id	sid	tid	token	lemma	pos
ejpam-1224	1	1	7_wang.dvi	7_wang.dvi	NUM
ejpam-1224	1	2	european	european	ADJ
ejpam-1224	1	3	journal	journal	NOUN
ejpam-1224	1	4	of	of	ADP
ejpam-1224	1	5	pure	pure	ADJ
ejpam-1224	1	6	and	and	CCONJ
ejpam-1224	1	7	applied	apply	VERB
ejpam-1224	1	8	mathematics	mathematic	NOUN
ejpam-1224	1	9	vol	vol	NOUN
ejpam-1224	1	10	.	.	PROPN
ejpam-1224	2	1	5	5	NUM
ejpam-1224	2	2	,	,	PUNCT
ejpam-1224	2	3	no	no	INTJ
ejpam-1224	2	4	.	.	NOUN
ejpam-1224	2	5	4	4	NUM
ejpam-1224	2	6	,	,	PUNCT
ejpam-1224	2	7	2012	2012	NUM
ejpam-1224	2	8	,	,	PUNCT
ejpam-1224	2	9	511	511	NUM
ejpam-1224	2	10	-	-	SYM
ejpam-1224	2	11	539	539	NUM
ejpam-1224	2	12	issn	issn	PROPN
ejpam-1224	2	13	1307	1307	NUM
ejpam-1224	2	14	-	-	SYM
ejpam-1224	2	15	5543	5543	NUM
ejpam-1224	2	16	–	–	PUNCT
ejpam-1224	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1224	2	18	koszul	koszul	ADJ
ejpam-1224	2	19	duality	duality	NOUN
ejpam-1224	2	20	for	for	ADP
ejpam-1224	2	21	multigraded	multigrade	VERB
ejpam-1224	2	22	algebras	algebras	PROPN
ejpam-1224	2	23	f.	f.	PROPN
ejpam-1224	2	24	t.	t.	PROPN
ejpam-1224	2	25	hawwa	hawwa	PROPN
ejpam-1224	3	1	1	1	NUM
ejpam-1224	3	2	,	,	PUNCT
ejpam-1224	3	3	j.	j.	PROPN
ejpam-1224	3	4	william	william	PROPN
ejpam-1224	3	5	hoffman1	hoffman1	PROPN
ejpam-1224	3	6	,	,	PUNCT
ejpam-1224	3	7	haohao	haohao	PROPN
ejpam-1224	3	8	wang	wang	PROPN
ejpam-1224	3	9	2,∗	2,∗	NUM
ejpam-1224	3	10	1	1	NUM
ejpam-1224	3	11	department	department	NOUN
ejpam-1224	3	12	of	of	ADP
ejpam-1224	3	13	mathematics	mathematics	PROPN
ejpam-1224	3	14	,	,	PUNCT
ejpam-1224	3	15	louisiana	louisiana	PROPN
ejpam-1224	3	16	state	state	PROPN
ejpam-1224	3	17	university	university	PROPN
ejpam-1224	3	18	,	,	PUNCT
ejpam-1224	3	19	baton	baton	NOUN
ejpam-1224	3	20	rouge	rouge	NOUN
ejpam-1224	3	21	,	,	PUNCT
ejpam-1224	3	22	la	la	PROPN
ejpam-1224	3	23	,	,	PUNCT
ejpam-1224	3	24	usa	usa	PROPN
ejpam-1224	3	25	2	2	NUM
ejpam-1224	3	26	department	department	NOUN
ejpam-1224	3	27	of	of	ADP
ejpam-1224	3	28	mathematics	mathematic	NOUN
ejpam-1224	3	29	,	,	PUNCT
ejpam-1224	3	30	southeast	southeast	PROPN
ejpam-1224	3	31	missouri	missouri	PROPN
ejpam-1224	3	32	state	state	PROPN
ejpam-1224	3	33	university	university	PROPN
ejpam-1224	3	34	,	,	PUNCT
ejpam-1224	3	35	cape	cape	PROPN
ejpam-1224	3	36	girardeau	girardeau	PROPN
ejpam-1224	3	37	,	,	PUNCT
ejpam-1224	3	38	mo	mo	PROPN
ejpam-1224	3	39	,	,	PUNCT
ejpam-1224	3	40	usa	usa	PROPN
ejpam-1224	3	41	abstract	abstract	PROPN
ejpam-1224	3	42	.	.	PUNCT
ejpam-1224	4	1	classical	classical	ADJ
ejpam-1224	4	2	koszul	koszul	ADJ
ejpam-1224	4	3	duality	duality	NOUN
ejpam-1224	4	4	sets	set	VERB
ejpam-1224	4	5	up	up	ADP
ejpam-1224	4	6	an	an	DET
ejpam-1224	4	7	adjoint	adjoint	NOUN
ejpam-1224	4	8	pair	pair	NOUN
ejpam-1224	4	9	of	of	ADP
ejpam-1224	4	10	functors	functor	NOUN
ejpam-1224	4	11	,	,	PUNCT
ejpam-1224	4	12	establishing	establish	VERB
ejpam-1224	4	13	an	an	DET
ejpam-1224	4	14	equivalence	equivalence	NOUN
ejpam-1224	4	15	f	f	X
ejpam-1224	4	16	:	:	PUNCT
ejpam-1224	4	17	db(a	db(a	NOUN
ejpam-1224	4	18	)	)	PUNCT
ejpam-1224	4	19	⇆	⇆	NOUN
ejpam-1224	4	20	db(a	db(a	NOUN
ejpam-1224	4	21	!	!	PUNCT
ejpam-1224	4	22	)	)	PUNCT
ejpam-1224	4	23	:	:	PUNCT
ejpam-1224	5	1	g	g	X
ejpam-1224	5	2	,	,	PUNCT
ejpam-1224	5	3	where	where	SCONJ
ejpam-1224	5	4	a	a	PRON
ejpam-1224	5	5	is	be	AUX
ejpam-1224	5	6	a	a	DET
ejpam-1224	5	7	quadratic	quadratic	ADJ
ejpam-1224	5	8	algebra	algebra	NOUN
ejpam-1224	5	9	,	,	PUNCT
ejpam-1224	5	10	a	a	PRON
ejpam-1224	5	11	!	!	PUNCT
ejpam-1224	5	12	is	be	AUX
ejpam-1224	5	13	the	the	DET
ejpam-1224	5	14	quadratic	quadratic	ADJ
ejpam-1224	5	15	dual	dual	ADJ
ejpam-1224	5	16	,	,	PUNCT
ejpam-1224	5	17	and	and	CCONJ
ejpam-1224	5	18	db	db	PROPN
ejpam-1224	5	19	refers	refer	VERB
ejpam-1224	5	20	to	to	ADP
ejpam-1224	5	21	the	the	DET
ejpam-1224	5	22	bounded	bound	VERB
ejpam-1224	5	23	derived	derive	VERB
ejpam-1224	5	24	category	category	NOUN
ejpam-1224	5	25	of	of	ADP
ejpam-1224	5	26	complexes	complex	NOUN
ejpam-1224	5	27	of	of	ADP
ejpam-1224	5	28	graded	grade	VERB
ejpam-1224	5	29	modules	module	NOUN
ejpam-1224	5	30	over	over	ADP
ejpam-1224	5	31	the	the	DET
ejpam-1224	5	32	graded	grade	VERB
ejpam-1224	5	33	algebra	algebra	NOUN
ejpam-1224	5	34	(	(	PUNCT
ejpam-1224	5	35	i.e.	i.e.	X
ejpam-1224	5	36	,	,	PUNCT
ejpam-1224	5	37	a	a	PRON
ejpam-1224	5	38	or	or	CCONJ
ejpam-1224	5	39	a	a	PRON
ejpam-1224	5	40	!	!	PUNCT
ejpam-1224	5	41	)	)	PUNCT
ejpam-1224	5	42	.	.	PUNCT
ejpam-1224	6	1	this	this	DET
ejpam-1224	6	2	duality	duality	NOUN
ejpam-1224	6	3	can	can	AUX
ejpam-1224	6	4	be	be	AUX
ejpam-1224	6	5	extended	extend	VERB
ejpam-1224	6	6	in	in	ADP
ejpam-1224	6	7	many	many	ADJ
ejpam-1224	6	8	ways	way	NOUN
ejpam-1224	6	9	.	.	PUNCT
ejpam-1224	7	1	we	we	PRON
ejpam-1224	7	2	consider	consider	VERB
ejpam-1224	7	3	here	here	ADV
ejpam-1224	7	4	two	two	NUM
ejpam-1224	7	5	extensions	extension	NOUN
ejpam-1224	7	6	:	:	PUNCT
ejpam-1224	7	7	first	first	ADV
ejpam-1224	7	8	we	we	PRON
ejpam-1224	7	9	wish	wish	VERB
ejpam-1224	7	10	to	to	PART
ejpam-1224	7	11	allow	allow	VERB
ejpam-1224	7	12	a	a	DET
ejpam-1224	7	13	λ	λ	NOUN
ejpam-1224	7	14	-	-	PUNCT
ejpam-1224	7	15	graded	grade	VERB
ejpam-1224	7	16	algebra	algebra	NOUN
ejpam-1224	7	17	,	,	PUNCT
ejpam-1224	7	18	where	where	SCONJ
ejpam-1224	7	19	λ	λ	PROPN
ejpam-1224	7	20	is	be	AUX
ejpam-1224	7	21	any	any	DET
ejpam-1224	7	22	abelian	abelian	ADJ
ejpam-1224	7	23	group	group	NOUN
ejpam-1224	7	24	(	(	PUNCT
ejpam-1224	7	25	not	not	PART
ejpam-1224	7	26	just	just	ADV
ejpam-1224	7	27	z	z	NOUN
ejpam-1224	7	28	)	)	PUNCT
ejpam-1224	7	29	.	.	PUNCT
ejpam-1224	8	1	second	second	ADJ
ejpam-1224	8	2	,	,	PUNCT
ejpam-1224	8	3	we	we	PRON
ejpam-1224	8	4	will	will	AUX
ejpam-1224	8	5	allow	allow	VERB
ejpam-1224	8	6	filtered	filter	VERB
ejpam-1224	8	7	algebras	algebra	NOUN
ejpam-1224	8	8	.	.	PUNCT
ejpam-1224	9	1	in	in	ADP
ejpam-1224	9	2	fact	fact	NOUN
ejpam-1224	9	3	we	we	PRON
ejpam-1224	9	4	are	be	AUX
ejpam-1224	9	5	considering	consider	VERB
ejpam-1224	9	6	filtered	filter	VERB
ejpam-1224	9	7	quadratic	quadratic	ADJ
ejpam-1224	9	8	algebras	algebra	NOUN
ejpam-1224	9	9	with	with	ADP
ejpam-1224	9	10	an	an	DET
ejpam-1224	9	11	(	(	PUNCT
ejpam-1224	9	12	internal	internal	ADJ
ejpam-1224	9	13	)	)	PUNCT
ejpam-1224	9	14	λ	λ	NOUN
ejpam-1224	9	15	-	-	PUNCT
ejpam-1224	9	16	grading	grade	VERB
ejpam-1224	9	17	.	.	PUNCT
ejpam-1224	10	1	2010	2010	NUM
ejpam-1224	10	2	mathematics	mathematic	NOUN
ejpam-1224	10	3	subject	subject	NOUN
ejpam-1224	10	4	classifications	classification	NOUN
ejpam-1224	10	5	:	:	PUNCT
ejpam-1224	10	6	14f05	14f05	NUM
ejpam-1224	10	7	,	,	PUNCT
ejpam-1224	10	8	16e05	16e05	NUM
ejpam-1224	10	9	,	,	PUNCT
ejpam-1224	10	10	13d25	13d25	NUM
ejpam-1224	10	11	,	,	PUNCT
ejpam-1224	10	12	13d02	13d02	NUM
ejpam-1224	10	13	,	,	PUNCT
ejpam-1224	10	14	18e30	18e30	NUM
ejpam-1224	10	15	.	.	PUNCT
ejpam-1224	11	1	key	key	ADJ
ejpam-1224	11	2	words	word	NOUN
ejpam-1224	11	3	and	and	CCONJ
ejpam-1224	11	4	phrases	phrase	NOUN
ejpam-1224	11	5	:	:	PUNCT
ejpam-1224	11	6	multigraded	multigrade	VERB
ejpam-1224	11	7	module	module	NOUN
ejpam-1224	11	8	,	,	PUNCT
ejpam-1224	11	9	functors	functor	NOUN
ejpam-1224	11	10	,	,	PUNCT
ejpam-1224	11	11	koszul	koszul	ADJ
ejpam-1224	11	12	duality	duality	NOUN
ejpam-1224	11	13	,	,	PUNCT
ejpam-1224	11	14	bgg	bgg	NOUN
ejpam-1224	11	15	correspondence	correspondence	NOUN
ejpam-1224	11	16	,	,	PUNCT
ejpam-1224	11	17	derived	derive	VERB
ejpam-1224	11	18	category	category	NOUN
ejpam-1224	11	19	1	1	NUM
ejpam-1224	11	20	.	.	PUNCT
ejpam-1224	12	1	introduction	introduction	NOUN
ejpam-1224	12	2	koszul	koszul	ADJ
ejpam-1224	12	3	duality	duality	NOUN
ejpam-1224	12	4	originated	originate	VERB
ejpam-1224	12	5	from	from	ADP
ejpam-1224	12	6	bernstein	bernstein	PROPN
ejpam-1224	12	7	-	-	PUNCT
ejpam-1224	12	8	gelfand	gelfand	PROPN
ejpam-1224	12	9	-	-	PUNCT
ejpam-1224	12	10	gelfand	gelfand	PROPN
ejpam-1224	12	11	[	[	X
ejpam-1224	12	12	2	2	NUM
ejpam-1224	12	13	]	]	PUNCT
ejpam-1224	12	14	in	in	ADP
ejpam-1224	12	15	the	the	DET
ejpam-1224	12	16	mid	mid	ADJ
ejpam-1224	12	17	1970s	1970	NOUN
ejpam-1224	12	18	.	.	PUNCT
ejpam-1224	13	1	it	it	PRON
ejpam-1224	13	2	led	lead	VERB
ejpam-1224	13	3	to	to	ADP
ejpam-1224	13	4	the	the	DET
ejpam-1224	13	5	observation	observation	NOUN
ejpam-1224	13	6	that	that	SCONJ
ejpam-1224	13	7	for	for	ADP
ejpam-1224	13	8	certain	certain	ADJ
ejpam-1224	13	9	pairs	pair	NOUN
ejpam-1224	13	10	of	of	ADP
ejpam-1224	13	11	associative	associative	ADJ
ejpam-1224	13	12	algebras	algebra	NOUN
ejpam-1224	13	13	a	a	PRON
ejpam-1224	13	14	and	and	CCONJ
ejpam-1224	13	15	a	a	PRON
ejpam-1224	13	16	!	!	PUNCT
ejpam-1224	13	17	,	,	PUNCT
ejpam-1224	13	18	there	there	PRON
ejpam-1224	13	19	is	be	VERB
ejpam-1224	13	20	a	a	DET
ejpam-1224	13	21	relationship	relationship	NOUN
ejpam-1224	13	22	between	between	ADP
ejpam-1224	13	23	the	the	DET
ejpam-1224	13	24	categories	category	NOUN
ejpam-1224	13	25	of	of	ADP
ejpam-1224	13	26	a	a	DET
ejpam-1224	13	27	-	-	PUNCT
ejpam-1224	13	28	modules	module	NOUN
ejpam-1224	13	29	and	and	CCONJ
ejpam-1224	13	30	a!-modules	a!-module	NOUN
ejpam-1224	13	31	.	.	PUNCT
ejpam-1224	14	1	an	an	DET
ejpam-1224	14	2	example	example	NOUN
ejpam-1224	14	3	of	of	ADP
ejpam-1224	14	4	such	such	DET
ejpam-1224	14	5	a	a	DET
ejpam-1224	14	6	pair	pair	NOUN
ejpam-1224	14	7	is	be	AUX
ejpam-1224	14	8	s	s	PROPN
ejpam-1224	14	9	=	=	SYM
ejpam-1224	14	10	k[x1	k[x1	PROPN
ejpam-1224	14	11	,	,	PUNCT
ejpam-1224	14	12	x2	x2	PROPN
ejpam-1224	14	13	,	,	PUNCT
ejpam-1224	14	14	.	.	PUNCT
ejpam-1224	14	15	.	.	PUNCT
ejpam-1224	15	1	.	.	PUNCT
ejpam-1224	16	1	,	,	PUNCT
ejpam-1224	16	2	xn	xn	PROPN
ejpam-1224	16	3	]	]	X
ejpam-1224	16	4	,	,	PUNCT
ejpam-1224	16	5	the	the	DET
ejpam-1224	16	6	polynomial	polynomial	ADJ
ejpam-1224	16	7	algebra	algebra	NOUN
ejpam-1224	16	8	over	over	ADP
ejpam-1224	16	9	a	a	DET
ejpam-1224	16	10	field	field	NOUN
ejpam-1224	16	11	k	k	NOUN
ejpam-1224	16	12	,	,	PUNCT
ejpam-1224	16	13	and	and	CCONJ
ejpam-1224	16	14	e	e	X
ejpam-1224	16	15	=	=	SYM
ejpam-1224	16	16	∧	∧	PROPN
ejpam-1224	16	17	k(e1	k(e1	NOUN
ejpam-1224	16	18	,	,	PUNCT
ejpam-1224	16	19	e2	e2	PROPN
ejpam-1224	16	20	,	,	PUNCT
ejpam-1224	16	21	.	.	PUNCT
ejpam-1224	16	22	.	.	PUNCT
ejpam-1224	16	23	.	.	PUNCT
ejpam-1224	17	1	,	,	PUNCT
ejpam-1224	17	2	en	en	X
ejpam-1224	17	3	)	)	PUNCT
ejpam-1224	17	4	,	,	PUNCT
ejpam-1224	17	5	the	the	DET
ejpam-1224	17	6	exterior	exterior	ADJ
ejpam-1224	17	7	algebra	algebra	NOUN
ejpam-1224	17	8	over	over	ADP
ejpam-1224	17	9	k.	k.	PROPN
ejpam-1224	17	10	bernstein	bernstein	PROPN
ejpam-1224	17	11	-	-	PUNCT
ejpam-1224	17	12	gelfand	gelfand	PROPN
ejpam-1224	17	13	-	-	PUNCT
ejpam-1224	17	14	gelfand	gelfand	PROPN
ejpam-1224	17	15	constructed	construct	VERB
ejpam-1224	17	16	an	an	DET
ejpam-1224	17	17	adjoint	adjoint	NOUN
ejpam-1224	17	18	pair	pair	NOUN
ejpam-1224	17	19	of	of	ADP
ejpam-1224	17	20	functors	functor	NOUN
ejpam-1224	17	21	between	between	ADP
ejpam-1224	17	22	the	the	DET
ejpam-1224	17	23	categories	category	NOUN
ejpam-1224	17	24	of	of	ADP
ejpam-1224	17	25	bounded	bounded	ADJ
ejpam-1224	17	26	chain	chain	NOUN
ejpam-1224	17	27	complexes	complex	NOUN
ejpam-1224	17	28	of	of	ADP
ejpam-1224	17	29	s	s	NOUN
ejpam-1224	17	30	-	-	PUNCT
ejpam-1224	17	31	modules	module	NOUN
ejpam-1224	17	32	and	and	CCONJ
ejpam-1224	17	33	bounded	bound	VERB
ejpam-1224	17	34	chain	chain	NOUN
ejpam-1224	17	35	complexes	complex	NOUN
ejpam-1224	17	36	of	of	ADP
ejpam-1224	17	37	e	e	NOUN
ejpam-1224	17	38	-	-	NOUN
ejpam-1224	17	39	modules	module	NOUN
ejpam-1224	17	40	which	which	PRON
ejpam-1224	17	41	induce	induce	VERB
ejpam-1224	17	42	an	an	DET
ejpam-1224	17	43	equivalence	equivalence	NOUN
ejpam-1224	17	44	of	of	ADP
ejpam-1224	17	45	the	the	DET
ejpam-1224	17	46	corresponding	corresponding	ADJ
ejpam-1224	17	47	derived	derived	ADJ
ejpam-1224	17	48	categories	category	NOUN
ejpam-1224	17	49	.	.	PUNCT
ejpam-1224	18	1	this	this	PRON
ejpam-1224	18	2	means	mean	VERB
ejpam-1224	18	3	that	that	SCONJ
ejpam-1224	18	4	problems	problem	NOUN
ejpam-1224	18	5	of	of	ADP
ejpam-1224	18	6	homological	homological	ADJ
ejpam-1224	18	7	algebra	algebra	NOUN
ejpam-1224	18	8	for	for	ADP
ejpam-1224	18	9	s	s	NOUN
ejpam-1224	18	10	-	-	PUNCT
ejpam-1224	18	11	modules	module	NOUN
ejpam-1224	18	12	can	can	AUX
ejpam-1224	18	13	be	be	AUX
ejpam-1224	18	14	translated	translate	VERB
ejpam-1224	18	15	into	into	ADP
ejpam-1224	18	16	problems	problem	NOUN
ejpam-1224	18	17	of	of	ADP
ejpam-1224	18	18	homological	homological	ADJ
ejpam-1224	18	19	algebra	algebra	NOUN
ejpam-1224	18	20	for	for	ADP
ejpam-1224	18	21	e	e	NOUN
ejpam-1224	18	22	-	-	NOUN
ejpam-1224	18	23	modules	module	NOUN
ejpam-1224	18	24	and	and	CCONJ
ejpam-1224	18	25	vice	vice	NOUN
ejpam-1224	18	26	-	-	NOUN
ejpam-1224	18	27	versa	versa	NOUN
ejpam-1224	18	28	.	.	PUNCT
ejpam-1224	19	1	a	a	DET
ejpam-1224	19	2	key	key	ADJ
ejpam-1224	19	3	fact	fact	NOUN
ejpam-1224	19	4	underlying	underlie	VERB
ejpam-1224	19	5	this	this	PRON
ejpam-1224	19	6	is	be	AUX
ejpam-1224	19	7	that	that	SCONJ
ejpam-1224	19	8	the	the	DET
ejpam-1224	19	9	koszul	koszul	ADJ
ejpam-1224	19	10	complex	complex	NOUN
ejpam-1224	19	11	of	of	ADP
ejpam-1224	19	12	s	s	PRON
ejpam-1224	19	13	and	and	CCONJ
ejpam-1224	19	14	e	e	X
ejpam-1224	19	15	which	which	PRON
ejpam-1224	19	16	is	be	AUX
ejpam-1224	19	17	given	give	VERB
ejpam-1224	19	18	by	by	ADP
ejpam-1224	19	19	·	·	PUNCT
ejpam-1224	19	20	·	·	PUNCT
ejpam-1224	19	21	·	·	PUNCT
ejpam-1224	20	1	→	→	PUNCT
ejpam-1224	20	2	si	si	PROPN
ejpam-1224	20	3	⊗	⊗	PROPN
ejpam-1224	20	4	en→	en→	ADV
ejpam-1224	20	5	si+1	si+1	VERB
ejpam-1224	20	6	⊗	⊗	NOUN
ejpam-1224	20	7	en−1→	en−1→	NOUN
ejpam-1224	20	8	·	·	PUNCT
ejpam-1224	20	9	·	·	PUNCT
ejpam-1224	20	10	·	·	PUNCT
ejpam-1224	21	1	∗corresponding	∗corresponde	VERB
ejpam-1224	21	2	author	author	NOUN
ejpam-1224	21	3	.	.	PUNCT
ejpam-1224	22	1	email	email	NOUN
ejpam-1224	22	2	addresses	address	NOUN
ejpam-1224	22	3	:	:	PUNCT
ejpam-1224	22	4	fhawwa�math.lsu.edu	fhawwa�math.lsu.edu	PROPN
ejpam-1224	22	5	(	(	PUNCT
ejpam-1224	22	6	f.	f.	PROPN
ejpam-1224	22	7	hawwa	hawwa	PROPN
ejpam-1224	22	8	)	)	PUNCT
ejpam-1224	22	9	,	,	PUNCT
ejpam-1224	22	10	hoffman�math.lsu.edu	hoffman�math.lsu.edu	PROPN
ejpam-1224	22	11	(	(	PUNCT
ejpam-1224	22	12	j.	j.	PROPN
ejpam-1224	22	13	hoffman	hoffman	PROPN
ejpam-1224	22	14	)	)	PUNCT
ejpam-1224	22	15	,	,	PUNCT
ejpam-1224	22	16	hwang�semo.edu	hwang�semo.edu	PROPN
ejpam-1224	22	17	(	(	PUNCT
ejpam-1224	22	18	h.	h.	PROPN
ejpam-1224	22	19	wang	wang	PROPN
ejpam-1224	22	20	)	)	PUNCT
ejpam-1224	22	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1224	23	1	511	511	NUM
ejpam-1224	23	2	c	c	X
ejpam-1224	23	3	©	©	VERB
ejpam-1224	23	4	2012	2012	NUM
ejpam-1224	23	5	ejpam	ejpam	VERB
ejpam-1224	23	6	all	all	DET
ejpam-1224	23	7	rights	right	NOUN
ejpam-1224	23	8	reserved	reserve	VERB
ejpam-1224	23	9	.	.	PUNCT
ejpam-1224	24	1	f.	f.	PROPN
ejpam-1224	24	2	hawwa	hawwa	PROPN
ejpam-1224	24	3	,	,	PUNCT
ejpam-1224	24	4	j.	j.	PROPN
ejpam-1224	24	5	hoffman	hoffman	PROPN
ejpam-1224	24	6	,	,	PUNCT
ejpam-1224	24	7	and	and	CCONJ
ejpam-1224	24	8	h.	h.	PROPN
ejpam-1224	24	9	wang	wang	PROPN
ejpam-1224	24	10	,	,	PUNCT
ejpam-1224	24	11	/	/	SYM
ejpam-1224	24	12	eur	eur	NOUN
ejpam-1224	24	13	.	.	PUNCT
ejpam-1224	25	1	j.	j.	PROPN
ejpam-1224	25	2	pure	pure	PROPN
ejpam-1224	25	3	appl	appl	PROPN
ejpam-1224	25	4	.	.	PROPN
ejpam-1224	25	5	math	math	PROPN
ejpam-1224	25	6	,	,	PUNCT
ejpam-1224	25	7	5	5	NUM
ejpam-1224	25	8	(	(	PUNCT
ejpam-1224	25	9	2012	2012	NUM
ejpam-1224	25	10	)	)	PUNCT
ejpam-1224	25	11	,	,	PUNCT
ejpam-1224	25	12	511	511	NUM
ejpam-1224	25	13	-	-	SYM
ejpam-1224	25	14	539	539	NUM
ejpam-1224	25	15	512	512	NUM
ejpam-1224	25	16	with	with	ADP
ejpam-1224	25	17	differential	differential	ADJ
ejpam-1224	25	18	d	d	PROPN
ejpam-1224	25	19	(	(	PUNCT
