18	amod	_	_
16	1	1	NUM	CD	NumType=Card	18	nummod	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	cells	cell	NOUN	NNS	Number=Plur	4	attr	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	opmonoidal	opmonoidal	ADJ	JJ	Degree=Pos	23	amod	_	_
21	2	2	NUM	CD	NumType=Card	23	nummod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	cells	cell	NOUN	NNS	Number=Plur	18	conj	_	_
24	in	in	ADP	IN	_	23	prep	_	_
25	$ M $	$ m $	SYM	$	_	24	pobj	_	_
26	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = Extending a construction due to Aguiar and Mahajan for $ M = Cat $ , we may apply the first construction $ p $ times and the second one $ q $ times (in any order).
1	Extending	extend	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	advcl	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	construction	construction	NOUN	NN	Number=Sing	1	dobj	_	_
4	due	due	ADP	IN	_	1	prep	_	_
5	to	to	ADP	IN	_	4	pcomp	_	_
6	Aguiar	Aguiar	PROPN	NNP	Number=Sing	4	pobj	_	_
7	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
8	Mahajan	Mahajan	PROPN	NNP	Number=Sing	6	conj	_	_
9	for	for	ADP	IN	_	1	prep	_	_
10	$ M = Cat $	$ m = cat $	SYM	$	_	9	pobj	_	_
11	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
12	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
13	may	may	AUX	MD	VerbForm=Fin	14	aux	_	_
14	apply	apply	VERB	VB	VerbForm=Inf	0	ROOT	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	first	first	ADJ	JJ	Degree=Pos	17	amod	_	_
17	construction	construction	NOUN	NN	Number=Sing	14	dobj	_	_
18	$ p $	$ p $	SYM	$	_	19	nmod	_	_
19	times	time	NOUN	NNS	Number=Plur	14	npadvmod	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	second	second	ADJ	JJ	Degree=Pos	23	amod	_	_
23	one	one	NUM	CD	NumType=Card	19	conj	_	_
24	$ q $	$ q $	SYM	$	_	25	nmod	_	_
25	times	time	NOUN	NNS	Number=Plur	23	npadvmod	_	_
26	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	23	punct	_	SpaceAfter=No
27	in	in	ADP	IN	_	23	prep	_	_
28	any	any	DET	DT	_	29	det	_	_
29	order	order	NOUN	NN	Number=Sing	27	pobj	_	SpaceAfter=No
30	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	14	punct	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# sent_id = 5
# text = It yields a 2 - category $ M_{pq} $ .
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	yields	yield	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
4	2	2	NUM	CD	NumType=Card	6	nummod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	category	category	NOUN	NN	Number=Sing	7	compound	_	_
7	$ M_{pq} $	$ m_{pq} $	SYM	$	_	2	dobj	_	_
8	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 6
# text = A 0 - cell therein is an object $ A $ of $ M $ together with $ p+q $ compatible pseudomonoid structures; it is termed a $ (p+q) $ - oidal object in $ M $ .
1	A	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
2	0	0	NUM	CD	NumType=Card	4	nummod	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	cell	cell	NOUN	NN	Number=Sing	5	compound	_	_
5	therein	therein	ADV	RB	_	6	advmod	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	21	ccomp	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	object	object	NOUN	NN	Number=Sing	6	attr	_	_
9	$ A $	$ a $	SYM	$	_	8	prep	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	$ M $	$ m $	SYM	$	_	10	pobj	_	_
12	together	together	ADV	RB	_	8	advmod	_	_
13	with	with	ADP	IN	_	8	prep	_	_
14	$ p+q $	$ p+q $	SYM	$	_	17	nmod	_	_
15	compatible	compatible	ADJ	JJ	Degree=Pos	17	amod	_	_
16	pseudomonoid	pseudomonoid	NOUN	NN	Number=Sing	17	compound	_	_
17	structures	structure	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
18	;	;	PUNCT	:	_	21	punct	_	_
19	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	21	nsubjpass	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	21	auxpass	_	_
21	termed	term	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
23	$ (p+q) $	$ (p+q) $	NUM	CD	NumType=Card	25	amod	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	oidal	oidal	ADJ	JJ	Degree=Pos	26	amod	_	_
26	object	object	NOUN	NN	Number=Sing	21	oprd	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	$ M $	$ m $	SYM	$	_	27	pobj	_	_
29	.	.	PUNCT	.	PunctType=Peri	21	punct	_	SpaceAfter=No

# sent_id = 7
# text = A monad in $ M_{pq} $ is called a $ (p, q) $ - oidal monad in $ M $ ; it is a monad $ t $ on $ A $ in $ M $ together with $ p $ monoidal, and $ q $ opmonoidal structures in a compatible way.
1	A	a	DET	DT	Definite=Ind|PronType=Art	2	det	_	_
2	monad	monad	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	$ M_{pq} $	$ m_{pq} $	SYM	$	_	3	pobj	_	_
5	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	called	call	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	ccomp	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	$ (p, q) $	$ (p, q) $	NUM	CD	NumType=Card	10	amod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	oidal	oidal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	monad	monad	NOUN	NNS	Number=Plur	6	oprd	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	$ M $	$ m $	SYM	$	_	12	pobj	_	_
14	;	;	PUNCT	:	_	16	punct	_	_
15	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	16	nsubj	_	_
16	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	monad	monad	NOUN	NNS	Number=Plur	16	attr	_	_
19	$ t $	$ t $	SYM	$	_	18	appos	_	_
20	on	on	ADP	IN	_	18	prep	_	_
21	$ A $	$ a $	SYM	$	_	20	pobj	_	_
22	in	in	ADP	IN	_	20	prep	_	_
23	$ M $	$ m $	SYM	$	_	22	pobj	_	_
24	together	together	ADV	RB	_	18	advmod	_	_
25	with	with	ADP	IN	_	18	prep	_	_
26	$ p $	$ p $	SYM	$	_	27	nmod	_	_
27	monoidal	monoidal	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
30	$ q $	$ q $	SYM	$	_	32	nummod	_	_
31	opmonoidal	opmonoidal	NOUN	NN	Number=Sing	32	compound	_	_
32	structures	structure	NOUN	NNS	Number=Plur	18	conj	_	_
33	in	in	ADP	IN	_	16	prep	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
35	compatible	compatible	ADJ	JJ	Degree=Pos	36	amod	_	_
36	way	way	NOUN	NN	Number=Sing	33	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 8
# text = If $ M $ has monoidal Eilenberg - Moore construction, and certain (Linton type) stable coequalizers exist, then a $ (p+q) $ - oidal structure on the Eilenberg - Moore object $ A^t $ of a $ (p, q) $ - oidal monad $ (A, t) $ is shown to arise via a symmetric strict monoidal double functor to Ehresmann's double category $ Sqr(M) $ of squares in $ M $ , from the double category of monads in $ Sqr(M) $ in the sense of Fiore, Gambino and Kock.
1	If	if	SCONJ	IN	_	3	mark	_	_
2	$ M $	$ m $	SYM	$	_	3	nsubj	_	_
3	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	31	advcl	_	_
4	monoidal	monoidal	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
5	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	7	compound	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	Moore	Moore	PROPN	NNP	Number=Sing	8	compound	_	_
8	construction	construction	NOUN	NN	Number=Sing	3	dobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
11	certain	certain	ADJ	JJ	Degree=Pos	14	amod	_	_
12	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	14	punct	_	SpaceAfter=No
13	Linton	Linton	PROPN	NNP	Number=Sing	14	compound	_	_
14	type	type	NOUN	NN	Number=Sing	18	nsubj	_	SpaceAfter=No
15	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	14	punct	_	_
16	stable	stable	ADJ	JJ	Degree=Pos	17	amod	_	_
17	coequalizers	coequalizer	NOUN	NNS	Number=Plur	18	nsubj	_	_
18	exist	exist	VERB	VBP	Tense=Pres|VerbForm=Fin	3	conj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	then	then	ADV	RB	PronType=Dem	25	advmod	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
22	$ (p+q) $	$ (p+q) $	SYM	$	_	24	amod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	oidal	oidal	ADJ	JJ	Degree=Pos	25	amod	_	_
25	structure	structure	NOUN	NN	Number=Sing	31	nsubj	_	_
26	on	on	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
28	Eilenberg	Eilenberg	PROPN	NNP	Number=Sing	30	compound	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	Moore	Moore	PROPN	NNP	Number=Sing	26	pobj	_	_
31	object	object	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
32	$ A^t $	$ a^t $	SYM	$	_	31	dobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	a	a	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
35	$ (p, q) $	$ (p, q) $	SYM	$	_	37	amod	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	oidal	oidal	ADJ	JJ	Degree=Pos	38	amod	_	_
38	monad	monad	NOUN	NNS	Number=Plur	33	pobj	_	_
39	$ (A, t) $	$ (a, t) $	SYM	$	_	41	nsubjpass	_	_
40	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	41	auxpass	_	_
41	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	38	relcl	_	_
42	to	to	PART	TO	_	43	aux	_	_
43	arise	arise	VERB	VB	VerbForm=Inf	41	xcomp	_	_
44	via	via	ADP	IN	_	43	prep	_	_
45	a	a	DET	DT	Definite=Ind|PronType=Art	50	det	_	_
46	symmetric	symmetric	ADJ	JJ	Degree=Pos	50	amod	_	_
47	strict	strict	ADJ	JJ	Degree=Pos	50	amod	_	_
48	monoidal	monoidal	ADJ	JJ	Degree=Pos	50	amod	_	_
49	double	double	ADJ	JJ	Degree=Pos	50	amod	_	_
50	functor	functor	NOUN	NN	Number=Sing	44	pobj	_	_
51	to	to	ADP	IN	_	43	prep	_	_
52	Ehresmann	Ehresmann	PROPN	NNP	Number=Sing	55	poss	_	SpaceAfter=No
53	's	's	PART	POS	_	52	case	_	_
54	double	double	ADJ	JJ	Degree=Pos	55	amod	_	_
55	category	category	NOUN	NN	Number=Sing	51	pobj	_	_
56	$ Sqr(M) $	$ sqr(m) $	SYM	$	_	55	appos	_	_
57	of	of	ADP	IN	_	56	prep	_	_
58	squares	square	NOUN	NNS	Number=Plur	57	pobj	_	_
59	in	in	ADP	IN	_	55	prep	_	_
60	$ M $	$ m $	SYM	$	_	59	pobj	_	_
61	,	,	PUNCT	,	PunctType=Comm	41	punct	_	_
62	from	from	ADP	IN	_	41	prep	_	_
63	the	the	DET	DT	Definite=Def|PronType=Art	65	det	_	_
64	double	double	ADJ	JJ	Degree=Pos	65	amod	_	_
65	category	category	NOUN	NN	Number=Sing	62	pobj	_	_
66	of	of	ADP	IN	_	65	prep	_	_
67	monads	monad	NOUN	NNS	Number=Plur	66	pobj	_	_
68	in	in	ADP	IN	_	65	prep	_	_
69	$ Sqr(M) $	$ sqr(m) $	SYM	$	_	68	pobj	_	_
70	in	in	ADP	IN	_	62	prep	_	_
71	the	the	DET	DT	Definite=Def|PronType=Art	72	det	_	_
72	sense	sense	NOUN	NN	Number=Sing	70	pobj	_	_
73	of	of	ADP	IN	_	72	prep	_	_
74	Fiore	Fiore	PROPN	NNP	Number=Sing	73	pobj	_	SpaceAfter=No
75	,	,	PUNCT	,	PunctType=Comm	74	punct	_	_
76	Gambino	Gambino	PROPN	NNP	Number=Sing	74	conj	_	_
77	and	and	CCONJ	CC	ConjType=Cmp	76	cc	_	_
78	Kock	Kock	PROPN	NNP	Number=Sing	76	conj	_	SpaceAfter=No
79	.	.	PUNCT	.	PunctType=Peri	31	punct	_	SpaceAfter=No

# sent_id = 9
# text = While $ q $ ones of the pseudomonoid structures of $ A^t $ are lifted along the `forgetful' 1 - cell $ A^t - > A $ , the other $ p $ ones are lifted along its left adjoint.
1	While	while	SCONJ	IN	_	11	mark	_	_
2	$ q $	$ q $	SYM	$	_	3	nummod	_	_
3	ones	one	NOUN	NNS	Number=Plur	11	nsubjpass	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
6	pseudomonoid	pseudomonoid	NOUN	NN	Number=Sing	7	compound	_	_
7	structures	structure	NOUN	NNS	Number=Plur	4	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	$ A^t $	$ a^t $	SYM	$	_	8	pobj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	11	auxpass	_	_
11	lifted	lift	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	advcl	_	_
12	along	along	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
14	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	19	punct	_	SpaceAfter=No
15	forgetful	forgetful	ADJ	JJ	Degree=Pos	19	amod	_	SpaceAfter=No
16	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	19	punct	_	_
17	1	1	NUM	CD	NumType=Card	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	cell	cell	NOUN	NN	Number=Sing	12	pobj	_	_
20	$ A^t - > A $	$ a^t - > a $	SYM	$	_	19	appos	_	_
21	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
23	other	other	ADJ	JJ	Degree=Pos	25	amod	_	_
24	$ p $	$ p $	SYM	$	_	23	cc	_	_
25	ones	one	NOUN	NNS	Number=Plur	27	nsubjpass	_	_
26	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	27	auxpass	_	_
27	lifted	lift	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
28	along	along	ADP	IN	_	27	prep	_	_
29	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	31	poss	_	_
30	left	left	ADJ	JJ	Degree=Pos	31	amod	_	_
31	adjoint	adjoint	NOUN	NN	Number=Sing	28	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	27	punct	_	SpaceAfter=No

# sent_id = 10
# text = In the particular example when $ M $ is an appropriate 2 - subcategory of $ Cat $ , this yields a conceptually different proof of some recent results due to Aguiar, Haim and Lopez Franco.
1	In	in	ADP	IN	_	17	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	particular	particular	ADJ	JJ	Degree=Pos	4	amod	_	_
4	example	example	NOUN	NN	Number=Sing	1	pobj	_	_
5	when	when	SCONJ	WRB	_	7	advmod	_	_
6	$ M $	$ m $	SYM	$	_	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	advcl	_	_
8	an	an	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
9	appropriate	appropriate	ADJ	JJ	Degree=Pos	12	amod	_	_
10	2	2	NUM	CD	NumType=Card	12	nummod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	subcategory	subcategory	NOUN	NN	Number=Sing	7	attr	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	$ Cat $	$ cat $	SYM	$	_	13	pobj	_	_
15	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
16	this	this	PRON	DT	Number=Sing|PronType=Dem	17	nsubj	_	_
17	yields	yield	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
19	conceptually	conceptually	ADV	RB	_	20	advmod	_	_
20	different	different	ADJ	JJ	Degree=Pos	21	amod	_	_
21	proof	proof	NOUN	NN	Number=Sing	17	dobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	some	some	DET	DT	_	25	det	_	_
24	recent	recent	ADJ	JJ	Degree=Pos	25	amod	_	_
25	results	result	NOUN	NNS	Number=Plur	22	pobj	_	_
26	due	due	ADJ	JJ	Degree=Pos	25	amod	_	_
27	to	to	ADP	IN	_	26	pcomp	_	_
28	Aguiar	Aguiar	PROPN	NNP	Number=Sing	27	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
30	Haim	Haim	PROPN	NNP	Number=Sing	28	conj	_	_
31	and	and	CCONJ	CC	ConjType=Cmp	30	cc	_	_
32	Lopez	Lopez	PROPN	NNP	Number=Sing	33	compound	_	_
33	Franco	Franco	PROPN	NNP	Number=Sing	30	conj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# doc_id = 727
# sent_id = 1
# text = We give necessary and sufficient conditions on a presentable $ infty $ - category $ C $ so that families of objects of $ C $ form an $ infty $ - topos.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	necessary	necessary	ADJ	JJ	Degree=Pos	6	amod	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
5	sufficient	sufficient	ADJ	JJ	Degree=Pos	3	conj	_	_
6	conditions	condition	NOUN	NNS	Number=Plur	2	dobj	_	_
7	on	on	ADP	IN	_	2	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
9	presentable	presentable	ADJ	JJ	Degree=Pos	12	amod	_	_
10	$ infty $	$ infty $	SYM	$	_	12	nmod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
13	$ C $	$ c $	SYM	$	_	14	nmod	_	_
14	so	so	SCONJ	IN	_	2	dative	_	_
15	that	that	SCONJ	IN	_	21	mark	_	_
16	families	family	NOUN	NNS	Number=Plur	21	nsubj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	objects	object	NOUN	NNS	Number=Plur	17	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	$ C $	$ c $	SYM	$	_	19	pobj	_	_
21	form	form	VERB	VB	VerbForm=Inf	2	ccomp	_	_
22	an	an	DET	DT	Definite=Ind|PronType=Art	25	det	_	_
23	$ infty $	$ infty $	SYM	$	_	25	compound	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	topos	topos	NOUN	NN	Number=Sing	21	dobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In particular, we prove a conjecture of Joyal that this is the case whenever $ C $ is stable.
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	conjecture	conjecture	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	Joyal	Joyal	PROPN	NNP	Number=Sing	8	pobj	_	_
10	that	that	SCONJ	IN	_	12	mark	_	_
11	this	this	PRON	DT	Number=Sing|PronType=Dem	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	acl	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	case	case	NOUN	NN	Number=Sing	12	attr	_	_
15	whenever	whenever	SCONJ	WRB	_	17	advmod	_	_
16	$ C $	$ c $	SYM	$	_	17	nsubj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	advcl	_	_
18	stable	stable	ADJ	JJ	Degree=Pos	17	acomp	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# doc_id = 728
# sent_id = 1
# text = In this paper, we introduce the notion of a pre - Lie 2 - algebra, which is the categorification of a pre - Lie algebra.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	notion	notion	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
11	pre	pre	ADJ	JJ	Degree=Pos	13	nmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	Lie	lie	NOUN	NN	Number=Sing	16	nmod	_	_
14	2	2	NUM	CD	NumType=Card	16	nummod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	algebra	algebra	PROPN	NNP	Number=Sing	9	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	which	which	PRON	WDT	_	19	nsubj	_	_
19	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	16	relcl	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
21	categorification	categorification	NOUN	NN	Number=Sing	19	attr	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
24	pre	pre	ADJ	JJ	Degree=Pos	26	amod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	Lie	lie	NOUN	NN	Number=Sing	27	compound	_	_
27	algebra	algebra	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = We prove that the category of pre - Lie 2 - algebras and the category of 2 - term pre - Lie $ _infty $ - algebras are equivalent.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	26	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	category	category	NOUN	NN	Number=Sing	26	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	pre	pre	ADJ	JJ	Degree=Pos	9	nmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	Lie	lie	NOUN	NN	Number=Sing	6	pobj	_	_
10	2	2	NUM	CD	NumType=Card	12	nummod	_	_
11	-	-	PUNCT	HYPH	PunctType=Dash	12	punct	_	_
12	algebras	algebra	NOUN	NNS	Number=Plur	6	pobj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
15	category	category	NOUN	NN	Number=Sing	12	conj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	2	2	NUM	CD	NumType=Card	19	nummod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	term	term	NOUN	NN	Number=Sing	16	pobj	_	_
20	pre	pre	NOUN	NN	Number=Sing	26	nsubj	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	Lie	lie	VERB	VB	VerbForm=Inf	20	nmod	_	_
23	$ _infty $	$ _infty $	SYM	$	_	25	compound	_	_
24	-	-	PUNCT	HYPH	PunctType=Dash	25	punct	_	_
25	algebras	algebra	NOUN	NNS	Number=Plur	26	nsubj	_	_
26	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
27	equivalent	equivalent	ADJ	JJ	Degree=Pos	26	acomp	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = We classify skeletal pre - Lie 2 - algebras by the third cohomology group of a pre - Lie algebra.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	classify	classify	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	skeletal	skeletal	ADJ	JJ	Degree=Pos	9	amod	_	_
4	pre	pre	ADJ	AFX	Hyph=Yes	6	amod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	Lie	lie	NOUN	NN	Number=Sing	3	nmod	_	_
7	2	2	NUM	CD	NumType=Card	9	nummod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	algebras	algebra	NOUN	NNS	Number=Plur	2	dobj	_	_
10	by	by	ADP	IN	_	2	prep	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
12	third	third	ADJ	JJ	Degree=Pos	14	amod	_	_
13	cohomology	cohomology	NOUN	NN	Number=Sing	14	compound	_	_
14	group	group	NOUN	NN	Number=Sing	10	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
17	pre	pre	ADJ	JJ	Degree=Pos	19	amod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	Lie	lie	NOUN	NN	Number=Sing	20	compound	_	_
20	algebra	algebra	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = We prove that crossed modules of pre - Lie algebras are in one - to - one correspondence with strict pre - Lie 2 - algebras.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	4	nsubj	_	_
4	crossed	cross	VERB	VBD	Tense=Past|VerbForm=Fin	2	ccomp	_	_
5	modules	module	NOUN	NNS	Number=Plur	4	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	pre	pre	ADJ	JJ	Degree=Pos	9	amod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	Lie	lie	ADJ	JJ	Degree=Pos	10	compound	_	_
10	algebras	algebra	NOUN	NNS	Number=Plur	6	pobj	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	one	one	NUM	CD	NumType=Card	18	nummod	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
15	to	to	ADP	IN	_	13	prep	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
17	one	one	NUM	CD	NumType=Card	15	pobj	_	_
18	correspondence	correspondence	NOUN	NN	Number=Sing	12	pobj	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	strict	strict	ADJ	JJ	Degree=Pos	26	amod	_	_
21	pre	pre	ADJ	AFX	Hyph=Yes	23	compound	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	Lie	lie	NOUN	NN	Number=Sing	20	nmod	_	_
24	2	2	NUM	CD	NumType=Card	26	nummod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	algebras	algebra	NOUN	NNS	Number=Plur	19	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = O - operators on Lie 2 - algebras are introduced, which can be used to construct pre - Lie 2 - algebras.
1	O	o	NOUN	NN	Number=Sing	3	compound	_	_
2	-	-	PUNCT	HYPH	PunctType=Dash	3	punct	_	_
3	operators	operator	NOUN	NNS	Number=Plur	10	nsubjpass	_	_
4	on	on	ADP	IN	_	3	prep	_	_
5	Lie	Lie	PROPN	NNP	Number=Sing	4	pobj	_	_
6	2	2	NUM	CD	NumType=Card	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	algebras	algebra	NOUN	NNS	Number=Plur	10	nsubjpass	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	10	auxpass	_	_
10	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	which	which	PRON	WDT	_	15	nsubjpass	_	_
13	can	can	AUX	MD	VerbForm=Fin	15	aux	_	_
14	be	be	AUX	VB	VerbForm=Inf	15	auxpass	_	_
15	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	relcl	_	_
16	to	to	PART	TO	_	17	aux	_	_
17	construct	construct	VERB	VB	VerbForm=Inf	15	xcomp	_	_
18	pre	pre	ADJ	JJ	Degree=Pos	20	advmod	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	Lie	lie	NOUN	NN	Number=Sing	17	dobj	_	_
21	2	2	NUM	CD	NumType=Card	23	nummod	_	_
22	-	-	PUNCT	HYPH	PunctType=Dash	23	punct	_	_
23	algebras	algebra	NOUN	NNS	Number=Plur	17	dobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 6
# text = As an application, we give solutions of 2 - graded classical Yang - Baxter equations in some semidirect product Lie 2 - algebras.
1	As	as	ADP	IN	_	6	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	solutions	solution	NOUN	NNS	Number=Plur	6	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	2	2	NUM	CD	NumType=Card	11	npadvmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	graded	grade	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
12	classical	classical	ADJ	JJ	Degree=Pos	16	amod	_	_
13	Yang	Yang	PROPN	NNP	Number=Sing	15	compound	_	_
14	-	-	PUNCT	HYPH	PunctType=Dash	15	punct	_	_
15	Baxter	Baxter	PROPN	NNP	Number=Sing	16	compound	_	_
16	equations	equation	NOUN	NNS	Number=Plur	8	pobj	_	_
17	in	in	ADP	IN	_	6	prep	_	_
18	some	some	DET	DT	_	21	det	_	_
19	semidirect	semidirect	NOUN	NN	Number=Sing	20	compound	_	_
20	product	product	NOUN	NN	Number=Sing	21	compound	_	_
21	Lie	lie	NOUN	NN	Number=Sing	17	pobj	_	_
22	2	2	NUM	CD	NumType=Card	24	nummod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	algebras	algebra	NOUN	NNS	Number=Plur	6	dobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 729
# sent_id = 1
# text = We introduce the notion of a majority category—the categorical counterpart of varieties of universal algebras admitting a majority term.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
7	majority	majority	NOUN	NN	Number=Sing	8	compound	_	_
8	category	category	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
9	—	—	PUNCT	:	_	8	punct	_	SpaceAfter=No
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	categorical	categorical	ADJ	JJ	Degree=Pos	12	amod	_	_
12	counterpart	counterpart	NOUN	NN	Number=Sing	8	appos	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	varieties	variety	NOUN	NNS	Number=Plur	13	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	universal	universal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	algebras	algebra	NOUN	NNS	Number=Plur	15	pobj	_	_
18	admitting	admit	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	acl	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
20	majority	majority	NOUN	NN	Number=Sing	21	compound	_	_
21	term	term	NOUN	NN	Number=Sing	18	dobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = This notion can be thought to capture properties of the category of lattices, in a way that parallels how Maltsev categories capture properties of the category of groups.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	notion	notion	NOUN	NN	Number=Sing	5	nsubjpass	_	_
3	can	can	AUX	MD	VerbForm=Fin	5	aux	_	_
4	be	be	AUX	VB	VerbForm=Inf	5	auxpass	_	_
5	thought	think	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	to	to	PART	TO	_	7	aux	_	_
7	capture	capture	VERB	VB	VerbForm=Inf	5	xcomp	_	_
8	properties	property	NOUN	NNS	Number=Plur	7	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	lattices	lattice	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
15	in	in	ADP	IN	_	7	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
17	way	way	NOUN	NN	Number=Sing	15	pobj	_	_
18	that	that	PRON	WDT	PronType=Rel	19	nsubj	_	_
19	parallels	parallel	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
20	how	how	SCONJ	WRB	_	23	advmod	_	_
21	Maltsev	maltsev	ADJ	JJ	Degree=Pos	22	amod	_	_
22	categories	category	NOUN	NNS	Number=Plur	23	nsubj	_	_
23	capture	capture	VERB	VBP	Tense=Pres|VerbForm=Fin	19	ccomp	_	_
24	properties	property	NOUN	NNS	Number=Plur	23	dobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	category	category	NOUN	NN	Number=Sing	25	pobj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	groups	group	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = Among algebraic majority categories are the categories of lattices, Boolean algebras and Heyting algebras.
1	Among	among	ADP	IN	_	5	prep	_	_
2	algebraic	algebraic	ADJ	JJ	Degree=Pos	4	amod	_	_
3	majority	majority	NOUN	NN	Number=Sing	4	compound	_	_
4	categories	category	NOUN	NNS	Number=Plur	1	pobj	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	categories	category	NOUN	NNS	Number=Plur	5	nsubj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	lattices	lattice	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	Boolean	boolean	ADJ	JJ	Degree=Pos	12	amod	_	_
12	algebras	algebra	NOUN	NNS	Number=Plur	9	conj	_	_
13	and	and	CCONJ	CC	ConjType=Cmp	12	cc	_	_
14	Heyting	Heyting	PROPN	NNP	Number=Sing	12	conj	_	_
15	algebras	algebra	NOUN	NNS	Number=Plur	12	conj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = Many geometric categories such as the category of topological spaces, metric spaces, ordered sets, any topos, et cetera, are comajority categories (that is, their duals are majority categories), and we show that, under mild assumptions, the only categories which are both majority and comajority, are the preorders.
1	Many	many	ADJ	JJ	Degree=Pos	3	amod	_	_
2	geometric	geometric	ADJ	JJ	Degree=Pos	3	amod	_	_
3	categories	category	NOUN	NNS	Number=Plur	24	nsubj	_	_
4	such	such	ADJ	JJ	Degree=Pos	5	amod	_	_
5	as	as	ADP	IN	_	3	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	category	category	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	topological	topological	ADJ	JJ	Degree=Pos	10	amod	_	_
10	spaces	space	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	metric	metric	ADJ	JJ	Degree=Pos	13	amod	_	_
13	spaces	space	NOUN	NNS	Number=Plur	10	conj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	ordered	order	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
16	sets	set	NOUN	NNS	Number=Plur	13	conj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	any	any	DET	DT	_	19	det	_	_
19	topos	topos	NOUN	NN	Number=Sing	16	conj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
21	et	et	NOUN	NN	Number=Sing	22	compound	_	_
22	cetera	cetera	PROPN	NNP	Number=Sing	7	appos	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
24	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	33	ccomp	_	_
25	comajority	comajority	NOUN	NN	Number=Sing	26	compound	_	_
26	categories	category	NOUN	NNS	Number=Plur	24	attr	_	_
27	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	26	punct	_	SpaceAfter=No
28	that	that	ADV	RB	_	29	advmod	_	_
29	is	is	ADV	RB	_	33	advmod	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
31	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	32	poss	_	_
32	duals	dual	NOUN	NNS	Number=Plur	33	nsubj	_	_
33	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
34	majority	majority	NOUN	NN	Number=Sing	35	compound	_	_
35	categories	category	NOUN	NNS	Number=Plur	33	attr	_	SpaceAfter=No
36	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	33	punct	_	SpaceAfter=No
37	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
38	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
39	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	40	nsubj	_	_
40	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	33	conj	_	_
41	that	that	SCONJ	IN	_	57	mark	_	SpaceAfter=No
42	,	,	PUNCT	,	PunctType=Comm	57	punct	_	_
43	under	under	ADP	IN	_	57	prep	_	_
44	mild	mild	ADJ	JJ	Degree=Pos	45	amod	_	_
45	assumptions	assumption	NOUN	NNS	Number=Plur	43	pobj	_	SpaceAfter=No
46	,	,	PUNCT	,	PunctType=Comm	57	punct	_	_
47	the	the	DET	DT	Definite=Def|PronType=Art	49	det	_	_
48	only	only	ADJ	JJ	Degree=Pos	49	amod	_	_
49	categories	category	NOUN	NNS	Number=Plur	57	nsubj	_	_
50	which	which	PRON	WDT	_	51	nsubj	_	_
51	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	49	relcl	_	_
52	both	both	PRON	DT	_	51	dep	_	_
53	majority	majority	NOUN	NN	Number=Sing	51	attr	_	_
54	and	and	CCONJ	CC	ConjType=Cmp	53	cc	_	_
55	comajority	comajority	NOUN	NN	Number=Sing	53	conj	_	SpaceAfter=No
56	,	,	PUNCT	,	PunctType=Comm	49	punct	_	_
57	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	40	ccomp	_	_
58	the	the	DET	DT	Definite=Def|PronType=Art	59	det	_	_
59	preorders	preorder	NOUN	NNS	Number=Plur	57	attr	_	SpaceAfter=No
60	.	.	PUNCT	.	PunctType=Peri	40	punct	_	SpaceAfter=No

