id	sid	tid	token	lemma	pos
ejpam-3905	1	1	european	european	PROPN
ejpam-3905	1	2	journal	journal	PROPN
ejpam-3905	1	3	of	of	ADP
ejpam-3905	1	4	pure	pure	ADJ
ejpam-3905	1	5	and	and	CCONJ
ejpam-3905	1	6	applied	apply	VERB
ejpam-3905	1	7	mathematics	mathematic	NOUN
ejpam-3905	1	8	vol	vol	NOUN
ejpam-3905	1	9	.	.	PUNCT
ejpam-3905	2	1	14	14	NUM
ejpam-3905	2	2	,	,	PUNCT
ejpam-3905	2	3	no	no	INTJ
ejpam-3905	2	4	.	.	NOUN
ejpam-3905	2	5	2	2	NUM
ejpam-3905	2	6	,	,	PUNCT
ejpam-3905	2	7	2021	2021	NUM
ejpam-3905	2	8	,	,	PUNCT
ejpam-3905	2	9	480	480	NUM
ejpam-3905	2	10	-	-	SYM
ejpam-3905	2	11	492	492	NUM
ejpam-3905	2	12	issn	issn	PROPN
ejpam-3905	2	13	1307	1307	NUM
ejpam-3905	2	14	-	-	SYM
ejpam-3905	2	15	5543	5543	NUM
ejpam-3905	2	16	–	–	PUNCT
ejpam-3905	2	17	ejpam.com	ejpam.com	X
ejpam-3905	2	18	published	publish	VERB
ejpam-3905	2	19	by	by	ADP
ejpam-3905	2	20	new	new	PROPN
ejpam-3905	2	21	york	york	PROPN
ejpam-3905	2	22	business	business	PROPN
ejpam-3905	2	23	global	global	PROPN
ejpam-3905	2	24	on	on	ADP
ejpam-3905	2	25	the	the	DET
ejpam-3905	2	26	e	e	NOUN
ejpam-3905	2	27	-	-	NOUN
ejpam-3905	2	28	infinity	infinity	NOUN
ejpam-3905	2	29	algebras	algebras	PROPN
ejpam-3905	2	30	alaa	alaa	PROPN
ejpam-3905	2	31	hassan	hassan	PROPN
ejpam-3905	2	32	noreldeen	noreldeen	PROPN
ejpam-3905	2	33	mohamed1,∗	mohamed1,∗	PROPN
ejpam-3905	2	34	,	,	PUNCT
ejpam-3905	2	35	samar	samar	PROPN
ejpam-3905	2	36	a.	a.	NOUN
ejpam-3905	2	37	abo	abo	PROPN
ejpam-3905	2	38	quota1	quota1	NOUN
ejpam-3905	2	39	1	1	NUM
ejpam-3905	2	40	department	department	NOUN
ejpam-3905	2	41	of	of	ADP
ejpam-3905	2	42	mathematics	mathematic	NOUN
ejpam-3905	2	43	,	,	PUNCT
ejpam-3905	2	44	faculty	faculty	NOUN
ejpam-3905	2	45	of	of	ADP
ejpam-3905	2	46	science	science	NOUN
ejpam-3905	2	47	,	,	PUNCT
ejpam-3905	2	48	aswan	aswan	PROPN
ejpam-3905	2	49	university	university	PROPN
ejpam-3905	2	50	,	,	PUNCT
ejpam-3905	2	51	egypt	egypt	PROPN
ejpam-3905	2	52	abstract	abstract	PROPN
ejpam-3905	2	53	.	.	PUNCT
ejpam-3905	3	1	in	in	ADP
ejpam-3905	3	2	this	this	DET
ejpam-3905	3	3	paper	paper	NOUN
ejpam-3905	3	4	we	we	PRON
ejpam-3905	3	5	study	study	VERB
ejpam-3905	3	6	an	an	DET
ejpam-3905	3	7	elementary	elementary	ADJ
ejpam-3905	3	8	use	use	NOUN
ejpam-3905	3	9	of	of	ADP
ejpam-3905	3	10	e	e	NOUN
ejpam-3905	3	11	-	-	NOUN
ejpam-3905	3	12	infinity	infinity	NOUN
ejpam-3905	3	13	modules	module	NOUN
ejpam-3905	3	14	and	and	CCONJ
ejpam-3905	3	15	e	e	NOUN
ejpam-3905	3	16	-	-	NOUN
ejpam-3905	3	17	infinity	infinity	NOUN
ejpam-3905	3	18	algebras	algebra	NOUN
ejpam-3905	3	19	as	as	SCONJ
ejpam-3905	3	20	together	together	ADV
ejpam-3905	3	21	they	they	PRON
ejpam-3905	3	22	have	have	VERB
ejpam-3905	3	23	a	a	DET
ejpam-3905	3	24	use	use	NOUN
ejpam-3905	3	25	in	in	ADP
ejpam-3905	3	26	terms	term	NOUN
ejpam-3905	3	27	of	of	ADP
ejpam-3905	3	28	describing	describe	VERB
ejpam-3905	3	29	triangulated	triangulate	VERB
ejpam-3905	3	30	categories	category	NOUN
ejpam-3905	3	31	.	.	PUNCT
ejpam-3905	4	1	also	also	ADV
ejpam-3905	4	2	,	,	PUNCT
ejpam-3905	4	3	we	we	PRON
ejpam-3905	4	4	show	show	VERB
ejpam-3905	4	5	an	an	DET
ejpam-3905	4	6	interpretation	interpretation	NOUN
ejpam-3905	4	7	of	of	ADP
ejpam-3905	4	8	e	e	NOUN
ejpam-3905	4	9	-	-	NOUN
ejpam-3905	4	10	infinity	infinity	NOUN
ejpam-3905	4	11	algebras	algebra	NOUN
ejpam-3905	4	12	where	where	SCONJ
ejpam-3905	4	13	the	the	DET
ejpam-3905	4	14	modules	module	NOUN
ejpam-3905	4	15	are	be	AUX
ejpam-3905	4	16	fibrant	fibrant	ADJ
ejpam-3905	4	17	objects	object	NOUN
ejpam-3905	4	18	within	within	ADP
ejpam-3905	4	19	the	the	DET
ejpam-3905	4	20	categories	category	NOUN
ejpam-3905	4	21	of	of	ADP
ejpam-3905	4	22	differential	differential	NOUN
ejpam-3905	4	23	graded	grade	VERB
ejpam-3905	4	24	co	co	NOUN
ejpam-3905	4	25	-	-	NOUN
ejpam-3905	4	26	algebras	algebra	NOUN
ejpam-3905	4	27	and	and	CCONJ
ejpam-3905	4	28	co	co	NOUN
ejpam-3905	4	29	-	-	NOUN
ejpam-3905	4	30	modules	module	NOUN
ejpam-3905	4	31	.	.	PUNCT
ejpam-3905	5	1	2020	2020	NUM
ejpam-3905	5	2	mathematics	mathematic	NOUN
ejpam-3905	5	3	subject	subject	NOUN
ejpam-3905	5	4	classifications	classification	NOUN
ejpam-3905	5	5	:	:	PUNCT
ejpam-3905	5	6	55q05	55q05	NUM
ejpam-3905	5	7	,	,	PUNCT
ejpam-3905	5	8	57q10	57q10	NUM
ejpam-3905	5	9	key	key	ADJ
ejpam-3905	5	10	words	word	NOUN
ejpam-3905	5	11	and	and	CCONJ
ejpam-3905	5	12	phrases	phrase	NOUN
ejpam-3905	5	13	:	:	PUNCT
ejpam-3905	5	14	coalgebra	coalgebra	PROPN
ejpam-3905	5	15	,	,	PUNCT
ejpam-3905	5	16	dg	dg	NOUN
ejpam-3905	5	17	-	-	PUNCT
ejpam-3905	5	18	algebras	algebras	X
ejpam-3905	5	19	,	,	PUNCT
ejpam-3905	5	20	e	e	NOUN
ejpam-3905	5	21	-	-	NOUN
ejpam-3905	5	22	infinity	infinity	ADJ
ejpam-3905	5	23	algebra	algebra	NOUN
ejpam-3905	5	24	,	,	PUNCT
ejpam-3905	5	25	modules	module	NOUN
ejpam-3905	5	26	1	1	NUM
ejpam-3905	5	27	.	.	PUNCT
ejpam-3905	5	28	introduction	introduction	NOUN
ejpam-3905	5	29	an	an	DET
ejpam-3905	5	30	operad	operad	ADJ
ejpam-3905	5	31	homology	homology	NOUN
ejpam-3905	5	32	theory	theory	NOUN
ejpam-3905	5	33	appeared	appear	VERB
ejpam-3905	5	34	in	in	ADP
ejpam-3905	5	35	mays	may	NOUN
ejpam-3905	5	36	investigation	investigation	NOUN
ejpam-3905	5	37	of	of	ADP
ejpam-3905	5	38	iterated	iterated	ADJ
ejpam-3905	5	39	loop	loop	NOUN
ejpam-3905	5	40	spaces	space	NOUN
ejpam-3905	5	41	in	in	ADP
ejpam-3905	5	42	[	[	X
ejpam-3905	5	43	11	11	NUM
ejpam-3905	5	44	]	]	PUNCT
ejpam-3905	5	45	.	.	PUNCT
ejpam-3905	6	1	the	the	DET
ejpam-3905	6	2	operad	operad	PROPN
ejpam-3905	6	3	model	model	NOUN
ejpam-3905	6	4	has	have	VERB
ejpam-3905	6	5	some	some	DET
ejpam-3905	6	6	properties	property	NOUN
ejpam-3905	6	7	of	of	ADP
ejpam-3905	6	8	the	the	DET
ejpam-3905	6	9	operations	operation	NOUN
ejpam-3905	6	10	there	there	ADV
ejpam-3905	6	11	in	in	ADP
ejpam-3905	6	12	,	,	PUNCT
ejpam-3905	6	13	for	for	ADP
ejpam-3905	6	14	example	example	NOUN
ejpam-3905	6	15	,	,	PUNCT
ejpam-3905	6	16	commutativity	commutativity	NOUN
ejpam-3905	6	17	and	and	CCONJ
ejpam-3905	6	18	associativity	associativity	NOUN
ejpam-3905	6	19	encoded	encode	VERB
ejpam-3905	6	20	in	in	ADP
ejpam-3905	6	21	every	every	DET
ejpam-3905	6	22	operad	operad	NOUN
ejpam-3905	6	23	as	as	SCONJ
ejpam-3905	6	24	realized	realize	VERB
ejpam-3905	6	25	by	by	ADP
ejpam-3905	6	26	the	the	DET
ejpam-3905	6	27	algebra	algebra	NOUN
ejpam-3905	6	28	involved	involve	VERB
ejpam-3905	6	29	.	.	PUNCT
ejpam-3905	7	1	the	the	DET
ejpam-3905	7	2	classification	classification	NOUN
ejpam-3905	7	3	of	of	ADP
ejpam-3905	7	4	the	the	DET
ejpam-3905	7	5	dg	dg	NOUN
ejpam-3905	7	6	-	-	PUNCT
ejpam-3905	7	7	modules	module	NOUN
ejpam-3905	7	8	over	over	ADP
ejpam-3905	7	9	ring	ring	NOUN
ejpam-3905	7	10	k	k	PROPN
ejpam-3905	7	11	is	be	AUX
ejpam-3905	7	12	defined	define	VERB
ejpam-3905	7	13	by	by	ADP
ejpam-3905	7	14	dg	dg	NOUN
ejpam-3905	7	15	-	-	PUNCT
ejpam-3905	7	16	mod	mod	PROPN
ejpam-3905	7	17	.	.	PUNCT
ejpam-3905	8	1	examples	example	NOUN
ejpam-3905	8	2	of	of	ADP
ejpam-3905	8	3	algebra	algebra	NOUN
ejpam-3905	8	4	over	over	ADP
ejpam-3905	8	5	the	the	DET
ejpam-3905	8	6	operads	operad	NOUN
ejpam-3905	8	7	in	in	ADP
ejpam-3905	8	8	dg	dg	PROPN
ejpam-3905	8	9	-	-	PUNCT
ejpam-3905	8	10	mod	mod	NOUN
ejpam-3905	8	11	include	include	VERB
ejpam-3905	8	12	a∞-algebras	a∞-algebra	NOUN
ejpam-3905	8	13	and	and	CCONJ
ejpam-3905	8	14	e∞-algebras	e∞-algebra	NOUN
ejpam-3905	8	15	generalizing	generalize	VERB
ejpam-3905	8	16	the	the	DET
ejpam-3905	8	17	concept	concept	NOUN
ejpam-3905	8	18	of	of	ADP
ejpam-3905	8	19	associativity	associativity	NOUN
ejpam-3905	8	20	and	and	CCONJ
ejpam-3905	8	21	commutativity.an	commutativity.an	NOUN
ejpam-3905	8	22	e∞-algebra	e∞-algebra	NOUN
ejpam-3905	8	23	is	be	AUX
ejpam-3905	8	24	a	a	DET
ejpam-3905	8	25	dg	dg	NOUN
ejpam-3905	8	26	-	-	PUNCT
ejpam-3905	8	27	module	module	NOUN
ejpam-3905	8	28	with	with	ADP
ejpam-3905	8	29	multiplication	multiplication	NOUN
ejpam-3905	8	30	present	present	ADJ
ejpam-3905	8	31	which	which	PRON
ejpam-3905	8	32	is	be	AUX
ejpam-3905	8	33	the	the	DET
ejpam-3905	8	34	associativity	associativity	NOUN
ejpam-3905	8	35	and	and	CCONJ
ejpam-3905	8	36	commutativity	commutativity	NOUN
ejpam-3905	8	37	up	up	ADP
ejpam-3905	8	38	to	to	ADP
ejpam-3905	8	39	all	all	DET
ejpam-3905	8	40	higher	high	ADJ
ejpam-3905	8	41	homotopies	homotopie	NOUN
ejpam-3905	8	42	.	.	PUNCT
ejpam-3905	9	1	an	an	DET
ejpam-3905	9	2	example	example	NOUN
ejpam-3905	9	3	of	of	ADP
ejpam-3905	9	4	e∞-algebras	e∞-algebras	PROPN
ejpam-3905	9	5	corresponding	correspond	VERB
ejpam-3905	9	6	to	to	ADP
ejpam-3905	9	7	n	n	PROPN
ejpam-3905	9	8	=	=	SYM
ejpam-3905	9	9	∞	∞	PROPN
ejpam-3905	9	10	has	have	AUX
ejpam-3905	9	11	been	be	AUX
ejpam-3905	9	12	given	give	VERB
ejpam-3905	9	13	in	in	ADP
ejpam-3905	9	14	[	[	PUNCT
ejpam-3905	9	15	1].we	1].we	NUM
ejpam-3905	9	16	present	present	VERB
ejpam-3905	9	17	the	the	DET
ejpam-3905	9	18	essential	essential	ADJ
ejpam-3905	9	19	explanations	explanation	NOUN
ejpam-3905	9	20	and	and	CCONJ
ejpam-3905	9	21	meaningsof	meaningsof	NOUN
ejpam-3905	9	22	e∞-algebras	e∞-algebra	NOUN
ejpam-3905	9	23	,	,	PUNCT
ejpam-3905	9	24	e∞-modulesand	e∞-modulesand	VERB
ejpam-3905	9	25	their	their	PRON
ejpam-3905	9	26	fundamental	fundamental	ADJ
ejpam-3905	9	27	properties	property	NOUN
ejpam-3905	9	28	in	in	ADP
ejpam-3905	9	29	this	this	DET
ejpam-3905	9	30	study	study	NOUN
ejpam-3905	9	31	.	.	PUNCT
ejpam-3905	10	1	this	this	PRON
ejpam-3905	10	2	is	be	AUX
ejpam-3905	10	3	in	in	ADP
ejpam-3905	10	4	addition	addition	NOUN
ejpam-3905	10	5	to	to	ADP
ejpam-3905	10	6	the	the	DET
ejpam-3905	10	7	presentation	presentation	NOUN
ejpam-3905	10	8	of	of	ADP
ejpam-3905	10	9	aderived	aderived	ADJ
ejpam-3905	10	10	category	category	NOUN
ejpam-3905	10	11	,	,	PUNCT
ejpam-3905	10	12	finishing	finish	VERB
ejpam-3905	10	13	up	up	ADP
ejpam-3905	10	14	with	with	ADP
ejpam-3905	10	15	the	the	DET
ejpam-3905	10	16	depiction	depiction	NOUN
ejpam-3905	10	17	of	of	ADP
ejpam-3905	10	18	triangulated	triangulate	VERB
ejpam-3905	10	19	classes	class	NOUN
ejpam-3905	10	20	using	use	VERB
ejpam-3905	10	21	e∞-algebras	e∞-algebra	NOUN
ejpam-3905	10	22	.	.	PUNCT
ejpam-3905	11	1	we	we	PRON
ejpam-3905	11	2	present	present	VERB
ejpam-3905	11	3	an	an	DET
ejpam-3905	11	4	understanding	understanding	NOUN
ejpam-3905	11	5	of	of	ADP
ejpam-3905	11	6	e∞-algebras	e∞-algebra	NOUN
ejpam-3905	11	7	and	and	CCONJ
ejpam-3905	11	8	e∞-modules	e∞-module	NOUN
ejpam-3905	11	9	as	as	ADP
ejpam-3905	11	10	the	the	DET
ejpam-3905	11	11	fibrant	fibrant	ADJ
ejpam-3905	11	12	objects	object	NOUN
ejpam-3905	11	13	in	in	ADP
ejpam-3905	11	14	the	the	DET
ejpam-3905	11	15	category	category	NOUN
ejpam-3905	11	16	of	of	ADP
ejpam-3905	11	17	the	the	DET
ejpam-3905	11	18	model	model	NOUN
ejpam-3905	11	19	of	of	ADP
ejpam-3905	11	20	certain	certain	ADJ
ejpam-3905	11	21	dg	dg	PROPN
ejpam-3905	11	22	-	-	PUNCT
ejpam-3905	11	23	co	co	NOUN
ejpam-3905	11	24	-	-	NOUN
ejpam-3905	11	25	algebras	algebras	X
ejpam-3905	11	26	(	(	PUNCT
ejpam-3905	11	27	co	co	NOUN
ejpam-3905	11	28	-	-	NOUN
ejpam-3905	11	29	modules	module	NOUN
ejpam-3905	11	30	)	)	PUNCT
ejpam-3905	11	31	following	follow	VERB
ejpam-3905	11	32	[	[	X
ejpam-3905	11	33	9	9	NUM
ejpam-3905	11	34	]	]	PUNCT
ejpam-3905	11	35	.	.	PUNCT
ejpam-3905	12	1	from	from	ADP
ejpam-3905	12	2	the	the	DET
ejpam-3905	12	3	idea	idea	NOUN
ejpam-3905	12	4	of	of	ADP
ejpam-3905	12	5	[	[	X
ejpam-3905	12	6	9	9	NUM
ejpam-3905	12	7	]	]	PUNCT
ejpam-3905	12	8	,	,	PUNCT
ejpam-3905	12	9	we	we	PRON
ejpam-3905	12	10	provide	provide	VERB
ejpam-3905	12	11	conceptual	conceptual	ADJ
ejpam-3905	12	12	construction	construction	NOUN
ejpam-3905	12	13	of	of	ADP
ejpam-3905	12	14	the	the	DET
ejpam-3905	12	15	e∞-functor	e∞-functor	NOUN
ejpam-3905	12	16	categories	category	NOUN
ejpam-3905	12	17	and	and	CCONJ
ejpam-3905	12	18	use	use	VERB
ejpam-3905	12	19	it	it	PRON
ejpam-3905	12	20	to	to	PART
ejpam-3905	12	21	construct	construct	VERB
ejpam-3905	12	22	the	the	DET
ejpam-3905	12	23	canonical	canonical	ADJ
ejpam-3905	12	24	bi	bi	ADJ
ejpam-3905	12	25	-	-	ADJ
ejpam-3905	12	26	algebra	algebra	ADJ
ejpam-3905	12	27	structure	structure	NOUN
ejpam-3905	12	28	of	of	ADP
ejpam-3905	12	29	the	the	DET
ejpam-3905	12	30	cobar	cobar	NOUN
ejpam-3905	12	31	-	-	PUNCT
ejpam-3905	12	32	construction	construction	NOUN
ejpam-3905	12	33	of	of	ADP
ejpam-3905	12	34	the	the	DET
ejpam-3905	12	35	simplicial	simplicial	ADJ
ejpam-3905	12	36	complex	complex	NOUN
ejpam-3905	12	37	of	of	ADP
ejpam-3905	12	38	an	an	DET
ejpam-3905	12	39	associative	associative	ADJ
ejpam-3905	12	40	algebra	algebra	NOUN
ejpam-3905	12	41	.	.	PUNCT
ejpam-3905	13	1	in	in	ADP
ejpam-3905	13	2	the	the	DET
ejpam-3905	13	3	second	second	ADJ
ejpam-3905	13	4	section	section	NOUN
ejpam-3905	13	5	,	,	PUNCT
ejpam-3905	13	6	we	we	PRON
ejpam-3905	13	7	will	will	AUX
ejpam-3905	13	8	present	present	VERB
ejpam-3905	13	9	the	the	DET
ejpam-3905	13	10	definition	definition	NOUN
ejpam-3905	13	11	of	of	ADP
ejpam-3905	13	12	e∞-algebra	e∞-algebra	NOUN
ejpam-3905	13	13	with	with	ADP
ejpam-3905	13	14	some	some	DET
ejpam-3905	13	15	examples	example	NOUN
ejpam-3905	13	16	and	and	CCONJ
ejpam-3905	13	17	study	study	VERB
ejpam-3905	13	18	some	some	DET
ejpam-3905	13	19	theories	theory	NOUN
ejpam-3905	13	20	and	and	CCONJ
ejpam-3905	13	21	properties	property	NOUN
ejpam-3905	13	22	of	of	ADP
ejpam-3905	13	23	it	it	PRON
ejpam-3905	13	24	.	.	PUNCT
ejpam-3905	14	1	in	in	ADP
ejpam-3905	14	2	the	the	DET
ejpam-3905	14	3	third	third	ADJ
ejpam-3905	14	4	part	part	NOUN
ejpam-3905	14	5	:	:	PUNCT
ejpam-3905	14	6	we	we	PRON
ejpam-3905	14	7	explain	explain	VERB
ejpam-3905	14	8	the	the	DET
ejpam-3905	14	9	idea	idea	NOUN
ejpam-3905	14	10	of	of	ADP
ejpam-3905	14	11	co	co	NOUN
ejpam-3905	14	12	-	-	NOUN
ejpam-3905	14	13	algebras	algebra	NOUN
ejpam-3905	14	14	and	and	CCONJ
ejpam-3905	14	15	the	the	DET
ejpam-3905	14	16	bar	bar	NOUN
ejpam-3905	14	17	-	-	PUNCT
ejpam-3905	14	18	cobar	cobar	NOUN
ejpam-3905	14	19	construction	construction	NOUN
ejpam-3905	14	20	.	.	PUNCT
ejpam-3905	15	1	this	this	DET
ejpam-3905	15	2	∗corresponding	∗corresponde	VERB
ejpam-3905	15	3	author	author	NOUN
ejpam-3905	15	4	.	.	PUNCT
ejpam-3905	16	1	doi	doi	NOUN
ejpam-3905	16	2	:	:	PUNCT
ejpam-3905	16	3	https://doi.org/10.29020/nybg.ejpam.v14i2.3905	https://doi.org/10.29020/nybg.ejpam.v14i2.3905	ADJ
ejpam-3905	16	4	email	email	NOUN
ejpam-3905	16	5	addresses	address	NOUN
ejpam-3905	16	6	:	:	PUNCT
ejpam-3905	16	7	ala2222000@yahoo.com	ala2222000@yahoo.com	X
ejpam-3905	16	8	(	(	PUNCT
ejpam-3905	16	9	a.	a.	NOUN
ejpam-3905	16	10	noreldeen	noreldeen	PROPN
ejpam-3905	16	11	)	)	PUNCT
ejpam-3905	16	12	,	,	PUNCT
ejpam-3905	16	13	scientist	scientist	NOUN
ejpam-3905	16	14	samar@yahoo.com	samar@yahoo.com	PROPN
ejpam-3905	16	15	(	(	PUNCT
ejpam-3905	16	16	s.	s.	PROPN
ejpam-3905	16	17	abo	abo	PROPN
ejpam-3905	16	18	quota	quota	NOUN
ejpam-3905	16	19	)	)	PUNCT
ejpam-3905	16	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3905	17	1	480	480	NUM
ejpam-3905	17	2	c	c	X
ejpam-3905	17	3	©	©	PROPN
ejpam-3905	17	4	2021	2021	NUM
ejpam-3905	17	5	ejpam	ejpam	VERB
ejpam-3905	17	6	all	all	DET
ejpam-3905	17	7	rights	right	NOUN
ejpam-3905	17	8	reserved	reserve	VERB
ejpam-3905	17	9	.	.	PUNCT
ejpam-3905	18	1	a.	a.	PROPN
ejpam-3905	18	2	noreldeen	noreldeen	PROPN
ejpam-3905	18	3	,	,	PUNCT
ejpam-3905	18	4	s.	s.	PROPN
ejpam-3905	18	5	abo	abo	VERB
ejpam-3905	18	6	quota	quota	PROPN
ejpam-3905	18	7	/	/	SYM
ejpam-3905	18	8	eur	eur	NOUN
ejpam-3905	18	9	.	.	PUNCT
ejpam-3905	19	1	j.	j.	PROPN
ejpam-3905	19	2	pure	pure	PROPN
ejpam-3905	19	3	appl	appl	PROPN
ejpam-3905	19	4	.	.	PROPN
ejpam-3905	19	5	math	math	PROPN
ejpam-3905	19	6	,	,	PUNCT
ejpam-3905	19	7	14	14	NUM
ejpam-3905	19	8	(	(	PUNCT
ejpam-3905	19	9	2	2	NUM
ejpam-3905	19	10	)	)	PUNCT
ejpam-3905	19	11	(	(	PUNCT
ejpam-3905	19	12	2021	2021	NUM
ejpam-3905	19	13	)	)	PUNCT
ejpam-3905	19	14	,	,	PUNCT
ejpam-3905	19	15	480	480	NUM
ejpam-3905	19	16	-	-	SYM
ejpam-3905	19	17	492	492	NUM
ejpam-3905	19	18	481	481	NUM
ejpam-3905	19	19	is	be	AUX
ejpam-3905	19	20	followed	follow	VERB
ejpam-3905	19	21	by	by	ADP
ejpam-3905	19	22	some	some	DET
ejpam-3905	19	23	relationships	relationship	NOUN
ejpam-3905	19	24	and	and	CCONJ
ejpam-3905	19	25	examples	example	NOUN
ejpam-3905	19	26	.	.	PUNCT
ejpam-3905	20	1	the	the	DET
ejpam-3905	20	2	fourth	fourth	ADJ
ejpam-3905	20	3	section	section	NOUN
ejpam-3905	20	4	is	be	AUX
ejpam-3905	20	5	concerned	concern	VERB
ejpam-3905	20	6	with	with	ADP
ejpam-3905	20	7	the	the	DET
ejpam-3905	20	8	study	study	NOUN
ejpam-3905	20	9	of	of	ADP
ejpam-3905	20	10	morphisms	morphism	NOUN
ejpam-3905	20	11	and	and	CCONJ
ejpam-3905	20	12	relationships	relationship	NOUN
ejpam-3905	20	13	in	in	ADP
ejpam-3905	20	14	e∞algebra	e∞algebra	PROPN
ejpam-3905	20	15	.	.	PUNCT
ejpam-3905	21	1	in	in	ADP
ejpam-3905	21	2	the	the	DET
ejpam-3905	21	3	fifth	fifth	ADJ
ejpam-3905	21	4	section	section	NOUN
ejpam-3905	21	5	,	,	PUNCT
ejpam-3905	21	6	we	we	PRON
ejpam-3905	21	7	will	will	AUX
ejpam-3905	21	8	discuss	discuss	VERB
ejpam-3905	21	9	some	some	DET
ejpam-3905	21	10	important	important	ADJ
ejpam-3905	21	11	theories	theory	NOUN
ejpam-3905	21	12	in	in	ADP
ejpam-3905	21	13	e∞-algebra	e∞-algebra	NOUN
ejpam-3905	21	14	with	with	ADP
ejpam-3905	21	15	its	its	PRON
ejpam-3905	21	16	proof	proof	NOUN
ejpam-3905	21	17	,	,	PUNCT
ejpam-3905	21	18	and	and	CCONJ
ejpam-3905	21	19	we	we	PRON
ejpam-3905	21	20	will	will	AUX
ejpam-3905	21	21	also	also	ADV
ejpam-3905	21	22	present	present	VERB
ejpam-3905	21	23	examples	example	NOUN
ejpam-3905	21	24	as	as	ADP
ejpam-3905	21	25	an	an	DET
ejpam-3905	21	26	application	application	NOUN
ejpam-3905	21	27	.	.	PUNCT
ejpam-3905	22	1	2	2	X
ejpam-3905	22	2	.	.	X
ejpam-3905	22	3	mathematical	mathematical	ADJ
ejpam-3905	22	4	background	background	NOUN
ejpam-3905	22	5	we	we	PRON
ejpam-3905	22	6	start	start	VERB
ejpam-3905	22	7	by	by	ADP
ejpam-3905	22	8	briefly	briefly	ADV
ejpam-3905	22	9	recalling	recall	VERB
ejpam-3905	22	10	the	the	DET
ejpam-3905	22	11	fundamental	fundamental	ADJ
ejpam-3905	22	12	definitions	definition	NOUN
ejpam-3905	22	13	of	of	ADP
ejpam-3905	22	14	e∞-algebras	e∞-algebras	PROPN
ejpam-3905	22	15	and	and	CCONJ
ejpam-3905	22	16	e∞modules	e∞modules	PROPN
ejpam-3905	22	17	.	.	PUNCT
ejpam-3905	23	1	this	this	PRON
ejpam-3905	23	2	is	be	AUX
ejpam-3905	23	3	to	to	PART
ejpam-3905	23	4	build	build	VERB
ejpam-3905	23	5	up	up	ADP
ejpam-3905	23	6	a	a	DET
ejpam-3905	23	7	picture	picture	NOUN
ejpam-3905	23	8	of	of	ADP
ejpam-3905	23	9	the	the	DET
ejpam-3905	23	10	different	different	ADJ
ejpam-3905	23	11	relations	relation	NOUN
ejpam-3905	23	12	between	between	ADP
ejpam-3905	23	13	them	they	PRON
ejpam-3905	23	14	.	.	PUNCT
ejpam-3905	24	1	we‘ll	we‘ll	AUX
ejpam-3905	24	2	provide	provide	VERB
ejpam-3905	24	3	and	and	CCONJ
ejpam-3905	24	4	concentrate	concentrate	VERB
ejpam-3905	24	5	on	on	ADP
ejpam-3905	24	6	the	the	DET
ejpam-3905	24	7	interpretation	interpretation	NOUN
ejpam-3905	24	8	of	of	ADP
ejpam-3905	24	9	the	the	DET
ejpam-3905	24	10	fibrant	fibrant	ADJ
ejpam-3905	24	11	objects	object	NOUN
ejpam-3905	24	12	of	of	ADP
ejpam-3905	24	13	the	the	DET
ejpam-3905	24	14	e∞-algebras	e∞-algebra	NOUN
ejpam-3905	24	15	as	as	ADP
ejpam-3905	24	16	in	in	ADP
ejpam-3905	24	17	the	the	DET
ejpam-3905	24	18	model	model	NOUN
ejpam-3905	24	19	category	category	NOUN
ejpam-3905	24	20	of	of	ADP
ejpam-3905	24	21	the	the	DET
ejpam-3905	24	22	differential	differential	NOUN
ejpam-3905	24	23	graded	grade	VERB
ejpam-3905	24	24	co	co	NOUN
ejpam-3905	24	25	-	-	NOUN
ejpam-3905	24	26	algebras	algebras	X
ejpam-3905	24	27	.	.	PUNCT
ejpam-3905	25	1	for	for	ADP
ejpam-3905	25	2	a	a	DET
ejpam-3905	25	3	gentler	gentle	ADJ
ejpam-3905	25	4	introduction	introduction	NOUN
ejpam-3905	25	5	,	,	PUNCT
ejpam-3905	25	6	see	see	VERB
ejpam-3905	25	7	[	[	X
ejpam-3905	25	8	3	3	NUM
ejpam-3905	25	9	]	]	PUNCT
ejpam-3905	25	10	,	,	PUNCT
ejpam-3905	25	11	[	[	X
ejpam-3905	25	12	2	2	NUM
ejpam-3905	25	13	]	]	PUNCT
ejpam-3905	25	14	and	and	CCONJ
ejpam-3905	25	15	[	[	X
ejpam-3905	25	16	10	10	NUM
ejpam-3905	25	17	]	]	PUNCT
ejpam-3905	25	18	.	.	PUNCT
ejpam-3905	26	1	for	for	ADP
ejpam-3905	26	2	the	the	DET
ejpam-3905	26	3	associated	associated	ADJ
ejpam-3905	26	4	absolute	absolute	ADJ
ejpam-3905	26	5	field	field	NOUN
ejpam-3905	26	6	,	,	PUNCT
ejpam-3905	26	7	we	we	PRON
ejpam-3905	26	8	have	have	AUX
ejpam-3905	26	9	used	use	VERB
ejpam-3905	26	10	f	f	PROPN
ejpam-3905	26	11	.	.	PUNCT
ejpam-3905	27	1	since	since	SCONJ
ejpam-3905	27	2	w	w	PROPN
ejpam-3905	27	3	is	be	AUX
ejpam-3905	27	4	denoted	denote	VERB
ejpam-3905	27	5	as	as	ADP
ejpam-3905	27	6	the	the	DET
ejpam-3905	27	7	graded	grade	VERB
ejpam-3905	27	8	vector	vector	NOUN
ejpam-3905	27	9	space	space	NOUN
ejpam-3905	27	10	,	,	PUNCT
ejpam-3905	27	11	i.e.	i.e.	X
ejpam-3905	27	12	w	w	X
ejpam-3905	27	13	=	=	SYM
ejpam-3905	27	14	⊗	⊗	PROPN
ejpam-3905	27	15	p∈z	p∈z	NOUN
ejpam-3905	27	16	wp	wp	PROPN
ejpam-3905	27	17	,	,	PUNCT
ejpam-3905	27	18	we	we	PRON
ejpam-3905	27	19	define	define	VERB
ejpam-3905	27	20	sw	sw	PROPN
ejpam-3905	27	21	or	or	CCONJ
ejpam-3905	27	22	w[1	w[1	PRON
ejpam-3905	27	23	]	]	PUNCT
ejpam-3905	27	24	as	as	SCONJ
ejpam-3905	27	25	the	the	DET
ejpam-3905	27	26	graded	grade	VERB
ejpam-3905	27	27	space	space	NOUN
ejpam-3905	27	28	with	with	ADP
ejpam-3905	27	29	(	(	PUNCT
ejpam-3905	27	30	sw)p	sw)p	NOUN
ejpam-3905	27	31	=	=	PUNCT
ejpam-3905	27	32	wp+1	wp+1	NOUN
ejpam-3905	27	33	for	for	ADP
ejpam-3905	27	34	each	each	DET
ejpam-3905	27	35	p	p	PROPN
ejpam-3905	27	36	∈	∈	PROPN
ejpam-3905	27	37	z.	z.	PROPN
ejpam-3905	27	38	sw	sw	PROPN
ejpam-3905	27	39	is	be	AUX
ejpam-3905	27	40	the	the	DET
ejpam-3905	27	41	shift	shift	NOUN
ejpam-3905	27	42	of	of	ADP
ejpam-3905	27	43	w.	w.	PROPN
ejpam-3905	27	44	definition	definition	NOUN
ejpam-3905	27	45	1	1	NUM
ejpam-3905	27	46	.	.	PUNCT
ejpam-3905	28	1	[	[	X
ejpam-3905	28	2	12	12	NUM
ejpam-3905	28	3	]	]	PUNCT
ejpam-3905	28	4	an	an	DET
ejpam-3905	28	5	operad	operad	NOUN
ejpam-3905	28	6	=	=	PRON
ejpam-3905	28	7	is	be	AUX
ejpam-3905	28	8	comprised	comprise	VERB
ejpam-3905	28	9	of	of	ADP
ejpam-3905	28	10	a	a	DET
ejpam-3905	28	11	symmetric	symmetric	ADJ
ejpam-3905	28	12	monoidal	monoidal	ADJ
ejpam-3905	28	13	category	category	NOUN
ejpam-3905	28	14	as	as	ADP
ejpam-3905	28	15	part	part	NOUN
ejpam-3905	28	16	of	of	ADP
ejpam-3905	28	17	a	a	DET
ejpam-3905	28	18	collection	collection	NOUN
ejpam-3905	28	19	=(	=(	NOUN
ejpam-3905	28	20	j)j≥0	j)j≥0	PROPN
ejpam-3905	28	21	.	.	PUNCT
ejpam-3905	29	1	each	each	DET
ejpam-3905	29	2	=(	=(	PROPN
ejpam-3905	29	3	j	j	PROPN
ejpam-3905	29	4	)	)	PUNCT
ejpam-3905	29	5	is	be	AUX
ejpam-3905	29	6	enriched	enrich	VERB
ejpam-3905	29	7	by	by	ADP
ejpam-3905	29	8	the	the	DET
ejpam-3905	29	9	activity	activity	NOUN
ejpam-3905	29	10	of	of	ADP
ejpam-3905	29	11	the	the	DET
ejpam-3905	29	12	symmetric	symmetric	ADJ
ejpam-3905	29	13	group	group	NOUN
ejpam-3905	29	14	,	,	PUNCT
ejpam-3905	29	15	σj	σj	ADJ
ejpam-3905	29	16	and	and	CCONJ
ejpam-3905	29	17	that	that	PRON
ejpam-3905	29	18	of	of	ADP
ejpam-3905	29	19	the	the	DET
ejpam-3905	29	20	morphisms	morphism	NOUN
ejpam-3905	29	21	.	.	PUNCT
ejpam-3905	30	1	γs	γs	VERB
ejpam-3905	30	2	,	,	PUNCT
ejpam-3905	30	3	r1,r2	r1,r2	PROPN
ejpam-3905	30	4	,	,	PUNCT
ejpam-3905	30	5	·	·	PUNCT
ejpam-3905	30	6	·	·	PUNCT
ejpam-3905	30	7	·	·	PUNCT
ejpam-3905	30	8	,	,	PUNCT
ejpam-3905	30	9	rs	rs	INTJ
ejpam-3905	30	10	:	:	PUNCT
ejpam-3905	30	11	=(	=(	PROPN
ejpam-3905	30	12	s)⊗=(r1)⊗	s)⊗=(r1)⊗	PROPN
ejpam-3905	30	13	·	·	PUNCT
ejpam-3905	30	14	·	·	PUNCT
ejpam-3905	30	15	·	·	PUNCT
ejpam-3905	31	1	⊗	⊗	NUM
ejpam-3905	31	2	=(	=(	NOUN
ejpam-3905	31	3	rs	rs	NOUN
ejpam-3905	31	4	)	)	PUNCT
ejpam-3905	31	5	−→	−→	NOUN
ejpam-3905	31	6	=(	=(	NOUN
ejpam-3905	31	7	r1	r1	PROPN
ejpam-3905	31	8	+	+	X
ejpam-3905	31	9	·	·	PUNCT
ejpam-3905	31	10	·	·	PUNCT
ejpam-3905	31	11	·	·	PUNCT
ejpam-3905	31	12	rs	rs	X
ejpam-3905	31	13	)	)	PUNCT
ejpam-3905	31	14	(	(	PUNCT