ejpam-1224	25	20	f	f	PROPN
ejpam-1224	25	21	⊗	⊗	PROPN
ejpam-1224	25	22	ei1	ei1	PROPN
ejpam-1224	26	1	∧	∧	NOUN
ejpam-1224	26	2	ei2	ei2	NOUN
ejpam-1224	26	3	∧	∧	PROPN
ejpam-1224	26	4	·	·	PUNCT
ejpam-1224	26	5	·	·	PUNCT
ejpam-1224	26	6	·	·	PUNCT
ejpam-1224	27	1	∧	∧	NOUN
ejpam-1224	27	2	eim	eim	X
ejpam-1224	27	3	)	)	PUNCT
ejpam-1224	27	4	=	=	PUNCT
ejpam-1224	28	1	m∑	m∑	CCONJ
ejpam-1224	28	2	j=1	j=1	NOUN
ejpam-1224	28	3	(	(	PUNCT
ejpam-1224	28	4	−1)mx	−1)mx	NUM
ejpam-1224	28	5	i	i	PRON
ejpam-1224	28	6	j	j	PROPN
ejpam-1224	28	7	f	f	PROPN
ejpam-1224	28	8	(	(	PUNCT
ejpam-1224	28	9	ei1	ei1	PROPN
ejpam-1224	28	10	∧	∧	PROPN
ejpam-1224	28	11	·	·	PUNCT
ejpam-1224	28	12	·	·	PUNCT
ejpam-1224	28	13	·	·	PUNCT
ejpam-1224	28	14	∧cei	∧cei	NOUN
ejpam-1224	28	15	j	j	PROPN
ejpam-1224	28	16	∧	∧	PROPN
ejpam-1224	28	17	·	·	PUNCT
ejpam-1224	28	18	·	·	PUNCT
ejpam-1224	28	19	·	·	PUNCT
ejpam-1224	29	1	∧	∧	NOUN
ejpam-1224	29	2	eim	eim	PROPN
ejpam-1224	29	3	)	)	PUNCT
ejpam-1224	29	4	is	be	AUX
ejpam-1224	29	5	acyclic	acyclic	ADJ
ejpam-1224	29	6	in	in	ADP
ejpam-1224	29	7	all	all	DET
ejpam-1224	29	8	degrees	degree	NOUN
ejpam-1224	29	9	greater	great	ADJ
ejpam-1224	29	10	than	than	ADP
ejpam-1224	29	11	zero	zero	NUM
ejpam-1224	29	12	.	.	PUNCT
ejpam-1224	30	1	given	give	VERB
ejpam-1224	30	2	this	this	DET
ejpam-1224	30	3	fact	fact	NOUN
ejpam-1224	30	4	we	we	PRON
ejpam-1224	30	5	say	say	VERB
ejpam-1224	30	6	that	that	PRON
ejpam-1224	30	7	s	s	VERB
ejpam-1224	30	8	and	and	CCONJ
ejpam-1224	30	9	e	e	NOUN
ejpam-1224	30	10	are	be	AUX
ejpam-1224	30	11	koszul	koszul	ADJ
ejpam-1224	30	12	algebras	algebra	NOUN
ejpam-1224	30	13	.	.	PUNCT
ejpam-1224	31	1	this	this	DET
ejpam-1224	31	2	theory	theory	NOUN
ejpam-1224	31	3	has	have	AUX
ejpam-1224	31	4	been	be	AUX
ejpam-1224	31	5	generalized	generalize	VERB
ejpam-1224	31	6	by	by	ADP
ejpam-1224	31	7	a	a	DET
ejpam-1224	31	8	number	number	NOUN
ejpam-1224	31	9	of	of	ADP
ejpam-1224	31	10	people	people	NOUN
ejpam-1224	31	11	to	to	PART
ejpam-1224	31	12	algebras	algebras	PROPN
ejpam-1224	31	13	defined	define	VERB
ejpam-1224	31	14	by	by	ADP
ejpam-1224	31	15	homogeneous	homogeneous	ADJ
ejpam-1224	31	16	relations	relation	NOUN
ejpam-1224	31	17	.	.	PUNCT
ejpam-1224	32	1	a	a	DET
ejpam-1224	32	2	general	general	ADJ
ejpam-1224	32	3	reference	reference	NOUN
ejpam-1224	32	4	is	be	AUX
ejpam-1224	32	5	[	[	X
ejpam-1224	32	6	5	5	NUM
ejpam-1224	32	7	]	]	PUNCT
ejpam-1224	32	8	for	for	ADP
ejpam-1224	32	9	background	background	NOUN
ejpam-1224	32	10	on	on	ADP
ejpam-1224	32	11	quadratic	quadratic	ADJ
ejpam-1224	32	12	algebras	algebra	NOUN
ejpam-1224	32	13	and	and	CCONJ
ejpam-1224	32	14	koszul	koszul	ADJ
ejpam-1224	32	15	duality	duality	NOUN
ejpam-1224	32	16	.	.	PUNCT
ejpam-1224	33	1	consider	consider	VERB
ejpam-1224	33	2	the	the	DET
ejpam-1224	33	3	free	free	ADJ
ejpam-1224	33	4	k	k	NOUN
ejpam-1224	33	5	-	-	NOUN
ejpam-1224	33	6	algebra	algebra	NOUN
ejpam-1224	33	7	k	k	X
ejpam-1224	33	8	<	<	X
ejpam-1224	33	9	x1	x1	PROPN
ejpam-1224	33	10	,	,	PUNCT
ejpam-1224	33	11	x2	x2	PROPN
ejpam-1224	33	12	,	,	PUNCT
ejpam-1224	33	13	.	.	PUNCT
ejpam-1224	33	14	.	.	PUNCT
ejpam-1224	34	1	.	.	PUNCT
ejpam-1224	35	1	,	,	PUNCT
ejpam-1224	35	2	xn	xn	PROPN
ejpam-1224	35	3	>	>	PUNCT
ejpam-1224	35	4	and	and	CCONJ
ejpam-1224	35	5	define	define	VERB
ejpam-1224	35	6	a	a	DET
ejpam-1224	35	7	=	=	SYM
ejpam-1224	35	8	k	k	X
ejpam-1224	35	9	<	<	X
ejpam-1224	35	10	x1	x1	PROPN
ejpam-1224	35	11	,	,	PUNCT
ejpam-1224	35	12	x2	x2	PROPN
ejpam-1224	35	13	,	,	PUNCT
ejpam-1224	35	14	.	.	PUNCT
ejpam-1224	35	15	.	.	PUNCT
ejpam-1224	35	16	.	.	PUNCT
ejpam-1224	36	1	,	,	PUNCT
ejpam-1224	37	1	xn	xn	PROPN
ejpam-1224	37	2	>	>	X
ejpam-1224	38	1	/r	/r	X
ejpam-1224	38	2	,	,	PUNCT
ejpam-1224	38	3	where	where	SCONJ
ejpam-1224	38	4	r	r	NOUN
ejpam-1224	38	5	is	be	AUX
ejpam-1224	38	6	the	the	DET
ejpam-1224	38	7	ideal	ideal	NOUN
ejpam-1224	38	8	generated	generate	VERB
ejpam-1224	38	9	by	by	ADP
ejpam-1224	38	10	homogeneous	homogeneous	ADJ
ejpam-1224	38	11	quadratic	quadratic	ADJ
ejpam-1224	38	12	relations	relation	NOUN
ejpam-1224	38	13	of	of	ADP
ejpam-1224	38	14	the	the	DET
ejpam-1224	38	15	form	form	NOUN
ejpam-1224	38	16	σci	σci	VERB
ejpam-1224	38	17	j	j	NOUN
ejpam-1224	38	18	x	x	INTJ
ejpam-1224	38	19	i	i	NOUN
ejpam-1224	38	20	x	x	X
ejpam-1224	38	21	j	j	PROPN
ejpam-1224	38	22	=	=	NOUN
ejpam-1224	38	23	0	0	PROPN
ejpam-1224	38	24	.	.	PUNCT
ejpam-1224	39	1	in	in	ADP
ejpam-1224	39	2	our	our	PRON
ejpam-1224	39	3	example	example	NOUN
ejpam-1224	39	4	above	above	ADV
ejpam-1224	39	5	,	,	PUNCT
ejpam-1224	39	6	the	the	DET
ejpam-1224	39	7	algebra	algebra	NOUN
ejpam-1224	39	8	s	s	VERB
ejpam-1224	39	9	is	be	AUX
ejpam-1224	39	10	defined	define	VERB
ejpam-1224	39	11	by	by	ADP
ejpam-1224	39	12	the	the	DET
ejpam-1224	39	13	quadratic	quadratic	ADJ
ejpam-1224	39	14	relation	relation	NOUN
ejpam-1224	39	15	x	x	PUNCT
ejpam-1224	40	1	i	i	NOUN
ejpam-1224	40	2	x	x	X
ejpam-1224	40	3	j	j	NOUN
ejpam-1224	41	1	−	−	NOUN
ejpam-1224	41	2	x	x	SYM
ejpam-1224	42	1	j	j	NOUN
ejpam-1224	42	2	x	x	PUNCT
ejpam-1224	42	3	i	i	NOUN
ejpam-1224	42	4	=	=	PUNCT
ejpam-1224	42	5	0	0	NUM
ejpam-1224	42	6	and	and	CCONJ
ejpam-1224	42	7	the	the	DET
ejpam-1224	42	8	algebra	algebra	NOUN
ejpam-1224	42	9	e	e	NOUN
ejpam-1224	42	10	is	be	AUX
ejpam-1224	42	11	defined	define	VERB
ejpam-1224	42	12	by	by	ADP
ejpam-1224	42	13	x	x	PROPN
ejpam-1224	42	14	i	i	NOUN
ejpam-1224	42	15	x	x	PROPN
ejpam-1224	42	16	j	j	PROPN
ejpam-1224	43	1	+	+	CCONJ
ejpam-1224	43	2	x	x	SYM
ejpam-1224	43	3	j	j	NOUN
ejpam-1224	43	4	x	x	PUNCT
ejpam-1224	43	5	i	i	NOUN
ejpam-1224	43	6	=	=	PUNCT
ejpam-1224	43	7	0	0	PUNCT
ejpam-1224	44	1	and	and	CCONJ
ejpam-1224	44	2	x2	x2	INTJ
ejpam-1224	44	3	i	i	NOUN
ejpam-1224	44	4	=	=	NOUN
ejpam-1224	44	5	0	0	X
ejpam-1224	44	6	.	.	PUNCT
ejpam-1224	45	1	more	more	ADV
ejpam-1224	45	2	generally	generally	ADV
ejpam-1224	45	3	s	s	PRON
ejpam-1224	45	4	and	and	CCONJ
ejpam-1224	45	5	e	e	NOUN
ejpam-1224	45	6	can	can	AUX
ejpam-1224	45	7	be	be	AUX
ejpam-1224	45	8	replaced	replace	VERB
ejpam-1224	45	9	by	by	ADP
ejpam-1224	45	10	a	a	DET
ejpam-1224	45	11	pair	pair	NOUN
ejpam-1224	45	12	of	of	ADP
ejpam-1224	45	13	dual	dual	ADJ
ejpam-1224	45	14	quadratic	quadratic	ADJ
ejpam-1224	45	15	algebras	algebra	NOUN
ejpam-1224	45	16	a	a	PRON
ejpam-1224	45	17	and	and	CCONJ
ejpam-1224	45	18	a	a	PRON
ejpam-1224	45	19	!	!	PUNCT
ejpam-1224	45	20	.	.	PUNCT
ejpam-1224	46	1	note	note	VERB
ejpam-1224	46	2	that	that	SCONJ
ejpam-1224	46	3	this	this	DET
ejpam-1224	46	4	relation	relation	NOUN
ejpam-1224	46	5	is	be	AUX
ejpam-1224	46	6	symmetric	symmetric	ADJ
ejpam-1224	46	7	,	,	PUNCT
ejpam-1224	46	8	(	(	PUNCT
ejpam-1224	46	9	a	a	X
ejpam-1224	46	10	!	!	PUNCT
ejpam-1224	46	11	)	)	PUNCT
ejpam-1224	46	12	!	!	PUNCT
ejpam-1224	47	1	=	=	PUNCT
ejpam-1224	48	1	a.	a.	NOUN
ejpam-1224	48	2	here	here	ADV
ejpam-1224	48	3	a	a	PRON
ejpam-1224	48	4	and	and	CCONJ
ejpam-1224	48	5	a	a	PRON
ejpam-1224	48	6	!	!	PUNCT
ejpam-1224	48	7	are	be	AUX
ejpam-1224	48	8	quadratic	quadratic	ADJ
ejpam-1224	48	9	algebras	algebra	NOUN
ejpam-1224	48	10	meaning	mean	VERB
ejpam-1224	48	11	that	that	SCONJ
ejpam-1224	48	12	each	each	PRON
ejpam-1224	48	13	is	be	AUX
ejpam-1224	48	14	the	the	DET
ejpam-1224	48	15	quotient	quotient	NOUN
ejpam-1224	48	16	of	of	ADP
ejpam-1224	48	17	a	a	DET
ejpam-1224	48	18	free	free	ADJ
ejpam-1224	48	19	k	k	NOUN
ejpam-1224	48	20	-	-	NOUN
ejpam-1224	48	21	algebra	algebra	NOUN
ejpam-1224	48	22	by	by	ADP
ejpam-1224	48	23	homogeneous	homogeneous	ADJ
ejpam-1224	48	24	quadratic	quadratic	ADJ
ejpam-1224	48	25	relations	relation	NOUN
ejpam-1224	48	26	.	.	PUNCT
ejpam-1224	49	1	given	give	VERB
ejpam-1224	49	2	a	a	DET
ejpam-1224	49	3	pair	pair	NOUN
ejpam-1224	49	4	of	of	ADP
ejpam-1224	49	5	quadratic	quadratic	ADJ
ejpam-1224	49	6	algebras	algebra	NOUN
ejpam-1224	49	7	we	we	PRON
ejpam-1224	49	8	may	may	AUX
ejpam-1224	49	9	form	form	VERB
ejpam-1224	49	10	the	the	DET
ejpam-1224	49	11	koszul	koszul	ADJ
ejpam-1224	49	12	complex	complex	NOUN
ejpam-1224	49	13	given	give	VERB
ejpam-1224	49	14	by	by	ADP
ejpam-1224	49	15	.	.	PUNCT
ejpam-1224	49	16	.	.	PUNCT
ejpam-1224	50	1	.→	.→	X
ejpam-1224	51	1	a⊗	a⊗	NOUN
ejpam-1224	51	2	(	(	PUNCT
ejpam-1224	51	3	a	a	NOUN
ejpam-1224	51	4	!	!	NOUN
ejpam-1224	51	5	2	2	NUM
ejpam-1224	51	6	)	)	PUNCT
ejpam-1224	51	7	∗→	∗→	ADJ
ejpam-1224	51	8	a⊗	a⊗	NOUN
ejpam-1224	51	9	(	(	PUNCT
ejpam-1224	51	10	a	a	NOUN
ejpam-1224	51	11	!	!	NOUN
ejpam-1224	51	12	1	1	NUM
ejpam-1224	51	13	)	)	PUNCT
ejpam-1224	51	14	∗→	∗→	VERB
ejpam-1224	51	15	a	a	PRON
ejpam-1224	52	1	and	and	CCONJ
ejpam-1224	52	2	we	we	PRON
ejpam-1224	52	3	say	say	VERB
ejpam-1224	52	4	that	that	SCONJ
ejpam-1224	52	5	a	a	PRON
ejpam-1224	52	6	is	be	AUX
ejpam-1224	52	7	a	a	DET
ejpam-1224	52	8	koszul	koszul	ADJ
ejpam-1224	52	9	algebra	algebra	NOUN
ejpam-1224	52	10	if	if	SCONJ
ejpam-1224	52	11	the	the	DET
ejpam-1224	52	12	koszul	koszul	ADJ
ejpam-1224	52	13	complex	complex	NOUN
ejpam-1224	52	14	is	be	AUX
ejpam-1224	52	15	exact	exact	ADJ
ejpam-1224	52	16	in	in	ADP
ejpam-1224	52	17	nonzero	nonzero	PROPN
ejpam-1224	52	18	degrees	degree	NOUN
ejpam-1224	52	19	.	.	PUNCT
ejpam-1224	53	1	by	by	ADP
ejpam-1224	53	2	symmetry	symmetry	NOUN
ejpam-1224	53	3	,	,	PUNCT
ejpam-1224	53	4	if	if	SCONJ
ejpam-1224	53	5	a	a	PRON
ejpam-1224	53	6	is	be	AUX
ejpam-1224	53	7	koszul	koszul	ADJ
ejpam-1224	53	8	then	then	ADV
ejpam-1224	53	9	a	a	DET
ejpam-1224	53	10	!	!	PUNCT
ejpam-1224	53	11	is	be	AUX
ejpam-1224	53	12	also	also	ADV
ejpam-1224	53	13	koszul	koszul	ADJ
ejpam-1224	53	14	.	.	PUNCT
ejpam-1224	54	1	koszul	koszul	ADJ
ejpam-1224	54	2	duality	duality	NOUN
ejpam-1224	54	3	is	be	AUX
ejpam-1224	54	4	a	a	DET
ejpam-1224	54	5	relation	relation	NOUN
ejpam-1224	54	6	between	between	ADP
ejpam-1224	54	7	the	the	DET
ejpam-1224	54	8	complexes	complex	NOUN
ejpam-1224	54	9	of	of	ADP
ejpam-1224	54	10	a	a	DET
ejpam-1224	54	11	-	-	PUNCT
ejpam-1224	54	12	modules	module	NOUN
ejpam-1224	54	13	and	and	CCONJ
ejpam-1224	54	14	the	the	DET
ejpam-1224	54	15	complexes	complex	NOUN
ejpam-1224	54	16	of	of	ADP
ejpam-1224	54	17	a!-modules	a!-module	NOUN
ejpam-1224	54	18	and	and	CCONJ
ejpam-1224	54	19	this	this	PRON
ejpam-1224	54	20	establishes	establish	VERB
ejpam-1224	54	21	an	an	DET
ejpam-1224	54	22	equivalence	equivalence	NOUN
ejpam-1224	54	23	of	of	ADP
ejpam-1224	54	24	categories	category	NOUN
ejpam-1224	54	25	f	f	NOUN
ejpam-1224	54	26	:	:	PUNCT
ejpam-1224	54	27	db(a	db(a	NOUN
ejpam-1224	54	28	)	)	PUNCT
ejpam-1224	54	29	⇆	⇆	NOUN
ejpam-1224	54	30	db(a	db(a	NOUN
ejpam-1224	54	31	!	!	PUNCT
ejpam-1224	54	32	)	)	PUNCT
ejpam-1224	54	33	:	:	PUNCT
ejpam-1224	55	1	g	g	ADP
ejpam-1224	55	2	where	where	SCONJ
ejpam-1224	55	3	db	db	PROPN
ejpam-1224	55	4	refers	refer	VERB
ejpam-1224	55	5	to	to	ADP
ejpam-1224	55	6	the	the	DET
ejpam-1224	55	7	bounded	bound	VERB
ejpam-1224	55	8	derived	derive	VERB
ejpam-1224	55	9	category	category	NOUN
ejpam-1224	55	10	of	of	ADP
ejpam-1224	55	11	complexes	complex	NOUN
ejpam-1224	55	12	of	of	ADP
ejpam-1224	55	13	graded	grade	VERB
ejpam-1224	55	14	modules	module	NOUN
ejpam-1224	55	15	over	over	ADP
ejpam-1224	55	16	the	the	DET
ejpam-1224	55	17	graded	grade	VERB
ejpam-1224	55	18	algebra	algebra	NOUN
ejpam-1224	55	19	a	a	PRON
ejpam-1224	55	20	(	(	PUNCT
ejpam-1224	55	21	or	or	CCONJ
ejpam-1224	55	22	a	a	PRON
ejpam-1224	55	23	!	!	PUNCT
ejpam-1224	55	24	)	)	PUNCT
ejpam-1224	55	25	.	.	PUNCT
ejpam-1224	56	1	for	for	ADP
ejpam-1224	56	2	m	m	PROPN
ejpam-1224	56	3	∈	∈	PROPN
ejpam-1224	56	4	c	c	X
ejpam-1224	56	5	b(a	b(a	NOUN
ejpam-1224	56	6	)	)	PUNCT
ejpam-1224	56	7	where	where	SCONJ
ejpam-1224	56	8	c	c	PROPN
ejpam-1224	56	9	b(a	b(a	X
ejpam-1224	56	10	)	)	PUNCT
ejpam-1224	56	11	is	be	AUX
ejpam-1224	56	12	the	the	DET
ejpam-1224	56	13	category	category	NOUN
ejpam-1224	56	14	of	of	ADP
ejpam-1224	56	15	bounded	bounded	ADJ
ejpam-1224	56	16	chain	chain	NOUN
ejpam-1224	56	17	complexes	complex	NOUN
ejpam-1224	56	18	of	of	ADP
ejpam-1224	56	19	graded	grade	VERB
ejpam-1224	56	20	left	leave	VERB
ejpam-1224	56	21	a	a	DET
ejpam-1224	56	22	-	-	PUNCT
ejpam-1224	56	23	modules	module	NOUN
ejpam-1224	56	24	,	,	PUNCT
ejpam-1224	56	25	the	the	DET
ejpam-1224	56	26	functor	functor	PROPN
ejpam-1224	56	27	f	f	PROPN
ejpam-1224	56	28	is	be	AUX
ejpam-1224	56	29	given	give	VERB
ejpam-1224	56	30	by	by	ADP
ejpam-1224	56	31	(	(	PUNCT
ejpam-1224	56	32	f	f	PROPN
ejpam-1224	56	33	m)pq	m)pq	PROPN
ejpam-1224	56	34	=	=	PROPN
ejpam-1224	56	35	⊕	⊕	PROPN
ejpam-1224	56	36	p	p	NOUN
ejpam-1224	56	37	=	=	PROPN
ejpam-1224	56	38	i+	i+	NOUN
ejpam-1224	56	39	j	j	NOUN
ejpam-1224	56	40	q	q	NOUN
ejpam-1224	56	41	=	=	VERB
ejpam-1224	56	42	l−	l−	NOUN
ejpam-1224	56	43	j	j	PROPN
ejpam-1224	56	44	a	a	X
ejpam-1224	56	45	!	!	PUNCT
ejpam-1224	57	1	l	l	NOUN
ejpam-1224	57	2	⊗m	⊗m	NOUN
ejpam-1224	58	1	i	i	PRON
ejpam-1224	58	2	j	j	PROPN
ejpam-1224	58	3	.	.	PUNCT
ejpam-1224	59	1	for	for	ADP
ejpam-1224	59	2	n	n	DET
ejpam-1224	59	3	∈	∈	PROPN
ejpam-1224	59	4	c	c	X
ejpam-1224	59	5	b(a	b(a	PROPN
ejpam-1224	59	6	!	!	PUNCT
ejpam-1224	59	7	)	)	PUNCT
ejpam-1224	59	8	,	,	PUNCT
ejpam-1224	59	9	the	the	DET
ejpam-1224	59	10	functor	functor	PROPN
ejpam-1224	59	11	g	g	PROPN
ejpam-1224	59	12	is	be	AUX
ejpam-1224	59	13	explicitly	explicitly	ADV
ejpam-1224	59	14	described	describe	VERB
ejpam-1224	59	15	as	as	ADP
ejpam-1224	59	16	(	(	PUNCT
ejpam-1224	59	17	gn)pq	gn)pq	PROPN
ejpam-1224	59	18	=	=	PROPN
ejpam-1224	59	19	⊕	⊕	PROPN
ejpam-1224	59	20	p	p	NOUN
ejpam-1224	59	21	=	=	PROPN
ejpam-1224	59	22	i+	i+	NOUN
ejpam-1224	59	23	j	j	NOUN
ejpam-1224	59	24	q	q	NOUN
ejpam-1224	59	25	=	=	VERB
ejpam-1224	59	26	l−	l−	NOUN
ejpam-1224	59	27	j	j	NOUN
ejpam-1224	59	28	homk(a−l	homk(a−l	PROPN
ejpam-1224	59	29	,	,	PUNCT
ejpam-1224	59	30	n	n	CCONJ
ejpam-1224	59	31	i	i	PRON
ejpam-1224	59	32	j	j	PROPN
ejpam-1224	59	33	)	)	PUNCT
ejpam-1224	59	34	.	.	PUNCT
ejpam-1224	60	1	another	another	DET
ejpam-1224	60	2	example	example	NOUN
ejpam-1224	60	3	concerns	concern	VERB
ejpam-1224	60	4	a	a	DET
ejpam-1224	60	5	nondegenerate	nondegenerate	ADJ
ejpam-1224	60	6	quadratic	quadratic	ADJ
ejpam-1224	60	7	form	form	NOUN
ejpam-1224	60	8	,	,	PUNCT
ejpam-1224	60	9	q	q	X
ejpam-1224	60	10	,	,	PUNCT
ejpam-1224	60	11	in	in	ADP
ejpam-1224	60	12	variables	variable	NOUN
ejpam-1224	60	13	x0	x0	PROPN
ejpam-1224	60	14	,	,	PUNCT
ejpam-1224	60	15	x1	x1	PROPN
ejpam-1224	60	16	,	,	PUNCT
ejpam-1224	60	17	.	.	PUNCT
ejpam-1224	60	18	.	.	PUNCT
ejpam-1224	61	1	.	.	PUNCT
ejpam-1224	62	1	,	,	PUNCT
ejpam-1224	62	2	xn	xn	X
ejpam-1224	62	3	.	.	PUNCT
ejpam-1224	63	1	let	let	VERB
ejpam-1224	63	2	a=	a=	VERB
ejpam-1224	63	3	k[x0	k[x0	ADV
ejpam-1224	63	4	,	,	PUNCT
ejpam-1224	63	5	x1	x1	PROPN
ejpam-1224	63	6	,	,	PUNCT
ejpam-1224	63	7	.	.	PUNCT
ejpam-1224	63	8	.	.	PUNCT
ejpam-1224	64	1	.	.	PUNCT
ejpam-1224	65	1	,	,	PUNCT
ejpam-1224	65	2	xn]/q	xn]/q	PROPN
ejpam-1224	65	3	=	=	SYM
ejpam-1224	65	4	sym(v	sym(v	ADJ
ejpam-1224	65	5	)	)	PUNCT
ejpam-1224	65	6	/q	/q	X
ejpam-1224	66	1	be	be	AUX
ejpam-1224	66	2	the	the	DET
ejpam-1224	66	3	homogeneous	homogeneous	ADJ
ejpam-1224	66	4	coordinate	coordinate	NOUN
ejpam-1224	66	5	ring	ring	NOUN
ejpam-1224	66	6	of	of	ADP
ejpam-1224	66	7	the	the	DET
ejpam-1224	66	8	quadric	quadric	ADJ
ejpam-1224	66	9	q	q	NOUN
ejpam-1224	66	10	=	=	SYM
ejpam-1224	66	11	0	0	NUM
ejpam-1224	66	12	in	in	ADP
ejpam-1224	66	13	projective	projective	ADJ
ejpam-1224	66	14	space	space	NOUN
ejpam-1224	66	15	pn	pn	PROPN
ejpam-1224	66	16	k	k	PROPN
ejpam-1224	66	17	.	.	PUNCT
ejpam-1224	67	1	the	the	DET
ejpam-1224	67	2	dual	dual	ADJ
ejpam-1224	67	3	a	a	PRON
ejpam-1224	67	4	!	!	PUNCT
ejpam-1224	67	5	is	be	AUX
ejpam-1224	67	6	the	the	DET
ejpam-1224	67	7	graded	grade	VERB
ejpam-1224	67	8	clifford	clifford	PROPN
ejpam-1224	67	9	algebra	algebra	PROPN
ejpam-1224	67	10	attached	attach	VERB
ejpam-1224	67	11	to	to	ADP