# sent_id = 5
# text = Maltsev majority categories provide an alternative generalization of arithmetical categories to protoarithmetical categories in the sense of Bourn.
1	Maltsev	maltsev	ADJ	JJ	Degree=Pos	3	amod	_	_
2	majority	majority	NOUN	NN	Number=Sing	3	compound	_	_
3	categories	category	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	provide	provide	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	alternative	alternative	ADJ	JJ	Degree=Pos	7	amod	_	_
7	generalization	generalization	NOUN	NN	Number=Sing	4	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	arithmetical	arithmetical	ADJ	JJ	Degree=Pos	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	_
11	to	to	ADP	IN	_	4	dative	_	_
12	protoarithmetical	protoarithmetical	ADJ	JJ	Degree=Pos	13	amod	_	_
13	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	_
14	in	in	ADP	IN	_	4	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	sense	sense	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	Bourn	Bourn	PROPN	NNP	Number=Sing	17	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 6
# text = We show that every Maltsev majority category is protoarithmetical, provide a counter - example for the converse implication, and show that in the Barr - exact context, the converse implication also holds.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	8	mark	_	_
4	every	every	DET	DT	_	7	det	_	_
5	Maltsev	Maltsev	PROPN	NNP	Number=Sing	7	compound	_	_
6	majority	majority	NOUN	NN	Number=Sing	7	compound	_	_
7	category	category	NOUN	NN	Number=Sing	8	nsubj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
9	protoarithmetical	protoarithmetical	ADJ	JJ	Degree=Pos	8	acomp	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
11	provide	provide	VERB	VB	VerbForm=Inf	8	conj	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	counter	counter	NOUN	NN	Number=Sing	11	dobj	_	_
14	-	-	NOUN	NN	Number=Sing	15	punct	_	_
15	example	example	NOUN	NN	Number=Sing	11	dobj	_	_
16	for	for	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	converse	converse	NOUN	NN	Number=Sing	19	compound	_	_
19	implication	implication	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
20	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
22	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	11	conj	_	_
23	that	that	SCONJ	IN	_	35	mark	_	_
24	in	in	ADP	IN	_	35	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
26	Barr	Barr	PROPN	NNP	Number=Sing	28	npadvmod	_	_
27	-	-	PUNCT	HYPH	PunctType=Dash	28	punct	_	_
28	exact	exact	ADJ	JJ	Degree=Pos	29	amod	_	_
29	context	context	NOUN	NN	Number=Sing	24	pobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	converse	converse	NOUN	NN	Number=Sing	33	compound	_	_
33	implication	implication	NOUN	NN	Number=Sing	35	nsubj	_	_
34	also	also	ADV	RB	_	35	advmod	_	_
35	holds	hold	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	ccomp	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 7
# text = We can then conclude that a category is arithmetical if and only if it is a Barr - exact Maltsev majority category, recovering in the varietal context a well known result of Pixley.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
2	can	can	AUX	MD	VerbForm=Fin	4	aux	_	_
3	then	then	ADV	RB	PronType=Dem	4	advmod	_	_
4	conclude	conclude	VERB	VB	VerbForm=Inf	0	ROOT	_	_
5	that	that	SCONJ	IN	_	8	mark	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	category	category	NOUN	NN	Number=Sing	8	nsubj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	ccomp	_	_
9	arithmetical	arithmetical	ADJ	JJ	Degree=Pos	8	acomp	_	_
10	if	if	SCONJ	IN	_	15	mark	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
12	only	only	ADV	RB	_	15	advmod	_	_
13	if	if	SCONJ	IN	_	15	mark	_	_
14	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	15	nsubj	_	_
15	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	advcl	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
17	Barr	Barr	PROPN	NNP	Number=Sing	19	npadvmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	exact	exact	ADJ	JJ	Degree=Pos	22	amod	_	_
20	Maltsev	Maltsev	PROPN	NNP	Number=Sing	22	compound	_	_
21	majority	majority	NOUN	NN	Number=Sing	22	compound	_	_
22	category	category	NOUN	NN	Number=Sing	15	attr	_	SpaceAfter=No
23	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
24	recovering	recover	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	15	advcl	_	_
25	in	in	ADP	IN	_	24	prep	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	varietal	varietal	ADJ	JJ	Degree=Pos	28	amod	_	_
28	context	context	NOUN	NN	Number=Sing	25	pobj	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
30	well	well	ADV	RB	Degree=Pos	31	advmod	_	_
31	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	32	amod	_	_
32	result	result	NOUN	NN	Number=Sing	24	dobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	Pixley	Pixley	PROPN	NNP	Number=Sing	33	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 730
# sent_id = 1
# text = We define and study a probability monad on the category of complete metric spaces and short maps.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	study	study	VERB	VB	VerbForm=Inf	2	conj	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	probability	probability	NOUN	NN	Number=Sing	7	compound	_	_
7	monad	monad	NOUN	NNS	Number=Plur	4	dobj	_	_
8	on	on	ADP	IN	_	4	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	category	category	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	complete	complete	ADJ	JJ	Degree=Pos	14	amod	_	_
13	metric	metric	ADJ	JJ	Degree=Pos	14	amod	_	_
14	spaces	space	NOUN	NNS	Number=Plur	11	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	14	cc	_	_
16	short	short	ADJ	JJ	Degree=Pos	17	amod	_	_
17	maps	map	NOUN	NNS	Number=Plur	14	conj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = It assigns to each space the space of Radon probability measures on it with finite first moment, equipped with the Kantorovich - Wasserstein distance.
1	It	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	2	nsubj	_	_
2	assigns	assign	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	each	each	DET	DT	_	5	det	_	_
5	space	space	NOUN	NN	Number=Sing	3	pobj	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	space	space	NOUN	NN	Number=Sing	2	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	Radon	Radon	PROPN	NNP	Number=Sing	11	compound	_	_
10	probability	probability	NOUN	NN	Number=Sing	11	compound	_	_
11	measures	measure	NOUN	NNS	Number=Plur	8	pobj	_	_
12	on	on	ADP	IN	_	11	prep	_	_
13	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	12	pobj	_	_
14	with	with	ADP	IN	_	7	prep	_	_
15	finite	finite	PROPN	NNP	Number=Sing	17	nmod	_	_
16	first	first	ADJ	JJ	Degree=Pos	17	amod	_	_
17	moment	moment	NOUN	NN	Number=Sing	14	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
19	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	acl	_	_
20	with	with	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
22	Kantorovich	Kantorovich	PROPN	NNP	Number=Sing	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	Wasserstein	Wasserstein	PROPN	NNP	Number=Sing	25	compound	_	_
25	distance	distance	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = This monad is analogous to the Giry monad on the category of Polish spaces, and it extends a construction due to van Breugel for compact and for 1 - bounded complete metric spaces.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	monad	monad	NOUN	NNS	Number=Plur	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	analogous	analogous	ADJ	JJ	Degree=Pos	3	acomp	_	_
5	to	to	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
7	Giry	Giry	PROPN	NNP	Number=Sing	8	compound	_	_
8	monad	monad	NOUN	NNS	Number=Plur	5	pobj	_	_
9	on	on	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	Polish	polish	ADJ	JJ	Degree=Pos	14	amod	_	_
14	spaces	space	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
17	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	18	nsubj	_	_
18	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	construction	construction	NOUN	NN	Number=Sing	18	dobj	_	_
21	due	due	ADP	IN	_	18	prep	_	_
22	to	to	ADP	IN	_	21	pcomp	_	_
23	van	van	PROPN	NNP	Number=Sing	24	compound	_	_
24	Breugel	Breugel	PROPN	NNP	Number=Sing	21	pobj	_	_
25	for	for	ADP	IN	_	18	prep	_	_
26	compact	compact	ADJ	JJ	Degree=Pos	25	amod	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	25	cc	_	_
28	for	for	ADP	IN	_	25	conj	_	_
29	1	1	NUM	CD	NumType=Card	31	npadvmod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	bounded	bound	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	34	amod	_	_
32	complete	complete	ADJ	JJ	Degree=Pos	34	amod	_	_
33	metric	metric	ADJ	JJ	Degree=Pos	34	amod	_	_
34	spaces	space	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	18	punct	_	SpaceAfter=No

# sent_id = 4
# text = We prove that this Kantorovich monad arises from a colimit construction on finite power - like constructions, which formalizes the intuition that probability measures are limits of finite samples.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
5	Kantorovich	Kantorovich	PROPN	NNP	Number=Sing	6	compound	_	_
6	monad	monad	NOUN	NNS	Number=Plur	7	nsubj	_	_
7	arises	arise	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	from	from	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	colimit	colimit	NOUN	NN	Number=Sing	11	compound	_	_
11	construction	construction	NOUN	NN	Number=Sing	8	pobj	_	_
12	on	on	ADP	IN	_	11	prep	_	_
13	finite	finite	ADJ	JJ	Degree=Pos	17	amod	_	_
14	power	power	NOUN	NN	Number=Sing	16	npadvmod	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	like	like	ADJ	JJ	Degree=Pos	17	amod	_	_
17	constructions	construction	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	which	which	PRON	WDT	_	20	nsubj	_	_
20	formalizes	formalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	intuition	intuition	NOUN	NN	Number=Sing	20	dobj	_	_
23	that	that	SCONJ	IN	_	26	mark	_	_
24	probability	probability	NOUN	NN	Number=Sing	25	compound	_	_
25	measures	measure	NOUN	NNS	Number=Plur	26	nsubj	_	_
26	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	22	acl	_	_
27	limits	limit	NOUN	NNS	Number=Plur	26	attr	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	finite	finite	ADJ	JJ	Degree=Pos	30	amod	_	_
30	samples	sample	NOUN	NNS	Number=Plur	28	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = The proof relies on a criterion for when an ordinary left Kan extension of lax monoidal functors is a monoidal Kan extension.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	proof	proof	NOUN	NN	Number=Sing	3	nsubj	_	_
3	relies	rely	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	on	on	ADP	IN	_	3	prep	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	criterion	criterion	NOUN	NN	Number=Sing	4	pobj	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	when	when	SCONJ	WRB	_	11	advmod	_	_
9	an	an	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
10	ordinary	ordinary	ADJ	JJ	Degree=Pos	11	nsubj	_	_
11	left	leave	VERB	VBD	Tense=Past|VerbForm=Fin	7	pcomp	_	_
12	Kan	Kan	PROPN	NNP	Number=Sing	13	compound	_	_
13	extension	extension	NOUN	NN	Number=Sing	11	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	lax	lax	ADJ	JJ	Degree=Pos	17	amod	_	_
16	monoidal	monoidal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	functors	functor	NOUN	NNS	Number=Plur	14	pobj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
20	monoidal	monoidal	ADJ	JJ	Degree=Pos	22	amod	_	_
21	Kan	Kan	PROPN	NNP	Number=Sing	22	compound	_	_
22	extension	extension	NOUN	NN	Number=Sing	18	attr	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 6
# text = The colimit characterization allows the development of integration theory and the treatment of measures on spaces of measures, without measure theory.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	colimit	colimit	NOUN	NN	Number=Sing	3	compound	_	_
3	characterization	characterization	NOUN	NN	Number=Sing	4	nsubj	_	_
4	allows	allow	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	development	development	NOUN	NN	Number=Sing	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	integration	integration	NOUN	NN	Number=Sing	9	compound	_	_
9	theory	theory	NOUN	NN	Number=Sing	7	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
12	treatment	treatment	NOUN	NN	Number=Sing	6	conj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	measures	measure	NOUN	NNS	Number=Plur	13	pobj	_	_
15	on	on	ADP	IN	_	14	prep	_	_
16	spaces	space	NOUN	NNS	Number=Plur	15	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	measures	measure	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
20	without	without	ADP	IN	_	6	prep	_	_
21	measure	measure	NOUN	NN	Number=Sing	22	compound	_	_
22	theory	theory	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 7
# text = We also show that the category of algebras of the Kantorovich monad is equivalent to the category of closed convex subsets of Banach spaces with short affine maps as morphisms.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	13	mark	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	category	category	NOUN	NN	Number=Sing	13	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	algebras	algebra	NOUN	NNS	Number=Plur	7	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	Kantorovich	Kantorovich	PROPN	NNP	Number=Sing	12	compound	_	_
12	monad	monad	NOUN	NNS	Number=Plur	9	pobj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
14	equivalent	equivalent	ADJ	JJ	Degree=Pos	13	acomp	_	_
15	to	to	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	category	category	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	closed	closed	ADJ	JJ	Degree=Pos	21	amod	_	_
20	convex	convex	ADJ	JJ	Degree=Pos	21	compound	_	_
21	subsets	subset	NOUN	NNS	Number=Plur	18	pobj	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	Banach	Banach	PROPN	NNP	Number=Sing	24	compound	_	_
24	spaces	space	NOUN	NNS	Number=Plur	22	pobj	_	_
25	with	with	ADP	IN	_	21	prep	_	_
26	short	short	ADJ	JJ	Degree=Pos	28	amod	_	_
27	affine	affine	NOUN	NN	Number=Sing	28	compound	_	_
28	maps	map	NOUN	NNS	Number=Plur	25	pobj	_	_
29	as	as	ADP	IN	_	17	prep	_	_
30	morphisms	morphism	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
31	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 731
# sent_id = 1
# text = Let $ (C, E, s) $ be an extriangulated category.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ (C, E, s) $	$ (c, e, s) $	SYM	$	_	3	nsubj	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
5	extriangulated	extriangulated	ADJ	JJ	Degree=Pos	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	3	attr	_	SpaceAfter=No
7	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that certain quotient categories of extriangulated categories are equivalent to module categories by some restriction of functor $ E $ , and in some cases, they are abelian.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	10	mark	_	_
4	certain	certain	ADJ	JJ	Degree=Pos	6	amod	_	_
5	quotient	quotient	ADJ	JJ	Degree=Pos	6	amod	_	_
6	categories	category	NOUN	NNS	Number=Plur	10	nsubj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	extriangulated	extriangulate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
10	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
11	equivalent	equivalent	ADJ	JJ	Degree=Pos	10	acomp	_	_
12	to	to	PART	TO	_	13	aux	_	_
13	module	module	VERB	VB	VerbForm=Inf	11	xcomp	_	_
14	categories	category	NOUN	NNS	Number=Plur	13	dobj	_	_
15	by	by	ADP	IN	_	13	prep	_	_
16	some	some	DET	DT	_	17	det	_	_
17	restriction	restriction	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	functor	functor	NOUN	NN	Number=Sing	18	pobj	_	_
20	$ E $	$ e $	SYM	$	_	13	advmod	_	_
21	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
23	in	in	ADP	IN	_	28	prep	_	_
24	some	some	DET	DT	_	25	det	_	_
25	cases	case	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
27	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	28	nsubj	_	_
28	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	10	conj	_	_
29	abelian	abelian	ADJ	JJ	Degree=Pos	28	attr	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = This result can be regarded as a simultaneous generalization of Koenig - Zhu and Demonet - Liu.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	result	result	NOUN	NN	Number=Sing	5	nsubjpass	_	_
3	can	can	AUX	MD	VerbForm=Fin	5	aux	_	_
4	be	be	AUX	VB	VerbForm=Inf	5	auxpass	_	_
5	regarded	regard	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
6	as	as	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	simultaneous	simultaneous	ADJ	JJ	Degree=Pos	9	amod	_	_
9	generalization	generalization	NOUN	NN	Number=Sing	6	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	Koenig	Koenig	PROPN	NNP	Number=Sing	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	Zhu	Zhu	PROPN	NNP	Number=Sing	10	pobj	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	13	cc	_	_
15	Demonet	Demonet	PROPN	NNP	Number=Sing	17	compound	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	Liu	Liu	PROPN	NNP	Number=Sing	13	conj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = In addition, we introduce the notion of maximal rigid subcategories in extriangulated categories.
1	In	in	ADP	IN	_	5	prep	_	_
2	addition	addition	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	notion	notion	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	maximal	maximal	ADJ	JJ	Degree=Pos	11	amod	_	_
10	rigid	rigid	ADJ	JJ	Degree=Pos	11	amod	_	_
11	subcategories	subcategorie	NOUN	NNS	Number=Plur	8	pobj	_	_
12	in	in	ADP	IN	_	11	prep	_	_
13	extriangulated	extriangulated	ADJ	JJ	Degree=Pos	14	amod	_	_
14	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 5
# text = Cluster tilting subcategories are obviously strongly functorially finite maximal rigid subcategories, we prove that the converse is true if the 2 - Calabi - Yau extriangulated categories admit a cluster tilting subcategories, which generalizes a result of Buan - Iyama - Reiten - Scott and Zhou - Zhu.
1	Cluster	cluster	NOUN	NN	Number=Sing	3	compound	_	_
2	tilting	tilting	NOUN	NN	Number=Sing	3	compound	_	_
3	subcategories	subcategorie	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	14	ccomp	_	_
5	obviously	obviously	ADV	RB	_	4	advmod	_	_
6	strongly	strongly	ADV	RB	_	7	advmod	_	_
7	functorially	functorially	ADV	RB	_	4	advmod	_	_
8	finite	finite	ADJ	JJ	Degree=Pos	11	nmod	_	_
9	maximal	maximal	ADJ	JJ	Degree=Pos	11	amod	_	_
10	rigid	rigid	ADJ	JJ	Degree=Pos	11	amod	_	_
11	subcategories	subcategorie	NOUN	NNS	Number=Plur	4	attr	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
13	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	14	nsubj	_	_
14	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
15	that	that	SCONJ	IN	_	18	mark	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	converse	converse	NOUN	NN	Number=Sing	18	nsubj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	ccomp	_	_
19	true	true	ADJ	JJ	Degree=Pos	18	acomp	_	_
20	if	if	SCONJ	IN	_	29	mark	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
22	2	2	NUM	CD	NumType=Card	24	nummod	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	Calabi	calabi	NOUN	NN	Number=Sing	26	nmod	_	_
25	-	-	PUNCT	HYPH	PunctType=Dash	26	punct	_	_
26	Yau	yau	NOUN	NN	Number=Sing	28	nmod	_	_
27	extriangulated	extriangulated	ADJ	JJ	Degree=Pos	28	amod	_	_
28	categories	category	NOUN	NNS	Number=Plur	29	nsubj	_	_
29	admit	admit	VERB	VBP	Tense=Pres|VerbForm=Fin	18	advcl	_	_
30	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
31	cluster	cluster	NOUN	NN	Number=Sing	32	compound	_	_
32	tilting	tilting	NOUN	NN	Number=Sing	33	compound	_	_
33	subcategories	subcategorie	NOUN	NNS	Number=Plur	29	dobj	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
35	which	which	PRON	WDT	_	36	nsubj	_	_
36	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	33	relcl	_	_
37	a	a	DET	DT	Definite=Ind|PronType=Art	38	det	_	_
38	result	result	NOUN	NN	Number=Sing	36	dobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	Buan	Buan	PROPN	NNP	Number=Sing	42	compound	_	_
41	-	-	PUNCT	HYPH	PunctType=Dash	42	punct	_	_
42	Iyama	Iyama	PROPN	NNP	Number=Sing	46	nmod	_	_
43	-	-	PUNCT	HYPH	PunctType=Dash	46	punct	_	_
44	Reiten	Reiten	PROPN	NNP	Number=Sing	46	compound	_	_
45	-	-	PUNCT	HYPH	PunctType=Dash	46	punct	_	_
46	Scott	Scott	PROPN	NNP	Number=Sing	39	pobj	_	_
47	and	and	CCONJ	CC	ConjType=Cmp	46	cc	_	_
48	Zhou	Zhou	PROPN	NNP	Number=Sing	50	compound	_	_
49	-	-	PUNCT	HYPH	PunctType=Dash	50	punct	_	_
50	Zhu	Zhu	PROPN	NNP	Number=Sing	46	conj	_	SpaceAfter=No
51	.	.	PUNCT	.	PunctType=Peri	14	punct	_	SpaceAfter=No