ejpam-3905	31	15	1	1	X
ejpam-3905	31	16	)	)	PUNCT
ejpam-3905	31	17	for	for	ADP
ejpam-3905	31	18	every	every	DET
ejpam-3905	31	19	decision	decision	NOUN
ejpam-3905	31	20	of	of	ADP
ejpam-3905	31	21	the	the	DET
ejpam-3905	31	22	components	component	NOUN
ejpam-3905	31	23	;	;	PUNCT
ejpam-3905	31	24	s	s	X
ejpam-3905	31	25	,	,	PUNCT
ejpam-3905	31	26	r1	r1	NOUN
ejpam-3905	31	27	,	,	PUNCT
ejpam-3905	31	28	·	·	PUNCT
ejpam-3905	31	29	·	·	PUNCT
ejpam-3905	31	30	·	·	PUNCT
ejpam-3905	31	31	,	,	PUNCT
ejpam-3905	31	32	rs	rs	X
ejpam-3905	31	33	≥	≥	NOUN
ejpam-3905	31	34	0	0	NUM
ejpam-3905	31	35	,	,	PUNCT
ejpam-3905	31	36	to	to	ADP
ejpam-3905	31	37	the	the	DET
ejpam-3905	31	38	associativity	associativity	NOUN
ejpam-3905	31	39	and	and	CCONJ
ejpam-3905	31	40	unit	unit	NOUN
ejpam-3905	31	41	axioms	axiom	NOUN
ejpam-3905	31	42	,	,	PUNCT
ejpam-3905	31	43	are	be	AUX
ejpam-3905	31	44	fulfilled	fulfil	VERB
ejpam-3905	31	45	.	.	PUNCT
ejpam-3905	32	1	an	an	DET
ejpam-3905	32	2	e∞	e∞	PROPN
ejpam-3905	32	3	f	f	X
ejpam-3905	32	4	-	-	PUNCT
ejpam-3905	32	5	algebra	algebra	NOUN
ejpam-3905	32	6	a	a	PRON
ejpam-3905	32	7	is	be	AUX
ejpam-3905	32	8	a	a	DET
ejpam-3905	32	9	graded	grade	VERB
ejpam-3905	32	10	space	space	NOUN
ejpam-3905	32	11	with	with	ADP
ejpam-3905	32	12	a	a	DET
ejpam-3905	32	13	map	map	NOUN
ejpam-3905	32	14	,	,	PUNCT
ejpam-3905	32	15	θj	θj	ADV
ejpam-3905	32	16	:	:	PUNCT
ejpam-3905	32	17	=(	=(	PROPN
ejpam-3905	32	18	j	j	PROPN
ejpam-3905	32	19	)	)	PUNCT
ejpam-3905	32	20	⊗	⊗	PROPN
ejpam-3905	32	21	(	(	PUNCT
ejpam-3905	32	22	sa)(j	sa)(j	PROPN
ejpam-3905	32	23	)	)	PUNCT
ejpam-3905	32	24	−→	−→	NOUN
ejpam-3905	32	25	(	(	PUNCT
ejpam-3905	32	26	sa	sa	NOUN
ejpam-3905	32	27	)	)	PUNCT
ejpam-3905	32	28	and	and	CCONJ
ejpam-3905	32	29	unit	unit	NOUN
ejpam-3905	32	30	,	,	PUNCT
ejpam-3905	32	31	η	η	PROPN
ejpam-3905	32	32	:	:	PUNCT
ejpam-3905	32	33	x	x	PUNCT
ejpam-3905	32	34	−→	−→	ADP
ejpam-3905	32	35	a	a	PRON
ejpam-3905	32	36	to	to	ADP
ejpam-3905	32	37	such	such	DET
ejpam-3905	32	38	an	an	DET
ejpam-3905	32	39	extent	extent	NOUN
ejpam-3905	32	40	that	that	SCONJ
ejpam-3905	32	41	the	the	DET
ejpam-3905	32	42	clear	clear	ADJ
ejpam-3905	32	43	associativity	associativity	NOUN
ejpam-3905	32	44	,	,	PUNCT
ejpam-3905	32	45	commutativity	commutativity	NOUN
ejpam-3905	32	46	and	and	CCONJ
ejpam-3905	32	47	the	the	DET
ejpam-3905	32	48	unit	unit	NOUN
ejpam-3905	32	49	diagrams	diagram	NOUN
ejpam-3905	32	50	are	be	AUX
ejpam-3905	32	51	commutative	commutative	ADJ
ejpam-3905	32	52	.	.	PUNCT
ejpam-3905	32	53	example	example	NOUN
ejpam-3905	33	1	1	1	NUM
ejpam-3905	33	2	.	.	PUNCT
ejpam-3905	34	1	[	[	X
ejpam-3905	34	2	2	2	X
ejpam-3905	34	3	]	]	PUNCT
ejpam-3905	34	4	a	a	DET
ejpam-3905	34	5	graded	grade	VERB
ejpam-3905	34	6	space	space	NOUN
ejpam-3905	34	7	a	a	DET
ejpam-3905	34	8	=	=	SYM
ejpam-3905	34	9	m[ε]/(ε2	m[ε]/(ε2	NOUN
ejpam-3905	34	10	)	)	PUNCT
ejpam-3905	34	11	with	with	ADP
ejpam-3905	34	12	the	the	DET
ejpam-3905	34	13	trivial	trivial	ADJ
ejpam-3905	34	14	a	a	DET
ejpam-3905	34	15	-	-	PUNCT
ejpam-3905	34	16	infinity	infinity	NOUN
ejpam-3905	34	17	structure	structure	NOUN
ejpam-3905	34	18	given	give	VERB
ejpam-3905	34	19	by	by	ADP
ejpam-3905	34	20	map	map	NOUN
ejpam-3905	34	21	m2	m2	PROPN
ejpam-3905	34	22	by	by	ADP
ejpam-3905	34	23	multiplication	multiplication	PROPN
ejpam-3905	34	24	ofm	ofm	PROPN
ejpam-3905	34	25	,	,	PUNCT
ejpam-3905	34	26	since	since	SCONJ
ejpam-3905	34	27	the	the	DET
ejpam-3905	34	28	maps	map	NOUN
ejpam-3905	34	29	mn	mn	PROPN
ejpam-3905	34	30	=	=	PUNCT
ejpam-3905	34	31	0	0	PROPN
ejpam-3905	34	32	for	for	ADP
ejpam-3905	34	33	each	each	DET
ejpam-3905	34	34	value	value	NOUN
ejpam-3905	34	35	n	n	CCONJ
ejpam-3905	34	36	6=	6=	NUM
ejpam-3905	34	37	2	2	NUM
ejpam-3905	34	38	,	,	PUNCT
ejpam-3905	34	39	wherem	wherem	PROPN
ejpam-3905	34	40	is	be	AUX
ejpam-3905	34	41	the	the	DET
ejpam-3905	34	42	ordinary	ordinary	ADJ
ejpam-3905	34	43	algebra	algebra	NOUN
ejpam-3905	34	44	for	for	ADP
ejpam-3905	34	45	n	n	PRON
ejpam-3905	34	46	≥	≥	NOUN
ejpam-3905	34	47	1	1	NUM
ejpam-3905	34	48	and	and	CCONJ
ejpam-3905	34	49	ε	ε	PROPN
ejpam-3905	34	50	be	be	AUX
ejpam-3905	34	51	uncertain	uncertain	ADJ
ejpam-3905	34	52	of	of	ADP
ejpam-3905	34	53	degree	degree	NOUN
ejpam-3905	34	54	(	(	PUNCT
ejpam-3905	34	55	2	2	NUM
ejpam-3905	34	56	−n	−n	NUM
ejpam-3905	34	57	)	)	PUNCT
ejpam-3905	34	58	.	.	PUNCT
ejpam-3905	35	1	we	we	PRON
ejpam-3905	35	2	characterize	characterize	VERB
ejpam-3905	35	3	the	the	DET
ejpam-3905	35	4	linear	linear	ADJ
ejpam-3905	35	5	map	map	NOUN
ejpam-3905	36	1	f	f	NOUN
ejpam-3905	36	2	:	:	PUNCT
ejpam-3905	36	3	m⊗n	m⊗n	PROPN
ejpam-3905	36	4	−→m	−→m	X
ejpam-3905	36	5	and	and	CCONJ
ejpam-3905	36	6	the	the	DET
ejpam-3905	36	7	deformed	deform	VERB
ejpam-3905	36	8	multiplication	multiplication	NOUN
ejpam-3905	36	9	,	,	PUNCT
ejpam-3905	36	10	m	m	VERB
ejpam-3905	36	11	′	′	NUM
ejpam-3905	37	1	n	n	NOUN
ejpam-3905	37	2	=	=	PRON
ejpam-3905	37	3	{	{	PUNCT
ejpam-3905	37	4	mn	mn	PROPN
ejpam-3905	37	5	n	n	PROPN
ejpam-3905	37	6	6=	6=	PROPN
ejpam-3905	37	7	n	n	PROPN
ejpam-3905	37	8	mn	mn	PROPN
ejpam-3905	38	1	+	+	CCONJ
ejpam-3905	38	2	εf	εf	PROPN
ejpam-3905	38	3	n	n	NOUN
ejpam-3905	38	4	=	=	CCONJ
ejpam-3905	38	5	n	n	PROPN
ejpam-3905	38	6	}	}	PUNCT
ejpam-3905	38	7	a	a	DET
ejpam-3905	38	8	endowed	endowed	ADJ
ejpam-3905	38	9	with	with	ADP
ejpam-3905	38	10	m	m	PROPN
ejpam-3905	38	11	′	′	NUM
ejpam-3905	38	12	n	n	NOUN
ejpam-3905	38	13	is	be	AUX
ejpam-3905	38	14	a	a	DET
ejpam-3905	38	15	-	-	PUNCT
ejpam-3905	38	16	infinity	infinity	NOUN
ejpam-3905	38	17	algebra	algebra	NOUN
ejpam-3905	38	18	if	if	SCONJ
ejpam-3905	38	19	and	and	CCONJ
ejpam-3905	38	20	only	only	ADV
ejpam-3905	38	21	if	if	SCONJ
ejpam-3905	38	22	f	f	PROPN
ejpam-3905	38	23	is	be	AUX
ejpam-3905	38	24	hochschild	hochschild	ADJ
ejpam-3905	38	25	cocycle	cocycle	NOUN
ejpam-3905	38	26	for	for	ADP
ejpam-3905	38	27	m.	m.	NOUN
ejpam-3905	38	28	definition	definition	NOUN
ejpam-3905	38	29	2	2	NUM
ejpam-3905	38	30	.	.	PUNCT
ejpam-3905	39	1	a	a	DET
ejpam-3905	39	2	weak	weak	ADJ
ejpam-3905	39	3	e∞-f	e∞-f	NOUN
ejpam-3905	39	4	-	-	PUNCT
ejpam-3905	39	5	algebra	algebra	NOUN
ejpam-3905	39	6	a	a	PRON
ejpam-3905	39	7	is	be	AUX
ejpam-3905	39	8	the	the	DET
ejpam-3905	39	9	graded	grade	VERB
ejpam-3905	39	10	space	space	NOUN
ejpam-3905	39	11	with	with	ADP
ejpam-3905	39	12	map	map	NOUN
ejpam-3905	39	13	,	,	PUNCT
ejpam-3905	39	14	θ0	θ0	PROPN
ejpam-3905	39	15	:	:	PUNCT
ejpam-3905	39	16	=(	=(	PROPN
ejpam-3905	39	17	j	j	PROPN
ejpam-3905	39	18	)	)	PUNCT
ejpam-3905	40	1	⊗	⊗	NOUN
ejpam-3905	40	2	x	x	PUNCT
ejpam-3905	40	3	−→	−→	NOUN
ejpam-3905	40	4	(	(	PUNCT
ejpam-3905	40	5	sa	sa	PROPN
ejpam-3905	40	6	)	)	PUNCT
ejpam-3905	40	7	,	,	PUNCT
ejpam-3905	40	8	θj	θj	INTJ
ejpam-3905	40	9	,	,	PUNCT
ejpam-3905	40	10	j	j	PROPN
ejpam-3905	40	11	≥	≥	PROPN
ejpam-3905	40	12	0	0	NUM
ejpam-3905	40	13	.	.	PUNCT
ejpam-3905	41	1	the	the	DET
ejpam-3905	41	2	morphisms	morphism	NOUN
ejpam-3905	41	3	,	,	PUNCT
ejpam-3905	41	4	f	f	X
ejpam-3905	41	5	:	:	PUNCT
ejpam-3905	41	6	a	a	DET
ejpam-3905	41	7	−→	−→	NOUN
ejpam-3905	41	8	b	b	PROPN
ejpam-3905	41	9	of	of	ADP
ejpam-3905	41	10	e∞-algebras	e∞-algebra	NOUN
ejpam-3905	41	11	are	be	AUX
ejpam-3905	41	12	the	the	DET
ejpam-3905	41	13	maps	map	NOUN
ejpam-3905	41	14	θn	θn	PROPN
ejpam-3905	41	15	:	:	PUNCT
ejpam-3905	41	16	=(	=(	PROPN
ejpam-3905	41	17	j	j	PROPN
ejpam-3905	41	18	)	)	PUNCT
ejpam-3905	42	1	⊗	⊗	PROPN
ejpam-3905	42	2	(	(	PUNCT
ejpam-3905	42	3	sa)(n	sa)(n	PROPN
ejpam-3905	42	4	)	)	PUNCT
ejpam-3905	42	5	−→	−→	NOUN
ejpam-3905	42	6	(	(	PUNCT
ejpam-3905	42	7	sa	sa	NOUN
ejpam-3905	42	8	)	)	PUNCT
ejpam-3905	42	9	homogeneous	homogeneous	ADJ
ejpam-3905	42	10	of	of	ADP
ejpam-3905	42	11	the	the	DET
ejpam-3905	42	12	degree	degree	NOUN
ejpam-3905	42	13	zero	zero	NUM
ejpam-3905	42	14	with	with	ADP
ejpam-3905	42	15	the	the	DET
ejpam-3905	42	16	ultimate	ultimate	ADJ
ejpam-3905	42	17	objective	objective	NOUN
ejpam-3905	42	18	that	that	PRON
ejpam-3905	42	19	,	,	PUNCT
ejpam-3905	42	20	∀	∀	X
ejpam-3905	42	21	n	n	PRON
ejpam-3905	42	22	≥	≥	NOUN
ejpam-3905	42	23	1	1	NUM
ejpam-3905	42	24	we	we	PRON
ejpam-3905	42	25	get	get	VERB
ejpam-3905	42	26	;	;	PUNCT
ejpam-3905	42	27	∑	∑	PUNCT
ejpam-3905	42	28	i+j+l	i+j+l	NOUN
ejpam-3905	42	29	=	=	SYM
ejpam-3905	42	30	n	n	NOUN
ejpam-3905	42	31	fi+1+l	fi+1+l	PRON
ejpam-3905	42	32	◦	◦	NOUN
ejpam-3905	42	33	(	(	PUNCT
ejpam-3905	42	34	1⊗i	1⊗i	NOUN
ejpam-3905	42	35	⊗	⊗	PROPN
ejpam-3905	42	36	bj	bj	ADP
ejpam-3905	42	37	⊗	⊗	PROPN
ejpam-3905	42	38	1⊗l	1⊗l	NUM
ejpam-3905	42	39	)	)	PUNCT
ejpam-3905	43	1	=	=	PUNCT
ejpam-3905	43	2	∑	∑	PUNCT
ejpam-3905	43	3	i1+···+is	i1+···+is	X
ejpam-3905	43	4	=	=	NOUN
ejpam-3905	43	5	n	n	ADV
ejpam-3905	43	6	bs	bs	NOUN
ejpam-3905	43	7	◦	◦	NOUN
ejpam-3905	43	8	(	(	PUNCT
ejpam-3905	43	9	fi1	fi1	ADJ
ejpam-3905	43	10	⊗	⊗	PROPN
ejpam-3905	43	11	·	·	PUNCT
ejpam-3905	43	12	·	·	PUNCT
ejpam-3905	43	13	·	·	PUNCT
ejpam-3905	44	1	⊗	⊗	NUM
ejpam-3905	44	2	fis	fis	PROPN
ejpam-3905	44	3	)	)	PUNCT
ejpam-3905	44	4	(	(	PUNCT
ejpam-3905	44	5	2	2	X
ejpam-3905	44	6	)	)	PUNCT
ejpam-3905	44	7	a.	a.	NOUN
ejpam-3905	44	8	noreldeen	noreldeen	PROPN
ejpam-3905	44	9	,	,	PUNCT
ejpam-3905	44	10	s.	s.	PROPN
ejpam-3905	44	11	abo	abo	VERB
ejpam-3905	44	12	quota	quota	PROPN
ejpam-3905	44	13	/	/	SYM
ejpam-3905	44	14	eur	eur	NOUN
ejpam-3905	44	15	.	.	PUNCT
ejpam-3905	45	1	j.	j.	PROPN
ejpam-3905	45	2	pure	pure	PROPN
ejpam-3905	45	3	appl	appl	PROPN
ejpam-3905	45	4	.	.	PROPN
ejpam-3905	45	5	math	math	PROPN
ejpam-3905	45	6	,	,	PUNCT
ejpam-3905	45	7	14	14	NUM
ejpam-3905	45	8	(	(	PUNCT
ejpam-3905	45	9	2	2	NUM
ejpam-3905	45	10	)	)	PUNCT
ejpam-3905	45	11	(	(	PUNCT
ejpam-3905	45	12	2021	2021	NUM
ejpam-3905	45	13	)	)	PUNCT
ejpam-3905	45	14	,	,	PUNCT
ejpam-3905	45	15	480	480	NUM
ejpam-3905	45	16	-	-	SYM
ejpam-3905	45	17	492	492	NUM
ejpam-3905	45	18	482	482	NUM
ejpam-3905	45	19	for	for	ADP
ejpam-3905	45	20	any	any	DET
ejpam-3905	45	21	two	two	NUM
ejpam-3905	45	22	morphisms	morphism	NOUN
ejpam-3905	45	23	(	(	PUNCT
ejpam-3905	45	24	f	f	X
ejpam-3905	45	25	,	,	PUNCT
ejpam-3905	45	26	g	g	NOUN
ejpam-3905	45	27	)	)	PUNCT
ejpam-3905	45	28	as	as	ADP
ejpam-3905	45	29	(	(	PUNCT
ejpam-3905	45	30	f	f	X
ejpam-3905	45	31	◦	◦	NOUN
ejpam-3905	45	32	g	g	NOUN
ejpam-3905	45	33	)	)	PUNCT
ejpam-3905	45	34	is	be	AUX
ejpam-3905	45	35	given	give	VERB
ejpam-3905	45	36	as	as	ADP
ejpam-3905	45	37	,	,	PUNCT
ejpam-3905	45	38	(	(	PUNCT
ejpam-3905	45	39	f	f	X
ejpam-3905	45	40	◦	◦	NOUN
ejpam-3905	45	41	g)j	g)j	NOUN
ejpam-3905	45	42	=	=	X
ejpam-3905	45	43	∑	∑	PUNCT
ejpam-3905	45	44	i1+···+is	i1+···+is	PROPN
ejpam-3905	45	45	=	=	NOUN
ejpam-3905	45	46	j	j	PROPN
ejpam-3905	45	47	fs	fs	PART
ejpam-3905	45	48	◦	◦	NOUN
ejpam-3905	45	49	(	(	PUNCT
ejpam-3905	45	50	gi1	gi1	PROPN
ejpam-3905	45	51	⊗	⊗	X
ejpam-3905	45	52	·	·	PUNCT
ejpam-3905	45	53	·	·	PUNCT
ejpam-3905	45	54	·	·	PUNCT
ejpam-3905	46	1	⊗	⊗	PROPN
ejpam-3905	46	2	gis	gis	PROPN
ejpam-3905	46	3	)	)	PUNCT
ejpam-3905	46	4	(	(	PUNCT
ejpam-3905	46	5	3	3	X
ejpam-3905	46	6	)	)	PUNCT
ejpam-3905	46	7	proposition	proposition	NOUN
ejpam-3905	46	8	1	1	NUM
ejpam-3905	46	9	.	.	PUNCT
ejpam-3905	47	1	[	[	X
ejpam-3905	47	2	10	10	NUM
ejpam-3905	47	3	]	]	PUNCT
ejpam-3905	47	4	for	for	ADP
ejpam-3905	47	5	each	each	DET
ejpam-3905	47	6	e	e	NOUN
ejpam-3905	47	7	-	-	NOUN
ejpam-3905	47	8	infinity	infinity	NOUN
ejpam-3905	47	9	algebra	algebra	NOUN
ejpam-3905	47	10	a	a	X
ejpam-3905	47	11	,	,	PUNCT
ejpam-3905	47	12	there	there	PRON
ejpam-3905	47	13	is	be	VERB
ejpam-3905	47	14	the	the	DET
ejpam-3905	47	15	universal	universal	ADJ
ejpam-3905	47	16	e	e	NOUN
ejpam-3905	47	17	-	-	NOUN
ejpam-3905	47	18	infinity	infinity	ADJ
ejpam-3905	47	19	algebra	algebra	NOUN
ejpam-3905	47	20	morphism	morphism	NOUN
ejpam-3905	47	21	φ	φ	PROPN
ejpam-3905	47	22	:	:	PUNCT
ejpam-3905	47	23	u(a	u(a	PROPN
ejpam-3905	47	24	)	)	PUNCT
ejpam-3905	47	25	−→	−→	NOUN
ejpam-3905	47	26	a	a	PRON
ejpam-3905	47	27	to	to	ADP
ejpam-3905	47	28	a	a	DET
ejpam-3905	47	29	differential	differential	NOUN
ejpam-3905	47	30	graded	grade	VERB
ejpam-3905	47	31	algebra	algebra	NOUN
ejpam-3905	47	32	u(a	u(a	PROPN
ejpam-3905	47	33	)	)	PUNCT
ejpam-3905	47	34	.	.	PUNCT
ejpam-3905	48	1	moreover	moreover	ADV
ejpam-3905	48	2	,	,	PUNCT
ejpam-3905	48	3	the	the	DET
ejpam-3905	48	4	morphism	morphism	NOUN
ejpam-3905	48	5	φ	φ	PROPN
ejpam-3905	48	6	is	be	AUX
ejpam-3905	48	7	an	an	DET
ejpam-3905	48	8	e	e	NOUN
ejpam-3905	48	9	-	-	NOUN
ejpam-3905	48	10	infinity	infinity	ADJ
ejpam-3905	48	11	quasi	quasi	ADJ
ejpam-3905	48	12	isomorphism	isomorphism	NOUN
ejpam-3905	48	13	.	.	PUNCT
ejpam-3905	49	1	proposition	proposition	NOUN
ejpam-3905	49	2	2	2	NUM
ejpam-3905	49	3	.	.	PUNCT
ejpam-3905	50	1	if	if	SCONJ
ejpam-3905	50	2	a	a	PRON
ejpam-3905	50	3	be	be	AUX
ejpam-3905	50	4	e	e	NOUN
ejpam-3905	50	5	-	-	NOUN
ejpam-3905	50	6	infinity	infinity	ADJ
ejpam-3905	50	7	algebra	algebra	NOUN
ejpam-3905	50	8	and	and	CCONJ
ejpam-3905	50	9	f1	f1	NOUN
ejpam-3905	50	10	:	:	PUNCT
ejpam-3905	50	11	a	a	DET
ejpam-3905	50	12	−→	−→	NOUN
ejpam-3905	50	13	v	v	NOUN
ejpam-3905	50	14	is	be	AUX
ejpam-3905	50	15	a	a	DET
ejpam-3905	50	16	quasi	quasi	NOUN
ejpam-3905	50	17	-	-	NOUN
ejpam-3905	50	18	isomorphism	isomorphism	ADJ
ejpam-3905	50	19	(	(	PUNCT
ejpam-3905	50	20	semiisomorphism	semiisomorphism	NOUN
ejpam-3905	50	21	)	)	PUNCT
ejpam-3905	50	22	of	of	ADP
ejpam-3905	50	23	complexes	complex	NOUN
ejpam-3905	50	24	since	since	SCONJ
ejpam-3905	50	25	v	v	NUM
ejpam-3905	50	26	is	be	AUX
ejpam-3905	50	27	the	the	DET
ejpam-3905	50	28	complex	complex	NOUN
ejpam-3905	50	29	.	.	PUNCT
ejpam-3905	51	1	then	then	ADV
ejpam-3905	51	2	the	the	DET
ejpam-3905	51	3	complex	complex	ADJ
ejpam-3905	51	4	v	v	NOUN
ejpam-3905	51	5	admits	admit	VERB
ejpam-3905	51	6	a	a	DET
ejpam-3905	51	7	structure	structure	NOUN
ejpam-3905	51	8	of	of	ADP
ejpam-3905	51	9	e	e	NOUN
ejpam-3905	51	10	-	-	NOUN
ejpam-3905	51	11	infinity	infinity	NOUN
ejpam-3905	51	12	algebra	algebra	NOUN
ejpam-3905	51	13	s.h	s.h	PROPN
ejpam-3905	51	14	.	.	PROPN
ejpam-3905	51	15	f1	f1	PROPN
ejpam-3905	51	16	extends	extend	VERB
ejpam-3905	51	17	to	to	ADP
ejpam-3905	51	18	an	an	DET
ejpam-3905	51	19	e	e	NOUN
ejpam-3905	51	20	-	-	NOUN
ejpam-3905	51	21	infinity	infinity	ADJ
ejpam-3905	51	22	quasi	quasi	ADJ
ejpam-3905	51	23	-	-	ADJ
ejpam-3905	51	24	isomorphism	isomorphism	ADJ
ejpam-3905	51	25	f1	f1	NOUN
ejpam-3905	51	26	:	:	PUNCT
ejpam-3905	51	27	a	a	DET
ejpam-3905	51	28	−→	−→	NOUN
ejpam-3905	51	29	v.	v.	ADP
ejpam-3905	51	30	theorem	theorem	NOUN
ejpam-3905	51	31	1	1	X
ejpam-3905	51	32	.	.	PUNCT
ejpam-3905	52	1	if	if	SCONJ
ejpam-3905	52	2	a	a	PRON
ejpam-3905	52	3	is	be	AUX
ejpam-3905	52	4	an	an	DET
ejpam-3905	52	5	e	e	NOUN
ejpam-3905	52	6	-	-	NOUN
ejpam-3905	52	7	infinity	infinity	ADJ
ejpam-3905	52	8	algebra	algebra	NOUN
ejpam-3905	52	9	,	,	PUNCT
ejpam-3905	52	10	then	then	ADV
ejpam-3905	52	11	h∗(a	h∗(a	PROPN
ejpam-3905	52	12	)	)	PUNCT
ejpam-3905	52	13	admits	admit	VERB
ejpam-3905	52	14	an	an	DET
ejpam-3905	52	15	e	e	NOUN
ejpam-3905	52	16	-	-	NOUN
ejpam-3905	52	17	infinity	infinity	ADJ
ejpam-3905	52	18	algebra	algebra	NOUN
ejpam-3905	52	19	structure	structure	NOUN
ejpam-3905	52	20	since	since	SCONJ
ejpam-3905	52	21	:	:	PUNCT
ejpam-3905	52	22	(	(	PUNCT
ejpam-3905	52	23	1	1	X
ejpam-3905	52	24	)	)	PUNCT
ejpam-3905	52	25	b1	b1	NOUN
ejpam-3905	52	26	=	=	SYM
ejpam-3905	52	27	0	0	NUM
ejpam-3905	52	28	,	,	PUNCT
ejpam-3905	52	29	b2	b2	NOUN
ejpam-3905	52	30	is	be	AUX
ejpam-3905	52	31	induced	induce	VERB
ejpam-3905	52	32	from	from	ADP
ejpam-3905	52	33	ba2	ba2	PROPN
ejpam-3905	52	34	,	,	PUNCT
ejpam-3905	52	35	(	(	PUNCT
ejpam-3905	52	36	2	2	X
ejpam-3905	52	37	)	)	PUNCT
ejpam-3905	52	38	the	the	DET
ejpam-3905	52	39	identity	identity	NOUN
ejpam-3905	52	40	element	element	NOUN
ejpam-3905	52	41	in	in	ADP
ejpam-3905	52	42	the	the	DET
ejpam-3905	52	43	homology	homology	NOUN
ejpam-3905	52	44	is	be	AUX
ejpam-3905	52	45	induced	induce	VERB
ejpam-3905	52	46	by	by	ADP
ejpam-3905	52	47	the	the	DET
ejpam-3905	52	48	e	e	NOUN
ejpam-3905	52	49	-	-	NOUN
ejpam-3905	52	50	infinity	infinity	ADJ
ejpam-3905	52	51	quasi	quasi	NOUN
ejpam-3905	52	52	-	-	NOUN
ejpam-3905	52	53	isomorphism	isomorphism	VERB
ejpam-3905	52	54	a	a	DET
ejpam-3905	52	55	−→	−→	NOUN
ejpam-3905	52	56	h∗(a	h∗(a	PROPN
ejpam-3905	52	57	)	)	PUNCT
ejpam-3905	52	58	.	.	PUNCT
ejpam-3905	53	1	note	note	VERB
ejpam-3905	53	2	that	that	SCONJ
ejpam-3905	53	3	e∞-quasi	e∞-quasi	NOUN
ejpam-3905	53	4	-	-	PUNCT
ejpam-3905	53	5	isomorphism	isomorphism	NOUN
ejpam-3905	53	6	is	be	AUX
ejpam-3905	53	7	trivial	trivial	ADJ
ejpam-3905	53	8	.	.	PUNCT
ejpam-3905	54	1	if	if	SCONJ
ejpam-3905	54	2	,	,	PUNCT
ejpam-3905	54	3	b1	b1	NOUN
ejpam-3905	54	4	=	=	SYM
ejpam-3905	54	5	0	0	PUNCT
ejpam-3905	54	6	then	then	ADV
ejpam-3905	54	7	e∞-algebra	e∞-algebra	VERB
ejpam-3905	54	8	is	be	AUX
ejpam-3905	54	9	minimal	minimal	ADJ
ejpam-3905	54	10	.	.	PUNCT
ejpam-3905	55	1	the	the	DET
ejpam-3905	55	2	minimal	minimal	ADJ
ejpam-3905	55	3	model	model	NOUN
ejpam-3905	55	4	of	of	ADP
ejpam-3905	55	5	an	an	DET
ejpam-3905	55	6	e	e	NOUN
ejpam-3905	55	7	-	-	NOUN
ejpam-3905	55	8	infinity	infinity	NOUN
ejpam-3905	55	9	algebra	algebra	NOUN
ejpam-3905	55	10	a	a	PRON
ejpam-3905	55	11	is	be	AUX
ejpam-3905	55	12	the	the	DET
ejpam-3905	55	13	space	space	NOUN
ejpam-3905	55	14	h∗(a	h∗(a	PROPN
ejpam-3905	55	15	)	)	PUNCT
ejpam-3905	55	16	endowed	endow	VERB
ejpam-3905	55	17	by	by	ADP
ejpam-3905	55	18	the	the	DET
ejpam-3905	55	19	structure	structure	NOUN
ejpam-3905	55	20	provided	provide	VERB
ejpam-3905	55	21	by	by	ADP
ejpam-3905	55	22	the	the	DET
ejpam-3905	55	23	theorem	theorem	PROPN
ejpam-3905	55	24	.	.	PROPN
ejpam-3905	56	1	definition	definition	NOUN
ejpam-3905	56	2	3	3	NUM
ejpam-3905	56	3	.	.	PUNCT
ejpam-3905	57	1	the	the	DET
ejpam-3905	57	2	yoneda	yoneda	PROPN
ejpam-3905	57	3	product	product	NOUN
ejpam-3905	57	4	is	be	AUX
ejpam-3905	57	5	characterized	characterize	VERB
ejpam-3905	57	6	between	between	ADP
ejpam-3905	57	7	ext	ext	NOUN
ejpam-3905	57	8	-	-	PUNCT
ejpam-3905	57	9	groups	group	NOUN
ejpam-3905	57	10	over	over	ADP
ejpam-3905	57	11	general	general	ADJ
ejpam-3905	57	12	rings	ring	NOUN
ejpam-3905	57	13	.	.	PUNCT
ejpam-3905	58	1	however	however	ADV
ejpam-3905	58	2	,	,	PUNCT
ejpam-3905	58	3	for	for	ADP
ejpam-3905	58	4	algebras	algebra	NOUN
ejpam-3905	58	5	over	over	ADP
ejpam-3905	58	6	fields	field	NOUN
ejpam-3905	58	7	,	,	PUNCT
ejpam-3905	58	8	the	the	DET
ejpam-3905	58	9	presentation	presentation	NOUN
ejpam-3905	58	10	can	can	AUX
ejpam-3905	58	11	be	be	AUX
ejpam-3905	58	12	simplified	simplify	VERB
ejpam-3905	58	13	using	use	VERB
ejpam-3905	58	14	canonical	canonical	ADJ
ejpam-3905	58	15	resolutions	resolution	NOUN
ejpam-3905	58	16	.	.	PUNCT
ejpam-3905	59	1	for	for	ADP
ejpam-3905	59	2	any	any	DET
ejpam-3905	59	3	associative	associative	ADJ
ejpam-3905	59	4	algebra	algebra	NOUN
ejpam-3905	59	5	b	b	NOUN
ejpam-3905	59	6	with	with	ADP
ejpam-3905	59	7	a	a	DET
ejpam-3905	59	8	unital	unital	ADJ
ejpam-3905	59	9	,	,	PUNCT
ejpam-3905	59	10	there	there	PRON
ejpam-3905	59	11	is	be	VERB
ejpam-3905	59	12	a	a	DET
ejpam-3905	59	13	projective	projective	ADJ
ejpam-3905	59	14	resolution	resolution	NOUN
ejpam-3905	59	15	p	p	PROPN
ejpam-3905	59	16	−→m	−→m	PROPN
ejpam-3905	59	17	and	and	CCONJ
ejpam-3905	59	18	a	a	DET
ejpam-3905	59	19	right	right	ADJ
ejpam-3905	59	20	b	b	NOUN
ejpam-3905	59	21	-	-	PUNCT
ejpam-3905	59	22	module	module	NOUN
ejpam-3905	59	23	m.	m.	NOUN
ejpam-3905	59	24	let	let	VERB
ejpam-3905	59	25	the	the	DET
ejpam-3905	59	26	dg	dg	NOUN
ejpam-3905	59	27	-	-	PUNCT
ejpam-3905	59	28	endomorphism	endomorphism	PROPN
ejpam-3905	59	29	algebra	algebra	NOUN
ejpam-3905	59	30	a	a	DET
ejpam-3905	59	31	=	=	SYM
ejpam-3905	59	32	homb(p	homb(p	PROPN
ejpam-3905	59	33	,	,	PUNCT
ejpam-3905	59	34	p	p	NOUN
ejpam-3905	59	35	)	)	PUNCT
ejpam-3905	59	36	of	of	ADP
ejpam-3905	59	37	p	p	NOUN
ejpam-3905	59	38	with	with	ADP
ejpam-3905	59	39	the	the	DET
ejpam-3905	59	40	nth	nth	NOUN
ejpam-3905	59	41	part	part	NOUN
ejpam-3905	59	42	of	of	ADP
ejpam-3905	59	43	a	a	DET
ejpam-3905	59	44	comprise	comprise	NOUN
ejpam-3905	59	45	of	of	ADP
ejpam-3905	59	46	the	the	DET
ejpam-3905	59	47	graded	grade	VERB
ejpam-3905	59	48	object	object	NOUN
ejpam-3905	59	49	morphisms	morphism	NOUN
ejpam-3905	59	50	of	of	ADP
ejpam-3905	59	51	degree	degree	NOUN
ejpam-3905	59	52	n	n	ADP
ejpam-3905	59	53	where	where	SCONJ
ejpam-3905	59	54	its	its	PRON
ejpam-3905	59	55	differential	differential	NOUN
ejpam-3905	59	56	is	be	AUX
ejpam-3905	59	57	the	the	DET
ejpam-3905	59	58	super	super	ADJ
ejpam-3905	59	59	commutator	commutator	NOUN
ejpam-3905	59	60	with	with	ADP
ejpam-3905	59	61	a	a	DET
ejpam-3905	59	62	differential	differential	NOUN
ejpam-3905	59	63	of	of	ADP
ejpam-3905	59	64	p	p	NOUN
ejpam-3905	59	65	.	.	PUNCT
ejpam-3905	60	1	thus	thus	ADV
ejpam-3905	60	2	,	,	PUNCT
ejpam-3905	60	3	a	a	PRON
ejpam-3905	60	4	is	be	AUX
ejpam-3905	60	5	specifically	specifically	ADV
ejpam-3905	60	6	an	an	DET
ejpam-3905	60	7	e	e	NOUN
ejpam-3905	60	8	-	-	NOUN
ejpam-3905	60	9	infinity	infinity	ADJ
ejpam-3905	60	10	algebra	algebra	NOUN
ejpam-3905	60	11	with	with	ADP
ejpam-3905	60	12	a	a	DET
ejpam-3905	60	13	minimal	minimal	ADJ
ejpam-3905	60	14	model	model	NOUN
ejpam-3905	60	15	.	.	PUNCT
ejpam-3905	61	1	the	the	DET
ejpam-3905	61	2	homology	homology	NOUN
ejpam-3905	61	3	hen	hen	PROPN
ejpam-3905	61	4	∗	∗	NOUN
ejpam-3905	61	5	(	(	PUNCT
ejpam-3905	61	6	a	a	NOUN
ejpam-3905	61	7	)	)	PUNCT
ejpam-3905	61	8	is	be	AUX
ejpam-3905	61	9	isomorphic	isomorphic	ADJ
ejpam-3905	61	10	for	for	SCONJ
ejpam-3905	61	11	m2	m2	PROPN
ejpam-3905	61	12	to	to	PART
ejpam-3905	61	13	ext∗b(m	ext∗b(m	VERB
ejpam-3905	61	14	,	,	PUNCT
ejpam-3905	61	15	m	m	PROPN
ejpam-3905	61	16	)	)	PUNCT
ejpam-3905	61	17	,	,	PUNCT
ejpam-3905	61	18	which	which	PRON
ejpam-3905	61	19	is	be	AUX
ejpam-3905	61	20	the	the	DET
ejpam-3905	61	21	yoneda	yoneda	PROPN
ejpam-3905	61	22	algebra	algebra	PROPN
ejpam-3905	61	23	.	.	PUNCT
ejpam-3905	62	1	definition	definition	NOUN
ejpam-3905	62	2	4	4	NUM
ejpam-3905	62	3	.	.	PUNCT
ejpam-3905	62	4	let	let	VERB
ejpam-3905	62	5	a	a	PRON
ejpam-3905	62	6	be	be	AUX
ejpam-3905	62	7	the	the	DET
ejpam-3905	62	8	strict	strict	ADJ
ejpam-3905	62	9	unit	unit	NOUN
ejpam-3905	62	10	for	for	ADP
ejpam-3905	62	11	an	an	DET
ejpam-3905	62	12	e	e	NOUN
ejpam-3905	62	13	-	-	NOUN
ejpam-3905	62	14	infinity	infinity	ADJ
ejpam-3905	62	15	algebra	algebra	NOUN
ejpam-3905	62	16	.	.	PUNCT
ejpam-3905	63	1	it	it	PRON
ejpam-3905	63	2	is	be	AUX
ejpam-3905	63	3	an	an	DET
ejpam-3905	63	4	element	element	NOUN
ejpam-3905	63	5	,	,	PUNCT
ejpam-3905	63	6	1	1	NUM
ejpam-3905	63	7	∈	∈	PROPN
ejpam-3905	63	8	e0	e0	NOUN
ejpam-3905	63	9	,	,	PUNCT
ejpam-3905	63	10	which	which	PRON
ejpam-3905	63	11	is	be	AUX
ejpam-3905	63	12	the	the	DET
ejpam-3905	63	13	unit	unit	NOUN
ejpam-3905	63	14	of	of	ADP
ejpam-3905	63	15	m2	m2	PROPN
ejpam-3905	63	16	and	and	CCONJ
ejpam-3905	63	17	such	such	ADJ
ejpam-3905	63	18	that	that	DET
ejpam-3905	63	19	,	,	PUNCT
ejpam-3905	63	20	for	for	ADP
ejpam-3905	63	21	n	n	PROPN
ejpam-3905	63	22	6=	6=	NUM
ejpam-3905	63	23	2	2	NUM
ejpam-3905	63	24	,	,	PUNCT
ejpam-3905	63	25	the	the	DET
ejpam-3905	63	26	map	map	NOUN
ejpam-3905	63	27	bn	bn	NOUN
ejpam-3905	63	28	takes	take	VERB
ejpam-3905	63	29	the	the	DET
ejpam-3905	63	30	value	value	NOUN
ejpam-3905	63	31	0	0	PUNCT
ejpam-3905	63	32	when	when	SCONJ
ejpam-3905	63	33	one	one	NUM
ejpam-3905	63	34	of	of	ADP
ejpam-3905	63	35	its	its	PRON
ejpam-3905	63	36	contentions	contention	NOUN
ejpam-3905	63	37	rises	rise	VERB
ejpam-3905	63	38	to	to	ADP
ejpam-3905	63	39	1	1	NUM
ejpam-3905	63	40	.	.	PUNCT
ejpam-3905	64	1	hen	hen	NOUN
ejpam-3905	64	2	∗	∗	NOUN
ejpam-3905	64	3	(	(	PUNCT
ejpam-3905	64	4	a	a	NOUN
ejpam-3905	64	5	)	)	PUNCT
ejpam-3905	64	6	is	be	AUX
ejpam-3905	64	7	the	the	DET
ejpam-3905	64	8	homological	homological	ADJ
ejpam-3905	64	9	unit	unit	NOUN