ejpam-1224	67	12	q.	q.	NOUN
ejpam-1224	67	13	this	this	PRON
ejpam-1224	67	14	is	be	AUX
ejpam-1224	67	15	generated	generate	VERB
ejpam-1224	67	16	by	by	ADP
ejpam-1224	67	17	elements	element	NOUN
ejpam-1224	67	18	ξ	ξ	PROPN
ejpam-1224	67	19	∈	∈	PROPN
ejpam-1224	67	20	v	v	ADP
ejpam-1224	67	21	∗	∗	NOUN
ejpam-1224	67	22	of	of	ADP
ejpam-1224	67	23	tensor	tensor	NOUN
ejpam-1224	67	24	degree	degree	NOUN
ejpam-1224	67	25	1	1	NUM
ejpam-1224	67	26	and	and	CCONJ
ejpam-1224	67	27	an	an	DET
ejpam-1224	67	28	element	element	ADJ
ejpam-1224	67	29	h	h	NOUN
ejpam-1224	67	30	of	of	ADP
ejpam-1224	67	31	tensor	tensor	NOUN
ejpam-1224	67	32	degree	degree	NOUN
ejpam-1224	67	33	2	2	NUM
ejpam-1224	67	34	with	with	ADP
ejpam-1224	67	35	the	the	DET
ejpam-1224	67	36	relations	relation	NOUN
ejpam-1224	67	37	ξη+ηξ	ξη+ηξ	PROPN
ejpam-1224	67	38	=	=	SYM
ejpam-1224	67	39	2q(ξ	2q(ξ	PROPN
ejpam-1224	67	40	,	,	PUNCT
ejpam-1224	67	41	η)h	η)h	NOUN
ejpam-1224	67	42	,	,	PUNCT
ejpam-1224	67	43	ξ	ξ	PROPN
ejpam-1224	67	44	,	,	PUNCT
ejpam-1224	67	45	η	η	PROPN
ejpam-1224	67	46	∈	∈	PROPN
ejpam-1224	67	47	v	v	ADP
ejpam-1224	67	48	∗.	∗.	PROPN
ejpam-1224	67	49	f.	f.	PROPN
ejpam-1224	67	50	hawwa	hawwa	PROPN
ejpam-1224	67	51	,	,	PUNCT
ejpam-1224	67	52	j.	j.	PROPN
ejpam-1224	67	53	hoffman	hoffman	PROPN
ejpam-1224	67	54	,	,	PUNCT
ejpam-1224	67	55	and	and	CCONJ
ejpam-1224	67	56	h.	h.	PROPN
ejpam-1224	67	57	wang	wang	PROPN
ejpam-1224	67	58	,	,	PUNCT
ejpam-1224	67	59	/	/	SYM
ejpam-1224	67	60	eur	eur	NOUN
ejpam-1224	67	61	.	.	PUNCT
ejpam-1224	68	1	j.	j.	PROPN
ejpam-1224	68	2	pure	pure	PROPN
ejpam-1224	68	3	appl	appl	PROPN
ejpam-1224	68	4	.	.	PROPN
ejpam-1224	68	5	math	math	PROPN
ejpam-1224	68	6	,	,	PUNCT
ejpam-1224	68	7	5	5	NUM
ejpam-1224	68	8	(	(	PUNCT
ejpam-1224	68	9	2012	2012	NUM
ejpam-1224	68	10	)	)	PUNCT
ejpam-1224	68	11	,	,	PUNCT
ejpam-1224	68	12	511	511	NUM
ejpam-1224	68	13	-	-	SYM
ejpam-1224	68	14	539	539	NUM
ejpam-1224	68	15	513	513	NUM
ejpam-1224	68	16	the	the	DET
ejpam-1224	68	17	ring	ring	NOUN
ejpam-1224	68	18	a	a	PRON
ejpam-1224	68	19	is	be	AUX
ejpam-1224	68	20	proven	prove	VERB
ejpam-1224	68	21	to	to	PART
ejpam-1224	68	22	be	be	AUX
ejpam-1224	68	23	a	a	DET
ejpam-1224	68	24	koszul	koszul	ADJ
ejpam-1224	68	25	ring	ring	NOUN
ejpam-1224	68	26	in	in	ADP
ejpam-1224	68	27	[	[	X
ejpam-1224	68	28	4	4	NUM
ejpam-1224	68	29	]	]	PUNCT
ejpam-1224	68	30	.	.	PUNCT
ejpam-1224	69	1	not	not	PART
ejpam-1224	69	2	every	every	DET
ejpam-1224	69	3	quadratic	quadratic	ADJ
ejpam-1224	69	4	algebra	algebra	NOUN
ejpam-1224	69	5	is	be	AUX
ejpam-1224	69	6	koszul	koszul	ADJ
ejpam-1224	69	7	.	.	PUNCT
ejpam-1224	70	1	a	a	DET
ejpam-1224	70	2	counterexample	counterexample	NOUN
ejpam-1224	70	3	is	be	AUX
ejpam-1224	70	4	a=	a=	ADJ
ejpam-1224	70	5	∧	∧	PROPN
ejpam-1224	70	6	k	k	PROPN
ejpam-1224	70	7	(	(	PUNCT
ejpam-1224	70	8	x	x	INTJ
ejpam-1224	70	9	,	,	PUNCT
ejpam-1224	70	10	y	y	PROPN
ejpam-1224	70	11	,	,	PUNCT
ejpam-1224	70	12	z	z	PROPN
ejpam-1224	70	13	,	,	PUNCT
ejpam-1224	70	14	w)/(x	w)/(x	PROPN
ejpam-1224	70	15	y	y	PROPN
ejpam-1224	70	16	+	+	PROPN
ejpam-1224	70	17	zw	zw	PROPN
ejpam-1224	70	18	)	)	PUNCT
ejpam-1224	70	19	.	.	PUNCT
ejpam-1224	71	1	using	use	VERB
ejpam-1224	71	2	the	the	DET
ejpam-1224	71	3	software	software	NOUN
ejpam-1224	71	4	package	package	NOUN
ejpam-1224	71	5	singular	singular	NOUN
ejpam-1224	71	6	to	to	PART
ejpam-1224	71	7	calculate	calculate	VERB
ejpam-1224	71	8	the	the	DET
ejpam-1224	71	9	minimal	minimal	ADJ
ejpam-1224	71	10	free	free	ADJ
ejpam-1224	71	11	resolution	resolution	NOUN
ejpam-1224	71	12	of	of	ADP
ejpam-1224	71	13	a	a	PRON
ejpam-1224	71	14	,	,	PUNCT
ejpam-1224	71	15	we	we	PRON
ejpam-1224	71	16	observed	observe	VERB
ejpam-1224	71	17	that	that	SCONJ
ejpam-1224	71	18	quadratic	quadratic	ADJ
ejpam-1224	71	19	entries	entry	NOUN
ejpam-1224	71	20	appear	appear	VERB
ejpam-1224	71	21	within	within	ADP
ejpam-1224	71	22	the	the	DET
ejpam-1224	71	23	matrices	matrix	NOUN
ejpam-1224	71	24	,	,	PUNCT
ejpam-1224	71	25	violating	violate	VERB
ejpam-1224	71	26	the	the	DET
ejpam-1224	71	27	property	property	NOUN
ejpam-1224	71	28	that	that	PRON
ejpam-1224	71	29	an	an	DET
ejpam-1224	71	30	algebra	algebra	NOUN
ejpam-1224	71	31	is	be	AUX
ejpam-1224	71	32	koszul	koszul	ADJ
ejpam-1224	71	33	if	if	SCONJ
ejpam-1224	71	34	and	and	CCONJ
ejpam-1224	71	35	only	only	ADV
ejpam-1224	71	36	if	if	SCONJ
ejpam-1224	71	37	k	k	PROPN
ejpam-1224	71	38	has	have	VERB
ejpam-1224	71	39	a	a	DET
ejpam-1224	71	40	linear	linear	ADJ
ejpam-1224	71	41	free	free	ADJ
ejpam-1224	71	42	a	a	DET
ejpam-1224	71	43	-	-	PUNCT
ejpam-1224	71	44	module	module	NOUN
ejpam-1224	71	45	resolution	resolution	NOUN
ejpam-1224	71	46	.	.	PUNCT
ejpam-1224	72	1	if	if	SCONJ
ejpam-1224	72	2	we	we	PRON
ejpam-1224	72	3	now	now	ADV
ejpam-1224	72	4	allow	allow	VERB
ejpam-1224	72	5	the	the	DET
ejpam-1224	72	6	relations	relation	NOUN
ejpam-1224	72	7	,	,	PUNCT
ejpam-1224	72	8	r	r	NOUN
ejpam-1224	72	9	,	,	PUNCT
ejpam-1224	72	10	of	of	ADP
ejpam-1224	72	11	an	an	DET
ejpam-1224	72	12	algebra	algebra	NOUN
ejpam-1224	72	13	a	a	DET
ejpam-1224	72	14	=	=	X
ejpam-1224	72	15	k	k	X
ejpam-1224	72	16	<	<	X
ejpam-1224	72	17	x1	x1	PROPN
ejpam-1224	72	18	,	,	PUNCT
ejpam-1224	72	19	x2	x2	PROPN
ejpam-1224	72	20	,	,	PUNCT
ejpam-1224	72	21	.	.	PUNCT
ejpam-1224	72	22	.	.	PUNCT
ejpam-1224	73	1	.	.	PUNCT
ejpam-1224	74	1	,	,	PUNCT
ejpam-1224	74	2	xn	xn	PROPN
ejpam-1224	74	3	>	>	X
ejpam-1224	74	4	/r	/r	PUNCT
ejpam-1224	74	5	to	to	PART
ejpam-1224	74	6	be	be	AUX
ejpam-1224	74	7	nonhomogeneous	nonhomogeneous	ADJ
ejpam-1224	74	8	,	,	PUNCT
ejpam-1224	74	9	a	a	PRON
ejpam-1224	74	10	will	will	AUX
ejpam-1224	74	11	no	no	ADV
ejpam-1224	74	12	longer	long	ADV
ejpam-1224	74	13	be	be	AUX
ejpam-1224	74	14	a	a	DET
ejpam-1224	74	15	graded	grade	VERB
ejpam-1224	74	16	algebra	algebra	NOUN
ejpam-1224	74	17	,	,	PUNCT
ejpam-1224	74	18	but	but	CCONJ
ejpam-1224	74	19	rather	rather	ADV
ejpam-1224	74	20	a	a	DET
ejpam-1224	74	21	filtered	filter	VERB
ejpam-1224	74	22	algebra	algebra	NOUN
ejpam-1224	74	23	.	.	PUNCT
ejpam-1224	75	1	the	the	DET
ejpam-1224	75	2	dual	dual	ADJ
ejpam-1224	75	3	of	of	ADP
ejpam-1224	75	4	a	a	DET
ejpam-1224	75	5	will	will	NOUN
ejpam-1224	75	6	no	no	ADV
ejpam-1224	75	7	longer	long	ADV
ejpam-1224	75	8	be	be	AUX
ejpam-1224	75	9	the	the	DET
ejpam-1224	75	10	quadratic	quadratic	ADJ
ejpam-1224	75	11	algebra	algebra	NOUN
ejpam-1224	75	12	a	a	PRON
ejpam-1224	75	13	!	!	PUNCT
ejpam-1224	75	14	,	,	PUNCT
ejpam-1224	75	15	but	but	CCONJ
ejpam-1224	75	16	rather	rather	ADV
ejpam-1224	75	17	the	the	DET
ejpam-1224	75	18	curved	curved	ADJ
ejpam-1224	75	19	differential	differential	NOUN
ejpam-1224	75	20	graded	grade	VERB
ejpam-1224	75	21	algebra	algebra	NOUN
ejpam-1224	75	22	(	(	PUNCT
ejpam-1224	75	23	cdga	cdga	PROPN
ejpam-1224	75	24	)	)	PUNCT
ejpam-1224	75	25	(	(	PUNCT
ejpam-1224	75	26	a	a	X
ejpam-1224	75	27	!	!	PUNCT
ejpam-1224	75	28	,	,	PUNCT
ejpam-1224	75	29	d	d	X
ejpam-1224	75	30	,	,	PUNCT
ejpam-1224	75	31	c	c	NOUN
ejpam-1224	75	32	)	)	PUNCT
ejpam-1224	75	33	.	.	PUNCT
ejpam-1224	76	1	that	that	PRON
ejpam-1224	76	2	is	be	AUX
ejpam-1224	76	3	,	,	PUNCT
ejpam-1224	76	4	we	we	PRON
ejpam-1224	76	5	have	have	VERB
ejpam-1224	76	6	a	a	DET
ejpam-1224	76	7	differential	differential	NOUN
ejpam-1224	76	8	d	d	NOUN
ejpam-1224	76	9	:	:	PUNCT
ejpam-1224	76	10	(	(	PUNCT
ejpam-1224	76	11	a!)n	a!)n	PROPN
ejpam-1224	76	12	→	→	PUNCT
ejpam-1224	76	13	(	(	PUNCT
ejpam-1224	76	14	a!)n+1	a!)n+1	VERB
ejpam-1224	76	15	with	with	ADP
ejpam-1224	76	16	the	the	DET
ejpam-1224	76	17	usual	usual	ADJ
ejpam-1224	76	18	property	property	NOUN
ejpam-1224	76	19	that	that	PRON
ejpam-1224	76	20	d(x	d(x	PROPN
ejpam-1224	76	21	y	y	PROPN
ejpam-1224	76	22	)	)	PUNCT
ejpam-1224	76	23	=	=	PUNCT
ejpam-1224	77	1	d	d	X
ejpam-1224	77	2	x(y	x(y	PROPN
ejpam-1224	77	3	)	)	PUNCT
ejpam-1224	77	4	±	±	NOUN
ejpam-1224	77	5	(	(	PUNCT
ejpam-1224	77	6	x)d	x)d	NOUN
ejpam-1224	77	7	y	y	PROPN
ejpam-1224	77	8	but	but	CCONJ
ejpam-1224	77	9	with	with	ADP
ejpam-1224	77	10	d2(x	d2(x	NOUN
ejpam-1224	77	11	)	)	PUNCT
ejpam-1224	77	12	=	=	PUNCT
ejpam-1224	78	1	[	[	X
ejpam-1224	78	2	c	c	X
ejpam-1224	78	3	,	,	PUNCT
ejpam-1224	78	4	x	x	X
ejpam-1224	78	5	]	]	X
ejpam-1224	78	6	=	=	SYM
ejpam-1224	78	7	cx	cx	PROPN
ejpam-1224	78	8	±	±	NUM
ejpam-1224	78	9	xc	xc	PROPN
ejpam-1224	78	10	,	,	PUNCT
ejpam-1224	78	11	where	where	SCONJ
ejpam-1224	78	12	c	c	PROPN
ejpam-1224	78	13	∈	∈	PROPN
ejpam-1224	78	14	(	(	PUNCT
ejpam-1224	78	15	a	a	NOUN
ejpam-1224	78	16	!	!	NOUN
ejpam-1224	78	17	2	2	NUM
ejpam-1224	78	18	)	)	PUNCT
ejpam-1224	78	19	∗	∗	NOUN
ejpam-1224	78	20	is	be	AUX
ejpam-1224	78	21	the	the	DET
ejpam-1224	78	22	curvature	curvature	NOUN
ejpam-1224	78	23	.	.	PUNCT
ejpam-1224	79	1	in	in	ADP
ejpam-1224	79	2	the	the	DET
ejpam-1224	79	3	case	case	NOUN
ejpam-1224	79	4	where	where	SCONJ
ejpam-1224	79	5	c	c	NOUN
ejpam-1224	79	6	=	=	SYM
ejpam-1224	79	7	0	0	NUM
ejpam-1224	79	8	we	we	PRON
ejpam-1224	79	9	refer	refer	VERB
ejpam-1224	79	10	to	to	ADP
ejpam-1224	79	11	a	a	DET
ejpam-1224	79	12	cdga	cdga	NOUN
ejpam-1224	79	13	as	as	ADP
ejpam-1224	79	14	just	just	ADV
ejpam-1224	79	15	a	a	DET
ejpam-1224	79	16	dga	dga	NOUN
ejpam-1224	79	17	(	(	PUNCT
ejpam-1224	79	18	differential	differential	NOUN
ejpam-1224	79	19	graded	grade	VERB
ejpam-1224	79	20	algebra	algebra	NOUN
ejpam-1224	79	21	)	)	PUNCT
ejpam-1224	79	22	.	.	PUNCT
ejpam-1224	80	1	two	two	NUM
ejpam-1224	80	2	canonical	canonical	ADJ
ejpam-1224	80	3	examples	example	NOUN
ejpam-1224	80	4	of	of	ADP
ejpam-1224	80	5	dgas	dgas	PROPN
ejpam-1224	80	6	are	be	AUX
ejpam-1224	80	7	the	the	DET
ejpam-1224	80	8	koszul	koszul	ADJ
ejpam-1224	80	9	complex	complex	NOUN
ejpam-1224	80	10	and	and	CCONJ
ejpam-1224	80	11	the	the	DET
ejpam-1224	80	12	derham	derham	PROPN
ejpam-1224	80	13	complex	complex	NOUN
ejpam-1224	80	14	.	.	PUNCT
ejpam-1224	81	1	let	let	VERB
ejpam-1224	81	2	us	we	PRON
ejpam-1224	81	3	consider	consider	VERB
ejpam-1224	81	4	an	an	DET
ejpam-1224	81	5	example	example	NOUN
ejpam-1224	81	6	that	that	PRON
ejpam-1224	81	7	illustrates	illustrate	VERB
ejpam-1224	81	8	dualizing	dualize	VERB
ejpam-1224	81	9	a	a	DET
ejpam-1224	81	10	nonhomogeneous	nonhomogeneous	ADJ
ejpam-1224	81	11	quadratic	quadratic	ADJ
ejpam-1224	81	12	algebra	algebra	NOUN
ejpam-1224	81	13	.	.	PUNCT
ejpam-1224	82	1	consider	consider	VERB
ejpam-1224	82	2	the	the	DET
ejpam-1224	82	3	algebra	algebra	NOUN
ejpam-1224	82	4	,	,	PUNCT
ejpam-1224	82	5	u	u	NOUN
ejpam-1224	82	6	=	=	X
ejpam-1224	82	7	k	k	X
ejpam-1224	82	8	<	<	X
ejpam-1224	82	9	x	x	X
ejpam-1224	82	10	,	,	PUNCT
ejpam-1224	82	11	y	y	PROPN
ejpam-1224	82	12	>	>	PUNCT
ejpam-1224	82	13	/p	/p	X
ejpam-1224	82	14	,	,	PUNCT
ejpam-1224	82	15	p	p	NOUN
ejpam-1224	82	16	=	=	X
ejpam-1224	82	17	(	(	PUNCT
ejpam-1224	82	18	x2−	x2−	PROPN
ejpam-1224	82	19	y	y	PROPN
ejpam-1224	82	20	,	,	PUNCT
ejpam-1224	82	21	x	x	PROPN
ejpam-1224	82	22	y	y	NOUN
ejpam-1224	82	23	−	−	PROPN
ejpam-1224	82	24	y	y	PROPN
ejpam-1224	82	25	x	x	PROPN
ejpam-1224	82	26	)	)	PUNCT
ejpam-1224	82	27	.	.	PUNCT
ejpam-1224	83	1	the	the	DET
ejpam-1224	83	2	associated	associate	VERB
ejpam-1224	83	3	graded	grade	VERB
ejpam-1224	83	4	algebra	algebra	NOUN
ejpam-1224	83	5	to	to	ADP
ejpam-1224	83	6	u	u	PRON
ejpam-1224	83	7	will	will	AUX
ejpam-1224	83	8	be	be	AUX
ejpam-1224	83	9	a	a	DET
ejpam-1224	83	10	=	=	X
ejpam-1224	83	11	k	k	X
ejpam-1224	83	12	<	<	X
ejpam-1224	83	13	x	x	X
ejpam-1224	83	14	,	,	PUNCT
ejpam-1224	83	15	y	y	PROPN
ejpam-1224	83	16	>	>	X
ejpam-1224	83	17	/(x2	/(x2	PROPN
ejpam-1224	83	18	,	,	PUNCT
ejpam-1224	83	19	x	x	VERB
ejpam-1224	84	1	y	y	NOUN
ejpam-1224	84	2	−	−	PROPN
ejpam-1224	84	3	y	y	PROPN
ejpam-1224	84	4	x	x	PROPN
ejpam-1224	84	5	)	)	PUNCT
ejpam-1224	84	6	which	which	PRON
ejpam-1224	84	7	is	be	AUX
ejpam-1224	84	8	dual	dual	ADJ
ejpam-1224	84	9	to	to	ADP
ejpam-1224	84	10	a	a	PRON
ejpam-1224	84	11	!	!	PUNCT
ejpam-1224	85	1	=	=	PUNCT
ejpam-1224	86	1	k	k	X
ejpam-1224	86	2	<	<	X
ejpam-1224	86	3	ξ	ξ	PROPN
ejpam-1224	86	4	,	,	PUNCT
ejpam-1224	86	5	η	η	PROPN
ejpam-1224	86	6	>	>	X
ejpam-1224	86	7	/(η2,ξη+	/(η2,ξη+	SYM
ejpam-1224	86	8	ηξ	ηξ	PROPN
ejpam-1224	86	9	)	)	PUNCT
ejpam-1224	86	10	which	which	PRON
ejpam-1224	86	11	can	can	AUX
ejpam-1224	86	12	be	be	AUX
ejpam-1224	86	13	seen	see	VERB
ejpam-1224	86	14	to	to	PART
ejpam-1224	86	15	be	be	AUX
ejpam-1224	86	16	a	a	DET
ejpam-1224	86	17	curved	curved	ADJ
ejpam-1224	86	18	differential	differential	NOUN
ejpam-1224	86	19	graded	grade	VERB
ejpam-1224	86	20	algebra	algebra	NOUN
ejpam-1224	86	21	(	(	PUNCT
ejpam-1224	86	22	a	a	PROPN
ejpam-1224	86	23	!	!	PUNCT
ejpam-1224	86	24	,	,	PUNCT
ejpam-1224	86	25	d	d	X
ejpam-1224	86	26	,	,	PUNCT
ejpam-1224	86	27	c	c	NOUN
ejpam-1224	86	28	)	)	PUNCT
ejpam-1224	86	29	with	with	ADP
ejpam-1224	86	30	c	c	NOUN
ejpam-1224	86	31	=	=	SYM
ejpam-1224	86	32	0	0	NUM
ejpam-1224	86	33	,	,	PUNCT
ejpam-1224	86	34	dξ=	dξ=	NOUN
ejpam-1224	86	35	0	0	NUM
ejpam-1224	86	36	and	and	CCONJ
ejpam-1224	86	37	dη=	dη=	PROPN
ejpam-1224	86	38	−ξ2	−ξ2	PROPN
ejpam-1224	86	39	.	.	PUNCT
ejpam-1224	87	1	a	a	DET
ejpam-1224	87	2	canonical	canonical	ADJ
ejpam-1224	87	3	example	example	NOUN
ejpam-1224	87	4	of	of	ADP
ejpam-1224	87	5	a	a	DET
ejpam-1224	87	6	nonhomogeneous	nonhomogeneous	ADJ
ejpam-1224	87	7	quadratic	quadratic	ADJ
ejpam-1224	87	8	algebra	algebra	NOUN
ejpam-1224	87	9	which	which	PRON
ejpam-1224	87	10	is	be	AUX
ejpam-1224	87	11	filtered	filter	VERB
ejpam-1224	87	12	by	by	ADP
ejpam-1224	87	13	tensor	tensor	NOUN
ejpam-1224	87	14	degree	degree	NOUN
ejpam-1224	87	15	is	be	AUX
ejpam-1224	87	16	u	u	PROPN
ejpam-1224	87	17	=	=	SYM
ejpam-1224	87	18	ug	ug	PROPN
ejpam-1224	87	19	,	,	PUNCT
ejpam-1224	87	20	the	the	DET
ejpam-1224	87	21	universal	universal	ADJ
ejpam-1224	87	22	enveloping	enveloping	NOUN
ejpam-1224	87	23	algebra	algebra	NOUN
ejpam-1224	87	24	of	of	ADP
ejpam-1224	87	25	a	a	DET
ejpam-1224	87	26	lie	lie	NOUN
ejpam-1224	87	27	algebra	algebra	NOUN
ejpam-1224	87	28	g.	g.	NOUN
ejpam-1224	88	1	the	the	DET
ejpam-1224	88	2	dual	dual	ADJ
ejpam-1224	88	3	of	of	ADP
ejpam-1224	88	4	ug	ug	ADV
ejpam-1224	88	5	is	be	AUX
ejpam-1224	88	6	the	the	DET
ejpam-1224	88	7	chevellay	chevellay	NOUN
ejpam-1224	88	8	-	-	PUNCT
ejpam-1224	88	9	eilenberg	eilenberg	PROPN
ejpam-1224	88	10	complex	complex	NOUN
ejpam-1224	88	11	which	which	PRON
ejpam-1224	88	12	is	be	AUX
ejpam-1224	88	13	a	a	DET
ejpam-1224	88	14	cdga	cdga	NOUN
ejpam-1224	88	15	(	(	PUNCT
ejpam-1224	88	16	more	more	ADV
ejpam-1224	88	17	specifically	specifically	ADV
ejpam-1224	88	18	it	it	PRON
ejpam-1224	88	19	is	be	AUX
ejpam-1224	88	20	a	a	DET
ejpam-1224	88	21	dga	dga	NOUN
ejpam-1224	88	22	since	since	SCONJ
ejpam-1224	88	23	c	c	PROPN
ejpam-1224	88	24	=	=	SYM
ejpam-1224	88	25	0	0	NUM
ejpam-1224	88	26	)	)	PUNCT
ejpam-1224	88	27	.	.	PUNCT
ejpam-1224	89	1	given	give	VERB
ejpam-1224	89	2	a	a	DET
ejpam-1224	89	3	filtered	filter	VERB
ejpam-1224	89	4	algebra	algebra	NOUN
ejpam-1224	89	5	,	,	PUNCT
ejpam-1224	89	6	we	we	PRON
ejpam-1224	89	7	can	can	AUX
ejpam-1224	89	8	add	add	VERB
ejpam-1224	89	9	a	a	DET
ejpam-1224	89	10	λ	λ	NOUN
ejpam-1224	89	11	-	-	NOUN
ejpam-1224	89	12	grading	grading	NOUN
ejpam-1224	89	13	to	to	ADP
ejpam-1224	89	14	it	it	PRON
ejpam-1224	89	15	.	.	PUNCT
ejpam-1224	90	1	a	a	DET
ejpam-1224	90	2	λ	λ	NOUN
ejpam-1224	90	3	-	-	PUNCT
ejpam-1224	90	4	graded	grade	VERB
ejpam-1224	90	5	filtered	filter	VERB
ejpam-1224	90	6	algebra	algebra	NOUN
ejpam-1224	90	7	,	,	PUNCT
ejpam-1224	90	8	u	u	NOUN
ejpam-1224	90	9	,	,	PUNCT
ejpam-1224	90	10	is	be	AUX
ejpam-1224	90	11	an	an	DET
ejpam-1224	90	12	algebra	algebra	NOUN
ejpam-1224	90	13	with	with	ADP
ejpam-1224	90	14	a	a	DET
ejpam-1224	90	15	filtration	filtration	NOUN
ejpam-1224	90	16	,	,	PUNCT
ejpam-1224	90	17	fi	fi	NOUN
ejpam-1224	90	18	,	,	PUNCT
ejpam-1224	90	19	and	and	CCONJ
ejpam-1224	90	20	also	also	ADV
ejpam-1224	90	21	a	a	DET