# doc_id = 732
# sent_id = 1
# text = This paper shows that generalizations of operads equipped with their respective bar/cobar dualities are related by a six operations formalism analogous to that of classical contexts in algebraic geometry.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	paper	paper	NOUN	NN	Number=Sing	3	nsubj	_	_
3	shows	show	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	17	mark	_	_
5	generalizations	generalization	NOUN	NNS	Number=Plur	17	nsubjpass	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	operads	operad	NOUN	NNS	Number=Plur	6	pobj	_	_
8	equipped	equip	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	acl	_	_
9	with	with	ADP	IN	_	8	prep	_	_
10	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	15	poss	_	_
11	respective	respective	ADJ	JJ	Degree=Pos	15	amod	_	_
12	bar	bar	NOUN	NN	Number=Sing	14	nmod	_	SpaceAfter=No
13	/	/	SYM	SYM	_	14	punct	_	SpaceAfter=No
14	cobar	cobar	NOUN	NN	Number=Sing	15	compound	_	_
15	dualities	duality	NOUN	NNS	Number=Plur	9	pobj	_	_
16	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	17	auxpass	_	_
17	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	ccomp	_	_
18	by	by	ADP	IN	_	17	agent	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	22	det	_	_
20	six	six	NUM	CD	NumType=Card	21	nummod	_	_
21	operations	operation	NOUN	NNS	Number=Plur	22	compound	_	_
22	formalism	formalism	NOUN	NN	Number=Sing	18	pobj	_	_
23	analogous	analogous	ADJ	JJ	Degree=Pos	22	amod	_	_
24	to	to	ADP	IN	_	23	prep	_	_
25	that	that	PRON	DT	Number=Sing|PronType=Dem	24	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	classical	classical	ADJ	JJ	Degree=Pos	28	amod	_	_
28	contexts	context	NOUN	NNS	Number=Plur	26	pobj	_	_
29	in	in	ADP	IN	_	28	prep	_	_
30	algebraic	algebraic	ADJ	JJ	Degree=Pos	31	amod	_	_
31	geometry	geometry	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 2
# text = As a consequence of our constructions, we prove intertwining theorems which govern derived Koszul duality of push - forwards and pull - backs.
1	As	as	ADP	IN	_	9	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	consequence	consequence	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	6	poss	_	_
6	constructions	construction	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	intertwining	intertwining	ADJ	JJ	Degree=Pos	11	amod	_	_
11	theorems	theorem	NOUN	NNS	Number=Plur	9	dobj	_	_
12	which	which	PRON	WDT	_	13	nsubj	_	_
13	govern	govern	VERB	VBP	Tense=Pres|VerbForm=Fin	11	relcl	_	_
14	derived	derive	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
15	Koszul	koszul	ADJ	JJ	Degree=Pos	16	amod	_	_
16	duality	duality	NOUN	NN	Number=Sing	13	dobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	push	push	NOUN	NN	Number=Sing	20	compound	_	_
19	-	-	PUNCT	HYPH	PunctType=Dash	20	punct	_	_
20	forwards	forward	NOUN	NNS	Number=Plur	17	pobj	_	_
21	and	and	CCONJ	CC	ConjType=Cmp	20	cc	_	_
22	pull	pull	VERB	VB	VerbForm=Inf	24	compound	_	_
23	-	-	PUNCT	HYPH	PunctType=Dash	24	punct	_	_
24	backs	back	NOUN	NNS	Number=Plur	20	conj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 733
# sent_id = 1
# text = In this note we prove that distributors between groupoids in a Barr - exact category $ E $ form the bicategory of relations relative to the comprehensive factorization system in $ Gpd(E) $ .
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	note	note	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	that	that	SCONJ	IN	_	17	mark	_	_
7	distributors	distributor	NOUN	NNS	Number=Plur	17	nsubj	_	_
8	between	between	ADP	IN	_	7	prep	_	_
9	groupoids	groupoid	NOUN	NNS	Number=Plur	8	pobj	_	_
10	in	in	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
12	Barr	Barr	PROPN	NNP	Number=Sing	14	npadvmod	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	exact	exact	ADJ	JJ	Degree=Pos	15	amod	_	_
15	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
16	$ E $	$ e $	SYM	$	_	7	appos	_	_
17	form	form	VERB	VB	VerbForm=Inf	5	ccomp	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	bicategory	bicategory	NOUN	NN	Number=Sing	17	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	relations	relation	NOUN	NNS	Number=Plur	20	pobj	_	_
22	relative	relative	ADJ	JJ	Degree=Pos	21	amod	_	_
23	to	to	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
25	comprehensive	comprehensive	ADJ	JJ	Degree=Pos	27	amod	_	_
26	factorization	factorization	NOUN	NN	Number=Sing	27	compound	_	_
27	system	system	NOUN	NN	Number=Sing	23	pobj	_	_
28	in	in	ADP	IN	_	27	prep	_	_
29	$ Gpd(E) $	$ gpd(e) $	SYM	$	_	28	pobj	_	_
30	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = The case $ E = Set $ is of special interest.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	case	case	NOUN	NN	Number=Sing	4	nsubj	_	_
3	$ E = Set $	$ e = set $	SYM	$	_	2	appos	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	special	special	ADJ	JJ	Degree=Pos	7	amod	_	_
7	interest	interest	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
8	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 734
# sent_id = 1
# text = This is the first part of a series of papers studying the problem of existence of double categories for which horizontal bicategory and object category are given.
1	This	this	PRON	DT	Number=Sing|PronType=Dem	2	nsubj	_	_
2	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	first	first	ADJ	JJ	Degree=Pos	5	amod	_	_
5	part	part	NOUN	NN	Number=Sing	2	attr	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	series	series	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	papers	paper	NOUN	NNS	Number=Plur	9	pobj	_	_
11	studying	study	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	acl	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	problem	problem	NOUN	NN	Number=Sing	11	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	existence	existence	NOUN	NN	Number=Sing	14	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	double	double	ADJ	JJ	Degree=Pos	18	amod	_	_
18	categories	category	NOUN	NNS	Number=Plur	16	pobj	_	_
19	for	for	ADP	IN	_	27	prep	_	_
20	which	which	PRON	WDT	_	19	pobj	_	_
21	horizontal	horizontal	ADJ	JJ	Degree=Pos	22	amod	_	_
22	bicategory	bicategory	NOUN	NN	Number=Sing	27	nsubjpass	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	object	object	NOUN	NN	Number=Sing	22	conj	_	_
25	category	category	NOUN	NN	Number=Sing	22	conj	_	_
26	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	27	auxpass	_	_
27	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	18	relcl	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We refer to this problem as the problem of existence of internalizations for decorated bicategories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	refer	refer	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	5	det	_	_
5	problem	problem	NOUN	NN	Number=Sing	3	pobj	_	_
6	as	as	ADP	IN	_	2	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	problem	problem	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	existence	existence	NOUN	NN	Number=Sing	9	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	internalizations	internalization	NOUN	NNS	Number=Plur	11	pobj	_	_
13	for	for	ADP	IN	_	12	prep	_	_
14	decorated	decorate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
15	bicategories	bicategorie	NOUN	NNS	Number=Plur	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Motivated by this we introduce the condition of a double category being globularily generated.
1	Motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	5	advcl	_	_
2	by	by	ADP	IN	_	1	agent	_	_
3	this	this	PRON	DT	Number=Sing|PronType=Dem	2	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	condition	condition	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
10	double	double	ADJ	JJ	Degree=Pos	11	amod	_	_
11	category	category	NOUN	NN	Number=Sing	14	nsubjpass	_	_
12	being	be	AUX	VBG	VerbForm=Ger	14	auxpass	_	_
13	globularily	globularily	ADV	RB	_	14	advmod	_	_
14	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	pcomp	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = We prove that the problem of existence of internalizations for a decorated bicategory admits a solution if and only if it admits a globularily generated solution, and we prove that the condition of a double category being globularily generated is precisely the condition of a solution to the problem of existence of internalizations for a decorated bicategory being minimal in a sense which we will make precise.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	14	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	problem	problem	NOUN	NN	Number=Sing	14	nsubj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	existence	existence	NOUN	NN	Number=Sing	6	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	internalizations	internalization	NOUN	NNS	Number=Plur	8	pobj	_	_
10	for	for	ADP	IN	_	9	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	decorated	decorate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	amod	_	_
13	bicategory	bicategory	NOUN	NN	Number=Sing	10	pobj	_	_
14	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
15	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
16	solution	solution	NOUN	NN	Number=Sing	14	dobj	_	_
17	if	if	SCONJ	IN	_	22	mark	_	_
18	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
19	only	only	ADV	RB	_	22	advmod	_	_
20	if	if	SCONJ	IN	_	22	mark	_	_
21	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	22	nsubj	_	_
22	admits	admit	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	14	advcl	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
24	globularily	globularily	ADV	RB	_	25	advmod	_	_
25	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	26	amod	_	_
26	solution	solution	NOUN	NN	Number=Sing	22	dobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
29	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	30	nsubj	_	_
30	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	22	conj	_	_
31	that	that	SCONJ	IN	_	41	mark	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
33	condition	condition	NOUN	NN	Number=Sing	41	nsubj	_	_
34	of	of	ADP	IN	_	33	prep	_	_
35	a	a	DET	DT	Definite=Ind|PronType=Art	37	det	_	_
36	double	double	ADJ	JJ	Degree=Pos	37	amod	_	_
37	category	category	NOUN	NN	Number=Sing	34	pobj	_	_
38	being	be	AUX	VBG	VerbForm=Ger	40	auxpass	_	_
39	globularily	globularily	ADV	RB	_	40	advmod	_	_
40	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	37	acl	_	_
41	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	ccomp	_	_
42	precisely	precisely	ADV	RB	_	44	advmod	_	_
43	the	the	DET	DT	Definite=Def|PronType=Art	44	det	_	_
44	condition	condition	NOUN	NN	Number=Sing	41	attr	_	_
45	of	of	ADP	IN	_	44	prep	_	_
46	a	a	DET	DT	Definite=Ind|PronType=Art	47	det	_	_
47	solution	solution	NOUN	NN	Number=Sing	45	pobj	_	_
48	to	to	ADP	IN	_	47	prep	_	_
49	the	the	DET	DT	Definite=Def|PronType=Art	50	det	_	_
50	problem	problem	NOUN	NN	Number=Sing	48	pobj	_	_
51	of	of	ADP	IN	_	50	prep	_	_
52	existence	existence	NOUN	NN	Number=Sing	51	pobj	_	_
53	of	of	ADP	IN	_	52	prep	_	_
54	internalizations	internalization	NOUN	NNS	Number=Plur	53	pobj	_	_
55	for	for	ADP	IN	_	54	prep	_	_
56	a	a	DET	DT	Definite=Ind|PronType=Art	58	det	_	_
57	decorated	decorate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	58	amod	_	_
58	bicategory	bicategory	NOUN	NN	Number=Sing	55	pobj	_	_
59	being	be	AUX	VBG	VerbForm=Ger	58	acl	_	_
60	minimal	minimal	ADJ	JJ	Degree=Pos	59	acomp	_	_
61	in	in	ADP	IN	_	59	prep	_	_
62	a	a	DET	DT	Definite=Ind|PronType=Art	63	det	_	_
63	sense	sense	NOUN	NN	Number=Sing	61	pobj	_	_
64	which	which	PRON	WDT	_	67	pobj	_	_
65	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	67	nsubj	_	_
66	will	will	AUX	MD	VerbForm=Fin	67	aux	_	_
67	make	make	VERB	VB	VerbForm=Inf	63	relcl	_	_
68	precise	precise	ADJ	JJ	Degree=Pos	67	acomp	_	SpaceAfter=No
69	.	.	PUNCT	.	PunctType=Peri	30	punct	_	SpaceAfter=No

# sent_id = 5
# text = The study of the condition of a double category being globularily generated will thus be pivotal in our study of the problem of existence of internalizations.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	study	study	NOUN	NN	Number=Sing	15	nsubj	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	condition	condition	NOUN	NN	Number=Sing	3	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	double	double	ADJ	JJ	Degree=Pos	9	amod	_	_
9	category	category	NOUN	NN	Number=Sing	6	pobj	_	_
10	being	be	AUX	VBG	VerbForm=Ger	12	auxpass	_	_
11	globularily	globularily	ADV	RB	_	12	advmod	_	_
12	generated	generate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	acl	_	_
13	will	will	AUX	MD	VerbForm=Fin	15	aux	_	_
14	thus	thus	ADV	RB	_	15	advmod	_	_
15	be	be	AUX	VB	VerbForm=Inf	0	ROOT	_	_
16	pivotal	pivotal	ADJ	JJ	Degree=Pos	15	acomp	_	_
17	in	in	ADP	IN	_	15	prep	_	_
18	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	19	poss	_	_
19	study	study	NOUN	NN	Number=Sing	17	pobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	problem	problem	NOUN	NN	Number=Sing	20	pobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	existence	existence	NOUN	NN	Number=Sing	23	pobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	internalizations	internalization	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
27	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# doc_id = 735
# sent_id = 1
# text = Let $ (C, otimes, 1) $ be an abelian symmetric monoidal category satisfying certain exactness conditions.
1	Let	let	VERB	VB	VerbForm=Inf	0	ROOT	_	_
2	$ (C, otimes, 1) $	$ (c, otimes, 1) $	SYM	$	_	3	nsubj	_	_
3	be	be	AUX	VB	VerbForm=Inf	1	ccomp	_	_
4	an	an	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
5	abelian	abelian	ADJ	JJ	Degree=Pos	8	amod	_	_
6	symmetric	symmetric	ADJ	JJ	Degree=Pos	8	amod	_	_
7	monoidal	monoidal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	category	category	NOUN	NN	Number=Sing	3	attr	_	_
9	satisfying	satisfy	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	acl	_	_
10	certain	certain	ADJ	JJ	Degree=Pos	12	amod	_	_
11	exactness	exactness	ADJ	JJ	Degree=Pos	12	amod	_	_
12	conditions	condition	NOUN	NNS	Number=Plur	9	dobj	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	1	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper we define a presheaf $ Proj{C} $ on the category of commutative algebras in $ C $ and we prove that this functor is a $ C $ - scheme in the sense of Toen and Vaquie.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	presheaf	presheaf	NOUN	NN	Number=Sing	5	dobj	_	_
8	$ Proj{C} $	$ proj{c} $	SYM	$	_	5	dep	_	_
9	on	on	ADP	IN	_	5	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	commutative	commutative	ADJ	JJ	Degree=Pos	14	amod	_	_
14	algebras	algebra	NOUN	NNS	Number=Plur	12	pobj	_	_
15	in	in	ADP	IN	_	5	prep	_	_
16	$ C $	$ c $	SYM	$	_	15	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
18	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	19	nsubj	_	_
19	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	5	conj	_	_
20	that	that	SCONJ	IN	_	23	mark	_	_
21	this	this	DET	DT	Number=Sing|PronType=Dem	22	det	_	_
22	functor	functor	NOUN	NN	Number=Sing	23	nsubj	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	ccomp	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
25	$ C $	$ c $	SYM	$	_	27	nmod	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	scheme	scheme	NOUN	NN	Number=Sing	23	attr	_	_
28	in	in	ADP	IN	_	27	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
30	sense	sense	NOUN	NN	Number=Sing	28	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	Toen	Toen	PROPN	NNP	Number=Sing	31	pobj	_	_
33	and	and	CCONJ	CC	ConjType=Cmp	32	cc	_	_
34	Vaquie	Vaquie	PROPN	NNP	Number=Sing	32	conj	_	SpaceAfter=No
35	.	.	PUNCT	.	PunctType=Peri	19	punct	_	SpaceAfter=No

# sent_id = 3
# text = We give another definition and prove that they give isomorphic $ C $ - schemes.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	another	another	DET	DT	_	4	det	_	_
4	definition	definition	NOUN	NN	Number=Sing	2	dobj	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
6	prove	prove	VERB	VB	VerbForm=Inf	2	conj	_	_
7	that	that	SCONJ	IN	_	9	mark	_	_
8	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	9	nsubj	_	_
9	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	6	ccomp	_	_
10	isomorphic	isomorphic	ADJ	JJ	Degree=Pos	13	amod	_	_
11	$ C $	$ c $	SYM	$	_	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	schemes	scheme	NOUN	NNS	Number=Plur	9	dobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = This construction gives us a context of non - associative relative algebraic geometry.
1	This	this	DET	DT	Number=Sing|PronType=Dem	2	det	_	_
2	construction	construction	NOUN	NN	Number=Sing	3	nsubj	_	_
3	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	3	dative	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
6	context	context	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	non	non	ADJ	JJ	Degree=Pos	10	amod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	associative	associative	ADJ	JJ	Degree=Pos	13	amod	_	_
11	relative	relative	ADJ	JJ	Degree=Pos	13	amod	_	_
12	algebraic	algebraic	ADJ	JJ	Degree=Pos	13	amod	_	_
13	geometry	geometry	NOUN	NN	Number=Sing	7	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = The most important example of the construction is the octonionic projective space.
1	The	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
2	most	most	ADV	RBS	Degree=Sup	3	advmod	_	_
3	important	important	ADJ	JJ	Degree=Pos	4	amod	_	_
4	example	example	NOUN	NN	Number=Sing	8	nsubj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	construction	construction	NOUN	NN	Number=Sing	5	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
10	octonionic	octonionic	ADJ	JJ	Degree=Pos	12	amod	_	_
11	projective	projective	ADJ	JJ	Degree=Pos	12	amod	_	_
12	space	space	NOUN	NN	Number=Sing	8	attr	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# doc_id = 736
# sent_id = 1
# text = We give a unified direct proof of the lifting of PIE limits to the 2 - category of algebras and (pseudo) morphisms, which specifies precisely which of the projections of the lifted limit are strict and detect strictness.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	6	det	_	_
4	unified	unified	ADJ	JJ	Degree=Pos	6	amod	_	_
5	direct	direct	ADJ	JJ	Degree=Pos	6	amod	_	_
6	proof	proof	NOUN	NN	Number=Sing	2	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	lifting	lifting	NOUN	NN	Number=Sing	7	pobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	PIE	pie	NOUN	NN	Number=Sing	12	compound	_	_
12	limits	limit	NOUN	NNS	Number=Plur	10	pobj	_	_
13	to	to	ADP	IN	_	6	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
15	2	2	NUM	CD	NumType=Card	17	nummod	_	_
16	-	-	PUNCT	HYPH	PunctType=Dash	17	punct	_	_
17	category	category	NOUN	NN	Number=Sing	13	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	algebras	algebra	NOUN	NNS	Number=Plur	18	pobj	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	19	cc	_	_
21	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	22	punct	_	SpaceAfter=No
22	pseudo	pseudo	NOUN	NN	Number=Sing	19	conj	_	SpaceAfter=No
23	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	19	punct	_	_
24	morphisms	morphism	NOUN	NNS	Number=Plur	19	appos	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	which	which	PRON	WDT	_	27	nsubj	_	_
27	specifies	specify	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	24	relcl	_	_
28	precisely	precisely	ADV	RB	_	29	advmod	_	_
29	which	which	PRON	WDT	_	27	dobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	32	det	_	_
32	projections	projection	NOUN	NNS	Number=Plur	30	pobj	_	_
33	of	of	ADP	IN	_	32	prep	_	_
34	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
35	lifted	lift	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	36	amod	_	_
36	limit	limit	NOUN	NN	Number=Sing	33	pobj	_	_
37	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	conj	_	_
38	strict	strict	ADJ	JJ	Degree=Pos	37	acomp	_	_
39	and	and	CCONJ	CC	ConjType=Cmp	38	cc	_	_
40	detect	detect	VERB	VB	VerbForm=Inf	38	conj	_	_
41	strictness	strictness	NOUN	NN	Number=Sing	40	dobj	_	SpaceAfter=No
42	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = In the literature, these limits were lifted one by one, so as to keep track of these projections in each case.
1	In	in	ADP	IN	_	8	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
3	literature	literature	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
5	these	these	DET	DT	Number=Plur|PronType=Dem	6	det	_	_
6	limits	limit	NOUN	NNS	Number=Plur	8	nsubjpass	_	_
7	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	8	auxpass	_	_
8	lifted	lift	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
9	one	one	NUM	CD	NumType=Card	8	npadvmod	_	_
10	by	by	ADP	IN	_	9	prep	_	_
11	one	one	NUM	CD	NumType=Card	10	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
13	so	so	SCONJ	IN	_	16	mark	_	_
14	as	as	SCONJ	IN	_	16	mark	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	keep	keep	VERB	VB	VerbForm=Inf	8	advcl	_	_
17	track	track	NOUN	NN	Number=Sing	16	dobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	these	these	DET	DT	Number=Plur|PronType=Dem	20	det	_	_
20	projections	projection	NOUN	NNS	Number=Plur	18	pobj	_	_
21	in	in	ADP	IN	_	16	prep	_	_
22	each	each	DET	DT	_	23	det	_	_
23	case	case	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 3
# text = We work in the more general context of weak algebra morphisms, so as to include lax morphisms as well.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	work	work	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	in	in	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	more	more	ADV	RBR	Degree=Cmp	6	advmod	_	_
6	general	general	ADJ	JJ	Degree=Pos	7	amod	_	_
7	context	context	NOUN	NN	Number=Sing	3	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	weak	weak	ADJ	JJ	Degree=Pos	11	amod	_	_
10	algebra	algebra	NOUN	NN	Number=Sing	11	compound	_	_
11	morphisms	morphism	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
13	so	so	SCONJ	IN	_	16	mark	_	_
14	as	as	SCONJ	IN	_	16	mark	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	include	include	VERB	VB	VerbForm=Inf	2	advcl	_	_
17	lax	lax	ADJ	JJ	Degree=Pos	18	amod	_	_
18	morphisms	morphism	NOUN	NNS	Number=Plur	16	dobj	_	_
19	as	as	ADV	RB	_	20	advmod	_	_
20	well	well	ADV	RB	Degree=Pos	16	advmod	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 4
# text = PIE limits are also all simultaneously lifted in this case, provided some specified arrows of the diagram are pseudo morphisms.
1	PIE	pie	NOUN	NN	Number=Sing	2	compound	_	_
2	limits	limit	NOUN	NNS	Number=Plur	7	nsubjpass	_	_
3	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	auxpass	_	_
4	also	also	ADV	RB	_	3	advmod	_	_
5	all	all	PRON	DT	_	7	dep	_	_
6	simultaneously	simultaneously	ADV	RB	_	7	advmod	_	_
7	lifted	lift	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	this	this	DET	DT	Number=Sing|PronType=Dem	10	det	_	_
10	case	case	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
12	provided	provide	VERB	VBD	Tense=Past|VerbForm=Fin	7	prep	_	_
13	some	some	DET	DT	_	15	det	_	_
14	specified	specify	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	amod	_	_
15	arrows	arrow	NOUN	NNS	Number=Plur	12	pobj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
18	diagram	diagram	NOUN	NN	Number=Sing	16	pobj	_	_
19	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	conj	_	_
20	pseudo	pseudo	NOUN	NN	Number=Sing	21	compound	_	_
21	morphisms	morphism	NOUN	NNS	Number=Plur	19	attr	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 5
# text = Again, this unifies the previously known lifting of many particular PIE limits, which were also treated separately.
1	Again	again	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	this	this	PRON	DT	Number=Sing|PronType=Dem	4	nsubj	_	_
4	unifies	unify	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
6	previously	previously	ADV	RB	_	7	advmod	_	_
7	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	amod	_	_
8	lifting	lifting	NOUN	NN	Number=Sing	4	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	many	many	ADJ	JJ	Degree=Pos	13	amod	_	_
11	particular	particular	ADJ	JJ	Degree=Pos	13	amod	_	_
12	PIE	PIE	PROPN	NNP	Number=Sing	13	compound	_	_
13	limits	limit	NOUN	NNS	Number=Plur	9	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	which	which	PRON	WDT	_	18	nsubjpass	_	_
16	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	18	auxpass	_	_
17	also	also	ADV	RB	_	18	advmod	_	_
18	treated	treat	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	13	relcl	_	_
19	separately	separately	ADV	RB	_	18	advmod	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 737
# sent_id = 1
# text = Involutive category theory provides a flexible framework to describe involutive structures on algebraic objects, such as anti - linear involutions on complex vector spaces.
1	Involutive	involutive	ADJ	JJ	Degree=Pos	3	amod	_	_
2	category	category	NOUN	NN	Number=Sing	3	compound	_	_
3	theory	theory	NOUN	NN	Number=Sing	4	nsubj	_	_
4	provides	provide	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	flexible	flexible	ADJ	JJ	Degree=Pos	7	amod	_	_
7	framework	framework	NOUN	NN	Number=Sing	4	dobj	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	describe	describe	VERB	VB	VerbForm=Inf	7	acl	_	_
10	involutive	involutive	ADJ	JJ	Degree=Pos	11	amod	_	_
11	structures	structure	NOUN	NNS	Number=Plur	9	dobj	_	_
12	on	on	ADP	IN	_	9	prep	_	_
13	algebraic	algebraic	ADJ	JJ	Degree=Pos	14	amod	_	_
14	objects	object	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
16	such	such	ADJ	JJ	Degree=Pos	17	amod	_	_
17	as	as	ADP	IN	_	14	prep	_	_
18	anti	anti	ADJ	JJ	Degree=Pos	21	amod	_	_
19	-	-	ADJ	JJ	Degree=Pos	21	amod	_	_
20	linear	linear	ADJ	JJ	Degree=Pos	21	amod	_	_
21	involutions	involution	NOUN	NNS	Number=Plur	17	pobj	_	_
22	on	on	ADP	IN	_	21	prep	_	_
23	complex	complex	ADJ	JJ	Degree=Pos	25	amod	_	_
24	vector	vector	NOUN	NN	Number=Sing	25	compound	_	_
25	spaces	space	NOUN	NNS	Number=Plur	22	pobj	_	SpaceAfter=No
26	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = Motivated by the prominent role of involutions in quantum (field) theory, we develop the involutive analogs of colored operads and their algebras, named colored $ * $ - operads and $ * $ - algebras.
1	Motivated	motivate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	advcl	_	_
2	by	by	ADP	IN	_	1	agent	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	prominent	prominent	ADJ	JJ	Degree=Pos	5	amod	_	_
5	role	role	NOUN	NN	Number=Sing	2	pobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	involutions	involution	NOUN	NNS	Number=Plur	6	pobj	_	_
8	in	in	ADP	IN	_	7	prep	_	_
9	quantum	quantum	PROPN	NNP	Number=Sing	8	pobj	_	_
10	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	9	punct	_	SpaceAfter=No
11	field	field	NOUN	NN	Number=Sing	9	appos	_	SpaceAfter=No
12	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	9	punct	_	_
13	theory	theory	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
15	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	16	nsubj	_	_
16	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	involutive	involutive	ADJ	JJ	Degree=Pos	19	amod	_	_
19	analogs	analog	NOUN	NNS	Number=Plur	16	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	colored	colored	ADJ	JJ	Degree=Pos	22	amod	_	_
22	operads	operad	NOUN	NNS	Number=Plur	20	pobj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	25	poss	_	_
25	algebras	algebra	NOUN	NNS	Number=Plur	22	conj	_	SpaceAfter=No
26	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
27	named	name	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	25	acl	_	_
28	colored	color	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	amod	_	_
29	$ * $	$ * $	SYM	$	_	31	nmod	_	_
30	-	-	PUNCT	HYPH	PunctType=Dash	31	punct	_	_
31	operads	operad	NOUN	NNS	Number=Plur	27	oprd	_	_
32	and	and	CCONJ	CC	ConjType=Cmp	31	cc	_	_
33	$ * $	$ * $	SYM	$	_	35	compound	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	algebras	algebra	NOUN	NNS	Number=Plur	31	conj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	16	punct	_	SpaceAfter=No