ejpam-3905	64	10	for	for	ADP
ejpam-3905	64	11	associative	associative	ADJ
ejpam-3905	64	12	algebra	algebra	NOUN
ejpam-3905	64	13	a	a	PRON
ejpam-3905	64	14	with	with	ADP
ejpam-3905	64	15	the	the	DET
ejpam-3905	64	16	multiplication	multiplication	NOUN
ejpam-3905	64	17	induced	induce	VERB
ejpam-3905	64	18	by	by	ADP
ejpam-3905	64	19	m2	m2	PROPN
ejpam-3905	64	20	.	.	PUNCT
ejpam-3905	65	1	consequently	consequently	ADV
ejpam-3905	65	2	,	,	PUNCT
ejpam-3905	65	3	the	the	DET
ejpam-3905	65	4	homological	homological	ADJ
ejpam-3905	65	5	unitality	unitality	NOUN
ejpam-3905	65	6	is	be	AUX
ejpam-3905	65	7	saved	save	VERB
ejpam-3905	65	8	under	under	ADP
ejpam-3905	65	9	e	e	NOUN
ejpam-3905	65	10	-	-	NOUN
ejpam-3905	65	11	infinity	infinity	ADJ
ejpam-3905	65	12	quasi	quasi	NOUN
ejpam-3905	65	13	-	-	NOUN
ejpam-3905	65	14	isomorphism	isomorphism	NOUN
ejpam-3905	65	15	.	.	PUNCT
ejpam-3905	66	1	proposition	proposition	NOUN
ejpam-3905	66	2	3	3	NUM
ejpam-3905	66	3	.	.	PUNCT
ejpam-3905	67	1	each	each	DET
ejpam-3905	67	2	homologically	homologically	ADV
ejpam-3905	67	3	unital	unital	ADJ
ejpam-3905	67	4	e	e	NOUN
ejpam-3905	67	5	-	-	NOUN
ejpam-3905	67	6	infinity	infinity	ADJ
ejpam-3905	67	7	algebra	algebra	NOUN
ejpam-3905	67	8	is	be	AUX
ejpam-3905	67	9	e	e	NOUN
ejpam-3905	67	10	-	-	NOUN
ejpam-3905	67	11	infinity	infinity	ADJ
ejpam-3905	67	12	quasi	quasi	NOUN
ejpam-3905	67	13	-	-	ADJ
ejpam-3905	67	14	isomorphic	isomorphic	ADJ
ejpam-3905	67	15	to	to	ADP
ejpam-3905	67	16	a	a	DET
ejpam-3905	67	17	strictly	strictly	ADV
ejpam-3905	67	18	unital	unital	ADJ
ejpam-3905	67	19	e	e	ADJ
ejpam-3905	67	20	-	-	NOUN
ejpam-3905	67	21	infinity	infinity	ADJ
ejpam-3905	67	22	algebra	algebra	NOUN
ejpam-3905	67	23	.	.	PUNCT
ejpam-3905	68	1	an	an	DET
ejpam-3905	68	2	e	e	NOUN
ejpam-3905	68	3	-	-	NOUN
ejpam-3905	68	4	infinity	infinity	NOUN
ejpam-3905	68	5	module	module	NOUN
ejpam-3905	68	6	over	over	ADP
ejpam-3905	68	7	a	a	PRON
ejpam-3905	68	8	is	be	AUX
ejpam-3905	68	9	a	a	DET
ejpam-3905	68	10	spectrum	spectrum	NOUN
ejpam-3905	68	11	m	m	NOUN
ejpam-3905	68	12	with	with	ADP
ejpam-3905	68	13	maps	map	NOUN
ejpam-3905	68	14	,	,	PUNCT
ejpam-3905	68	15	λj	λj	INTJ
ejpam-3905	68	16	:	:	PUNCT
ejpam-3905	68	17	=(	=(	ADV
ejpam-3905	68	18	j)×	j)×	PROPN
ejpam-3905	68	19	(	(	PUNCT
ejpam-3905	68	20	aj−1	aj−1	NOUN
ejpam-3905	68	21	∧m	∧m	PROPN
ejpam-3905	68	22	)	)	PUNCT
ejpam-3905	68	23	−→m	−→m	PROPN
ejpam-3905	68	24	(	(	PUNCT
ejpam-3905	68	25	4	4	NUM
ejpam-3905	68	26	)	)	PUNCT
ejpam-3905	68	27	that	that	PRON
ejpam-3905	68	28	are	be	AUX
ejpam-3905	68	29	λj	λj	PROPN
ejpam-3905	68	30	,	,	PUNCT
ejpam-3905	68	31	namely	namely	ADV
ejpam-3905	68	32	suitably	suitably	ADV
ejpam-3905	68	33	,	,	PUNCT
ejpam-3905	68	34	unital	unital	ADJ
ejpam-3905	68	35	,	,	PUNCT
ejpam-3905	68	36	associative	associative	ADJ
ejpam-3905	68	37	,	,	PUNCT
ejpam-3905	68	38	and	and	CCONJ
ejpam-3905	68	39	equivalent	equivalent	ADJ
ejpam-3905	68	40	.	.	PUNCT
ejpam-3905	69	1	an	an	DET
ejpam-3905	69	2	e	e	NOUN
ejpam-3905	69	3	-	-	NOUN
ejpam-3905	69	4	infinity	infinity	NOUN
ejpam-3905	69	5	module	module	NOUN
ejpam-3905	69	6	m	m	NOUN
ejpam-3905	69	7	is	be	AUX
ejpam-3905	69	8	an	an	DET
ejpam-3905	69	9	f	f	NOUN
ejpam-3905	69	10	-	-	PUNCT
ejpam-3905	69	11	module	module	NOUN
ejpam-3905	69	12	with	with	ADP
ejpam-3905	69	13	the	the	DET
ejpam-3905	69	14	unital	unital	ADJ
ejpam-3905	69	15	,	,	PUNCT
ejpam-3905	69	16	equivariant	equivariant	ADJ
ejpam-3905	69	17	,	,	PUNCT
ejpam-3905	69	18	and	and	CCONJ
ejpam-3905	69	19	associative	associative	ADJ
ejpam-3905	69	20	systems	system	NOUN
ejpam-3905	69	21	within	within	ADP
ejpam-3905	69	22	the	the	DET
ejpam-3905	69	23	action	action	NOUN
ejpam-3905	69	24	maps	map	NOUN
ejpam-3905	69	25	λj	λj	PROPN
ejpam-3905	69	26	:	:	PUNCT
ejpam-3905	69	27	=(	=(	NOUN
ejpam-3905	69	28	j)⊗aj−1	j)⊗aj−1	PROPN
ejpam-3905	70	1	⊗	⊗	PROPN
ejpam-3905	70	2	sm	sm	INTJ
ejpam-3905	71	1	−→	−→	NOUN
ejpam-3905	71	2	sm	sm	INTJ
ejpam-3905	71	3	(	(	PUNCT
ejpam-3905	71	4	5	5	NUM
ejpam-3905	71	5	)	)	PUNCT
ejpam-3905	71	6	a.	a.	NOUN
ejpam-3905	71	7	noreldeen	noreldeen	PROPN
ejpam-3905	71	8	,	,	PUNCT
ejpam-3905	71	9	s.	s.	PROPN
ejpam-3905	71	10	abo	abo	VERB
ejpam-3905	71	11	quota	quota	PROPN
ejpam-3905	71	12	/	/	SYM
ejpam-3905	71	13	eur	eur	NOUN
ejpam-3905	71	14	.	.	PUNCT
ejpam-3905	72	1	j.	j.	PROPN
ejpam-3905	72	2	pure	pure	PROPN
ejpam-3905	72	3	appl	appl	PROPN
ejpam-3905	72	4	.	.	PROPN
ejpam-3905	72	5	math	math	PROPN
ejpam-3905	72	6	,	,	PUNCT
ejpam-3905	72	7	14	14	NUM
ejpam-3905	72	8	(	(	PUNCT
ejpam-3905	72	9	2	2	NUM
ejpam-3905	72	10	)	)	PUNCT
ejpam-3905	72	11	(	(	PUNCT
ejpam-3905	72	12	2021	2021	NUM
ejpam-3905	72	13	)	)	PUNCT
ejpam-3905	72	14	,	,	PUNCT
ejpam-3905	72	15	480	480	NUM
ejpam-3905	72	16	-	-	SYM
ejpam-3905	72	17	492	492	NUM
ejpam-3905	72	18	483	483	NUM
ejpam-3905	72	19	that	that	PRON
ejpam-3905	72	20	homogeneous	homogeneous	ADJ
ejpam-3905	72	21	of	of	ADP
ejpam-3905	72	22	degree	degree	NOUN
ejpam-3905	72	23	1	1	NUM
ejpam-3905	72	24	is	be	AUX
ejpam-3905	72	25	such	such	ADJ
ejpam-3905	72	26	that	that	SCONJ
ejpam-3905	72	27	the	the	DET
ejpam-3905	72	28	identity	identity	NOUN
ejpam-3905	72	29	of	of	ADP
ejpam-3905	72	30	the	the	DET
ejpam-3905	72	31	definition	definition	NOUN
ejpam-3905	72	32	1	1	NUM
ejpam-3905	72	33	holds	hold	VERB
ejpam-3905	72	34	for	for	ADP
ejpam-3905	72	35	j	j	PROPN
ejpam-3905	72	36	≥	≥	PROPN
ejpam-3905	72	37	1	1	NUM
ejpam-3905	72	38	.	.	PUNCT
ejpam-3905	73	1	we	we	PRON
ejpam-3905	73	2	define	define	VERB
ejpam-3905	73	3	an	an	DET
ejpam-3905	73	4	∞-algebra	∞-algebra	NOUN
ejpam-3905	73	5	a	a	PRON
ejpam-3905	73	6	as	as	ADP
ejpam-3905	73	7	a	a	DET
ejpam-3905	73	8	module	module	NOUN
ejpam-3905	73	9	over	over	ADP
ejpam-3905	73	10	itself	itself	PRON
ejpam-3905	73	11	.	.	PUNCT
ejpam-3905	74	1	the	the	DET
ejpam-3905	74	2	map	map	NOUN
ejpam-3905	74	3	of	of	ADP
ejpam-3905	74	4	a	a	DET
ejpam-3905	74	5	-	-	PUNCT
ejpam-3905	74	6	modules	module	NOUN
ejpam-3905	74	7	is	be	AUX
ejpam-3905	74	8	semi	semi	ADJ
ejpam-3905	74	9	-	-	ADJ
ejpam-3905	74	10	isomorphic	isomorphic	ADJ
ejpam-3905	74	11	if	if	SCONJ
ejpam-3905	74	12	there	there	PRON
ejpam-3905	74	13	is	be	VERB
ejpam-3905	74	14	an	an	DET
ejpam-3905	74	15	actuating	actuate	VERB
ejpam-3905	74	16	isomorphism	isomorphism	NOUN
ejpam-3905	74	17	on	on	ADP
ejpam-3905	74	18	the	the	DET
ejpam-3905	74	19	homology	homology	NOUN
ejpam-3905	74	20	.	.	PUNCT
ejpam-3905	75	1	definition	definition	NOUN
ejpam-3905	75	2	5	5	NUM
ejpam-3905	75	3	.	.	PUNCT
ejpam-3905	76	1	a	a	DET
ejpam-3905	76	2	derived	derive	VERB
ejpam-3905	76	3	category	category	NOUN
ejpam-3905	76	4	is	be	AUX
ejpam-3905	76	5	characterized	characterize	VERB
ejpam-3905	76	6	as	as	ADP
ejpam-3905	76	7	the	the	DET
ejpam-3905	76	8	stable	stable	ADJ
ejpam-3905	76	9	homotopic	homotopic	ADJ
ejpam-3905	76	10	category	category	NOUN
ejpam-3905	76	11	of	of	ADP
ejpam-3905	76	12	spectra	spectra	PROPN
ejpam-3905	76	13	and	and	CCONJ
ejpam-3905	76	14	signified	signify	VERB
ejpam-3905	76	15	by	by	ADP
ejpam-3905	76	16	h̄=.	h̄=.	NOUN
ejpam-3905	76	17	if	if	SCONJ
ejpam-3905	76	18	the	the	DET
ejpam-3905	76	19	map	map	NOUN
ejpam-3905	76	20	of	of	ADP
ejpam-3905	76	21	spectra	spectra	PROPN
ejpam-3905	76	22	induces	induce	VERB
ejpam-3905	76	23	an	an	DET
ejpam-3905	76	24	isomorphism	isomorphism	NOUN
ejpam-3905	76	25	in	in	ADP
ejpam-3905	76	26	the	the	DET
ejpam-3905	76	27	homotopy	homotopy	NOUN
ejpam-3905	76	28	groups	group	NOUN
ejpam-3905	76	29	,	,	PUNCT
ejpam-3905	76	30	then	then	ADV
ejpam-3905	76	31	it	it	PRON
ejpam-3905	76	32	is	be	AUX
ejpam-3905	76	33	weak	weak	ADJ
ejpam-3905	76	34	equivalence	equivalence	NOUN
ejpam-3905	76	35	and	and	CCONJ
ejpam-3905	76	36	h̄=	h̄=	NOUN
ejpam-3905	76	37	is	be	AUX
ejpam-3905	76	38	constructed	construct	VERB
ejpam-3905	76	39	from	from	ADP
ejpam-3905	76	40	a	a	DET
ejpam-3905	76	41	homotopy	homotopy	NOUN
ejpam-3905	76	42	category	category	NOUN
ejpam-3905	76	43	of	of	ADP
ejpam-3905	76	44	the	the	DET
ejpam-3905	76	45	spectra	spectra	NOUN
ejpam-3905	76	46	by	by	ADP
ejpam-3905	76	47	formally	formally	ADV
ejpam-3905	76	48	altering	alter	VERB
ejpam-3905	76	49	the	the	DET
ejpam-3905	76	50	weak	weak	ADJ
ejpam-3905	76	51	equivalences	equivalence	NOUN
ejpam-3905	76	52	.	.	PUNCT
ejpam-3905	77	1	the	the	DET
ejpam-3905	77	2	derived	derived	ADJ
ejpam-3905	77	3	category	category	NOUN
ejpam-3905	77	4	of	of	ADP
ejpam-3905	77	5	a	a	DET
ejpam-3905	77	6	-	-	PUNCT
ejpam-3905	77	7	modules	module	NOUN
ejpam-3905	77	8	da	da	NOUN
ejpam-3905	77	9	=	=	PUNCT
ejpam-3905	77	10	h̄ma	h̄ma	NOUN
ejpam-3905	77	11	is	be	AUX
ejpam-3905	77	12	constructed	construct	VERB
ejpam-3905	77	13	from	from	ADP
ejpam-3905	77	14	the	the	DET
ejpam-3905	77	15	homotopy	homotopy	NOUN
ejpam-3905	77	16	category	category	NOUN
ejpam-3905	77	17	of	of	ADP
ejpam-3905	77	18	a	a	DET
ejpam-3905	77	19	-	-	PUNCT
ejpam-3905	77	20	modules	module	NOUN
ejpam-3905	77	21	by	by	ADP
ejpam-3905	77	22	formally	formally	ADV
ejpam-3905	77	23	altering	alter	VERB
ejpam-3905	77	24	a	a	DET
ejpam-3905	77	25	semi	semi	NOUN
ejpam-3905	77	26	-	-	NOUN
ejpam-3905	77	27	isomorphisms	isomorphisms	X
ejpam-3905	77	28	.	.	PUNCT
ejpam-3905	78	1	the	the	DET
ejpam-3905	78	2	exact	exact	ADJ
ejpam-3905	78	3	triangle	triangle	NOUN
ejpam-3905	78	4	sequence	sequence	NOUN
ejpam-3905	78	5	,	,	PUNCT
ejpam-3905	78	6	m	m	PROPN
ejpam-3905	78	7	f−→	f−→	NOUN
ejpam-3905	78	8	n	n	CCONJ
ejpam-3905	78	9	−→	−→	NOUN
ejpam-3905	78	10	cf	cf	NOUN
ejpam-3905	78	11	−→	−→	NOUN
ejpam-3905	78	12	∑	∑	PUNCT
ejpam-3905	78	13	m	m	VERB
ejpam-3905	78	14	prompts	prompt	VERB
ejpam-3905	78	15	a	a	DET
ejpam-3905	78	16	triangulation	triangulation	NOUN
ejpam-3905	78	17	of	of	ADP
ejpam-3905	78	18	the	the	DET
ejpam-3905	78	19	derived	derive	VERB
ejpam-3905	78	20	category	category	NOUN
ejpam-3905	78	21	,	,	PUNCT
ejpam-3905	78	22	for	for	ADP
ejpam-3905	78	23	a	a	DET
ejpam-3905	78	24	map	map	NOUN
ejpam-3905	78	25	f	f	X
ejpam-3905	78	26	:	:	PUNCT
ejpam-3905	78	27	m−→	m−→	ADJ
ejpam-3905	78	28	n	n	NOUN
ejpam-3905	78	29	.	.	PUNCT
ejpam-3905	79	1	definition	definition	NOUN
ejpam-3905	79	2	6	6	NUM
ejpam-3905	79	3	.	.	PUNCT
ejpam-3905	80	1	[	[	X
ejpam-3905	80	2	9	9	NUM
ejpam-3905	80	3	]	]	PUNCT
ejpam-3905	80	4	the	the	DET
ejpam-3905	80	5	derived	derived	ADJ
ejpam-3905	80	6	category	category	NOUN
ejpam-3905	80	7	d∞(a	d∞(a	NOUN
ejpam-3905	80	8	)	)	PUNCT
ejpam-3905	80	9	is	be	AUX
ejpam-3905	80	10	the	the	DET
ejpam-3905	80	11	localization	localization	NOUN
ejpam-3905	80	12	of	of	ADP
ejpam-3905	80	13	the	the	DET
ejpam-3905	80	14	category	category	NOUN
ejpam-3905	80	15	e	e	NOUN
ejpam-3905	80	16	-	-	NOUN
ejpam-3905	80	17	infinity	infinity	ADJ
ejpam-3905	80	18	modules	module	NOUN
ejpam-3905	80	19	with	with	ADP
ejpam-3905	80	20	degree	degree	NOUN
ejpam-3905	80	21	0	0	NUM
ejpam-3905	80	22	morphisms	morphism	NOUN
ejpam-3905	80	23	regarding	regard	VERB
ejpam-3905	80	24	a	a	DET
ejpam-3905	80	25	class	class	NOUN
ejpam-3905	80	26	of	of	ADP
ejpam-3905	80	27	a	a	DET
ejpam-3905	80	28	quasi	quasi	NOUN
ejpam-3905	80	29	-	-	NOUN
ejpam-3905	80	30	isomorphisms	isomorphisms	X
ejpam-3905	80	31	.	.	PUNCT
ejpam-3905	81	1	note	note	VERB
ejpam-3905	81	2	that	that	SCONJ
ejpam-3905	81	3	,	,	PUNCT
ejpam-3905	81	4	the	the	DET
ejpam-3905	81	5	objects	object	NOUN
ejpam-3905	81	6	of	of	ADP
ejpam-3905	81	7	the	the	DET
ejpam-3905	81	8	derived	derived	ADJ
ejpam-3905	81	9	category	category	NOUN
ejpam-3905	81	10	d∞(a	d∞(a	NOUN
ejpam-3905	81	11	)	)	PUNCT
ejpam-3905	81	12	are	be	AUX
ejpam-3905	81	13	e	e	NOUN
ejpam-3905	81	14	-	-	NOUN
ejpam-3905	81	15	infinity	infinity	ADJ
ejpam-3905	81	16	modules	module	NOUN
ejpam-3905	81	17	,	,	PUNCT
ejpam-3905	81	18	and	and	CCONJ
ejpam-3905	81	19	its	its	PRON
ejpam-3905	81	20	morphisms	morphism	NOUN
ejpam-3905	81	21	are	be	AUX
ejpam-3905	81	22	obtained	obtain	VERB
ejpam-3905	81	23	from	from	ADP
ejpam-3905	81	24	the	the	DET
ejpam-3905	81	25	morphisms	morphism	NOUN
ejpam-3905	81	26	of	of	ADP
ejpam-3905	81	27	e	e	NOUN
ejpam-3905	81	28	-	-	NOUN
ejpam-3905	81	29	infinity	infinity	NOUN
ejpam-3905	81	30	modules	module	NOUN
ejpam-3905	81	31	by	by	ADP
ejpam-3905	81	32	formally	formally	ADV
ejpam-3905	81	33	rearranging	rearrange	VERB
ejpam-3905	81	34	every	every	DET
ejpam-3905	81	35	single	single	ADJ
ejpam-3905	81	36	semi	semi	ADJ
ejpam-3905	81	37	isomorphisms	isomorphisms	PROPN
ejpam-3905	81	38	and	and	CCONJ
ejpam-3905	81	39	,	,	PUNCT
ejpam-3905	81	40	d(moda	d(moda	PROPN
ejpam-3905	81	41	)	)	PUNCT
ejpam-3905	81	42	−→	−→	NOUN
ejpam-3905	81	43	d∞a	d∞a	NOUN
ejpam-3905	81	44	.	.	PUNCT
ejpam-3905	82	1	theorem	theorem	NOUN
ejpam-3905	82	2	2	2	NUM
ejpam-3905	82	3	.	.	PUNCT
ejpam-3905	83	1	[	[	X
ejpam-3905	83	2	11	11	NUM
ejpam-3905	83	3	]	]	PUNCT
ejpam-3905	83	4	the	the	DET
ejpam-3905	83	5	category	category	NOUN
ejpam-3905	83	6	of	of	ADP
ejpam-3905	83	7	f	f	PROPN
ejpam-3905	83	8	-	-	PUNCT
ejpam-3905	83	9	linear	linear	NOUN
ejpam-3905	83	10	algebraiclly	algebraiclly	ADV
ejpam-3905	83	11	triangulated	triangulate	VERB
ejpam-3905	83	12	t	t	PROPN
ejpam-3905	83	13	with	with	ADP
ejpam-3905	83	14	the	the	DET
ejpam-3905	83	15	split	split	ADJ
ejpam-3905	83	16	idempotent	idempotent	NOUN
ejpam-3905	83	17	and	and	CCONJ
ejpam-3905	83	18	the	the	DET
ejpam-3905	83	19	generator	generator	NOUN
ejpam-3905	83	20	g.	g.	PROPN
ejpam-3905	83	21	then	then	ADV
ejpam-3905	83	22	for	for	ADP
ejpam-3905	83	23	m1	m1	PROPN
ejpam-3905	83	24	=	=	SYM
ejpam-3905	83	25	0	0	PROPN
ejpam-3905	83	26	,	,	PUNCT
ejpam-3905	83	27	the	the	DET
ejpam-3905	83	28	structure	structure	NOUN
ejpam-3905	83	29	of	of	ADP
ejpam-3905	83	30	e	e	NOUN
ejpam-3905	83	31	-	-	NOUN
ejpam-3905	83	32	infinity	infinity	ADJ
ejpam-3905	83	33	algebra	algebra	NOUN
ejpam-3905	83	34	is	be	AUX
ejpam-3905	83	35	as	as	SCONJ
ejpam-3905	83	36	follows	follow	VERB
ejpam-3905	83	37	:	:	PUNCT
ejpam-3905	84	1	a	a	DET
ejpam-3905	84	2	=	=	X
ejpam-3905	84	3	⊗	⊗	NUM
ejpam-3905	84	4	n∈zhomt	n∈zhomt	INTJ
ejpam-3905	84	5	(	(	PUNCT
ejpam-3905	84	6	g	g	NOUN
ejpam-3905	84	7	,	,	PUNCT
ejpam-3905	84	8	g[n	g[n	PRON
ejpam-3905	84	9	]	]	PUNCT
ejpam-3905	84	10	)	)	PUNCT
ejpam-3905	84	11	(	(	PUNCT
ejpam-3905	84	12	6	6	X
ejpam-3905	84	13	)	)	PUNCT
ejpam-3905	84	14	m2	m2	PROPN
ejpam-3905	84	15	is	be	AUX
ejpam-3905	84	16	given	give	VERB
ejpam-3905	84	17	as	as	ADP
ejpam-3905	84	18	composition	composition	NOUN
ejpam-3905	84	19	and	and	CCONJ
ejpam-3905	84	20	that	that	SCONJ
ejpam-3905	84	21	the	the	DET
ejpam-3905	84	22	functor	functor	NOUN
ejpam-3905	84	23	;	;	PUNCT
ejpam-3905	84	24	t	t	PROPN
ejpam-3905	84	25	−→	−→	NOUN
ejpam-3905	84	26	grmod(a	grmod(a	PROPN
ejpam-3905	84	27	,	,	PUNCT
ejpam-3905	84	28	m2	m2	PROPN
ejpam-3905	84	29	)	)	PUNCT
ejpam-3905	84	30	,	,	PUNCT
ejpam-3905	84	31	u	u	NOUN
ejpam-3905	84	32	7−→	7−→	NOUN
ejpam-3905	84	33	⊗	⊗	ADJ
ejpam-3905	85	1	n∈zhomt	n∈zhomt	INTJ
ejpam-3905	85	2	(	(	PUNCT
ejpam-3905	85	3	g	g	NOUN
ejpam-3905	85	4	,	,	PUNCT
ejpam-3905	85	5	g[n	g[n	PRON
ejpam-3905	85	6	]	]	PUNCT
ejpam-3905	85	7	)	)	PUNCT
ejpam-3905	85	8	wgich	wgich	PRON
ejpam-3905	85	9	lifts	lift	VERB
ejpam-3905	85	10	to	to	ADP
ejpam-3905	85	11	the	the	DET
ejpam-3905	85	12	triangle	triangle	NOUN
ejpam-3905	85	13	equivalence	equivalence	NOUN
ejpam-3905	85	14	,	,	PUNCT
ejpam-3905	85	15	t	t	PROPN
ejpam-3905	85	16	−→	−→	NOUN
ejpam-3905	85	17	per(a	per(a	PROPN
ejpam-3905	85	18	)	)	PUNCT
ejpam-3905	85	19	.	.	PUNCT
ejpam-3905	86	1	definition	definition	NOUN
ejpam-3905	86	2	7	7	NUM
ejpam-3905	86	3	.	.	PUNCT
ejpam-3905	87	1	[	[	X
ejpam-3905	87	2	8	8	NUM
ejpam-3905	87	3	]	]	PUNCT
ejpam-3905	87	4	a	a	DET
ejpam-3905	87	5	cyclic	cyclic	ADJ
ejpam-3905	87	6	fibration	fibration	NOUN
ejpam-3905	87	7	(	(	PUNCT
ejpam-3905	87	8	co	co	NOUN
ejpam-3905	87	9	-	-	NOUN
ejpam-3905	87	10	fibration	fibration	NOUN
ejpam-3905	87	11	)	)	PUNCT
ejpam-3905	87	12	is	be	AUX
ejpam-3905	87	13	the	the	DET
ejpam-3905	87	14	map	map	NOUN
ejpam-3905	87	15	with	with	ADP
ejpam-3905	87	16	fibration	fibration	NOUN
ejpam-3905	87	17	(	(	PUNCT
ejpam-3905	87	18	co	co	NOUN
ejpam-3905	87	19	-	-	NOUN
ejpam-3905	87	20	fibration	fibration	ADJ
ejpam-3905	87	21	)	)	PUNCT
ejpam-3905	87	22	and	and	CCONJ
ejpam-3905	87	23	weak	weak	ADJ
ejpam-3905	87	24	equivalence	equivalence	NOUN
ejpam-3905	87	25	.	.	PUNCT
ejpam-3905	88	1	a	a	DET
ejpam-3905	88	2	cofibrant	cofibrant	ADJ
ejpam-3905	88	3	object	object	NOUN
ejpam-3905	88	4	is	be	AUX
ejpam-3905	88	5	a	a	DET
ejpam-3905	88	6	one	one	NUM
ejpam-3905	88	7	of	of	ADP
ejpam-3905	88	8	a	a	DET
ejpam-3905	88	9	kind	kind	ADJ
ejpam-3905	88	10	morphism	morphism	NOUN
ejpam-3905	88	11	(	(	PUNCT
ejpam-3905	88	12	φ	φ	X
ejpam-3905	88	13	−→	−→	NOUN
ejpam-3905	88	14	x	x	SYM
ejpam-3905	88	15	)	)	PUNCT
ejpam-3905	88	16	from	from	ADP
ejpam-3905	88	17	the	the	DET
ejpam-3905	88	18	underlying	underlie	VERB
ejpam-3905	88	19	item	item	NOUN
ejpam-3905	88	20	that	that	PRON
ejpam-3905	88	21	is	be	AUX
ejpam-3905	88	22	a	a	DET
ejpam-3905	88	23	co	co	NOUN
ejpam-3905	88	24	-	-	NOUN
ejpam-3905	88	25	fibration	fibration	NOUN
ejpam-3905	88	26	.	.	PUNCT
ejpam-3905	89	1	the	the	DET
ejpam-3905	89	2	fibrant	fibrant	ADJ
ejpam-3905	89	3	object	object	NOUN
ejpam-3905	89	4	is	be	AUX
ejpam-3905	89	5	the	the	DET
ejpam-3905	89	6	special	special	ADJ
ejpam-3905	89	7	morphism	morphism	NOUN
ejpam-3905	89	8	(	(	PUNCT
ejpam-3905	89	9	x	x	NOUN
ejpam-3905	89	10	−→	−→	NOUN
ejpam-3905	89	11	∗	∗	NOUN
ejpam-3905	89	12	)	)	PUNCT
ejpam-3905	89	13	concerning	concern	VERB
ejpam-3905	89	14	the	the	DET
ejpam-3905	89	15	terminal	terminal	ADJ
ejpam-3905	89	16	object	object	NOUN
ejpam-3905	89	17	which	which	PRON
ejpam-3905	89	18	is	be	AUX
ejpam-3905	89	19	a	a	DET
ejpam-3905	89	20	fibration	fibration	NOUN
ejpam-3905	89	21	.	.	PUNCT
ejpam-3905	90	1	definition	definition	NOUN
ejpam-3905	90	2	8	8	NUM
ejpam-3905	90	3	.	.	PUNCT
ejpam-3905	91	1	the	the	DET
ejpam-3905	91	2	classes	class	NOUN
ejpam-3905	91	3	are	be	AUX
ejpam-3905	91	4	supposed	suppose	VERB
ejpam-3905	91	5	to	to	PART
ejpam-3905	91	6	satisfy	satisfy	VERB
ejpam-3905	91	7	the	the	DET
ejpam-3905	91	8	quillen	quillen	ADJ
ejpam-3905	91	9	axioms	axiom	NOUN
ejpam-3905	91	10	as	as	ADP
ejpam-3905	91	11	following	follow	VERB
ejpam-3905	91	12	:	:	PUNCT
ejpam-3905	91	13	(	(	PUNCT
ejpam-3905	91	14	1	1	X
ejpam-3905	91	15	)	)	PUNCT
ejpam-3905	91	16	c	c	NOUN
ejpam-3905	91	17	have	have	VERB
ejpam-3905	91	18	limits	limit	NOUN
ejpam-3905	91	19	and	and	CCONJ
ejpam-3905	91	20	co	co	NOUN
ejpam-3905	91	21	-	-	NOUN
ejpam-3905	91	22	limits	limit	NOUN
ejpam-3905	91	23	which	which	PRON
ejpam-3905	91	24	is	be	AUX
ejpam-3905	91	25	finite	finite	ADJ
ejpam-3905	91	26	.	.	PUNCT
ejpam-3905	92	1	(	(	PUNCT
ejpam-3905	92	2	2	2	X
ejpam-3905	92	3	)	)	PUNCT
ejpam-3905	92	4	if	if	SCONJ
ejpam-3905	92	5	µ	µ	NUM
ejpam-3905	92	6	and	and	CCONJ
ejpam-3905	92	7	γ	γ	NOUN
ejpam-3905	92	8	are	be	AUX
ejpam-3905	92	9	composable	composable	ADJ
ejpam-3905	92	10	in	in	ADP
ejpam-3905	92	11	c	c	NOUN
ejpam-3905	92	12	,	,	PUNCT
ejpam-3905	92	13	and	and	CCONJ
ejpam-3905	92	14	for	for	ADP
ejpam-3905	92	15	any	any	DET
ejpam-3905	92	16	two	two	NUM
ejpam-3905	92	17	of	of	ADP
ejpam-3905	92	18	µ	µ	NUM
ejpam-3905	92	19	,	,	PUNCT
ejpam-3905	92	20	γ	γ	NOUN
ejpam-3905	92	21	and	and	CCONJ
ejpam-3905	92	22	µ	µ	NOUN
ejpam-3905	92	23	,	,	PUNCT
ejpam-3905	92	24	γ	γ	NOUN
ejpam-3905	92	25	are	be	AUX
ejpam-3905	92	26	weak	weak	ADJ
ejpam-3905	92	27	equivalences	equivalence	NOUN
ejpam-3905	92	28	,	,	PUNCT
ejpam-3905	92	29	at	at	ADP
ejpam-3905	92	30	that	that	DET
ejpam-3905	92	31	point	point	NOUN
ejpam-3905	92	32	also	also	ADV
ejpam-3905	92	33	is	be	AUX
ejpam-3905	92	34	the	the	DET
ejpam-3905	92	35	third	third	ADJ
ejpam-3905	92	36	.	.	PUNCT
ejpam-3905	93	1	(	(	PUNCT
ejpam-3905	93	2	3	3	X
ejpam-3905	93	3	)	)	PUNCT
ejpam-3905	93	4	a	a	DET
ejpam-3905	93	5	the	the	DET
ejpam-3905	93	6	draw	draw	NOUN
ejpam-3905	93	7	in	in	ADP
ejpam-3905	93	8	the	the	DET
ejpam-3905	93	9	morphism	morphism	NOUN
ejpam-3905	93	10	’s	’s	PART
ejpam-3905	93	11	category	category	NOUN
ejpam-3905	93	12	of	of	ADP
ejpam-3905	93	13	c	c	PROPN
ejpam-3905	93	14	of	of	ADP
ejpam-3905	93	15	a	a	DET
ejpam-3905	93	16	weak	weak	ADJ
ejpam-3905	93	17	equivalence	equivalence	NOUN
ejpam-3905	93	18	,	,	PUNCT
ejpam-3905	93	19	fibration	fibration	NOUN
ejpam-3905	93	20	,	,	PUNCT
ejpam-3905	93	21	or	or	CCONJ
ejpam-3905	93	22	a.	a.	NOUN
ejpam-3905	93	23	noreldeen	noreldeen	PROPN
ejpam-3905	93	24	,	,	PUNCT
ejpam-3905	93	25	s.	s.	PROPN
ejpam-3905	93	26	abo	abo	VERB
ejpam-3905	93	27	quota	quota	PROPN
ejpam-3905	93	28	/	/	SYM
ejpam-3905	93	29	eur	eur	NOUN
ejpam-3905	93	30	.	.	PUNCT
ejpam-3905	94	1	j.	j.	PROPN
ejpam-3905	94	2	pure	pure	PROPN
ejpam-3905	94	3	appl	appl	PROPN
ejpam-3905	94	4	.	.	PROPN
ejpam-3905	94	5	math	math	PROPN
ejpam-3905	94	6	,	,	PUNCT
ejpam-3905	94	7	14	14	NUM
ejpam-3905	94	8	(	(	PUNCT
ejpam-3905	94	9	2	2	NUM
ejpam-3905	94	10	)	)	PUNCT
ejpam-3905	94	11	(	(	PUNCT
ejpam-3905	94	12	2021	2021	NUM
ejpam-3905	94	13	)	)	PUNCT
ejpam-3905	94	14	,	,	PUNCT
ejpam-3905	94	15	480	480	NUM
ejpam-3905	94	16	-	-	SYM
ejpam-3905	94	17	492	492	NUM
ejpam-3905	94	18	484	484	NUM
ejpam-3905	94	19	cofibration	cofibration	NOUN
ejpam-3905	94	20	is	be	AUX
ejpam-3905	94	21	individually	individually	ADV
ejpam-3905	94	22	a	a	DET
ejpam-3905	94	23	weak	weak	ADJ
ejpam-3905	94	24	equivalence	equivalence	NOUN
ejpam-3905	94	25	,	,	PUNCT
ejpam-3905	94	26	fibration	fibration	NOUN
ejpam-3905	94	27	,	,	PUNCT
ejpam-3905	94	28	or	or	CCONJ
ejpam-3905	94	29	cofibration	cofibration	NOUN
ejpam-3905	94	30	.	.	PUNCT
ejpam-3905	95	1	(	(	PUNCT
ejpam-3905	95	2	4	4	X
ejpam-3905	95	3	)	)	PUNCT
ejpam-3905	95	4	the	the	DET
ejpam-3905	95	5	following	follow	VERB
ejpam-3905	95	6	commuting	commute	VERB
ejpam-3905	95	7	arrow	arrow	NOUN
ejpam-3905	95	8	diagram	diagram	NOUN
ejpam-3905	95	9	a	a	DET
ejpam-3905	95	10	−→	−→	NOUN
ejpam-3905	95	11	x	x	PUNCT
ejpam-3905	95	12	i	i	PRON
ejpam-3905	95	13	↓	↓	PROPN
ejpam-3905	95	14	l	l	PROPN
ejpam-3905	95	15	↗	↗	PROPN
ejpam-3905	95	16	↓	↓	PROPN
ejpam-3905	96	1	p	p	X
ejpam-3905	96	2	b	b	PROPN
ejpam-3905	96	3	−→	−→	ADJ
ejpam-3905	96	4	y	y	PROPN
ejpam-3905	96	5	(	(	PUNCT
ejpam-3905	96	6	7	7	NUM
ejpam-3905	96	7	)	)	PUNCT
ejpam-3905	96	8	with	with	ADP
ejpam-3905	96	9	a	a	DET
ejpam-3905	96	10	cofibration	cofibration	NOUN
ejpam-3905	96	11	i	i	PRON
ejpam-3905	96	12	and	and	CCONJ
ejpam-3905	96	13	a	a	DET
ejpam-3905	96	14	fibration	fibration	NOUN
ejpam-3905	96	15	p	p	NOUN
ejpam-3905	96	16	,	,	PUNCT
ejpam-3905	96	17	if	if	SCONJ
ejpam-3905	96	18	i	i	PRON
ejpam-3905	96	19	or	or	CCONJ
ejpam-3905	96	20	p	p	NOUN
ejpam-3905	96	21	is	be	AUX
ejpam-3905	96	22	weak	weak	ADJ
ejpam-3905	96	23	equivalence	equivalence	NOUN
ejpam-3905	96	24	,	,	PUNCT
ejpam-3905	96	25	then	then	ADV
ejpam-3905	96	26	the	the	DET
ejpam-3905	96	27	lifting	lift	VERB
ejpam-3905	96	28	l	l	NOUN
ejpam-3905	96	29	exists	exist	VERB
ejpam-3905	96	30	making	make	VERB
ejpam-3905	96	31	both	both	DET
ejpam-3905	96	32	triangles	triangle	NOUN
ejpam-3905	96	33	commute	commute	NOUN
ejpam-3905	96	34	.	.	PUNCT
ejpam-3905	97	1	every	every	DET
ejpam-3905	97	2	morphism	morphism	NOUN
ejpam-3905	97	3	can	can	AUX
ejpam-3905	97	4	be	be	AUX
ejpam-3905	97	5	considered	consider	VERB
ejpam-3905	97	6	as	as	ADP
ejpam-3905	97	7	(	(	PUNCT
ejpam-3905	97	8	1	1	X
ejpam-3905	97	9	)	)	PUNCT
ejpam-3905	97	10	a	a	DET
ejpam-3905	97	11	cyclic	cyclic	ADJ
ejpam-3905	97	12	cofibration	cofibration	NOUN
ejpam-3905	97	13	taken	take	VERB
ejpam-3905	97	14	after	after	ADP
ejpam-3905	97	15	by	by	ADP
ejpam-3905	97	16	a	a	DET
ejpam-3905	97	17	fibration	fibration	NOUN
ejpam-3905	97	18	,	,	PUNCT
ejpam-3905	97	19	and	and	CCONJ
ejpam-3905	97	20	as	as	ADP
ejpam-3905	97	21	(	(	PUNCT
ejpam-3905	97	22	2	2	NUM
ejpam-3905	97	23	)	)	PUNCT
ejpam-3905	97	24	a	a	DET
ejpam-3905	97	25	cofibration	cofibration	NOUN
ejpam-3905	97	26	took	take	VERB
ejpam-3905	97	27	after	after	ADV
ejpam-3905	97	28	by	by	ADP
ejpam-3905	97	29	a	a	DET