ejpam-1224	90	22	grading	grade	VERB
ejpam-1224	90	23	u	u	NOUN
ejpam-1224	90	24	=	=	PROPN
ejpam-1224	90	25	⊕	⊕	PROPN
ejpam-1224	90	26	λ∈λ	λ∈λ	NOUN
ejpam-1224	90	27	uλ	uλ	ADP
ejpam-1224	90	28	for	for	ADP
ejpam-1224	90	29	some	some	DET
ejpam-1224	90	30	abelian	abelian	ADJ
ejpam-1224	90	31	group	group	PROPN
ejpam-1224	90	32	λ	λ	PROPN
ejpam-1224	90	33	.	.	PUNCT
ejpam-1224	91	1	if	if	SCONJ
ejpam-1224	91	2	we	we	PRON
ejpam-1224	91	3	allow	allow	VERB
ejpam-1224	91	4	v	v	NOUN
ejpam-1224	91	5	to	to	PART
ejpam-1224	91	6	be	be	AUX
ejpam-1224	91	7	λ	λ	NOUN
ejpam-1224	91	8	-	-	VERB
ejpam-1224	91	9	graded	grade	VERB
ejpam-1224	91	10	,	,	PUNCT
ejpam-1224	91	11	and	and	CCONJ
ejpam-1224	91	12	p	p	NOUN
ejpam-1224	91	13	is	be	AUX
ejpam-1224	91	14	λ	λ	NOUN
ejpam-1224	91	15	-	-	ADJ
ejpam-1224	91	16	homogeneous	homogeneous	ADJ
ejpam-1224	91	17	,	,	PUNCT
ejpam-1224	91	18	then	then	ADV
ejpam-1224	91	19	we	we	PRON
ejpam-1224	91	20	know	know	VERB
ejpam-1224	91	21	that	that	SCONJ
ejpam-1224	91	22	u	u	PROPN
ejpam-1224	91	23	=	=	PROPN
ejpam-1224	91	24	t	t	PROPN
ejpam-1224	91	25	(	(	PUNCT
ejpam-1224	91	26	v	v	NOUN
ejpam-1224	91	27	)	)	PUNCT
ejpam-1224	91	28	/p	/p	PUNCT
ejpam-1224	91	29	will	will	AUX
ejpam-1224	91	30	be	be	AUX
ejpam-1224	91	31	filtered	filter	VERB
ejpam-1224	91	32	by	by	ADP
ejpam-1224	91	33	tensor	tensor	NOUN
ejpam-1224	91	34	degree	degree	NOUN
ejpam-1224	91	35	and	and	CCONJ
ejpam-1224	91	36	λ	λ	NOUN
ejpam-1224	91	37	-	-	PUNCT
ejpam-1224	91	38	graded	grade	VERB
ejpam-1224	91	39	.	.	PUNCT
ejpam-1224	92	1	two	two	NUM
ejpam-1224	92	2	examples	example	NOUN
ejpam-1224	92	3	of	of	ADP
ejpam-1224	92	4	λ	λ	NOUN
ejpam-1224	92	5	-	-	PUNCT
ejpam-1224	92	6	graded	grade	VERB
ejpam-1224	92	7	algebras	algebra	NOUN
ejpam-1224	92	8	are	be	AUX
ejpam-1224	92	9	the	the	DET
ejpam-1224	92	10	universal	universal	ADJ
ejpam-1224	92	11	enveloping	enveloping	NOUN
ejpam-1224	92	12	algebra	algebra	NOUN
ejpam-1224	92	13	of	of	ADP
ejpam-1224	92	14	a	a	DET
ejpam-1224	92	15	semisimple	semisimple	ADJ
ejpam-1224	92	16	lie	lie	NOUN
ejpam-1224	92	17	algebra	algebra	NOUN
ejpam-1224	92	18	,	,	PUNCT
ejpam-1224	92	19	and	and	CCONJ
ejpam-1224	92	20	the	the	DET
ejpam-1224	92	21	coordinate	coordinate	NOUN
ejpam-1224	92	22	ring	ring	NOUN
ejpam-1224	92	23	of	of	ADP
ejpam-1224	92	24	a	a	DET
ejpam-1224	92	25	projective	projective	ADJ
ejpam-1224	92	26	toric	toric	ADJ
ejpam-1224	92	27	variety	variety	NOUN
ejpam-1224	92	28	.	.	PUNCT
ejpam-1224	93	1	there	there	PRON
ejpam-1224	93	2	is	be	VERB
ejpam-1224	93	3	no	no	DET
ejpam-1224	93	4	obvious	obvious	ADJ
ejpam-1224	93	5	way	way	NOUN
ejpam-1224	93	6	to	to	PART
ejpam-1224	93	7	extend	extend	VERB
ejpam-1224	93	8	koszul	koszul	ADJ
ejpam-1224	93	9	duality	duality	NOUN
ejpam-1224	93	10	to	to	ADP
ejpam-1224	93	11	a	a	DET
ejpam-1224	93	12	λ	λ	NOUN
ejpam-1224	93	13	-	-	PUNCT
ejpam-1224	93	14	graded	grade	VERB
ejpam-1224	93	15	situation	situation	NOUN
ejpam-1224	93	16	when	when	SCONJ
ejpam-1224	93	17	λ	λ	PROPN
ejpam-1224	93	18	6=	6=	PROPN
ejpam-1224	93	19	z.	z.	PROPN
ejpam-1224	93	20	consider	consider	VERB
ejpam-1224	93	21	the	the	DET
ejpam-1224	93	22	functor	functor	PROPN
ejpam-1224	93	23	f	f	PROPN
ejpam-1224	93	24	given	give	VERB
ejpam-1224	93	25	by	by	ADP
ejpam-1224	93	26	(	(	PUNCT
ejpam-1224	93	27	f	f	PROPN
ejpam-1224	93	28	m)pq	m)pq	PROPN
ejpam-1224	93	29	=	=	PROPN
ejpam-1224	93	30	⊕	⊕	PROPN
ejpam-1224	93	31	p	p	NOUN
ejpam-1224	93	32	=	=	PROPN
ejpam-1224	93	33	i+	i+	NOUN
ejpam-1224	93	34	j	j	NOUN
ejpam-1224	93	35	q	q	NOUN
ejpam-1224	93	36	=	=	VERB
ejpam-1224	93	37	l−	l−	NOUN
ejpam-1224	93	38	j	j	PROPN
ejpam-1224	93	39	a	a	X
ejpam-1224	93	40	!	!	PUNCT
ejpam-1224	94	1	l	l	NOUN
ejpam-1224	94	2	⊗m	⊗m	NOUN
ejpam-1224	95	1	i	i	PRON
ejpam-1224	95	2	j	j	PROPN
ejpam-1224	95	3	.	.	PUNCT
ejpam-1224	96	1	f.	f.	PROPN
ejpam-1224	96	2	hawwa	hawwa	PROPN
ejpam-1224	96	3	,	,	PUNCT
ejpam-1224	96	4	j.	j.	PROPN
ejpam-1224	96	5	hoffman	hoffman	PROPN
ejpam-1224	96	6	,	,	PUNCT
ejpam-1224	96	7	and	and	CCONJ
ejpam-1224	96	8	h.	h.	PROPN
ejpam-1224	96	9	wang	wang	PROPN
ejpam-1224	96	10	,	,	PUNCT
ejpam-1224	96	11	/	/	SYM
ejpam-1224	96	12	eur	eur	NOUN
ejpam-1224	96	13	.	.	PUNCT
ejpam-1224	97	1	j.	j.	PROPN
ejpam-1224	97	2	pure	pure	PROPN
ejpam-1224	97	3	appl	appl	PROPN
ejpam-1224	97	4	.	.	PROPN
ejpam-1224	97	5	math	math	PROPN
ejpam-1224	97	6	,	,	PUNCT
ejpam-1224	97	7	5	5	NUM
ejpam-1224	97	8	(	(	PUNCT
ejpam-1224	97	9	2012	2012	NUM
ejpam-1224	97	10	)	)	PUNCT
ejpam-1224	97	11	,	,	PUNCT
ejpam-1224	97	12	511	511	NUM
ejpam-1224	97	13	-	-	SYM
ejpam-1224	97	14	539	539	NUM
ejpam-1224	97	15	514	514	NUM
ejpam-1224	97	16	this	this	DET
ejpam-1224	97	17	functor	functor	NOUN
ejpam-1224	97	18	is	be	AUX
ejpam-1224	97	19	well	well	ADV
ejpam-1224	97	20	defined	define	VERB
ejpam-1224	97	21	for	for	ADP
ejpam-1224	97	22	the	the	DET
ejpam-1224	97	23	case	case	NOUN
ejpam-1224	97	24	λ	λ	X
ejpam-1224	97	25	=	=	SYM
ejpam-1224	98	1	z	z	NOUN
ejpam-1224	99	1	but	but	CCONJ
ejpam-1224	99	2	if	if	SCONJ
ejpam-1224	99	3	a	a	PRON
ejpam-1224	99	4	is	be	AUX
ejpam-1224	99	5	λ	λ	NOUN
ejpam-1224	99	6	-	-	PUNCT
ejpam-1224	99	7	graded	grade	VERB
ejpam-1224	99	8	then	then	ADV
ejpam-1224	99	9	we	we	PRON
ejpam-1224	99	10	would	would	AUX
ejpam-1224	99	11	have	have	VERB
ejpam-1224	99	12	i	i	PRON
ejpam-1224	99	13	∈	∈	PROPN
ejpam-1224	99	14	z	z	NOUN
ejpam-1224	100	1	but	but	CCONJ
ejpam-1224	100	2	j	j	PROPN
ejpam-1224	100	3	∈	∈	PROPN
ejpam-1224	100	4	λ	λ	PROPN
ejpam-1224	100	5	.	.	PUNCT
ejpam-1224	101	1	now	now	ADV
ejpam-1224	101	2	the	the	DET
ejpam-1224	101	3	addition	addition	NOUN
ejpam-1224	101	4	i	i	PRON
ejpam-1224	102	1	+	+	NUM
ejpam-1224	102	2	j	j	NOUN
ejpam-1224	102	3	no	no	ADV
ejpam-1224	102	4	longer	long	ADV
ejpam-1224	102	5	makes	make	VERB
ejpam-1224	102	6	sense	sense	NOUN
ejpam-1224	102	7	since	since	SCONJ
ejpam-1224	102	8	i	i	PRON
ejpam-1224	102	9	is	be	AUX
ejpam-1224	102	10	a	a	DET
ejpam-1224	102	11	scalar	scalar	ADJ
ejpam-1224	102	12	and	and	CCONJ
ejpam-1224	102	13	j	j	PROPN
ejpam-1224	102	14	is	be	AUX
ejpam-1224	102	15	a	a	DET
ejpam-1224	102	16	vector	vector	NOUN
ejpam-1224	102	17	.	.	PUNCT
ejpam-1224	103	1	the	the	DET
ejpam-1224	103	2	key	key	ADJ
ejpam-1224	103	3	step	step	NOUN
ejpam-1224	103	4	to	to	ADP
ejpam-1224	103	5	our	our	PRON
ejpam-1224	103	6	extension	extension	NOUN
ejpam-1224	103	7	of	of	ADP
ejpam-1224	103	8	koszul	koszul	ADJ
ejpam-1224	103	9	duality	duality	NOUN
ejpam-1224	103	10	is	be	AUX
ejpam-1224	103	11	considering	consider	VERB
ejpam-1224	103	12	a	a	PRON
ejpam-1224	103	13	!	!	PUNCT
ejpam-1224	104	1	l	l	NOUN
ejpam-1224	104	2	not	not	PART
ejpam-1224	104	3	as	as	ADP
ejpam-1224	104	4	a	a	DET
ejpam-1224	104	5	quadratic	quadratic	ADJ
ejpam-1224	104	6	algebra	algebra	NOUN
ejpam-1224	104	7	but	but	CCONJ
ejpam-1224	104	8	as	as	ADP
ejpam-1224	104	9	a	a	DET
ejpam-1224	104	10	cdga	cdga	NOUN
ejpam-1224	104	11	,	,	PUNCT
ejpam-1224	104	12	meaning	mean	VERB
ejpam-1224	104	13	a	a	PRON
ejpam-1224	104	14	!	!	PUNCT
ejpam-1224	105	1	l	l	NOUN
ejpam-1224	106	1	=	=	PUNCT
ejpam-1224	106	2	(	(	PUNCT
ejpam-1224	106	3	a!)lλ	a!)lλ	PROPN
ejpam-1224	106	4	l	l	PROPN
ejpam-1224	106	5	∈	∈	PROPN
ejpam-1224	106	6	z	z	PROPN
ejpam-1224	106	7	,	,	PUNCT
ejpam-1224	106	8	λ	λ	PROPN
ejpam-1224	106	9	∈	∈	PROPN
ejpam-1224	106	10	λ	λ	PROPN
ejpam-1224	106	11	,	,	PUNCT
ejpam-1224	106	12	with	with	ADP
ejpam-1224	106	13	the	the	DET
ejpam-1224	106	14	multiplication	multiplication	NOUN
ejpam-1224	106	15	(	(	PUNCT
ejpam-1224	106	16	a!)lλ	a!)lλ	ADJ
ejpam-1224	106	17	×	×	NOUN
ejpam-1224	106	18	(	(	PUNCT
ejpam-1224	106	19	a	a	PRON
ejpam-1224	106	20	!	!	PUNCT
ejpam-1224	106	21	)	)	PUNCT
ejpam-1224	106	22	mµ	mµ	ADP
ejpam-1224	106	23	−→	−→	NOUN
ejpam-1224	106	24	(	(	PUNCT
ejpam-1224	106	25	a	a	PRON
ejpam-1224	106	26	!	!	PUNCT
ejpam-1224	106	27	)	)	PUNCT
ejpam-1224	106	28	l+m	l+m	X
ejpam-1224	107	1	λ+µ	λ+µ	X
ejpam-1224	107	2	.	.	PUNCT
ejpam-1224	108	1	the	the	DET
ejpam-1224	108	2	benefit	benefit	NOUN
ejpam-1224	108	3	of	of	ADP
ejpam-1224	108	4	switching	switch	VERB
ejpam-1224	108	5	over	over	ADP
ejpam-1224	108	6	from	from	ADP
ejpam-1224	108	7	a	a	DET
ejpam-1224	108	8	quadratic	quadratic	ADJ
ejpam-1224	108	9	algebra	algebra	NOUN
ejpam-1224	108	10	point	point	NOUN
ejpam-1224	108	11	of	of	ADP
ejpam-1224	108	12	view	view	NOUN
ejpam-1224	108	13	to	to	ADP
ejpam-1224	108	14	a	a	DET
ejpam-1224	108	15	cdga	cdga	ADJ
ejpam-1224	108	16	point	point	NOUN
ejpam-1224	108	17	of	of	ADP
ejpam-1224	108	18	view	view	NOUN
ejpam-1224	108	19	is	be	AUX
ejpam-1224	108	20	that	that	SCONJ
ejpam-1224	108	21	now	now	ADV
ejpam-1224	108	22	we	we	PRON
ejpam-1224	108	23	are	be	AUX
ejpam-1224	108	24	allowed	allow	VERB
ejpam-1224	108	25	two	two	NUM
ejpam-1224	108	26	new	new	ADJ
ejpam-1224	108	27	levels	level	NOUN
ejpam-1224	108	28	of	of	ADP
ejpam-1224	108	29	freedom	freedom	NOUN
ejpam-1224	108	30	.	.	PUNCT
ejpam-1224	109	1	first	first	ADV
ejpam-1224	109	2	we	we	PRON
ejpam-1224	109	3	may	may	AUX
ejpam-1224	109	4	insert	insert	VERB
ejpam-1224	109	5	a	a	DET
ejpam-1224	109	6	λ	λ	NOUN
ejpam-1224	109	7	-	-	PUNCT
ejpam-1224	109	8	grading	grade	VERB
ejpam-1224	109	9	and	and	CCONJ
ejpam-1224	109	10	second	second	ADV
ejpam-1224	109	11	we	we	PRON
ejpam-1224	109	12	can	can	AUX
ejpam-1224	109	13	now	now	ADV
ejpam-1224	109	14	let	let	VERB
ejpam-1224	109	15	a	a	PRON
ejpam-1224	109	16	be	be	AUX
ejpam-1224	109	17	a	a	DET
ejpam-1224	109	18	nonhomogeneous	nonhomogeneous	ADJ
ejpam-1224	109	19	filtered	filter	VERB
ejpam-1224	109	20	algebra	algebra	NOUN
ejpam-1224	109	21	.	.	PUNCT
ejpam-1224	110	1	we	we	PRON
ejpam-1224	110	2	define	define	VERB
ejpam-1224	110	3	comλ(a	comλ(a	ADP
ejpam-1224	110	4	!	!	PUNCT
ejpam-1224	110	5	,	,	PUNCT
ejpam-1224	111	1	d	d	X
ejpam-1224	111	2	,	,	PUNCT
ejpam-1224	111	3	c	c	NOUN
ejpam-1224	111	4	)	)	PUNCT
ejpam-1224	111	5	to	to	PART
ejpam-1224	111	6	be	be	AUX
ejpam-1224	111	7	the	the	DET
ejpam-1224	111	8	category	category	NOUN
ejpam-1224	111	9	of	of	ADP
ejpam-1224	111	10	curved	curved	ADJ
ejpam-1224	111	11	differential	differential	NOUN
ejpam-1224	111	12	graded	grade	VERB
ejpam-1224	111	13	modules	module	NOUN
ejpam-1224	111	14	over	over	ADP
ejpam-1224	111	15	the	the	DET
ejpam-1224	111	16	cdga	cdga	NOUN
ejpam-1224	111	17	(	(	PUNCT
ejpam-1224	111	18	a	a	PROPN
ejpam-1224	111	19	!	!	PUNCT
ejpam-1224	111	20	,	,	PUNCT
ejpam-1224	111	21	d	d	X
ejpam-1224	111	22	,	,	PUNCT
ejpam-1224	111	23	c	c	NOUN
ejpam-1224	111	24	)	)	PUNCT
ejpam-1224	111	25	.	.	PUNCT
ejpam-1224	112	1	we	we	PRON
ejpam-1224	112	2	define	define	VERB
ejpam-1224	112	3	comλ(u	comλ(u	NOUN
ejpam-1224	112	4	)	)	PUNCT
ejpam-1224	112	5	to	to	PART
ejpam-1224	112	6	be	be	AUX
ejpam-1224	112	7	the	the	DET
ejpam-1224	112	8	category	category	NOUN
ejpam-1224	112	9	of	of	ADP
ejpam-1224	112	10	complexes	complex	NOUN
ejpam-1224	112	11	of	of	ADP
ejpam-1224	112	12	λ	λ	NOUN
ejpam-1224	112	13	-	-	PUNCT
ejpam-1224	112	14	graded	grade	VERB
ejpam-1224	112	15	left	leave	VERB
ejpam-1224	112	16	u	u	NOUN
ejpam-1224	112	17	-	-	NOUN
ejpam-1224	112	18	modules	module	NOUN
ejpam-1224	112	19	.	.	PUNCT
ejpam-1224	113	1	the	the	DET
ejpam-1224	113	2	version	version	NOUN
ejpam-1224	113	3	of	of	ADP
ejpam-1224	113	4	koszul	koszul	ADJ
ejpam-1224	113	5	duality	duality	NOUN
ejpam-1224	113	6	that	that	SCONJ
ejpam-1224	113	7	we	we	PRON
ejpam-1224	113	8	are	be	AUX
ejpam-1224	113	9	most	most	ADV
ejpam-1224	113	10	interested	interested	ADJ
ejpam-1224	113	11	in	in	ADP
ejpam-1224	113	12	is	be	AUX
ejpam-1224	113	13	that	that	SCONJ
ejpam-1224	113	14	introduced	introduce	VERB
ejpam-1224	113	15	by	by	ADP
ejpam-1224	113	16	floystad	floystad	NOUN
ejpam-1224	113	17	[	[	X
ejpam-1224	113	18	3	3	NUM
ejpam-1224	113	19	]	]	PUNCT
ejpam-1224	113	20	concerning	concern	VERB
ejpam-1224	113	21	the	the	DET
ejpam-1224	113	22	pair	pair	NOUN
ejpam-1224	113	23	of	of	ADP
ejpam-1224	113	24	adjoint	adjoint	PROPN
ejpam-1224	113	25	functors	functors	PROPN
ejpam-1224	113	26	f	f	X
ejpam-1224	113	27	:	:	PUNCT
ejpam-1224	113	28	comλ(a	comλ(a	INTJ
ejpam-1224	113	29	!	!	PUNCT
ejpam-1224	113	30	,	,	PUNCT
ejpam-1224	114	1	d	d	X
ejpam-1224	114	2	,	,	PUNCT
ejpam-1224	114	3	c	c	NOUN
ejpam-1224	114	4	)	)	PUNCT
ejpam-1224	114	5	⇆	⇆	PROPN
ejpam-1224	114	6	comλ(u	comλ(u	NOUN
ejpam-1224	114	7	)	)	PUNCT
ejpam-1224	114	8	:	:	PUNCT
ejpam-1224	115	1	g.	g.	PROPN
ejpam-1224	115	2	here	here	ADV
ejpam-1224	115	3	u	u	NOUN
ejpam-1224	115	4	is	be	AUX
ejpam-1224	115	5	a	a	DET
ejpam-1224	115	6	λ	λ	NOUN
ejpam-1224	115	7	-	-	PUNCT
ejpam-1224	115	8	graded	grade	VERB
ejpam-1224	115	9	filtered	filter	VERB
ejpam-1224	115	10	quadratic	quadratic	ADJ
ejpam-1224	115	11	algebra	algebra	NOUN
ejpam-1224	115	12	and	and	CCONJ
ejpam-1224	115	13	(	(	PUNCT
ejpam-1224	115	14	a	a	PROPN
ejpam-1224	115	15	!	!	PUNCT
ejpam-1224	115	16	,	,	PUNCT
ejpam-1224	115	17	d	d	X
ejpam-1224	115	18	,	,	PUNCT
ejpam-1224	115	19	c	c	X
ejpam-1224	115	20	)	)	PUNCT
ejpam-1224	115	21	is	be	AUX
ejpam-1224	115	22	a	a	DET
ejpam-1224	115	23	curved	curved	ADJ
ejpam-1224	115	24	differential	differential	NOUN
ejpam-1224	115	25	graded	grade	VERB
ejpam-1224	115	26	algebra	algebra	NOUN
ejpam-1224	115	27	(	(	PUNCT
ejpam-1224	115	28	cdga	cdga	PROPN
ejpam-1224	115	29	)	)	PUNCT
ejpam-1224	115	30	which	which	PRON
ejpam-1224	115	31	is	be	AUX
ejpam-1224	115	32	dual	dual	ADJ
ejpam-1224	115	33	to	to	ADP
ejpam-1224	115	34	u	u	PRON
ejpam-1224	115	35	.	.	PUNCT
ejpam-1224	116	1	we	we	PRON
ejpam-1224	116	2	have	have	AUX
ejpam-1224	116	3	generalized	generalize	VERB
ejpam-1224	116	4	the	the	DET
ejpam-1224	116	5	functors	functors	PROPN
ejpam-1224	116	6	f	f	PROPN
ejpam-1224	116	7	and	and	CCONJ
ejpam-1224	116	8	g	g	PROPN
ejpam-1224	116	9	for	for	ADP
ejpam-1224	116	10	this	this	DET
ejpam-1224	116	11	λ	λ	NOUN
ejpam-1224	116	12	-	-	PUNCT
ejpam-1224	116	13	graded	grade	VERB
ejpam-1224	116	14	situation	situation	NOUN
ejpam-1224	116	15	,	,	PUNCT
ejpam-1224	116	16	i.e.	i.e.	X
ejpam-1224	116	17	,	,	PUNCT
ejpam-1224	116	18	f(n	f(n	PROPN
ejpam-1224	116	19	)	)	PUNCT
ejpam-1224	116	20	p	p	X
ejpam-1224	116	21	λ	λ	X
ejpam-1224	116	22	=	=	PROPN
ejpam-1224	116	23	⊕	⊕	PROPN
ejpam-1224	116	24	µ+ν	µ+ν	NOUN
ejpam-1224	116	25	=	=	SYM
ejpam-1224	116	26	λ	λ	X
ejpam-1224	116	27	uµ	uµ	NOUN
ejpam-1224	116	28	⊗k	⊗k	ADJ
ejpam-1224	116	29	n	n	CCONJ
ejpam-1224	116	30	p	p	NOUN
ejpam-1224	116	31	ν	ν	NOUN
ejpam-1224	116	32	g(m	g(m	PROPN
ejpam-1224	116	33	)	)	PUNCT
ejpam-1224	116	34	p	p	X
ejpam-1224	116	35	λ	λ	X
ejpam-1224	116	36	=	=	SYM
ejpam-1224	116	37	∏	∏	PROPN
ejpam-1224	116	38	r≥0	r≥0	PROPN
ejpam-1224	116	39	∏	∏	PROPN
ejpam-1224	116	40	µ	µ	PROPN
ejpam-1224	116	41	homk((a	homk((a	NUM
ejpam-1224	116	42	!	!	PUNCT
ejpam-1224	116	43	)	)	PUNCT
ejpam-1224	117	1	rµ	rµ	VERB
ejpam-1224	117	2	,	,	PUNCT
ejpam-1224	117	3	m	m	PROPN
ejpam-1224	117	4	p+r	p+r	NOUN
ejpam-1224	117	5	λ+µ	λ+µ	PRON
ejpam-1224	117	6	)	)	PUNCT
ejpam-1224	117	7	.	.	PUNCT
ejpam-1224	118	1	notice	notice	VERB
ejpam-1224	118	2	that	that	SCONJ
ejpam-1224	118	3	now	now	ADV
ejpam-1224	118	4	integers	integer	NOUN
ejpam-1224	118	5	are	be	AUX
ejpam-1224	118	6	added	add	VERB
ejpam-1224	118	7	to	to	ADP
ejpam-1224	118	8	integers	integer	NOUN
ejpam-1224	118	9	and	and	CCONJ
ejpam-1224	118	10	elements	element	NOUN
ejpam-1224	118	11	of	of	ADP
ejpam-1224	118	12	λ	λ	NOUN
ejpam-1224	118	13	are	be	AUX
ejpam-1224	118	14	added	add	VERB
ejpam-1224	118	15	to	to	ADP
ejpam-1224	118	16	other	other	ADJ
ejpam-1224	118	17	elements	element	NOUN
ejpam-1224	118	18	of	of	ADP
ejpam-1224	118	19	λ	λ	PROPN
ejpam-1224	118	20	.	.	PUNCT
ejpam-1224	119	1	let	let	VERB
ejpam-1224	119	2	kλ(a	kλ(a	NOUN
ejpam-1224	119	3	!	!	PUNCT
ejpam-1224	119	4	,	,	PUNCT
ejpam-1224	120	1	d	d	X
ejpam-1224	120	2	,	,	PUNCT
ejpam-1224	120	3	c	c	AUX
ejpam-1224	120	4	)	)	PUNCT
ejpam-1224	120	5	be	be	AUX
ejpam-1224	120	6	the	the	DET
ejpam-1224	120	7	category	category	NOUN