# sent_id = 3
# text = Central to the definition of colored $ * $ - operads is the involutive monoidal category of symmetric sequences, which we obtain from a general product - exponential 2 - adjunction whose right adjoint forms involutive functor categories.
1	Central	central	ADJ	JJ	Degree=Pos	10	acomp	_	_
2	to	to	ADP	IN	_	1	prep	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	definition	definition	NOUN	NN	Number=Sing	2	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	colored	color	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	amod	_	_
7	$ * $	$ * $	SYM	$	_	9	nmod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	operads	operad	NOUN	NNS	Number=Plur	5	pobj	_	_
10	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
12	involutive	involutive	ADJ	JJ	Degree=Pos	14	amod	_	_
13	monoidal	monoidal	ADJ	JJ	Degree=Pos	14	amod	_	_
14	category	category	NOUN	NN	Number=Sing	10	attr	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	symmetric	symmetric	ADJ	JJ	Degree=Pos	17	amod	_	_
17	sequences	sequence	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
19	which	which	PRON	WDT	_	21	dobj	_	_
20	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	21	nsubj	_	_
21	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	14	relcl	_	_
22	from	from	ADP	IN	_	21	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
24	general	general	ADJ	JJ	Degree=Pos	25	amod	_	_
25	product	product	NOUN	NN	Number=Sing	27	compound	_	_
26	-	-	PUNCT	HYPH	PunctType=Dash	27	punct	_	_
27	exponential	exponential	NOUN	NN	Number=Sing	30	compound	_	_
28	2	2	NUM	CD	NumType=Card	30	nummod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	adjunction	adjunction	NOUN	NN	Number=Sing	22	pobj	_	_
31	whose	whose	DET	WP$	Poss=Yes	34	poss	_	_
32	right	right	ADJ	JJ	Degree=Pos	33	amod	_	_
33	adjoint	adjoint	NOUN	NN	Number=Sing	34	compound	_	_
34	forms	form	NOUN	NNS	Number=Plur	35	nsubj	_	_
35	involutive	involutive	PROPN	NNP	Number=Sing	37	compound	_	_
36	functor	functor	NOUN	NN	Number=Sing	37	compound	_	_
37	categories	category	NOUN	NNS	Number=Plur	30	appos	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 4
# text = For $ * $ - algebras over $ * $ - operads we obtain involutive analogs of the usual change of color and operad adjunctions.
1	For	for	ADP	IN	_	0	ROOT	_	_
2	$ * $	$ * $	SYM	$	_	4	dep	_	_
3	-	-	PUNCT	HYPH	PunctType=Dash	4	punct	_	_
4	algebras	algebra	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	1	pobj	_	_
5	over	over	ADP	IN	_	8	advmod	_	_
6	$ * $	$ * $	SYM	$	_	8	compound	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	operads	operad	NOUN	NNS	Number=Plur	1	pobj	_	_
9	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
10	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	8	relcl	_	_
11	involutive	involutive	ADJ	JJ	Degree=Pos	12	amod	_	_
12	analogs	analog	NOUN	NNS	Number=Plur	10	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
15	usual	usual	ADJ	JJ	Degree=Pos	16	amod	_	_
16	change	change	NOUN	NN	Number=Sing	13	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	color	color	NOUN	NN	Number=Sing	21	amod	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	operad	operad	ADJ	JJ	Degree=Pos	18	conj	_	_
21	adjunctions	adjunction	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# sent_id = 5
# text = As an application, we turn the colored operads for algebraic quantum field theory into colored $ * $ - operads.
1	As	as	ADP	IN	_	6	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	application	application	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	turn	turn	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	colored	colored	ADJ	JJ	Degree=Pos	9	amod	_	_
9	operads	operad	NOUN	NNS	Number=Plur	6	dobj	_	_
10	for	for	ADP	IN	_	9	prep	_	_
11	algebraic	algebraic	ADJ	JJ	Degree=Pos	14	amod	_	_
12	quantum	quantum	PROPN	NNP	Number=Sing	13	compound	_	_
13	field	field	NOUN	NN	Number=Sing	14	compound	_	_
14	theory	theory	NOUN	NN	Number=Sing	10	pobj	_	_
15	into	into	ADP	IN	_	14	prep	_	_
16	colored	color	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	19	amod	_	_
17	$ * $	$ * $	SYM	$	_	19	nmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	operads	operad	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 6
# text = The simplest instance is the associative $ * $ - operad, whose $ * $ - algebras are unital and associative $ * $ - algebras.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	simplest	simple	ADJ	JJS	Degree=Sup	3	amod	_	_
3	instance	instance	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
6	associative	associative	ADJ	JJ	Degree=Pos	9	amod	_	_
7	$ * $	$ * $	SYM	$	_	9	dep	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	operad	operad	NOUN	NN	Number=Sing	4	attr	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	whose	whose	DET	WP$	Poss=Yes	14	poss	_	_
12	$ * $	$ * $	SYM	$	_	14	compound	_	_
13	-	-	PUNCT	HYPH	PunctType=Dash	14	punct	_	_
14	algebras	algebra	NOUN	NNS	Number=Plur	15	nsubj	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	relcl	_	_
16	unital	unital	ADJ	JJ	Degree=Pos	15	acomp	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	associative	associative	VERB	VB	VerbForm=Inf	16	conj	_	_
19	$ * $	$ * $	SYM	$	_	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	algebras	algebra	NOUN	NNS	Number=Plur	9	appos	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 738
# sent_id = 1
# text = We explain how, in the context of a semi - abelian category, the concept of an internal crossed square may be used to set up an intrinsic approach to the Brown - Loday non - abelian tensor product.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	explain	explain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	how	how	SCONJ	WRB	_	24	advmod	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
5	in	in	ADP	IN	_	24	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	context	context	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
10	semi	semi	ADJ	JJ	Degree=Pos	13	amod	_	_
11	-	-	ADJ	JJ	Degree=Pos	13	amod	_	_
12	abelian	abelian	ADJ	JJ	Degree=Pos	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	concept	concept	NOUN	NN	Number=Sing	24	nsubjpass	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	an	an	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
19	internal	internal	ADJ	JJ	Degree=Pos	21	amod	_	_
20	crossed	crossed	ADJ	JJ	Degree=Pos	21	amod	_	_
21	square	square	NOUN	NN	Number=Sing	17	pobj	_	_
22	may	may	AUX	MD	VerbForm=Fin	24	aux	_	_
23	be	be	AUX	VB	VerbForm=Inf	24	auxpass	_	_
24	used	use	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
25	to	to	PART	TO	_	26	aux	_	_
26	set	set	VERB	VB	VerbForm=Inf	24	xcomp	_	_
27	up	up	ADP	RP	_	26	prt	_	_
28	an	an	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
29	intrinsic	intrinsic	ADJ	JJ	Degree=Pos	30	amod	_	_
30	approach	approach	NOUN	NN	Number=Sing	26	dobj	_	_
31	to	to	ADP	IN	_	30	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
33	Brown	Brown	PROPN	NNP	Number=Sing	35	compound	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	Loday	Loday	PROPN	NNP	Number=Sing	40	nmod	_	_
36	non	non	PROPN	NNP	Number=Sing	38	amod	_	_
37	-	-	PUNCT	HYPH	PunctType=Dash	38	punct	_	_
38	abelian	abelian	PROPN	NNP	Number=Sing	40	amod	_	_
39	tensor	tensor	NOUN	NN	Number=Sing	40	compound	_	_
40	product	product	NOUN	NN	Number=Sing	31	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 739
# sent_id = 1
# text = In this paper we develop a theory of Segal enriched categories.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	theory	theory	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	Segal	segal	ADJ	JJ	Degree=Pos	11	amod	_	_
10	enriched	enriched	ADJ	JJ	Degree=Pos	11	amod	_	_
11	categories	category	NOUN	NNS	Number=Plur	8	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = Our motivation was to generalize the notion of up - to - homotopy monoid in a monoidal category, introduced by Leinster.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	motivation	motivation	NOUN	NN	Number=Sing	3	nsubj	_	_
3	was	be	AUX	VBD	Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin	0	ROOT	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	generalize	generalize	VERB	VB	VerbForm=Inf	3	xcomp	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	notion	notion	NOUN	NN	Number=Sing	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	up	up	ADP	IN	_	14	nmod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
11	to	to	ADP	IN	_	9	prep	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
13	homotopy	homotopy	NOUN	NN	Number=Sing	11	pobj	_	_
14	monoid	monoid	NOUN	NN	Number=Sing	8	pobj	_	_
15	in	in	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	monoidal	monoidal	ADJ	JJ	Degree=Pos	18	amod	_	_
18	category	category	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	14	punct	_	_
20	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	14	acl	_	_
21	by	by	ADP	IN	_	20	agent	_	_
22	Leinster	Leinster	PROPN	NNP	Number=Sing	21	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = Our formalism generalizes the classical theory of Segal categories and extends the theory of categories enriched over a 2 - category.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	formalism	formalism	NOUN	NN	Number=Sing	3	nsubj	_	_
3	generalizes	generalize	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	classical	classical	ADJ	JJ	Degree=Pos	6	amod	_	_
6	theory	theory	NOUN	NN	Number=Sing	3	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	Segal	segal	ADJ	JJ	Degree=Pos	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	7	pobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
11	extends	extend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	conj	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	theory	theory	NOUN	NN	Number=Sing	11	dobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	categories	category	NOUN	NNS	Number=Plur	14	pobj	_	_
16	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	acl	_	_
17	over	over	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
19	2	2	NUM	CD	NumType=Card	21	nummod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	category	category	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = We introduce Segal dg - categories which did not exist so far.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	Segal	Segal	PROPN	NNP	Number=Sing	6	compound	_	_
4	dg	dg	NOUN	NN	Number=Sing	6	compound	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	categories	category	NOUN	NNS	Number=Plur	2	dobj	_	_
7	which	which	PRON	WDT	_	10	nsubj	_	_
8	did	do	AUX	VBD	Tense=Past|VerbForm=Fin	10	aux	_	_
9	not	not	PART	RB	Polarity=Neg	10	neg	_	_
10	exist	exist	VERB	VB	VerbForm=Inf	6	relcl	_	_
11	so	so	ADV	RB	_	12	advmod	_	_
12	far	far	ADV	RB	_	10	advmod	_	SpaceAfter=No
13	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = We show that the homotopy transfer problem for algebras leads directly to a Leinster - Segal algebra.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	10	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	homotopy	homotopy	NOUN	NN	Number=Sing	6	compound	_	_
6	transfer	transfer	NOUN	NN	Number=Sing	7	compound	_	_
7	problem	problem	NOUN	NN	Number=Sing	10	nsubj	_	_
8	for	for	ADP	IN	_	7	prep	_	_
9	algebras	algebra	NOUN	NNS	Number=Plur	8	pobj	_	_
10	leads	lead	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
11	directly	directly	ADV	RB	_	10	advmod	_	_
12	to	to	ADP	IN	_	10	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	17	det	_	_
14	Leinster	Leinster	PROPN	NNP	Number=Sing	16	compound	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	Segal	Segal	PROPN	NNP	Number=Sing	17	compound	_	_
17	algebra	algebra	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
18	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 740
# sent_id = 1
# text = We consider pre - exponentiable objects of a pre - cartesian double category $ D $ , that is, objects $ Y $ such that the lax functor $ - x Y: D - - > D $ has a right adjoint in the 2 - category LxDbl of double categories and lax functors.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	pre	pre	ADJ	JJ	Degree=Pos	6	amod	_	_
4	-	-	ADJ	JJ	Degree=Pos	6	amod	_	_
5	exponentiable	exponentiable	ADJ	JJ	Degree=Pos	6	amod	_	_
6	objects	object	NOUN	NNS	Number=Plur	2	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
9	pre	pre	ADJ	JJ	Degree=Pos	11	amod	_	_
10	-	-	ADJ	JJ	Degree=Pos	11	punct	_	_
11	cartesian	cartesian	ADJ	JJ	Degree=Pos	13	amod	_	_
12	double	double	ADJ	JJ	Degree=Pos	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	7	pobj	_	_
14	$ D $	$ d $	SYM	$	_	13	appos	_	_
15	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
16	that	that	ADV	RB	_	17	advmod	_	_
17	is	is	ADV	RB	_	19	advmod	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	19	punct	_	_
19	objects	object	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
20	$ Y $	$ y $	SYM	$	_	21	nmod	_	_
21	such	such	ADJ	JJ	Degree=Pos	19	dobj	_	_
22	that	that	SCONJ	IN	_	27	mark	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
24	lax	lax	PROPN	NNP	Number=Sing	25	compound	_	_
25	functor	functor	PROPN	NNP	Number=Sing	27	nsubj	_	_
26	$ - x Y: D - - > D $	$ - x y: d - - > d $	SYM	$	_	25	appos	_	_
27	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	ccomp	_	_
28	a	a	DET	DT	Definite=Ind|PronType=Art	30	det	_	_
29	right	right	ADJ	JJ	Degree=Pos	30	amod	_	_
30	adjoint	adjoint	NOUN	NN	Number=Sing	27	dobj	_	_
31	in	in	ADP	IN	_	30	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
33	2	2	NUM	CD	NumType=Card	35	nummod	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	category	category	NOUN	NN	Number=Sing	36	compound	_	_
36	LxDbl	LxDbl	PROPN	NNP	Number=Sing	31	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	double	double	ADJ	JJ	Degree=Pos	39	amod	_	_
39	categories	category	NOUN	NNS	Number=Plur	37	pobj	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	39	cc	_	_
41	lax	lax	ADJ	JJ	Degree=Pos	42	amod	_	_
42	functors	functor	NOUN	NNS	Number=Plur	39	conj	_	SpaceAfter=No
43	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = When $ D $ has 2 - glueing, we show that $ Y $ is pre - exponentiable in $ D $ if and only if $ Y $ is exponentiable in $ D_0 $ and $ - x Y $ is an oplax functor.
1	When	when	SCONJ	WRB	_	3	advmod	_	_
2	$ D $	$ d $	SYM	$	_	3	nsubj	_	_
3	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	advcl	_	_
4	2	2	NUM	CD	NumType=Card	6	nummod	_	_
5	-	-	PUNCT	HYPH	PunctType=Dash	6	punct	_	_
6	glueing	glueing	NOUN	NN	Number=Sing	3	dobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
8	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	9	nsubj	_	_
9	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	that	that	SCONJ	IN	_	12	mark	_	_
11	$ Y $	$ y $	SYM	$	_	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	ccomp	_	_
13	pre	pre	ADJ	JJ	Degree=Pos	12	acomp	_	_
14	-	-	ADJ	JJ	Degree=Pos	12	acomp	_	_
15	exponentiable	exponentiable	ADJ	JJ	Degree=Pos	12	acomp	_	_
16	in	in	ADP	IN	_	15	prep	_	_
17	$ D $	$ d $	SYM	$	_	16	pobj	_	_
18	if	if	SCONJ	IN	_	12	dep	_	_
19	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
20	only	only	ADV	RB	_	23	advmod	_	_
21	if	if	SCONJ	IN	_	23	mark	_	_
22	$ Y $	$ y $	SYM	$	_	23	nsubj	_	_
23	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	29	advcl	_	_
24	exponentiable	exponentiable	ADJ	JJ	Degree=Pos	23	acomp	_	_
25	in	in	ADP	IN	_	24	prep	_	_
26	$ D_0 $	$ d_0 $	SYM	$	_	25	pobj	_	_
27	and	and	CCONJ	CC	ConjType=Cmp	26	cc	_	_
28	$ - x Y $	$ - x y $	SYM	$	_	29	nsubj	_	_
29	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	conj	_	_
30	an	an	DET	DT	Definite=Ind|PronType=Art	32	det	_	_
31	oplax	oplax	NOUN	NN	Number=Sing	32	compound	_	_
32	functor	functor	NOUN	NN	Number=Sing	29	attr	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 3
# text = Thus, such a $ D $ is pre - cartesian closed as a double category if and only if $ D_0 $ is a cartesian closed category.
1	Thus	thus	ADV	RB	_	6	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
3	such	such	DET	PDT	_	5	predet	_	_
4	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
5	$ D $	$ d $	SYM	$	_	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	pre	pre	ADJ	JJ	Degree=Pos	10	amod	_	_
8	-	-	ADJ	JJ	Degree=Pos	10	amod	_	_
9	cartesian	cartesian	ADJ	JJ	Degree=Pos	10	nsubj	_	_
10	closed	close	VERB	VBD	Tense=Past|VerbForm=Fin	6	acomp	_	_
11	as	as	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
13	double	double	ADJ	JJ	Degree=Pos	14	amod	_	_
14	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
15	if	if	SCONJ	IN	_	20	mark	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	only	only	ADV	RB	_	20	advmod	_	_
18	if	if	SCONJ	IN	_	20	mark	_	_
19	$ D_0 $	$ d_0 $	SYM	$	_	20	nsubj	_	_
20	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	advcl	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
22	cartesian	cartesian	ADJ	JJ	Degree=Pos	23	advmod	_	_
23	closed	closed	ADJ	JJ	Degree=Pos	24	amod	_	_
24	category	category	NOUN	NN	Number=Sing	20	attr	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 4
# text = Applications include the double categories $ cat $ , $ pos $ , $ spaces $ , $ loc $ , and $ topos $ , whose objects are small categories, posets, topological space, locales, and toposes, respectively.
1	Applications	application	NOUN	NNS	Number=Plur	2	nsubj	_	_
2	include	include	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	double	double	ADJ	JJ	Degree=Pos	5	amod	_	_
5	categories	category	NOUN	NNS	Number=Plur	2	dobj	_	_
6	$ cat $	$ cat $	SYM	$	_	5	appos	_	_
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	$ pos $	$ pos $	SYM	$	_	5	appos	_	_
9	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
10	$ spaces $	$ spaces $	SYM	$	_	8	conj	_	_
11	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
12	$ loc $	$ loc $	SYM	$	_	8	conj	_	_
13	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	5	cc	_	_
15	$ topos $	$ topos $	SYM	$	_	5	conj	_	_
16	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
17	whose	whose	DET	WP$	Poss=Yes	18	poss	_	_
18	objects	object	NOUN	NNS	Number=Plur	19	nsubj	_	_
19	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	5	relcl	_	_
20	small	small	ADJ	JJ	Degree=Pos	21	amod	_	_
21	categories	category	NOUN	NNS	Number=Plur	19	attr	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	posets	poset	NOUN	NNS	Number=Plur	21	conj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	23	punct	_	_
25	topological	topological	ADJ	JJ	Degree=Pos	26	amod	_	_
26	space	space	NOUN	NN	Number=Sing	23	conj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
28	locales	locale	NOUN	NNS	Number=Plur	26	conj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	28	punct	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	28	cc	_	_
31	toposes	topos	NOUN	NNS	Number=Plur	28	conj	_	SpaceAfter=No
32	,	,	PUNCT	,	PunctType=Comm	31	punct	_	_
33	respectively	respectively	ADV	RB	_	31	advmod	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 741
# sent_id = 1
# text = In previous work, we introduced an axiomatic framework within which to prove theorems about many varieties of infinite - dimensional categories simultaneously.
1	In	in	ADP	IN	_	6	prep	_	_
2	previous	previous	ADJ	JJ	Degree=Pos	3	amod	_	_
3	work	work	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	introduced	introduce	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
7	an	an	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	axiomatic	axiomatic	ADJ	JJ	Degree=Pos	9	amod	_	_
9	framework	framework	NOUN	NN	Number=Sing	6	dobj	_	_
10	within	within	ADP	IN	_	13	prep	_	_
11	which	which	PRON	WDT	_	10	pobj	_	_
12	to	to	PART	TO	_	13	aux	_	_
13	prove	prove	VERB	VB	VerbForm=Inf	9	relcl	_	_
14	theorems	theorem	NOUN	NNS	Number=Plur	13	dobj	_	_
15	about	about	ADP	IN	_	13	prep	_	_
16	many	many	ADJ	JJ	Degree=Pos	17	amod	_	_
17	varieties	variety	NOUN	NNS	Number=Plur	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	infinite	infinite	ADJ	JJ	Degree=Pos	21	amod	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	dimensional	dimensional	ADJ	JJ	Degree=Pos	22	amod	_	_
22	categories	category	NOUN	NNS	Number=Plur	18	pobj	_	_
23	simultaneously	simultaneously	ADV	RB	_	13	advmod	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper, we establish criteria implying that an $ infty $ - category—for instance, a quasi - category, a complete Segal space, or a Segal category—is complete and cocomplete, admitting limits and colimits indexed by any small simplicial set.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	establish	establish	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	criteria	criterion	NOUN	NNS	Number=Plur	6	dobj	_	_
8	implying	imply	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	7	acl	_	_
9	that	that	SCONJ	IN	_	33	mark	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	$ infty $	$ infty $	SYM	$	_	13	compound	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	category	category	NOUN	NN	Number=Sing	33	nsubj	_	SpaceAfter=No
14	—	—	PUNCT	:	_	13	punct	_	SpaceAfter=No
15	for	for	ADP	IN	_	13	prep	_	_
16	instance	instance	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	quasi	quasi	ADJ	JJ	Degree=Pos	13	appos	_	_
20	-	-	NOUN	NN	Number=Sing	13	conj	_	_
21	category	category	NOUN	NN	Number=Sing	13	appos	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	26	det	_	_
24	complete	complete	ADJ	JJ	Degree=Pos	26	amod	_	_
25	Segal	Segal	PROPN	NNP	Number=Sing	26	amod	_	_
26	space	space	NOUN	NN	Number=Sing	21	conj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
28	or	or	CCONJ	CC	ConjType=Cmp	26	cc	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	Segal	Segal	PROPN	NNP	Number=Sing	31	compound	_	_
31	category	category	NOUN	NN	Number=Sing	26	conj	_	SpaceAfter=No
32	—	—	PUNCT	:	_	13	punct	_	SpaceAfter=No
33	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	ccomp	_	_
34	complete	complete	ADJ	JJ	Degree=Pos	33	acomp	_	_
35	and	and	CCONJ	CC	ConjType=Cmp	34	cc	_	_
36	cocomplete	cocomplete	ADJ	JJ	Degree=Pos	34	conj	_	SpaceAfter=No
37	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
38	admitting	admit	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	33	advcl	_	_
39	limits	limit	NOUN	NNS	Number=Plur	38	dobj	_	_
40	and	and	CCONJ	CC	ConjType=Cmp	39	cc	_	_
41	colimits	colimit	NOUN	NNS	Number=Plur	39	conj	_	_
42	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	39	acl	_	_
43	by	by	ADP	IN	_	42	agent	_	_
44	any	any	DET	DT	_	47	det	_	_
45	small	small	ADJ	JJ	Degree=Pos	47	amod	_	_
46	simplicial	simplicial	ADJ	JJ	Degree=Pos	47	amod	_	_
47	set	set	NOUN	NN	Number=Sing	43	pobj	_	SpaceAfter=No
48	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = Our strategy is to build (co)limits of diagrams indexed by a simplicial set inductively from (co)limits of restricted diagrams indexed by the pieces of its skeletal filtration.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	strategy	strategy	NOUN	NN	Number=Sing	3	nsubj	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	build	build	VERB	VB	VerbForm=Inf	3	xcomp	_	_
6	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	5	punct	_	SpaceAfter=No
7	co)limits	co)limit	NOUN	NNS	Number=Plur	5	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	diagrams	diagram	NOUN	NNS	Number=Plur	8	pobj	_	_
10	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	9	acl	_	_
11	by	by	ADP	IN	_	10	agent	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	simplicial	simplicial	NOUN	NN	Number=Sing	11	pobj	_	_
14	set	set	NOUN	NN	Number=Sing	13	acl	_	_
15	inductively	inductively	ADV	RB	_	14	advmod	_	_
16	from	from	ADP	IN	_	14	prep	_	_
17	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	16	punct	_	SpaceAfter=No
18	co)limits	co)limit	NOUN	NNS	Number=Plur	16	pobj	_	_
19	of	of	ADP	IN	_	18	prep	_	_
20	restricted	restricted	ADJ	JJ	Degree=Pos	21	amod	_	_
21	diagrams	diagram	NOUN	NNS	Number=Plur	19	pobj	_	_
22	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	21	acl	_	_
23	by	by	ADP	IN	_	22	agent	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	pieces	piece	NOUN	NNS	Number=Plur	23	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	29	poss	_	_
28	skeletal	skeletal	ADJ	JJ	Degree=Pos	29	amod	_	_
29	filtration	filtration	NOUN	NN	Number=Sing	26	pobj	_	SpaceAfter=No
30	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show directly that the modules that express the universal properties of (co)limits of diagrams of these shapes are reconstructible as limits of the modules that express the universal properties of (co)limits of the restricted diagrams.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	directly	directly	ADV	RB	_	2	advmod	_	_
4	that	that	SCONJ	IN	_	20	mark	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	modules	module	NOUN	NNS	Number=Plur	20	nsubj	_	_
7	that	that	PRON	WDT	PronType=Rel	8	nsubj	_	_
8	express	express	VERB	VBP	Tense=Pres|VerbForm=Fin	6	relcl	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
10	universal	universal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	properties	property	NOUN	NNS	Number=Plur	8	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	12	punct	_	SpaceAfter=No
14	co)limits	co)limit	NOUN	NNS	Number=Plur	12	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	diagrams	diagram	NOUN	NNS	Number=Plur	15	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	these	these	DET	DT	Number=Plur|PronType=Dem	19	det	_	_
19	shapes	shape	NOUN	NNS	Number=Plur	17	pobj	_	_
20	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
21	reconstructible	reconstructible	ADJ	JJ	Degree=Pos	20	acomp	_	_
22	as	as	ADP	IN	_	20	prep	_	_
23	limits	limit	NOUN	NNS	Number=Plur	22	pobj	_	_
24	of	of	ADP	IN	_	23	prep	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	modules	module	NOUN	NNS	Number=Plur	24	pobj	_	_
27	that	that	PRON	WDT	PronType=Rel	28	nsubj	_	_
28	express	express	VERB	VBP	Tense=Pres|VerbForm=Fin	26	relcl	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
30	universal	universal	ADJ	JJ	Degree=Pos	31	amod	_	_
31	properties	property	NOUN	NNS	Number=Plur	28	dobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	32	punct	_	SpaceAfter=No
34	co)limits	co)limit	NOUN	NNS	Number=Plur	32	pobj	_	_
35	of	of	ADP	IN	_	34	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
37	restricted	restricted	ADJ	JJ	Degree=Pos	38	amod	_	_
38	diagrams	diagram	NOUN	NNS	Number=Plur	35	pobj	_	SpaceAfter=No
39	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = We also prove that the Yoneda embedding preserves and reflects limits in a suitable sense, and deduce our main theorems as a consequence.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	10	mark	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
6	Yoneda	Yoneda	PROPN	NNP	Number=Sing	8	nmod	_	_
7	embedding	embed	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	amod	_	_
8	preserves	preserve	NOUN	NNS	Number=Plur	10	nsubj	_	_
9	and	and	CCONJ	CC	ConjType=Cmp	8	cc	_	_
10	reflects	reflect	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	3	ccomp	_	_
11	limits	limit	NOUN	NNS	Number=Plur	10	dobj	_	_
12	in	in	ADP	IN	_	10	prep	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	suitable	suitable	ADJ	JJ	Degree=Pos	15	amod	_	_
15	sense	sense	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	3	punct	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
18	deduce	deduce	VERB	VB	VerbForm=Inf	3	conj	_	_
19	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	21	poss	_	_
20	main	main	ADJ	JJ	Degree=Pos	21	amod	_	_
21	theorems	theorem	NOUN	NNS	Number=Plur	18	dobj	_	_
22	as	as	ADP	IN	_	18	prep	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	consequence	consequence	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
25	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 742
# sent_id = 1
# text = We determine the largest submonoid of the monoid of continuous endomorphisms of the unit interval $ [0, 1] $ on which the finite partitions form the basis of a Grothendieck topology, and thus determine a cohesive topos over sets.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	determine	determine	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	largest	large	ADJ	JJS	Degree=Sup	5	amod	_	_
5	submonoid	submonoid	NOUN	NN	Number=Sing	2	dobj	_	_
6	of	of	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	monoid	monoid	NOUN	NN	Number=Sing	6	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	continuous	continuous	ADJ	JJ	Degree=Pos	11	amod	_	_
11	endomorphisms	endomorphism	NOUN	NNS	Number=Plur	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	15	det	_	_
14	unit	unit	NOUN	NN	Number=Sing	15	compound	_	_
15	interval	interval	NOUN	NN	Number=Sing	12	pobj	_	_
16	$ [0, 1] $	$ [0, 1] $	SYM	$	_	15	appos	_	_
17	on	on	ADP	IN	_	22	prep	_	_
18	which	which	PRON	WDT	_	17	pobj	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	finite	finite	PROPN	NNP	Number=Sing	21	compound	_	_
21	partitions	partition	NOUN	NNS	Number=Plur	22	nsubj	_	_
22	form	form	VERB	VBP	Tense=Pres|VerbForm=Fin	16	relcl	_	_
23	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
24	basis	basis	NOUN	NN	Number=Sing	22	dobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
27	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	28	compound	_	_
28	topology	topology	NOUN	NN	Number=Sing	25	pobj	_	SpaceAfter=No
29	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
30	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
31	thus	thus	ADV	RB	_	32	advmod	_	_
32	determine	determine	VERB	VB	VerbForm=Inf	22	conj	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	35	det	_	_
34	cohesive	cohesive	ADJ	JJ	Degree=Pos	35	amod	_	_
35	topos	topos	NOUN	NN	Number=Sing	32	dobj	_	_
36	over	over	ADP	IN	_	35	prep	_	_
37	sets	set	NOUN	NNS	Number=Plur	36	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We analyze some of the sheaf theoretic aspects of this topos.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	analyze	analyze	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	some	some	PRON	DT	_	2	dobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
6	sheaf	sheaf	NOUN	NN	Number=Sing	7	compound	_	_
7	theoretic	theoretic	ADJ	JJ	Degree=Pos	8	amod	_	_
8	aspects	aspect	NOUN	NNS	Number=Plur	4	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	this	this	DET	DT	Number=Sing|PronType=Dem	11	det	_	_
11	topos	topos	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Furthermore, we adapt the constructions of Menni to include another model of axiomatic cohesion.
1	Furthermore	furthermore	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	adapt	adapt	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	constructions	construction	NOUN	NNS	Number=Plur	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	Menni	Menni	PROPN	NNP	Number=Sing	7	pobj	_	_
9	to	to	PART	TO	_	10	aux	_	_
10	include	include	VERB	VB	VerbForm=Inf	4	advcl	_	_
11	another	another	DET	DT	_	12	det	_	_
12	model	model	NOUN	NN	Number=Sing	10	dobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	axiomatic	axiomatic	ADJ	JJ	Degree=Pos	15	amod	_	_
15	cohesion	cohesion	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = We conclude the paper with a proof of the fact that a sufficiently cohesive topos of presheaves does not satisfy the continuity axiom.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	conclude	conclude	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	paper	paper	NOUN	NN	Number=Sing	2	dobj	_	_
5	with	with	ADP	IN	_	2	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	proof	proof	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	fact	fact	NOUN	NN	Number=Sing	8	pobj	_	_
11	that	that	SCONJ	IN	_	20	mark	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	sufficiently	sufficiently	ADV	RB	_	14	advmod	_	_
14	cohesive	cohesive	ADJ	JJ	Degree=Pos	15	amod	_	_
15	topos	topos	NOUN	NN	Number=Sing	20	nsubj	_	_
16	of	of	ADP	IN	_	15	prep	_	_
17	presheaves	presheave	NOUN	NNS	Number=Plur	16	pobj	_	_
18	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	20	aux	_	_
19	not	not	PART	RB	Polarity=Neg	20	neg	_	_
20	satisfy	satisfy	VERB	VB	VerbForm=Inf	10	acl	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
22	continuity	continuity	NOUN	NN	Number=Sing	23	compound	_	_
23	axiom	axiom	NOUN	NN	Number=Sing	20	dobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 743
# sent_id = 1
# text = We lift the standard equivalence between fibrations and indexed categories to an equivalence between monoidal fibrations and monoidal indexed categories, namely lax monoidal pseudofunctors to the 2 - category of categories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	lift	lift	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
4	standard	standard	ADJ	JJ	Degree=Pos	5	amod	_	_
5	equivalence	equivalence	NOUN	NN	Number=Sing	2	dobj	_	_
6	between	between	ADP	IN	_	5	prep	_	_
7	fibrations	fibration	NOUN	NNS	Number=Plur	6	pobj	_	_
8	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
9	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	amod	_	_
10	categories	category	NOUN	NNS	Number=Plur	7	conj	_	_
11	to	to	ADP	IN	_	2	prep	_	_
12	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
13	equivalence	equivalence	NOUN	NN	Number=Sing	11	pobj	_	_
14	between	between	ADP	IN	_	13	prep	_	_
15	monoidal	monoidal	ADJ	JJ	Degree=Pos	16	amod	_	_
16	fibrations	fibration	NOUN	NNS	Number=Plur	14	pobj	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	16	cc	_	_
18	monoidal	monoidal	ADJ	JJ	Degree=Pos	20	amod	_	_
19	indexed	index	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	amod	_	_
20	categories	category	NOUN	NNS	Number=Plur	16	conj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	namely	namely	ADV	RB	_	23	advmod	_	_
23	lax	lax	ADJ	JJ	Degree=Pos	25	amod	_	_
24	monoidal	monoidal	ADJ	JJ	Degree=Pos	25	amod	_	_
25	pseudofunctors	pseudofunctor	NOUN	NNS	Number=Plur	20	appos	_	_
26	to	to	ADP	IN	_	2	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
28	2	2	NUM	CD	NumType=Card	30	nummod	_	_
29	-	-	PUNCT	HYPH	PunctType=Dash	30	punct	_	_
30	category	category	NOUN	NN	Number=Sing	26	pobj	_	_
31	of	of	ADP	IN	_	30	prep	_	_
32	categories	category	NOUN	NNS	Number=Plur	31	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Furthermore, we investigate the relation between this `global' monoidal version where the total category is monoidal and the fibration strictly preserves the structure, and a `fibrewise' one where the fibres are monoidal and the reindexing functors strongly preserve the structure, first hinted by Shulman.
1	Furthermore	furthermore	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	investigate	investigate	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	relation	relation	NOUN	NN	Number=Sing	4	dobj	_	_
7	between	between	ADP	IN	_	6	prep	_	_
8	this	this	DET	DT	Number=Sing|PronType=Dem	13	det	_	_
9	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	13	punct	_	SpaceAfter=No
10	global	global	ADJ	JJ	Degree=Pos	13	amod	_	SpaceAfter=No
11	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	13	punct	_	_
12	monoidal	monoidal	ADJ	JJ	Degree=Pos	13	amod	_	_
13	version	version	NOUN	NN	Number=Sing	7	pobj	_	_
14	where	where	SCONJ	WRB	_	18	advmod	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
16	total	total	ADJ	JJ	Degree=Pos	17	amod	_	_
17	category	category	NOUN	NN	Number=Sing	18	nsubj	_	_
18	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	13	relcl	_	_
19	monoidal	monoidal	ADJ	JJ	Degree=Pos	18	acomp	_	_
20	and	and	CCONJ	CC	ConjType=Cmp	18	cc	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	fibration	fibration	NOUN	NN	Number=Sing	24	nsubj	_	_
23	strictly	strictly	ADV	RB	_	24	advmod	_	_
24	preserves	preserve	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	conj	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	structure	structure	NOUN	NN	Number=Sing	24	dobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
28	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	31	punct	_	SpaceAfter=No
31	fibrewise	fibrewise	NOUN	NN	Number=Sing	24	conj	_	SpaceAfter=No
32	'	'	PUNCT	''	PunctSide=Fin|PunctType=Quot	31	punct	_	_
33	one	one	NOUN	NN	Number=Sing	31	appos	_	_
34	where	where	SCONJ	WRB	_	37	advmod	_	_
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	_	_
36	fibres	fibre	NOUN	NNS	Number=Plur	37	nsubj	_	_
37	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	33	relcl	_	_
38	monoidal	monoidal	ADJ	JJ	Degree=Pos	37	acomp	_	_
39	and	and	CCONJ	CC	ConjType=Cmp	33	cc	_	_
40	the	the	DET	DT	Definite=Def|PronType=Art	42	det	_	_
41	reindexing	reindexe	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	42	amod	_	_
42	functors	functor	NOUN	NNS	Number=Plur	44	nsubj	_	_
43	strongly	strongly	ADV	RB	_	44	advmod	_	_
44	preserve	preserve	VERB	VBP	Tense=Pres|VerbForm=Fin	24	conj	_	_
45	the	the	DET	DT	Definite=Def|PronType=Art	46	det	_	_
46	structure	structure	NOUN	NN	Number=Sing	44	dobj	_	SpaceAfter=No
47	,	,	PUNCT	,	PunctType=Comm	44	punct	_	_
48	first	first	ADV	RB	_	49	advmod	_	_
49	hinted	hint	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	44	advcl	_	_
50	by	by	ADP	IN	_	49	agent	_	_
51	Shulman	Shulman	PROPN	NNP	Number=Sing	50	pobj	_	SpaceAfter=No
52	.	.	PUNCT	.	PunctType=Peri	24	punct	_	SpaceAfter=No