ejpam-3905	97	30	cyclic	cyclic	ADJ
ejpam-3905	97	31	fibration	fibration	NOUN
ejpam-3905	97	32	.	.	PUNCT
ejpam-3905	98	1	definition	definition	NOUN
ejpam-3905	98	2	9	9	NUM
ejpam-3905	98	3	.	.	PUNCT
ejpam-3905	99	1	[	[	X
ejpam-3905	99	2	12	12	NUM
ejpam-3905	99	3	]	]	PUNCT
ejpam-3905	99	4	the	the	DET
ejpam-3905	99	5	morphisms	morphism	NOUN
ejpam-3905	99	6	(	(	PUNCT
ejpam-3905	99	7	w	w	PROPN
ejpam-3905	99	8	∩	∩	ADJ
ejpam-3905	99	9	fib	fib	NOUN
ejpam-3905	99	10	)	)	PUNCT
ejpam-3905	99	11	of	of	ADP
ejpam-3905	99	12	w	w	PROPN
ejpam-3905	99	13	are	be	AUX
ejpam-3905	99	14	called	call	VERB
ejpam-3905	99	15	trivial	trivial	ADJ
ejpam-3905	99	16	fibrations	fibration	NOUN
ejpam-3905	99	17	.	.	PUNCT
ejpam-3905	100	1	the	the	DET
ejpam-3905	100	2	morphisms	morphism	NOUN
ejpam-3905	100	3	in	in	ADP
ejpam-3905	100	4	(	(	PUNCT
ejpam-3905	100	5	w	w	PROPN
ejpam-3905	100	6	∩	∩	ADJ
ejpam-3905	100	7	c	c	NOUN
ejpam-3905	100	8	)	)	PUNCT
ejpam-3905	100	9	of	of	ADP
ejpam-3905	100	10	w	w	PROPN
ejpam-3905	100	11	called	call	VERB
ejpam-3905	100	12	trivial	trivial	ADJ
ejpam-3905	100	13	cofibrations	cofibration	NOUN
ejpam-3905	100	14	.	.	PUNCT
ejpam-3905	101	1	fibration	fibration	NOUN
ejpam-3905	101	2	involves	involve	VERB
ejpam-3905	101	3	the	the	DET
ejpam-3905	101	4	morphisms	morphism	NOUN
ejpam-3905	101	5	with	with	ADP
ejpam-3905	101	6	privilege	privilege	NOUN
ejpam-3905	101	7	lifting	lifting	NOUN
ejpam-3905	101	8	property	property	NOUN
ejpam-3905	101	9	for	for	ADP
ejpam-3905	101	10	any	any	DET
ejpam-3905	101	11	trivial	trivial	ADJ
ejpam-3905	101	12	cofibrations	cofibration	NOUN
ejpam-3905	101	13	and	and	CCONJ
ejpam-3905	101	14	complex	complex	ADJ
ejpam-3905	101	15	c	c	NOUN
ejpam-3905	101	16	of	of	ADP
ejpam-3905	101	17	the	the	DET
ejpam-3905	101	18	morphisms	morphism	NOUN
ejpam-3905	101	19	with	with	ADP
ejpam-3905	101	20	the	the	DET
ejpam-3905	101	21	left	left	ADJ
ejpam-3905	101	22	lifting	lift	VERB
ejpam-3905	101	23	property	property	NOUN
ejpam-3905	101	24	concerning	concern	VERB
ejpam-3905	101	25	all	all	DET
ejpam-3905	101	26	trivial	trivial	ADJ
ejpam-3905	101	27	fibration	fibration	NOUN
ejpam-3905	101	28	.	.	PUNCT
ejpam-3905	102	1	a	a	DET
ejpam-3905	102	2	left	left	ADJ
ejpam-3905	102	3	(	(	PUNCT
ejpam-3905	102	4	right	right	ADJ
ejpam-3905	102	5	)	)	PUNCT
ejpam-3905	102	6	legitimate	legitimate	ADJ
ejpam-3905	102	7	model	model	NOUN
ejpam-3905	102	8	class	class	NOUN
ejpam-3905	102	9	is	be	AUX
ejpam-3905	102	10	a	a	DET
ejpam-3905	102	11	one	one	NUM
ejpam-3905	102	12	where	where	SCONJ
ejpam-3905	102	13	the	the	DET
ejpam-3905	102	14	weak	weak	ADJ
ejpam-3905	102	15	equivalences	equivalence	NOUN
ejpam-3905	102	16	are	be	AUX
ejpam-3905	102	17	steady	steady	ADJ
ejpam-3905	102	18	under	under	ADP
ejpam-3905	102	19	push	push	NOUN
ejpam-3905	102	20	forward	forward	ADV
ejpam-3905	102	21	along	along	ADP
ejpam-3905	102	22	cofibrations	cofibration	NOUN
ejpam-3905	102	23	.	.	PUNCT
ejpam-3905	103	1	example	example	NOUN
ejpam-3905	104	1	2	2	NUM
ejpam-3905	104	2	.	.	PUNCT
ejpam-3905	105	1	[	[	X
ejpam-3905	105	2	11	11	NUM
ejpam-3905	105	3	]	]	PUNCT
ejpam-3905	105	4	the	the	DET
ejpam-3905	105	5	class	class	NOUN
ejpam-3905	105	6	on	on	ADP
ejpam-3905	105	7	the	the	DET
ejpam-3905	105	8	form	form	NOUN
ejpam-3905	105	9	c	c	NOUN
ejpam-3905	105	10	=	=	SYM
ejpam-3905	105	11	c+(moda	c+(moda	PROPN
ejpam-3905	105	12	)	)	PUNCT
ejpam-3905	105	13	of	of	ADP
ejpam-3905	105	14	the	the	DET
ejpam-3905	105	15	left	left	ADJ
ejpam-3905	105	16	bounded	bounded	ADJ
ejpam-3905	105	17	complex	complex	ADJ
ejpam-3905	105	18	·	·	PUNCT
ejpam-3905	105	19	·	·	PUNCT
ejpam-3905	105	20	·	·	PUNCT
ejpam-3905	106	1	−→	−→	NOUN
ejpam-3905	106	2	0	0	NUM
ejpam-3905	106	3	−→	−→	NOUN
ejpam-3905	106	4	·	·	PUNCT
ejpam-3905	106	5	·	·	PUNCT
ejpam-3905	106	6	·	·	PUNCT
ejpam-3905	107	1	−→	−→	NOUN
ejpam-3905	107	2	xp	xp	INTJ
ejpam-3905	107	3	−→	−→	NOUN
ejpam-3905	107	4	xp+1	xp+1	NOUN
ejpam-3905	107	5	−→	−→	NOUN
ejpam-3905	107	6	·	·	PUNCT
ejpam-3905	107	7	·	·	PUNCT
ejpam-3905	107	8	·	·	PUNCT
ejpam-3905	108	1	of	of	ADP
ejpam-3905	108	2	right	right	ADJ
ejpam-3905	108	3	modules	module	NOUN
ejpam-3905	108	4	over	over	ADP
ejpam-3905	108	5	the	the	DET
ejpam-3905	108	6	ring	ring	NOUN
ejpam-3905	108	7	a.	a.	NOUN
ejpam-3905	108	8	for	for	ADP
ejpam-3905	108	9	an	an	DET
ejpam-3905	108	10	arbitrary	arbitrary	ADJ
ejpam-3905	108	11	w	w	AUX
ejpam-3905	108	12	be	be	AUX
ejpam-3905	108	13	a	a	DET
ejpam-3905	108	14	class	class	NOUN
ejpam-3905	108	15	of	of	ADP
ejpam-3905	108	16	a	a	DET
ejpam-3905	108	17	semi	semi	NOUN
ejpam-3905	108	18	-	-	NOUN
ejpam-3905	108	19	isomorphisms	isomorphism	NOUN
ejpam-3905	108	20	c	c	NOUN
ejpam-3905	108	21	,	,	PUNCT
ejpam-3905	108	22	the	the	DET
ejpam-3905	108	23	set	set	NOUN
ejpam-3905	108	24	of	of	ADP
ejpam-3905	108	25	morphism	morphism	NOUN
ejpam-3905	108	26	i	i	PRON
ejpam-3905	108	27	:	:	PUNCT
ejpam-3905	108	28	x	x	X
ejpam-3905	108	29	−→	−→	NOUN
ejpam-3905	108	30	y	y	PROPN
ejpam-3905	108	31	,	,	PUNCT
ejpam-3905	108	32	∀	∀	VERB
ejpam-3905	108	33	in	in	ADP
ejpam-3905	108	34	,	,	PUNCT
ejpam-3905	108	35	n	n	PROPN
ejpam-3905	108	36	∈	∈	PROPN
ejpam-3905	108	37	z	z	NOUN
ejpam-3905	108	38	,	,	PUNCT
ejpam-3905	108	39	is	be	AUX
ejpam-3905	108	40	injective	injective	ADJ
ejpam-3905	108	41	and	and	CCONJ
ejpam-3905	108	42	fib	fib	NOUN
ejpam-3905	108	43	is	be	AUX
ejpam-3905	108	44	the	the	DET
ejpam-3905	108	45	set	set	NOUN
ejpam-3905	108	46	of	of	ADP
ejpam-3905	108	47	morphisms	morphism	NOUN
ejpam-3905	108	48	p	p	NOUN
ejpam-3905	108	49	:	:	PUNCT
ejpam-3905	108	50	x	x	PUNCT
ejpam-3905	108	51	−→	−→	NOUN
ejpam-3905	108	52	y	y	PROPN
ejpam-3905	108	53	with	with	ADP
ejpam-3905	108	54	morphism	morphism	PROPN
ejpam-3905	108	55	pn	pn	PROPN
ejpam-3905	108	56	,	,	PUNCT
ejpam-3905	108	57	n	n	PROPN
ejpam-3905	108	58	∈	∈	PROPN
ejpam-3905	108	59	z	z	NOUN
ejpam-3905	108	60	,	,	PUNCT
ejpam-3905	108	61	is	be	AUX
ejpam-3905	108	62	surjective	surjective	ADJ
ejpam-3905	108	63	.	.	PUNCT
ejpam-3905	109	1	from	from	ADP
ejpam-3905	109	2	[	[	X
ejpam-3905	109	3	10	10	NUM
ejpam-3905	109	4	]	]	PUNCT
ejpam-3905	109	5	,	,	PUNCT
ejpam-3905	109	6	we	we	PRON
ejpam-3905	109	7	get	get	VERB
ejpam-3905	109	8	c	c	NOUN
ejpam-3905	109	9	is	be	AUX
ejpam-3905	109	10	a	a	DET
ejpam-3905	109	11	model	model	NOUN
ejpam-3905	109	12	classification	classification	NOUN
ejpam-3905	109	13	.	.	PUNCT
ejpam-3905	110	1	since	since	SCONJ
ejpam-3905	110	2	c	c	PROPN
ejpam-3905	110	3	is	be	AUX
ejpam-3905	110	4	the	the	DET
ejpam-3905	110	5	underlying	underlying	ADJ
ejpam-3905	110	6	and	and	CCONJ
ejpam-3905	110	7	the	the	DET
ejpam-3905	110	8	terminal	terminal	ADJ
ejpam-3905	110	9	protest	protest	NOUN
ejpam-3905	110	10	,	,	PUNCT
ejpam-3905	110	11	consequently	consequently	ADV
ejpam-3905	110	12	the	the	DET
ejpam-3905	110	13	morphism	morphism	NOUN
ejpam-3905	110	14	0	0	NUM
ejpam-3905	110	15	−→	−→	NOUN
ejpam-3905	110	16	x	x	PUNCT
ejpam-3905	110	17	is	be	AUX
ejpam-3905	110	18	dependably	dependably	ADV
ejpam-3905	110	19	a	a	DET
ejpam-3905	110	20	cofibration	cofibration	NOUN
ejpam-3905	110	21	,	,	PUNCT
ejpam-3905	110	22	since	since	SCONJ
ejpam-3905	110	23	the	the	DET
ejpam-3905	110	24	morphism	morphism	NOUN
ejpam-3905	110	25	x	x	PUNCT
ejpam-3905	110	26	−→	−→	NOUN
ejpam-3905	110	27	0	0	NUM
ejpam-3905	110	28	is	be	AUX
ejpam-3905	110	29	fibration	fibration	PROPN
ejpam-3905	110	30	iff	iff	VERB
ejpam-3905	110	31	the	the	DET
ejpam-3905	110	32	all	all	DET
ejpam-3905	110	33	components	component	NOUN
ejpam-3905	110	34	x	x	SYM
ejpam-3905	110	35	n	n	CCONJ
ejpam-3905	110	36	,	,	PUNCT
ejpam-3905	110	37	n	n	PROPN
ejpam-3905	110	38	∈	∈	PROPN
ejpam-3905	110	39	z	z	NOUN
ejpam-3905	110	40	are	be	AUX
ejpam-3905	110	41	injective	injective	ADJ
ejpam-3905	110	42	x	x	SYM
ejpam-3905	110	43	−→	−→	ADJ
ejpam-3905	110	44	0	0	NUM
ejpam-3905	110	45	∼	∼	NOUN
ejpam-3905	110	46	↘	↘	PROPN
ejpam-3905	110	47	↗	↗	PROPN
ejpam-3905	110	48	i	i	PROPN
ejpam-3905	110	49	(	(	PUNCT
ejpam-3905	110	50	8)	8)	NUM
ejpam-3905	110	51	for	for	ADP
ejpam-3905	110	52	a	a	DET
ejpam-3905	110	53	self	self	NOUN
ejpam-3905	110	54	-	-	PUNCT
ejpam-3905	110	55	assertive	assertive	ADJ
ejpam-3905	110	56	class	class	NOUN
ejpam-3905	110	57	c	c	NOUN
ejpam-3905	110	58	,	,	PUNCT
ejpam-3905	110	59	an	an	DET
ejpam-3905	110	60	object	object	NOUN
ejpam-3905	110	61	x	x	PUNCT
ejpam-3905	110	62	is	be	AUX
ejpam-3905	110	63	fibrant	fibrant	ADJ
ejpam-3905	110	64	if	if	SCONJ
ejpam-3905	110	65	the	the	DET
ejpam-3905	110	66	morphism	morphism	NOUN
ejpam-3905	110	67	x	x	PUNCT
ejpam-3905	110	68	−→	−→	ADJ
ejpam-3905	110	69	∗	∗	NOUN
ejpam-3905	110	70	is	be	AUX
ejpam-3905	110	71	a	a	DET
ejpam-3905	110	72	fibration	fibration	NOUN
ejpam-3905	110	73	.	.	PUNCT
ejpam-3905	111	1	correspondingly	correspondingly	ADV
ejpam-3905	111	2	,	,	PUNCT
ejpam-3905	111	3	if	if	SCONJ
ejpam-3905	111	4	the	the	DET
ejpam-3905	111	5	morphism	morphism	NOUN
ejpam-3905	111	6	φ	φ	PROPN
ejpam-3905	111	7	−→	−→	PROPN
ejpam-3905	111	8	y	y	PROPN
ejpam-3905	111	9	is	be	AUX
ejpam-3905	111	10	a	a	DET
ejpam-3905	111	11	cofibration	cofibration	NOUN
ejpam-3905	111	12	,	,	PUNCT
ejpam-3905	111	13	then	then	ADV
ejpam-3905	111	14	the	the	DET
ejpam-3905	111	15	object	object	NOUN
ejpam-3905	111	16	y	y	PROPN
ejpam-3905	111	17	is	be	AUX
ejpam-3905	111	18	cofibrant	cofibrant	NOUN
ejpam-3905	111	19	.	.	PUNCT
ejpam-3905	112	1	all	all	DET
ejpam-3905	112	2	complexes	complex	NOUN
ejpam-3905	112	3	x	x	VERB
ejpam-3905	112	4	are	be	AUX
ejpam-3905	112	5	cofibrant	cofibrant	NOUN
ejpam-3905	112	6	and	and	CCONJ
ejpam-3905	112	7	a	a	DET
ejpam-3905	112	8	complex	complex	ADJ
ejpam-3905	112	9	y	y	NOUN
ejpam-3905	112	10	is	be	AUX
ejpam-3905	112	11	fibrant	fibrant	ADJ
ejpam-3905	112	12	if	if	SCONJ
ejpam-3905	112	13	and	and	CCONJ
ejpam-3905	112	14	only	only	ADV
ejpam-3905	112	15	if	if	SCONJ
ejpam-3905	112	16	it	it	PRON
ejpam-3905	112	17	has	have	VERB
ejpam-3905	112	18	injective	injective	ADJ
ejpam-3905	112	19	parts	part	NOUN
ejpam-3905	112	20	.	.	PUNCT
ejpam-3905	113	1	in	in	ADP
ejpam-3905	113	2	the	the	DET
ejpam-3905	113	3	following	following	ADJ
ejpam-3905	113	4	section	section	NOUN
ejpam-3905	113	5	,	,	PUNCT
ejpam-3905	113	6	we	we	PRON
ejpam-3905	113	7	study	study	VERB
ejpam-3905	113	8	the	the	DET
ejpam-3905	113	9	co	co	NOUN
ejpam-3905	113	10	-	-	NOUN
ejpam-3905	113	11	algebras	algebra	VERB
ejpam-3905	113	12	with	with	ADP
ejpam-3905	113	13	examples	example	NOUN
ejpam-3905	113	14	illustrated	illustrate	VERB
ejpam-3905	113	15	.	.	PUNCT
ejpam-3905	114	1	3	3	X
ejpam-3905	114	2	.	.	X
ejpam-3905	114	3	co	co	VERB
ejpam-3905	114	4	-	-	NOUN
ejpam-3905	114	5	algebras	algebra	NOUN
ejpam-3905	114	6	and	and	CCONJ
ejpam-3905	114	7	the	the	DET
ejpam-3905	114	8	cobar	cobar	NOUN
ejpam-3905	114	9	construction	construction	NOUN
ejpam-3905	114	10	in	in	ADP
ejpam-3905	114	11	this	this	DET
ejpam-3905	114	12	part	part	NOUN
ejpam-3905	114	13	,	,	PUNCT
ejpam-3905	114	14	we	we	PRON
ejpam-3905	114	15	recall	recall	VERB
ejpam-3905	114	16	the	the	DET
ejpam-3905	114	17	idea	idea	NOUN
ejpam-3905	114	18	of	of	ADP
ejpam-3905	114	19	co	co	NOUN
ejpam-3905	114	20	-	-	NOUN
ejpam-3905	114	21	algebras	algebra	NOUN
ejpam-3905	114	22	and	and	CCONJ
ejpam-3905	114	23	the	the	DET
ejpam-3905	114	24	bar	bar	NOUN
ejpam-3905	114	25	-	-	PUNCT
ejpam-3905	114	26	cobar	cobar	NOUN
ejpam-3905	114	27	construction	construction	NOUN
ejpam-3905	114	28	.	.	PUNCT
ejpam-3905	115	1	this	this	PRON
ejpam-3905	115	2	is	be	AUX
ejpam-3905	115	3	followed	follow	VERB
ejpam-3905	115	4	by	by	ADP
ejpam-3905	115	5	some	some	DET
ejpam-3905	115	6	relations	relation	NOUN
ejpam-3905	115	7	and	and	CCONJ
ejpam-3905	115	8	examples	example	NOUN
ejpam-3905	115	9	.	.	PUNCT
ejpam-3905	116	1	the	the	DET
ejpam-3905	116	2	fundamental	fundamental	ADJ
ejpam-3905	116	3	references	reference	NOUN
ejpam-3905	116	4	are	be	AUX
ejpam-3905	116	5	[	[	X
ejpam-3905	116	6	13],[5	13],[5	X
ejpam-3905	116	7	]	]	X
ejpam-3905	116	8	and	and	CCONJ
ejpam-3905	116	9	[	[	X
ejpam-3905	116	10	14	14	NUM
ejpam-3905	116	11	]	]	PUNCT
ejpam-3905	116	12	.	.	PUNCT
ejpam-3905	117	1	a.	a.	PROPN
ejpam-3905	117	2	noreldeen	noreldeen	PROPN
ejpam-3905	117	3	,	,	PUNCT
ejpam-3905	117	4	s.	s.	PROPN
ejpam-3905	117	5	abo	abo	VERB
ejpam-3905	117	6	quota	quota	PROPN
ejpam-3905	117	7	/	/	SYM
ejpam-3905	117	8	eur	eur	NOUN
ejpam-3905	117	9	.	.	PUNCT
ejpam-3905	118	1	j.	j.	PROPN
ejpam-3905	118	2	pure	pure	PROPN
ejpam-3905	118	3	appl	appl	PROPN
ejpam-3905	118	4	.	.	PROPN
ejpam-3905	118	5	math	math	PROPN
ejpam-3905	118	6	,	,	PUNCT
ejpam-3905	118	7	14	14	NUM
ejpam-3905	118	8	(	(	PUNCT
ejpam-3905	118	9	2	2	NUM
ejpam-3905	118	10	)	)	PUNCT
ejpam-3905	118	11	(	(	PUNCT
ejpam-3905	118	12	2021	2021	NUM
ejpam-3905	118	13	)	)	PUNCT
ejpam-3905	118	14	,	,	PUNCT
ejpam-3905	118	15	480	480	NUM
ejpam-3905	118	16	-	-	SYM
ejpam-3905	118	17	492	492	NUM
ejpam-3905	118	18	485	485	NUM
ejpam-3905	118	19	definition	definition	NOUN
ejpam-3905	118	20	10	10	NUM
ejpam-3905	118	21	.	.	PUNCT
ejpam-3905	119	1	an	an	DET
ejpam-3905	119	2	algebraic	algebraic	PROPN
ejpam-3905	119	3	operad	operad	PROPN
ejpam-3905	119	4	comprises	comprise	VERB
ejpam-3905	119	5	a	a	DET
ejpam-3905	119	6	gathering	gathering	NOUN
ejpam-3905	119	7	of	of	ADP
ejpam-3905	119	8	the	the	DET
ejpam-3905	119	9	chain	chain	NOUN
ejpam-3905	119	10	complexes	complex	NOUN
ejpam-3905	119	11	,	,	PUNCT
ejpam-3905	119	12	o(n	o(n	NOUN
ejpam-3905	119	13	)	)	PUNCT
ejpam-3905	119	14	,	,	PUNCT
ejpam-3905	119	15	n	n	X
ejpam-3905	119	16	≥	≥	NOUN
ejpam-3905	119	17	0	0	NUM
ejpam-3905	119	18	,	,	PUNCT
ejpam-3905	119	19	an	an	DET
ejpam-3905	119	20	accumulation	accumulation	NOUN
ejpam-3905	119	21	of	of	ADP
ejpam-3905	119	22	a	a	DET
ejpam-3905	119	23	chain	chain	NOUN
ejpam-3905	119	24	maps	map	NOUN
ejpam-3905	119	25	γ	γ	NOUN
ejpam-3905	119	26	:	:	PUNCT
ejpam-3905	119	27	o(k)⊗o(j1)⊗	o(k)⊗o(j1)⊗	PROPN
ejpam-3905	119	28	·	·	PUNCT
ejpam-3905	119	29	·	·	PUNCT
ejpam-3905	119	30	·	·	PUNCT
ejpam-3905	119	31	o(jk	o(jk	NUM
ejpam-3905	119	32	)	)	PUNCT
ejpam-3905	119	33	−→	−→	NOUN
ejpam-3905	119	34	o(j1	o(j1	NOUN
ejpam-3905	119	35	+	+	X
ejpam-3905	119	36	·	·	PUNCT
ejpam-3905	119	37	·	·	PUNCT
ejpam-3905	119	38	·	·	PUNCT
ejpam-3905	119	39	+	+	NUM
ejpam-3905	119	40	jk	jk	PROPN
ejpam-3905	119	41	)	)	PUNCT
ejpam-3905	119	42	(	(	PUNCT
ejpam-3905	119	43	9	9	X
ejpam-3905	119	44	)	)	PUNCT
ejpam-3905	119	45	an	an	DET
ejpam-3905	119	46	o	o	NOUN
ejpam-3905	119	47	-	-	NOUN
ejpam-3905	119	48	coalgebra	coalgebra	NOUN
ejpam-3905	119	49	is	be	AUX
ejpam-3905	119	50	a	a	DET
ejpam-3905	119	51	chain	chain	NOUN
ejpam-3905	119	52	complex	complex	NOUN
ejpam-3905	119	53	c	c	PROPN
ejpam-3905	119	54	together	together	ADV
ejpam-3905	119	55	with	with	ADP
ejpam-3905	119	56	chain	chain	NOUN
ejpam-3905	119	57	maps	map	NOUN
ejpam-3905	119	58	θ	θ	PROPN
ejpam-3905	119	59	:	:	PUNCT
ejpam-3905	119	60	o(j)⊗	o(j)⊗	NOUN
ejpam-3905	119	61	c	c	AUX
ejpam-3905	119	62	−→	−→	NOUN
ejpam-3905	119	63	cj	cj	NOUN
ejpam-3905	119	64	where	where	SCONJ
ejpam-3905	119	65	,	,	PUNCT
ejpam-3905	119	66	o	o	PROPN
ejpam-3905	119	67	is	be	AUX
ejpam-3905	119	68	an	an	DET
ejpam-3905	119	69	operad	operad	ADJ
ejpam-3905	119	70	,	,	PUNCT
ejpam-3905	119	71	fulfilling	fulfil	VERB
ejpam-3905	119	72	the	the	DET
ejpam-3905	119	73	conditions	condition	NOUN
ejpam-3905	119	74	;	;	PUNCT
ejpam-3905	119	75	(	(	PUNCT
ejpam-3905	119	76	i	i	NOUN
ejpam-3905	119	77	)	)	PUNCT
ejpam-3905	119	78	associativity	associativity	NOUN
ejpam-3905	119	79	:	:	PUNCT
ejpam-3905	119	80	for	for	ADP
ejpam-3905	119	81	∑k	∑k	PROPN
ejpam-3905	119	82	s=1	s=1	X
ejpam-3905	119	83	js	js	PROPN
ejpam-3905	119	84	=	=	SYM
ejpam-3905	119	85	j	j	PROPN
ejpam-3905	119	86	,	,	PUNCT
ejpam-3905	119	87	then	then	ADV
ejpam-3905	119	88	the	the	DET
ejpam-3905	119	89	diagram	diagram	NOUN
ejpam-3905	119	90	;	;	PUNCT
ejpam-3905	119	91	o(k)⊗o(j1)⊗	o(k)⊗o(j1)⊗	PROPN
ejpam-3905	119	92	·	·	PUNCT
ejpam-3905	119	93	·	·	PUNCT
ejpam-3905	119	94	·	·	PUNCT
ejpam-3905	119	95	o(jk)⊗	o(jk)⊗	NOUN
ejpam-3905	119	96	c	c	NOUN
ejpam-3905	119	97	γ⊗id	γ⊗id	NOUN
ejpam-3905	119	98	−→	−→	NOUN
ejpam-3905	119	99	o(j)⊗	o(j)⊗	NOUN
ejpam-3905	119	100	c	c	X
ejpam-3905	119	101	↓	↓	NOUN
ejpam-3905	119	102	θ	θ	PROPN
ejpam-3905	119	103	id⊗	id⊗	PROPN
ejpam-3905	119	104	θ	θ	PROPN
ejpam-3905	119	105	↓	↓	PROPN
ejpam-3905	119	106	cj	cj	PROPN
ejpam-3905	119	107	↑	↑	PROPN
ejpam-3905	119	108	θk	θk	PROPN
ejpam-3905	119	109	o(j1)⊗	o(j1)⊗	X
ejpam-3905	119	110	·	·	PUNCT
ejpam-3905	119	111	·	·	PUNCT
ejpam-3905	120	1	·	·	PUNCT
ejpam-3905	120	2	o(jk)⊗	o(jk)⊗	NOUN
ejpam-3905	120	3	ck	ck	INTJ
ejpam-3905	120	4	−→	−→	NOUN
ejpam-3905	120	5	shuffle	shuffle	NOUN
ejpam-3905	120	6	o(j1)⊗	o(j1)⊗	PROPN
ejpam-3905	120	7	·	·	PUNCT
ejpam-3905	120	8	·	·	PUNCT
ejpam-3905	120	9	·	·	PUNCT
ejpam-3905	120	10	o(jk)⊗	o(jk)⊗	PROPN
ejpam-3905	120	11	c	c	X
ejpam-3905	120	12	(	(	PUNCT
ejpam-3905	120	13	10	10	NUM
ejpam-3905	120	14	)	)	PUNCT
ejpam-3905	120	15	is	be	AUX
ejpam-3905	120	16	commutes	commute	NOUN
ejpam-3905	120	17	.	.	PUNCT
ejpam-3905	121	1	(	(	PUNCT
ejpam-3905	121	2	ii	ii	NOUN
ejpam-3905	121	3	)	)	PUNCT
ejpam-3905	121	4	unity	unity	NOUN
ejpam-3905	121	5	:	:	PUNCT
ejpam-3905	121	6	the	the	DET
ejpam-3905	121	7	accompanying	accompanying	ADJ
ejpam-3905	121	8	diagram	diagram	NOUN
ejpam-3905	121	9	commutes	commute	NOUN
ejpam-3905	121	10	:	:	PUNCT
ejpam-3905	121	11	r⊗	r⊗	NOUN
ejpam-3905	121	12	c	c	NOUN
ejpam-3905	121	13	∼=	∼=	PROPN
ejpam-3905	121	14	−→	−→	NOUN
ejpam-3905	121	15	c	c	NOUN
ejpam-3905	121	16	γ	γ	PROPN
ejpam-3905	121	17	⊗	⊗	PROPN
ejpam-3905	121	18	i	i	PROPN
ejpam-3905	121	19	d	d	PROPN
ejpam-3905	121	20	↓	↓	PROPN
ejpam-3905	121	21	↗	↗	PROPN
ejpam-3905	121	22	θ	θ	PROPN
ejpam-3905	121	23	o(1)⊗	o(1)⊗	PROPN
ejpam-3905	121	24	c	c	PROPN
ejpam-3905	122	1	(	(	PUNCT
ejpam-3905	122	2	11	11	NUM
ejpam-3905	122	3	)	)	PUNCT
ejpam-3905	122	4	(	(	PUNCT
ejpam-3905	122	5	iii	iii	X
ejpam-3905	122	6	)	)	PUNCT
ejpam-3905	122	7	equivariance	equivariance	NOUN
ejpam-3905	122	8	:	:	PUNCT
ejpam-3905	122	9	for	for	ADP
ejpam-3905	122	10	a	a	DET
ejpam-3905	122	11	discretionary	discretionary	ADJ
ejpam-3905	122	12	component	component	NOUN
ejpam-3905	122	13	σ	σ	PROPN
ejpam-3905	122	14	∈	∈	PROPN
ejpam-3905	122	15	σj	σj	NOUN
ejpam-3905	122	16	,	,	PUNCT
ejpam-3905	122	17	the	the	DET
ejpam-3905	122	18	accompanying	accompanying	ADJ
ejpam-3905	122	19	graph	graph	NOUN
ejpam-3905	122	20	commutes	commute	NOUN
ejpam-3905	122	21	:	:	PUNCT
ejpam-3905	122	22	o(j)⊗	o(j)⊗	NOUN
ejpam-3905	122	23	c	c	PART
ejpam-3905	122	24	σ⊗id	σ⊗id	NOUN
ejpam-3905	122	25	−→	−→	NOUN
ejpam-3905	122	26	o(j)⊗	o(j)⊗	NOUN
ejpam-3905	122	27	c	c	NOUN
ejpam-3905	122	28	θ	θ	NOUN
ejpam-3905	122	29	↓	↓	PROPN
ejpam-3905	122	30	↓	↓	PROPN
ejpam-3905	122	31	θ	θ	PROPN
ejpam-3905	122	32	cj	cj	X
ejpam-3905	122	33	−→	−→	PROPN
ejpam-3905	122	34	σ	σ	X
ejpam-3905	122	35	cj	cj	PROPN
ejpam-3905	123	1	(	(	PUNCT
ejpam-3905	123	2	12	12	NUM
ejpam-3905	123	3	)	)	PUNCT
ejpam-3905	123	4	the	the	DET
ejpam-3905	123	5	morphism	morphism	NOUN
ejpam-3905	123	6	in	in	ADP
ejpam-3905	123	7	o	o	PROPN
ejpam-3905	123	8	-	-	NOUN
ejpam-3905	123	9	coalgebras	coalgebra	NOUN
ejpam-3905	123	10	are	be	AUX
ejpam-3905	123	11	the	the	DET
ejpam-3905	123	12	map	map	NOUN
ejpam-3905	123	13	commuting	commute	VERB
ejpam-3905	123	14	strictly	strictly	ADV
ejpam-3905	123	15	with	with	ADP
ejpam-3905	123	16	the	the	DET
ejpam-3905	123	17	above	above	ADJ
ejpam-3905	123	18	structure	structure	NOUN
ejpam-3905	123	19	.	.	PUNCT
ejpam-3905	124	1	the	the	DET
ejpam-3905	124	2	class	class	NOUN
ejpam-3905	124	3	o	o	NOUN
ejpam-3905	124	4	-	-	NOUN
ejpam-3905	124	5	coalgebras	coalgebras	ADJ
ejpam-3905	124	6	will	will	AUX
ejpam-3905	124	7	be	be	AUX
ejpam-3905	124	8	referred	refer	VERB
ejpam-3905	124	9	to	to	ADP
ejpam-3905	124	10	by	by	ADP
ejpam-3905	124	11	coalgo	coalgo	NOUN
ejpam-3905	124	12	.	.	PUNCT
ejpam-3905	125	1	we	we	PRON
ejpam-3905	125	2	characterize	characterize	VERB
ejpam-3905	125	3	w	w	ADP
ejpam-3905	125	4	as	as	ADP
ejpam-3905	125	5	the	the	DET
ejpam-3905	125	6	class	class	NOUN
ejpam-3905	125	7	semi	semi	NOUN
ejpam-3905	125	8	-	-	NOUN
ejpam-3905	125	9	isomorphisms	isomorphism	NOUN
ejpam-3905	125	10	and	and	CCONJ
ejpam-3905	125	11	fib	fib	VERB
ejpam-3905	125	12	as	as	ADP
ejpam-3905	125	13	the	the	DET
ejpam-3905	125	14	arrangement	arrangement	NOUN
ejpam-3905	125	15	of	of	ADP
ejpam-3905	125	16	surjective	surjective	ADJ
ejpam-3905	125	17	morphisms	morphism	NOUN
ejpam-3905	125	18	.	.	PUNCT
ejpam-3905	126	1	consider	consider	VERB
ejpam-3905	126	2	(	(	PUNCT
ejpam-3905	126	3	c	c	NOUN
ejpam-3905	126	4	◦	◦	NOUN
ejpam-3905	126	5	f	f	X
ejpam-3905	126	6	)	)	PUNCT
ejpam-3905	126	7	as	as	ADP
ejpam-3905	126	8	the	the	DET
ejpam-3905	126	9	set	set	NOUN
ejpam-3905	126	10	of	of	ADP
ejpam-3905	126	11	morphisms	morphism	NOUN
ejpam-3905	126	12	i	i	PRON
ejpam-3905	126	13	to	to	ADP
ejpam-3905	126	14	such	such	DET
ejpam-3905	126	15	an	an	DET
ejpam-3905	126	16	extent	extent	NOUN
ejpam-3905	126	17	that	that	SCONJ
ejpam-3905	126	18	it	it	PRON
ejpam-3905	126	19	is	be	AUX
ejpam-3905	126	20	present	present	ADJ
ejpam-3905	126	21	in	in	ADP
ejpam-3905	126	22	each	each	DET
ejpam-3905	126	23	commutative	commutative	ADJ
ejpam-3905	126	24	square	square	NOUN
ejpam-3905	126	25	of	of	ADP
ejpam-3905	126	26	strong	strong	ADJ
ejpam-3905	126	27	bolts	bolt	NOUN
ejpam-3905	126	28	in	in	ADP
ejpam-3905	126	29	alg	alg	PROPN
ejpam-3905	126	30	.	.	PUNCT
ejpam-3905	127	1	definition	definition	NOUN
ejpam-3905	127	2	11	11	NUM
ejpam-3905	127	3	.	.	PUNCT
ejpam-3905	128	1	[	[	X
ejpam-3905	128	2	7	7	X
ejpam-3905	128	3	]	]	X
ejpam-3905	128	4	a	a	DET
ejpam-3905	128	5	graded	grade	VERB
ejpam-3905	128	6	coalgebra	coalgebra	NOUN
ejpam-3905	128	7	over	over	ADP
ejpam-3905	128	8	k	k	PROPN
ejpam-3905	128	9	is	be	AUX
ejpam-3905	128	10	graded	grade	VERB
ejpam-3905	128	11	k	k	NOUN
ejpam-3905	128	12	-	-	NOUN
ejpam-3905	128	13	module	module	NOUN
ejpam-3905	128	14	c	c	NOUN
ejpam-3905	128	15	with	with	ADP
ejpam-3905	128	16	a	a	DET
ejpam-3905	128	17	comultiplication	comultiplication	NOUN
ejpam-3905	128	18	of	of	ADP
ejpam-3905	128	19	degree	degree	NOUN
ejpam-3905	128	20	0	0	NUM
ejpam-3905	128	21	,	,	PUNCT
ejpam-3905	128	22	to	to	ADP
ejpam-3905	128	23	such	such	DET
ejpam-3905	128	24	an	an	DET
ejpam-3905	128	25	extent	extent	NOUN
ejpam-3905	128	26	that	that	SCONJ
ejpam-3905	128	27	the	the	DET
ejpam-3905	128	28	accompanying	accompanying	ADJ
ejpam-3905	128	29	diagram	diagram	NOUN
ejpam-3905	128	30	commutes	commute	NOUN
ejpam-3905	128	31	:	:	PUNCT
ejpam-3905	128	32	c	c	NOUN
ejpam-3905	128	33	4	4	NUM
ejpam-3905	128	34	−→	−→	NOUN
ejpam-3905	129	1	c	c	PROPN
ejpam-3905	129	2	⊗	⊗	PROPN
ejpam-3905	129	3	c	c	NOUN
ejpam-3905	129	4	4	4	NUM
ejpam-3905	129	5	↓	↓	NOUN
ejpam-3905	129	6	↓	↓	NOUN
ejpam-3905	129	7	4	4	NUM
ejpam-3905	129	8	c	c	NOUN
ejpam-3905	129	9	⊗	⊗	PROPN
ejpam-3905	129	10	c	c	PROPN
ejpam-3905	129	11	1⊗4	1⊗4	NUM
ejpam-3905	129	12	−→	−→	NOUN
ejpam-3905	130	1	c	c	PROPN
ejpam-3905	131	1	⊗	⊗	PROPN
ejpam-3905	131	2	c	c	PROPN
ejpam-3905	132	1	⊗	⊗	PROPN
ejpam-3905	132	2	c	c	PROPN
ejpam-3905	133	1	this	this	PRON
ejpam-3905	133	2	called	call	VERB
ejpam-3905	133	3	co	co	NOUN
ejpam-3905	133	4	-	-	NOUN
ejpam-3905	133	5	associativit	associativit	ADJ
ejpam-3905	133	6	a	a	DET
ejpam-3905	133	7	coderivation	coderivation	NOUN
ejpam-3905	133	8	on	on	ADP
ejpam-3905	133	9	co	co	NOUN
ejpam-3905	133	10	-	-	NOUN
ejpam-3905	133	11	algebra	algebra	ADJ
ejpam-3905	133	12	is	be	AUX
ejpam-3905	133	13	the	the	DET
ejpam-3905	133	14	map	map	NOUN
ejpam-3905	133	15	g	g	NOUN
ejpam-3905	133	16	:	:	PUNCT
ejpam-3905	133	17	c	c	AUX
ejpam-3905	133	18	−→	−→	NOUN
ejpam-3905	133	19	c	c	AUX
ejpam-3905	133	20	satisfying	satisfy	VERB
ejpam-3905	133	21	co	co	ADJ
ejpam-3905	133	22	-	-	ADJ
ejpam-3905	133	23	leibnizs	leibnizs	ADJ
ejpam-3905	133	24	rule	rule	NOUN
ejpam-3905	133	25	,	,	PUNCT
ejpam-3905	133	26	that	that	ADV
ejpam-3905	133	27	is	is	ADV
ejpam-3905	133	28	,	,	PUNCT