ejpam-1224	120	8	comλ(a	comλ(a	ADV
ejpam-1224	120	9	!	!	PUNCT
ejpam-1224	120	10	,	,	PUNCT
ejpam-1224	121	1	d	d	X
ejpam-1224	121	2	,	,	PUNCT
ejpam-1224	121	3	c	c	NOUN
ejpam-1224	121	4	)	)	PUNCT
ejpam-1224	121	5	with	with	ADP
ejpam-1224	121	6	morphisms	morphism	NOUN
ejpam-1224	121	7	being	be	AUX
ejpam-1224	121	8	chain	chain	NOUN
ejpam-1224	121	9	homotopy	homotopy	NOUN
ejpam-1224	121	10	equivalence	equivalence	NOUN
ejpam-1224	121	11	classes	class	NOUN
ejpam-1224	121	12	of	of	ADP
ejpam-1224	121	13	maps	map	NOUN
ejpam-1224	121	14	.	.	PUNCT
ejpam-1224	122	1	the	the	DET
ejpam-1224	122	2	null	null	ADJ
ejpam-1224	122	3	system	system	NOUN
ejpam-1224	122	4	,	,	PUNCT
ejpam-1224	122	5	n	n	X
ejpam-1224	122	6	,	,	PUNCT
ejpam-1224	122	7	of	of	ADP
ejpam-1224	122	8	kλ(a	kλ(a	NOUN
ejpam-1224	122	9	!	!	PUNCT
ejpam-1224	122	10	,	,	PUNCT
ejpam-1224	123	1	d	d	X
ejpam-1224	123	2	,	,	PUNCT
ejpam-1224	123	3	c	c	X
ejpam-1224	123	4	)	)	PUNCT
ejpam-1224	123	5	is	be	AUX
ejpam-1224	123	6	defined	define	VERB
ejpam-1224	123	7	to	to	PART
ejpam-1224	123	8	be	be	AUX
ejpam-1224	123	9	all	all	PRON
ejpam-1224	123	10	of	of	ADP
ejpam-1224	123	11	the	the	DET
ejpam-1224	123	12	complexes	complex	NOUN
ejpam-1224	123	13	,	,	PUNCT
ejpam-1224	123	14	x	x	INTJ
ejpam-1224	123	15	,	,	PUNCT
ejpam-1224	123	16	such	such	ADJ
ejpam-1224	123	17	that	that	SCONJ
ejpam-1224	123	18	f(x	f(x	PROPN
ejpam-1224	123	19	)	)	PUNCT
ejpam-1224	123	20	is	be	AUX
ejpam-1224	123	21	acyclic	acyclic	ADJ
ejpam-1224	123	22	.	.	PUNCT
ejpam-1224	124	1	a	a	DET
ejpam-1224	124	2	similar	similar	ADJ
ejpam-1224	124	3	definition	definition	NOUN
ejpam-1224	124	4	is	be	AUX
ejpam-1224	124	5	given	give	VERB
ejpam-1224	124	6	for	for	ADP
ejpam-1224	124	7	the	the	DET
ejpam-1224	124	8	null	null	ADJ
ejpam-1224	124	9	system	system	NOUN
ejpam-1224	124	10	of	of	ADP
ejpam-1224	124	11	kλ(u	kλ(u	NUM
ejpam-1224	124	12	)	)	PUNCT
ejpam-1224	124	13	.	.	PUNCT
ejpam-1224	125	1	we	we	PRON
ejpam-1224	125	2	define	define	VERB
ejpam-1224	125	3	dλ(a	dλ(a	NOUN
ejpam-1224	125	4	!	!	PUNCT
ejpam-1224	125	5	,	,	PUNCT
ejpam-1224	126	1	d	d	X
ejpam-1224	126	2	,	,	PUNCT
ejpam-1224	126	3	c	c	NOUN
ejpam-1224	126	4	)	)	PUNCT
ejpam-1224	126	5	to	to	PART
ejpam-1224	126	6	be	be	AUX
ejpam-1224	126	7	the	the	DET
ejpam-1224	126	8	category	category	NOUN
ejpam-1224	126	9	kλ(a	kλ(a	X
ejpam-1224	126	10	!	!	PUNCT
ejpam-1224	126	11	,	,	PUNCT
ejpam-1224	127	1	d	d	X
ejpam-1224	127	2	,	,	PUNCT
ejpam-1224	127	3	c)/n	c)/n	PROPN
ejpam-1224	127	4	where	where	SCONJ
ejpam-1224	127	5	n	n	X
ejpam-1224	127	6	is	be	AUX
ejpam-1224	127	7	the	the	DET
ejpam-1224	127	8	null	null	ADJ
ejpam-1224	127	9	system	system	NOUN
ejpam-1224	127	10	of	of	ADP
ejpam-1224	127	11	comλ(a	comλ(a	PROPN
ejpam-1224	127	12	!	!	PUNCT
ejpam-1224	127	13	,	,	PUNCT
ejpam-1224	128	1	d	d	X
ejpam-1224	128	2	,	,	PUNCT
ejpam-1224	128	3	c	c	NOUN
ejpam-1224	128	4	)	)	PUNCT
ejpam-1224	128	5	.	.	PUNCT
ejpam-1224	129	1	we	we	PRON
ejpam-1224	129	2	also	also	ADV
ejpam-1224	129	3	define	define	VERB
ejpam-1224	129	4	dλ(u	dλ(u	NOUN
ejpam-1224	129	5	)	)	PUNCT
ejpam-1224	129	6	to	to	PART
ejpam-1224	129	7	be	be	AUX
ejpam-1224	129	8	the	the	DET
ejpam-1224	129	9	category	category	NOUN
ejpam-1224	129	10	kλ(u)/n	kλ(u)/n	VERB
ejpam-1224	129	11	where	where	SCONJ
ejpam-1224	129	12	n	n	PRON
ejpam-1224	129	13	is	be	AUX
ejpam-1224	129	14	the	the	DET
ejpam-1224	129	15	null	null	ADJ
ejpam-1224	129	16	system	system	NOUN
ejpam-1224	129	17	of	of	ADP
ejpam-1224	129	18	comλ(u	comλ(u	NOUN
ejpam-1224	129	19	)	)	PUNCT
ejpam-1224	129	20	.	.	PUNCT
ejpam-1224	130	1	the	the	DET
ejpam-1224	130	2	main	main	ADJ
ejpam-1224	130	3	result	result	NOUN
ejpam-1224	130	4	of	of	ADP
ejpam-1224	130	5	this	this	DET
ejpam-1224	130	6	paper	paper	NOUN
ejpam-1224	130	7	is	be	AUX
ejpam-1224	130	8	that	that	SCONJ
ejpam-1224	130	9	the	the	DET
ejpam-1224	130	10	functors	functors	PROPN
ejpam-1224	130	11	f	f	PROPN
ejpam-1224	130	12	and	and	CCONJ
ejpam-1224	130	13	g	g	PROPN
ejpam-1224	130	14	given	give	VERB
ejpam-1224	130	15	in	in	ADP
ejpam-1224	130	16	proposition	proposition	NOUN
ejpam-1224	130	17	4	4	NUM
ejpam-1224	130	18	induce	induce	VERB
ejpam-1224	130	19	an	an	DET
ejpam-1224	130	20	equivalence	equivalence	NOUN
ejpam-1224	130	21	of	of	ADP
ejpam-1224	130	22	categories	category	NOUN
ejpam-1224	130	23	between	between	ADP
ejpam-1224	130	24	the	the	DET
ejpam-1224	130	25	quotient	quotient	NOUN
ejpam-1224	130	26	categories	category	NOUN
ejpam-1224	130	27	dλ(a	dλ(a	PRON
ejpam-1224	130	28	!	!	PUNCT
ejpam-1224	130	29	,	,	PUNCT
ejpam-1224	131	1	d	d	X
ejpam-1224	131	2	,	,	PUNCT
ejpam-1224	131	3	c	c	NOUN
ejpam-1224	131	4	)	)	PUNCT
ejpam-1224	131	5	and	and	CCONJ
ejpam-1224	131	6	dλ(u	dλ(u	NUM
ejpam-1224	131	7	)	)	PUNCT
ejpam-1224	131	8	.	.	PUNCT
ejpam-1224	132	1	2	2	X
ejpam-1224	132	2	.	.	X
ejpam-1224	132	3	graded	grade	VERB
ejpam-1224	132	4	and	and	CCONJ
ejpam-1224	132	5	filtered	filter	VERB
ejpam-1224	132	6	algebras	algebras	PROPN
ejpam-1224	132	7	floystad	floystad	PROPN
ejpam-1224	132	8	’s	’s	PART
ejpam-1224	132	9	koszul	koszul	ADJ
ejpam-1224	132	10	duality	duality	NOUN
ejpam-1224	132	11	concerns	concern	VERB
ejpam-1224	132	12	a	a	DET
ejpam-1224	132	13	pair	pair	NOUN
ejpam-1224	132	14	of	of	ADP
ejpam-1224	132	15	adjoint	adjoint	PROPN
ejpam-1224	132	16	functors	functors	PROPN
ejpam-1224	133	1	f	f	X
ejpam-1224	133	2	:	:	PUNCT
ejpam-1224	133	3	comλ(a	comλ(a	INTJ
ejpam-1224	133	4	!	!	PUNCT
ejpam-1224	133	5	,	,	PUNCT
ejpam-1224	134	1	d	d	X
ejpam-1224	134	2	,	,	PUNCT
ejpam-1224	134	3	c	c	NOUN
ejpam-1224	134	4	)	)	PUNCT
ejpam-1224	134	5	⇆	⇆	PROPN
ejpam-1224	134	6	comλ(u	comλ(u	NOUN
ejpam-1224	134	7	)	)	PUNCT
ejpam-1224	134	8	:	:	PUNCT
ejpam-1224	135	1	g	g	PROPN
ejpam-1224	135	2	f.	f.	PROPN
ejpam-1224	135	3	hawwa	hawwa	PROPN
ejpam-1224	135	4	,	,	PUNCT
ejpam-1224	135	5	j.	j.	PROPN
ejpam-1224	135	6	hoffman	hoffman	PROPN
ejpam-1224	135	7	,	,	PUNCT
ejpam-1224	135	8	and	and	CCONJ
ejpam-1224	135	9	h.	h.	PROPN
ejpam-1224	135	10	wang	wang	PROPN
ejpam-1224	135	11	,	,	PUNCT
ejpam-1224	135	12	/	/	SYM
ejpam-1224	135	13	eur	eur	NOUN
ejpam-1224	135	14	.	.	PUNCT
ejpam-1224	136	1	j.	j.	PROPN
ejpam-1224	136	2	pure	pure	PROPN
ejpam-1224	136	3	appl	appl	PROPN
ejpam-1224	136	4	.	.	PROPN
ejpam-1224	136	5	math	math	PROPN
ejpam-1224	136	6	,	,	PUNCT
ejpam-1224	136	7	5	5	NUM
ejpam-1224	136	8	(	(	PUNCT
ejpam-1224	136	9	2012	2012	NUM
ejpam-1224	136	10	)	)	PUNCT
ejpam-1224	136	11	,	,	PUNCT
ejpam-1224	136	12	511	511	NUM
ejpam-1224	136	13	-	-	SYM
ejpam-1224	136	14	539	539	NUM
ejpam-1224	136	15	515	515	NUM
ejpam-1224	136	16	which	which	PRON
ejpam-1224	136	17	induce	induce	VERB
ejpam-1224	136	18	an	an	DET
ejpam-1224	136	19	equivalence	equivalence	NOUN
ejpam-1224	136	20	of	of	ADP
ejpam-1224	136	21	homotopy	homotopy	NOUN
ejpam-1224	136	22	categories	category	NOUN
ejpam-1224	136	23	.	.	PUNCT
ejpam-1224	137	1	here	here	ADV
ejpam-1224	137	2	u	u	NOUN
ejpam-1224	137	3	is	be	AUX
ejpam-1224	137	4	a	a	DET
ejpam-1224	137	5	λ	λ	NOUN
ejpam-1224	137	6	-	-	PUNCT
ejpam-1224	137	7	graded	grade	VERB
ejpam-1224	137	8	filtered	filter	VERB
ejpam-1224	137	9	quadratic	quadratic	ADJ
ejpam-1224	137	10	algebra	algebra	NOUN
ejpam-1224	137	11	,	,	PUNCT
ejpam-1224	137	12	and	and	CCONJ
ejpam-1224	137	13	(	(	PUNCT
ejpam-1224	137	14	a	a	NOUN
ejpam-1224	137	15	!	!	PUNCT
ejpam-1224	137	16	,	,	PUNCT
ejpam-1224	137	17	d	d	X
ejpam-1224	137	18	,	,	PUNCT
ejpam-1224	137	19	c	c	X
ejpam-1224	137	20	)	)	PUNCT
ejpam-1224	137	21	is	be	AUX
ejpam-1224	137	22	a	a	DET
ejpam-1224	137	23	curved	curved	ADJ
ejpam-1224	137	24	differential	differential	NOUN
ejpam-1224	137	25	graded	grade	VERB
ejpam-1224	137	26	algebra	algebra	NOUN
ejpam-1224	137	27	(	(	PUNCT
ejpam-1224	137	28	cdga	cdga	ADJ
ejpam-1224	137	29	)	)	PUNCT
ejpam-1224	137	30	dual	dual	ADJ
ejpam-1224	137	31	to	to	ADP
ejpam-1224	137	32	u	u	PRON
ejpam-1224	137	33	.	.	PUNCT
ejpam-1224	138	1	here	here	ADV
ejpam-1224	138	2	comλ(u	comλ(u	NOUN
ejpam-1224	138	3	)	)	PUNCT
ejpam-1224	138	4	is	be	AUX
ejpam-1224	138	5	the	the	DET
ejpam-1224	138	6	category	category	NOUN
ejpam-1224	138	7	of	of	ADP
ejpam-1224	138	8	complexes	complex	NOUN
ejpam-1224	138	9	of	of	ADP
ejpam-1224	138	10	λ	λ	NOUN
ejpam-1224	138	11	-	-	PUNCT
ejpam-1224	138	12	graded	grade	VERB
ejpam-1224	138	13	left	leave	VERB
ejpam-1224	138	14	u	u	NOUN
ejpam-1224	138	15	-	-	NOUN
ejpam-1224	138	16	modules	module	NOUN
ejpam-1224	138	17	(	(	PUNCT
ejpam-1224	138	18	of	of	ADP
ejpam-1224	138	19	finite	finite	ADJ
ejpam-1224	138	20	type	type	NOUN
ejpam-1224	138	21	)	)	PUNCT
ejpam-1224	138	22	.	.	PUNCT
ejpam-1224	139	1	we	we	PRON
ejpam-1224	139	2	let	let	VERB
ejpam-1224	139	3	comλ(a	comλ(a	ADP
ejpam-1224	139	4	!	!	PUNCT
ejpam-1224	139	5	,	,	PUNCT
ejpam-1224	140	1	d	d	X
ejpam-1224	140	2	,	,	PUNCT
ejpam-1224	140	3	c	c	AUX
ejpam-1224	140	4	)	)	PUNCT
ejpam-1224	140	5	be	be	AUX
ejpam-1224	140	6	the	the	DET
ejpam-1224	140	7	category	category	NOUN
ejpam-1224	140	8	of	of	ADP
ejpam-1224	140	9	curved	curved	ADJ
ejpam-1224	140	10	differential	differential	NOUN
ejpam-1224	140	11	graded	grade	VERB
ejpam-1224	140	12	left	leave	VERB
ejpam-1224	140	13	modules	module	NOUN
ejpam-1224	140	14	over	over	ADP
ejpam-1224	140	15	the	the	DET
ejpam-1224	140	16	cdga	cdga	NOUN
ejpam-1224	141	1	(	(	PUNCT
ejpam-1224	141	2	a	a	PROPN
ejpam-1224	141	3	!	!	PUNCT
ejpam-1224	141	4	,	,	PUNCT
ejpam-1224	141	5	d	d	X
ejpam-1224	141	6	,	,	PUNCT
ejpam-1224	141	7	c	c	NOUN
ejpam-1224	141	8	)	)	PUNCT
ejpam-1224	141	9	.	.	PUNCT
ejpam-1224	142	1	when	when	SCONJ
ejpam-1224	142	2	c	c	NOUN
ejpam-1224	142	3	=	=	SYM
ejpam-1224	142	4	0	0	NUM
ejpam-1224	142	5	these	these	PRON
ejpam-1224	142	6	are	be	AUX
ejpam-1224	142	7	just	just	ADV
ejpam-1224	142	8	the	the	DET
ejpam-1224	142	9	usual	usual	ADJ
ejpam-1224	142	10	differential	differential	NOUN
ejpam-1224	142	11	graded	grade	VERB
ejpam-1224	142	12	algebras	algebra	NOUN
ejpam-1224	142	13	.	.	PUNCT
ejpam-1224	143	1	it	it	PRON
ejpam-1224	143	2	is	be	AUX
ejpam-1224	143	3	important	important	ADJ
ejpam-1224	143	4	to	to	PART
ejpam-1224	143	5	note	note	VERB
ejpam-1224	143	6	that	that	SCONJ
ejpam-1224	143	7	this	this	DET
ejpam-1224	143	8	form	form	NOUN
ejpam-1224	143	9	of	of	ADP
ejpam-1224	143	10	duality	duality	NOUN
ejpam-1224	143	11	is	be	AUX
ejpam-1224	143	12	not	not	PART
ejpam-1224	143	13	symmetrical	symmetrical	ADJ
ejpam-1224	143	14	.	.	PUNCT
ejpam-1224	144	1	we	we	PRON
ejpam-1224	144	2	will	will	AUX
ejpam-1224	144	3	explain	explain	VERB
ejpam-1224	144	4	how	how	SCONJ
ejpam-1224	144	5	classical	classical	ADJ
ejpam-1224	144	6	koszul	koszul	ADJ
ejpam-1224	144	7	duality	duality	NOUN
ejpam-1224	144	8	relates	relate	VERB
ejpam-1224	144	9	to	to	ADP
ejpam-1224	144	10	floystad	floystad	PROPN
ejpam-1224	144	11	’s	’s	PART
ejpam-1224	144	12	koszul	koszul	ADJ
ejpam-1224	144	13	duality	duality	NOUN
ejpam-1224	144	14	in	in	ADP
ejpam-1224	144	15	the	the	DET
ejpam-1224	144	16	special	special	ADJ
ejpam-1224	144	17	case	case	NOUN
ejpam-1224	144	18	u	u	NOUN
ejpam-1224	144	19	=	=	NOUN
ejpam-1224	144	20	a	a	PRON
ejpam-1224	144	21	is	be	AUX
ejpam-1224	144	22	a	a	DET
ejpam-1224	144	23	z	z	NOUN
ejpam-1224	144	24	-	-	PUNCT
ejpam-1224	144	25	graded	grade	VERB
ejpam-1224	144	26	koszul	koszul	ADJ
ejpam-1224	144	27	quadratic	quadratic	ADJ
ejpam-1224	144	28	algebra	algebra	NOUN
ejpam-1224	144	29	.	.	PUNCT
ejpam-1224	145	1	so	so	ADV
ejpam-1224	145	2	first	first	ADV
ejpam-1224	145	3	let	let	VERB
ejpam-1224	145	4	us	we	PRON
ejpam-1224	145	5	recall	recall	VERB
ejpam-1224	145	6	the	the	DET
ejpam-1224	145	7	definitions	definition	NOUN
ejpam-1224	145	8	of	of	ADP
ejpam-1224	145	9	some	some	PRON
ejpam-1224	145	10	of	of	ADP
ejpam-1224	145	11	the	the	DET
ejpam-1224	145	12	key	key	ADJ
ejpam-1224	145	13	terms	term	NOUN
ejpam-1224	145	14	we	we	PRON
ejpam-1224	145	15	will	will	AUX
ejpam-1224	145	16	be	be	AUX
ejpam-1224	145	17	using	use	VERB
ejpam-1224	145	18	.	.	PUNCT
ejpam-1224	146	1	definition	definition	NOUN
ejpam-1224	146	2	1	1	NUM
ejpam-1224	146	3	.	.	PUNCT
ejpam-1224	147	1	let	let	VERB
ejpam-1224	147	2	k	k	PRON
ejpam-1224	147	3	be	be	AUX
ejpam-1224	147	4	a	a	DET
ejpam-1224	147	5	field	field	NOUN
ejpam-1224	147	6	.	.	PUNCT
ejpam-1224	148	1	a	a	DET
ejpam-1224	148	2	λ	λ	NOUN
ejpam-1224	148	3	-	-	PUNCT
ejpam-1224	148	4	graded	grade	VERB
ejpam-1224	148	5	associative	associative	ADJ
ejpam-1224	148	6	k	k	NOUN
ejpam-1224	148	7	-	-	NOUN
ejpam-1224	148	8	algebra	algebra	NOUN
ejpam-1224	148	9	a	a	PRON
ejpam-1224	148	10	with	with	ADP
ejpam-1224	148	11	unit	unit	NOUN
ejpam-1224	148	12	is	be	AUX
ejpam-1224	148	13	an	an	DET
ejpam-1224	148	14	algebra	algebra	NOUN
ejpam-1224	148	15	together	together	ADV
ejpam-1224	148	16	with	with	ADP
ejpam-1224	148	17	a	a	DET
ejpam-1224	148	18	decomposition	decomposition	NOUN
ejpam-1224	148	19	into	into	ADP
ejpam-1224	148	20	k	k	NOUN
ejpam-1224	148	21	-	-	NOUN
ejpam-1224	148	22	subspaces	subspace	NOUN
ejpam-1224	148	23	,	,	PUNCT
ejpam-1224	148	24	a=	a=	PROPN
ejpam-1224	148	25	⊕	⊕	NOUN
ejpam-1224	148	26	λ∈λ	λ∈λ	NOUN
ejpam-1224	148	27	aλ	aλ	ADP
ejpam-1224	148	28	which	which	PRON
ejpam-1224	148	29	obeys	obey	VERB
ejpam-1224	148	30	the	the	DET
ejpam-1224	148	31	multiplication	multiplication	NOUN
ejpam-1224	148	32	law	law	NOUN
ejpam-1224	148	33	aλ	aλ	PROPN
ejpam-1224	148	34	·	·	PUNCT
ejpam-1224	148	35	aµ	aµ	PROPN
ejpam-1224	148	36	⊂	⊂	PROPN
ejpam-1224	148	37	aλ+µ.	aλ+µ.	PART
ejpam-1224	148	38	definition	definition	NOUN
ejpam-1224	148	39	2	2	NUM
ejpam-1224	148	40	.	.	PUNCT
ejpam-1224	149	1	a	a	DET
ejpam-1224	149	2	λ	λ	NOUN
ejpam-1224	149	3	-	-	PUNCT
ejpam-1224	149	4	graded	grade	VERB
ejpam-1224	149	5	filtered	filter	VERB
ejpam-1224	149	6	algebra	algebra	NOUN
ejpam-1224	149	7	u	u	NOUN
ejpam-1224	149	8	over	over	ADP
ejpam-1224	149	9	a	a	DET
ejpam-1224	149	10	field	field	NOUN
ejpam-1224	149	11	k	k	X
ejpam-1224	149	12	is	be	AUX
ejpam-1224	149	13	a	a	DET
ejpam-1224	149	14	λ	λ	NOUN
ejpam-1224	149	15	-	-	PUNCT
ejpam-1224	149	16	graded	grade	VERB
ejpam-1224	149	17	algebra	algebra	NOUN
ejpam-1224	149	18	which	which	PRON
ejpam-1224	149	19	has	have	VERB
ejpam-1224	149	20	an	an	DET
ejpam-1224	149	21	increasing	increase	VERB
ejpam-1224	149	22	sequence	sequence	NOUN
ejpam-1224	149	23	0⊂	0⊂	NUM
ejpam-1224	150	1	f0	f0	PROPN
ejpam-1224	150	2	⊂	⊂	PROPN
ejpam-1224	150	3	f1	f1	PROPN
ejpam-1224	150	4	⊂	⊂	PROPN
ejpam-1224	150	5	·	·	PUNCT
ejpam-1224	150	6	·	·	PUNCT
ejpam-1224	150	7	·	·	PUNCT
ejpam-1224	150	8	fi	fi	NOUN
ejpam-1224	151	1	⊂	⊂	PROPN
ejpam-1224	151	2	·	·	PUNCT
ejpam-1224	151	3	·	·	PUNCT
ejpam-1224	151	4	·	·	PUNCT
ejpam-1224	151	5	⊂	⊂	PRON
ejpam-1224	151	6	u	u	PROPN
ejpam-1224	151	7	of	of	ADP
ejpam-1224	151	8	k	k	NOUN
ejpam-1224	151	9	-	-	NOUN
ejpam-1224	151	10	subspaces	subspace	NOUN
ejpam-1224	151	11	of	of	ADP
ejpam-1224	151	12	u	u	PRON
ejpam-1224	151	13	such	such	ADJ
ejpam-1224	151	14	that	that	DET
ejpam-1224	151	15	u	u	NOUN
ejpam-1224	151	16	=	=	NOUN
ejpam-1224	151	17	⋃	⋃	NOUN
ejpam-1224	151	18	i∈n	i∈n	NOUN
ejpam-1224	151	19	fi	fi	NOUN
ejpam-1224	151	20	and	and	CCONJ
ejpam-1224	151	21	the	the	DET
ejpam-1224	151	22	following	follow	VERB
ejpam-1224	151	23	property	property	NOUN
ejpam-1224	151	24	of	of	ADP
ejpam-1224	151	25	the	the	DET
ejpam-1224	151	26	algebra	algebra	NOUN
ejpam-1224	151	27	multiplication	multiplication	NOUN
ejpam-1224	151	28	holds	hold	VERB
ejpam-1224	151	29	:	:	PUNCT
ejpam-1224	152	1	∀m	∀m	NUM
ejpam-1224	152	2	,	,	PUNCT
ejpam-1224	152	3	n	n	PROPN
ejpam-1224	152	4	∈	∈	PROPN
ejpam-1224	152	5	n	n	CCONJ
ejpam-1224	152	6	,	,	PUNCT
ejpam-1224	152	7	fm	fm	PROPN
ejpam-1224	152	8	·	·	PUNCT
ejpam-1224	152	9	fn	fn	PROPN
ejpam-1224	152	10	⊂	⊂	PROPN
ejpam-1224	152	11	fn+m	fn+m	PROPN
ejpam-1224	152	12	.	.	PUNCT
ejpam-1224	153	1	in	in	ADP
ejpam-1224	153	2	addition	addition	NOUN
ejpam-1224	153	3	,	,	PUNCT
ejpam-1224	153	4	the	the	DET