# sent_id = 3
# text = In particular, when the domain is cocartesian monoidal, we show how lax monoidal structures on a pseudofunctor to $ Cat $ bijectively correspond to lifts of the pseudofunctor to $ MonCat $ .
1	In	in	ADP	IN	_	12	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
4	when	when	SCONJ	WRB	_	7	advmod	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	domain	domain	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	advcl	_	_
8	cocartesian	cocartesian	ADJ	JJ	Degree=Pos	9	amod	_	_
9	monoidal	monoidal	NOUN	NN	Number=Sing	7	attr	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
11	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	12	nsubj	_	_
12	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	how	how	SCONJ	WRB	_	14	advmod	_	_
14	lax	lax	ADJ	JJ	Degree=Pos	16	amod	_	_
15	monoidal	monoidal	ADJ	JJ	Degree=Pos	16	amod	_	_
16	structures	structure	NOUN	NNS	Number=Plur	23	nsubj	_	_
17	on	on	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	19	det	_	_
19	pseudofunctor	pseudofunctor	NOUN	NN	Number=Sing	17	pobj	_	_
20	to	to	ADP	IN	_	16	prep	_	_
21	$ Cat $	$ cat $	SYM	$	_	20	pobj	_	_
22	bijectively	bijectively	ADV	RB	_	23	advmod	_	_
23	correspond	correspond	VERB	VBP	Tense=Pres|VerbForm=Fin	12	ccomp	_	_
24	to	to	ADP	IN	_	23	prep	_	_
25	lifts	lift	NOUN	NNS	Number=Plur	24	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	pseudofunctor	pseudofunctor	NOUN	NN	Number=Sing	26	pobj	_	_
29	to	to	ADP	IN	_	23	prep	_	_
30	$ MonCat $	$ moncat $	SYM	$	_	29	pobj	_	_
31	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 4
# text = Finally, we give some examples where this correspondence appears, spanning from the fundamental and family fibrations to network models and systems.
1	Finally	finally	ADV	RB	_	4	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	some	some	DET	DT	_	6	det	_	_
6	examples	example	NOUN	NNS	Number=Plur	4	dobj	_	_
7	where	where	SCONJ	WRB	_	10	advmod	_	_
8	this	this	DET	DT	Number=Sing|PronType=Dem	9	det	_	_
9	correspondence	correspondence	NOUN	NN	Number=Sing	10	nsubj	_	_
10	appears	appear	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	6	relcl	_	SpaceAfter=No
11	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
12	spanning	span	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	4	advcl	_	_
13	from	from	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	18	det	_	_
15	fundamental	fundamental	ADJ	JJ	Degree=Pos	18	amod	_	_
16	and	and	CCONJ	CC	ConjType=Cmp	15	cc	_	_
17	family	family	NOUN	NN	Number=Sing	15	conj	_	_
18	fibrations	fibration	NOUN	NNS	Number=Plur	13	pobj	_	_
19	to	to	ADP	IN	_	18	prep	_	_
20	network	network	NOUN	NN	Number=Sing	21	compound	_	_
21	models	model	NOUN	NNS	Number=Plur	19	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	21	cc	_	_
23	systems	system	NOUN	NNS	Number=Plur	21	conj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 744
# sent_id = 1
# text = In this paper we prove an equivalence theorem originally observed by Robert MacPherson.
1	In	in	ADP	IN	_	5	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	an	an	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	equivalence	equivalence	NOUN	NN	Number=Sing	8	nsubj	_	_
8	theorem	theorem	ADJ	JJ	Degree=Pos	5	ccomp	_	_
9	originally	originally	ADV	RB	_	10	advmod	_	_
10	observed	observe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	acl	_	_
11	by	by	ADP	IN	_	10	agent	_	_
12	Robert	Robert	PROPN	NNP	Number=Sing	13	compound	_	_
13	MacPherson	MacPherson	PROPN	NNP	Number=Sing	11	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 2
# text = On one side of the equivalence is the category of cosheaves that are constructible with respect to a locally cone - like stratification.
1	On	on	ADP	IN	_	7	prep	_	_
2	one	one	NUM	CD	NumType=Card	3	nummod	_	_
3	side	side	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
6	equivalence	equivalence	NOUN	NN	Number=Sing	4	pobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
9	category	category	NOUN	NN	Number=Sing	7	attr	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	cosheaves	cosheave	NOUN	NNS	Number=Plur	10	pobj	_	_
12	that	that	PRON	WDT	PronType=Rel	13	nsubj	_	_
13	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	11	relcl	_	_
14	constructible	constructible	ADJ	JJ	Degree=Pos	13	acomp	_	_
15	with	with	ADP	IN	_	14	prep	_	_
16	respect	respect	NOUN	NN	Number=Sing	15	pobj	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	23	det	_	_
19	locally	locally	ADV	RB	_	22	advmod	_	_
20	cone	cone	NOUN	NN	Number=Sing	22	npadvmod	_	_
21	-	-	PUNCT	HYPH	PunctType=Dash	22	punct	_	_
22	like	like	ADJ	JJ	Degree=Pos	23	amod	_	_
23	stratification	stratification	NOUN	NN	Number=Sing	17	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = Our constructibility condition is new and only requires that certain inclusions of open sets are sent to isomorphisms.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	3	poss	_	_
2	constructibility	constructibility	NOUN	NN	Number=Sing	3	compound	_	_
3	condition	condition	NOUN	NN	Number=Sing	4	nsubj	_	_
4	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	new	new	ADJ	JJ	Degree=Pos	4	acomp	_	_
6	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
7	only	only	ADV	RB	_	8	advmod	_	_
8	requires	require	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	conj	_	_
9	that	that	SCONJ	IN	_	16	mark	_	_
10	certain	certain	ADJ	JJ	Degree=Pos	11	amod	_	_
11	inclusions	inclusion	NOUN	NNS	Number=Plur	16	nsubjpass	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	open	open	ADJ	JJ	Degree=Pos	14	amod	_	_
14	sets	set	NOUN	NNS	Number=Plur	12	pobj	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	16	auxpass	_	_
16	sent	send	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	8	ccomp	_	_
17	to	to	ADP	IN	_	16	prep	_	_
18	isomorphisms	isomorphism	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = On the other side of the equivalence is the category of functors from the entrance path category, which has points for objects and certain homotopy classes of paths for morphisms.
1	On	on	ADP	IN	_	8	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	other	other	ADJ	JJ	Degree=Pos	4	amod	_	_
4	side	side	NOUN	NN	Number=Sing	1	pobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	equivalence	equivalence	NOUN	NN	Number=Sing	5	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	category	category	NOUN	NN	Number=Sing	8	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	functors	functor	NOUN	NNS	Number=Plur	11	pobj	_	_
13	from	from	ADP	IN	_	12	prep	_	_
14	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
15	entrance	entrance	NOUN	NN	Number=Sing	16	compound	_	_
16	path	path	NOUN	NN	Number=Sing	17	compound	_	_
17	category	category	NOUN	NN	Number=Sing	13	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	which	which	PRON	WDT	_	20	nsubj	_	_
20	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
21	points	point	NOUN	NNS	Number=Plur	20	dobj	_	_
22	for	for	ADP	IN	_	21	prep	_	_
23	objects	object	NOUN	NNS	Number=Plur	22	pobj	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	23	cc	_	_
25	certain	certain	ADJ	JJ	Degree=Pos	27	amod	_	_
26	homotopy	homotopy	NOUN	NN	Number=Sing	27	compound	_	_
27	classes	class	NOUN	NNS	Number=Plur	23	conj	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	paths	path	NOUN	NNS	Number=Plur	28	pobj	_	_
30	for	for	ADP	IN	_	23	prep	_	_
31	morphisms	morphism	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
32	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 5
# text = When our constructible cosheaves are valued in Set we prove an additional equivalence with the category of stratified coverings.
1	When	when	SCONJ	WRB	_	6	advmod	_	_
2	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	4	poss	_	_
3	constructible	constructible	ADJ	JJ	Degree=Pos	4	amod	_	_
4	cosheaves	cosheave	NOUN	NNS	Number=Plur	6	nsubjpass	_	_
5	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	6	auxpass	_	_
6	valued	value	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	10	advcl	_	_
7	in	in	ADP	IN	_	6	prep	_	_
8	Set	Set	PROPN	NNP	Number=Sing	7	pobj	_	_
9	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	10	nsubj	_	_
10	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
11	an	an	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
12	additional	additional	ADJ	JJ	Degree=Pos	13	amod	_	_
13	equivalence	equivalence	NOUN	NN	Number=Sing	10	dobj	_	_
14	with	with	ADP	IN	_	13	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	category	category	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	stratified	stratified	ADJ	JJ	Degree=Pos	19	amod	_	_
19	coverings	covering	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
20	.	.	PUNCT	.	PunctType=Peri	10	punct	_	SpaceAfter=No

# doc_id = 745
# sent_id = 1
# text = We show that the various higher Segal conditions of Dyckerhoff and Kapranov can all be characterized in purely categorical terms by higher excision conditions (in the spirit of Goodwillie - - Weiss manifold calculus) on the simplex category $ Delta $ and the cyclic category $ Lambda $ .
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	16	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
5	various	various	ADJ	JJ	Degree=Pos	8	amod	_	_
6	higher	high	ADJ	JJR	Degree=Cmp	8	amod	_	_
7	Segal	Segal	PROPN	NNP	Number=Sing	8	compound	_	_
8	conditions	condition	NOUN	NNS	Number=Plur	16	nsubjpass	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	Dyckerhoff	Dyckerhoff	PROPN	NNP	Number=Sing	9	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
12	Kapranov	Kapranov	PROPN	NNP	Number=Sing	10	conj	_	_
13	can	can	AUX	MD	VerbForm=Fin	16	aux	_	_
14	all	all	ADV	RB	_	16	dep	_	_
15	be	be	AUX	VB	VerbForm=Inf	16	auxpass	_	_
16	characterized	characterize	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
17	in	in	ADP	IN	_	16	prep	_	_
18	purely	purely	ADV	RB	_	19	advmod	_	_
19	categorical	categorical	ADJ	JJ	Degree=Pos	20	amod	_	_
20	terms	term	NOUN	NNS	Number=Plur	17	pobj	_	_
21	by	by	ADP	IN	_	20	prep	_	_
22	higher	high	ADJ	JJR	Degree=Cmp	23	amod	_	_
23	excision	excision	NOUN	NN	Number=Sing	24	compound	_	_
24	conditions	condition	NOUN	NNS	Number=Plur	21	pobj	_	_
25	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	24	punct	_	SpaceAfter=No
26	in	in	ADP	IN	_	24	prep	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
28	spirit	spirit	NOUN	NN	Number=Sing	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	Goodwillie	Goodwillie	PROPN	NNP	Number=Sing	33	nmod	_	_
31	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
32	-	-	PUNCT	HYPH	PunctType=Dash	33	punct	_	_
33	Weiss	Weiss	PROPN	NNP	Number=Sing	35	nmod	_	_
34	manifold	manifold	ADJ	JJ	Degree=Pos	35	amod	_	_
35	calculus	calculus	NOUN	NN	Number=Sing	29	pobj	_	SpaceAfter=No
36	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	35	punct	_	_
37	on	on	ADP	IN	_	28	prep	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
39	simplex	simplex	NOUN	NN	Number=Sing	40	compound	_	_
40	category	category	NOUN	NN	Number=Sing	37	pobj	_	_
41	$ Delta $	$ delta $	SYM	$	_	40	appos	_	_
42	and	and	CCONJ	CC	ConjType=Cmp	40	cc	_	_
43	the	the	DET	DT	Definite=Def|PronType=Art	45	det	_	_
44	cyclic	cyclic	ADJ	JJ	Degree=Pos	45	amod	_	_
45	category	category	NOUN	NN	Number=Sing	40	conj	_	_
46	$ Lambda $	$ lambda $	SYM	$	_	45	appos	_	_
47	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 746
# sent_id = 1
# text = The task of constructing compositional semantics for network - style diagrammatic languages, such as electrical circuits or chemical reaction networks, has been dubbed the black boxing problem, as it gives semantics that describes the properties of each network that can be observed externally, through composition, while discarding the internal structure.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	task	task	NOUN	NN	Number=Sing	25	nsubjpass	_	_
3	of	of	ADP	IN	_	2	prep	_	_
4	constructing	construct	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	3	pcomp	_	_
5	compositional	compositional	ADJ	JJ	Degree=Pos	6	amod	_	_
6	semantics	semantic	NOUN	NNS	Number=Plur	4	dobj	_	_
7	for	for	ADP	IN	_	6	prep	_	_
8	network	network	NOUN	NN	Number=Sing	10	nmod	_	_
9	-	-	PUNCT	HYPH	PunctType=Dash	10	punct	_	_
10	style	style	NOUN	NN	Number=Sing	12	compound	_	_
11	diagrammatic	diagrammatic	NOUN	NN	Number=Sing	12	compound	_	_
12	languages	language	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	such	such	ADJ	JJ	Degree=Pos	15	amod	_	_
15	as	as	ADP	IN	_	12	prep	_	_
16	electrical	electrical	ADJ	JJ	Degree=Pos	17	amod	_	_
17	circuits	circuit	NOUN	NNS	Number=Plur	15	pobj	_	_
18	or	or	CCONJ	CC	ConjType=Cmp	17	cc	_	_
19	chemical	chemical	ADJ	JJ	Degree=Pos	20	compound	_	_
20	reaction	reaction	NOUN	NN	Number=Sing	21	compound	_	_
21	networks	network	NOUN	NNS	Number=Plur	17	conj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
23	has	have	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	aux	_	_
24	been	be	AUX	VBN	Tense=Past|VerbForm=Part	25	auxpass	_	_
25	dubbed	dub	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
27	black	black	ADJ	JJ	Degree=Pos	29	amod	_	_
28	boxing	boxing	NOUN	NN	Number=Sing	29	compound	_	_
29	problem	problem	NOUN	NN	Number=Sing	25	oprd	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	25	punct	_	_
31	as	as	SCONJ	IN	_	33	mark	_	_
32	it	it	PRON	PRP	Case=Nom|Gender=Neut|Number=Sing|Person=3|PronType=Prs	33	nsubj	_	_
33	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	25	advcl	_	_
34	semantics	semantic	NOUN	NNS	Number=Plur	33	dobj	_	_
35	that	that	PRON	WDT	PronType=Rel	36	nsubj	_	_
36	describes	describe	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	34	relcl	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	38	det	_	_
38	properties	property	NOUN	NNS	Number=Plur	36	dobj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	each	each	DET	DT	_	41	det	_	_
41	network	network	NOUN	NN	Number=Sing	39	pobj	_	_
42	that	that	PRON	WDT	PronType=Rel	45	nsubjpass	_	_
43	can	can	AUX	MD	VerbForm=Fin	45	aux	_	_
44	be	be	AUX	VB	VerbForm=Inf	45	auxpass	_	_
45	observed	observe	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	38	relcl	_	_
46	externally	externally	ADV	RB	_	45	advmod	_	SpaceAfter=No
47	,	,	PUNCT	,	PunctType=Comm	45	punct	_	_
48	through	through	ADP	IN	_	45	prep	_	_
49	composition	composition	NOUN	NN	Number=Sing	48	pobj	_	SpaceAfter=No
50	,	,	PUNCT	,	PunctType=Comm	45	punct	_	_
51	while	while	SCONJ	IN	_	52	mark	_	_
52	discarding	discard	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	45	advcl	_	_
53	the	the	DET	DT	Definite=Def|PronType=Art	55	det	_	_
54	internal	internal	ADJ	JJ	Degree=Pos	55	amod	_	_
55	structure	structure	NOUN	NN	Number=Sing	52	dobj	_	SpaceAfter=No
56	.	.	PUNCT	.	PunctType=Peri	25	punct	_	SpaceAfter=No