ejpam-3905	133	29	the	the	DET
ejpam-3905	133	30	accompanying	accompanying	ADJ
ejpam-3905	133	31	diagram	diagram	NOUN
ejpam-3905	133	32	commutes	commute	NOUN
ejpam-3905	133	33	:	:	PUNCT
ejpam-3905	133	34	a.	a.	NOUN
ejpam-3905	133	35	noreldeen	noreldeen	PROPN
ejpam-3905	133	36	,	,	PUNCT
ejpam-3905	133	37	s.	s.	PROPN
ejpam-3905	133	38	abo	abo	VERB
ejpam-3905	133	39	quota	quota	PROPN
ejpam-3905	133	40	/	/	SYM
ejpam-3905	133	41	eur	eur	NOUN
ejpam-3905	133	42	.	.	PUNCT
ejpam-3905	134	1	j.	j.	PROPN
ejpam-3905	134	2	pure	pure	PROPN
ejpam-3905	134	3	appl	appl	PROPN
ejpam-3905	134	4	.	.	PROPN
ejpam-3905	134	5	math	math	PROPN
ejpam-3905	134	6	,	,	PUNCT
ejpam-3905	134	7	14	14	NUM
ejpam-3905	134	8	(	(	PUNCT
ejpam-3905	134	9	2	2	NUM
ejpam-3905	134	10	)	)	PUNCT
ejpam-3905	134	11	(	(	PUNCT
ejpam-3905	134	12	2021	2021	NUM
ejpam-3905	134	13	)	)	PUNCT
ejpam-3905	134	14	,	,	PUNCT
ejpam-3905	134	15	480	480	NUM
ejpam-3905	134	16	-	-	SYM
ejpam-3905	134	17	492	492	NUM
ejpam-3905	134	18	486	486	NUM
ejpam-3905	134	19	c	c	NOUN
ejpam-3905	134	20	g	g	NOUN
ejpam-3905	134	21	−→	−→	NOUN
ejpam-3905	134	22	c	c	NOUN
ejpam-3905	134	23	4	4	NUM
ejpam-3905	134	24	↓	↓	NOUN
ejpam-3905	134	25	↓	↓	NOUN
ejpam-3905	134	26	4	4	NUM
ejpam-3905	134	27	c	c	NOUN
ejpam-3905	134	28	⊗	⊗	PROPN
ejpam-3905	134	29	c	c	NOUN
ejpam-3905	134	30	g⊗+1⊗g	g⊗+1⊗g	PROPN
ejpam-3905	134	31	−→	−→	ADV
ejpam-3905	134	32	c	c	PROPN
ejpam-3905	134	33	⊗	⊗	PROPN
ejpam-3905	134	34	c	c	PROPN
ejpam-3905	134	35	definition	definition	NOUN
ejpam-3905	134	36	12	12	NUM
ejpam-3905	134	37	.	.	PUNCT
ejpam-3905	135	1	[	[	X
ejpam-3905	135	2	4	4	X
ejpam-3905	135	3	]	]	X
ejpam-3905	135	4	a	a	DET
ejpam-3905	135	5	dg	dg	NOUN
ejpam-3905	135	6	-	-	PUNCT
ejpam-3905	135	7	coalgebra	coalgebra	NOUN
ejpam-3905	135	8	is	be	AUX
ejpam-3905	135	9	graded	grade	VERB
ejpam-3905	135	10	coalgebra	coalgebra	NOUN
ejpam-3905	135	11	with	with	ADP
ejpam-3905	135	12	co	co	NOUN
ejpam-3905	135	13	-	-	NOUN
ejpam-3905	135	14	derivation	derivation	ADJ
ejpam-3905	135	15	p	p	NOUN
ejpam-3905	135	16	:	:	PUNCT
ejpam-3905	135	17	c	c	AUX
ejpam-3905	135	18	−→	−→	NOUN
ejpam-3905	135	19	c	c	PROPN
ejpam-3905	135	20	of	of	ADP
ejpam-3905	135	21	degree	degree	NOUN
ejpam-3905	135	22	(	(	PUNCT
ejpam-3905	135	23	-1	-1	INTJ
ejpam-3905	135	24	)	)	PUNCT
ejpam-3905	135	25	such	such	ADJ
ejpam-3905	135	26	that	that	SCONJ
ejpam-3905	135	27	,	,	PUNCT
ejpam-3905	135	28	p	p	NOUN
ejpam-3905	135	29	2	2	NUM
ejpam-3905	135	30	=	=	SYM
ejpam-3905	135	31	0	0	PROPN
ejpam-3905	135	32	.	.	NOUN
ejpam-3905	135	33	example	example	NOUN
ejpam-3905	136	1	3	3	X
ejpam-3905	136	2	.	.	PUNCT
ejpam-3905	137	1	the	the	DET
ejpam-3905	137	2	fundamental	fundamental	ADJ
ejpam-3905	137	3	cause	cause	NOUN
ejpam-3905	137	4	of	of	ADP
ejpam-3905	137	5	an	an	DET
ejpam-3905	137	6	evaluated	evaluate	VERB
ejpam-3905	137	7	graded	grade	VERB
ejpam-3905	137	8	co	co	NOUN
ejpam-3905	137	9	-	-	NOUN
ejpam-3905	137	10	algebra	algebra	NOUN
ejpam-3905	137	11	is	be	AUX
ejpam-3905	137	12	co	co	ADJ
ejpam-3905	137	13	-	-	NOUN
ejpam-3905	137	14	tensor	tensor	ADJ
ejpam-3905	137	15	coalgebra	coalgebra	NOUN
ejpam-3905	137	16	of	of	ADP
ejpam-3905	137	17	graded	grade	VERB
ejpam-3905	137	18	k	k	NOUN
ejpam-3905	137	19	-	-	NOUN
ejpam-3905	137	20	module	module	NOUN
ejpam-3905	137	21	:	:	PUNCT
ejpam-3905	137	22	t	t	PROPN
ejpam-3905	137	23	(	(	PUNCT
ejpam-3905	137	24	v	v	NOUN
ejpam-3905	137	25	)	)	PUNCT
ejpam-3905	137	26	=	=	PUNCT
ejpam-3905	138	1	∞∑	∞∑	NUM
ejpam-3905	138	2	n=0	n=0	NUM
ejpam-3905	138	3	v	v	NUM
ejpam-3905	138	4	⊗n	⊗n	NOUN
ejpam-3905	138	5	(	(	PUNCT
ejpam-3905	138	6	13	13	NUM
ejpam-3905	138	7	)	)	PUNCT
ejpam-3905	138	8	the	the	DET
ejpam-3905	138	9	co	co	NOUN
ejpam-3905	138	10	-	-	NOUN
ejpam-3905	138	11	multiplication	multiplication	NOUN
ejpam-3905	138	12	is	be	AUX
ejpam-3905	138	13	formed	form	VERB
ejpam-3905	138	14	as	as	ADP
ejpam-3905	138	15	;	;	PUNCT
ejpam-3905	138	16	4(v1	4(v1	NUM
ejpam-3905	138	17	,	,	PUNCT
ejpam-3905	138	18	·	·	PUNCT
ejpam-3905	138	19	·	·	PUNCT
ejpam-3905	138	20	·	·	PUNCT
ejpam-3905	138	21	,	,	PUNCT
ejpam-3905	138	22	vn	vn	X
ejpam-3905	138	23	)	)	PUNCT
ejpam-3905	139	1	=	=	SYM
ejpam-3905	139	2	n∑	n∑	PROPN
ejpam-3905	139	3	i=0	i=0	PROPN
ejpam-3905	139	4	⊗(vi+1	⊗(vi+1	PROPN
ejpam-3905	139	5	,	,	PUNCT
ejpam-3905	139	6	·	·	PUNCT
ejpam-3905	139	7	·	·	PUNCT
ejpam-3905	139	8	·	·	PUNCT
ejpam-3905	139	9	,	,	PUNCT
ejpam-3905	139	10	vn	vn	PROPN
ejpam-3905	139	11	)	)	PUNCT
ejpam-3905	139	12	(	(	PUNCT
ejpam-3905	139	13	14	14	NUM
ejpam-3905	139	14	)	)	PUNCT
ejpam-3905	139	15	since	since	SCONJ
ejpam-3905	139	16	(	(	PUNCT
ejpam-3905	139	17	v1	v1	NOUN
ejpam-3905	139	18	,	,	PUNCT
ejpam-3905	139	19	·	·	PUNCT
ejpam-3905	139	20	·	·	PUNCT
ejpam-3905	139	21	·	·	PUNCT
ejpam-3905	139	22	,	,	PUNCT
ejpam-3905	139	23	vn	vn	PROPN
ejpam-3905	139	24	)	)	PUNCT
ejpam-3905	139	25	stands	stand	VERB
ejpam-3905	139	26	for	for	ADP
ejpam-3905	139	27	v1	v1	PROPN
ejpam-3905	139	28	⊗	⊗	PROPN
ejpam-3905	139	29	·	·	PUNCT
ejpam-3905	139	30	·	·	PUNCT
ejpam-3905	139	31	·	·	PUNCT
ejpam-3905	140	1	⊗	⊗	NUM
ejpam-3905	140	2	vn	vn	PROPN
ejpam-3905	140	3	.	.	PUNCT
ejpam-3905	141	1	so	so	ADV
ejpam-3905	141	2	,	,	PUNCT
ejpam-3905	141	3	for	for	ADP
ejpam-3905	141	4	every	every	PRON
ejpam-3905	141	5	graded	grade	VERB
ejpam-3905	141	6	co	co	NOUN
ejpam-3905	141	7	-	-	NOUN
ejpam-3905	141	8	algebra	algebra	ADJ
ejpam-3905	141	9	c	c	NOUN
ejpam-3905	141	10	and	and	CCONJ
ejpam-3905	141	11	the	the	DET
ejpam-3905	141	12	linear	linear	ADJ
ejpam-3905	141	13	map	map	NOUN
ejpam-3905	141	14	c	c	AUX
ejpam-3905	141	15	−→	−→	NOUN
ejpam-3905	141	16	v	v	NOUN
ejpam-3905	141	17	,	,	PUNCT
ejpam-3905	141	18	there	there	PRON
ejpam-3905	141	19	is	be	VERB
ejpam-3905	141	20	one	one	NUM
ejpam-3905	141	21	of	of	ADP
ejpam-3905	141	22	a	a	DET
ejpam-3905	141	23	kind	kind	ADJ
ejpam-3905	141	24	expansion	expansion	NOUN
ejpam-3905	141	25	to	to	ADP
ejpam-3905	141	26	co	co	VERB
ejpam-3905	141	27	-	-	NOUN
ejpam-3905	141	28	algebra	algebra	ADJ
ejpam-3905	141	29	map	map	NOUN
ejpam-3905	141	30	c	c	PROPN
ejpam-3905	141	31	−→	−→	NOUN
ejpam-3905	141	32	t	t	PROPN
ejpam-3905	141	33	(	(	PUNCT
ejpam-3905	141	34	v	v	NOUN
ejpam-3905	141	35	)	)	PUNCT
ejpam-3905	141	36	with	with	ADP
ejpam-3905	141	37	the	the	DET
ejpam-3905	141	38	end	end	NOUN
ejpam-3905	141	39	goal	goal	NOUN
ejpam-3905	141	40	that	that	SCONJ
ejpam-3905	141	41	the	the	DET
ejpam-3905	141	42	diagram	diagram	NOUN
ejpam-3905	141	43	;	;	PUNCT
ejpam-3905	141	44	c	c	PROPN
ejpam-3905	141	45	−→	−→	NOUN
ejpam-3905	141	46	t	t	PROPN
ejpam-3905	141	47	(	(	PUNCT
ejpam-3905	141	48	v	v	NOUN
ejpam-3905	141	49	)	)	PUNCT
ejpam-3905	141	50	↓	↓	NOUN
ejpam-3905	141	51	↓	↓	PROPN
ejpam-3905	141	52	v	v	PROPN
ejpam-3905	141	53	=	=	SYM
ejpam-3905	141	54	v	v	NOUN
ejpam-3905	141	55	is	be	AUX
ejpam-3905	141	56	commutes	commute	NOUN
ejpam-3905	141	57	.	.	PUNCT
ejpam-3905	142	1	definition	definition	NOUN
ejpam-3905	142	2	13	13	NUM
ejpam-3905	142	3	.	.	PUNCT
ejpam-3905	143	1	[	[	X
ejpam-3905	143	2	12	12	NUM
ejpam-3905	143	3	]	]	PUNCT
ejpam-3905	143	4	a	a	DET
ejpam-3905	143	5	co	co	NOUN
ejpam-3905	143	6	-	-	NOUN
ejpam-3905	143	7	algebra	algebra	ADJ
ejpam-3905	143	8	c	c	NOUN
ejpam-3905	143	9	is	be	AUX
ejpam-3905	143	10	a	a	DET
ejpam-3905	143	11	co	co	NOUN
ejpam-3905	143	12	-	-	NOUN
ejpam-3905	143	13	complete	complete	ADJ
ejpam-3905	143	14	if	if	SCONJ
ejpam-3905	143	15	the	the	DET
ejpam-3905	143	16	union	union	NOUN
ejpam-3905	143	17	of	of	ADP
ejpam-3905	143	18	the	the	DET
ejpam-3905	143	19	compositions	composition	NOUN
ejpam-3905	143	20	of	of	ADP
ejpam-3905	143	21	the	the	DET
ejpam-3905	143	22	canonical	canonical	ADJ
ejpam-3905	143	23	projection	projection	NOUN
ejpam-3905	143	24	as	as	SCONJ
ejpam-3905	143	25	the	the	DET
ejpam-3905	143	26	kernel	kernel	NOUN
ejpam-3905	143	27	’s	’s	PART
ejpam-3905	143	28	maps	map	NOUN
ejpam-3905	143	29	c	c	AUX
ejpam-3905	143	30	−→	−→	VERB
ejpam-3905	143	31	c⊗n	c⊗n	NOUN
ejpam-3905	143	32	−→	−→	NOUN
ejpam-3905	143	33	(	(	PUNCT
ejpam-3905	143	34	ck	ck	NOUN
ejpam-3905	143	35	)	)	PUNCT
ejpam-3905	143	36	⊗n	⊗n	NOUN
ejpam-3905	143	37	,	,	PUNCT
ejpam-3905	143	38	n	n	PRON
ejpam-3905	143	39	≥	≥	NOUN
ejpam-3905	143	40	2	2	NUM
ejpam-3905	143	41	with	with	ADP
ejpam-3905	143	42	the	the	DET
ejpam-3905	143	43	iterated	iterated	ADJ
ejpam-3905	143	44	co	co	NOUN
ejpam-3905	143	45	-	-	NOUN
ejpam-3905	143	46	multiplication	multiplication	NOUN
ejpam-3905	143	47	.	.	PUNCT
ejpam-3905	144	1	definition	definition	NOUN
ejpam-3905	144	2	14	14	NUM
ejpam-3905	144	3	.	.	PUNCT
ejpam-3905	145	1	[	[	X
ejpam-3905	145	2	11	11	NUM
ejpam-3905	145	3	]	]	PUNCT
ejpam-3905	145	4	for	for	ADP
ejpam-3905	145	5	the	the	DET
ejpam-3905	145	6	nth	nth	NOUN
ejpam-3905	145	7	complex	complex	ADJ
ejpam-3905	145	8	hom•k(c	hom•k(c	NOUN
ejpam-3905	145	9	,	,	PUNCT
ejpam-3905	145	10	a	a	PRON
ejpam-3905	145	11	)	)	PUNCT
ejpam-3905	145	12	is	be	AUX
ejpam-3905	145	13	n	n	PRON
ejpam-3905	145	14	degree	degree	NOUN
ejpam-3905	145	15	space	space	NOUN
ejpam-3905	145	16	of	of	ADP
ejpam-3905	145	17	homogeneous	homogeneous	ADJ
ejpam-3905	145	18	k	k	ADJ
ejpam-3905	145	19	-	-	PUNCT
ejpam-3905	145	20	linear	linear	PROPN
ejpam-3905	145	21	maps	map	NOUN
ejpam-3905	145	22	f	f	X
ejpam-3905	145	23	:	:	PUNCT
ejpam-3905	145	24	c	c	AUX
ejpam-3905	145	25	−→	−→	ADV
ejpam-3905	145	26	a	a	DET
ejpam-3905	145	27	and	and	CCONJ
ejpam-3905	145	28	differential	differential	ADJ
ejpam-3905	145	29	maps	map	NOUN
ejpam-3905	145	30	f	f	PROPN
ejpam-3905	145	31	to	to	PART
ejpam-3905	145	32	(	(	PUNCT
ejpam-3905	145	33	d	d	PART
ejpam-3905	145	34	◦	◦	NOUN
ejpam-3905	145	35	f	f	X
ejpam-3905	146	1	−	−	PROPN
ejpam-3905	146	2	(	(	PUNCT
ejpam-3905	146	3	−1)nf	−1)nf	NUM
ejpam-3905	146	4	◦	◦	NOUN
ejpam-3905	146	5	d	d	NOUN
ejpam-3905	146	6	)	)	PUNCT
ejpam-3905	146	7	.	.	PUNCT
ejpam-3905	147	1	this	this	DET
ejpam-3905	147	2	complex	complex	ADJ
ejpam-3905	147	3	turns	turn	VERB
ejpam-3905	147	4	into	into	ADP
ejpam-3905	147	5	a	a	DET
ejpam-3905	147	6	differential	differential	NOUN
ejpam-3905	147	7	graded	grade	VERB
ejpam-3905	147	8	algebra	algebra	NOUN
ejpam-3905	147	9	for	for	ADP
ejpam-3905	147	10	the	the	DET
ejpam-3905	147	11	convolution	convolution	NOUN
ejpam-3905	147	12	characterized	characterize	VERB
ejpam-3905	147	13	by	by	ADP
ejpam-3905	147	14	;	;	PUNCT
ejpam-3905	147	15	f	f	PROPN
ejpam-3905	147	16	∗	∗	NOUN
ejpam-3905	147	17	g	g	PROPN
ejpam-3905	147	18	=	=	SYM
ejpam-3905	147	19	µ	µ	X
ejpam-3905	147	20	◦	◦	NOUN
ejpam-3905	147	21	(	(	PUNCT
ejpam-3905	147	22	f	f	PROPN
ejpam-3905	147	23	⊗	⊗	PROPN
ejpam-3905	147	24	g	g	NOUN
ejpam-3905	147	25	)	)	PUNCT
ejpam-3905	147	26	◦	◦	NOUN
ejpam-3905	147	27	4	4	NUM
ejpam-3905	147	28	the	the	DET
ejpam-3905	147	29	maps	map	NOUN
ejpam-3905	147	30	τ	τ	X
ejpam-3905	147	31	:	:	PUNCT
ejpam-3905	147	32	c	c	AUX
ejpam-3905	147	33	−→	−→	ADV
ejpam-3905	147	34	a	a	PRON
ejpam-3905	147	35	,	,	PUNCT
ejpam-3905	147	36	which	which	PRON
ejpam-3905	147	37	is	be	AUX
ejpam-3905	147	38	homogeneous	homogeneous	ADJ
ejpam-3905	147	39	k	k	NOUN
ejpam-3905	147	40	-	-	NOUN
ejpam-3905	147	41	linear	linear	NOUN
ejpam-3905	147	42	of	of	ADP
ejpam-3905	147	43	degree	degree	NOUN
ejpam-3905	147	44	1	1	NUM
ejpam-3905	147	45	,	,	PUNCT
ejpam-3905	147	46	is	be	AUX
ejpam-3905	147	47	twisting	twist	VERB
ejpam-3905	147	48	cochain	cochain	NOUN
ejpam-3905	147	49	if	if	SCONJ
ejpam-3905	147	50	it	it	PRON
ejpam-3905	147	51	is	be	AUX
ejpam-3905	147	52	homogeneous	homogeneous	ADJ
ejpam-3905	147	53	and	and	CCONJ
ejpam-3905	147	54	fulfills	fulfill	VERB
ejpam-3905	147	55	d(τ	d(τ	PROPN
ejpam-3905	147	56	)	)	PUNCT
ejpam-3905	147	57	+	+	CCONJ
ejpam-3905	148	1	τ	τ	PROPN
ejpam-3905	148	2	∗	∗	NOUN
ejpam-3905	148	3	τ	τ	X
ejpam-3905	148	4	=	=	SYM
ejpam-3905	148	5	0	0	PROPN
ejpam-3905	148	6	,	,	PUNCT
ejpam-3905	148	7	ε	ε	PROPN
ejpam-3905	148	8	◦	◦	NOUN
ejpam-3905	148	9	τ	τ	PUNCT
ejpam-3905	148	10	◦	◦	NOUN
ejpam-3905	148	11	ε	ε	PROPN
ejpam-3905	148	12	=	=	SYM
ejpam-3905	148	13	0	0	NUM
ejpam-3905	148	14	(	(	PUNCT
ejpam-3905	148	15	15	15	NUM
ejpam-3905	148	16	)	)	PUNCT
ejpam-3905	148	17	a.	a.	NOUN
ejpam-3905	148	18	noreldeen	noreldeen	PROPN
ejpam-3905	148	19	,	,	PUNCT
ejpam-3905	148	20	s.	s.	PROPN
ejpam-3905	148	21	abo	abo	VERB
ejpam-3905	148	22	quota	quota	PROPN
ejpam-3905	148	23	/	/	SYM
ejpam-3905	148	24	eur	eur	NOUN
ejpam-3905	148	25	.	.	PUNCT
ejpam-3905	149	1	j.	j.	PROPN
ejpam-3905	149	2	pure	pure	PROPN
ejpam-3905	149	3	appl	appl	PROPN
ejpam-3905	149	4	.	.	PROPN
ejpam-3905	149	5	math	math	PROPN
ejpam-3905	149	6	,	,	PUNCT
ejpam-3905	149	7	14	14	NUM
ejpam-3905	149	8	(	(	PUNCT
ejpam-3905	149	9	2	2	NUM
ejpam-3905	149	10	)	)	PUNCT
ejpam-3905	149	11	(	(	PUNCT
ejpam-3905	149	12	2021	2021	NUM
ejpam-3905	149	13	)	)	PUNCT
ejpam-3905	149	14	,	,	PUNCT
ejpam-3905	149	15	480	480	NUM
ejpam-3905	149	16	-	-	SYM
ejpam-3905	149	17	492	492	NUM
ejpam-3905	149	18	487	487	NUM
ejpam-3905	149	19	proposition	proposition	NOUN
ejpam-3905	149	20	4	4	NUM
ejpam-3905	149	21	.	.	PUNCT
ejpam-3905	150	1	[	[	X
ejpam-3905	150	2	14	14	NUM
ejpam-3905	150	3	]	]	X
ejpam-3905	150	4	define	define	NOUN
ejpam-3905	150	5	tw(c	tw(c	PUNCT
ejpam-3905	150	6	,	,	PUNCT
ejpam-3905	150	7	a	a	PRON
ejpam-3905	150	8	)	)	PUNCT
ejpam-3905	150	9	a	a	DET
ejpam-3905	150	10	class	class	NOUN
ejpam-3905	150	11	of	of	ADP
ejpam-3905	150	12	the	the	DET
ejpam-3905	150	13	twisting	twisting	NOUN
ejpam-3905	150	14	cochains	cochain	NOUN
ejpam-3905	150	15	.	.	PUNCT
ejpam-3905	151	1	then	then	ADV
ejpam-3905	151	2	for	for	ADP
ejpam-3905	151	3	a	a	DET
ejpam-3905	151	4	∈	∈	PROPN
ejpam-3905	151	5	alg	alg	PROPN
ejpam-3905	151	6	,	,	PUNCT
ejpam-3905	151	7	the	the	DET
ejpam-3905	151	8	functor	functor	PROPN
ejpam-3905	151	9	c	c	PROPN
ejpam-3905	151	10	◦	◦	NOUN
ejpam-3905	151	11	g	g	NOUN
ejpam-3905	151	12	−→	−→	NOUN
ejpam-3905	151	13	sets	set	NOUN
ejpam-3905	151	14	,	,	PUNCT
ejpam-3905	151	15	c	c	PROPN
ejpam-3905	151	16	7−→	7−→	NUM
ejpam-3905	151	17	tw(c	tw(c	PUNCT
ejpam-3905	151	18	,	,	PUNCT
ejpam-3905	151	19	a	a	PRON
ejpam-3905	151	20	)	)	PUNCT
ejpam-3905	151	21	is	be	AUX
ejpam-3905	151	22	representable	representable	ADJ
ejpam-3905	151	23	.	.	PUNCT
ejpam-3905	152	1	in	in	ADP
ejpam-3905	152	2	the	the	DET
ejpam-3905	152	3	following	following	ADJ
ejpam-3905	152	4	section	section	NOUN
ejpam-3905	152	5	,	,	PUNCT
ejpam-3905	152	6	we	we	PRON
ejpam-3905	152	7	study	study	VERB
ejpam-3905	152	8	the	the	DET
ejpam-3905	152	9	relation	relation	NOUN
ejpam-3905	152	10	and	and	CCONJ
ejpam-3905	152	11	morphisms	morphism	NOUN
ejpam-3905	152	12	in	in	ADP
ejpam-3905	152	13	e∞-algebra	e∞-algebra	NOUN
ejpam-3905	152	14	and	and	CCONJ
ejpam-3905	152	15	we	we	PRON
ejpam-3905	152	16	introduce	introduce	VERB
ejpam-3905	152	17	the	the	DET
ejpam-3905	152	18	definition	definition	NOUN
ejpam-3905	152	19	of	of	ADP
ejpam-3905	152	20	massy	massy	ADJ
ejpam-3905	152	21	sequence	sequence	NOUN
ejpam-3905	152	22	and	and	CCONJ
ejpam-3905	152	23	massy	massy	ADJ
ejpam-3905	152	24	product	product	NOUN
ejpam-3905	152	25	.	.	PUNCT
ejpam-3905	153	1	4	4	X
ejpam-3905	153	2	.	.	X
ejpam-3905	153	3	basic	basic	ADJ
ejpam-3905	153	4	statement	statement	NOUN
ejpam-3905	153	5	on	on	ADP
ejpam-3905	153	6	e	e	NOUN
ejpam-3905	153	7	-	-	NOUN
ejpam-3905	153	8	infinity	infinity	ADJ
ejpam-3905	153	9	algebras	algebra	NOUN
ejpam-3905	153	10	in	in	ADP
ejpam-3905	153	11	the	the	DET
ejpam-3905	153	12	current	current	ADJ
ejpam-3905	153	13	part	part	NOUN
ejpam-3905	153	14	,	,	PUNCT
ejpam-3905	153	15	we	we	PRON
ejpam-3905	153	16	consider	consider	VERB
ejpam-3905	153	17	the	the	DET
ejpam-3905	153	18	fundamental	fundamental	ADJ
ejpam-3905	153	19	relations	relation	NOUN
ejpam-3905	153	20	in	in	ADP
ejpam-3905	153	21	the	the	DET
ejpam-3905	153	22	e∞-modules	e∞-module	NOUN
ejpam-3905	153	23	.	.	PUNCT
ejpam-3905	154	1	the	the	DET
ejpam-3905	154	2	augmented	augment	VERB
ejpam-3905	154	3	e∞-algebra	e∞-algebra	NOUN
ejpam-3905	154	4	is	be	AUX
ejpam-3905	154	5	equipped	equip	VERB
ejpam-3905	154	6	with	with	ADP
ejpam-3905	154	7	morphism	morphism	NOUN
ejpam-3905	154	8	ε	ε	PROPN
ejpam-3905	154	9	:	:	PUNCT
ejpam-3905	154	10	a	a	DET
ejpam-3905	154	11	−→	−→	NOUN
ejpam-3905	154	12	k.	k.	NOUN
ejpam-3905	154	13	definition	definition	NOUN
ejpam-3905	154	14	15	15	NUM
ejpam-3905	154	15	.	.	PUNCT
ejpam-3905	155	1	[	[	X
ejpam-3905	155	2	13	13	NUM
ejpam-3905	155	3	]	]	PUNCT
ejpam-3905	155	4	the	the	DET
ejpam-3905	155	5	complex	complex	ADJ
ejpam-3905	155	6	h•k(c	h•k(c	NOUN
ejpam-3905	155	7	,	,	PUNCT
ejpam-3905	155	8	a	a	PRON
ejpam-3905	155	9	)	)	PUNCT
ejpam-3905	155	10	becomes	become	VERB
ejpam-3905	155	11	an	an	DET
ejpam-3905	155	12	augmented	augment	VERB
ejpam-3905	155	13	e∞-algebra	e∞-algebra	NOUN
ejpam-3905	155	14	for	for	ADP
ejpam-3905	155	15	the	the	DET
ejpam-3905	155	16	convolution	convolution	NOUN
ejpam-3905	155	17	operation	operation	NOUN
ejpam-3905	155	18	;	;	PUNCT
ejpam-3905	155	19	bn(g1	bn(g1	X
ejpam-3905	155	20	,	,	PUNCT
ejpam-3905	155	21	·	·	PUNCT
ejpam-3905	155	22	·	·	PUNCT
ejpam-3905	155	23	·	·	PUNCT
ejpam-3905	155	24	,	,	PUNCT
ejpam-3905	155	25	gn	gn	PROPN
ejpam-3905	155	26	)	)	PUNCT
ejpam-3905	155	27	=	=	PUNCT
ejpam-3905	155	28	ban	ban	NOUN
ejpam-3905	155	29	◦	◦	NOUN
ejpam-3905	155	30	(	(	PUNCT
ejpam-3905	155	31	g1	g1	PROPN
ejpam-3905	155	32	⊗	⊗	PROPN
ejpam-3905	155	33	·	·	PUNCT
ejpam-3905	155	34	·	·	PUNCT
ejpam-3905	155	35	·	·	PUNCT
ejpam-3905	156	1	⊗	⊗	NUM
ejpam-3905	156	2	g)n	g)n	NOUN
ejpam-3905	156	3	)	)	PUNCT
ejpam-3905	156	4	◦	◦	NOUN
ejpam-3905	156	5	4(n	4(n	NUM
ejpam-3905	156	6	)	)	PUNCT
ejpam-3905	156	7	(	(	PUNCT
ejpam-3905	156	8	16	16	NUM
ejpam-3905	156	9	)	)	PUNCT
ejpam-3905	156	10	where	where	SCONJ
ejpam-3905	156	11	,	,	PUNCT
ejpam-3905	156	12	4(n	4(n	NUM
ejpam-3905	156	13	)	)	PUNCT
ejpam-3905	156	14	is	be	AUX
ejpam-3905	156	15	iterate	iterate	NOUN
ejpam-3905	156	16	of	of	ADP
ejpam-3905	156	17	taking	take	VERB
ejpam-3905	156	18	values	value	NOUN
ejpam-3905	156	19	in	in	ADP
ejpam-3905	156	20	⊗n	⊗n	PROPN
ejpam-3905	156	21	for	for	ADP
ejpam-3905	156	22	a	a	DET
ejpam-3905	156	23	coalgebra	coalgebra	NOUN
ejpam-3905	156	24	∈	∈	PROPN
ejpam-3905	156	25	◦	◦	NOUN
ejpam-3905	156	26	g	g	NOUN
ejpam-3905	156	27	and	and	CCONJ
ejpam-3905	156	28	an	an	DET
ejpam-3905	156	29	augmented	augment	VERB
ejpam-3905	156	30	∞-algebra	∞-algebra	NOUN
ejpam-3905	156	31	a.	a.	NOUN
ejpam-3905	156	32	let	let	VERB
ejpam-3905	156	33	∞	∞	PROPN
ejpam-3905	156	34	(	(	PUNCT
ejpam-3905	156	35	,	,	PUNCT
ejpam-3905	156	36	a	a	PRON
ejpam-3905	156	37	)	)	PUNCT
ejpam-3905	156	38	be	be	AUX
ejpam-3905	156	39	the	the	DET
ejpam-3905	156	40	arrangement	arrangement	NOUN
ejpam-3905	156	41	of	of	ADP
ejpam-3905	156	42	all	all	DET
ejpam-3905	156	43	arrangement	arrangement	NOUN
ejpam-3905	156	44	of	of	ADP
ejpam-3905	156	45	the	the	DET
ejpam-3905	156	46	”	"	PUNCT
ejpam-3905	156	47	maurer	maurer	NOUN
ejpam-3905	156	48	-	-	PUNCT
ejpam-3905	156	49	cartan	cartan	PROPN
ejpam-3905	156	50	equation”,∑	equation”,∑	PROPN
ejpam-3905	156	51	n≥1	n≥1	NOUN
ejpam-3905	156	52	bn(τ	bn(τ	PUNCT
ejpam-3905	156	53	,	,	PUNCT
ejpam-3905	156	54	·	·	PUNCT
ejpam-3905	156	55	·	·	PUNCT
ejpam-3905	156	56	·	·	PUNCT
ejpam-3905	156	57	,	,	PUNCT
ejpam-3905	156	58	τ	τ	X
ejpam-3905	156	59	)	)	PUNCT
ejpam-3905	156	60	=	=	SYM
ejpam-3905	157	1	0	0	NUM
ejpam-3905	157	2	proposition	proposition	NOUN
ejpam-3905	157	3	5	5	NUM
ejpam-3905	157	4	.	.	PUNCT
ejpam-3905	158	1	[	[	X
ejpam-3905	158	2	2	2	NUM
ejpam-3905	158	3	]	]	PUNCT
ejpam-3905	158	4	b∞a	b∞a	NOUN
ejpam-3905	158	5	is	be	AUX
ejpam-3905	158	6	t	t	NOUN
ejpam-3905	158	7	c(sa	c(sa	PROPN
ejpam-3905	158	8	)	)	PUNCT
ejpam-3905	158	9	enriched	enrich	VERB
ejpam-3905	158	10	with	with	ADP
ejpam-3905	158	11	the	the	DET
ejpam-3905	158	12	one	one	NUM
ejpam-3905	158	13	of	of	ADP
ejpam-3905	158	14	a	a	DET
ejpam-3905	158	15	kind	kind	ADJ
ejpam-3905	158	16	co	co	NOUN
ejpam-3905	158	17	-	-	NOUN
ejpam-3905	158	18	derivation	derivation	NOUN
ejpam-3905	158	19	whose	whose	DET
ejpam-3905	158	20	composition	composition	NOUN
ejpam-3905	158	21	with	with	ADP
ejpam-3905	158	22	a	a	DET
ejpam-3905	158	23	basic	basic	ADJ
ejpam-3905	158	24	projection	projection	NOUN
ejpam-3905	158	25	ba	ba	PROPN
ejpam-3905	158	26	↓	↓	PROPN
ejpam-3905	158	27	sa	sa	PROPN
ejpam-3905	158	28	has	have	VERB
ejpam-3905	158	29	the	the	DET
ejpam-3905	158	30	segments	segment	NOUN
ejpam-3905	158	31	bn	bn	INTJ
ejpam-3905	158	32	:	:	PUNCT
ejpam-3905	158	33	(	(	PUNCT
ejpam-3905	158	34	sa)⊗n	sa)⊗n	X
ejpam-3905	158	35	−→	−→	PROPN
ejpam-3905	158	36	sa	sa	PROPN
ejpam-3905	158	37	,	,	PUNCT
ejpam-3905	158	38	n	n	X
ejpam-3905	158	39	≥	≥	NUM
ejpam-3905	158	40	1	1	NUM
ejpam-3905	158	41	(	(	PUNCT
ejpam-3905	158	42	17	17	NUM
ejpam-3905	158	43	)	)	PUNCT
ejpam-3905	158	44	example	example	NOUN
ejpam-3905	158	45	4	4	NUM
ejpam-3905	158	46	.	.	PUNCT
ejpam-3905	159	1	let	let	VERB
ejpam-3905	159	2	a	a	DET
ejpam-3905	159	3	=	=	NOUN
ejpam-3905	159	4	tv	tv	NOUN
ejpam-3905	159	5	,	,	PUNCT
ejpam-3905	159	6	where	where	SCONJ
ejpam-3905	159	7	v	v	AUX
ejpam-3905	159	8	=	=	SYM
ejpam-3905	159	9	k	k	PROPN
ejpam-3905	159	10	is	be	AUX
ejpam-3905	159	11	concentrated	concentrate	VERB
ejpam-3905	159	12	with	with	ADP
ejpam-3905	159	13	degree	degree	NOUN
ejpam-3905	159	14	1	1	NUM
ejpam-3905	159	15	.	.	PUNCT
ejpam-3905	159	16	endow	endow	VERB
ejpam-3905	159	17	a	a	PRON
ejpam-3905	159	18	with	with	ADP
ejpam-3905	159	19	the	the	DET
ejpam-3905	159	20	novel	novel	ADJ
ejpam-3905	159	21	differential	differential	NOUN
ejpam-3905	159	22	whose	whose	DET
ejpam-3905	159	23	confinement	confinement	NOUN
ejpam-3905	159	24	to	to	ADP
ejpam-3905	159	25	v	v	PROPN
ejpam-3905	159	26	⊂	⊂	PROPN
ejpam-3905	159	27	tv	tv	NOUN
ejpam-3905	159	28	is	be	AUX
ejpam-3905	159	29	v	v	NOUN
ejpam-3905	159	30	=	=	SYM
ejpam-3905	159	31	k∼−→k	k∼−→k	NOUN
ejpam-3905	160	1	⊗	⊗	PROPN
ejpam-3905	160	2	k	k	PROPN
ejpam-3905	160	3	=	=	PUNCT
ejpam-3905	160	4	v	v	X
ejpam-3905	160	5	⊗2	⊗2	NUM
ejpam-3905	160	6	⊂	⊂	PROPN
ejpam-3905	160	7	tv	tv	NOUN
ejpam-3905	160	8	(	(	PUNCT
ejpam-3905	160	9	18	18	NUM
ejpam-3905	160	10	)	)	PUNCT
ejpam-3905	160	11	then	then	ADV
ejpam-3905	160	12	a	a	PRON
ejpam-3905	160	13	is	be	AUX
ejpam-3905	160	14	the	the	DET
ejpam-3905	160	15	semi	semi	ADJ
ejpam-3905	160	16	isomorphic	isomorphic	ADJ
ejpam-3905	160	17	to	to	ADP
ejpam-3905	160	18	its	its	PRON
ejpam-3905	160	19	sub	sub	NOUN
ejpam-3905	160	20	-	-	NOUN
ejpam-3905	160	21	algebra	algebra	ADJ
ejpam-3905	160	22	k	k	NOUN
ejpam-3905	160	23	,	,	PUNCT
ejpam-3905	160	24	which	which	PRON
ejpam-3905	160	25	is	be	AUX
ejpam-3905	160	26	fibrant	fibrant	ADJ
ejpam-3905	160	27	-	-	PUNCT
ejpam-3905	160	28	cofibrant	cofibrant	NOUN
ejpam-3905	160	29	.	.	PUNCT
ejpam-3905	161	1	if	if	SCONJ
ejpam-3905	161	2	a	a	PRON
ejpam-3905	161	3	was	be	AUX
ejpam-3905	161	4	fibrant	fibrant	NOUN
ejpam-3905	161	5	-	-	PUNCT
ejpam-3905	161	6	cofibrant	cofibrant	NOUN
ejpam-3905	161	7	,	,	PUNCT
ejpam-3905	161	8	then	then	ADV
ejpam-3905	161	9	the	the	DET
ejpam-3905	161	10	inclusion	inclusion	NOUN
ejpam-3905	161	11	k	k	PROPN
ejpam-3905	161	12	−→	−→	ADJ
ejpam-3905	161	13	tv	tv	NOUN
ejpam-3905	161	14	should	should	AUX
ejpam-3905	161	15	admit	admit	VERB
ejpam-3905	161	16	a	a	DET
ejpam-3905	161	17	left	left	ADJ
ejpam-3905	161	18	inverse	inverse	NOUN
ejpam-3905	161	19	up	up	ADP
ejpam-3905	161	20	to	to	PART
ejpam-3905	161	21	homotopy	homotopy	VERB
ejpam-3905	161	22	in	in	ADP
ejpam-3905	161	23	the	the	DET
ejpam-3905	161	24	feeling	feeling	NOUN
ejpam-3905	161	25	of	of	ADP
ejpam-3905	161	26	c.	c.	NOUN
ejpam-3905	161	27	since	since	SCONJ
ejpam-3905	161	28	there	there	PRON
ejpam-3905	161	29	are	be	VERB
ejpam-3905	161	30	non	non	ADJ
ejpam-3905	161	31	-	-	ADJ
ejpam-3905	161	32	zero	zero	NUM
ejpam-3905	161	33	maps	map	NOUN
ejpam-3905	161	34	h	h	NOUN
ejpam-3905	161	35	:	:	PUNCT
ejpam-3905	161	36	a	a	DET
ejpam-3905	161	37	−→	−→	NOUN
ejpam-3905	161	38	k	k	X
ejpam-3905	161	39	with	with	ADP
ejpam-3905	161	40	degree	degree	NOUN
ejpam-3905	161	41	-1	-1	PUNCT