ejpam-1224	153	5	grading	grading	NOUN
ejpam-1224	153	6	must	must	AUX
ejpam-1224	153	7	be	be	AUX
ejpam-1224	153	8	compatible	compatible	ADJ
ejpam-1224	153	9	with	with	ADP
ejpam-1224	153	10	the	the	DET
ejpam-1224	153	11	filtration	filtration	NOUN
ejpam-1224	153	12	,	,	PUNCT
ejpam-1224	153	13	meaning	meaning	NOUN
ejpam-1224	153	14	fi	fi	NOUN
ejpam-1224	153	15	=	=	SYM
ejpam-1224	153	16	⊕	⊕	PROPN
ejpam-1224	153	17	λ∈λ	λ∈λ	NOUN
ejpam-1224	153	18	(	(	PUNCT
ejpam-1224	153	19	fi	fi	NOUN
ejpam-1224	153	20	∩	∩	X
ejpam-1224	153	21	uλ	uλ	NOUN
ejpam-1224	153	22	)	)	PUNCT
ejpam-1224	153	23	given	give	VERB
ejpam-1224	153	24	the	the	DET
ejpam-1224	153	25	grading	grade	VERB
ejpam-1224	153	26	u	u	NOUN
ejpam-1224	153	27	=	=	PROPN
ejpam-1224	153	28	⊕	⊕	PROPN
ejpam-1224	153	29	λ∈λ	λ∈λ	PROPN
ejpam-1224	153	30	uλ	uλ	NOUN
ejpam-1224	153	31	.	.	PUNCT
ejpam-1224	154	1	definition	definition	NOUN
ejpam-1224	154	2	3	3	NUM
ejpam-1224	154	3	.	.	PUNCT
ejpam-1224	155	1	if	if	SCONJ
ejpam-1224	155	2	u	u	NOUN
ejpam-1224	155	3	is	be	AUX
ejpam-1224	155	4	a	a	DET
ejpam-1224	155	5	λ	λ	NOUN
ejpam-1224	155	6	-	-	PUNCT
ejpam-1224	155	7	graded	grade	VERB
ejpam-1224	155	8	ring	ring	NOUN
ejpam-1224	155	9	,	,	PUNCT
ejpam-1224	155	10	then	then	ADV
ejpam-1224	155	11	a	a	DET
ejpam-1224	155	12	λ	λ	NOUN
ejpam-1224	155	13	-	-	PUNCT
ejpam-1224	155	14	graded	grade	VERB
ejpam-1224	155	15	module	module	NOUN
ejpam-1224	155	16	m	m	NOUN
ejpam-1224	155	17	is	be	AUX
ejpam-1224	155	18	a	a	DET
ejpam-1224	155	19	left	left	ADJ
ejpam-1224	155	20	u	u	NOUN
ejpam-1224	155	21	-	-	NOUN
ejpam-1224	155	22	module	module	NOUN
ejpam-1224	155	23	with	with	ADP
ejpam-1224	155	24	a	a	DET
ejpam-1224	155	25	decomposition	decomposition	NOUN
ejpam-1224	155	26	m	m	NOUN
ejpam-1224	155	27	=	=	SYM
ejpam-1224	155	28	⊕	⊕	PROPN
ejpam-1224	155	29	λ∈λ	λ∈λ	PROPN
ejpam-1224	155	30	mλ	mλ	INTJ
ejpam-1224	155	31	into	into	ADP
ejpam-1224	155	32	k	k	NOUN
ejpam-1224	155	33	-	-	NOUN
ejpam-1224	155	34	subspaces	subspace	NOUN
ejpam-1224	155	35	such	such	ADJ
ejpam-1224	155	36	that	that	SCONJ
ejpam-1224	155	37	uλ	uλ	NOUN
ejpam-1224	155	38	·	·	PUNCT
ejpam-1224	155	39	mµ	mµ	ADP
ejpam-1224	155	40	⊂	⊂	PROPN
ejpam-1224	155	41	mλ+µ.	mλ+µ.	NOUN
ejpam-1224	155	42	remark	remark	NOUN
ejpam-1224	155	43	1	1	NUM
ejpam-1224	155	44	.	.	PUNCT
ejpam-1224	156	1	we	we	PRON
ejpam-1224	156	2	allow	allow	VERB
ejpam-1224	156	3	the	the	DET
ejpam-1224	156	4	case	case	NOUN
ejpam-1224	156	5	where	where	SCONJ
ejpam-1224	156	6	there	there	PRON
ejpam-1224	156	7	is	be	VERB
ejpam-1224	156	8	no	no	DET
ejpam-1224	156	9	λ	λ	NOUN
ejpam-1224	156	10	-	-	PUNCT
ejpam-1224	156	11	grading	grading	NOUN
ejpam-1224	156	12	in	in	ADP
ejpam-1224	156	13	which	which	DET
ejpam-1224	156	14	case	case	NOUN
ejpam-1224	156	15	the	the	DET
ejpam-1224	156	16	algebra	algebra	NOUN
ejpam-1224	156	17	(	(	PUNCT
ejpam-1224	156	18	resp	resp	NOUN
ejpam-1224	156	19	.	.	PUNCT
ejpam-1224	156	20	module	module	NOUN
ejpam-1224	156	21	)	)	PUNCT
ejpam-1224	156	22	u	u	NOUN
ejpam-1224	156	23	is	be	AUX
ejpam-1224	156	24	just	just	ADV
ejpam-1224	156	25	considered	consider	VERB
ejpam-1224	156	26	a	a	DET
ejpam-1224	156	27	filtered	filter	VERB
ejpam-1224	156	28	algebra	algebra	NOUN
ejpam-1224	156	29	(	(	PUNCT
ejpam-1224	156	30	resp	resp	NOUN
ejpam-1224	156	31	.	.	PUNCT
ejpam-1224	156	32	module	module	NOUN
ejpam-1224	156	33	)	)	PUNCT
ejpam-1224	156	34	.	.	PUNCT
ejpam-1224	157	1	we	we	PRON
ejpam-1224	157	2	also	also	ADV
ejpam-1224	157	3	will	will	AUX
ejpam-1224	157	4	allow	allow	VERB
ejpam-1224	157	5	the	the	DET
ejpam-1224	157	6	case	case	NOUN
ejpam-1224	157	7	where	where	SCONJ
ejpam-1224	157	8	there	there	PRON
ejpam-1224	157	9	is	be	VERB
ejpam-1224	157	10	neither	neither	CCONJ
ejpam-1224	157	11	a	a	DET
ejpam-1224	157	12	filtration	filtration	NOUN
ejpam-1224	157	13	nor	nor	CCONJ
ejpam-1224	157	14	a	a	DET
ejpam-1224	157	15	grading	grading	NOUN
ejpam-1224	157	16	in	in	ADP
ejpam-1224	157	17	which	which	DET
ejpam-1224	157	18	case	case	NOUN
ejpam-1224	157	19	u	u	NOUN
ejpam-1224	157	20	is	be	AUX
ejpam-1224	157	21	just	just	ADV
ejpam-1224	157	22	an	an	DET
ejpam-1224	157	23	algebra	algebra	NOUN
ejpam-1224	157	24	.	.	PUNCT
ejpam-1224	158	1	definition	definition	NOUN
ejpam-1224	158	2	4	4	NUM
ejpam-1224	158	3	.	.	PUNCT
ejpam-1224	159	1	let	let	VERB
ejpam-1224	159	2	comλ(u	comλ(u	NOUN
ejpam-1224	159	3	)	)	PUNCT
ejpam-1224	159	4	be	be	AUX
ejpam-1224	159	5	the	the	DET
ejpam-1224	159	6	category	category	NOUN
ejpam-1224	159	7	of	of	ADP
ejpam-1224	159	8	chain	chain	NOUN
ejpam-1224	159	9	complexes	complex	NOUN
ejpam-1224	159	10	of	of	ADP
ejpam-1224	159	11	λ	λ	NOUN
ejpam-1224	159	12	-	-	PUNCT
ejpam-1224	159	13	graded	grade	VERB
ejpam-1224	159	14	left	leave	VERB
ejpam-1224	159	15	u	u	NOUN
ejpam-1224	159	16	-	-	NOUN
ejpam-1224	159	17	modules	module	NOUN
ejpam-1224	159	18	m	m	VERB
ejpam-1224	159	19	p	p	NOUN
ejpam-1224	159	20	(	(	PUNCT
ejpam-1224	159	21	of	of	ADP
ejpam-1224	159	22	finite	finite	ADJ
ejpam-1224	159	23	type	type	NOUN
ejpam-1224	159	24	)	)	PUNCT
ejpam-1224	159	25	.	.	PUNCT
ejpam-1224	160	1	the	the	DET
ejpam-1224	160	2	differentials	differential	NOUN
ejpam-1224	160	3	will	will	AUX
ejpam-1224	160	4	be	be	AUX
ejpam-1224	160	5	u	u	ADJ
ejpam-1224	160	6	-	-	ADJ
ejpam-1224	160	7	linear	linear	ADJ
ejpam-1224	160	8	maps	map	NOUN
ejpam-1224	160	9	which	which	PRON
ejpam-1224	160	10	preserve	preserve	VERB
ejpam-1224	160	11	the	the	DET
ejpam-1224	160	12	λ	λ	NOUN
ejpam-1224	160	13	degree	degree	NOUN
ejpam-1224	160	14	,	,	PUNCT
ejpam-1224	160	15	i.e.	i.e.	X
ejpam-1224	160	16	,	,	PUNCT
ejpam-1224	160	17	m	m	VERB
ejpam-1224	160	18	p	p	NOUN
ejpam-1224	160	19	λ	λ	X
ejpam-1224	160	20	d	d	NOUN
ejpam-1224	160	21	−→	−→	NOUN
ejpam-1224	160	22	m	m	VERB
ejpam-1224	160	23	p+1	p+1	NOUN
ejpam-1224	161	1	λ	λ	INTJ
ejpam-1224	161	2	.	.	PUNCT
ejpam-1224	162	1	if	if	SCONJ
ejpam-1224	162	2	there	there	PRON
ejpam-1224	162	3	is	be	VERB
ejpam-1224	162	4	no	no	DET
ejpam-1224	162	5	λ	λ	NOUN
ejpam-1224	162	6	-	-	PUNCT
ejpam-1224	162	7	grading	grade	VERB
ejpam-1224	162	8	then	then	ADV
ejpam-1224	162	9	we	we	PRON
ejpam-1224	162	10	use	use	VERB
ejpam-1224	162	11	com(u	com(u	PROPN
ejpam-1224	162	12	)	)	PUNCT
ejpam-1224	162	13	to	to	PART
ejpam-1224	162	14	denote	denote	VERB
ejpam-1224	162	15	the	the	DET
ejpam-1224	162	16	category	category	NOUN
ejpam-1224	162	17	of	of	ADP
ejpam-1224	162	18	chain	chain	NOUN
ejpam-1224	162	19	complexes	complex	NOUN
ejpam-1224	162	20	of	of	ADP
ejpam-1224	162	21	left	leave	VERB
ejpam-1224	162	22	u	u	NOUN
ejpam-1224	162	23	-	-	NOUN
ejpam-1224	162	24	modules	module	NOUN
ejpam-1224	162	25	.	.	PUNCT
ejpam-1224	163	1	f.	f.	PROPN
ejpam-1224	163	2	hawwa	hawwa	PROPN
ejpam-1224	163	3	,	,	PUNCT
ejpam-1224	163	4	j.	j.	PROPN
ejpam-1224	163	5	hoffman	hoffman	PROPN
ejpam-1224	163	6	,	,	PUNCT
ejpam-1224	163	7	and	and	CCONJ
ejpam-1224	163	8	h.	h.	PROPN
ejpam-1224	163	9	wang	wang	PROPN
ejpam-1224	163	10	,	,	PUNCT
ejpam-1224	163	11	/	/	SYM
ejpam-1224	163	12	eur	eur	NOUN
ejpam-1224	163	13	.	.	PUNCT
ejpam-1224	164	1	j.	j.	PROPN
ejpam-1224	164	2	pure	pure	PROPN
ejpam-1224	164	3	appl	appl	PROPN
ejpam-1224	164	4	.	.	PROPN
ejpam-1224	164	5	math	math	PROPN
ejpam-1224	164	6	,	,	PUNCT
ejpam-1224	164	7	5	5	NUM
ejpam-1224	164	8	(	(	PUNCT
ejpam-1224	164	9	2012	2012	NUM
ejpam-1224	164	10	)	)	PUNCT
ejpam-1224	164	11	,	,	PUNCT
ejpam-1224	164	12	511	511	NUM
ejpam-1224	164	13	-	-	SYM
ejpam-1224	164	14	539	539	NUM
ejpam-1224	164	15	516	516	NUM
ejpam-1224	164	16	a	a	DET
ejpam-1224	164	17	general	general	ADJ
ejpam-1224	164	18	construction	construction	NOUN
ejpam-1224	164	19	that	that	PRON
ejpam-1224	164	20	we	we	PRON
ejpam-1224	164	21	will	will	AUX
ejpam-1224	164	22	be	be	AUX
ejpam-1224	164	23	utilizing	utilize	VERB
ejpam-1224	164	24	is	be	AUX
ejpam-1224	164	25	that	that	PRON
ejpam-1224	164	26	of	of	ADP
ejpam-1224	164	27	a	a	DET
ejpam-1224	164	28	quadratic	quadratic	ADJ
ejpam-1224	164	29	filtered	filter	VERB
ejpam-1224	164	30	algebra	algebra	NOUN
ejpam-1224	164	31	.	.	PUNCT
ejpam-1224	165	1	let	let	VERB
ejpam-1224	165	2	k	k	PRON
ejpam-1224	165	3	be	be	AUX
ejpam-1224	165	4	a	a	DET
ejpam-1224	165	5	field	field	NOUN
ejpam-1224	165	6	,	,	PUNCT
ejpam-1224	165	7	λ	λ	X
ejpam-1224	165	8	an	an	DET
ejpam-1224	165	9	abelian	abelian	ADJ
ejpam-1224	165	10	group	group	NOUN
ejpam-1224	165	11	,	,	PUNCT
ejpam-1224	165	12	and	and	CCONJ
ejpam-1224	165	13	v	v	ADP
ejpam-1224	165	14	a	a	DET
ejpam-1224	165	15	λ	λ	NOUN
ejpam-1224	165	16	-	-	PUNCT
ejpam-1224	165	17	graded	grade	VERB
ejpam-1224	165	18	,	,	PUNCT
ejpam-1224	165	19	finite	finite	ADJ
ejpam-1224	165	20	dimensional	dimensional	ADJ
ejpam-1224	165	21	vector	vector	NOUN
ejpam-1224	165	22	space	space	NOUN
ejpam-1224	165	23	over	over	ADP
ejpam-1224	165	24	k	k	PROPN
ejpam-1224	165	25	,	,	PUNCT
ejpam-1224	165	26	i.e.	i.e.	X
ejpam-1224	165	27	,	,	PUNCT
ejpam-1224	165	28	v	v	NOUN
ejpam-1224	165	29	=	=	SYM
ejpam-1224	165	30	⊕	⊕	PROPN
ejpam-1224	165	31	λ∈λ	λ∈λ	NOUN
ejpam-1224	166	1	vλ	vλ	INTJ
ejpam-1224	166	2	.	.	PUNCT
ejpam-1224	167	1	we	we	PRON
ejpam-1224	167	2	can	can	AUX
ejpam-1224	167	3	form	form	VERB
ejpam-1224	167	4	the	the	DET
ejpam-1224	167	5	tensor	tensor	NOUN
ejpam-1224	167	6	algebra	algebra	NOUN
ejpam-1224	167	7	t	t	PROPN
ejpam-1224	167	8	(	(	PUNCT
ejpam-1224	167	9	v	v	NOUN
ejpam-1224	167	10	)	)	PUNCT
ejpam-1224	167	11	=	=	SYM
ejpam-1224	167	12	v	v	NUM
ejpam-1224	167	13	⊕	⊕	PROPN
ejpam-1224	167	14	(	(	PUNCT
ejpam-1224	167	15	v	v	NOUN
ejpam-1224	167	16	⊗	⊗	PROPN
ejpam-1224	167	17	v	v	NOUN
ejpam-1224	167	18	)	)	PUNCT
ejpam-1224	167	19	⊕	⊕	PROPN
ejpam-1224	167	20	(	(	PUNCT
ejpam-1224	167	21	v	v	PROPN
ejpam-1224	167	22	⊗	⊗	PROPN
ejpam-1224	167	23	v	v	ADP
ejpam-1224	167	24	⊗	⊗	PROPN
ejpam-1224	167	25	v	v	NOUN
ejpam-1224	167	26	)	)	PUNCT
ejpam-1224	167	27	⊕	⊕	PROPN
ejpam-1224	167	28	·	·	PUNCT
ejpam-1224	167	29	·	·	PUNCT
ejpam-1224	167	30	·	·	PUNCT
ejpam-1224	167	31	which	which	PRON
ejpam-1224	167	32	will	will	AUX
ejpam-1224	167	33	also	also	ADV
ejpam-1224	167	34	be	be	AUX
ejpam-1224	167	35	λ	λ	NOUN
ejpam-1224	167	36	-	-	PUNCT
ejpam-1224	167	37	graded	grade	VERB
ejpam-1224	167	38	.	.	PUNCT
ejpam-1224	168	1	for	for	ADP
ejpam-1224	168	2	each	each	DET
ejpam-1224	168	3	v1	v1	PROPN
ejpam-1224	168	4	⊗	⊗	PROPN
ejpam-1224	168	5	.	.	PUNCT
ejpam-1224	168	6	.	.	PUNCT
ejpam-1224	168	7	.	.	PUNCT
ejpam-1224	169	1	⊗	⊗	PROPN
ejpam-1224	169	2	vn	vn	PROPN
ejpam-1224	169	3	∈	∈	PROPN
ejpam-1224	169	4	t	t	PROPN
ejpam-1224	169	5	(	(	PUNCT
ejpam-1224	169	6	v	v	NOUN
ejpam-1224	169	7	)	)	PUNCT
ejpam-1224	169	8	,	,	PUNCT
ejpam-1224	169	9	each	each	DET
ejpam-1224	169	10	vi	vi	PROPN
ejpam-1224	169	11	has	have	VERB
ejpam-1224	169	12	a	a	DET
ejpam-1224	169	13	λ	λ	NOUN
ejpam-1224	169	14	grading	grade	VERB
ejpam-1224	169	15	,	,	PUNCT
ejpam-1224	169	16	λi	λi	ADP
ejpam-1224	169	17	,	,	PUNCT
ejpam-1224	169	18	and	and	CCONJ
ejpam-1224	169	19	the	the	DET
ejpam-1224	169	20	total	total	ADJ
ejpam-1224	169	21	degree	degree	NOUN
ejpam-1224	169	22	will	will	AUX
ejpam-1224	169	23	be	be	AUX
ejpam-1224	169	24	the	the	DET
ejpam-1224	169	25	sum	sum	NOUN
ejpam-1224	169	26	of	of	ADP
ejpam-1224	169	27	all	all	DET
ejpam-1224	169	28	the	the	DET
ejpam-1224	169	29	λi	λi	NOUN
ejpam-1224	169	30	.	.	NOUN
ejpam-1224	169	31	let	let	VERB
ejpam-1224	169	32	p	p	PRON
ejpam-1224	169	33	be	be	AUX
ejpam-1224	169	34	a	a	DET
ejpam-1224	169	35	λ	λ	NOUN
ejpam-1224	169	36	-	-	PUNCT
ejpam-1224	169	37	graded	grade	VERB
ejpam-1224	169	38	sub	sub	ADJ
ejpam-1224	169	39	-	-	ADJ
ejpam-1224	169	40	vector	vector	ADJ
ejpam-1224	169	41	space	space	NOUN
ejpam-1224	169	42	of	of	ADP
ejpam-1224	169	43	k⊕	k⊕	PROPN
ejpam-1224	169	44	v	v	PROPN
ejpam-1224	169	45	⊕	⊕	PROPN
ejpam-1224	169	46	(	(	PUNCT
ejpam-1224	169	47	v	v	NOUN
ejpam-1224	169	48	⊗	⊗	PROPN
ejpam-1224	169	49	v	v	NOUN
ejpam-1224	169	50	)	)	PUNCT
ejpam-1224	169	51	such	such	ADJ
ejpam-1224	169	52	that	that	SCONJ
ejpam-1224	169	53	p	p	PROPN
ejpam-1224	169	54	∩	∩	NOUN
ejpam-1224	169	55	(	(	PUNCT
ejpam-1224	169	56	k⊕	k⊕	NOUN
ejpam-1224	169	57	v	v	NOUN
ejpam-1224	169	58	)	)	PUNCT
ejpam-1224	170	1	=	=	SYM
ejpam-1224	170	2	0	0	X
ejpam-1224	170	3	.	.	PUNCT
ejpam-1224	170	4	let	let	VERB
ejpam-1224	170	5	p0(p	p0(p	NOUN
ejpam-1224	170	6	)	)	PUNCT
ejpam-1224	170	7	,	,	PUNCT
ejpam-1224	170	8	p1(p	p1(p	PROPN
ejpam-1224	170	9	)	)	PUNCT
ejpam-1224	170	10	,	,	PUNCT
ejpam-1224	170	11	and	and	CCONJ
ejpam-1224	170	12	p2(p	p2(p	NOUN
ejpam-1224	170	13	)	)	PUNCT
ejpam-1224	170	14	be	be	VERB
ejpam-1224	170	15	the	the	DET
ejpam-1224	170	16	projections	projection	NOUN
ejpam-1224	170	17	of	of	ADP
ejpam-1224	170	18	p	p	NOUN
ejpam-1224	170	19	onto	onto	ADP
ejpam-1224	170	20	k	k	PROPN
ejpam-1224	170	21	,	,	PUNCT
ejpam-1224	170	22	v	v	NOUN
ejpam-1224	170	23	,	,	PUNCT
ejpam-1224	170	24	and	and	CCONJ
ejpam-1224	170	25	(	(	PUNCT
ejpam-1224	170	26	v	v	NOUN
ejpam-1224	170	27	⊗	⊗	PROPN
ejpam-1224	170	28	v	v	NOUN
ejpam-1224	170	29	)	)	PUNCT
ejpam-1224	170	30	respectively	respectively	ADV
ejpam-1224	170	31	.	.	PUNCT
ejpam-1224	171	1	let	let	VERB
ejpam-1224	171	2	r=	r=	PRON
ejpam-1224	171	3	p2(p	p2(p	NUM
ejpam-1224	171	4	)	)	PUNCT
ejpam-1224	171	5	,	,	PUNCT
ejpam-1224	171	6	now	now	ADV
ejpam-1224	171	7	we	we	PRON
ejpam-1224	171	8	may	may	AUX
ejpam-1224	171	9	then	then	ADV
ejpam-1224	171	10	define	define	VERB
ejpam-1224	171	11	u	u	NOUN
ejpam-1224	171	12	=	=	PROPN
ejpam-1224	171	13	t	t	PROPN
ejpam-1224	171	14	(	(	PUNCT
ejpam-1224	171	15	v	v	NOUN
ejpam-1224	171	16	)	)	PUNCT
ejpam-1224	171	17	/	/	SYM
ejpam-1224	172	1	<	<	X
ejpam-1224	172	2	p	p	X
ejpam-1224	172	3	>	>	X
ejpam-1224	172	4	to	to	PART
ejpam-1224	172	5	be	be	AUX
ejpam-1224	172	6	filtered	filter	VERB
ejpam-1224	172	7	by	by	ADP
ejpam-1224	172	8	tensor	tensor	NOUN
ejpam-1224	172	9	powers	power	NOUN
ejpam-1224	172	10	and	and	CCONJ
ejpam-1224	172	11	λ	λ	NOUN
ejpam-1224	172	12	-	-	PUNCT
ejpam-1224	172	13	graded	grade	VERB
ejpam-1224	172	14	.	.	PUNCT
ejpam-1224	173	1	in	in	ADP
ejpam-1224	173	2	the	the	DET
ejpam-1224	173	3	case	case	NOUN
ejpam-1224	173	4	where	where	SCONJ
ejpam-1224	173	5	p	p	NOUN
ejpam-1224	173	6	=	=	SYM
ejpam-1224	173	7	r	r	NOUN
ejpam-1224	173	8	,	,	PUNCT
ejpam-1224	173	9	u	u	NOUN
ejpam-1224	173	10	=	=	NOUN
ejpam-1224	173	11	a	a	PRON
ejpam-1224	173	12	is	be	AUX
ejpam-1224	173	13	said	say	VERB
ejpam-1224	173	14	to	to	PART
ejpam-1224	173	15	be	be	AUX
ejpam-1224	173	16	a	a	DET
ejpam-1224	173	17	quadratic	quadratic	ADJ
ejpam-1224	173	18	algebra	algebra	NOUN
ejpam-1224	173	19	defined	define	VERB
ejpam-1224	173	20	by	by	ADP
ejpam-1224	173	21	r	r	NOUN
ejpam-1224	173	22	and	and	CCONJ
ejpam-1224	173	23	this	this	DET
ejpam-1224	173	24	quotient	quotient	NOUN
ejpam-1224	173	25	induces	induce	VERB
ejpam-1224	173	26	an	an	DET
ejpam-1224	173	27	epimorphism	epimorphism	NOUN
ejpam-1224	173	28	φ	φ	NOUN
ejpam-1224	173	29	:	:	PUNCT
ejpam-1224	173	30	a→	a→	PROPN
ejpam-1224	173	31	gru	gru	NOUN
ejpam-1224	173	32	.	.	PUNCT
ejpam-1224	174	1	here	here	ADV
ejpam-1224	174	2	gru	gru	PROPN
ejpam-1224	174	3	is	be	AUX
ejpam-1224	174	4	the	the	DET
ejpam-1224	174	5	associated	associate	VERB
ejpam-1224	174	6	graded	grade	VERB
ejpam-1224	174	7	algebra	algebra	NOUN
ejpam-1224	174	8	of	of	ADP
ejpam-1224	174	9	u	u	NOUN
ejpam-1224	174	10	defined	define	VERB
ejpam-1224	174	11	by	by	ADP
ejpam-1224	174	12	u	u	PROPN
ejpam-1224	174	13	=	=	PROPN
ejpam-1224	174	14	⊕	⊕	PROPN
ejpam-1224	174	15	i∈z	i∈z	PROPN
ejpam-1224	174	16	fi+1	fi+1	NOUN
ejpam-1224	174	17	/	/	SYM
ejpam-1224	174	18	fi	fi	NOUN
ejpam-1224	174	19	.	.	PUNCT
ejpam-1224	175	1	if	if	SCONJ
ejpam-1224	175	2	φ	φ	PROPN
ejpam-1224	175	3	is	be	AUX
ejpam-1224	175	4	an	an	DET
ejpam-1224	175	5	isomorphism	isomorphism	NOUN
ejpam-1224	175	6	then	then	ADV
ejpam-1224	175	7	we	we	PRON
ejpam-1224	175	8	say	say	VERB
ejpam-1224	175	9	that	that	SCONJ
ejpam-1224	175	10	u	u	PROPN