# sent_id = 2
# text = One way to solve these problems is to formalise the diagrams and their semantics using hypergraph categories, with semantic interpretation a hypergraph functor, called the black box functor, between them.
1	One	one	NUM	CD	NumType=Card	2	nummod	_	_
2	way	way	NOUN	NN	Number=Sing	7	nsubj	_	_
3	to	to	PART	TO	_	4	aux	_	_
4	solve	solve	VERB	VB	VerbForm=Inf	2	relcl	_	_
5	these	these	DET	DT	Number=Plur|PronType=Dem	6	det	_	_
6	problems	problem	NOUN	NNS	Number=Plur	4	dobj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	to	to	PART	TO	_	9	aux	_	_
9	formalise	formalise	VERB	VB	VerbForm=Inf	7	xcomp	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	diagrams	diagram	NOUN	NNS	Number=Plur	9	dobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	14	poss	_	_
14	semantics	semantic	NOUN	NNS	Number=Plur	11	conj	_	_
15	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	acl	_	_
16	hypergraph	hypergraph	ADJ	JJ	Degree=Pos	17	amod	_	_
17	categories	category	NOUN	NNS	Number=Plur	15	dobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
19	with	with	ADP	IN	_	9	prep	_	_
20	semantic	semantic	ADJ	JJ	Degree=Pos	21	amod	_	_
21	interpretation	interpretation	NOUN	NN	Number=Sing	19	pobj	_	_
22	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
23	hypergraph	hypergraph	NOUN	NN	Number=Sing	24	compound	_	_
24	functor	functor	NOUN	NN	Number=Sing	9	dobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
26	called	call	VERB	VBD	Tense=Past|VerbForm=Fin	24	acl	_	_
27	the	the	DET	DT	Definite=Def|PronType=Art	30	det	_	_
28	black	black	ADJ	JJ	Degree=Pos	29	compound	_	_
29	box	box	NOUN	NN	Number=Sing	30	compound	_	_
30	functor	functor	NOUN	NN	Number=Sing	26	oprd	_	SpaceAfter=No
31	,	,	PUNCT	,	PunctType=Comm	24	punct	_	_
32	between	between	ADP	IN	_	24	prep	_	_
33	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	32	pobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 3
# text = Building on a previous method for constructing hypergraph categories and functors, known as decorated corelations, in this paper we construct a category of decorating data, and show that the decorated corelations method is itself functorial, with a universal property characterised by a left Kan extension.
1	Building	build	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	22	advcl	_	_
2	on	on	ADP	IN	_	1	prep	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	previous	previous	ADJ	JJ	Degree=Pos	5	amod	_	_
5	method	method	NOUN	NN	Number=Sing	2	pobj	_	_
6	for	for	ADP	IN	_	5	prep	_	_
7	constructing	construct	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	pcomp	_	_
8	hypergraph	hypergraph	ADJ	JJ	Degree=Pos	9	amod	_	_
9	categories	category	NOUN	NNS	Number=Plur	7	dobj	_	_
10	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
11	functors	functor	NOUN	NNS	Number=Plur	9	conj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
13	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	7	advcl	_	_
14	as	as	ADP	IN	_	13	prep	_	_
15	decorated	decorate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
16	corelations	corelation	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
18	in	in	ADP	IN	_	22	prep	_	_
19	this	this	DET	DT	Number=Sing|PronType=Dem	20	det	_	_
20	paper	paper	NOUN	NN	Number=Sing	18	pobj	_	_
21	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	22	nsubj	_	_
22	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
23	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
24	category	category	NOUN	NN	Number=Sing	22	dobj	_	_
25	of	of	ADP	IN	_	24	prep	_	_
26	decorating	decorate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	25	pcomp	_	_
27	data	datum	NOUN	NNS	Number=Plur	26	dobj	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
29	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
30	show	show	VERB	VB	VerbForm=Inf	22	conj	_	_
31	that	that	SCONJ	IN	_	36	mark	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	34	det	_	_
33	decorated	decorate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	34	amod	_	_
34	corelations	corelation	NOUN	NNS	Number=Plur	35	compound	_	_
35	method	method	NOUN	NN	Number=Sing	36	nsubj	_	_
36	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	30	ccomp	_	_
37	itself	itself	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs|Reflex=Yes	36	attr	_	_
38	functorial	functorial	NOUN	NN	Number=Sing	36	acomp	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	36	punct	_	_
40	with	with	ADP	IN	_	36	prep	_	_
41	a	a	DET	DT	Definite=Ind|PronType=Art	43	det	_	_
42	universal	universal	ADJ	JJ	Degree=Pos	43	amod	_	_
43	property	property	NOUN	NN	Number=Sing	40	pobj	_	_
44	characterised	characterise	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	43	acl	_	_
45	by	by	ADP	IN	_	44	agent	_	_
46	a	a	DET	DT	Definite=Ind|PronType=Art	49	det	_	_
47	left	leave	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	49	amod	_	_
48	Kan	Kan	PROPN	NNP	Number=Sing	49	compound	_	_
49	extension	extension	NOUN	NN	Number=Sing	45	pobj	_	SpaceAfter=No
50	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# sent_id = 4
# text = We then show that any hypergraph category can be presented in terms of decorating data, and hence argue that the category of decorating data is a good setting in which to construct any hypergraph functor.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	then	then	ADV	RB	PronType=Dem	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	10	mark	_	_
5	any	any	DET	DT	_	7	det	_	_
6	hypergraph	hypergraph	ADJ	JJ	Degree=Pos	7	amod	_	_
7	category	category	NOUN	NN	Number=Sing	10	nsubjpass	_	_
8	can	can	AUX	MD	VerbForm=Fin	10	aux	_	_
9	be	be	AUX	VB	VerbForm=Inf	10	auxpass	_	_
10	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	3	ccomp	_	_
11	in	in	ADP	IN	_	10	prep	_	_
12	terms	term	NOUN	NNS	Number=Plur	11	pobj	_	_
13	of	of	ADP	IN	_	12	prep	_	_
14	decorating	decorate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	13	pcomp	_	_
15	data	datum	NOUN	NNS	Number=Plur	14	dobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	10	punct	_	_
17	and	and	CCONJ	CC	ConjType=Cmp	10	cc	_	_
18	hence	hence	ADV	RB	_	19	advmod	_	_
19	argue	argue	VERB	VBP	Tense=Pres|VerbForm=Fin	10	conj	_	_
20	that	that	SCONJ	IN	_	26	mark	_	_
21	the	the	DET	DT	Definite=Def|PronType=Art	22	det	_	_
22	category	category	NOUN	NN	Number=Sing	26	nsubj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	decorating	decorate	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	23	pcomp	_	_
25	data	datum	NOUN	NNS	Number=Plur	24	dobj	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	19	ccomp	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	good	good	ADJ	JJ	Degree=Pos	29	amod	_	_
29	setting	setting	NOUN	NN	Number=Sing	26	attr	_	_
30	in	in	ADP	IN	_	33	prep	_	_
31	which	which	PRON	WDT	_	30	pobj	_	_
32	to	to	PART	TO	_	33	aux	_	_
33	construct	construct	VERB	VB	VerbForm=Inf	29	relcl	_	_
34	any	any	DET	DT	_	36	det	_	_
35	hypergraph	hypergraph	NOUN	NN	Number=Sing	36	compound	_	_
36	functor	functor	NOUN	NN	Number=Sing	33	dobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 5
# text = As an example, we give a new construction of Baez and Pollard's black box functor for reaction networks.
1	As	as	ADP	IN	_	6	prep	_	_
2	an	an	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	example	example	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	9	det	_	_
8	new	new	ADJ	JJ	Degree=Pos	9	amod	_	_
9	construction	construction	NOUN	NN	Number=Sing	6	dobj	_	_
10	of	of	ADP	IN	_	9	prep	_	_
11	Baez	Baez	PROPN	NNP	Number=Sing	10	pobj	_	_
12	and	and	CCONJ	CC	ConjType=Cmp	11	cc	_	_
13	Pollard	Pollard	PROPN	NNP	Number=Sing	17	poss	_	SpaceAfter=No
14	's	's	PART	POS	_	13	case	_	_
15	black	black	ADJ	JJ	Degree=Pos	16	amod	_	_
16	box	box	NOUN	NN	Number=Sing	17	compound	_	_
17	functor	functor	NOUN	NN	Number=Sing	11	conj	_	_
18	for	for	ADP	IN	_	6	prep	_	_
19	reaction	reaction	NOUN	NN	Number=Sing	20	compound	_	_
20	networks	network	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 747
# sent_id = 1
# text = For a diagram of simplicial combinatorial model categories, we show that the associated lax limit, endowed with the projective model structure, is a presentation of the lax limit of the underlying $ infty $ - categories.
1	For	for	ADP	IN	_	11	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	diagram	diagram	NOUN	NN	Number=Sing	1	pobj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	simplicial	simplicial	ADJ	JJ	Degree=Pos	8	amod	_	_
6	combinatorial	combinatorial	ADJ	JJ	Degree=Pos	7	amod	_	_
7	model	model	NOUN	NN	Number=Sing	8	compound	_	_
8	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
10	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	11	nsubj	_	_
11	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
12	that	that	SCONJ	IN	_	25	mark	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
14	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	amod	_	_
15	lax	lax	PROPN	NNP	Number=Sing	16	compound	_	_
16	limit	limit	NOUN	NN	Number=Sing	25	nsubj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	endowed	endow	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	acl	_	_
19	with	with	ADP	IN	_	18	prep	_	_
20	the	the	DET	DT	Definite=Def|PronType=Art	23	det	_	_
21	projective	projective	ADJ	JJ	Degree=Pos	23	amod	_	_
22	model	model	NOUN	NN	Number=Sing	23	compound	_	_
23	structure	structure	NOUN	NN	Number=Sing	19	pobj	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
25	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	ccomp	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	presentation	presentation	NOUN	NN	Number=Sing	25	attr	_	_
28	of	of	ADP	IN	_	27	prep	_	_
29	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
30	lax	lax	ADJ	JJ	Degree=Pos	31	amod	_	_
31	limit	limit	NOUN	NN	Number=Sing	28	pobj	_	_
32	of	of	ADP	IN	_	31	prep	_	_
33	the	the	DET	DT	Definite=Def|PronType=Art	37	det	_	_
34	underlying	underlie	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	37	amod	_	_
35	$ infty $	$ infty $	SYM	$	_	37	compound	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	categories	category	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
38	.	.	PUNCT	.	PunctType=Peri	11	punct	_	SpaceAfter=No

# sent_id = 2
# text = Our approach can also allow for the indexing category to be simplicial, as long as the diagram factors through its homotopy category.
1	Our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	2	poss	_	_
2	approach	approach	NOUN	NN	Number=Sing	5	nsubj	_	_
3	can	can	AUX	MD	VerbForm=Fin	5	aux	_	_
4	also	also	ADV	RB	_	5	advmod	_	_
5	allow	allow	VERB	VB	VerbForm=Inf	0	ROOT	_	_
6	for	for	SCONJ	IN	_	11	mark	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
8	indexing	indexing	NOUN	NN	Number=Sing	9	compound	_	_
9	category	category	NOUN	NN	Number=Sing	11	nsubj	_	_
10	to	to	PART	TO	_	11	aux	_	_
11	be	be	AUX	VB	VerbForm=Inf	5	ccomp	_	_
12	simplicial	simplicial	ADJ	JJ	Degree=Pos	11	acomp	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
14	as	as	ADV	RB	_	15	advmod	_	_
15	long	long	ADV	RB	_	11	advmod	_	_
16	as	as	SCONJ	IN	_	19	mark	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	diagram	diagram	NOUN	NN	Number=Sing	19	compound	_	_
19	factors	factor	NOUN	NNS	Number=Plur	15	advcl	_	_
20	through	through	ADP	IN	_	19	prep	_	_
21	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	23	poss	_	_
22	homotopy	homotopy	NOUN	NN	Number=Sing	23	compound	_	_
23	category	category	NOUN	NN	Number=Sing	20	pobj	_	SpaceAfter=No
24	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 3
# text = Analogous results for the associated homotopy limit (and other intermediate limits) directly follow.
1	Analogous	analogous	ADJ	JJ	Degree=Pos	2	amod	_	_
2	results	result	NOUN	NNS	Number=Plur	15	nsubj	_	_
3	for	for	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
5	associated	associate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	6	amod	_	_
6	homotopy	homotopy	NOUN	NN	Number=Sing	7	compound	_	_
7	limit	limit	NOUN	NN	Number=Sing	3	pobj	_	_
8	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	7	punct	_	SpaceAfter=No
9	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
10	other	other	ADJ	JJ	Degree=Pos	12	amod	_	_
11	intermediate	intermediate	ADJ	JJ	Degree=Pos	12	amod	_	_
12	limits	limit	NOUN	NNS	Number=Plur	15	nsubj	_	SpaceAfter=No
13	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	12	punct	_	_
14	directly	directly	ADV	RB	_	15	advmod	_	_
15	follow	follow	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# doc_id = 748
# sent_id = 1
# text = We introduce a notion of "weak model category" which is a weakening of the notion of Quillen model category, still sufficient to define a homotopy category, Quillen adjunctions, Quillen equivalences, and most of the usual constructions of categorical homotopy theory.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	9	punct	_	SpaceAfter=No
7	weak	weak	ADJ	JJ	Degree=Pos	9	amod	_	_
8	model	model	NOUN	NN	Number=Sing	9	compound	_	_
9	category	category	NOUN	NN	Number=Sing	5	pobj	_	SpaceAfter=No
10	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	9	punct	_	_
11	which	which	PRON	WDT	_	12	nsubj	_	_
12	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	relcl	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
14	weakening	weakening	NOUN	NN	Number=Sing	12	attr	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	notion	notion	NOUN	NN	Number=Sing	15	pobj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	Quillen	quillen	ADJ	JJ	Degree=Pos	21	amod	_	_
20	model	model	NOUN	NN	Number=Sing	21	compound	_	_
21	category	category	NOUN	NN	Number=Sing	18	pobj	_	SpaceAfter=No
22	,	,	PUNCT	,	PunctType=Comm	21	punct	_	_
23	still	still	ADV	RB	_	24	advmod	_	_
24	sufficient	sufficient	ADJ	JJ	Degree=Pos	21	amod	_	_
25	to	to	PART	TO	_	26	aux	_	_
26	define	define	VERB	VB	VerbForm=Inf	24	xcomp	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
28	homotopy	homotopy	NOUN	NN	Number=Sing	29	compound	_	_
29	category	category	NOUN	NN	Number=Sing	26	dobj	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
31	Quillen	quillen	ADJ	JJ	Degree=Pos	32	amod	_	_
32	adjunctions	adjunction	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
33	,	,	PUNCT	,	PunctType=Comm	32	punct	_	_
34	Quillen	quillen	ADJ	JJ	Degree=Pos	35	amod	_	_
35	equivalences	equivalence	NOUN	NNS	Number=Plur	32	conj	_	SpaceAfter=No
36	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
37	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	_
38	most	most	ADJ	JJS	Degree=Sup	35	conj	_	_
39	of	of	ADP	IN	_	38	prep	_	_
40	the	the	DET	DT	Definite=Def|PronType=Art	42	det	_	_
41	usual	usual	ADJ	JJ	Degree=Pos	42	amod	_	_
42	constructions	construction	NOUN	NNS	Number=Plur	39	pobj	_	_
43	of	of	ADP	IN	_	42	prep	_	_
44	categorical	categorical	ADJ	JJ	Degree=Pos	45	amod	_	_
45	homotopy	homotopy	NOUN	NN	Number=Sing	46	compound	_	_
46	theory	theory	NOUN	NN	Number=Sing	43	pobj	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Both left and right semi - model categories are weak model categories, and the opposite of a weak model category is again a weak model category.
1	Both	both	PRON	DT	_	2	preconj	_	_
2	left	leave	VERB	VBD	Tense=Past|VerbForm=Fin	8	amod	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	right	right	ADJ	JJ	Degree=Pos	8	amod	_	_
5	semi	semi	ADJ	JJ	Degree=Pos	7	amod	_	_
6	-	-	PUNCT	HYPH	PunctType=Dash	7	punct	_	_
7	model	model	ADJ	JJ	Degree=Pos	8	amod	_	_
8	categories	category	NOUN	NNS	Number=Plur	9	nsubj	_	_
9	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
10	weak	weak	ADJ	JJ	Degree=Pos	12	amod	_	_
11	model	model	NOUN	NN	Number=Sing	12	compound	_	_
12	categories	category	NOUN	NNS	Number=Plur	9	attr	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
14	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	opposite	opposite	NOUN	NN	Number=Sing	22	nsubj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
19	weak	weak	ADJ	JJ	Degree=Pos	21	amod	_	_
20	model	model	NOUN	NN	Number=Sing	21	compound	_	_
21	category	category	NOUN	NN	Number=Sing	17	pobj	_	_
22	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	conj	_	_
23	again	again	ADV	RB	_	22	advmod	_	_
24	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
25	weak	weak	ADJ	JJ	Degree=Pos	27	amod	_	_
26	model	model	NOUN	NN	Number=Sing	27	compound	_	_
27	category	category	NOUN	NN	Number=Sing	22	attr	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# sent_id = 3
# text = The main advantage of weak model categories is that they are easier to construct than Quillen model categories.
1	The	the	DET	DT	Definite=Def|PronType=Art	3	det	_	_
2	main	main	ADJ	JJ	Degree=Pos	3	amod	_	_
3	advantage	advantage	NOUN	NN	Number=Sing	8	nsubj	_	_
4	of	of	ADP	IN	_	3	prep	_	_
5	weak	weak	ADJ	JJ	Degree=Pos	7	amod	_	_
6	model	model	NOUN	NN	Number=Sing	7	compound	_	_
7	categories	category	NOUN	NNS	Number=Plur	4	pobj	_	_
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
9	that	that	SCONJ	IN	_	11	mark	_	_
10	they	they	PRON	PRP	Case=Nom|Number=Plur|Person=3|PronType=Prs	11	nsubj	_	_
11	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	8	ccomp	_	_
12	easier	easy	ADJ	JJR	Degree=Cmp	11	acomp	_	_
13	to	to	PART	TO	_	14	aux	_	_
14	construct	construct	VERB	VB	VerbForm=Inf	12	xcomp	_	_
15	than	than	ADP	IN	_	14	prep	_	_
16	Quillen	quillen	ADJ	JJ	Degree=Pos	18	amod	_	_
17	model	model	NOUN	NN	Number=Sing	18	compound	_	_
18	categories	category	NOUN	NNS	Number=Plur	15	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	8	punct	_	SpaceAfter=No

# sent_id = 4
# text = In particular we give some simple criteria on two weak factorization systems for them to form a weak model category.
1	In	in	ADP	IN	_	4	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	_
3	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	4	nsubj	_	_
4	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	some	some	DET	DT	_	7	det	_	_
6	simple	simple	ADJ	JJ	Degree=Pos	7	amod	_	_
7	criteria	criterion	NOUN	NNS	Number=Plur	4	dobj	_	_
8	on	on	ADP	IN	_	7	prep	_	_
9	two	two	NUM	CD	NumType=Card	12	nummod	_	_
10	weak	weak	ADJ	JJ	Degree=Pos	12	amod	_	_
11	factorization	factorization	NOUN	NN	Number=Sing	12	compound	_	_
12	systems	system	NOUN	NNS	Number=Plur	8	pobj	_	_
13	for	for	SCONJ	IN	_	16	mark	_	_
14	them	they	PRON	PRP	Case=Acc|Number=Plur|Person=3|PronType=Prs	16	nsubj	_	_
15	to	to	PART	TO	_	16	aux	_	_
16	form	form	VERB	VB	VerbForm=Inf	4	advcl	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
18	weak	weak	ADJ	JJ	Degree=Pos	20	amod	_	_
19	model	model	NOUN	NN	Number=Sing	20	compound	_	_
20	category	category	NOUN	NN	Number=Sing	16	dobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 5
# text = The theory is developed in a very weak constructive, even predicative, framework and we use it to give constructive proofs of the existence of weak versions of various standard model categories, including the Kan - Quillen model structure, Lurie's variant of the Joyal model structure on marked simplicial sets, and the Verity model structure for weak complicial sets.
1	The	the	DET	DT	Definite=Def|PronType=Art	2	det	_	_
2	theory	theory	NOUN	NN	Number=Sing	4	nsubjpass	_	_
3	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	4	auxpass	_	_
4	developed	develop	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
7	very	very	ADV	RB	_	8	advmod	_	_
8	weak	weak	ADJ	JJ	Degree=Pos	12	advmod	_	_
9	constructive	constructive	ADJ	JJ	Degree=Pos	12	amod	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
11	even	even	ADV	RB	_	12	advmod	_	_
12	predicative	predicative	ADJ	JJ	Degree=Pos	14	amod	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	framework	framework	NOUN	NN	Number=Sing	5	pobj	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	4	cc	_	_
16	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	17	nsubj	_	_
17	use	use	VERB	VBP	Tense=Pres|VerbForm=Fin	4	conj	_	_
18	it	it	PRON	PRP	Case=Acc|Gender=Neut|Number=Sing|Person=3|PronType=Prs	17	dobj	_	_
19	to	to	PART	TO	_	20	aux	_	_
20	give	give	VERB	VB	VerbForm=Inf	17	xcomp	_	_
21	constructive	constructive	ADJ	JJ	Degree=Pos	22	amod	_	_
22	proofs	proof	NOUN	NNS	Number=Plur	20	dobj	_	_
23	of	of	ADP	IN	_	22	prep	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
25	existence	existence	NOUN	NN	Number=Sing	23	pobj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	weak	weak	ADJ	JJ	Degree=Pos	28	amod	_	_
28	versions	version	NOUN	NNS	Number=Plur	26	pobj	_	_
29	of	of	ADP	IN	_	28	prep	_	_
30	various	various	ADJ	JJ	Degree=Pos	33	amod	_	_
31	standard	standard	ADJ	JJ	Degree=Pos	33	amod	_	_
32	model	model	NOUN	NN	Number=Sing	33	compound	_	_
33	categories	category	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
34	,	,	PUNCT	,	PunctType=Comm	33	punct	_	_
35	including	include	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	33	prep	_	_
36	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
37	Kan	Kan	PROPN	NNP	Number=Sing	39	compound	_	_
38	-	-	PUNCT	HYPH	PunctType=Dash	39	punct	_	_
39	Quillen	Quillen	PROPN	NNP	Number=Sing	41	amod	_	_
40	model	model	NOUN	NN	Number=Sing	41	compound	_	_
41	structure	structure	NOUN	NN	Number=Sing	35	pobj	_	SpaceAfter=No
42	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
43	Lurie	Lurie	PROPN	NNP	Number=Sing	45	poss	_	SpaceAfter=No
44	's	's	PART	POS	_	43	case	_	_
45	variant	variant	NOUN	NN	Number=Sing	17	dobj	_	_
46	of	of	ADP	IN	_	45	prep	_	_
47	the	the	DET	DT	Definite=Def|PronType=Art	50	det	_	_
48	Joyal	joyal	ADJ	JJ	Degree=Pos	50	amod	_	_
49	model	model	NOUN	NN	Number=Sing	50	compound	_	_
50	structure	structure	NOUN	NN	Number=Sing	46	pobj	_	_
51	on	on	ADP	IN	_	50	prep	_	_
52	marked	marked	ADJ	JJ	Degree=Pos	54	amod	_	_
53	simplicial	simplicial	ADJ	JJ	Degree=Pos	54	amod	_	_
54	sets	set	NOUN	NNS	Number=Plur	51	pobj	_	SpaceAfter=No
55	,	,	PUNCT	,	PunctType=Comm	45	punct	_	_
56	and	and	CCONJ	CC	ConjType=Cmp	45	cc	_	_
57	the	the	DET	DT	Definite=Def|PronType=Art	60	det	_	_
58	Verity	verity	NOUN	NN	Number=Sing	59	compound	_	_
59	model	model	NOUN	NN	Number=Sing	60	compound	_	_
60	structure	structure	NOUN	NN	Number=Sing	45	conj	_	_
61	for	for	ADP	IN	_	60	prep	_	_
62	weak	weak	ADJ	JJ	Degree=Pos	64	amod	_	_
63	complicial	complicial	ADJ	JJ	Degree=Pos	64	amod	_	_
64	sets	set	NOUN	NNS	Number=Plur	61	pobj	_	SpaceAfter=No
65	.	.	PUNCT	.	PunctType=Peri	17	punct	_	SpaceAfter=No