ejpam-3905	161	42	such	such	ADJ
ejpam-3905	161	43	that	that	DET
ejpam-3905	161	44	ε	ε	PROPN
ejpam-3905	161	45	◦	◦	NOUN
ejpam-3905	161	46	h	h	NOUN
ejpam-3905	161	47	=	=	SYM
ejpam-3905	161	48	0	0	NUM
ejpam-3905	161	49	,	,	PUNCT
ejpam-3905	161	50	then	then	ADV
ejpam-3905	161	51	a	a	PRON
ejpam-3905	161	52	can	can	AUX
ejpam-3905	161	53	not	not	PART
ejpam-3905	161	54	be	be	AUX
ejpam-3905	161	55	fibrant	fibrant	ADJ
ejpam-3905	161	56	or	or	CCONJ
ejpam-3905	161	57	cofibrant	cofibrant	NOUN
ejpam-3905	161	58	,	,	PUNCT
ejpam-3905	161	59	since	since	SCONJ
ejpam-3905	161	60	a	a	PRON
ejpam-3905	161	61	is	be	AUX
ejpam-3905	161	62	the	the	DET
ejpam-3905	161	63	cobra	cobra	NOUN
ejpam-3905	161	64	construction	construction	NOUN
ejpam-3905	161	65	on	on	ADP
ejpam-3905	161	66	a	a	DET
ejpam-3905	161	67	non	non	ADJ
ejpam-3905	161	68	-	-	ADJ
ejpam-3905	161	69	complete	complete	ADJ
ejpam-3905	161	70	dg	dg	NOUN
ejpam-3905	161	71	-	-	PUNCT
ejpam-3905	161	72	coalgebra	coalgebra	NOUN
ejpam-3905	161	73	.	.	PUNCT
ejpam-3905	162	1	definition	definition	NOUN
ejpam-3905	162	2	16	16	NUM
ejpam-3905	162	3	.	.	PUNCT
ejpam-3905	163	1	a	a	DET
ejpam-3905	163	2	c	c	NOUN
ejpam-3905	163	3	-	-	PUNCT
ejpam-3905	163	4	comodule	comodule	NOUN
ejpam-3905	163	5	is	be	AUX
ejpam-3905	163	6	a	a	DET
ejpam-3905	163	7	chain	chain	NOUN
ejpam-3905	163	8	complex	complex	NOUN
ejpam-3905	163	9	d	d	PROPN
ejpam-3905	163	10	together	together	ADV
ejpam-3905	163	11	with	with	ADP
ejpam-3905	163	12	chains	chain	NOUN
ejpam-3905	163	13	maps	map	NOUN
ejpam-3905	163	14	,	,	PUNCT
ejpam-3905	163	15	λ	λ	X
ejpam-3905	163	16	:	:	PUNCT
ejpam-3905	163	17	o(j)⊗	o(j)⊗	NOUN
ejpam-3905	164	1	d	d	X
ejpam-3905	164	2	−→	−→	NOUN
ejpam-3905	164	3	d	d	PROPN
ejpam-3905	164	4	⊗	⊗	PROPN
ejpam-3905	164	5	cj−1	cj−1	NOUN
ejpam-3905	164	6	for	for	ADP
ejpam-3905	164	7	o	o	PROPN
ejpam-3905	164	8	is	be	AUX
ejpam-3905	164	9	an	an	DET
ejpam-3905	164	10	operad	operad	NOUN
ejpam-3905	164	11	and	and	CCONJ
ejpam-3905	164	12	c	c	PROPN
ejpam-3905	164	13	is	be	AUX
ejpam-3905	164	14	an	an	DET
ejpam-3905	164	15	o	o	NOUN
ejpam-3905	164	16	-	-	NOUN
ejpam-3905	164	17	coalgebra	coalgebra	NOUN
ejpam-3905	164	18	,	,	PUNCT
ejpam-3905	164	19	fulfilling	fulfil	VERB
ejpam-3905	164	20	the	the	DET
ejpam-3905	164	21	conditions	condition	NOUN
ejpam-3905	164	22	:	:	PUNCT
ejpam-3905	164	23	(	(	PUNCT
ejpam-3905	164	24	i	i	NOUN
ejpam-3905	164	25	)	)	PUNCT
ejpam-3905	164	26	associativity	associativity	NOUN
ejpam-3905	164	27	:	:	PUNCT
ejpam-3905	164	28	∑k	∑k	PROPN
ejpam-3905	165	1	s=1	s=1	X
ejpam-3905	165	2	js	js	PROPN
ejpam-3905	165	3	=	=	SYM
ejpam-3905	165	4	j	j	PROPN
ejpam-3905	165	5	,	,	PUNCT
ejpam-3905	165	6	and	and	CCONJ
ejpam-3905	165	7	a.	a.	PROPN
ejpam-3905	165	8	noreldeen	noreldeen	PROPN
ejpam-3905	165	9	,	,	PUNCT
ejpam-3905	165	10	s.	s.	PROPN
ejpam-3905	165	11	abo	abo	VERB
ejpam-3905	165	12	quota	quota	PROPN
ejpam-3905	165	13	/	/	SYM
ejpam-3905	165	14	eur	eur	NOUN
ejpam-3905	165	15	.	.	PUNCT
ejpam-3905	166	1	j.	j.	PROPN
ejpam-3905	166	2	pure	pure	PROPN
ejpam-3905	166	3	appl	appl	PROPN
ejpam-3905	166	4	.	.	PROPN
ejpam-3905	166	5	math	math	PROPN
ejpam-3905	166	6	,	,	PUNCT
ejpam-3905	166	7	14	14	NUM
ejpam-3905	166	8	(	(	PUNCT
ejpam-3905	166	9	2	2	NUM
ejpam-3905	166	10	)	)	PUNCT
ejpam-3905	166	11	(	(	PUNCT
ejpam-3905	166	12	2021	2021	NUM
ejpam-3905	166	13	)	)	PUNCT
ejpam-3905	166	14	,	,	PUNCT
ejpam-3905	166	15	480	480	NUM
ejpam-3905	166	16	-	-	SYM
ejpam-3905	166	17	492	492	NUM
ejpam-3905	166	18	488	488	NUM
ejpam-3905	166	19	o(k)⊗o(j1)⊗	o(k)⊗o(j1)⊗	PROPN
ejpam-3905	166	20	·	·	PUNCT
ejpam-3905	166	21	·	·	PUNCT
ejpam-3905	167	1	·	·	PUNCT
ejpam-3905	167	2	o(jk)⊗d	o(jk)⊗d	NOUN
ejpam-3905	167	3	γ⊗id	γ⊗id	NOUN
ejpam-3905	167	4	−→	−→	NOUN
ejpam-3905	167	5	o(j)⊗	o(j)⊗	NOUN
ejpam-3905	167	6	c	c	X
ejpam-3905	167	7	↓	↓	NOUN
ejpam-3905	167	8	θ	θ	X
ejpam-3905	168	1	id⊗	id⊗	PROPN
ejpam-3905	168	2	λ	λ	PROPN
ejpam-3905	168	3	↓	↓	PROPN
ejpam-3905	169	1	d	d	PROPN
ejpam-3905	169	2	⊗	⊗	PROPN
ejpam-3905	169	3	cj−1	cj−1	PROPN
ejpam-3905	169	4	↑	↑	PROPN
ejpam-3905	169	5	λ⊗	λ⊗	VERB
ejpam-3905	169	6	θk−1	θk−1	NOUN
ejpam-3905	169	7	o(j1)⊗	o(j1)⊗	X
ejpam-3905	169	8	·	·	PUNCT
ejpam-3905	169	9	·	·	PUNCT
ejpam-3905	169	10	·	·	PUNCT
ejpam-3905	169	11	o(jk)⊗d	o(jk)⊗d	NOUN
ejpam-3905	169	12	⊗	⊗	ADJ
ejpam-3905	169	13	ck−1	ck−1	PROPN
ejpam-3905	169	14	−→	−→	NOUN
ejpam-3905	169	15	shuffle	shuffle	NOUN
ejpam-3905	169	16	o(j1)⊗d	o(j1)⊗d	NOUN
ejpam-3905	169	17	⊗	⊗	PROPN
ejpam-3905	169	18	·	·	PUNCT
ejpam-3905	169	19	·	·	PUNCT
ejpam-3905	169	20	·	·	PUNCT
ejpam-3905	169	21	o(jk)⊗	o(jk)⊗	NOUN
ejpam-3905	169	22	c	c	NOUN
ejpam-3905	169	23	is	be	AUX
ejpam-3905	169	24	commutes	commute	NOUN
ejpam-3905	169	25	.	.	PUNCT
ejpam-3905	170	1	(	(	PUNCT
ejpam-3905	170	2	ii	ii	NOUN
ejpam-3905	170	3	)	)	PUNCT
ejpam-3905	170	4	unity	unity	NOUN
ejpam-3905	170	5	:	:	PUNCT
ejpam-3905	170	6	the	the	DET
ejpam-3905	170	7	accompanying	accompanying	ADJ
ejpam-3905	170	8	outline	outline	NOUN
ejpam-3905	170	9	commutes	commute	NOUN
ejpam-3905	170	10	:	:	PUNCT
ejpam-3905	170	11	r⊗d	r⊗d	NOUN
ejpam-3905	170	12	∼=	∼=	PART
ejpam-3905	170	13	−→	−→	NOUN
ejpam-3905	170	14	d	d	X
ejpam-3905	170	15	γ	γ	X
ejpam-3905	170	16	⊗	⊗	PROPN
ejpam-3905	170	17	i	i	PROPN
ejpam-3905	170	18	d	d	PROPN
ejpam-3905	170	19	↓	↓	PROPN
ejpam-3905	170	20	↗	↗	PROPN
ejpam-3905	170	21	θ	θ	PROPN
ejpam-3905	170	22	o(1)⊗d	o(1)⊗d	NOUN
ejpam-3905	170	23	(	(	PUNCT
ejpam-3905	170	24	iii	iii	NOUN
ejpam-3905	170	25	)	)	PUNCT
ejpam-3905	170	26	equivariance	equivariance	NOUN
ejpam-3905	170	27	:	:	PUNCT
ejpam-3905	170	28	let	let	VERB
ejpam-3905	170	29	σ	σ	X
ejpam-3905	170	30	∈	∈	PROPN
ejpam-3905	170	31	σj	σj	VERB
ejpam-3905	170	32	−	−	PROPN
ejpam-3905	170	33	1	1	NUM
ejpam-3905	170	34	⊂	⊂	PRON
ejpam-3905	170	35	σj	σj	ADJ
ejpam-3905	170	36	,	,	PUNCT
ejpam-3905	170	37	then	then	ADV
ejpam-3905	170	38	the	the	DET
ejpam-3905	170	39	accompanying	accompanying	ADJ
ejpam-3905	170	40	outline	outline	NOUN
ejpam-3905	170	41	is	be	AUX
ejpam-3905	170	42	a	a	DET
ejpam-3905	170	43	commute	commute	NOUN
ejpam-3905	170	44	:	:	PUNCT
ejpam-3905	170	45	o(j)⊗d	o(j)⊗d	NUM
ejpam-3905	170	46	σ⊗id	σ⊗id	NOUN
ejpam-3905	170	47	−→	−→	NOUN
ejpam-3905	171	1	o(j)⊗d	o(j)⊗d	NUM
ejpam-3905	171	2	θ	θ	NOUN
ejpam-3905	171	3	↓	↓	NOUN
ejpam-3905	172	1	↓	↓	PROPN
ejpam-3905	172	2	θ	θ	PROPN
ejpam-3905	172	3	d	d	PROPN
ejpam-3905	172	4	⊗	⊗	PROPN
ejpam-3905	172	5	cj−1	cj−1	PROPN
ejpam-3905	172	6	−→	−→	NOUN
ejpam-3905	172	7	id⊗σ	id⊗σ	NOUN
ejpam-3905	172	8	d	d	PROPN
ejpam-3905	172	9	⊗	⊗	PROPN
ejpam-3905	172	10	cj−1	cj−1	VERB
ejpam-3905	172	11	a	a	DET
ejpam-3905	172	12	morphism	morphism	NOUN
ejpam-3905	172	13	in	in	ADP
ejpam-3905	172	14	c	c	NOUN
ejpam-3905	172	15	-	-	PUNCT
ejpam-3905	172	16	comodules	comodule	NOUN
ejpam-3905	172	17	is	be	AUX
ejpam-3905	172	18	a	a	DET
ejpam-3905	172	19	homeomorphism	homeomorphism	NOUN
ejpam-3905	172	20	of	of	ADP
ejpam-3905	172	21	abelian	abelian	ADJ
ejpam-3905	172	22	groups	group	NOUN
ejpam-3905	172	23	commuting	commute	VERB
ejpam-3905	172	24	with	with	ADP
ejpam-3905	172	25	the	the	DET
ejpam-3905	172	26	above	above	ADJ
ejpam-3905	172	27	structure	structure	NOUN
ejpam-3905	172	28	,	,	PUNCT
ejpam-3905	172	29	see	see	VERB
ejpam-3905	172	30	[	[	X
ejpam-3905	172	31	10	10	NUM
ejpam-3905	172	32	]	]	PUNCT
ejpam-3905	172	33	.	.	PUNCT
ejpam-3905	173	1	definition	definition	NOUN
ejpam-3905	173	2	17	17	NUM
ejpam-3905	173	3	.	.	PUNCT
ejpam-3905	174	1	for	for	ADP
ejpam-3905	174	2	all	all	DET
ejpam-3905	174	3	classes	class	NOUN
ejpam-3905	174	4	of	of	ADP
ejpam-3905	174	5	all	all	DET
ejpam-3905	174	6	right	right	ADJ
ejpam-3905	174	7	dga	dga	NOUN
ejpam-3905	174	8	-	-	PUNCT
ejpam-3905	174	9	modules	module	NOUN
ejpam-3905	174	10	and	and	CCONJ
ejpam-3905	174	11	category	category	NOUN
ejpam-3905	174	12	dg	dg	PART
ejpam-3905	174	13	−c	−c	NOUN
ejpam-3905	174	14	-	-	PUNCT
ejpam-3905	174	15	comodules	comodule	NOUN
ejpam-3905	174	16	m	m	VERB
ejpam-3905	174	17	.	.	PUNCT
ejpam-3905	175	1	then	then	ADV
ejpam-3905	175	2	m	m	PROPN
ejpam-3905	175	3	is	be	AUX
ejpam-3905	175	4	co	co	ADJ
ejpam-3905	175	5	-	-	NOUN
ejpam-3905	175	6	complete	complete	ADJ
ejpam-3905	175	7	,	,	PUNCT
ejpam-3905	175	8	m	m	VERB
ejpam-3905	175	9	−→m	−→m	ADJ
ejpam-3905	175	10	⊗	⊗	NUM
ejpam-3905	175	11	c̄⊗n	c̄⊗n	NOUN
ejpam-3905	175	12	,	,	PUNCT
ejpam-3905	175	13	n	n	PRON
ejpam-3905	175	14	≥	≥	NOUN
ejpam-3905	175	15	2	2	NUM
ejpam-3905	175	16	.	.	PUNCT
ejpam-3905	176	1	then	then	ADV
ejpam-3905	176	2	the	the	DET
ejpam-3905	176	3	match	match	NOUN
ejpam-3905	176	4	moda	moda	PROPN
ejpam-3905	176	5	!	!	PUNCT
ejpam-3905	177	1	⊗τ	⊗τ	PROPN
ejpam-3905	177	2	a	a	DET
ejpam-3905	177	3	↑↓	↑↓	X
ejpam-3905	177	4	!	!	PUNCT
ejpam-3905	178	1	⊗τ	⊗τ	PROPN
ejpam-3905	178	2	c	c	PROPN
ejpam-3905	178	3	comcc	comcc	PROPN
ejpam-3905	178	4	is	be	AUX
ejpam-3905	178	5	a	a	DET
ejpam-3905	178	6	couple	couple	NOUN
ejpam-3905	178	7	of	of	ADP
ejpam-3905	178	8	adjoint	adjoint	PROPN
ejpam-3905	178	9	functors	functor	NOUN
ejpam-3905	178	10	.	.	PUNCT
ejpam-3905	179	1	theorem	theorem	NOUN
ejpam-3905	179	2	3	3	NUM
ejpam-3905	179	3	.	.	PUNCT
ejpam-3905	179	4	.	.	PUNCT
ejpam-3905	180	1	(	(	PUNCT
ejpam-3905	180	2	i	i	NOUN
ejpam-3905	180	3	)	)	PUNCT
ejpam-3905	180	4	the	the	DET
ejpam-3905	180	5	category	category	NOUN
ejpam-3905	180	6	comcc	comcc	NOUN
ejpam-3905	180	7	concedes	concede	VERB
ejpam-3905	180	8	to	to	ADP
ejpam-3905	180	9	a	a	DET
ejpam-3905	180	10	special	special	ADJ
ejpam-3905	180	11	structure	structure	NOUN
ejpam-3905	180	12	of	of	ADP
ejpam-3905	180	13	model	model	NOUN
ejpam-3905	180	14	category	category	NOUN
ejpam-3905	180	15	whose	whose	DET
ejpam-3905	180	16	weak	weak	ADJ
ejpam-3905	180	17	equivalences	equivalence	NOUN
ejpam-3905	180	18	are	be	AUX
ejpam-3905	180	19	the	the	DET
ejpam-3905	180	20	morphisms	morphism	NOUN
ejpam-3905	180	21	f	f	NOUN
ejpam-3905	180	22	such	such	ADJ
ejpam-3905	180	23	that	that	SCONJ
ejpam-3905	180	24	f	f	PROPN
ejpam-3905	180	25	⊗τ	⊗τ	VERB
ejpam-3905	180	26	a	a	DET
ejpam-3905	180	27	be	be	AUX
ejpam-3905	180	28	a	a	DET
ejpam-3905	180	29	semi	semi	ADJ
ejpam-3905	180	30	isomorphism	isomorphism	NOUN
ejpam-3905	180	31	and	and	CCONJ
ejpam-3905	180	32	whose	whose	DET
ejpam-3905	180	33	cofibrations	cofibration	NOUN
ejpam-3905	180	34	are	be	AUX
ejpam-3905	180	35	injective	injective	ADJ
ejpam-3905	180	36	morphisms	morphism	NOUN
ejpam-3905	180	37	.	.	PUNCT
ejpam-3905	181	1	(	(	PUNCT
ejpam-3905	181	2	ii	ii	X
ejpam-3905	181	3	)	)	PUNCT
ejpam-3905	181	4	the	the	DET
ejpam-3905	181	5	functors	functors	PROPN
ejpam-3905	181	6	!	!	PUNCT
ejpam-3905	182	1	⊗τ	⊗τ	PROPN
ejpam-3905	182	2	c	c	PROPN
ejpam-3905	182	3	and	and	CCONJ
ejpam-3905	182	4	!	!	PUNCT
ejpam-3905	182	5	⊗τ	⊗τ	VERB
ejpam-3905	182	6	a	a	DET
ejpam-3905	182	7	induce	induce	NOUN
ejpam-3905	182	8	semi	semi	ADJ
ejpam-3905	182	9	-	-	ADJ
ejpam-3905	182	10	inverse	inverse	ADJ
ejpam-3905	182	11	equivalences	equivalence	NOUN
ejpam-3905	182	12	d(a)∼−→d(c	d(a)∼−→d(c	NUM
ejpam-3905	182	13	)	)	PUNCT
ejpam-3905	182	14	since	since	SCONJ
ejpam-3905	182	15	d(c	d(c	PROPN
ejpam-3905	182	16	)	)	PUNCT
ejpam-3905	182	17	the	the	DET
ejpam-3905	182	18	localization	localization	NOUN
ejpam-3905	182	19	of	of	ADP
ejpam-3905	182	20	comcc	comcc	PROPN
ejpam-3905	182	21	is	be	AUX
ejpam-3905	182	22	regarding	regard	VERB
ejpam-3905	182	23	classes	class	NOUN
ejpam-3905	182	24	of	of	ADP
ejpam-3905	182	25	weak	weak	ADJ
ejpam-3905	182	26	equivalences	equivalence	NOUN
ejpam-3905	182	27	.	.	PUNCT
ejpam-3905	183	1	by	by	ADP
ejpam-3905	183	2	comparing	compare	VERB
ejpam-3905	183	3	the	the	DET
ejpam-3905	183	4	adjunction	adjunction	NOUN
ejpam-3905	183	5	morphism	morphism	NOUN
ejpam-3905	183	6	,	,	PUNCT
ejpam-3905	183	7	b∞a	b∞a	NOUN
ejpam-3905	183	8	=	=	PUNCT
ejpam-3905	183	9	c	c	NOUN
ejpam-3905	183	10	−→	−→	NOUN
ejpam-3905	183	11	bωc	bωc	NOUN
ejpam-3905	183	12	=	=	SYM
ejpam-3905	183	13	b∞(ωc	b∞(ωc	PROPN
ejpam-3905	183	14	)	)	PUNCT
ejpam-3905	184	1	to	to	ADP
ejpam-3905	184	2	canonical	canonical	ADJ
ejpam-3905	184	3	einfinity	einfinity	NOUN
ejpam-3905	184	4	morphism	morphism	NOUN
ejpam-3905	184	5	a	a	DET
ejpam-3905	184	6	−→	−→	NOUN
ejpam-3905	184	7	ωb∞a	ωb∞a	NOUN
ejpam-3905	184	8	,	,	PUNCT
ejpam-3905	184	9	which	which	PRON
ejpam-3905	184	10	is	be	AUX
ejpam-3905	184	11	a	a	DET
ejpam-3905	184	12	semi	semi	NOUN
ejpam-3905	184	13	-	-	NOUN
ejpam-3905	184	14	isomorphism	isomorphism	NOUN
ejpam-3905	184	15	which	which	PRON
ejpam-3905	184	16	is	be	AUX
ejpam-3905	184	17	universal	universal	ADJ
ejpam-3905	184	18	among	among	ADP
ejpam-3905	184	19	the	the	DET
ejpam-3905	184	20	e	e	NOUN
ejpam-3905	184	21	-	-	NOUN
ejpam-3905	184	22	infinity	infinity	ADJ
ejpam-3905	184	23	morphisms	morphism	NOUN
ejpam-3905	184	24	from	from	ADP
ejpam-3905	184	25	a	a	PRON
ejpam-3905	184	26	to	to	ADP
ejpam-3905	184	27	a	a	DET
ejpam-3905	184	28	dg	dg	NOUN
ejpam-3905	184	29	-	-	PUNCT
ejpam-3905	184	30	algebra	algebra	NOUN
ejpam-3905	184	31	,	,	PUNCT
ejpam-3905	184	32	since	since	SCONJ
ejpam-3905	184	33	a	a	DET
ejpam-3905	184	34	be	be	AUX
ejpam-3905	184	35	an	an	DET
ejpam-3905	184	36	augmented	augment	VERB
ejpam-3905	184	37	e∞-algebra	e∞-algebra	NOUN
ejpam-3905	184	38	and	and	CCONJ
ejpam-3905	184	39	b∞a	b∞a	NOUN
ejpam-3905	184	40	=	=	SYM
ejpam-3905	184	41	c.	c.	NOUN
ejpam-3905	184	42	definition	definition	NOUN
ejpam-3905	184	43	18	18	NUM
ejpam-3905	184	44	.	.	PUNCT
ejpam-3905	185	1	if	if	SCONJ
ejpam-3905	185	2	we	we	PRON
ejpam-3905	185	3	let	let	VERB
ejpam-3905	185	4	u(a	u(a	NOUN
ejpam-3905	185	5	)	)	PUNCT
ejpam-3905	185	6	=	=	PUNCT
ejpam-3905	186	1	ωb∞a	ωb∞a	NOUN
ejpam-3905	186	2	,	,	PUNCT
ejpam-3905	186	3	at	at	ADP
ejpam-3905	186	4	that	that	DET
ejpam-3905	186	5	point	point	NOUN
ejpam-3905	186	6	there	there	PRON
ejpam-3905	186	7	is	be	VERB
ejpam-3905	186	8	canonical	canonical	ADJ
ejpam-3905	186	9	cyclic	cyclic	ADJ
ejpam-3905	186	10	twisting	twisting	NOUN
ejpam-3905	186	11	cochain	cochain	NOUN
ejpam-3905	186	12	τ	τ	X
ejpam-3905	186	13	:	:	PUNCT
ejpam-3905	186	14	b∞(a	b∞(a	ADJ
ejpam-3905	186	15	)	)	PUNCT
ejpam-3905	186	16	−→	−→	PROPN
ejpam-3905	186	17	u(a	u(a	PROPN
ejpam-3905	186	18	)	)	PUNCT
ejpam-3905	186	19	.	.	PUNCT
ejpam-3905	187	1	from	from	ADP
ejpam-3905	187	2	theorem	theorem	NOUN
ejpam-3905	187	3	3	3	NUM
ejpam-3905	187	4	we	we	PRON
ejpam-3905	187	5	have	have	VERB
ejpam-3905	187	6	an	an	DET
ejpam-3905	187	7	equivalence	equivalence	NOUN
ejpam-3905	187	8	a.	a.	NOUN
ejpam-3905	187	9	noreldeen	noreldeen	PROPN
ejpam-3905	187	10	,	,	PUNCT
ejpam-3905	187	11	s.	s.	PROPN
ejpam-3905	187	12	abo	abo	VERB
ejpam-3905	187	13	quota	quota	PROPN
ejpam-3905	187	14	/	/	SYM
ejpam-3905	187	15	eur	eur	NOUN
ejpam-3905	187	16	.	.	PUNCT
ejpam-3905	188	1	j.	j.	PROPN
ejpam-3905	188	2	pure	pure	PROPN
ejpam-3905	188	3	appl	appl	PROPN
ejpam-3905	188	4	.	.	PROPN
ejpam-3905	188	5	math	math	PROPN
ejpam-3905	188	6	,	,	PUNCT
ejpam-3905	188	7	14	14	NUM
ejpam-3905	188	8	(	(	PUNCT
ejpam-3905	188	9	2	2	NUM
ejpam-3905	188	10	)	)	PUNCT
ejpam-3905	188	11	(	(	PUNCT
ejpam-3905	188	12	2021	2021	NUM
ejpam-3905	188	13	)	)	PUNCT
ejpam-3905	188	14	,	,	PUNCT
ejpam-3905	188	15	480	480	NUM
ejpam-3905	188	16	-	-	SYM
ejpam-3905	188	17	492	492	NUM
ejpam-3905	188	18	489	489	NUM
ejpam-3905	188	19	d(u(a))∼−→d(b∞(a	d(u(a))∼−→d(b∞(a	PROPN
ejpam-3905	188	20	)	)	PUNCT
ejpam-3905	188	21	)	)	PUNCT
ejpam-3905	188	22	definition	definition	NOUN
ejpam-3905	188	23	19	19	NUM
ejpam-3905	188	24	.	.	PUNCT
ejpam-3905	189	1	[	[	X
ejpam-3905	189	2	6	6	NUM
ejpam-3905	189	3	]	]	PUNCT
ejpam-3905	189	4	assume	assume	VERB
ejpam-3905	189	5	that	that	SCONJ
ejpam-3905	189	6	mod∞a	mod∞a	PROPN
ejpam-3905	189	7	is	be	AUX
ejpam-3905	189	8	the	the	DET
ejpam-3905	189	9	grouping	grouping	NOUN
ejpam-3905	189	10	of	of	ADP
ejpam-3905	189	11	e∞-modules	e∞-module	NOUN
ejpam-3905	189	12	over	over	ADP
ejpam-3905	189	13	abmn	abmn	ADJ
ejpam-3905	189	14	,	,	PUNCT
ejpam-3905	189	15	n	n	CCONJ
ejpam-3905	189	16	≥	≥	X
ejpam-3905	189	17	2	2	NUM
ejpam-3905	189	18	which	which	PRON
ejpam-3905	189	19	are	be	AUX
ejpam-3905	189	20	vanish	vanish	VERB
ejpam-3905	189	21	when	when	SCONJ
ejpam-3905	189	22	one	one	NUM
ejpam-3905	189	23	of	of	ADP
ejpam-3905	189	24	the	the	DET
ejpam-3905	189	25	contentions	contention	NOUN
ejpam-3905	189	26	is	be	AUX
ejpam-3905	189	27	1	1	NUM
ejpam-3905	189	28	.	.	PUNCT
ejpam-3905	190	1	the	the	DET
ejpam-3905	190	2	morphisms	morphisms	PROPN
ejpam-3905	190	3	gn	gn	PROPN
ejpam-3905	190	4	,	,	PUNCT
ejpam-3905	190	5	n	n	PRON
ejpam-3905	190	6	≥	≥	NOUN
ejpam-3905	190	7	2	2	NUM
ejpam-3905	190	8	are	be	AUX
ejpam-3905	190	9	strictly	strictly	ADV
ejpam-3905	190	10	unital	unital	ADJ
ejpam-3905	190	11	(	(	PUNCT
ejpam-3905	190	12	vanish	vanish	VERB
ejpam-3905	190	13	if	if	SCONJ
ejpam-3905	190	14	the	the	DET
ejpam-3905	190	15	arguments	argument	NOUN
ejpam-3905	190	16	is	be	AUX
ejpam-3905	190	17	1	1	NUM
ejpam-3905	190	18	)	)	PUNCT
ejpam-3905	190	19	.	.	PUNCT
ejpam-3905	191	1	this	this	DET
ejpam-3905	191	2	category	category	NOUN
ejpam-3905	191	3	is	be	AUX
ejpam-3905	191	4	isomorphic	isomorphic	ADJ
ejpam-3905	191	5	to	to	ADP
ejpam-3905	191	6	the	the	DET
ejpam-3905	191	7	order	order	NOUN
ejpam-3905	191	8	of	of	ADP
ejpam-3905	191	9	all	all	DET
ejpam-3905	191	10	e	e	NOUN
ejpam-3905	191	11	-	-	NOUN
ejpam-3905	191	12	infinity	infinity	ADJ
ejpam-3905	191	13	modules	module	NOUN
ejpam-3905	191	14	and	and	CCONJ
ejpam-3905	191	15	all	all	DET
ejpam-3905	191	16	e	e	NOUN
ejpam-3905	191	17	-	-	NOUN
ejpam-3905	191	18	infinity	infinity	ADJ
ejpam-3905	191	19	morphisms	morphism	NOUN
ejpam-3905	191	20	(	(	PUNCT
ejpam-3905	191	21	to	to	PART
ejpam-3905	191	22	more	more	ADV
ejpam-3905	191	23	see	see	VERB
ejpam-3905	191	24	[	[	X
ejpam-3905	191	25	11	11	NUM
ejpam-3905	191	26	]	]	NUM
ejpam-3905	191	27	)	)	PUNCT
ejpam-3905	191	28	.	.	PUNCT
ejpam-3905	192	1	suppose	suppose	VERB
ejpam-3905	192	2	that	that	SCONJ
ejpam-3905	192	3	m	m	NOUN
ejpam-3905	192	4	is	be	AUX
ejpam-3905	192	5	in	in	ADP
ejpam-3905	192	6	(	(	PUNCT
ejpam-3905	192	7	mod∞a	mod∞a	NOUN
ejpam-3905	192	8	)	)	PUNCT
ejpam-3905	192	9	.	.	PUNCT
ejpam-3905	193	1	the	the	DET
ejpam-3905	193	2	datum	datum	NOUN
ejpam-3905	193	3	of	of	ADP
ejpam-3905	193	4	the	the	DET
ejpam-3905	193	5	arbitrary	arbitrary	ADJ
ejpam-3905	193	6	e	e	NOUN
ejpam-3905	193	7	-	-	NOUN
ejpam-3905	193	8	infinity	infinity	NOUN
ejpam-3905	193	9	module	module	NOUN
ejpam-3905	193	10	structure	structure	NOUN
ejpam-3905	193	11	over	over	ADP
ejpam-3905	193	12	ā	ā	PROPN
ejpam-3905	193	13	and	and	CCONJ
ejpam-3905	193	14	the	the	DET
ejpam-3905	193	15	datum	datum	NOUN
ejpam-3905	193	16	of	of	ADP
ejpam-3905	193	17	its	its	PRON
ejpam-3905	193	18	strictly	strictly	ADV
ejpam-3905	193	19	unital	unital	ADJ
ejpam-3905	193	20	e	e	ADJ
ejpam-3905	193	21	-	-	NOUN
ejpam-3905	193	22	infinity	infinity	NOUN
ejpam-3905	193	23	module	module	NOUN
ejpam-3905	193	24	structure	structure	NOUN
ejpam-3905	193	25	over	over	ADP
ejpam-3905	193	26	a	a	PRON
ejpam-3905	193	27	are	be	AUX
ejpam-3905	193	28	equivalent	equivalent	ADJ
ejpam-3905	193	29	each	each	PRON
ejpam-3905	193	30	to	to	ADP
ejpam-3905	193	31	other	other	ADJ
ejpam-3905	193	32	.	.	PUNCT
ejpam-3905	194	1	it	it	PRON
ejpam-3905	194	2	is	be	AUX
ejpam-3905	194	3	also	also	ADV
ejpam-3905	194	4	equivalent	equivalent	ADJ
ejpam-3905	194	5	to	to	ADP
ejpam-3905	194	6	a	a	DET
ejpam-3905	194	7	co	co	NOUN
ejpam-3905	194	8	-	-	NOUN
ejpam-3905	194	9	module	module	ADJ
ejpam-3905	194	10	differential	differential	NOUN
ejpam-3905	194	11	in	in	ADP
ejpam-3905	194	12	the	the	DET
ejpam-3905	194	13	induced	induced	ADJ
ejpam-3905	194	14	co	co	NOUN
ejpam-3905	194	15	-	-	NOUN
ejpam-3905	194	16	module	module	NOUN
ejpam-3905	194	17	(	(	PUNCT
ejpam-3905	194	18	m⊗b∞a	m⊗b∞a	NOUN
ejpam-3905	194	19	)	)	PUNCT
ejpam-3905	194	20	.	.	PUNCT
ejpam-3905	195	1	(	(	PUNCT
ejpam-3905	195	2	b∞m	b∞m	NOUN
ejpam-3905	195	3	)	)	PUNCT
ejpam-3905	195	4	is	be	AUX
ejpam-3905	195	5	the	the	DET
ejpam-3905	195	6	induced	induced	ADJ
ejpam-3905	195	7	co	co	NOUN
ejpam-3905	195	8	-	-	NOUN
ejpam-3905	195	9	module	module	NOUN
ejpam-3905	195	10	supplied	supply	VERB
ejpam-3905	195	11	with	with	ADP
ejpam-3905	195	12	the	the	DET
ejpam-3905	195	13	differential	differential	NOUN
ejpam-3905	195	14	corresponding	correspond	VERB
ejpam-3905	195	15	to	to	ADP
ejpam-3905	195	16	a	a	DET
ejpam-3905	195	17	given	give	VERB
ejpam-3905	195	18	e	e	NOUN
ejpam-3905	195	19	-	-	NOUN
ejpam-3905	195	20	infinity	infinity	NOUN
ejpam-3905	195	21	module	module	NOUN
ejpam-3905	195	22	structure	structure	NOUN
ejpam-3905	195	23	on	on	ADP
ejpam-3905	195	24	m	m	PROPN
ejpam-3905	195	25	.	.	PUNCT
ejpam-3905	196	1	the	the	DET
ejpam-3905	196	2	functor	functor	PROPN
ejpam-3905	196	3	,	,	PUNCT
ejpam-3905	196	4	mod∞a	mod∞a	PROPN
ejpam-3905	196	5	−→	−→	ADJ
ejpam-3905	196	6	comcb∞(a),m	comcb∞(a),m	NUM
ejpam-3905	196	7	−→	−→	NOUN
ejpam-3905	196	8	b∞m	b∞m	NOUN
ejpam-3905	196	9	exists	exist	VERB
ejpam-3905	196	10	.	.	PUNCT
ejpam-3905	197	1	proposition	proposition	NOUN
ejpam-3905	197	2	6	6	NUM
ejpam-3905	197	3	.	.	PUNCT
ejpam-3905	198	1	[	[	X
ejpam-3905	198	2	1	1	X
ejpam-3905	198	3	]	]	PUNCT
ejpam-3905	198	4	the	the	DET
ejpam-3905	198	5	functor	functor	PROPN
ejpam-3905	198	6	m	m	PROPN
ejpam-3905	198	7	−→	−→	ADJ
ejpam-3905	198	8	b∞m	b∞m	NOUN
ejpam-3905	198	9	induces	induce	VERB
ejpam-3905	198	10	the	the	DET
ejpam-3905	198	11	following	follow	VERB
ejpam-3905	198	12	equivalence	equivalence	NOUN
ejpam-3905	198	13	:	:	PUNCT
ejpam-3905	198	14	(	(	PUNCT
ejpam-3905	198	15	i	i	NOUN
ejpam-3905	198	16	)	)	PUNCT
ejpam-3905	198	17	the	the	DET
ejpam-3905	198	18	equivalence	equivalence	NOUN
ejpam-3905	198	19	onto	onto	ADP
ejpam-3905	198	20	subcategory	subcategory	ADJ
ejpam-3905	198	21	fibrant	fibrant	NOUN
ejpam-3905	198	22	(	(	PUNCT
ejpam-3905	198	23	cofibrant	cofibrant	NOUN
ejpam-3905	198	24	)	)	PUNCT
ejpam-3905	198	25	objects	object	NOUN
ejpam-3905	198	26	(	(	PUNCT
ejpam-3905	198	27	comcb∞(a))cf	comcb∞(a))cf	PROPN
ejpam-3905	198	28	of	of	ADP
ejpam-3905	198	29	comcb∞(a	comcb∞(a	PROPN
ejpam-3905	198	30	)	)	PUNCT
ejpam-3905	198	31	.	.	PUNCT
ejpam-3905	199	1	(	(	PUNCT
ejpam-3905	199	2	ii	ii	NOUN
ejpam-3905	199	3	)	)	PUNCT
ejpam-3905	199	4	(	(	PUNCT
ejpam-3905	199	5	mod∞a)/homotopy∼−→d(c	mod∞a)/homotopy∼−→d(c	NOUN
ejpam-3905	199	6	)	)	PUNCT
ejpam-3905	199	7	.	.	PUNCT
ejpam-3905	200	1	definition	definition	NOUN
ejpam-3905	200	2	20	20	NUM
ejpam-3905	200	3	.	.	PUNCT
ejpam-3905	201	1	[	[	X
ejpam-3905	201	2	2	2	X
ejpam-3905	201	3	]	]	PUNCT
ejpam-3905	201	4	the	the	DET
ejpam-3905	201	5	derived	derived	ADJ
ejpam-3905	201	6	classification	classification	NOUN
ejpam-3905	201	7	for	for	ADP
ejpam-3905	201	8	a	a	DET
ejpam-3905	201	9	non	non	ADJ
ejpam-3905	201	10	-	-	ADJ
ejpam-3905	201	11	augmented	augmented	ADJ
ejpam-3905	201	12	e	e	NOUN
ejpam-3905	201	13	-	-	NOUN
ejpam-3905	201	14	infinity	infinity	ADJ
ejpam-3905	201	15	algebra	algebra	NOUN
ejpam-3905	201	16	d∞a	d∞a	NOUN
ejpam-3905	201	17	,	,	PUNCT
ejpam-3905	201	18	is	be	AUX
ejpam-3905	201	19	the	the	DET
ejpam-3905	201	20	kernel	kernel	NOUN
ejpam-3905	201	21	of	of	ADP
ejpam-3905	201	22	the	the	DET
ejpam-3905	201	23	functor	functor	PROPN
ejpam-3905	201	24	d∞(a+	d∞(a+	PROPN
ejpam-3905	201	25	)	)	PUNCT
ejpam-3905	201	26	−→	−→	NOUN
ejpam-3905	201	27	d∞(k	d∞(k	NOUN
ejpam-3905	201	28	)	)	PUNCT
ejpam-3905	201	29	,	,	PUNCT
ejpam-3905	201	30	since	since	SCONJ
ejpam-3905	201	31	a+	a+	PRON
ejpam-3905	201	32	=	=	PUNCT
ejpam-3905	201	33	a	a	DET
ejpam-3905	201	34	⊕	⊕	PROPN
ejpam-3905	201	35	k	k	PROPN
ejpam-3905	201	36	be	be	AUX
ejpam-3905	201	37	the	the	DET
ejpam-3905	201	38	increased	increase	VERB
ejpam-3905	201	39	e	e	NOUN
ejpam-3905	201	40	-	-	NOUN
ejpam-3905	201	41	infinity	infinity	ADJ
ejpam-3905	201	42	algebra	algebra	NOUN
ejpam-3905	201	43	obtained	obtain	VERB
ejpam-3905	201	44	by	by	ADP
ejpam-3905	201	45	adjoining	adjoin	VERB
ejpam-3905	201	46	k	k	PROPN
ejpam-3905	201	47	and	and	CCONJ
ejpam-3905	201	48	the	the	DET