ejpam-1224	175	11	is	be	AUX
ejpam-1224	175	12	of	of	ADP
ejpam-1224	175	13	poincaré-birkho	poincaré-birkho	ADJ
ejpam-1224	175	14	ff	ff	NOUN
ejpam-1224	175	15	-	-	PUNCT
ejpam-1224	175	16	witt	witt	ADJ
ejpam-1224	175	17	(	(	PUNCT
ejpam-1224	175	18	pbw	pbw	NOUN
ejpam-1224	175	19	)	)	PUNCT
ejpam-1224	175	20	type	type	NOUN
ejpam-1224	175	21	.	.	PUNCT
ejpam-1224	176	1	definition	definition	NOUN
ejpam-1224	176	2	5	5	NUM
ejpam-1224	176	3	.	.	PUNCT
ejpam-1224	177	1	given	give	VERB
ejpam-1224	177	2	a	a	DET
ejpam-1224	177	3	quadratic	quadratic	ADJ
ejpam-1224	177	4	algebra	algebra	NOUN
ejpam-1224	177	5	a	a	PRON
ejpam-1224	177	6	defined	define	VERB
ejpam-1224	177	7	by	by	ADP
ejpam-1224	177	8	r	r	PROPN
ejpam-1224	177	9	⊂	⊂	PROPN
ejpam-1224	177	10	v	v	ADP
ejpam-1224	177	11	⊗	⊗	PROPN
ejpam-1224	177	12	v	v	NOUN
ejpam-1224	177	13	,	,	PUNCT
ejpam-1224	177	14	we	we	PRON
ejpam-1224	177	15	may	may	AUX
ejpam-1224	177	16	dualize	dualize	VERB
ejpam-1224	177	17	this	this	DET
ejpam-1224	177	18	inclusion	inclusion	NOUN
ejpam-1224	177	19	and	and	CCONJ
ejpam-1224	177	20	get	get	VERB
ejpam-1224	177	21	an	an	DET
ejpam-1224	177	22	exact	exact	ADJ
ejpam-1224	177	23	sequence	sequence	NOUN
ejpam-1224	177	24	0→	0→	PROPN
ejpam-1224	177	25	r⊥→	r⊥→	ADJ
ejpam-1224	177	26	v	v	ADP
ejpam-1224	177	27	∗	∗	NOUN
ejpam-1224	177	28	⊗	⊗	PROPN
ejpam-1224	177	29	v	v	ADP
ejpam-1224	177	30	∗→	∗→	ADJ
ejpam-1224	177	31	r∗→	r∗→	PROPN
ejpam-1224	177	32	0	0	NUM
ejpam-1224	177	33	.	.	PUNCT
ejpam-1224	178	1	the	the	DET
ejpam-1224	178	2	algebra	algebra	NOUN
ejpam-1224	178	3	a	a	PRON
ejpam-1224	178	4	!	!	PUNCT
ejpam-1224	179	1	=	=	SYM
ejpam-1224	179	2	t	t	PROPN
ejpam-1224	179	3	(	(	PUNCT
ejpam-1224	179	4	v	v	NOUN
ejpam-1224	179	5	∗)/r⊥	∗)/r⊥	PROPN
ejpam-1224	179	6	is	be	AUX
ejpam-1224	179	7	called	call	VERB
ejpam-1224	179	8	the	the	DET
ejpam-1224	179	9	quadratic	quadratic	ADJ
ejpam-1224	179	10	dual	dual	ADJ
ejpam-1224	179	11	algebra	algebra	NOUN
ejpam-1224	179	12	of	of	ADP
ejpam-1224	179	13	a.	a.	NOUN
ejpam-1224	179	14	now	now	ADV
ejpam-1224	179	15	,	,	PUNCT
ejpam-1224	179	16	assuming	assume	VERB
ejpam-1224	179	17	that	that	SCONJ
ejpam-1224	179	18	(	(	PUNCT
ejpam-1224	179	19	k	k	PROPN
ejpam-1224	179	20	⊕	⊕	PROPN
ejpam-1224	179	21	v	v	NOUN
ejpam-1224	179	22	)	)	PUNCT
ejpam-1224	179	23	∩	∩	NOUN
ejpam-1224	179	24	p	p	NOUN
ejpam-1224	179	25	=	=	SYM
ejpam-1224	179	26	0	0	NUM
ejpam-1224	179	27	,	,	PUNCT
ejpam-1224	179	28	the	the	DET
ejpam-1224	179	29	map	map	NOUN
ejpam-1224	179	30	p	p	X
ejpam-1224	179	31	→	→	SYM
ejpam-1224	179	32	p2(p	p2(p	NOUN
ejpam-1224	179	33	)	)	PUNCT
ejpam-1224	179	34	=	=	SYM
ejpam-1224	179	35	r	r	NOUN
ejpam-1224	179	36	is	be	AUX
ejpam-1224	179	37	a	a	DET
ejpam-1224	179	38	bijection	bijection	NOUN
ejpam-1224	179	39	,	,	PUNCT
ejpam-1224	179	40	so	so	SCONJ
ejpam-1224	179	41	we	we	PRON
ejpam-1224	179	42	can	can	AUX
ejpam-1224	179	43	define	define	VERB
ejpam-1224	179	44	maps	map	NOUN
ejpam-1224	179	45	α	α	NOUN
ejpam-1224	179	46	:	:	PUNCT
ejpam-1224	179	47	r→	r→	PROPN
ejpam-1224	179	48	v	v	NOUN
ejpam-1224	179	49	and	and	CCONJ
ejpam-1224	179	50	β	β	X
ejpam-1224	179	51	:	:	PUNCT
ejpam-1224	179	52	r→	r→	PROPN
ejpam-1224	179	53	k	k	PROPN
ejpam-1224	179	54	as	as	ADP
ejpam-1224	179	55	α	α	NOUN
ejpam-1224	179	56	:	:	PUNCT
ejpam-1224	179	57	r	r	NOUN
ejpam-1224	179	58	p−1	p−1	PROPN
ejpam-1224	179	59	2−−−→	2−−−→	NUM
ejpam-1224	179	60	p	p	X
ejpam-1224	179	61	p1−−−→	p1−−−→	PROPN
ejpam-1224	179	62	v	v	PROPN
ejpam-1224	179	63	,	,	PUNCT
ejpam-1224	179	64	β	β	X
ejpam-1224	179	65	:	:	PUNCT
ejpam-1224	179	66	r	r	NOUN
ejpam-1224	179	67	p−1	p−1	PROPN
ejpam-1224	179	68	2−−−→	2−−−→	NUM
ejpam-1224	179	69	p	p	PROPN
ejpam-1224	179	70	p0−−−→	p0−−−→	PROPN
ejpam-1224	179	71	k.	k.	PROPN
ejpam-1224	179	72	then	then	ADV
ejpam-1224	179	73	p	p	PROPN
ejpam-1224	179	74	=	=	PUNCT
ejpam-1224	179	75	�	�	PROPN
ejpam-1224	179	76	x	x	SYM
ejpam-1224	180	1	+	+	ADJ
ejpam-1224	180	2	α(x)+	α(x)+	NOUN
ejpam-1224	180	3	β(x)|x	β(x)|x	NOUN
ejpam-1224	180	4	∈	∈	NOUN
ejpam-1224	180	5	r	r	NOUN
ejpam-1224	180	6	.	.	PUNCT
ejpam-1224	181	1	now	now	ADV
ejpam-1224	181	2	let	let	VERB
ejpam-1224	181	3	a	a	PRON
ejpam-1224	181	4	!	!	PUNCT
ejpam-1224	182	1	be	be	AUX
ejpam-1224	182	2	the	the	DET
ejpam-1224	182	3	dual	dual	ADJ
ejpam-1224	182	4	algebra	algebra	NOUN
ejpam-1224	182	5	of	of	ADP
ejpam-1224	182	6	a.	a.	NOUN
ejpam-1224	182	7	dualizing	dualize	VERB
ejpam-1224	182	8	the	the	DET
ejpam-1224	182	9	maps	map	NOUN
ejpam-1224	182	10	α	α	PROPN
ejpam-1224	182	11	and	and	CCONJ
ejpam-1224	182	12	β	β	X
ejpam-1224	182	13	we	we	PRON
ejpam-1224	182	14	have	have	VERB
ejpam-1224	182	15	a	a	PRON
ejpam-1224	182	16	!	!	NOUN
ejpam-1224	182	17	1	1	NUM
ejpam-1224	182	18	=	=	SYM
ejpam-1224	182	19	v	v	NOUN
ejpam-1224	182	20	∗	∗	NOUN
ejpam-1224	182	21	α∗	α∗	NOUN
ejpam-1224	182	22	−−−→	−−−→	VERB
ejpam-1224	182	23	a	a	DET
ejpam-1224	182	24	!	!	NOUN
ejpam-1224	182	25	2	2	NUM
ejpam-1224	182	26	=	=	SYM
ejpam-1224	182	27	r∗	r∗	PROPN
ejpam-1224	182	28	,	,	PUNCT
ejpam-1224	182	29	k	k	PROPN
ejpam-1224	182	30	β∗	β∗	NOUN
ejpam-1224	182	31	−−−→	−−−→	PROPN
ejpam-1224	182	32	a	a	DET
ejpam-1224	182	33	!	!	NOUN
ejpam-1224	182	34	2	2	NUM
ejpam-1224	182	35	=	=	NOUN
ejpam-1224	182	36	r∗.	r∗.	NOUN
ejpam-1224	182	37	example	example	NOUN
ejpam-1224	182	38	1	1	NUM
ejpam-1224	182	39	.	.	PUNCT
ejpam-1224	183	1	first	first	ADV
ejpam-1224	183	2	let	let	VERB
ejpam-1224	183	3	us	we	PRON
ejpam-1224	183	4	examine	examine	VERB
ejpam-1224	183	5	the	the	DET
ejpam-1224	183	6	classical	classical	ADJ
ejpam-1224	183	7	case	case	NOUN
ejpam-1224	183	8	.	.	PUNCT
ejpam-1224	184	1	consider	consider	VERB
ejpam-1224	184	2	the	the	DET
ejpam-1224	184	3	tensor	tensor	NOUN
ejpam-1224	184	4	algebra	algebra	NOUN
ejpam-1224	184	5	,	,	PUNCT
ejpam-1224	184	6	t	t	PROPN
ejpam-1224	184	7	(	(	PUNCT
ejpam-1224	184	8	v	v	NOUN
ejpam-1224	184	9	)	)	PUNCT
ejpam-1224	184	10	,	,	PUNCT
ejpam-1224	184	11	of	of	ADP
ejpam-1224	184	12	the	the	DET
ejpam-1224	184	13	λ	λ	NOUN
ejpam-1224	184	14	-	-	PUNCT
ejpam-1224	184	15	graded	grade	VERB
ejpam-1224	184	16	vector	vector	NOUN
ejpam-1224	184	17	space	space	NOUN
ejpam-1224	184	18	v	v	NOUN
ejpam-1224	184	19	,	,	PUNCT
ejpam-1224	184	20	where	where	SCONJ
ejpam-1224	184	21	λ	λ	X
ejpam-1224	184	22	=	=	SYM
ejpam-1224	184	23	z.	z.	PROPN
ejpam-1224	184	24	now	now	ADV
ejpam-1224	184	25	assign	assign	VERB
ejpam-1224	184	26	deg(v	deg(v	PROPN
ejpam-1224	184	27	)	)	PUNCT
ejpam-1224	184	28	=	=	SYM
ejpam-1224	184	29	1	1	NUM
ejpam-1224	184	30	for	for	ADP
ejpam-1224	184	31	v	v	NOUN
ejpam-1224	184	32	∈	∈	NOUN
ejpam-1224	184	33	v	v	NOUN
ejpam-1224	184	34	.	.	PUNCT
ejpam-1224	185	1	it	it	PRON
ejpam-1224	185	2	is	be	AUX
ejpam-1224	185	3	easy	easy	ADJ
ejpam-1224	185	4	to	to	PART
ejpam-1224	185	5	see	see	VERB
ejpam-1224	185	6	that	that	SCONJ
ejpam-1224	185	7	the	the	DET
ejpam-1224	185	8	λ	λ	NOUN
ejpam-1224	185	9	-	-	PUNCT
ejpam-1224	185	10	degree	degree	NOUN
ejpam-1224	185	11	will	will	AUX
ejpam-1224	185	12	equal	equal	VERB
ejpam-1224	185	13	the	the	DET
ejpam-1224	185	14	tensor	tensor	NOUN
ejpam-1224	185	15	degree	degree	NOUN
ejpam-1224	185	16	meaning	mean	VERB
ejpam-1224	185	17	that	that	SCONJ
ejpam-1224	185	18	the	the	DET
ejpam-1224	185	19	filtration	filtration	NOUN
ejpam-1224	185	20	and	and	CCONJ
ejpam-1224	185	21	grading	grading	NOUN
ejpam-1224	185	22	of	of	ADP
ejpam-1224	185	23	t	t	PROPN
ejpam-1224	185	24	(	(	PUNCT
ejpam-1224	185	25	v	v	NOUN
ejpam-1224	185	26	)	)	PUNCT
ejpam-1224	185	27	will	will	AUX
ejpam-1224	185	28	be	be	AUX
ejpam-1224	185	29	one	one	NUM
ejpam-1224	185	30	in	in	ADP
ejpam-1224	185	31	the	the	DET
ejpam-1224	185	32	same	same	ADJ
ejpam-1224	185	33	.	.	PUNCT
ejpam-1224	186	1	given	give	VERB
ejpam-1224	186	2	r⊂	r⊂	PROPN
ejpam-1224	186	3	v	v	ADP
ejpam-1224	186	4	⊗	⊗	PROPN
ejpam-1224	186	5	v	v	NOUN
ejpam-1224	186	6	,	,	PUNCT
ejpam-1224	186	7	u	u	NOUN
ejpam-1224	186	8	=	=	X
ejpam-1224	186	9	a=	a=	PROPN
ejpam-1224	186	10	t	t	X
ejpam-1224	186	11	(	(	PUNCT
ejpam-1224	186	12	v	v	NOUN
ejpam-1224	186	13	)	)	PUNCT
ejpam-1224	186	14	/	/	SYM
ejpam-1224	186	15	<	<	X
ejpam-1224	186	16	r	r	X
ejpam-1224	186	17	>	>	X
ejpam-1224	186	18	.	.	PUNCT
ejpam-1224	187	1	f.	f.	PROPN
ejpam-1224	187	2	hawwa	hawwa	PROPN
ejpam-1224	187	3	,	,	PUNCT
ejpam-1224	187	4	j.	j.	PROPN
ejpam-1224	187	5	hoffman	hoffman	PROPN
ejpam-1224	187	6	,	,	PUNCT
ejpam-1224	187	7	and	and	CCONJ
ejpam-1224	187	8	h.	h.	PROPN
ejpam-1224	187	9	wang	wang	PROPN
ejpam-1224	187	10	,	,	PUNCT
ejpam-1224	187	11	/	/	SYM
ejpam-1224	187	12	eur	eur	NOUN
ejpam-1224	187	13	.	.	PUNCT
ejpam-1224	188	1	j.	j.	PROPN
ejpam-1224	188	2	pure	pure	PROPN
ejpam-1224	188	3	appl	appl	PROPN
ejpam-1224	188	4	.	.	PROPN
ejpam-1224	188	5	math	math	PROPN
ejpam-1224	188	6	,	,	PUNCT
ejpam-1224	188	7	5	5	NUM
ejpam-1224	188	8	(	(	PUNCT
ejpam-1224	188	9	2012	2012	NUM
ejpam-1224	188	10	)	)	PUNCT
ejpam-1224	188	11	,	,	PUNCT
ejpam-1224	188	12	511	511	NUM
ejpam-1224	188	13	-	-	SYM
ejpam-1224	188	14	539	539	NUM
ejpam-1224	188	15	517	517	NUM
ejpam-1224	188	16	example	example	NOUN
ejpam-1224	188	17	2	2	NUM
ejpam-1224	188	18	.	.	PUNCT
ejpam-1224	188	19	now	now	ADV
ejpam-1224	188	20	let	let	VERB
ejpam-1224	188	21	us	we	PRON
ejpam-1224	188	22	examine	examine	VERB
ejpam-1224	188	23	a	a	DET
ejpam-1224	188	24	special	special	ADJ
ejpam-1224	188	25	case	case	NOUN
ejpam-1224	188	26	of	of	ADP
ejpam-1224	188	27	a	a	DET
ejpam-1224	188	28	λ	λ	NOUN
ejpam-1224	188	29	-	-	PUNCT
ejpam-1224	188	30	graded	grade	VERB
ejpam-1224	188	31	filtered	filter	VERB
ejpam-1224	188	32	algebra	algebra	NOUN
ejpam-1224	188	33	.	.	PUNCT
ejpam-1224	189	1	let	let	VERB
ejpam-1224	189	2	g	g	PRON
ejpam-1224	189	3	be	be	AUX
ejpam-1224	189	4	a	a	DET
ejpam-1224	189	5	semisimple	semisimple	ADJ
ejpam-1224	189	6	lie	lie	NOUN
ejpam-1224	189	7	algebra	algebra	NOUN
ejpam-1224	189	8	,	,	PUNCT
ejpam-1224	189	9	where	where	SCONJ
ejpam-1224	189	10	λ	λ	PROPN
ejpam-1224	189	11	is	be	AUX
ejpam-1224	189	12	the	the	DET
ejpam-1224	189	13	lattice	lattice	NOUN
ejpam-1224	189	14	of	of	ADP
ejpam-1224	189	15	weights	weight	NOUN
ejpam-1224	189	16	of	of	ADP
ejpam-1224	189	17	g.	g.	PROPN
ejpam-1224	190	1	it	it	PRON
ejpam-1224	190	2	is	be	AUX
ejpam-1224	190	3	known	know	VERB
ejpam-1224	190	4	that	that	SCONJ
ejpam-1224	190	5	we	we	PRON
ejpam-1224	190	6	have	have	VERB
ejpam-1224	190	7	a	a	DET
ejpam-1224	190	8	decomposition	decomposition	NOUN
ejpam-1224	190	9	g	g	NOUN
ejpam-1224	190	10	=	=	SYM
ejpam-1224	190	11	⊕	⊕	PROPN
ejpam-1224	190	12	λ∈λ	λ∈λ	NOUN
ejpam-1224	190	13	gλ	gλ	NOUN
ejpam-1224	190	14	,	,	PUNCT
ejpam-1224	190	15	[	[	X
ejpam-1224	190	16	gλ	gλ	NOUN
ejpam-1224	190	17	,	,	PUNCT
ejpam-1224	190	18	gµ]⊂	gµ]⊂	NOUN
ejpam-1224	190	19	gλ+µ	gλ+µ	NOUN
ejpam-1224	190	20	,	,	PUNCT
ejpam-1224	190	21	gλ	gλ	NOUN
ejpam-1224	190	22	=	=	SYM
ejpam-1224	190	23	{	{	PUNCT
ejpam-1224	190	24	x	x	SYM
ejpam-1224	190	25	∈	∈	PROPN
ejpam-1224	190	26	g	g	NOUN
ejpam-1224	191	1	|	|	PROPN
ejpam-1224	192	1	[	[	X
ejpam-1224	192	2	h	h	X
ejpam-1224	192	3	,	,	PUNCT
ejpam-1224	192	4	x	x	X
ejpam-1224	192	5	]	]	X
ejpam-1224	192	6	=	=	SYM
ejpam-1224	192	7	λ(h)x	λ(h)x	X
ejpam-1224	192	8	∀h	∀h	PROPN
ejpam-1224	192	9	∈	∈	PROPN
ejpam-1224	192	10	h	h	NOUN
ejpam-1224	192	11	}	}	PUNCT
ejpam-1224	192	12	where	where	SCONJ
ejpam-1224	192	13	h	h	NOUN
ejpam-1224	192	14	is	be	AUX
ejpam-1224	192	15	a	a	DET
ejpam-1224	192	16	cartan	cartan	ADJ
ejpam-1224	192	17	subalgebra	subalgebra	NOUN
ejpam-1224	192	18	.	.	PUNCT
ejpam-1224	193	1	if	if	SCONJ
ejpam-1224	193	2	we	we	PRON
ejpam-1224	193	3	consider	consider	VERB
ejpam-1224	193	4	the	the	DET
ejpam-1224	193	5	relation	relation	NOUN
ejpam-1224	193	6	x⊗	x⊗	VERB
ejpam-1224	193	7	y−	y−	NOUN
ejpam-1224	194	1	[	[	X
ejpam-1224	194	2	x	x	X
ejpam-1224	194	3	,	,	PUNCT
ejpam-1224	194	4	y	y	PROPN
ejpam-1224	194	5	]	]	X
ejpam-1224	194	6	for	for	ADP
ejpam-1224	194	7	x	x	PROPN
ejpam-1224	194	8	∈	∈	PROPN
ejpam-1224	194	9	gλ	gλ	NOUN
ejpam-1224	194	10	and	and	CCONJ
ejpam-1224	194	11	y	y	PROPN
ejpam-1224	194	12	∈	∈	PROPN
ejpam-1224	194	13	gµ	gµ	PROPN
ejpam-1224	194	14	,	,	PUNCT
ejpam-1224	194	15	we	we	PRON
ejpam-1224	194	16	can	can	AUX
ejpam-1224	194	17	see	see	VERB
ejpam-1224	194	18	that	that	SCONJ
ejpam-1224	194	19	deg(x	deg(x	PROPN
ejpam-1224	194	20	⊗	⊗	PROPN
ejpam-1224	194	21	y	y	NOUN
ejpam-1224	194	22	)	)	PUNCT
ejpam-1224	195	1	=	=	SYM
ejpam-1224	195	2	deg(([x	deg(([x	PROPN
ejpam-1224	195	3	,	,	PUNCT
ejpam-1224	195	4	y	y	PROPN
ejpam-1224	195	5	]	]	X
ejpam-1224	195	6	)	)	PUNCT
ejpam-1224	195	7	=	=	PRON
ejpam-1224	195	8	λ+	λ+	PUNCT
ejpam-1224	195	9	µ.	µ.	NOUN
ejpam-1224	195	10	by	by	ADP
ejpam-1224	195	11	definition	definition	NOUN
ejpam-1224	195	12	,	,	PUNCT
ejpam-1224	195	13	the	the	DET
ejpam-1224	195	14	universal	universal	ADJ
ejpam-1224	195	15	enveloping	enveloping	NOUN
ejpam-1224	195	16	algebra	algebra	NOUN
ejpam-1224	195	17	of	of	ADP
ejpam-1224	195	18	g	g	PROPN
ejpam-1224	195	19	is	be	AUX
ejpam-1224	195	20	u	u	NOUN
ejpam-1224	195	21	=	=	NOUN
ejpam-1224	195	22	ug	ug	ADP
ejpam-1224	195	23	=	=	SYM
ejpam-1224	195	24	tg	tg	PROPN
ejpam-1224	195	25	/	/	SYM
ejpam-1224	195	26	j	j	PROPN
ejpam-1224	195	27	where	where	SCONJ
ejpam-1224	195	28	tg	tg	PROPN
ejpam-1224	195	29	is	be	AUX
ejpam-1224	195	30	the	the	DET
ejpam-1224	195	31	tensor	tensor	NOUN
ejpam-1224	195	32	algebra	algebra	NOUN
ejpam-1224	195	33	on	on	ADP
ejpam-1224	195	34	g	g	PROPN
ejpam-1224	195	35	and	and	CCONJ
ejpam-1224	195	36	j	j	PROPN
ejpam-1224	196	1	=	=	X
ejpam-1224	196	2	<	<	X
ejpam-1224	196	3	x	x	X
ejpam-1224	196	4	⊗	⊗	NUM
ejpam-1224	196	5	y	y	PROPN
ejpam-1224	196	6	−	−	PROPN
ejpam-1224	197	1	[	[	X
ejpam-1224	197	2	x	x	X
ejpam-1224	197	3	,	,	PUNCT
ejpam-1224	197	4	y	y	PROPN
ejpam-1224	197	5	]	]	X
ejpam-1224	197	6	>	>	PUNCT
ejpam-1224	197	7	.	.	PUNCT
ejpam-1224	198	1	we	we	PRON
ejpam-1224	198	2	can	can	AUX
ejpam-1224	198	3	see	see	VERB
ejpam-1224	198	4	that	that	SCONJ
ejpam-1224	198	5	since	since	SCONJ
ejpam-1224	198	6	j	j	PROPN
ejpam-1224	198	7	is	be	AUX
ejpam-1224	198	8	generated	generate	VERB
ejpam-1224	198	9	by	by	ADP
ejpam-1224	198	10	homogeneous	homogeneous	ADJ
ejpam-1224	198	11	relations	relation	NOUN
ejpam-1224	198	12	,	,	PUNCT
ejpam-1224	198	13	u	u	NOUN
ejpam-1224	198	14	is	be	AUX
ejpam-1224	198	15	graded	grade	VERB
ejpam-1224	198	16	by	by	ADP
ejpam-1224	198	17	λ	λ	NOUN
ejpam-1224	198	18	and	and	CCONJ
ejpam-1224	198	19	is	be	AUX
ejpam-1224	198	20	filtered	filter	VERB
ejpam-1224	198	21	by	by	ADP
ejpam-1224	198	22	the	the	DET
ejpam-1224	198	23	tensor	tensor	NOUN
ejpam-1224	198	24	degree	degree	NOUN
ejpam-1224	198	25	.	.	PUNCT
ejpam-1224	199	1	3	3	X
ejpam-1224	199	2	.	.	X
ejpam-1224	199	3	curved	curved	ADJ
ejpam-1224	199	4	differential	differential	NOUN
ejpam-1224	199	5	graded	grade	VERB
ejpam-1224	199	6	algebras	algebra	NOUN
ejpam-1224	199	7	a	a	DET
ejpam-1224	199	8	λ	λ	NOUN
ejpam-1224	199	9	-	-	PUNCT
ejpam-1224	199	10	graded	grade	VERB
ejpam-1224	199	11	curved	curved	ADJ
ejpam-1224	199	12	differential	differential	NOUN
ejpam-1224	199	13	graded	grade	VERB
ejpam-1224	199	14	algebra	algebra	NOUN
ejpam-1224	199	15	(	(	PUNCT
ejpam-1224	199	16	cdga	cdga	PROPN
ejpam-1224	199	17	)	)	PUNCT
ejpam-1224	200	1	(	(	PUNCT
ejpam-1224	200	2	b	b	X
ejpam-1224	200	3	,	,	PUNCT
ejpam-1224	200	4	d	d	NOUN
ejpam-1224	200	5	,	,	PUNCT
ejpam-1224	200	6	c	c	NOUN
ejpam-1224	200	7	)	)	PUNCT
ejpam-1224	200	8	over	over	ADP
ejpam-1224	200	9	k	k	PROPN
ejpam-1224	200	10	is	be	AUX
ejpam-1224	200	11	a	a	DET
ejpam-1224	200	12	cohomologically	cohomologically	ADV
ejpam-1224	200	13	graded	grade	VERB
ejpam-1224	200	14	k	k	NOUN
ejpam-1224	200	15	-	-	NOUN
ejpam-1224	200	16	algebra	algebra	NOUN
ejpam-1224	200	17	such	such	ADJ
ejpam-1224	200	18	that	that	DET
ejpam-1224	200	19	b	b	X
ejpam-1224	200	20	=	=	PROPN
ejpam-1224	200	21	⊕	⊕	PROPN
ejpam-1224	200	22	p∈z	p∈z	NOUN
ejpam-1224	200	23	bp	bp	PROPN