# sent_id = 6
# text = We also construct semi - simplicial versions of all these.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	construct	construct	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	semi	semi	ADJ	JJ	Degree=Pos	7	amod	_	_
5	-	-	ADJ	JJ	Degree=Pos	6	punct	_	_
6	simplicial	simplicial	ADJ	JJ	Degree=Pos	7	amod	_	_
7	versions	version	NOUN	NNS	Number=Plur	3	dobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	all	all	DET	PDT	_	10	predet	_	_
10	these	these	PRON	DT	Number=Plur|PronType=Dem	8	pobj	_	SpaceAfter=No
11	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 749
# sent_id = 1
# text = Given a bicategory $ C $ and a family $ W $ of arrows of $ C $ , we give conditions on the pair $ (C, W) $ that allow us to construct the bicategorical localization with respect to $ W $ by dealing only with the 2 - cells, that is without adding objects or arrows to $ C $ .
1	Given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	15	prep	_	_
2	a	a	DET	DT	Definite=Ind|PronType=Art	3	det	_	_
3	bicategory	bicategory	NOUN	NN	Number=Sing	1	pobj	_	_
4	$ C $	$ c $	SYM	$	_	3	appos	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	3	cc	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	family	family	NOUN	NN	Number=Sing	3	conj	_	_
8	$ W $	$ w $	SYM	$	_	1	pobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	arrows	arrow	NOUN	NNS	Number=Plur	9	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	$ C $	$ c $	SYM	$	_	11	pobj	_	_
13	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
14	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	15	nsubj	_	_
15	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
16	conditions	condition	NOUN	NNS	Number=Plur	15	dobj	_	_
17	on	on	ADP	IN	_	16	prep	_	_
18	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
19	pair	pair	NOUN	NN	Number=Sing	17	pobj	_	_
20	$ (C, W) $	$ (c, w) $	SYM	$	_	15	dative	_	_
21	that	that	PRON	WDT	PronType=Rel	22	nsubj	_	_
22	allow	allow	VERB	VBP	Tense=Pres|VerbForm=Fin	20	relcl	_	_
23	us	we	PRON	PRP	Case=Acc|Number=Plur|Person=1|PronType=Prs	25	nsubj	_	_
24	to	to	PART	TO	_	25	aux	_	_
25	construct	construct	VERB	VB	VerbForm=Inf	22	ccomp	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	28	det	_	_
27	bicategorical	bicategorical	ADJ	JJ	Degree=Pos	28	amod	_	_
28	localization	localization	NOUN	NN	Number=Sing	25	dobj	_	_
29	with	with	ADP	IN	_	25	prep	_	_
30	respect	respect	NOUN	NN	Number=Sing	29	pobj	_	_
31	to	to	ADP	IN	_	30	prep	_	_
32	$ W $	$ w $	SYM	$	_	31	pobj	_	_
33	by	by	ADP	IN	_	25	prep	_	_
34	dealing	deal	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	33	pcomp	_	_
35	only	only	ADV	RB	_	36	advmod	_	_
36	with	with	ADP	IN	_	34	prep	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
38	2	2	NUM	CD	NumType=Card	40	nummod	_	_
39	-	-	PUNCT	HYPH	PunctType=Dash	40	punct	_	_
40	cells	cell	NOUN	NNS	Number=Plur	36	pobj	_	SpaceAfter=No
41	,	,	PUNCT	,	PunctType=Comm	40	punct	_	_
42	that	that	ADV	RB	_	43	nsubj	_	_
43	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	40	relcl	_	_
44	without	without	ADP	IN	_	43	prep	_	_
45	adding	add	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	44	pcomp	_	_
46	objects	object	NOUN	NNS	Number=Plur	45	dobj	_	_
47	or	or	CCONJ	CC	ConjType=Cmp	46	cc	_	_
48	arrows	arrow	NOUN	NNS	Number=Plur	46	conj	_	_
49	to	to	ADP	IN	_	45	prep	_	_
50	$ C $	$ c $	SYM	$	_	49	pobj	_	_
51	.	.	PUNCT	.	PunctType=Peri	15	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that in this case, the 2 - cells of the localization can be given by the homotopies with respect to $ W $ , a notion defined in this article which is closely related to Quillen's notion of homotopy for model categories but depends only on a single family of arrows.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	17	mark	_	_
4	in	in	ADP	IN	_	17	prep	_	_
5	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
6	case	case	NOUN	NN	Number=Sing	4	pobj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
8	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
9	2	2	NUM	CD	NumType=Card	11	nummod	_	_
10	-	-	PUNCT	HYPH	PunctType=Dash	11	punct	_	_
11	cells	cell	NOUN	NNS	Number=Plur	17	nsubjpass	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
14	localization	localization	NOUN	NN	Number=Sing	12	pobj	_	_
15	can	can	AUX	MD	VerbForm=Fin	17	aux	_	_
16	be	be	AUX	VB	VerbForm=Inf	17	auxpass	_	_
17	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
18	by	by	ADP	IN	_	17	agent	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	20	det	_	_
20	homotopies	homotopie	NOUN	NNS	Number=Plur	18	pobj	_	_
21	with	with	ADP	IN	_	17	prep	_	_
22	respect	respect	NOUN	NN	Number=Sing	21	pobj	_	_
23	to	to	ADP	IN	_	22	prep	_	_
24	$ W $	$ w $	SYM	$	_	23	pobj	_	_
25	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	27	det	_	_
27	notion	notion	NOUN	NN	Number=Sing	17	dobj	_	_
28	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	27	acl	_	_
29	in	in	ADP	IN	_	28	prep	_	_
30	this	this	DET	DT	Number=Sing|PronType=Dem	31	det	_	_
31	article	article	NOUN	NN	Number=Sing	29	pobj	_	_
32	which	which	PRON	WDT	_	35	nsubjpass	_	_
33	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	35	auxpass	_	_
34	closely	closely	ADV	RB	_	35	advmod	_	_
35	related	relate	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	31	relcl	_	_
36	to	to	ADP	IN	_	35	prep	_	_
37	Quillen	Quillen	PROPN	NNP	Number=Sing	39	poss	_	SpaceAfter=No
38	's	's	PART	POS	_	37	case	_	_
39	notion	notion	NOUN	NN	Number=Sing	36	pobj	_	_
40	of	of	ADP	IN	_	39	prep	_	_
41	homotopy	homotopy	NOUN	NN	Number=Sing	40	pobj	_	_
42	for	for	ADP	IN	_	41	prep	_	_
43	model	model	NOUN	NN	Number=Sing	44	compound	_	_
44	categories	category	NOUN	NNS	Number=Plur	42	pobj	_	_
45	but	but	CCONJ	CC	ConjType=Cmp	17	cc	_	_
46	depends	depend	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	conj	_	_
47	only	only	ADV	RB	_	48	advmod	_	_
48	on	on	ADP	IN	_	46	prep	_	_
49	a	a	DET	DT	Definite=Ind|PronType=Art	51	det	_	_
50	single	single	ADJ	JJ	Degree=Pos	51	amod	_	_
51	family	family	NOUN	NN	Number=Sing	48	pobj	_	_
52	of	of	ADP	IN	_	51	prep	_	_
53	arrows	arrow	NOUN	NNS	Number=Plur	52	pobj	_	SpaceAfter=No
54	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = This localization result has a natural application to the construction of the homotopy bicategory of a model bicategory, which we develop elsewhere, as the pair $ (C_{fc}, W) $ given by the weak equivalences between fibrant - cofibrant objects satisfies the conditions given in the present article.
1	This	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
2	localization	localization	NOUN	NN	Number=Sing	3	compound	_	_
3	result	result	NOUN	NN	Number=Sing	4	nsubj	_	_
4	has	have	VERB	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
6	natural	natural	ADJ	JJ	Degree=Pos	7	amod	_	_
7	application	application	NOUN	NN	Number=Sing	4	dobj	_	_
8	to	to	ADP	IN	_	7	prep	_	_
9	the	the	DET	DT	Definite=Def|PronType=Art	10	det	_	_
10	construction	construction	NOUN	NN	Number=Sing	8	pobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
13	homotopy	homotopy	NOUN	NN	Number=Sing	14	compound	_	_
14	bicategory	bicategory	NOUN	NN	Number=Sing	11	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
17	model	model	NOUN	NN	Number=Sing	18	compound	_	_
18	bicategory	bicategory	NOUN	NN	Number=Sing	15	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	18	punct	_	_
20	which	which	PRON	WDT	_	22	dobj	_	_
21	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	22	nsubj	_	_
22	develop	develop	VERB	VBP	Tense=Pres|VerbForm=Fin	18	relcl	_	_
23	elsewhere	elsewhere	ADV	RB	_	22	advmod	_	SpaceAfter=No
24	,	,	PUNCT	,	PunctType=Comm	4	punct	_	_
25	as	as	SCONJ	IN	_	29	mark	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	27	det	_	_
27	pair	pair	NOUN	NN	Number=Sing	25	pobj	_	_
28	$ (C_{fc}, W) $	$ (C_{fc}, W) $	PROPN	NNP	Number=Sing	29	nsubj	_	_
29	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	4	advcl	_	_
30	by	by	ADP	IN	_	29	agent	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	weak	weak	ADJ	JJ	Degree=Pos	33	amod	_	_
33	equivalences	equivalence	NOUN	NNS	Number=Plur	30	pobj	_	_
34	between	between	ADP	IN	_	33	prep	_	_
35	fibrant	fibrant	ADJ	JJ	Degree=Pos	37	amod	_	_
36	-	-	PUNCT	HYPH	PunctType=Dash	37	punct	_	_
37	cofibrant	cofibrant	NOUN	NN	Number=Sing	38	amod	_	_
38	objects	object	NOUN	NNS	Number=Plur	39	compound	_	_
39	satisfies	satisfie	NOUN	NNS	Number=Plur	34	pobj	_	_
40	the	the	DET	DT	Definite=Def|PronType=Art	41	det	_	_
41	conditions	condition	NOUN	NNS	Number=Plur	39	dobj	_	_
42	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	41	acl	_	_
43	in	in	ADP	IN	_	42	prep	_	_
44	the	the	DET	DT	Definite=Def|PronType=Art	46	det	_	_
45	present	present	ADJ	JJ	Degree=Pos	46	amod	_	_
46	article	article	NOUN	NN	Number=Sing	43	pobj	_	SpaceAfter=No
47	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# doc_id = 750
# sent_id = 1
# text = Restriction categories were introduced as a way of generalising the notion of partial map category.
1	Restriction	restriction	NOUN	NN	Number=Sing	2	compound	_	_
2	categories	category	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
3	were	be	AUX	VBD	Mood=Ind|Tense=Past|VerbForm=Fin	4	auxpass	_	_
4	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	as	as	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	way	way	NOUN	NN	Number=Sing	5	pobj	_	_
8	of	of	ADP	IN	_	7	prep	_	_
9	generalising	generalise	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	8	pcomp	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	notion	notion	NOUN	NN	Number=Sing	9	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	partial	partial	ADJ	JJ	Degree=Pos	15	amod	_	_
14	map	map	NOUN	NN	Number=Sing	15	compound	_	_
15	category	category	NOUN	NN	Number=Sing	12	pobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = In this paper, we define a notion of cocompleteness for restriction categories, and describe the free cocompletion of a small restriction category as a suitably defined category of restriction presheaves.
1	In	in	ADP	IN	_	6	prep	_	_
2	this	this	DET	DT	Number=Sing|PronType=Dem	3	det	_	_
3	paper	paper	NOUN	NN	Number=Sing	1	pobj	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
5	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	6	nsubj	_	_
6	define	define	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	8	det	_	_
8	notion	notion	NOUN	NN	Number=Sing	6	dobj	_	_
9	of	of	ADP	IN	_	8	prep	_	_
10	cocompleteness	cocompleteness	NOUN	NN	Number=Sing	9	pobj	_	_
11	for	for	ADP	IN	_	10	prep	_	_
12	restriction	restriction	NOUN	NN	Number=Sing	13	compound	_	_
13	categories	category	NOUN	NNS	Number=Plur	11	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
15	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
16	describe	describe	VERB	VB	VerbForm=Inf	6	conj	_	_
17	the	the	DET	DT	Definite=Def|PronType=Art	19	det	_	_
18	free	free	ADJ	JJ	Degree=Pos	19	amod	_	_
19	cocompletion	cocompletion	NOUN	NN	Number=Sing	16	dobj	_	_
20	of	of	ADP	IN	_	19	prep	_	_
21	a	a	DET	DT	Definite=Ind|PronType=Art	24	det	_	_
22	small	small	ADJ	JJ	Degree=Pos	23	amod	_	_
23	restriction	restriction	NOUN	NN	Number=Sing	24	compound	_	_
24	category	category	NOUN	NN	Number=Sing	20	pobj	_	_
25	as	as	ADP	IN	_	16	prep	_	_
26	a	a	DET	DT	Definite=Ind|PronType=Art	29	det	_	_
27	suitably	suitably	ADV	RB	_	28	advmod	_	_
28	defined	define	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	29	amod	_	_
29	category	category	NOUN	NN	Number=Sing	25	pobj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	restriction	restriction	NOUN	NN	Number=Sing	32	compound	_	_
32	presheaves	presheave	NOUN	NNS	Number=Plur	30	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# sent_id = 3
# text = We also consider free cocompletions in the case where our restriction category is only locally small.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	also	also	ADV	RB	_	3	advmod	_	_
3	consider	consider	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	free	free	ADJ	JJ	Degree=Pos	5	amod	_	_
5	cocompletions	cocompletion	NOUN	NNS	Number=Plur	3	dobj	_	_
6	in	in	ADP	IN	_	5	prep	_	_
7	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
8	case	case	NOUN	NN	Number=Sing	6	pobj	_	_
9	where	where	SCONJ	WRB	_	13	advmod	_	_
10	our	our	PRON	PRP$	Number=Plur|Person=1|Poss=Yes|PronType=Prs	12	poss	_	_
11	restriction	restriction	NOUN	NN	Number=Sing	12	compound	_	_
12	category	category	NOUN	NN	Number=Sing	13	nsubj	_	_
13	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	relcl	_	_
14	only	only	ADV	RB	_	16	advmod	_	_
15	locally	locally	ADV	RB	_	16	advmod	_	_
16	small	small	ADJ	JJ	Degree=Pos	13	acomp	_	SpaceAfter=No
17	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# doc_id = 751
# sent_id = 1
# text = We prove that the folk model category structure on the category of strict $ omega $ - categories, introduced by Lafont, Métayer and Worytkiewicz, is monoidal, first, for the Gray tensor product and, second, for the join of $ omega $ - categories, introduced by the first author and Maltsiniotis.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	26	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
5	folk	folk	NOUN	NN	Number=Sing	6	compound	_	_
6	model	model	NOUN	NN	Number=Sing	8	compound	_	_
7	category	category	NOUN	NN	Number=Sing	8	compound	_	_
8	structure	structure	NOUN	NN	Number=Sing	26	nsubj	_	_
9	on	on	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	11	det	_	_
11	category	category	NOUN	NN	Number=Sing	9	pobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	strict	strict	ADJ	JJ	Degree=Pos	16	amod	_	_
14	$ omega $	$ omega $	SYM	$	_	16	compound	_	_
15	-	-	PUNCT	HYPH	PunctType=Dash	16	punct	_	_
16	categories	category	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
17	,	,	PUNCT	,	PunctType=Comm	16	punct	_	_
18	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	16	acl	_	_
19	by	by	ADP	IN	_	18	agent	_	_
20	Lafont	Lafont	PROPN	NNP	Number=Sing	19	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	20	punct	_	_
22	Métayer	Métayer	PROPN	NNP	Number=Sing	20	conj	_	_
23	and	and	CCONJ	CC	ConjType=Cmp	22	cc	_	_
24	Worytkiewicz	Worytkiewicz	PROPN	NNP	Number=Sing	22	conj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	8	punct	_	_
26	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
27	monoidal	monoidal	ADJ	JJ	Degree=Pos	26	attr	_	SpaceAfter=No
28	,	,	PUNCT	,	PunctType=Comm	27	punct	_	_
29	first	first	ADV	RB	_	26	advmod	_	SpaceAfter=No
30	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
31	for	for	ADP	IN	_	26	prep	_	_
32	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
33	Gray	Gray	PROPN	NNP	Number=Sing	35	compound	_	_
34	tensor	tensor	NOUN	NN	Number=Sing	35	compound	_	_
35	product	product	NOUN	NN	Number=Sing	31	pobj	_	_
36	and	and	CCONJ	CC	ConjType=Cmp	35	cc	_	SpaceAfter=No
37	,	,	PUNCT	,	PunctType=Comm	35	punct	_	_
38	second	second	ADJ	JJ	Degree=Pos	26	acomp	_	SpaceAfter=No
39	,	,	PUNCT	,	PunctType=Comm	38	punct	_	_
40	for	for	ADP	IN	_	38	prep	_	_
41	the	the	DET	DT	Definite=Def|PronType=Art	42	det	_	_
42	join	join	NOUN	NN	Number=Sing	40	pobj	_	_
43	of	of	ADP	IN	_	42	prep	_	_
44	$ omega $	$ omega $	SYM	$	_	46	compound	_	_
45	-	-	PUNCT	HYPH	PunctType=Dash	46	punct	_	_
46	categories	category	NOUN	NNS	Number=Plur	43	pobj	_	SpaceAfter=No
47	,	,	PUNCT	,	PunctType=Comm	42	punct	_	_
48	introduced	introduce	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	42	acl	_	_
49	by	by	ADP	IN	_	48	agent	_	_
50	the	the	DET	DT	Definite=Def|PronType=Art	52	det	_	_
51	first	first	ADJ	JJ	Degree=Pos	52	amod	_	_
52	author	author	NOUN	NN	Number=Sing	49	pobj	_	_
53	and	and	CCONJ	CC	ConjType=Cmp	52	cc	_	_
54	Maltsiniotis	Maltsiniotis	PROPN	NNP	Number=Sing	52	conj	_	SpaceAfter=No
55	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = We moreover show that the Gray tensor product induces, by adjunction, a tensor product of strict $ (m, n) $ - categories and that this tensor product is also compatible with the folk model category structure.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	3	nsubj	_	_
2	moreover	moreover	ADV	RB	_	3	advmod	_	_
3	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
4	that	that	SCONJ	IN	_	9	mark	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	8	det	_	_
6	Gray	Gray	PROPN	NNP	Number=Sing	8	compound	_	_
7	tensor	tensor	NOUN	NN	Number=Sing	8	compound	_	_
8	product	product	NOUN	NN	Number=Sing	9	compound	_	_
9	induces	induce	NOUN	NNS	Number=Plur	3	ccomp	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
11	by	by	ADP	IN	_	9	prep	_	_
12	adjunction	adjunction	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	9	punct	_	_
14	a	a	DET	DT	Definite=Ind|PronType=Art	16	det	_	_
15	tensor	tensor	NOUN	NN	Number=Sing	16	compound	_	_
16	product	product	NOUN	NN	Number=Sing	9	appos	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	strict	strict	ADJ	JJ	Degree=Pos	21	amod	_	_
19	$ (m, n) $	$ (m, n) $	PROPN	NNP	Number=Sing	21	compound	_	_
20	-	-	PUNCT	HYPH	PunctType=Dash	21	punct	_	_
21	categories	category	NOUN	NNS	Number=Plur	17	pobj	_	_
22	and	and	CCONJ	CC	ConjType=Cmp	9	cc	_	_
23	that	that	SCONJ	IN	_	27	mark	_	_
24	this	this	DET	DT	Number=Sing|PronType=Dem	26	det	_	_
25	tensor	tensor	NOUN	NN	Number=Sing	26	compound	_	_
26	product	product	NOUN	NN	Number=Sing	27	nsubj	_	_
27	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	conj	_	_
28	also	also	ADV	RB	_	27	advmod	_	_
29	compatible	compatible	ADJ	JJ	Degree=Pos	27	acomp	_	_
30	with	with	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	35	det	_	_
32	folk	folk	NOUN	NN	Number=Sing	33	compound	_	_
33	model	model	NOUN	NN	Number=Sing	35	compound	_	_
34	category	category	NOUN	NN	Number=Sing	35	compound	_	_
35	structure	structure	NOUN	NN	Number=Sing	30	pobj	_	SpaceAfter=No
36	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = In particular, we get a monoidal model category structure on the category of strict $ omega $ - groupoids.
1	In	in	ADP	IN	_	5	prep	_	_
2	particular	particular	ADJ	JJ	Degree=Pos	1	amod	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	5	punct	_	_
4	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	5	nsubj	_	_
5	get	get	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
7	monoidal	monoidal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	model	model	NOUN	NN	Number=Sing	10	compound	_	_
9	category	category	NOUN	NN	Number=Sing	10	compound	_	_
10	structure	structure	NOUN	NN	Number=Sing	5	dobj	_	_
11	on	on	ADP	IN	_	10	prep	_	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	_	_
13	category	category	NOUN	NN	Number=Sing	11	pobj	_	_
14	of	of	ADP	IN	_	13	prep	_	_
15	strict	strict	ADJ	JJ	Degree=Pos	18	amod	_	_
16	$ omega $	$ omega $	SYM	$	_	18	compound	_	_
17	-	-	PUNCT	HYPH	PunctType=Dash	18	punct	_	_
18	groupoids	groupoid	NOUN	NNS	Number=Plur	14	pobj	_	SpaceAfter=No
19	.	.	PUNCT	.	PunctType=Peri	5	punct	_	SpaceAfter=No

# sent_id = 4
# text = We prove that this monoidal model category structure satisfies the monoid axiom, so that the category of Gray monoids, studied by the second author, bears a natural model category structure.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	prove	prove	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	9	mark	_	_
4	this	this	DET	DT	Number=Sing|PronType=Dem	9	det	_	_
5	monoidal	monoidal	ADJ	JJ	Degree=Pos	6	amod	_	_
6	model	model	NOUN	NN	Number=Sing	8	compound	_	_
7	category	category	NOUN	NN	Number=Sing	8	compound	_	_
8	structure	structure	NOUN	NN	Number=Sing	9	compound	_	_
9	satisfies	satisfie	NOUN	NNS	Number=Plur	2	ccomp	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	12	det	_	_
11	monoid	monoid	NOUN	NN	Number=Sing	12	compound	_	_
12	axiom	axiom	NOUN	NN	Number=Sing	9	dobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	so	so	SCONJ	IN	_	28	mark	_	_
15	that	that	SCONJ	IN	_	28	mark	_	_
16	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
17	category	category	NOUN	NN	Number=Sing	28	nsubj	_	_
18	of	of	ADP	IN	_	17	prep	_	_
19	Gray	Gray	PROPN	NNP	Number=Sing	20	compound	_	_
20	monoids	monoid	NOUN	NNS	Number=Plur	18	pobj	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
22	studied	study	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	17	acl	_	_
23	by	by	ADP	IN	_	22	agent	_	_
24	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
25	second	second	ADJ	JJ	Degree=Pos	26	amod	_	_
26	author	author	NOUN	NN	Number=Sing	23	pobj	_	SpaceAfter=No
27	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
28	bears	bear	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	9	advcl	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	33	det	_	_
30	natural	natural	ADJ	JJ	Degree=Pos	31	amod	_	_
31	model	model	NOUN	NN	Number=Sing	33	compound	_	_
32	category	category	NOUN	NN	Number=Sing	33	compound	_	_
33	structure	structure	NOUN	NN	Number=Sing	28	dobj	_	SpaceAfter=No
34	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# doc_id = 752
# sent_id = 1
# text = Cheng, Gurski, and Riehl constructed a cyclic double multicategory of multivariable adjunctions.
1	Cheng	Cheng	PROPN	NNP	Number=Sing	7	nsubj	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	1	punct	_	_
3	Gurski	Gurski	PROPN	NNP	Number=Sing	1	appos	_	SpaceAfter=No
4	,	,	PUNCT	,	PunctType=Comm	1	punct	_	_
5	and	and	CCONJ	CC	ConjType=Cmp	1	cc	_	_
6	Riehl	Riehl	PROPN	NNP	Number=Sing	7	nsubj	_	_
7	constructed	construct	VERB	VBD	Tense=Past|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
9	cyclic	cyclic	ADJ	JJ	Degree=Pos	11	amod	_	_
10	double	double	ADJ	JJ	Degree=Pos	11	amod	_	_
11	multicategory	multicategory	NOUN	NN	Number=Sing	7	dobj	_	_
12	of	of	ADP	IN	_	11	prep	_	_
13	multivariable	multivariable	ADJ	JJ	Degree=Pos	14	amod	_	_
14	adjunctions	adjunction	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 2
# text = We show that the same information is carried by a poly double category, in which opposite categories are polycategorical duals.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	8	mark	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
5	same	same	ADJ	JJ	Degree=Pos	6	amod	_	_
6	information	information	NOUN	NN	Number=Sing	8	nsubjpass	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	8	auxpass	_	_
8	carried	carry	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	2	ccomp	_	_
9	by	by	ADP	IN	_	8	agent	_	_
10	a	a	DET	DT	Definite=Ind|PronType=Art	13	det	_	_
11	poly	poly	ADJ	JJ	Degree=Pos	13	amod	_	_
12	double	double	ADJ	JJ	Degree=Pos	13	amod	_	_
13	category	category	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
14	,	,	PUNCT	,	PunctType=Comm	13	punct	_	_
15	in	in	ADP	IN	_	19	prep	_	_
16	which	which	PRON	WDT	_	15	pobj	_	_
17	opposite	opposite	ADJ	JJ	Degree=Pos	18	amod	_	_
18	categories	category	NOUN	NNS	Number=Plur	19	nsubj	_	_
19	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	13	relcl	_	_
20	polycategorical	polycategorical	ADJ	JJ	Degree=Pos	21	amod	_	_
21	duals	dual	NOUN	NNS	Number=Plur	19	attr	_	SpaceAfter=No
22	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Moreover, this poly double category is a full substructure of a double Chu construction, whose objects are a sort of polarized category, and which is a natural home for 2 - categorical dualities.
1	Moreover	moreover	ADV	RB	_	7	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
3	this	this	DET	DT	Number=Sing|PronType=Dem	6	det	_	_
4	poly	poly	ADJ	JJ	Degree=Pos	6	amod	_	_
5	double	double	ADJ	JJ	Degree=Pos	6	amod	_	_
6	category	category	NOUN	NN	Number=Sing	7	nsubj	_	_
7	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	10	det	_	_
9	full	full	ADJ	JJ	Degree=Pos	10	amod	_	_
10	substructure	substructure	NOUN	NN	Number=Sing	7	attr	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
13	double	double	ADJ	JJ	Degree=Pos	15	amod	_	_
14	Chu	Chu	PROPN	NNP	Number=Sing	15	compound	_	_
15	construction	construction	NOUN	NN	Number=Sing	11	pobj	_	SpaceAfter=No
16	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
17	whose	whose	DET	WP$	Poss=Yes	18	poss	_	_
18	objects	object	NOUN	NNS	Number=Plur	19	nsubj	_	_
19	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	15	relcl	_	_
20	a	a	DET	DT	Definite=Ind|PronType=Art	21	det	_	_
21	sort	sort	NOUN	NN	Number=Sing	19	attr	_	_
22	of	of	ADP	IN	_	21	prep	_	_
23	polarized	polarized	ADJ	JJ	Degree=Pos	24	amod	_	_
24	category	category	NOUN	NN	Number=Sing	22	pobj	_	SpaceAfter=No
25	,	,	PUNCT	,	PunctType=Comm	15	punct	_	_
26	and	and	CCONJ	CC	ConjType=Cmp	7	cc	_	_
27	which	which	PRON	WDT	_	28	nsubj	_	_
28	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	7	conj	_	_
29	a	a	DET	DT	Definite=Ind|PronType=Art	31	det	_	_
30	natural	natural	ADJ	JJ	Degree=Pos	31	amod	_	_
31	home	home	NOUN	NN	Number=Sing	28	attr	_	_
32	for	for	ADP	IN	_	31	prep	_	_
33	2	2	NUM	CD	NumType=Card	35	nummod	_	_
34	-	-	PUNCT	HYPH	PunctType=Dash	35	punct	_	_
35	categorical	categorical	ADJ	JJ	Degree=Pos	36	amod	_	_
36	dualities	duality	NOUN	NNS	Number=Plur	32	pobj	_	SpaceAfter=No
37	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No