ejpam-3905	201	49	augmentation	augmentation	NOUN
ejpam-3905	201	50	a+	a+	PUNCT
ejpam-3905	201	51	−→	−→	NOUN
ejpam-3905	201	52	k	k	PROPN
ejpam-3905	201	53	yields	yield	VERB
ejpam-3905	201	54	a	a	DET
ejpam-3905	201	55	functor	functor	NOUN
ejpam-3905	201	56	mod∞a	mod∞a	PROPN
ejpam-3905	201	57	+	+	CCONJ
ejpam-3905	201	58	−→mod∞k	−→mod∞k	X
ejpam-3905	201	59	proposition	proposition	NOUN
ejpam-3905	201	60	7	7	NUM
ejpam-3905	201	61	.	.	PUNCT
ejpam-3905	202	1	the	the	DET
ejpam-3905	202	2	cohomology	cohomology	NOUN
ejpam-3905	202	3	h∗(m	h∗(m	PROPN
ejpam-3905	202	4	)	)	PUNCT
ejpam-3905	202	5	is	be	AUX
ejpam-3905	202	6	unital	unital	ADJ
ejpam-3905	202	7	h∗(a)-module	h∗(a)-module	NOUN
ejpam-3905	202	8	i.e.	i.e.	X
ejpam-3905	202	9	m	m	VERB
ejpam-3905	202	10	includes	include	VERB
ejpam-3905	202	11	a	a	DET
ejpam-3905	202	12	place	place	NOUN
ejpam-3905	202	13	with	with	ADP
ejpam-3905	202	14	the	the	DET
ejpam-3905	202	15	kernel	kernel	PROPN
ejpam-3905	202	16	iff	iff	PROPN
ejpam-3905	202	17	m	m	PROPN
ejpam-3905	202	18	is	be	AUX
ejpam-3905	202	19	homologically	homologically	ADV
ejpam-3905	202	20	unital	unital	ADJ
ejpam-3905	202	21	since	since	SCONJ
ejpam-3905	202	22	a	a	PRON
ejpam-3905	202	23	is	be	AUX
ejpam-3905	202	24	homologically	homologically	ADV
ejpam-3905	202	25	unital	unital	ADJ
ejpam-3905	202	26	.	.	PUNCT
ejpam-3905	203	1	the	the	DET
ejpam-3905	203	2	category	category	NOUN
ejpam-3905	203	3	d∞(a	d∞(a	NOUN
ejpam-3905	203	4	)	)	PUNCT
ejpam-3905	203	5	is	be	AUX
ejpam-3905	203	6	compactly	compactly	ADV
ejpam-3905	203	7	created	create	VERB
ejpam-3905	203	8	a	a	DET
ejpam-3905	203	9	triangulated	triangulate	VERB
ejpam-3905	203	10	category	category	NOUN
ejpam-3905	203	11	and	and	CCONJ
ejpam-3905	203	12	has	have	VERB
ejpam-3905	203	13	the	the	DET
ejpam-3905	203	14	free	free	ADJ
ejpam-3905	203	15	a	a	PRON
ejpam-3905	203	16	-	-	PUNCT
ejpam-3905	203	17	module	module	NOUN
ejpam-3905	203	18	of	of	ADP
ejpam-3905	203	19	the	the	DET
ejpam-3905	203	20	rank	rank	NOUN
ejpam-3905	203	21	one	one	NUM
ejpam-3905	203	22	as	as	ADP
ejpam-3905	203	23	a	a	DET
ejpam-3905	203	24	generator	generator	NOUN
ejpam-3905	203	25	of	of	ADP
ejpam-3905	203	26	the	the	DET
ejpam-3905	203	27	compact	compact	NOUN
ejpam-3905	203	28	.	.	PUNCT
ejpam-3905	204	1	definition	definition	NOUN
ejpam-3905	204	2	21	21	NUM
ejpam-3905	204	3	.	.	PUNCT
ejpam-3905	205	1	[	[	X
ejpam-3905	205	2	9	9	NUM
ejpam-3905	205	3	]	]	PUNCT
ejpam-3905	205	4	let	let	VERB
ejpam-3905	205	5	b	b	PRON
ejpam-3905	205	6	be	be	AUX
ejpam-3905	205	7	a	a	DET
ejpam-3905	205	8	differential	differential	ADJ
ejpam-3905	205	9	polynormal	polynormal	ADJ
ejpam-3905	205	10	algebra	algebra	NOUN
ejpam-3905	205	11	with	with	ADP
ejpam-3905	205	12	,	,	PUNCT
ejpam-3905	205	13	b	b	X
ejpam-3905	205	14	=	=	SYM
ejpam-3905	205	15	b1	b1	PROPN
ejpam-3905	205	16	⊃	⊃	PROPN
ejpam-3905	205	17	b2	b2	PROPN
ejpam-3905	205	18	⊃	⊃	X
ejpam-3905	205	19	·	·	PUNCT
ejpam-3905	205	20	·	·	PUNCT
ejpam-3905	205	21	·	·	PUNCT
ejpam-3905	206	1	⊃	⊃	PROPN
ejpam-3905	206	2	bn	bn	NUM
ejpam-3905	206	3	⊃	⊃	X
ejpam-3905	206	4	·	·	PUNCT
ejpam-3905	206	5	·	·	PUNCT
ejpam-3905	206	6	·	·	PUNCT
ejpam-3905	206	7	(	(	PUNCT
ejpam-3905	206	8	19	19	NUM
ejpam-3905	206	9	)	)	PUNCT
ejpam-3905	206	10	if	if	SCONJ
ejpam-3905	206	11	a	a	DET
ejpam-3905	206	12	natural	natural	ADJ
ejpam-3905	206	13	map	map	NOUN
ejpam-3905	206	14	f	f	NOUN
ejpam-3905	206	15	:	:	PUNCT
ejpam-3905	206	16	b	b	X
ejpam-3905	206	17	−→	−→	NOUN
ejpam-3905	206	18	b̂	b̂	NOUN
ejpam-3905	206	19	is	be	AUX
ejpam-3905	206	20	an	an	DET
ejpam-3905	206	21	isomorphism	isomorphism	NOUN
ejpam-3905	206	22	,	,	PUNCT
ejpam-3905	206	23	then	then	ADV
ejpam-3905	206	24	b	b	NOUN
ejpam-3905	206	25	is	be	AUX
ejpam-3905	206	26	perfect	perfect	ADJ
ejpam-3905	206	27	algebra	algebra	NOUN
ejpam-3905	206	28	.	.	PUNCT
ejpam-3905	207	1	since	since	SCONJ
ejpam-3905	207	2	b̂	b̂	NOUN
ejpam-3905	207	3	is	be	AUX
ejpam-3905	207	4	polynormal	polynormal	ADJ
ejpam-3905	207	5	algebra	algebra	NOUN
ejpam-3905	207	6	and	and	CCONJ
ejpam-3905	207	7	given	give	VERB
ejpam-3905	207	8	by	by	ADP
ejpam-3905	207	9	;	;	PUNCT
ejpam-3905	207	10	b̂	b̂	NOUN
ejpam-3905	207	11	=	=	SYM
ejpam-3905	207	12	limb	limb	PROPN
ejpam-3905	207	13	/	/	SYM
ejpam-3905	207	14	bn	bn	NOUN
ejpam-3905	207	15	.	.	PUNCT
ejpam-3905	207	16	definition	definition	NOUN
ejpam-3905	207	17	22	22	NUM
ejpam-3905	207	18	.	.	PUNCT
ejpam-3905	208	1	let	let	VERB
ejpam-3905	208	2	the	the	DET
ejpam-3905	208	3	e∞-algebra	e∞-algebra	ADJ
ejpam-3905	208	4	a.	a.	NOUN
ejpam-3905	208	5	outline	outline	NOUN
ejpam-3905	208	6	the	the	DET
ejpam-3905	208	7	massy	massy	ADJ
ejpam-3905	208	8	sequence	sequence	NOUN
ejpam-3905	208	9	(	(	PUNCT
ejpam-3905	208	10	a2	a2	PROPN
ejpam-3905	208	11	,	,	PUNCT
ejpam-3905	208	12	·	·	PUNCT
ejpam-3905	208	13	·	·	PUNCT
ejpam-3905	208	14	·	·	PUNCT
ejpam-3905	208	15	,	,	PUNCT
ejpam-3905	208	16	an	an	X
ejpam-3905	208	17	)	)	PUNCT
ejpam-3905	208	18	of	of	ADP
ejpam-3905	208	19	the	the	DET
ejpam-3905	208	20	elements	element	NOUN
ejpam-3905	208	21	ai	ai	VERB
ejpam-3905	208	22	∈	∈	NOUN
ejpam-3905	208	23	sa⊗i	sa⊗i	NOUN
ejpam-3905	208	24	such	such	ADJ
ejpam-3905	208	25	that	that	PRON
ejpam-3905	208	26	,	,	PUNCT
ejpam-3905	208	27	(	(	PUNCT
ejpam-3905	208	28	π(2)⊗	π(2)⊗	PROPN
ejpam-3905	208	29	·	·	PUNCT
ejpam-3905	208	30	·	·	PUNCT
ejpam-3905	208	31	·	·	PUNCT
ejpam-3905	209	1	⊗	⊗	NUM
ejpam-3905	209	2	1	1	NUM
ejpam-3905	210	1	+	+	NUM
ejpam-3905	210	2	1⊗	1⊗	NUM
ejpam-3905	210	3	·	·	PUNCT
ejpam-3905	210	4	·	·	PUNCT
ejpam-3905	210	5	·	·	PUNCT
ejpam-3905	211	1	⊗	⊗	NUM
ejpam-3905	211	2	π(2))(an	π(2))(an	NUM
ejpam-3905	211	3	)	)	PUNCT
ejpam-3905	211	4	=	=	SYM
ejpam-3905	211	5	0	0	PUNCT
ejpam-3905	211	6	(	(	PUNCT
ejpam-3905	211	7	π(3)⊗	π(3)⊗	NOUN
ejpam-3905	211	8	·	·	PUNCT
ejpam-3905	211	9	·	·	PUNCT
ejpam-3905	211	10	·	·	PUNCT
ejpam-3905	212	1	⊗	⊗	NUM
ejpam-3905	212	2	1	1	NUM
ejpam-3905	213	1	+	+	NUM
ejpam-3905	213	2	1⊗	1⊗	NUM
ejpam-3905	213	3	·	·	PUNCT
ejpam-3905	213	4	·	·	PUNCT
ejpam-3905	213	5	·	·	PUNCT
ejpam-3905	214	1	⊗	⊗	NUM
ejpam-3905	214	2	π(3))(an	π(3))(an	NUM
ejpam-3905	214	3	)	)	PUNCT
ejpam-3905	215	1	+	+	CCONJ
ejpam-3905	215	2	(	(	PUNCT
ejpam-3905	215	3	π(2)⊗	π(2)⊗	PROPN
ejpam-3905	215	4	·	·	PUNCT
ejpam-3905	215	5	·	·	PUNCT
ejpam-3905	215	6	·	·	PUNCT
ejpam-3905	216	1	⊗	⊗	NUM
ejpam-3905	216	2	1	1	NUM
ejpam-3905	217	1	+	+	NUM
ejpam-3905	217	2	1⊗	1⊗	NUM
ejpam-3905	217	3	·	·	PUNCT
ejpam-3905	217	4	·	·	PUNCT
ejpam-3905	217	5	·	·	PUNCT
ejpam-3905	218	1	⊗	⊗	NUM
ejpam-3905	218	2	π(2))(an−1	π(2))(an−1	PROPN
ejpam-3905	218	3	)	)	PUNCT
ejpam-3905	218	4	=	=	SYM
ejpam-3905	218	5	0	0	NUM
ejpam-3905	218	6	a.	a.	NOUN
ejpam-3905	218	7	noreldeen	noreldeen	PROPN
ejpam-3905	218	8	,	,	PUNCT
ejpam-3905	218	9	s.	s.	PROPN
ejpam-3905	218	10	abo	abo	VERB
ejpam-3905	218	11	quota	quota	PROPN
ejpam-3905	218	12	/	/	SYM
ejpam-3905	218	13	eur	eur	NOUN
ejpam-3905	218	14	.	.	PUNCT
ejpam-3905	219	1	j.	j.	PROPN
ejpam-3905	219	2	pure	pure	PROPN
ejpam-3905	219	3	appl	appl	PROPN
ejpam-3905	219	4	.	.	PROPN
ejpam-3905	219	5	math	math	PROPN
ejpam-3905	219	6	,	,	PUNCT
ejpam-3905	219	7	14	14	NUM
ejpam-3905	219	8	(	(	PUNCT
ejpam-3905	219	9	2	2	NUM
ejpam-3905	219	10	)	)	PUNCT
ejpam-3905	219	11	(	(	PUNCT
ejpam-3905	219	12	2021	2021	NUM
ejpam-3905	219	13	)	)	PUNCT
ejpam-3905	219	14	,	,	PUNCT
ejpam-3905	219	15	480	480	NUM
ejpam-3905	219	16	-	-	SYM
ejpam-3905	219	17	492	492	NUM
ejpam-3905	219	18	490	490	NUM
ejpam-3905	219	19	·	·	PUNCT
ejpam-3905	219	20	·	·	PUNCT
ejpam-3905	219	21	·	·	PUNCT
ejpam-3905	219	22	·	·	PUNCT
ejpam-3905	219	23	·	·	PUNCT
ejpam-3905	219	24	·	·	PUNCT
ejpam-3905	219	25	·	·	PUNCT
ejpam-3905	219	26	·	·	PUNCT
ejpam-3905	219	27	·	·	PUNCT
ejpam-3905	219	28	·	·	PUNCT
ejpam-3905	219	29	·	·	PUNCT
ejpam-3905	219	30	·	·	PUNCT
ejpam-3905	219	31	·	·	PUNCT
ejpam-3905	219	32	·	·	PUNCT
ejpam-3905	219	33	·	·	PUNCT
ejpam-3905	219	34	·	·	PUNCT
ejpam-3905	219	35	·	·	PUNCT
ejpam-3905	219	36	·	·	PUNCT
ejpam-3905	219	37	·	·	PUNCT
ejpam-3905	219	38	·	·	PUNCT
ejpam-3905	219	39	·	·	PUNCT
ejpam-3905	219	40	·	·	PUNCT
ejpam-3905	219	41	·	·	PUNCT
ejpam-3905	219	42	·	·	PUNCT
ejpam-3905	219	43	·	·	PUNCT
ejpam-3905	219	44	·	·	PUNCT
ejpam-3905	219	45	·	·	PUNCT
ejpam-3905	219	46	·	·	PUNCT
ejpam-3905	219	47	·	·	PUNCT
ejpam-3905	219	48	·	·	PUNCT
ejpam-3905	219	49	·	·	PUNCT
ejpam-3905	219	50	·	·	PUNCT
ejpam-3905	219	51	·	·	PUNCT
ejpam-3905	219	52	·	·	PUNCT
ejpam-3905	219	53	·	·	PUNCT
ejpam-3905	219	54	·	·	PUNCT
ejpam-3905	219	55	·	·	PUNCT
ejpam-3905	219	56	·	·	PUNCT
ejpam-3905	219	57	·	·	PUNCT
ejpam-3905	219	58	·	·	PUNCT
ejpam-3905	219	59	·	·	PUNCT
ejpam-3905	219	60	·	·	PUNCT
ejpam-3905	219	61	·	·	PUNCT
ejpam-3905	219	62	·	·	PUNCT
ejpam-3905	219	63	·	·	PUNCT
ejpam-3905	219	64	·	·	PUNCT
ejpam-3905	219	65	·	·	PUNCT
ejpam-3905	219	66	·	·	PUNCT
ejpam-3905	219	67	·	·	PUNCT
ejpam-3905	219	68	·	·	PUNCT
ejpam-3905	219	69	·	·	PUNCT
ejpam-3905	220	1	(	(	PUNCT
ejpam-3905	220	2	π(n−	π(n−	NOUN
ejpam-3905	220	3	1)⊗	1)⊗	NUM
ejpam-3905	220	4	1	1	NUM
ejpam-3905	220	5	+	+	SYM
ejpam-3905	220	6	1⊗	1⊗	NUM
ejpam-3905	220	7	π(n−	π(n−	PROPN
ejpam-3905	220	8	1))(an	1))(an	NUM
ejpam-3905	220	9	)	)	PUNCT
ejpam-3905	221	1	+	+	CCONJ
ejpam-3905	221	2	(	(	PUNCT
ejpam-3905	221	3	π(n−	π(n−	PROPN
ejpam-3905	221	4	2)⊗	2)⊗	NUM
ejpam-3905	221	5	1	1	NUM
ejpam-3905	221	6	+	+	SYM
ejpam-3905	221	7	1⊗	1⊗	NUM
ejpam-3905	221	8	(	(	PUNCT
ejpam-3905	221	9	π(n−	π(n−	PROPN
ejpam-3905	221	10	2))(an−1	2))(an−1	NUM
ejpam-3905	221	11	)	)	PUNCT
ejpam-3905	221	12	+	+	CCONJ
ejpam-3905	221	13	·	·	PUNCT
ejpam-3905	221	14	·	·	PUNCT
ejpam-3905	221	15	·	·	PUNCT
ejpam-3905	221	16	+	+	CCONJ
ejpam-3905	221	17	(	(	PUNCT
ejpam-3905	221	18	π(2)⊗	π(2)⊗	PROPN
ejpam-3905	221	19	1	1	NUM
ejpam-3905	221	20	+	+	SYM
ejpam-3905	221	21	1⊗	1⊗	NUM
ejpam-3905	221	22	π(2))(a3	π(2))(a3	NOUN
ejpam-3905	221	23	)	)	PUNCT
ejpam-3905	221	24	=	=	SYM
ejpam-3905	221	25	0	0	NUM
ejpam-3905	221	26	and	and	CCONJ
ejpam-3905	221	27	the	the	DET
ejpam-3905	221	28	massy	massy	ADJ
ejpam-3905	221	29	product	product	NOUN
ejpam-3905	221	30	is	be	AUX
ejpam-3905	221	31	given	give	VERB
ejpam-3905	221	32	by	by	ADP
ejpam-3905	221	33	;	;	PUNCT
ejpam-3905	221	34	µ(a2	µ(a2	PROPN
ejpam-3905	221	35	,	,	PUNCT
ejpam-3905	221	36	·	·	PUNCT
ejpam-3905	221	37	·	·	PUNCT
ejpam-3905	221	38	·	·	PUNCT
ejpam-3905	221	39	,	,	PUNCT
ejpam-3905	221	40	an	an	X
ejpam-3905	221	41	)	)	PUNCT
ejpam-3905	221	42	=	=	SYM
ejpam-3905	221	43	π(2)(a2	π(2)(a2	NOUN
ejpam-3905	221	44	)	)	PUNCT
ejpam-3905	221	45	+	+	NUM
ejpam-3905	221	46	·	·	PUNCT
ejpam-3905	221	47	·	·	PUNCT
ejpam-3905	221	48	·	·	PUNCT
ejpam-3905	222	1	+	+	SYM
ejpam-3905	222	2	π(2)(an	π(2)(an	X
ejpam-3905	222	3	)	)	PUNCT
ejpam-3905	222	4	all	all	DET
ejpam-3905	222	5	parts	part	NOUN
ejpam-3905	222	6	in	in	ADP
ejpam-3905	222	7	a	a	PRON
ejpam-3905	222	8	are	be	AUX
ejpam-3905	222	9	decomposable	decomposable	ADJ
ejpam-3905	222	10	if	if	SCONJ
ejpam-3905	222	11	they	they	PRON
ejpam-3905	222	12	’re	’re	VERB
ejpam-3905	222	13	images	image	NOUN
ejpam-3905	222	14	of	of	ADP
ejpam-3905	222	15	massy	massy	ADJ
ejpam-3905	222	16	product	product	NOUN
ejpam-3905	222	17	.	.	PUNCT
ejpam-3905	223	1	and	and	CCONJ
ejpam-3905	223	2	therefore	therefore	ADV
ejpam-3905	223	3	,	,	PUNCT
ejpam-3905	223	4	the	the	DET
ejpam-3905	223	5	module	module	NOUN
ejpam-3905	223	6	of	of	ADP
ejpam-3905	223	7	the	the	DET
ejpam-3905	223	8	indecomposable	indecomposable	ADJ
ejpam-3905	223	9	elements	element	NOUN
ejpam-3905	223	10	ja	ja	PROPN
ejpam-3905	223	11	is	be	AUX
ejpam-3905	223	12	that	that	DET
ejpam-3905	223	13	factor	factor	NOUN
ejpam-3905	223	14	a	a	PRON
ejpam-3905	223	15	concerning	concern	VERB
ejpam-3905	223	16	the	the	DET
ejpam-3905	223	17	decomposable	decomposable	ADJ
ejpam-3905	223	18	elements	element	NOUN
ejpam-3905	223	19	.	.	PUNCT
ejpam-3905	224	1	definition	definition	NOUN
ejpam-3905	224	2	23	23	NUM
ejpam-3905	224	3	.	.	PUNCT
ejpam-3905	225	1	let	let	VERB
ejpam-3905	225	2	b	b	X
ejpam-3905	225	3	be	be	AUX
ejpam-3905	225	4	the	the	DET
ejpam-3905	225	5	graded	grade	VERB
ejpam-3905	225	6	e∞-algebra	e∞-algebra	NOUN
ejpam-3905	225	7	and	and	CCONJ
ejpam-3905	225	8	f̂b	f̂b	PROPN
ejpam-3905	225	9	is	be	AUX
ejpam-3905	225	10	that	that	SCONJ
ejpam-3905	225	11	the	the	DET
ejpam-3905	225	12	b	b	NOUN
ejpam-3905	225	13	-	-	PUNCT
ejpam-3905	225	14	construction	construction	NOUN
ejpam-3905	225	15	.	.	PUNCT
ejpam-3905	226	1	from	from	ADP
ejpam-3905	226	2	the	the	DET
ejpam-3905	226	3	short	short	ADJ
ejpam-3905	226	4	exact	exact	ADJ
ejpam-3905	226	5	sequence	sequence	NOUN
ejpam-3905	226	6	;	;	PUNCT
ejpam-3905	226	7	0	0	NUM
ejpam-3905	226	8	−→	−→	NOUN
ejpam-3905	226	9	f̂	f̂	NUM
ejpam-3905	226	10	1bi	1bi	ADJ
ejpam-3905	226	11	−→f̂b	−→f̂b	PROPN
ejpam-3905	226	12	p	p	NOUN
ejpam-3905	226	13	−→	−→	NOUN
ejpam-3905	226	14	−→	−→	NOUN
ejpam-3905	226	15	0	0	NUM
ejpam-3905	227	1	we	we	PRON
ejpam-3905	227	2	’ve	’ve	AUX
ejpam-3905	227	3	got	get	VERB
ejpam-3905	227	4	the	the	DET
ejpam-3905	227	5	long	long	ADJ
ejpam-3905	227	6	exact	exact	ADJ
ejpam-3905	227	7	sequence	sequence	NOUN
ejpam-3905	227	8	;	;	PUNCT
ejpam-3905	227	9	·	·	PUNCT
ejpam-3905	227	10	·	·	PUNCT
ejpam-3905	227	11	·	·	PUNCT
ejpam-3905	228	1	−→	−→	NOUN
ejpam-3905	228	2	hn(f̂b)pn−→b	hn(f̂b)pn−→b	PROPN
ejpam-3905	228	3	vn	vn	PROPN
ejpam-3905	228	4	−→hn(f̂	−→hn(f̂	PROPN
ejpam-3905	228	5	1b	1b	NUM
ejpam-3905	228	6	)	)	PUNCT
ejpam-3905	228	7	−→	−→	NOUN
ejpam-3905	228	8	·	·	PUNCT
ejpam-3905	228	9	·	·	PUNCT
ejpam-3905	228	10	·	·	PUNCT
ejpam-3905	228	11	(	(	PUNCT
ejpam-3905	228	12	20	20	NUM
ejpam-3905	228	13	)	)	PUNCT
ejpam-3905	228	14	with	with	ADP
ejpam-3905	228	15	the	the	DET
ejpam-3905	228	16	projections	projection	NOUN
ejpam-3905	228	17	;	;	PUNCT
ejpam-3905	228	18	i	i	PRON
ejpam-3905	228	19	:	:	PUNCT
ejpam-3905	228	20	f̂	f̂	VERB
ejpam-3905	228	21	1b	1b	NUM
ejpam-3905	228	22	−→	−→	PROPN
ejpam-3905	228	23	f̂b	f̂b	PROPN
ejpam-3905	228	24	,	,	PUNCT
ejpam-3905	228	25	p	p	X
ejpam-3905	228	26	:	:	PUNCT
ejpam-3905	228	27	f̂b	f̂b	PROPN
ejpam-3905	228	28	−→	−→	PROPN
ejpam-3905	228	29	b.	b.	PROPN
ejpam-3905	228	30	and	and	CCONJ
ejpam-3905	228	31	for	for	ADP
ejpam-3905	228	32	all	all	DET
ejpam-3905	228	33	x	x	SYM
ejpam-3905	228	34	∈	∈	PROPN
ejpam-3905	228	35	b	b	NOUN
ejpam-3905	228	36	,	,	PUNCT
ejpam-3905	228	37	if	if	SCONJ
ejpam-3905	228	38	x	x	SYM
ejpam-3905	228	39	∈	∈	PROPN
ejpam-3905	228	40	kervn	kervn	VERB
ejpam-3905	228	41	:	:	PUNCT
ejpam-3905	229	1	b	b	X
ejpam-3905	229	2	−→	−→	NOUN
ejpam-3905	229	3	hn(f̂	hn(f̂	PRON
ejpam-3905	229	4	1b	1b	NUM
ejpam-3905	229	5	)	)	PUNCT
ejpam-3905	229	6	.	.	PUNCT
ejpam-3905	230	1	then	then	ADV
ejpam-3905	230	2	x	x	PRON
ejpam-3905	230	3	is	be	AUX
ejpam-3905	230	4	a	a	DET
ejpam-3905	230	5	primitive	primitive	ADJ
ejpam-3905	230	6	element	element	NOUN
ejpam-3905	230	7	.	.	PUNCT
ejpam-3905	231	1	now	now	ADV
ejpam-3905	231	2	we	we	PRON
ejpam-3905	231	3	can	can	AUX
ejpam-3905	231	4	present	present	VERB
ejpam-3905	231	5	the	the	DET
ejpam-3905	231	6	results	result	NOUN
ejpam-3905	231	7	that	that	PRON
ejpam-3905	231	8	we	we	PRON
ejpam-3905	231	9	studied	study	VERB
ejpam-3905	231	10	to	to	PART
ejpam-3905	231	11	clarify	clarify	VERB
ejpam-3905	231	12	important	important	ADJ
ejpam-3905	231	13	relationships	relationship	NOUN
ejpam-3905	231	14	of	of	ADP
ejpam-3905	231	15	morphisms	morphism	NOUN
ejpam-3905	231	16	in	in	ADP
ejpam-3905	231	17	the	the	DET
ejpam-3905	231	18	homology	homology	NOUN
ejpam-3905	231	19	and	and	CCONJ
ejpam-3905	231	20	cohomology	cohomology	NOUN
ejpam-3905	231	21	theory	theory	NOUN
ejpam-3905	231	22	of	of	ADP
ejpam-3905	231	23	e∞-algebra	e∞-algebra	PROPN
ejpam-3905	231	24	.	.	PROPN
ejpam-3905	231	25	5	5	NUM
ejpam-3905	231	26	.	.	X
ejpam-3905	231	27	main	main	ADJ
ejpam-3905	231	28	result	result	NOUN
ejpam-3905	231	29	through	through	ADP
ejpam-3905	231	30	our	our	PRON
ejpam-3905	231	31	study	study	NOUN
ejpam-3905	231	32	of	of	ADP
ejpam-3905	231	33	e∞-algebra	e∞-algebra	NOUN
ejpam-3905	231	34	and	and	CCONJ
ejpam-3905	231	35	providing	provide	VERB
ejpam-3905	231	36	some	some	DET
ejpam-3905	231	37	definitions	definition	NOUN
ejpam-3905	231	38	of	of	ADP
ejpam-3905	231	39	perfect	perfect	ADJ
ejpam-3905	231	40	algebra	algebra	NOUN
ejpam-3905	231	41	and	and	CCONJ
ejpam-3905	231	42	primitive	primitive	ADJ
ejpam-3905	231	43	and	and	CCONJ
ejpam-3905	231	44	indecomposable	indecomposable	ADJ
ejpam-3905	231	45	elements	element	NOUN
ejpam-3905	231	46	,	,	PUNCT
ejpam-3905	231	47	we	we	PRON
ejpam-3905	231	48	will	will	AUX
ejpam-3905	231	49	study	study	VERB
ejpam-3905	231	50	and	and	CCONJ
ejpam-3905	231	51	prove	prove	VERB
ejpam-3905	231	52	the	the	DET
ejpam-3905	231	53	relationships	relationship	NOUN
ejpam-3905	231	54	between	between	ADP
ejpam-3905	231	55	them	they	PRON
ejpam-3905	231	56	in	in	ADP
ejpam-3905	231	57	the	the	DET
ejpam-3905	231	58	(	(	PUNCT
ejpam-3905	231	59	co)homology	co)homology	NOUN
ejpam-3905	231	60	theory	theory	NOUN
ejpam-3905	231	61	through	through	ADP
ejpam-3905	231	62	the	the	DET
ejpam-3905	231	63	following	follow	VERB
ejpam-3905	231	64	theories	theory	NOUN
ejpam-3905	231	65	:	:	PUNCT
ejpam-3905	231	66	theorem	theorem	NOUN
ejpam-3905	231	67	4	4	NUM
ejpam-3905	231	68	.	.	PUNCT
ejpam-3905	232	1	let	let	VERB
ejpam-3905	232	2	a	a	PRON
ejpam-3905	232	3	and	and	CCONJ
ejpam-3905	232	4	na	na	AUX
ejpam-3905	232	5	are	be	AUX
ejpam-3905	232	6	the	the	DET
ejpam-3905	232	7	perfect	perfect	ADJ
ejpam-3905	232	8	algebra	algebra	NOUN
ejpam-3905	232	9	and	and	CCONJ
ejpam-3905	232	10	n	n	DET
ejpam-3905	232	11	-construction	-construction	NOUN
ejpam-3905	232	12	,	,	PUNCT
ejpam-3905	232	13	respectively	respectively	ADV
ejpam-3905	232	14	.	.	PUNCT
ejpam-3905	233	1	for	for	ADP
ejpam-3905	233	2	the	the	DET
ejpam-3905	233	3	homology	homology	NOUN
ejpam-3905	233	4	of	of	ADP
ejpam-3905	233	5	na	na	PROPN
ejpam-3905	233	6	,	,	PUNCT
ejpam-3905	233	7	the	the	DET
ejpam-3905	233	8	space	space	NOUN
ejpam-3905	233	9	of	of	ADP
ejpam-3905	233	10	the	the	DET
ejpam-3905	233	11	primitive	primitive	ADJ
ejpam-3905	233	12	elements	element	NOUN
ejpam-3905	233	13	phn(na	phn(na	VERB
ejpam-3905	233	14	)	)	PUNCT
ejpam-3905	233	15	is	be	AUX
ejpam-3905	233	16	isomorphic	isomorphic	ADJ
ejpam-3905	233	17	to	to	ADP
ejpam-3905	233	18	indecomposable	indecomposable	ADJ
ejpam-3905	233	19	elements	element	NOUN
ejpam-3905	233	20	space	space	NOUN
ejpam-3905	233	21	;	;	PUNCT
ejpam-3905	233	22	phn(na	phn(na	NOUN
ejpam-3905	233	23	)	)	PUNCT
ejpam-3905	234	1	∼=	∼=	PROPN
ejpam-3905	234	2	ja	ja	PROPN
ejpam-3905	234	3	.	.	PUNCT
ejpam-3905	234	4	proof	proof	NOUN
ejpam-3905	234	5	.	.	PUNCT
ejpam-3905	235	1	since	since	SCONJ
ejpam-3905	235	2	phn(na	phn(na	NOUN
ejpam-3905	235	3	)	)	PUNCT
ejpam-3905	235	4	is	be	AUX
ejpam-3905	235	5	primitive	primitive	ADJ
ejpam-3905	235	6	space	space	NOUN
ejpam-3905	235	7	then	then	ADV
ejpam-3905	235	8	;	;	PUNCT
ejpam-3905	235	9	phn(na	phn(na	ADJ
ejpam-3905	235	10	)	)	PUNCT
ejpam-3905	235	11	=	=	SYM
ejpam-3905	235	12	im{hn(f̂hn(na	im{hn(f̂hn(na	ADJ
ejpam-3905	235	13	)	)	PUNCT
ejpam-3905	235	14	)	)	PUNCT
ejpam-3905	236	1	7−→	7−→	PROPN
ejpam-3905	236	2	hn(na	hn(na	PROPN
ejpam-3905	236	3	)	)	PUNCT
ejpam-3905	236	4	}	}	PUNCT
ejpam-3905	236	5	since	since	SCONJ
ejpam-3905	236	6	hn(f̂na	hn(f̂na	NOUN
ejpam-3905	236	7	)	)	PUNCT
ejpam-3905	236	8	∼=	∼=	NOUN
ejpam-3905	236	9	a	a	DET
ejpam-3905	236	10	,	,	PUNCT
ejpam-3905	236	11	then	then	ADV
ejpam-3905	236	12	phn(na	phn(na	VERB
ejpam-3905	236	13	)	)	PUNCT
ejpam-3905	236	14	∼=	∼=	PROPN
ejpam-3905	236	15	i	i	PRON
ejpam-3905	236	16	m	m	VERB
ejpam-3905	236	17	a	a	DET
ejpam-3905	236	18	−→	−→	ADJ
ejpam-3905	236	19	hn(na	hn(na	PROPN
ejpam-3905	236	20	)	)	PUNCT
ejpam-3905	237	1	∼=	∼=	PROPN
ejpam-3905	237	2	ja	ja	PROPN
ejpam-3905	237	3	.	.	PUNCT
ejpam-3905	237	4	theorem	theorem	PROPN
ejpam-3905	237	5	5	5	NUM
ejpam-3905	237	6	.	.	PUNCT
ejpam-3905	237	7	consider	consider	VERB
ejpam-3905	237	8	jhn(fu	jhn(fu	VERB
ejpam-3905	237	9	)	)	PUNCT
ejpam-3905	237	10	be	be	AUX
ejpam-3905	237	11	the	the	DET
ejpam-3905	237	12	space	space	NOUN
ejpam-3905	237	13	of	of	ADP
ejpam-3905	237	14	indecomposable	indecomposable	ADJ
ejpam-3905	237	15	components	component	NOUN
ejpam-3905	237	16	in	in	ADP
ejpam-3905	237	17	hn(fu	hn(fu	PROPN
ejpam-3905	237	18	)	)	PUNCT
ejpam-3905	237	19	,	,	PUNCT
ejpam-3905	237	20	wherever	wherever	SCONJ
ejpam-3905	237	21	u	u	NOUN
ejpam-3905	237	22	is	be	AUX
ejpam-3905	237	23	perfect	perfect	ADJ
ejpam-3905	237	24	algebra	algebra	NOUN
ejpam-3905	237	25	and	and	CCONJ
ejpam-3905	237	26	pu	pu	PROPN
ejpam-3905	237	27	be	be	AUX
ejpam-3905	237	28	the	the	DET
ejpam-3905	237	29	primitive	primitive	ADJ
ejpam-3905	237	30	space	space	NOUN
ejpam-3905	237	31	.	.	PUNCT
ejpam-3905	238	1	then	then	ADV
ejpam-3905	238	2	jhn(fu	jhn(fu	VERB
ejpam-3905	238	3	)	)	PUNCT
ejpam-3905	238	4	∼=	∼=	PROPN
ejpam-3905	238	5	pu	pu	NOUN
ejpam-3905	238	6	.	.	PUNCT
ejpam-3905	239	1	proof	proof	NOUN
ejpam-3905	239	2	.	.	PUNCT
ejpam-3905	240	1	for	for	ADP
ejpam-3905	240	2	the	the	DET
ejpam-3905	240	3	indecomposable	indecomposable	ADJ
ejpam-3905	240	4	elements	element	NOUN
ejpam-3905	240	5	of	of	ADP
ejpam-3905	240	6	e∞-algebra	e∞-algebra	NOUN
ejpam-3905	240	7	we	we	PRON
ejpam-3905	240	8	tend	tend	VERB
ejpam-3905	240	9	to	to	PART
ejpam-3905	240	10	get	get	VERB
ejpam-3905	240	11	;	;	PUNCT
ejpam-3905	240	12	jhn(fu	jhn(fu	X
ejpam-3905	240	13	)	)	PUNCT
ejpam-3905	240	14	=	=	SYM
ejpam-3905	240	15	im{hn(fu	im{hn(fu	NOUN
ejpam-3905	240	16	)	)	PUNCT
ejpam-3905	240	17	−→	−→	ADJ
ejpam-3905	240	18	hn(bhn(fu	hn(bhn(fu	NOUN
ejpam-3905	240	19	)	)	PUNCT
ejpam-3905	240	20	)	)	PUNCT
ejpam-3905	240	21	}	}	PUNCT
ejpam-3905	240	22	since	since	SCONJ
ejpam-3905	240	23	hn(bhn(fu	hn(bhn(fu	NOUN
ejpam-3905	240	24	)	)	PUNCT
ejpam-3905	240	25	)	)	PUNCT
ejpam-3905	241	1	=	=	SYM
ejpam-3905	241	2	u	u	NOUN
ejpam-3905	241	3	,	,	PUNCT
ejpam-3905	241	4	we	we	PRON
ejpam-3905	241	5	get	get	VERB
ejpam-3905	241	6	jhn(fu	jhn(fu	ADV
ejpam-3905	241	7	)	)	PUNCT
ejpam-3905	241	8	∼=	∼=	VERB
ejpam-3905	241	9	im{hn(fu	im{hn(fu	NOUN
ejpam-3905	241	10	)	)	PUNCT
ejpam-3905	241	11	−→	−→	NOUN
ejpam-3905	241	12	u	u	NOUN
ejpam-3905	241	13	}	}	PUNCT
ejpam-3905	241	14	∼=	∼=	PROPN
ejpam-3905	241	15	pa	pa	PROPN
ejpam-3905	241	16	a.	a.	PROPN
ejpam-3905	241	17	noreldeen	noreldeen	PROPN
ejpam-3905	241	18	,	,	PUNCT
ejpam-3905	241	19	s.	s.	PROPN
ejpam-3905	241	20	abo	abo	VERB
ejpam-3905	241	21	quota	quota	PROPN
ejpam-3905	241	22	/	/	SYM
ejpam-3905	241	23	eur	eur	NOUN
ejpam-3905	241	24	.	.	PUNCT
ejpam-3905	242	1	j.	j.	PROPN
ejpam-3905	242	2	pure	pure	PROPN
ejpam-3905	242	3	appl	appl	PROPN
ejpam-3905	242	4	.	.	PROPN
ejpam-3905	242	5	math	math	PROPN
ejpam-3905	242	6	,	,	PUNCT
ejpam-3905	242	7	14	14	NUM
ejpam-3905	242	8	(	(	PUNCT
ejpam-3905	242	9	2	2	NUM
ejpam-3905	242	10	)	)	PUNCT
ejpam-3905	242	11	(	(	PUNCT
ejpam-3905	242	12	2021	2021	NUM
ejpam-3905	242	13	)	)	PUNCT
ejpam-3905	242	14	,	,	PUNCT
ejpam-3905	242	15	480	480	NUM
ejpam-3905	242	16	-	-	SYM
ejpam-3905	242	17	492	492	NUM
ejpam-3905	242	18	491	491	NUM
ejpam-3905	242	19	theorem	theorem	NOUN
ejpam-3905	242	20	6	6	NUM
ejpam-3905	242	21	.	.	PUNCT
ejpam-3905	242	22	for	for	ADP
ejpam-3905	242	23	the	the	DET
ejpam-3905	242	24	ideal	ideal	ADJ
ejpam-3905	242	25	algebra	algebra	PROPN
ejpam-3905	242	26	u	u	NOUN
ejpam-3905	242	27	,	,	PUNCT
ejpam-3905	242	28	and	and	CCONJ
ejpam-3905	242	29	therefore	therefore	ADV
ejpam-3905	242	30	the	the	DET
ejpam-3905	242	31	nth	nth	NOUN
ejpam-3905	242	32	-	-	PUNCT
ejpam-3905	242	33	homology	homology	NOUN
ejpam-3905	242	34	un	un	PROPN
ejpam-3905	242	35	=	=	PROPN
ejpam-3905	242	36	hn(ba	hn(ba	PROPN
ejpam-3905	242	37	)	)	PUNCT
ejpam-3905	242	38	is	be	AUX
ejpam-3905	242	39	the	the	DET
ejpam-3905	242	40	graded	grade	VERB
ejpam-3905	242	41	space	space	NOUN
ejpam-3905	242	42	with	with	ADP
ejpam-3905	242	43	the	the	DET
ejpam-3905	242	44	approximation	approximation	NOUN
ejpam-3905	242	45	property	property	NOUN
ejpam-3905	242	46	.	.	PUNCT
ejpam-3905	243	1	then	then	ADV
ejpam-3905	243	2	we	we	PRON
ejpam-3905	243	3	get	get	VERB
ejpam-3905	243	4	of	of	ADP
ejpam-3905	243	5	un	un	PROPN
ejpam-3905	243	6	=	=	PROPN
ejpam-3905	243	7	hn(ba	hn(ba	PROPN
ejpam-3905	243	8	)	)	PUNCT
ejpam-3905	243	9	in	in	ADP
ejpam-3905	243	10	e∞-algebra	e∞-algebra	ADJ
ejpam-3905	243	11	as	as	ADP
ejpam-3905	243	12	,	,	PUNCT
ejpam-3905	243	13	∑	∑	ADV
ejpam-3905	243	14	n≥0	n≥0	PROPN
ejpam-3905	243	15	πn	πn	INTJ
ejpam-3905	243	16	(	(	PUNCT
ejpam-3905	243	17	¯q	¯q	PROPN
ejpam-3905	243	18	⊗	⊗	PROPN
ejpam-3905	243	19	·	·	PUNCT
ejpam-3905	243	20	·	·	PUNCT
ejpam-3905	243	21	·	·	PUNCT
ejpam-3905	244	1	⊗	⊗	PROPN
ejpam-3905	244	2	q)π̄(n+	q)π̄(n+	PROPN
ejpam-3905	244	3	2)(x	2)(x	NUM
ejpam-3905	244	4	)	)	PUNCT
ejpam-3905	244	5	=	=	SYM
ejpam-3905	244	6	0	0	NUM
ejpam-3905	244	7	,	,	PUNCT
ejpam-3905	244	8	x	x	SYM
ejpam-3905	244	9	∈	∈	PROPN
ejpam-3905	244	10	k̄	k̄	X
ejpam-3905	244	11	(	(	PUNCT
ejpam-3905	244	12	21	21	NUM
ejpam-3905	244	13	)	)	PUNCT
ejpam-3905	244	14	now	now	ADV
ejpam-3905	244	15	we	we	PRON
ejpam-3905	244	16	present	present	VERB
ejpam-3905	244	17	some	some	DET
ejpam-3905	244	18	examples	example	NOUN
ejpam-3905	244	19	as	as	ADP
ejpam-3905	244	20	an	an	DET
ejpam-3905	244	21	application	application	NOUN
ejpam-3905	244	22	to	to	ADP
ejpam-3905	244	23	what	what	PRON
ejpam-3905	244	24	we	we	PRON
ejpam-3905	244	25	got	get	VERB
ejpam-3905	244	26	as	as	ADP
ejpam-3905	244	27	results	result	NOUN
ejpam-3905	244	28	from	from	ADP
ejpam-3905	244	29	previous	previous	ADJ
ejpam-3905	244	30	theories	theory	NOUN
ejpam-3905	244	31	.	.	PUNCT
ejpam-3905	245	1	example	example	NOUN
ejpam-3905	245	2	5	5	NUM
ejpam-3905	245	3	.	.	X
ejpam-3905	245	4	consider	consider	VERB
ejpam-3905	245	5	perfect	perfect	ADJ
ejpam-3905	245	6	algebra	algebra	NOUN
ejpam-3905	245	7	u	u	NOUN
ejpam-3905	245	8	=	=	PROPN
ejpam-3905	245	9	=(	=(	PROPN
ejpam-3905	245	10	m	m	PROPN
ejpam-3905	245	11	)	)	PUNCT
ejpam-3905	245	12	1	1	NUM
ejpam-3905	245	13	.	.	PUNCT
ejpam-3905	246	1	for	for	ADP
ejpam-3905	246	2	the	the	DET
ejpam-3905	246	3	cohomology	cohomology	NOUN
ejpam-3905	246	4	hn(u	hn(u	NOUN
ejpam-3905	246	5	)	)	PUNCT
ejpam-3905	246	6	,	,	PUNCT
ejpam-3905	246	7	we	we	PRON
ejpam-3905	246	8	discover	discover	VERB
ejpam-3905	246	9	the	the	DET
ejpam-3905	246	10	generator	generator	NOUN
ejpam-3905	246	11	a1	a1	PROPN
ejpam-3905	246	12	∈	∈	PROPN
ejpam-3905	246	13	h1(u	h1(u	PROPN
ejpam-3905	246	14	)	)	PUNCT
ejpam-3905	246	15	corresponding	correspond	VERB
ejpam-3905	246	16	e1	e1	NOUN
ejpam-3905	246	17	∈	∈	NOUN
ejpam-3905	247	1	=	=	VERB
ejpam-3905	247	2	m1	m1	NOUN
ejpam-3905	247	3	and	and	CCONJ
ejpam-3905	247	4	satisfy	satisfy	VERB
ejpam-3905	247	5	that	that	PRON
ejpam-3905	247	6	,	,	PUNCT
ejpam-3905	247	7	πn−2(a1	πn−2(a1	PROPN
ejpam-3905	247	8	⊗	⊗	PROPN
ejpam-3905	247	9	·	·	PUNCT
ejpam-3905	247	10	·	·	PUNCT
ejpam-3905	247	11	·	·	PUNCT
ejpam-3905	247	12	⊗	⊗	PROPN
ejpam-3905	247	13	a2	a2	PROPN
ejpam-3905	247	14	)	)	PUNCT
ejpam-3905	247	15	=	=	SYM
ejpam-3905	247	16	0	0	NUM
ejpam-3905	247	17	,	,	PUNCT
ejpam-3905	247	18	2	2	NUM
ejpam-3905	247	19	≤	≤	NUM
ejpam-3905	247	20	n	n	PRON
ejpam-3905	247	21	≤	≤	NOUN
ejpam-3905	247	22	m	m	VERB
ejpam-3905	248	1	and	and	CCONJ
ejpam-3905	248	2	we	we	PRON
ejpam-3905	248	3	get	get	VERB
ejpam-3905	248	4	the	the	DET
ejpam-3905	248	5	even	even	ADV
ejpam-3905	248	6	-	-	PUNCT
ejpam-3905	248	7	dimensional	dimensional	ADJ
ejpam-3905	248	8	of	of	ADP
ejpam-3905	248	9	cohomologies	cohomologie	NOUN
ejpam-3905	248	10	have	have	VERB
ejpam-3905	248	11	the	the	DET
ejpam-3905	248	12	generators	generator	NOUN
ejpam-3905	248	13	an2	an2	PROPN
ejpam-3905	248	14	=	=	SYM
ejpam-3905	248	15	a2	a2	PROPN
ejpam-3905	248	16	·	·	PUNCT
ejpam-3905	248	17	·	·	PUNCT
ejpam-3905	249	1	·	·	PUNCT
ejpam-3905	249	2	a2	a2	PROPN
ejpam-3905	249	3	∈	∈	PROPN
ejpam-3905	249	4	h2n(u	h2n(u	PROPN
ejpam-3905	249	5	)	)	PUNCT
ejpam-3905	249	6	and	and	CCONJ
ejpam-3905	249	7	isomorphic	isomorphic	ADJ
ejpam-3905	249	8	to	to	ADP
ejpam-3905	249	9	c.	c.	PROPN
ejpam-3905	249	10	however	however	ADV
ejpam-3905	249	11	,	,	PUNCT
ejpam-3905	249	12	the	the	DET
ejpam-3905	249	13	odd	odd	ADV
ejpam-3905	249	14	-	-	PUNCT
ejpam-3905	249	15	dimensional	dimensional	ADJ
ejpam-3905	249	16	cohomology	cohomology	NOUN
ejpam-3905	249	17	has	have	VERB
ejpam-3905	249	18	the	the	DET
ejpam-3905	249	19	generators	generator	NOUN
ejpam-3905	249	20	an2	an2	PROPN
ejpam-3905	249	21	·	·	PUNCT
ejpam-3905	249	22	pa1	pa1	PROPN
ejpam-3905	249	23	∈	∈	PROPN
ejpam-3905	249	24	h2n+1(a	h2n+1(a	PROPN
ejpam-3905	249	25	)	)	PUNCT
ejpam-3905	249	26	and	and	CCONJ
ejpam-3905	249	27	isomorphic	isomorphic	ADJ
ejpam-3905	249	28	to	to	ADP
ejpam-3905	249	29	c.	c.	PROPN
ejpam-3905	249	30	example	example	NOUN
ejpam-3905	249	31	6	6	NUM
ejpam-3905	249	32	.	.	X
ejpam-3905	250	1	for	for	ADP
ejpam-3905	250	2	the	the	DET
ejpam-3905	250	3	ideal	ideal	ADJ
ejpam-3905	250	4	algebra	algebra	PROPN
ejpam-3905	250	5	u	u	NOUN
ejpam-3905	250	6	=	=	PROPN
ejpam-3905	250	7	=(	=(	PROPN
ejpam-3905	250	8	m	m	PROPN
ejpam-3905	250	9	)	)	PUNCT
ejpam-3905	250	10	1	1	NUM
ejpam-3905	250	11	and	and	CCONJ
ejpam-3905	250	12	also	also	ADV
ejpam-3905	250	13	the	the	DET
ejpam-3905	250	14	short	short	ADJ
ejpam-3905	250	15	exact	exact	ADJ
ejpam-3905	250	16	sequence	sequence	NOUN
ejpam-3905	250	17	0	0	NUM
ejpam-3905	250	18	−→	−→	ADJ
ejpam-3905	250	19	=(	=(	NOUN
ejpam-3905	250	20	m	m	NOUN
ejpam-3905	250	21	)	)	PUNCT
ejpam-3905	250	22	1	1	NUM
ejpam-3905	250	23	−→	−→	NOUN
ejpam-3905	250	24	=	=	SYM
ejpam-3905	250	25	1	1	NUM
ejpam-3905	250	26	−→	−→	NOUN
ejpam-3905	250	27	=	=	NOUN
ejpam-3905	250	28	m1	m1	NOUN
ejpam-3905	250	29	−→	−→	NOUN
ejpam-3905	250	30	0	0	NUM
ejpam-3905	250	31	,	,	PUNCT
ejpam-3905	250	32	we	we	PRON
ejpam-3905	250	33	discover	discover	VERB
ejpam-3905	250	34	that	that	SCONJ
ejpam-3905	250	35	the	the	DET
ejpam-3905	250	36	cohomology	cohomology	NOUN
ejpam-3905	250	37	h1(u	h1(u	PROPN
ejpam-3905	250	38	)	)	PUNCT
ejpam-3905	250	39	has	have	VERB
ejpam-3905	250	40	generators	generator	NOUN
ejpam-3905	250	41	am+1	am+1	PROPN
ejpam-3905	250	42	,	,	PUNCT
ejpam-3905	250	43	·	·	PUNCT
ejpam-3905	250	44	·	·	PUNCT
ejpam-3905	250	45	·	·	PUNCT
ejpam-3905	250	46	,	,	PUNCT
ejpam-3905	250	47	a2m+1	a2m+1	NOUN
ejpam-3905	251	1	that	that	SCONJ
ejpam-3905	251	2	like	like	ADP
ejpam-3905	251	3	em+1	em+1	PRON
ejpam-3905	251	4	,	,	PUNCT
ejpam-3905	251	5	·	·	PUNCT
ejpam-3905	251	6	·	·	PUNCT
ejpam-3905	251	7	·	·	PUNCT
ejpam-3905	251	8	,	,	PUNCT
ejpam-3905	251	9	e2m+1	e2m+1	PROPN
ejpam-3905	251	10	∈	∈	PROPN
ejpam-3905	251	11	u	u	NOUN
ejpam-3905	251	12	and	and	CCONJ
ejpam-3905	251	13	satisfy	satisfy	VERB
ejpam-3905	251	14	that	that	PRON
ejpam-3905	251	15	;	;	PUNCT
ejpam-3905	251	16	am+1am+1	am+1am+1	VERB
ejpam-3905	251	17	=	=	SYM
ejpam-3905	251	18	0	0	NUM
ejpam-3905	251	19	,	,	PUNCT
ejpam-3905	251	20	am+1am+2	am+1am+2	PRON
ejpam-3905	251	21	+	+	CCONJ
ejpam-3905	251	22	am+2am+1	am+2am+1	X
ejpam-3905	251	23	=	=	X
ejpam-3905	251	24	0	0	NUM
ejpam-3905	251	25	,	,	PUNCT
ejpam-3905	251	26	·	·	PUNCT
ejpam-3905	251	27	·	·	PUNCT
ejpam-3905	251	28	·	·	PUNCT
ejpam-3905	251	29	·	·	PUNCT
ejpam-3905	251	30	·	·	PUNCT
ejpam-3905	251	31	·	·	PUNCT
ejpam-3905	251	32	·	·	PUNCT
ejpam-3905	251	33	·	·	PUNCT
ejpam-3905	251	34	·	·	PUNCT
ejpam-3905	251	35	·	·	PUNCT
ejpam-3905	251	36	·	·	PUNCT
ejpam-3905	251	37	·	·	PUNCT
ejpam-3905	251	38	·	·	PUNCT
ejpam-3905	251	39	·	·	PUNCT
ejpam-3905	251	40	·	·	PUNCT
ejpam-3905	251	41	·	·	PUNCT
ejpam-3905	251	42	·	·	PUNCT
ejpam-3905	251	43	·	·	PUNCT
ejpam-3905	251	44	·	·	PUNCT
ejpam-3905	251	45	·	·	PUNCT
ejpam-3905	251	46	·	·	PUNCT
ejpam-3905	251	47	·	·	PUNCT
ejpam-3905	251	48	·	·	PUNCT
ejpam-3905	251	49	·	·	PUNCT
ejpam-3905	251	50	·	·	PUNCT
ejpam-3905	251	51	·	·	PUNCT
ejpam-3905	251	52	·	·	PUNCT
ejpam-3905	251	53	·	·	PUNCT
ejpam-3905	251	54	·	·	PUNCT
ejpam-3905	251	55	·	·	PUNCT
ejpam-3905	251	56	·	·	PUNCT
ejpam-3905	251	57	·	·	PUNCT
ejpam-3905	251	58	·	·	PUNCT
ejpam-3905	251	59	·	·	PUNCT
ejpam-3905	251	60	·	·	PUNCT
ejpam-3905	251	61	·	·	PUNCT
ejpam-3905	251	62	·	·	PUNCT
ejpam-3905	251	63	·	·	PUNCT
ejpam-3905	251	64	·	·	PUNCT
ejpam-3905	251	65	·	·	PUNCT
ejpam-3905	251	66	·	·	PUNCT
ejpam-3905	251	67	·	·	PUNCT
ejpam-3905	251	68	·	·	PUNCT
ejpam-3905	251	69	·	·	PUNCT
ejpam-3905	251	70	·	·	PUNCT
ejpam-3905	251	71	·	·	PUNCT
ejpam-3905	251	72	·	·	PUNCT
ejpam-3905	251	73	·	·	PUNCT
ejpam-3905	251	74	·	·	PUNCT
ejpam-3905	251	75	·	·	PUNCT
ejpam-3905	251	76	·	·	PUNCT
ejpam-3905	252	1	am+1a2m+1	am+1a2m+1	PUNCT
ejpam-3905	252	2	+	+	X
ejpam-3905	252	3	·	·	PUNCT
ejpam-3905	252	4	·	·	PUNCT
ejpam-3905	252	5	·	·	PUNCT
ejpam-3905	252	6	+	+	NUM
ejpam-3905	252	7	a2m+1am+1	a2m+1am+1	X
ejpam-3905	252	8	=	=	SYM
ejpam-3905	252	9	0	0	NUM
ejpam-3905	252	10	,	,	PUNCT
ejpam-3905	252	11	π1(am+1	π1(am+1	X
ejpam-3905	252	12	⊗	⊗	PROPN
ejpam-3905	252	13	am+1	am+1	PROPN
ejpam-3905	252	14	⊗	⊗	PROPN
ejpam-3905	252	15	am+1	am+1	PROPN
ejpam-3905	252	16	)	)	PUNCT
ejpam-3905	252	17	+	+	CCONJ
ejpam-3905	252	18	am+2a2m+1	am+2a2m+1	PROPN
ejpam-3905	252	19	+	+	CCONJ
ejpam-3905	252	20	·	·	PUNCT
ejpam-3905	252	21	·	·	PUNCT
ejpam-3905	252	22	·	·	PUNCT
ejpam-3905	252	23	+	+	NUM
ejpam-3905	252	24	a2m+1am+2	a2m+1am+2	NOUN
ejpam-3905	252	25	=	=	SYM
ejpam-3905	252	26	0	0	PUNCT
ejpam-3905	252	27	·	·	PUNCT
ejpam-3905	252	28	·	·	PUNCT
ejpam-3905	252	29	·	·	PUNCT
ejpam-3905	252	30	·	·	PUNCT
ejpam-3905	252	31	·	·	PUNCT
ejpam-3905	252	32	·	·	PUNCT
ejpam-3905	252	33	·	·	PUNCT
ejpam-3905	252	34	·	·	PUNCT
ejpam-3905	252	35	·	·	PUNCT
ejpam-3905	252	36	·	·	PUNCT
ejpam-3905	252	37	·	·	PUNCT
ejpam-3905	252	38	·	·	PUNCT
ejpam-3905	252	39	·	·	PUNCT
ejpam-3905	252	40	·	·	PUNCT
ejpam-3905	252	41	·	·	PUNCT
ejpam-3905	252	42	·	·	PUNCT
ejpam-3905	252	43	·	·	PUNCT
ejpam-3905	252	44	·	·	PUNCT
ejpam-3905	252	45	·	·	PUNCT
ejpam-3905	252	46	·	·	PUNCT
ejpam-3905	252	47	·	·	PUNCT
ejpam-3905	252	48	·	·	PUNCT
ejpam-3905	252	49	·	·	PUNCT
ejpam-3905	252	50	·	·	PUNCT
ejpam-3905	252	51	·	·	PUNCT
ejpam-3905	252	52	·	·	PUNCT
ejpam-3905	252	53	·	·	PUNCT
ejpam-3905	252	54	·	·	PUNCT
ejpam-3905	252	55	·	·	PUNCT
ejpam-3905	252	56	·	·	PUNCT
ejpam-3905	252	57	·	·	PUNCT
ejpam-3905	252	58	·	·	PUNCT
ejpam-3905	252	59	·	·	PUNCT
ejpam-3905	252	60	·	·	PUNCT
ejpam-3905	252	61	·	·	PUNCT
ejpam-3905	252	62	·	·	PUNCT
ejpam-3905	252	63	·	·	PUNCT
ejpam-3905	252	64	·	·	PUNCT
ejpam-3905	252	65	·	·	PUNCT
ejpam-3905	252	66	·	·	PUNCT
ejpam-3905	252	67	·	·	PUNCT
ejpam-3905	252	68	·	·	PUNCT
ejpam-3905	252	69	·	·	PUNCT
ejpam-3905	252	70	·	·	PUNCT
ejpam-3905	252	71	·	·	PUNCT
ejpam-3905	252	72	·	·	PUNCT
ejpam-3905	252	73	·	·	PUNCT
ejpam-3905	252	74	·	·	PUNCT
ejpam-3905	252	75	·	·	PUNCT
ejpam-3905	252	76	·	·	PUNCT
ejpam-3905	252	77	·	·	PUNCT
ejpam-3905	252	78	6	6	X
ejpam-3905	252	79	.	.	X
ejpam-3905	252	80	conclusion	conclusion	NOUN
ejpam-3905	252	81	we	we	PRON
ejpam-3905	252	82	have	have	AUX
ejpam-3905	252	83	studied	study	VERB
ejpam-3905	252	84	the	the	DET
ejpam-3905	252	85	basic	basic	ADJ
ejpam-3905	252	86	statements	statement	NOUN
ejpam-3905	252	87	previously	previously	ADV
ejpam-3905	252	88	made	make	VERB
ejpam-3905	252	89	on	on	ADP
ejpam-3905	252	90	e	e	NOUN
ejpam-3905	252	91	-	-	NOUN
ejpam-3905	252	92	infinity	infinity	NOUN
ejpam-3905	252	93	modules	module	NOUN
ejpam-3905	252	94	and	and	CCONJ
ejpam-3905	252	95	einfinity	einfinity	NOUN
ejpam-3905	252	96	algebras	algebras	X
ejpam-3905	252	97	.	.	PUNCT
ejpam-3905	253	1	we	we	PRON
ejpam-3905	253	2	also	also	ADV
ejpam-3905	253	3	demonstrate	demonstrate	VERB
ejpam-3905	253	4	an	an	DET
ejpam-3905	253	5	interpretation	interpretation	NOUN
ejpam-3905	253	6	of	of	ADP
ejpam-3905	253	7	the	the	DET
ejpam-3905	253	8	e	e	NOUN
ejpam-3905	253	9	-	-	NOUN
ejpam-3905	253	10	infinity	infinity	ADJ
ejpam-3905	253	11	algebras	algebra	NOUN
ejpam-3905	253	12	and	and	CCONJ
ejpam-3905	253	13	modules	module	NOUN
ejpam-3905	253	14	as	as	ADP
ejpam-3905	253	15	fibrant	fibrant	ADJ
ejpam-3905	253	16	objects	object	NOUN
ejpam-3905	253	17	within	within	ADP
ejpam-3905	253	18	the	the	DET
ejpam-3905	253	19	category	category	NOUN
ejpam-3905	253	20	differential	differential	NOUN
ejpam-3905	253	21	graded	grade	VERB
ejpam-3905	253	22	co	co	NOUN
ejpam-3905	253	23	-	-	NOUN
ejpam-3905	253	24	algebras	algebra	NOUN
ejpam-3905	253	25	and	and	CCONJ
ejpam-3905	253	26	comodules	comodule	NOUN
ejpam-3905	253	27	.	.	PUNCT
ejpam-3905	254	1	we	we	PRON
ejpam-3905	254	2	have	have	AUX
ejpam-3905	254	3	also	also	ADV
ejpam-3905	254	4	presented	present	VERB
ejpam-3905	254	5	new	new	ADJ
ejpam-3905	254	6	properties	property	NOUN
ejpam-3905	254	7	and	and	CCONJ
ejpam-3905	254	8	examples	example	NOUN
ejpam-3905	254	9	to	to	PART
ejpam-3905	254	10	explain	explain	VERB
ejpam-3905	254	11	the	the	DET
ejpam-3905	254	12	idea	idea	NOUN
ejpam-3905	254	13	.	.	PUNCT
ejpam-3905	255	1	acknowledgements	acknowledgement	VERB
ejpam-3905	255	2	the	the	DET
ejpam-3905	255	3	author	author	NOUN
ejpam-3905	255	4	expresses	express	VERB
ejpam-3905	255	5	special	special	ADJ
ejpam-3905	255	6	thanks	thank	NOUN
ejpam-3905	255	7	to	to	ADP
ejpam-3905	255	8	the	the	DET
ejpam-3905	255	9	referees	referee	NOUN
ejpam-3905	255	10	for	for	ADP
ejpam-3905	255	11	their	their	PRON
ejpam-3905	255	12	suggestions	suggestion	NOUN
ejpam-3905	255	13	and	and	CCONJ
ejpam-3905	255	14	assistance	assistance	NOUN
ejpam-3905	255	15	in	in	ADP
ejpam-3905	255	16	the	the	DET
ejpam-3905	255	17	chief	chief	ADJ
ejpam-3905	255	18	draft	draft	NOUN
ejpam-3905	255	19	of	of	ADP
ejpam-3905	255	20	the	the	DET
ejpam-3905	255	21	present	present	ADJ
ejpam-3905	255	22	work	work	NOUN
ejpam-3905	255	23	.	.	PUNCT
ejpam-3905	256	1	references	reference	NOUN
ejpam-3905	256	2	492	492	NUM
ejpam-3905	256	3	references	reference	NOUN
ejpam-3905	256	4	[	[	X
ejpam-3905	256	5	1	1	NUM
ejpam-3905	256	6	]	]	PUNCT
ejpam-3905	256	7	c.	c.	PROPN
ejpam-3905	256	8	berger	berger	PROPN
ejpam-3905	256	9	and	and	CCONJ
ejpam-3905	256	10	i.	i.	PROPN
ejpam-3905	256	11	moerdijk	moerdijk	PROPN
ejpam-3905	256	12	.	.	PUNCT
ejpam-3905	257	1	axiomatic	axiomatic	ADJ
ejpam-3905	257	2	homotopy	homotopy	PROPN
ejpam-3905	257	3	theory	theory	NOUN
ejpam-3905	257	4	for	for	ADP
ejpam-3905	257	5	operads	operad	NOUN
ejpam-3905	257	6	.	.	PUNCT
ejpam-3905	258	1	comment	comment	NOUN
ejpam-3905	258	2	.	.	PUNCT
ejpam-3905	259	1	math	math	NOUN
ejpam-3905	259	2	.	.	PUNCT
ejpam-3905	260	1	helv	helv	PROPN
ejpam-3905	260	2	.	.	PROPN
ejpam-3905	260	3	,	,	PUNCT
ejpam-3905	260	4	78:805831	78:805831	PROPN
ejpam-3905	260	5	,	,	PUNCT
ejpam-3905	260	6	2003	2003	NUM
ejpam-3905	260	7	.	.	PUNCT
ejpam-3905	261	1	[	[	X
ejpam-3905	261	2	2	2	NUM
ejpam-3905	261	3	]	]	X
ejpam-3905	261	4	b.	b.	PROPN
ejpam-3905	261	5	fresse	fresse	NOUN
ejpam-3905	261	6	.	.	PUNCT
ejpam-3905	262	1	the	the	DET
ejpam-3905	262	2	bar	bar	NOUN
ejpam-3905	262	3	complex	complex	NOUN
ejpam-3905	262	4	of	of	ADP
ejpam-3905	262	5	an	an	DET
ejpam-3905	262	6	e	e	NOUN
ejpam-3905	262	7	-	-	NOUN
ejpam-3905	262	8	infinity	infinity	ADJ
ejpam-3905	262	9	algebra	algebra	NOUN
ejpam-3905	262	10	.	.	PUNCT
ejpam-3905	263	1	adv	adv	PROPN
ejpam-3905	263	2	.	.	PUNCT
ejpam-3905	263	3	math	math	PROPN
ejpam-3905	263	4	.	.	PUNCT
ejpam-3905	263	5	,	,	PUNCT
ejpam-3905	263	6	223:2049–2096	223:2049–2096	NUM
ejpam-3905	263	7	,	,	PUNCT
ejpam-3905	263	8	2010	2010	NUM
ejpam-3905	263	9	.	.	PUNCT
ejpam-3905	264	1	[	[	X
ejpam-3905	264	2	3	3	X
ejpam-3905	264	3	]	]	X
ejpam-3905	264	4	b.	b.	PROPN
ejpam-3905	264	5	fresse	fresse	PROPN
ejpam-3905	264	6	.	.	PUNCT
ejpam-3905	265	1	iterated	iterate	VERB
ejpam-3905	265	2	bar	bar	NOUN
ejpam-3905	265	3	complexes	complex	NOUN
ejpam-3905	265	4	of	of	ADP
ejpam-3905	265	5	einfinity	einfinity	NOUN
ejpam-3905	265	6	algebras	algebra	NOUN
ejpam-3905	265	7	and	and	CCONJ
ejpam-3905	265	8	homology	homology	NOUN
ejpam-3905	265	9	theories	theory	NOUN
ejpam-3905	265	10	.	.	PUNCT
ejpam-3905	266	1	algebraic	algebraic	PROPN
ejpam-3905	266	2	&	&	CCONJ
ejpam-3905	266	3	geometric	geometric	ADJ
ejpam-3905	266	4	topology	topology	NOUN
ejpam-3905	266	5	,	,	PUNCT
ejpam-3905	266	6	11:747–838	11:747–838	PROPN
ejpam-3905	266	7	,	,	PUNCT
ejpam-3905	266	8	2011	2011	NUM
ejpam-3905	266	9	.	.	PUNCT
ejpam-3905	267	1	[	[	X
ejpam-3905	267	2	4	4	NUM
ejpam-3905	267	3	]	]	X
ejpam-3905	267	4	l.	l.	PROPN
ejpam-3905	267	5	lewis	lewis	PROPN
ejpam-3905	267	6	g.	g.	PROPN
ejpam-3905	267	7	,	,	PUNCT
ejpam-3905	267	8	j.	j.	PROPN
ejpam-3905	267	9	may	may	AUX
ejpam-3905	267	10	p.	p.	VERB
ejpam-3905	267	11	,	,	PUNCT
ejpam-3905	267	12	and	and	CCONJ
ejpam-3905	267	13	m.	m.	NOUN
ejpam-3905	267	14	steinberger	steinberger	PROPN
ejpam-3905	267	15	.	.	PUNCT
ejpam-3905	268	1	equivariant	equivariant	PROPN
ejpam-3905	268	2	stable	stable	PROPN
ejpam-3905	268	3	homotopy	homotopy	PROPN
ejpam-3905	268	4	theory	theory	NOUN
ejpam-3905	268	5	.	.	PUNCT
ejpam-3905	269	1	springer	springer	NOUN
ejpam-3905	269	2	lecture	lecture	NOUN
ejpam-3905	269	3	notes	note	NOUN
ejpam-3905	269	4	,	,	PUNCT
ejpam-3905	269	5	1213	1213	NUM
ejpam-3905	269	6	,	,	PUNCT
ejpam-3905	269	7	1986	1986	NUM
ejpam-3905	269	8	.	.	PUNCT
ejpam-3905	270	1	[	[	X
ejpam-3905	270	2	5	5	X
ejpam-3905	270	3	]	]	PUNCT
ejpam-3905	270	4	e.	e.	PROPN
ejpam-3905	270	5	getzler	getzler	PROPN
ejpam-3905	270	6	and	and	CCONJ
ejpam-3905	270	7	s.	s.	PROPN
ejpam-3905	270	8	petrack	petrack	PROPN
ejpam-3905	270	9	j.	j.	PROPN
ejpam-3905	270	10	jones	jones	PROPN
ejpam-3905	270	11	d.	d.	PROPN
ejpam-3905	270	12	differential	differential	PROPN
ejpam-3905	270	13	forms	form	NOUN
ejpam-3905	270	14	on	on	ADP
ejpam-3905	270	15	loop	loop	NOUN
ejpam-3905	270	16	spaces	space	NOUN
ejpam-3905	270	17	and	and	CCONJ
ejpam-3905	270	18	the	the	DET
ejpam-3905	270	19	cyclic	cyclic	ADJ
ejpam-3905	270	20	bar	bar	NOUN
ejpam-3905	270	21	complex	complex	NOUN
ejpam-3905	270	22	.	.	PUNCT
ejpam-3905	271	1	topology	topology	NOUN
ejpam-3905	271	2	,	,	PUNCT
ejpam-3905	271	3	30:339–371	30:339–371	PROPN
ejpam-3905	271	4	,	,	PUNCT
ejpam-3905	271	5	1990	1990	NUM
ejpam-3905	271	6	.	.	PUNCT
ejpam-3905	272	1	[	[	X
ejpam-3905	272	2	6	6	NUM
ejpam-3905	272	3	]	]	PUNCT
ejpam-3905	272	4	a.	a.	NOUN
ejpam-3905	272	5	hassan	hassan	PROPN
ejpam-3905	272	6	.	.	PUNCT
ejpam-3905	273	1	on	on	ADP
ejpam-3905	273	2	the	the	DET
ejpam-3905	273	3	hochschild	hochschild	ADJ
ejpam-3905	273	4	cohomology	cohomology	NOUN
ejpam-3905	273	5	theory	theory	NOUN
ejpam-3905	273	6	of	of	ADP
ejpam-3905	273	7	a∞-algebra	a∞-algebra	PROPN
ejpam-3905	273	8	.	.	PUNCT
ejpam-3905	274	1	scientific	scientific	ADJ
ejpam-3905	274	2	african	african	PROPN
ejpam-3905	274	3	,	,	PUNCT
ejpam-3905	274	4	69	69	NUM
ejpam-3905	274	5	,	,	PUNCT
ejpam-3905	274	6	2019	2019	NUM
ejpam-3905	274	7	.	.	PUNCT
ejpam-3905	275	1	[	[	X
ejpam-3905	275	2	7	7	X
ejpam-3905	275	3	]	]	PUNCT
ejpam-3905	275	4	a.	a.	NOUN
ejpam-3905	275	5	hassan	hassan	PROPN
ejpam-3905	275	6	.	.	PUNCT
ejpam-3905	276	1	perturbation	perturbation	NOUN
ejpam-3905	276	2	differential	differential	VERB
ejpam-3905	276	3	a	a	DET
ejpam-3905	276	4	-	-	PUNCT
ejpam-3905	276	5	infinity	infinity	NOUN
ejpam-3905	276	6	algebra	algebra	NOUN
ejpam-3905	276	7	.	.	PUNCT
ejpam-3905	277	1	appl	appl	PROPN
ejpam-3905	277	2	.	.	PROPN
ejpam-3905	278	1	math	math	PROPN
ejpam-3905	278	2	.	.	PUNCT
ejpam-3905	279	1	inf	inf	PROPN
ejpam-3905	279	2	.	.	PUNCT
ejpam-3905	280	1	sci	sci	PROPN
ejpam-3905	280	2	.	.	PROPN
ejpam-3905	280	3	,	,	PUNCT
ejpam-3905	280	4	14:1–5	14:1–5	NUM
ejpam-3905	280	5	,	,	PUNCT
ejpam-3905	280	6	2020	2020	NUM
ejpam-3905	280	7	.	.	PUNCT
ejpam-3905	281	1	[	[	X
ejpam-3905	281	2	8	8	NUM
ejpam-3905	281	3	]	]	X
ejpam-3905	281	4	m.	m.	NOUN
ejpam-3905	281	5	karoubi	karoubi	PROPN
ejpam-3905	281	6	.	.	PUNCT
ejpam-3905	282	1	quasi	quasi	ADJ
ejpam-3905	282	2	-	-	ADJ
ejpam-3905	282	3	commutative	commutative	ADJ
ejpam-3905	282	4	cochains	cochain	NOUN
ejpam-3905	282	5	in	in	ADP
ejpam-3905	282	6	algebraic	algebraic	PROPN
ejpam-3905	282	7	topology	topology	NOUN
ejpam-3905	282	8	.	.	PUNCT
ejpam-3905	283	1	preprint	preprint	NOUN
ejpam-3905	283	2	,	,	PUNCT
ejpam-3905	283	3	2005	2005	NUM
ejpam-3905	283	4	.	.	PUNCT
ejpam-3905	284	1	[	[	X
ejpam-3905	284	2	9	9	NUM
ejpam-3905	284	3	]	]	PUNCT
ejpam-3905	284	4	k.	k.	NOUN
ejpam-3905	284	5	leffevre	leffevre	PROPN
ejpam-3905	284	6	-	-	PUNCT
ejpam-3905	284	7	hasegawa	hasegawa	PROPN
ejpam-3905	284	8	.	.	PUNCT
ejpam-3905	285	1	sur	sur	PROPN
ejpam-3905	285	2	les	les	PROPN
ejpam-3905	285	3	a∞-categories	a∞-categorie	NOUN
ejpam-3905	285	4	.	.	PUNCT
ejpam-3905	286	1	phd	phd	NOUN
ejpam-3905	286	2	thesis	thesis	PROPN
ejpam-3905	286	3	,	,	PUNCT
ejpam-3905	286	4	university	university	NOUN
ejpam-3905	286	5	denis	denis	NOUN
ejpam-3905	286	6	diderot	diderot	NOUN
ejpam-3905	286	7	,	,	PUNCT
ejpam-3905	286	8	2003	2003	NUM
ejpam-3905	286	9	.	.	PUNCT
ejpam-3905	287	1	[	[	X
ejpam-3905	287	2	10	10	NUM
ejpam-3905	287	3	]	]	PUNCT
ejpam-3905	287	4	m.	m.	NOUN
ejpam-3905	287	5	mandell	mandell	PROPN
ejpam-3905	287	6	.	.	PUNCT
ejpam-3905	288	1	e∞-algebras	e∞-algebras	PROPN
ejpam-3905	288	2	and	and	CCONJ
ejpam-3905	288	3	p	p	ADJ
ejpam-3905	288	4	-	-	PUNCT
ejpam-3905	288	5	adichomotopy	adichomotopy	NOUN
ejpam-3905	288	6	theory	theory	NOUN
ejpam-3905	288	7	.	.	PUNCT
ejpam-3905	289	1	topology	topology	NOUN
ejpam-3905	289	2	,	,	PUNCT
ejpam-3905	289	3	40:4394	40:4394	NUM
ejpam-3905	289	4	,	,	PUNCT
ejpam-3905	289	5	2001	2001	NUM
ejpam-3905	289	6	.	.	PUNCT
ejpam-3905	290	1	[	[	X
ejpam-3905	290	2	11	11	NUM
ejpam-3905	290	3	]	]	PUNCT
ejpam-3905	290	4	j.	j.	PROPN
ejpam-3905	290	5	may	may	AUX
ejpam-3905	290	6	p.	p.	PROPN
ejpam-3905	290	7	e∞-ringspaces	e∞-ringspace	NOUN
ejpam-3905	290	8	and	and	CCONJ
ejpam-3905	290	9	e∞-ring	e∞-re	VERB
ejpam-3905	290	10	spectra	spectra	PROPN
ejpam-3905	290	11	.	.	PROPN
ejpam-3905	291	1	springer	springer	NOUN
ejpam-3905	291	2	lecture	lecture	NOUN
ejpam-3905	291	3	notes	note	NOUN
ejpam-3905	291	4	,	,	PUNCT
ejpam-3905	291	5	577	577	NUM
ejpam-3905	291	6	,	,	PUNCT
ejpam-3905	291	7	1977	1977	NUM
ejpam-3905	291	8	.	.	PUNCT
ejpam-3905	292	1	[	[	X
ejpam-3905	292	2	12	12	NUM
ejpam-3905	292	3	]	]	X
ejpam-3905	292	4	j.	j.	PROPN
ejpam-3905	292	5	may	may	PROPN
ejpam-3905	292	6	p.	p.	PROPN
ejpam-3905	292	7	multiplicative	multiplicative	PROPN
ejpam-3905	292	8	infinite	infinite	PROPN
ejpam-3905	292	9	loop	loop	NOUN
ejpam-3905	292	10	space	space	NOUN
ejpam-3905	292	11	theory	theory	NOUN
ejpam-3905	292	12	.	.	PUNCT
ejpam-3905	293	1	j.	j.	PROPN
ejpam-3905	293	2	pure	pure	ADJ
ejpam-3905	293	3	and	and	CCONJ
ejpam-3905	293	4	applied	applied	ADJ
ejpam-3905	293	5	algebra	algebra	NOUN
ejpam-3905	293	6	,	,	PUNCT
ejpam-3905	293	7	26:1–69	26:1–69	NUM
ejpam-3905	293	8	,	,	PUNCT
ejpam-3905	293	9	1982	1982	NUM
ejpam-3905	293	10	.	.	PUNCT
ejpam-3905	294	1	[	[	X
ejpam-3905	294	2	13	13	NUM
ejpam-3905	294	3	]	]	X
ejpam-3905	294	4	d.	d.	PROPN
ejpam-3905	294	5	quillen	quillen	PROPN
ejpam-3905	294	6	.	.	PUNCT
ejpam-3905	295	1	rational	rational	ADJ
ejpam-3905	295	2	homotopy	homotopy	PROPN
ejpam-3905	295	3	theory	theory	NOUN
ejpam-3905	295	4	.	.	PUNCT
ejpam-3905	296	1	annals	annal	NOUN
ejpam-3905	296	2	of	of	ADP
ejpam-3905	296	3	mathematics	mathematic	NOUN
ejpam-3905	296	4	(	(	PUNCT
ejpam-3905	296	5	2	2	NUM
ejpam-3905	296	6	)	)	PUNCT
ejpam-3905	296	7	,	,	PUNCT
ejpam-3905	296	8	90:205–295	90:205–295	NUM
ejpam-3905	296	9	,	,	PUNCT
ejpam-3905	296	10	1969	1969	NUM
ejpam-3905	296	11	.	.	PUNCT
ejpam-3905	297	1	[	[	X
ejpam-3905	297	2	14	14	NUM
ejpam-3905	297	3	]	]	PUNCT
ejpam-3905	297	4	j.	j.	PROPN
ejpam-3905	297	5	smith	smith	PROPN
ejpam-3905	297	6	r.	r.	PROPN
ejpam-3905	297	7	operads	operad	NOUN
ejpam-3905	297	8	and	and	CCONJ
ejpam-3905	297	9	algebraic	algebraic	PROPN
ejpam-3905	297	10	homotopy	homotopy	PROPN
ejpam-3905	297	11	.	.	PUNCT
ejpam-3905	298	1	preprint	preprint	NOUN
ejpam-3905	298	2	,	,	PUNCT
ejpam-3905	298	3	2000	2000	NUM
ejpam-3905	298	4	.	.	PUNCT