# sent_id = 4
# text = We obtain the double Chu construction using a general "Chu - Dialectica" construction on polycategories, which includes both the Chu construction and the categorical Dialectica construction of de Paiva.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	obtain	obtain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	6	det	_	_
4	double	double	ADJ	JJ	Degree=Pos	6	amod	_	_
5	Chu	Chu	PROPN	NNP	Number=Sing	6	compound	_	_
6	construction	construction	NOUN	NN	Number=Sing	2	dobj	_	_
7	using	use	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	6	acl	_	_
8	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
9	general	general	ADJ	JJ	Degree=Pos	15	amod	_	_
10	"	"	PUNCT	``	PunctSide=Ini|PunctType=Quot	15	punct	_	SpaceAfter=No
11	Chu	Chu	PROPN	NNP	Number=Sing	13	nmod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	Dialectica	Dialectica	PROPN	NNP	Number=Sing	15	nmod	_	SpaceAfter=No
14	"	"	PUNCT	''	PunctSide=Fin|PunctType=Quot	15	punct	_	_
15	construction	construction	NOUN	NN	Number=Sing	7	dobj	_	_
16	on	on	ADP	IN	_	15	prep	_	_
17	polycategories	polycategorie	NOUN	NNS	Number=Plur	16	pobj	_	SpaceAfter=No
18	,	,	PUNCT	,	PunctType=Comm	17	punct	_	_
19	which	which	PRON	WDT	_	20	nsubj	_	_
20	includes	include	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	17	relcl	_	_
21	both	both	CCONJ	CC	ConjType=Cmp	24	preconj	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	Chu	Chu	PROPN	NNP	Number=Sing	24	compound	_	_
24	construction	construction	NOUN	NN	Number=Sing	20	dobj	_	_
25	and	and	CCONJ	CC	ConjType=Cmp	24	cc	_	_
26	the	the	DET	DT	Definite=Def|PronType=Art	29	det	_	_
27	categorical	categorical	ADJ	JJ	Degree=Pos	29	amod	_	_
28	Dialectica	Dialectica	PROPN	NNP	Number=Sing	29	compound	_	_
29	construction	construction	NOUN	NN	Number=Sing	24	conj	_	_
30	of	of	ADP	IN	_	29	prep	_	_
31	de	de	PROPN	NNP	Number=Sing	32	compound	_	_
32	Paiva	Paiva	PROPN	NNP	Number=Sing	30	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = The Chu and Dialectica constructions each impose additional hypotheses making the resulting polycategory representable (hence $ * $ - autonomous), but for different reasons; this leads to their apparent differences.
1	The	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
2	Chu	Chu	PROPN	NNP	Number=Sing	5	nmod	_	_
3	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
4	Dialectica	Dialectica	PROPN	NNP	Number=Sing	2	conj	_	_
5	constructions	construction	NOUN	NNS	Number=Plur	7	nsubj	_	_
6	each	each	PRON	DT	_	7	nsubj	_	_
7	impose	impose	VERB	VBP	Tense=Pres|VerbForm=Fin	28	ccomp	_	_
8	additional	additional	ADJ	JJ	Degree=Pos	9	amod	_	_
9	hypotheses	hypothesis	NOUN	NNS	Number=Plur	7	dobj	_	_
10	making	make	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	9	acl	_	_
11	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
12	resulting	result	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	amod	_	_
13	polycategory	polycategory	NOUN	NN	Number=Sing	14	compound	_	_
14	representable	representable	NOUN	NN	Number=Sing	10	dobj	_	_
15	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	19	punct	_	SpaceAfter=No
16	hence	hence	ADV	RB	_	19	advmod	_	_
17	$ * $	$ * $	SYM	$	_	19	advmod	_	_
18	-	-	PUNCT	HYPH	PunctType=Dash	19	punct	_	_
19	autonomous	autonomous	ADJ	JJ	Degree=Pos	14	appos	_	SpaceAfter=No
20	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	14	punct	_	SpaceAfter=No
21	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
22	but	but	CCONJ	CC	ConjType=Cmp	7	cc	_	_
23	for	for	ADP	IN	_	7	conj	_	_
24	different	different	ADJ	JJ	Degree=Pos	25	amod	_	_
25	reasons	reason	NOUN	NNS	Number=Plur	23	pobj	_	SpaceAfter=No
26	;	;	PUNCT	:	_	28	punct	_	_
27	this	this	PRON	DT	Number=Sing|PronType=Dem	28	nsubj	_	_
28	leads	lead	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
29	to	to	ADP	IN	_	28	prep	_	_
30	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	32	poss	_	_
31	apparent	apparent	ADJ	JJ	Degree=Pos	32	amod	_	_
32	differences	difference	NOUN	NNS	Number=Plur	29	pobj	_	SpaceAfter=No
33	.	.	PUNCT	.	PunctType=Peri	28	punct	_	SpaceAfter=No

# doc_id = 753
# sent_id = 1
# text = Networks can be combined in various ways, such as overlaying one on top of another or setting two side by side.
1	Networks	network	NOUN	NNS	Number=Plur	4	nsubjpass	_	_
2	can	can	AUX	MD	VerbForm=Fin	4	aux	_	_
3	be	be	AUX	VB	VerbForm=Inf	4	auxpass	_	_
4	combined	combine	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
5	in	in	ADP	IN	_	4	prep	_	_
6	various	various	ADJ	JJ	Degree=Pos	7	amod	_	_
7	ways	way	NOUN	NNS	Number=Plur	5	pobj	_	SpaceAfter=No
8	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
9	such	such	ADJ	JJ	Degree=Pos	10	amod	_	_
10	as	as	ADP	IN	_	7	prep	_	_
11	overlaying	overlay	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	10	pcomp	_	_
12	one	one	NUM	CD	NumType=Card	11	dobj	_	_
13	on	on	ADP	IN	_	12	prep	_	_
14	top	top	NOUN	NN	Number=Sing	13	pobj	_	_
15	of	of	ADP	IN	_	14	prep	_	_
16	another	another	PRON	DT	_	15	pobj	_	_
17	or	or	CCONJ	CC	ConjType=Cmp	11	cc	_	_
18	setting	set	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	conj	_	_
19	two	two	NUM	CD	NumType=Card	20	nummod	_	_
20	side	side	NOUN	NN	Number=Sing	18	dobj	_	_
21	by	by	ADP	IN	_	18	prep	_	_
22	side	side	NOUN	NN	Number=Sing	21	pobj	_	SpaceAfter=No
23	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 2
# text = We introduce `network models' to encode these ways of combining networks.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	`	`	PUNCT	``	PunctSide=Ini|PunctType=Quot	5	punct	_	SpaceAfter=No
4	network	network	NOUN	NN	Number=Sing	5	compound	_	_
5	models	model	NOUN	NNS	Number=Plur	2	dobj	_	SpaceAfter=No
6	'	'	PART	POS	_	5	case	_	_
7	to	to	PART	TO	_	8	aux	_	_
8	encode	encode	VERB	VB	VerbForm=Inf	5	relcl	_	_
9	these	these	DET	DT	Number=Plur|PronType=Dem	10	det	_	_
10	ways	way	NOUN	NNS	Number=Plur	8	dobj	_	_
11	of	of	ADP	IN	_	10	prep	_	_
12	combining	combine	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	11	pcomp	_	_
13	networks	network	NOUN	NNS	Number=Plur	12	dobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 3
# text = Different network models describe different kinds of networks.
1	Different	different	ADJ	JJ	Degree=Pos	3	amod	_	_
2	network	network	NOUN	NN	Number=Sing	3	compound	_	_
3	models	model	NOUN	NNS	Number=Plur	4	nsubj	_	_
4	describe	describe	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
5	different	different	ADJ	JJ	Degree=Pos	6	amod	_	_
6	kinds	kind	NOUN	NNS	Number=Plur	4	dobj	_	_
7	of	of	ADP	IN	_	6	prep	_	_
8	networks	network	NOUN	NNS	Number=Plur	7	pobj	_	SpaceAfter=No
9	.	.	PUNCT	.	PunctType=Peri	4	punct	_	SpaceAfter=No

# sent_id = 4
# text = We show that each network model gives rise to an operad, whose operations are ways of assembling a network of the given kind from smaller parts.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	that	that	SCONJ	IN	_	7	mark	_	_
4	each	each	DET	DT	_	6	det	_	_
5	network	network	NOUN	NN	Number=Sing	6	compound	_	_
6	model	model	NOUN	NN	Number=Sing	7	nsubj	_	_
7	gives	give	VERB	VBZ	Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	2	ccomp	_	_
8	rise	rise	VERB	VB	VerbForm=Inf	7	dobj	_	_
9	to	to	ADP	IN	_	8	prep	_	_
10	an	an	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
11	operad	operad	NOUN	NN	Number=Sing	9	pobj	_	SpaceAfter=No
12	,	,	PUNCT	,	PunctType=Comm	11	punct	_	_
13	whose	whose	DET	WP$	Poss=Yes	14	poss	_	_
14	operations	operation	NOUN	NNS	Number=Plur	15	nsubj	_	_
15	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	11	relcl	_	_
16	ways	way	NOUN	NNS	Number=Plur	15	attr	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	assembling	assemble	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	17	pcomp	_	_
19	a	a	DET	DT	Definite=Ind|PronType=Art	20	det	_	_
20	network	network	NOUN	NN	Number=Sing	18	dobj	_	_
21	of	of	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	24	det	_	_
23	given	give	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	24	amod	_	_
24	kind	kind	NOUN	NN	Number=Sing	21	pobj	_	_
25	from	from	ADP	IN	_	18	prep	_	_
26	smaller	small	ADJ	JJR	Degree=Cmp	27	amod	_	_
27	parts	part	NOUN	NNS	Number=Plur	25	pobj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = Such operads, and their algebras, can serve as tools for designing networks.
1	Such	such	ADJ	JJ	Degree=Pos	2	amod	_	_
2	operads	operad	NOUN	NNS	Number=Plur	9	nsubj	_	SpaceAfter=No
3	,	,	PUNCT	,	PunctType=Comm	2	punct	_	_
4	and	and	CCONJ	CC	ConjType=Cmp	2	cc	_	_
5	their	their	PRON	PRP$	Number=Plur|Person=3|Poss=Yes|PronType=Prs	6	poss	_	_
6	algebras	algebra	NOUN	NNS	Number=Plur	2	conj	_	SpaceAfter=No
7	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
8	can	can	AUX	MD	VerbForm=Fin	9	aux	_	_
9	serve	serve	VERB	VB	VerbForm=Inf	0	ROOT	_	_
10	as	as	ADP	IN	_	9	prep	_	_
11	tools	tool	NOUN	NNS	Number=Plur	10	pobj	_	_
12	for	for	ADP	IN	_	11	prep	_	_
13	designing	designing	NOUN	NN	Number=Sing	14	compound	_	_
14	networks	network	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
15	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# sent_id = 6
# text = Technically, a network model is a lax symmetric monoidal functor from the free symmetric monoidal category on some set to $ Cat $ , and the construction of the corresponding operad proceeds via a symmetric monoidal version of the Grothendieck construction.
1	Technically	technically	ADV	RB	_	6	advmod	_	SpaceAfter=No
2	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
3	a	a	DET	DT	Definite=Ind|PronType=Art	5	det	_	_
4	network	network	NOUN	NN	Number=Sing	5	compound	_	_
5	model	model	NOUN	NN	Number=Sing	6	nsubj	_	_
6	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	0	ROOT	_	_
7	a	a	DET	DT	Definite=Ind|PronType=Art	11	det	_	_
8	lax	lax	ADJ	JJ	Degree=Pos	11	amod	_	_
9	symmetric	symmetric	ADJ	JJ	Degree=Pos	11	amod	_	_
10	monoidal	monoidal	ADJ	JJ	Degree=Pos	11	amod	_	_
11	functor	functor	NOUN	NN	Number=Sing	6	attr	_	_
12	from	from	ADP	IN	_	11	prep	_	_
13	the	the	DET	DT	Definite=Def|PronType=Art	17	det	_	_
14	free	free	ADJ	JJ	Degree=Pos	17	amod	_	_
15	symmetric	symmetric	ADJ	JJ	Degree=Pos	17	amod	_	_
16	monoidal	monoidal	ADJ	JJ	Degree=Pos	17	amod	_	_
17	category	category	NOUN	NN	Number=Sing	12	pobj	_	_
18	on	on	ADP	IN	_	17	prep	_	_
19	some	some	PRON	DT	_	18	pobj	_	_
20	set	set	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	11	acl	_	_
21	to	to	ADP	IN	_	20	prep	_	_
22	$ Cat $	$ cat $	SYM	$	_	21	pobj	_	_
23	,	,	PUNCT	,	PunctType=Comm	6	punct	_	_
24	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
25	the	the	DET	DT	Definite=Def|PronType=Art	26	det	_	_
26	construction	construction	NOUN	NN	Number=Sing	6	conj	_	_
27	of	of	ADP	IN	_	26	prep	_	_
28	the	the	DET	DT	Definite=Def|PronType=Art	31	det	_	_
29	corresponding	correspond	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	31	amod	_	_
30	operad	operad	NOUN	NN	Number=Sing	31	compound	_	_
31	proceeds	proceed	NOUN	NNS	Number=Plur	27	pobj	_	_
32	via	via	ADP	IN	_	31	prep	_	_
33	a	a	DET	DT	Definite=Ind|PronType=Art	36	det	_	_
34	symmetric	symmetric	ADJ	JJ	Degree=Pos	36	amod	_	_
35	monoidal	monoidal	ADJ	JJ	Degree=Pos	36	amod	_	_
36	version	version	NOUN	NN	Number=Sing	32	pobj	_	_
37	of	of	ADP	IN	_	36	prep	_	_
38	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
39	Grothendieck	Grothendieck	PROPN	NNP	Number=Sing	40	compound	_	_
40	construction	construction	NOUN	NN	Number=Sing	37	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	6	punct	_	SpaceAfter=No

# doc_id = 754
# sent_id = 1
# text = In contrast to the fact that every completely distributive lattice is necessarily continuous in the sense of Scott, it is shown that complete distributivity of a category enriched over the closed category obtained by endowing the unit interval with a continuous $ t $ - norm does not imply its continuity in general.
1	In	in	ADP	IN	_	22	prep	_	_
2	contrast	contrast	NOUN	NN	Number=Sing	1	pobj	_	_
3	to	to	ADP	IN	_	2	prep	_	_
4	the	the	DET	DT	Definite=Def|PronType=Art	5	det	_	_
5	fact	fact	NOUN	NN	Number=Sing	3	pobj	_	_
6	that	that	SCONJ	IN	_	11	mark	_	_
7	every	every	DET	DT	_	10	det	_	_
8	completely	completely	ADV	RB	_	9	advmod	_	_
9	distributive	distributive	ADJ	JJ	Degree=Pos	10	amod	_	_
10	lattice	lattice	NOUN	NN	Number=Sing	11	nsubj	_	_
11	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	5	acl	_	_
12	necessarily	necessarily	ADV	RB	_	11	advmod	_	_
13	continuous	continuous	ADJ	JJ	Degree=Pos	11	acomp	_	_
14	in	in	ADP	IN	_	11	prep	_	_
15	the	the	DET	DT	Definite=Def|PronType=Art	16	det	_	_
16	sense	sense	NOUN	NN	Number=Sing	14	pobj	_	_
17	of	of	ADP	IN	_	16	prep	_	_
18	Scott	Scott	PROPN	NNP	Number=Sing	17	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	22	punct	_	_
20	it	it	PRON	PRP	Gender=Neut|Number=Sing|Person=3|PronType=Prs	22	nsubjpass	_	_
21	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	22	auxpass	_	_
22	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
23	that	that	DET	DT	Number=Sing|PronType=Dem	25	det	_	_
24	complete	complete	ADJ	JJ	Degree=Pos	25	amod	_	_
25	distributivity	distributivity	NOUN	NN	Number=Sing	48	nsubj	_	_
26	of	of	ADP	IN	_	25	prep	_	_
27	a	a	DET	DT	Definite=Ind|PronType=Art	28	det	_	_
28	category	category	NOUN	NN	Number=Sing	26	pobj	_	_
29	enriched	enrich	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	28	acl	_	_
30	over	over	ADP	IN	_	29	prep	_	_
31	the	the	DET	DT	Definite=Def|PronType=Art	33	det	_	_
32	closed	closed	ADJ	JJ	Degree=Pos	33	amod	_	_
33	category	category	NOUN	NN	Number=Sing	30	pobj	_	_
34	obtained	obtain	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	33	acl	_	_
35	by	by	ADP	IN	_	34	prep	_	_
36	endowing	endow	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	35	pcomp	_	_
37	the	the	DET	DT	Definite=Def|PronType=Art	39	det	_	_
38	unit	unit	NOUN	NN	Number=Sing	39	compound	_	_
39	interval	interval	NOUN	NN	Number=Sing	36	dobj	_	_
40	with	with	ADP	IN	_	36	prep	_	_
41	a	a	DET	DT	Definite=Ind|PronType=Art	45	det	_	_
42	continuous	continuous	ADJ	JJ	Degree=Pos	45	amod	_	_
43	$ t $	$ t $	SYM	$	_	45	nummod	_	_
44	-	-	PUNCT	HYPH	PunctType=Dash	45	punct	_	_
45	norm	norm	NOUN	NN	Number=Sing	40	pobj	_	_
46	does	do	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	48	aux	_	_
47	not	not	PART	RB	Polarity=Neg	48	neg	_	_
48	imply	imply	VERB	VB	VerbForm=Inf	22	ccomp	_	_
49	its	its	PRON	PRP$	Gender=Neut|Number=Sing|Person=3|Poss=Yes|PronType=Prs	50	poss	_	_
50	continuity	continuity	NOUN	NN	Number=Sing	48	dobj	_	_
51	in	in	ADP	IN	_	50	prep	_	_
52	general	general	ADJ	JJ	Degree=Pos	51	amod	_	SpaceAfter=No
53	.	.	PUNCT	.	PunctType=Peri	22	punct	_	SpaceAfter=No

# sent_id = 2
# text = Necessary and sufficient conditions for the implication are presented.
1	Necessary	necessary	ADJ	JJ	Degree=Pos	4	amod	_	_
2	and	and	CCONJ	CC	ConjType=Cmp	1	cc	_	_
3	sufficient	sufficient	ADJ	JJ	Degree=Pos	1	conj	_	_
4	conditions	condition	NOUN	NNS	Number=Plur	9	nsubjpass	_	_
5	for	for	SCONJ	IN	_	9	mark	_	_
6	the	the	DET	DT	Definite=Def|PronType=Art	7	det	_	_
7	implication	implication	NOUN	NN	Number=Sing	9	nsubjpass	_	_
8	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	9	auxpass	_	_
9	presented	present	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	SpaceAfter=No
10	.	.	PUNCT	.	PunctType=Peri	9	punct	_	SpaceAfter=No

# doc_id = 755
# sent_id = 1
# text = We introduce the notion of a braiding on a skew monoidal category, whose curious feature is that the defining isomorphisms involve three objects rather than two.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	introduce	introduce	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
4	notion	notion	NOUN	NN	Number=Sing	2	dobj	_	_
5	of	of	ADP	IN	_	4	prep	_	_
6	a	a	DET	DT	Definite=Ind|PronType=Art	7	det	_	_
7	braiding	braiding	NOUN	NN	Number=Sing	5	pobj	_	_
8	on	on	ADP	IN	_	7	prep	_	_
9	a	a	DET	DT	Definite=Ind|PronType=Art	12	det	_	_
10	skew	skew	ADJ	JJ	Degree=Pos	12	amod	_	_
11	monoidal	monoidal	ADJ	JJ	Degree=Pos	12	amod	_	_
12	category	category	NOUN	NN	Number=Sing	8	pobj	_	SpaceAfter=No
13	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
14	whose	whose	DET	WP$	Poss=Yes	16	poss	_	_
15	curious	curious	ADJ	JJ	Degree=Pos	16	amod	_	_
16	feature	feature	NOUN	NN	Number=Sing	17	nsubj	_	_
17	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	12	relcl	_	_
18	that	that	SCONJ	IN	_	22	mark	_	_
19	the	the	DET	DT	Definite=Def|PronType=Art	21	det	_	_
20	defining	define	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	21	amod	_	_
21	isomorphisms	isomorphism	NOUN	NNS	Number=Plur	22	nsubj	_	_
22	involve	involve	VERB	VBP	Tense=Pres|VerbForm=Fin	17	ccomp	_	_
23	three	three	NUM	CD	NumType=Card	24	nummod	_	_
24	objects	object	NOUN	NNS	Number=Plur	22	dobj	_	_
25	rather	rather	ADV	RB	_	26	advmod	_	_
26	than	than	ADP	IN	_	24	cc	_	_
27	two	two	NUM	CD	NumType=Card	24	conj	_	SpaceAfter=No
28	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 2
# text = Examples are shown to arise from 2 - category theory and from bialgebras.
1	Examples	example	NOUN	NNS	Number=Plur	3	nsubjpass	_	_
2	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	3	auxpass	_	_
3	shown	show	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	0	ROOT	_	_
4	to	to	PART	TO	_	5	aux	_	_
5	arise	arise	VERB	VB	VerbForm=Inf	3	xcomp	_	_
6	from	from	ADP	IN	_	5	prep	_	_
7	2	2	NUM	CD	NumType=Card	9	nummod	_	_
8	-	-	PUNCT	HYPH	PunctType=Dash	9	punct	_	_
9	category	category	NOUN	NN	Number=Sing	10	compound	_	_
10	theory	theory	NOUN	NN	Number=Sing	6	pobj	_	_
11	and	and	CCONJ	CC	ConjType=Cmp	6	cc	_	_
12	from	from	ADP	IN	_	6	conj	_	_
13	bialgebras	bialgebra	NOUN	NNS	Number=Plur	12	pobj	_	SpaceAfter=No
14	.	.	PUNCT	.	PunctType=Peri	3	punct	_	SpaceAfter=No

# sent_id = 3
# text = In order to describe the 2 - categorical examples, we take a multicategorical approach.
1	In	in	ADP	IN	_	12	prep	_	_
2	order	order	NOUN	NN	Number=Sing	1	pobj	_	_
3	to	to	PART	TO	_	4	aux	_	_
4	describe	describe	VERB	VB	VerbForm=Inf	2	acl	_	_
5	the	the	DET	DT	Definite=Def|PronType=Art	9	det	_	_
6	2	2	NUM	CD	NumType=Card	8	nummod	_	_
7	-	-	PUNCT	HYPH	PunctType=Dash	8	punct	_	_
8	categorical	categorical	ADJ	JJ	Degree=Pos	9	amod	_	_
9	examples	example	NOUN	NNS	Number=Plur	4	dobj	_	SpaceAfter=No
10	,	,	PUNCT	,	PunctType=Comm	12	punct	_	_
11	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	12	nsubj	_	_
12	take	take	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
13	a	a	DET	DT	Definite=Ind|PronType=Art	15	det	_	_
14	multicategorical	multicategorical	ADJ	JJ	Degree=Pos	15	amod	_	_
15	approach	approach	NOUN	NN	Number=Sing	12	dobj	_	SpaceAfter=No
16	.	.	PUNCT	.	PunctType=Peri	12	punct	_	SpaceAfter=No

# sent_id = 4
# text = We explain how certain braided skew monoidal structures in the 2 - categorical setting give rise to braided monoidal bicategories.
1	We	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	2	nsubj	_	_
2	explain	explain	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
3	how	how	SCONJ	WRB	_	4	advmod	_	_
4	certain	certain	ADJ	JJ	Degree=Pos	8	amod	_	_
5	braided	braided	ADJ	JJ	Degree=Pos	8	amod	_	_
6	skew	skew	NOUN	NN	Number=Sing	8	nmod	_	_
7	monoidal	monoidal	ADJ	JJ	Degree=Pos	8	amod	_	_
8	structures	structure	NOUN	NNS	Number=Plur	15	nsubj	_	_
9	in	in	ADP	IN	_	8	prep	_	_
10	the	the	DET	DT	Definite=Def|PronType=Art	14	det	_	_
11	2	2	NUM	CD	NumType=Card	13	nummod	_	_
12	-	-	PUNCT	HYPH	PunctType=Dash	13	punct	_	_
13	categorical	categorical	ADJ	JJ	Degree=Pos	14	amod	_	_
14	setting	setting	NOUN	NN	Number=Sing	9	pobj	_	_
15	give	give	VERB	VBP	Tense=Pres|VerbForm=Fin	2	ccomp	_	_
16	rise	rise	NOUN	NN	Number=Sing	15	dobj	_	_
17	to	to	ADP	IN	_	15	prep	_	_
18	braided	braid	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	20	amod	_	_
19	monoidal	monoidal	ADJ	JJ	Degree=Pos	20	amod	_	_
20	bicategories	bicategorie	NOUN	NNS	Number=Plur	17	pobj	_	SpaceAfter=No
21	.	.	PUNCT	.	PunctType=Peri	2	punct	_	SpaceAfter=No

# sent_id = 5
# text = For the bialgebraic examples, we show that, for a skew monoidal category arising from a bialgebra, braidings on the skew monoidal category are in bijection with cobraidings (also known as coquasitriangular structures) on the bialgebra.
1	For	for	ADP	IN	_	7	prep	_	_
2	the	the	DET	DT	Definite=Def|PronType=Art	4	det	_	_
3	bialgebraic	bialgebraic	NOUN	NN	Number=Sing	4	compound	_	_
4	examples	example	NOUN	NNS	Number=Plur	1	pobj	_	SpaceAfter=No
5	,	,	PUNCT	,	PunctType=Comm	7	punct	_	_
6	we	we	PRON	PRP	Case=Nom|Number=Plur|Person=1|PronType=Prs	7	nsubj	_	_
7	show	show	VERB	VBP	Tense=Pres|VerbForm=Fin	0	ROOT	_	_
8	that	that	SCONJ	IN	_	26	mark	_	SpaceAfter=No
9	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
10	for	for	ADP	IN	_	26	prep	_	_
11	a	a	DET	DT	Definite=Ind|PronType=Art	14	det	_	_
12	skew	skew	ADJ	JJ	Degree=Pos	14	amod	_	_
13	monoidal	monoidal	ADJ	JJ	Degree=Pos	14	amod	_	_
14	category	category	NOUN	NN	Number=Sing	10	pobj	_	_
15	arising	arise	VERB	VBG	Aspect=Prog|Tense=Pres|VerbForm=Part	14	acl	_	_
16	from	from	ADP	IN	_	15	prep	_	_
17	a	a	DET	DT	Definite=Ind|PronType=Art	18	det	_	_
18	bialgebra	bialgebra	NOUN	NN	Number=Sing	16	pobj	_	SpaceAfter=No
19	,	,	PUNCT	,	PunctType=Comm	26	punct	_	_
20	braidings	braiding	NOUN	NNS	Number=Plur	26	nsubj	_	_
21	on	on	ADP	IN	_	20	prep	_	_
22	the	the	DET	DT	Definite=Def|PronType=Art	25	det	_	_
23	skew	skew	ADJ	JJ	Degree=Pos	25	amod	_	_
24	monoidal	monoidal	ADJ	JJ	Degree=Pos	25	amod	_	_
25	category	category	NOUN	NN	Number=Sing	21	pobj	_	_
26	are	be	AUX	VBP	Mood=Ind|Tense=Pres|VerbForm=Fin	7	ccomp	_	_
27	in	in	ADP	IN	_	26	prep	_	_
28	bijection	bijection	NOUN	NN	Number=Sing	27	pobj	_	_
29	with	with	ADP	IN	_	28	prep	_	_
30	cobraidings	cobraiding	NOUN	NNS	Number=Plur	29	pobj	_	_
31	(	(	PUNCT	-LRB-	PunctSide=Ini|PunctType=Brck	30	punct	_	SpaceAfter=No
32	also	also	ADV	RB	_	33	advmod	_	_
33	known	know	VERB	VBN	Aspect=Perf|Tense=Past|VerbForm=Part	30	acl	_	_
34	as	as	ADP	IN	_	33	prep	_	_
35	coquasitriangular	coquasitriangular	ADJ	JJ	Degree=Pos	36	amod	_	_
36	structures	structure	NOUN	NNS	Number=Plur	34	pobj	_	SpaceAfter=No
37	)	)	PUNCT	-RRB-	PunctSide=Fin|PunctType=Brck	30	punct	_	_
38	on	on	ADP	IN	_	26	prep	_	_
39	the	the	DET	DT	Definite=Def|PronType=Art	40	det	_	_
40	bialgebra	bialgebra	NOUN	NN	Number=Sing	38	pobj	_	SpaceAfter=No
41	.	.	PUNCT	.	PunctType=Peri	7	punct	_	SpaceAfter=No