ejpam-1224	200	24	,	,	PUNCT
ejpam-1224	200	25	bp	bp	PROPN
ejpam-1224	200	26	=	=	SYM
ejpam-1224	200	27	⊕	⊕	PROPN
ejpam-1224	200	28	λ∈λ	λ∈λ	NOUN
ejpam-1224	200	29	b	b	PROPN
ejpam-1224	200	30	p	p	PROPN
ejpam-1224	200	31	λ	λ	PROPN
ejpam-1224	200	32	,	,	PUNCT
ejpam-1224	200	33	bp	bp	PROPN
ejpam-1224	200	34	·	·	PUNCT
ejpam-1224	200	35	bq	bq	PROPN
ejpam-1224	200	36	⊂	⊂	PROPN
ejpam-1224	200	37	bp+q	bp+q	PROPN
ejpam-1224	200	38	,	,	PUNCT
ejpam-1224	201	1	b	b	PROPN
ejpam-1224	201	2	p	p	X
ejpam-1224	201	3	λ	λ	PROPN
ejpam-1224	201	4	·	·	PUNCT
ejpam-1224	201	5	bq	bq	PROPN
ejpam-1224	201	6	µ	µ	PROPN
ejpam-1224	201	7	=	=	SYM
ejpam-1224	201	8	b	b	PROPN
ejpam-1224	201	9	p+q	p+q	NUM
ejpam-1224	201	10	λ+µ	λ+µ	X
ejpam-1224	201	11	,	,	PUNCT
ejpam-1224	201	12	where	where	SCONJ
ejpam-1224	201	13	the	the	DET
ejpam-1224	201	14	differential	differential	NOUN
ejpam-1224	201	15	d	d	NOUN
ejpam-1224	201	16	is	be	AUX
ejpam-1224	201	17	a	a	DET
ejpam-1224	201	18	k	k	ADJ
ejpam-1224	201	19	-	-	PUNCT
ejpam-1224	201	20	linear	linear	ADJ
ejpam-1224	201	21	map	map	NOUN
ejpam-1224	201	22	such	such	ADJ
ejpam-1224	201	23	that	that	DET
ejpam-1224	201	24	d	d	NOUN
ejpam-1224	201	25	:	:	PUNCT
ejpam-1224	201	26	bp	bp	PROPN
ejpam-1224	201	27	→	→	SYM
ejpam-1224	201	28	bp+1	bp+1	PROPN
ejpam-1224	201	29	with	with	ADP
ejpam-1224	201	30	d2(b	d2(b	NOUN
ejpam-1224	201	31	)	)	PUNCT
ejpam-1224	201	32	=	=	PUNCT
ejpam-1224	202	1	[	[	X
ejpam-1224	202	2	c	c	X
ejpam-1224	202	3	,	,	PUNCT
ejpam-1224	202	4	b	b	NOUN
ejpam-1224	202	5	]	]	X
ejpam-1224	202	6	=	=	PUNCT
ejpam-1224	202	7	cb+	cb+	NOUN
ejpam-1224	202	8	(	(	PUNCT
ejpam-1224	202	9	−1)deg(b)deg(c)bc	−1)deg(b)deg(c)bc	PROPN
ejpam-1224	202	10	,	,	PUNCT
ejpam-1224	202	11	d(b1b2	d(b1b2	NOUN
ejpam-1224	202	12	)	)	PUNCT
ejpam-1224	202	13	=	=	PUNCT
ejpam-1224	202	14	d(b1)b2	d(b1)b2	NOUN
ejpam-1224	202	15	+	+	CCONJ
ejpam-1224	202	16	(	(	PUNCT
ejpam-1224	202	17	−1)|b1|b1d(b2	−1)|b1|b1d(b2	NOUN
ejpam-1224	202	18	)	)	PUNCT
ejpam-1224	202	19	.	.	PUNCT
ejpam-1224	203	1	note	note	VERB
ejpam-1224	203	2	that	that	SCONJ
ejpam-1224	203	3	when	when	SCONJ
ejpam-1224	203	4	λ	λ	X
ejpam-1224	203	5	=	=	SYM
ejpam-1224	203	6	0	0	NUM
ejpam-1224	203	7	we	we	PRON
ejpam-1224	203	8	have	have	VERB
ejpam-1224	203	9	the	the	DET
ejpam-1224	203	10	notion	notion	NOUN
ejpam-1224	203	11	of	of	ADP
ejpam-1224	203	12	a	a	DET
ejpam-1224	203	13	curved	curved	ADJ
ejpam-1224	203	14	differential	differential	NOUN
ejpam-1224	203	15	graded	grade	VERB
ejpam-1224	203	16	algebra	algebra	NOUN
ejpam-1224	203	17	,	,	PUNCT
ejpam-1224	203	18	if	if	SCONJ
ejpam-1224	203	19	c	c	NOUN
ejpam-1224	203	20	=	=	SYM
ejpam-1224	203	21	0	0	NUM
ejpam-1224	204	1	we	we	PRON
ejpam-1224	204	2	have	have	VERB
ejpam-1224	204	3	the	the	DET
ejpam-1224	204	4	notion	notion	NOUN
ejpam-1224	204	5	of	of	ADP
ejpam-1224	204	6	a	a	DET
ejpam-1224	204	7	λ	λ	NOUN
ejpam-1224	204	8	-	-	PUNCT
ejpam-1224	204	9	graded	grade	VERB
ejpam-1224	204	10	differential	differential	NOUN
ejpam-1224	204	11	graded	grade	VERB
ejpam-1224	204	12	algebra	algebra	NOUN
ejpam-1224	204	13	,	,	PUNCT
ejpam-1224	204	14	and	and	CCONJ
ejpam-1224	204	15	if	if	SCONJ
ejpam-1224	204	16	both	both	PRON
ejpam-1224	204	17	are	be	AUX
ejpam-1224	204	18	zero	zero	NUM
ejpam-1224	204	19	then	then	ADV
ejpam-1224	204	20	we	we	PRON
ejpam-1224	204	21	simply	simply	ADV
ejpam-1224	204	22	have	have	VERB
ejpam-1224	204	23	a	a	DET
ejpam-1224	204	24	differential	differential	ADJ
ejpam-1224	204	25	graded	grade	VERB
ejpam-1224	204	26	algebra	algebra	NOUN
ejpam-1224	204	27	.	.	PUNCT
ejpam-1224	205	1	definition	definition	NOUN
ejpam-1224	205	2	6	6	NUM
ejpam-1224	205	3	.	.	PUNCT
ejpam-1224	206	1	a	a	DET
ejpam-1224	206	2	λ	λ	NOUN
ejpam-1224	206	3	-	-	PUNCT
ejpam-1224	206	4	graded	grade	VERB
ejpam-1224	206	5	left	leave	VERB
ejpam-1224	206	6	curved	curved	ADJ
ejpam-1224	206	7	differential	differential	NOUN
ejpam-1224	206	8	graded	grade	VERB
ejpam-1224	206	9	module	module	NOUN
ejpam-1224	206	10	(	(	PUNCT
ejpam-1224	206	11	cdgm	cdgm	NOUN
ejpam-1224	206	12	)	)	PUNCT
ejpam-1224	206	13	(	(	PUNCT
ejpam-1224	206	14	n	n	X
ejpam-1224	206	15	,	,	PUNCT
ejpam-1224	206	16	d	d	X
ejpam-1224	206	17	,	,	PUNCT
ejpam-1224	206	18	c	c	NOUN
ejpam-1224	206	19	)	)	PUNCT
ejpam-1224	206	20	over	over	ADP
ejpam-1224	206	21	a	a	DET
ejpam-1224	206	22	cdga	cdga	NOUN
ejpam-1224	206	23	(	(	PUNCT
ejpam-1224	206	24	b	b	X
ejpam-1224	206	25	,	,	PUNCT
ejpam-1224	206	26	d	d	NOUN
ejpam-1224	206	27	,	,	PUNCT
ejpam-1224	206	28	c	c	X
ejpam-1224	206	29	)	)	PUNCT
ejpam-1224	206	30	is	be	AUX
ejpam-1224	206	31	a	a	DET
ejpam-1224	206	32	graded	grade	VERB
ejpam-1224	206	33	left	leave	VERB
ejpam-1224	206	34	b	b	NOUN
ejpam-1224	206	35	-	-	PUNCT
ejpam-1224	206	36	module	module	NOUN
ejpam-1224	206	37	n	n	NOUN
ejpam-1224	206	38	with	with	ADP
ejpam-1224	206	39	a	a	DET
ejpam-1224	206	40	k	k	ADJ
ejpam-1224	206	41	-	-	PUNCT
ejpam-1224	206	42	linear	linear	ADJ
ejpam-1224	206	43	map	map	NOUN
ejpam-1224	206	44	dn	dn	ADP
ejpam-1224	206	45	such	such	ADJ
ejpam-1224	206	46	that	that	SCONJ
ejpam-1224	206	47	n	n	NOUN
ejpam-1224	206	48	=	=	SYM
ejpam-1224	206	49	⊕	⊕	PROPN
ejpam-1224	206	50	i∈z	i∈z	PROPN
ejpam-1224	206	51	n	n	CCONJ
ejpam-1224	206	52	i	i	PRON
ejpam-1224	206	53	,	,	PUNCT
ejpam-1224	206	54	n	n	PROPN
ejpam-1224	207	1	i	i	NOUN
ejpam-1224	207	2	=	=	SYM
ejpam-1224	207	3	⊕	⊕	PROPN
ejpam-1224	207	4	λ∈λ	λ∈λ	NOUN
ejpam-1224	208	1	n	n	INTJ
ejpam-1224	208	2	i	i	PRON
ejpam-1224	208	3	λ	λ	PROPN
ejpam-1224	208	4	,	,	PUNCT
ejpam-1224	208	5	bi	bi	NOUN
ejpam-1224	208	6	λ	λ	PROPN
ejpam-1224	208	7	·	·	PUNCT
ejpam-1224	208	8	n	n	CCONJ
ejpam-1224	208	9	j	j	PROPN
ejpam-1224	208	10	µ	µ	X
ejpam-1224	208	11	⊂	⊂	PROPN
ejpam-1224	208	12	n	n	CCONJ
ejpam-1224	208	13	i+	i+	NOUN
ejpam-1224	208	14	j	j	PROPN
ejpam-1224	208	15	λ+µ	λ+µ	X
ejpam-1224	208	16	,	,	PUNCT
ejpam-1224	208	17	dn	dn	NOUN
ejpam-1224	208	18	:	:	PUNCT
ejpam-1224	208	19	n	n	CCONJ
ejpam-1224	208	20	i	i	PRON
ejpam-1224	208	21	λ→	λ→	PUNCT
ejpam-1224	208	22	n	n	CCONJ
ejpam-1224	208	23	i+1	i+1	NUM
ejpam-1224	208	24	λ	λ	PROPN
ejpam-1224	208	25	,	,	PUNCT
ejpam-1224	208	26	d2	d2	PROPN
ejpam-1224	208	27	n	n	CCONJ
ejpam-1224	208	28	(	(	PUNCT
ejpam-1224	208	29	n	n	CCONJ
ejpam-1224	208	30	)	)	PUNCT
ejpam-1224	209	1	=	=	SYM
ejpam-1224	209	2	cn	cn	PROPN
ejpam-1224	209	3	,	,	PUNCT
ejpam-1224	209	4	dn	dn	PROPN
ejpam-1224	209	5	(	(	PUNCT
ejpam-1224	209	6	bn	bn	NOUN
ejpam-1224	209	7	)	)	PUNCT
ejpam-1224	209	8	=	=	SYM
ejpam-1224	210	1	db(b)n+	db(b)n+	PROPN
ejpam-1224	210	2	(	(	PUNCT
ejpam-1224	210	3	−1)|b|bdn	−1)|b|bdn	PROPN
ejpam-1224	210	4	(	(	PUNCT
ejpam-1224	210	5	n	n	CCONJ
ejpam-1224	210	6	)	)	PUNCT
ejpam-1224	210	7	,	,	PUNCT
ejpam-1224	210	8	b	b	X
ejpam-1224	210	9	∈	∈	PROPN
ejpam-1224	210	10	b	b	PROPN
ejpam-1224	210	11	,	,	PUNCT
ejpam-1224	210	12	n	n	PROPN
ejpam-1224	210	13	∈	∈	PROPN
ejpam-1224	210	14	n	n	X
ejpam-1224	210	15	.	.	PUNCT
ejpam-1224	210	16	note	note	VERB
ejpam-1224	210	17	that	that	SCONJ
ejpam-1224	210	18	for	for	ADP
ejpam-1224	210	19	a	a	DET
ejpam-1224	210	20	λ	λ	NOUN
ejpam-1224	210	21	-	-	PUNCT
ejpam-1224	210	22	graded	grade	VERB
ejpam-1224	210	23	right	right	ADJ
ejpam-1224	210	24	curved	curve	VERB
ejpam-1224	210	25	differential	differential	NOUN
ejpam-1224	210	26	graded	grade	VERB
ejpam-1224	210	27	module	module	NOUN
ejpam-1224	210	28	we	we	PRON
ejpam-1224	210	29	have	have	VERB
ejpam-1224	210	30	n	n	PROPN
ejpam-1224	210	31	j	j	PROPN
ejpam-1224	210	32	µ	µ	X
ejpam-1224	211	1	·	·	PUNCT
ejpam-1224	211	2	b	b	X
ejpam-1224	212	1	i	i	PRON
ejpam-1224	212	2	λ	λ	VERB
ejpam-1224	212	3	⊂	⊂	PROPN
ejpam-1224	212	4	n	n	CCONJ
ejpam-1224	212	5	i+	i+	NOUN
ejpam-1224	212	6	j	j	PROPN
ejpam-1224	212	7	λ+µ	λ+µ	X
ejpam-1224	212	8	and	and	CCONJ
ejpam-1224	212	9	d2	d2	PROPN
ejpam-1224	212	10	n	n	CCONJ
ejpam-1224	212	11	(	(	PUNCT
ejpam-1224	212	12	n	n	CCONJ
ejpam-1224	212	13	)	)	PUNCT
ejpam-1224	212	14	=	=	SYM
ejpam-1224	212	15	−cn	−cn	NOUN
ejpam-1224	212	16	.	.	PUNCT
ejpam-1224	213	1	we	we	PRON
ejpam-1224	213	2	let	let	VERB
ejpam-1224	213	3	comλ(b	comλ(b	PROPN
ejpam-1224	213	4	,	,	PUNCT
ejpam-1224	213	5	d	d	X
ejpam-1224	213	6	,	,	PUNCT
ejpam-1224	213	7	c	c	X
ejpam-1224	213	8	)	)	PUNCT
ejpam-1224	213	9	be	be	AUX
ejpam-1224	213	10	the	the	DET
ejpam-1224	213	11	category	category	NOUN
ejpam-1224	213	12	of	of	ADP
ejpam-1224	213	13	these	these	DET
ejpam-1224	213	14	curved	curved	ADJ
ejpam-1224	213	15	differential	differential	NOUN
ejpam-1224	213	16	graded	grade	VERB
ejpam-1224	213	17	modules	module	NOUN
ejpam-1224	213	18	,	,	PUNCT
ejpam-1224	213	19	with	with	ADP
ejpam-1224	213	20	the	the	DET
ejpam-1224	213	21	evident	evident	ADJ
ejpam-1224	213	22	morphisms	morphism	NOUN
ejpam-1224	213	23	.	.	PUNCT
ejpam-1224	214	1	when	when	SCONJ
ejpam-1224	214	2	c	c	NOUN
ejpam-1224	214	3	=	=	SYM
ejpam-1224	214	4	0	0	NUM
ejpam-1224	214	5	,	,	PUNCT
ejpam-1224	214	6	we	we	PRON
ejpam-1224	214	7	have	have	VERB
ejpam-1224	214	8	simply	simply	ADV
ejpam-1224	214	9	a	a	DET
ejpam-1224	214	10	differential	differential	ADJ
ejpam-1224	214	11	graded	grade	VERB
ejpam-1224	214	12	module	module	NOUN
ejpam-1224	214	13	.	.	PUNCT
ejpam-1224	215	1	f.	f.	PROPN
ejpam-1224	215	2	hawwa	hawwa	PROPN
ejpam-1224	215	3	,	,	PUNCT
ejpam-1224	215	4	j.	j.	PROPN
ejpam-1224	215	5	hoffman	hoffman	PROPN
ejpam-1224	215	6	,	,	PUNCT
ejpam-1224	215	7	and	and	CCONJ
ejpam-1224	215	8	h.	h.	PROPN
ejpam-1224	215	9	wang	wang	PROPN
ejpam-1224	215	10	,	,	PUNCT
ejpam-1224	215	11	/	/	SYM
ejpam-1224	215	12	eur	eur	NOUN
ejpam-1224	215	13	.	.	PUNCT
ejpam-1224	216	1	j.	j.	PROPN
ejpam-1224	216	2	pure	pure	PROPN
ejpam-1224	216	3	appl	appl	PROPN
ejpam-1224	216	4	.	.	PROPN
ejpam-1224	216	5	math	math	PROPN
ejpam-1224	216	6	,	,	PUNCT
ejpam-1224	216	7	5	5	NUM
ejpam-1224	216	8	(	(	PUNCT
ejpam-1224	216	9	2012	2012	NUM
ejpam-1224	216	10	)	)	PUNCT
ejpam-1224	216	11	,	,	PUNCT
ejpam-1224	216	12	511	511	NUM
ejpam-1224	216	13	-	-	SYM
ejpam-1224	216	14	539	539	NUM
ejpam-1224	216	15	518	518	NUM
ejpam-1224	216	16	example	example	NOUN
ejpam-1224	216	17	3	3	NUM
ejpam-1224	216	18	.	.	PUNCT
ejpam-1224	217	1	the	the	DET
ejpam-1224	217	2	following	following	ADJ
ejpam-1224	217	3	example	example	NOUN
ejpam-1224	217	4	is	be	AUX
ejpam-1224	217	5	due	due	ADJ
ejpam-1224	217	6	to	to	ADP
ejpam-1224	217	7	floystad	floystad	NOUN
ejpam-1224	217	8	[	[	X
ejpam-1224	217	9	3	3	NUM
ejpam-1224	217	10	]	]	PUNCT
ejpam-1224	217	11	.	.	PUNCT
ejpam-1224	218	1	let	let	VERB
ejpam-1224	218	2	k	k	PRON
ejpam-1224	218	3	be	be	AUX
ejpam-1224	218	4	a	a	DET
ejpam-1224	218	5	field	field	NOUN
ejpam-1224	218	6	and	and	CCONJ
ejpam-1224	218	7	let	let	VERB
ejpam-1224	218	8	u	u	PRON
ejpam-1224	218	9	be	be	AUX
ejpam-1224	218	10	the	the	DET
ejpam-1224	218	11	following	follow	VERB
ejpam-1224	218	12	filtered	filter	VERB
ejpam-1224	218	13	quadratic	quadratic	ADJ
ejpam-1224	218	14	algebra	algebra	NOUN
ejpam-1224	218	15	,	,	PUNCT
ejpam-1224	218	16	u	u	PROPN
ejpam-1224	218	17	=	=	PROPN
ejpam-1224	218	18	k[x]/(x2−	k[x]/(x2−	PROPN
ejpam-1224	218	19	(	(	PUNCT
ejpam-1224	218	20	a−	a−	PROPN
ejpam-1224	218	21	b)x	b)x	X
ejpam-1224	218	22	+	+	CCONJ
ejpam-1224	218	23	ab	ab	X
ejpam-1224	218	24	)	)	PUNCT
ejpam-1224	218	25	=	=	SYM
ejpam-1224	218	26	k[x]/(x	k[x]/(x	NOUN
ejpam-1224	218	27	−	−	NOUN
ejpam-1224	218	28	a)⊕	a)⊕	VERB
ejpam-1224	218	29	k[x]/(x	k[x]/(x	NOUN
ejpam-1224	218	30	−	−	PROPN
ejpam-1224	218	31	b	b	NOUN
ejpam-1224	218	32	)	)	PUNCT
ejpam-1224	218	33	.	.	PUNCT
ejpam-1224	219	1	the	the	DET
ejpam-1224	219	2	dual	dual	ADJ
ejpam-1224	219	3	of	of	ADP
ejpam-1224	219	4	u	u	NOUN
ejpam-1224	219	5	will	will	AUX
ejpam-1224	219	6	be	be	AUX
ejpam-1224	219	7	a	a	PRON
ejpam-1224	219	8	!	!	PUNCT
ejpam-1224	220	1	=	=	SYM
ejpam-1224	220	2	k[ξ	k[ξ	X
ejpam-1224	220	3	]	]	PUNCT
ejpam-1224	220	4	which	which	PRON
ejpam-1224	220	5	is	be	AUX
ejpam-1224	220	6	the	the	DET
ejpam-1224	220	7	cdga	cdga	NOUN
ejpam-1224	220	8	with	with	ADP
ejpam-1224	220	9	differential	differential	NOUN
ejpam-1224	220	10	d(ξn	d(ξn	NOUN
ejpam-1224	220	11	)	)	PUNCT
ejpam-1224	220	12	=	=	SYM
ejpam-1224	220	13	(	(	PUNCT
ejpam-1224	220	14	−(a+	−(a+	NUM
ejpam-1224	220	15	b)ξn+1	b)ξn+1	NOUN
ejpam-1224	220	16	if	if	SCONJ
ejpam-1224	220	17	n	n	NOUN
ejpam-1224	220	18	is	be	AUX
ejpam-1224	220	19	odd	odd	ADJ
ejpam-1224	220	20	0	0	NUM
ejpam-1224	220	21	if	if	SCONJ
ejpam-1224	220	22	n	n	NOUN
ejpam-1224	220	23	is	be	AUX
ejpam-1224	220	24	even	even	ADV
ejpam-1224	220	25	and	and	CCONJ
ejpam-1224	220	26	curvature	curvature	VERB
ejpam-1224	220	27	c	c	NOUN
ejpam-1224	220	28	=	=	SYM
ejpam-1224	220	29	abξ2	abξ2	PROPN
ejpam-1224	220	30	.	.	PUNCT
ejpam-1224	221	1	more	more	ADJ
ejpam-1224	221	2	details	detail	NOUN
ejpam-1224	221	3	of	of	ADP
ejpam-1224	221	4	this	this	DET
ejpam-1224	221	5	cdga	cdga	NOUN
ejpam-1224	221	6	will	will	AUX
ejpam-1224	221	7	be	be	AUX
ejpam-1224	221	8	provided	provide	VERB
ejpam-1224	221	9	in	in	ADP
ejpam-1224	221	10	sections	section	NOUN
ejpam-1224	221	11	5	5	NUM
ejpam-1224	221	12	and	and	CCONJ
ejpam-1224	221	13	6	6	NUM
ejpam-1224	221	14	.	.	NOUN
ejpam-1224	221	15	4	4	NUM
ejpam-1224	221	16	.	.	X
ejpam-1224	221	17	koszul	koszul	ADJ
ejpam-1224	221	18	algebras	algebra	NOUN
ejpam-1224	221	19	let	let	VERB
ejpam-1224	221	20	a	a	PRON
ejpam-1224	221	21	be	be	AUX
ejpam-1224	221	22	a	a	DET
ejpam-1224	221	23	quadratic	quadratic	ADJ
ejpam-1224	221	24	algebra	algebra	NOUN
ejpam-1224	221	25	over	over	ADP
ejpam-1224	221	26	a	a	DET
ejpam-1224	221	27	field	field	NOUN
ejpam-1224	222	1	k	k	NOUN
ejpam-1224	222	2	,	,	PUNCT
ejpam-1224	222	3	so	so	ADV
ejpam-1224	222	4	a	a	DET
ejpam-1224	222	5	=	=	X
ejpam-1224	222	6	t	t	PROPN
ejpam-1224	222	7	(	(	PUNCT
ejpam-1224	222	8	v	v	NOUN
ejpam-1224	222	9	)	)	PUNCT
ejpam-1224	222	10	/(r	/(r	PUNCT
ejpam-1224	222	11	)	)	PUNCT
ejpam-1224	222	12	.	.	PUNCT
ejpam-1224	223	1	its	its	PRON
ejpam-1224	223	2	dual	dual	ADJ
ejpam-1224	223	3	a	a	PRON
ejpam-1224	223	4	!	!	PUNCT
ejpam-1224	223	5	is	be	AUX
ejpam-1224	223	6	the	the	DET
ejpam-1224	223	7	quadratic	quadratic	ADJ
ejpam-1224	223	8	algebra	algebra	NOUN
ejpam-1224	223	9	over	over	ADP
ejpam-1224	223	10	k	k	PROPN
ejpam-1224	223	11	given	give	VERB
ejpam-1224	223	12	by	by	ADP
ejpam-1224	223	13	a	a	PRON
ejpam-1224	223	14	!	!	PUNCT
ejpam-1224	224	1	=	=	SYM
ejpam-1224	224	2	t	t	PROPN
ejpam-1224	224	3	(	(	PUNCT
ejpam-1224	224	4	v	v	PROPN
ejpam-1224	224	5	∗)/(r⊥	∗)/(r⊥	PROPN
ejpam-1224	224	6	)	)	PUNCT
ejpam-1224	224	7	with	with	ADP
ejpam-1224	224	8	r⊥	r⊥	PROPN
ejpam-1224	224	9	⊂	⊂	PROPN
ejpam-1224	224	10	v	v	ADP
ejpam-1224	224	11	∗⊗	∗⊗	PROPN
ejpam-1224	224	12	v	v	ADP
ejpam-1224	224	13	∗	∗	NOUN
ejpam-1224	224	14	=	=	SYM
ejpam-1224	224	15	(	(	PUNCT
ejpam-1224	224	16	v	v	NOUN
ejpam-1224	224	17	⊗	⊗	PROPN
ejpam-1224	224	18	v	v	NOUN
ejpam-1224	224	19	)	)	PUNCT
ejpam-1224	225	1	∗.	∗.	PROPN
ejpam-1224	225	2	we	we	PRON
ejpam-1224	225	3	define	define	VERB
ejpam-1224	225	4	the	the	DET
ejpam-1224	225	5	koszul	koszul	ADJ
ejpam-1224	225	6	complex	complex	NOUN
ejpam-1224	225	7	of	of	ADP
ejpam-1224	225	8	a	a	PRON
ejpam-1224	225	9	to	to	PART
ejpam-1224	225	10	be	be	AUX
ejpam-1224	225	11	the	the	DET
ejpam-1224	225	12	complex	complex	ADJ
ejpam-1224	225	13	(	(	PUNCT
ejpam-1224	225	14	isomorphic	isomorphic	ADJ
ejpam-1224	225	15	to	to	ADP
ejpam-1224	225	16	)	)	PUNCT
ejpam-1224	225	17	.	.	PUNCT
ejpam-1224	225	18	.	.	PUNCT
ejpam-1224	226	1	.→	.→	X
ejpam-1224	227	1	a⊗	a⊗	NOUN
ejpam-1224	227	2	(	(	PUNCT
ejpam-1224	227	3	a	a	NOUN
ejpam-1224	227	4	!	!	NOUN
ejpam-1224	227	5	2	2	NUM
ejpam-1224	227	6	)	)	PUNCT
ejpam-1224	227	7	∗→	∗→	ADJ
ejpam-1224	227	8	a⊗	a⊗	NOUN
ejpam-1224	227	9	(	(	PUNCT
ejpam-1224	227	10	a	a	NOUN
ejpam-1224	227	11	!	!	NOUN
ejpam-1224	227	12	1	1	X
ejpam-1224	227	13	)	)	PUNCT
ejpam-1224	227	14	∗→	∗→	VERB
ejpam-1224	227	15	a	a	DET
ejpam-1224	227	16	where	where	SCONJ
ejpam-1224	227	17	(	(	PUNCT
ejpam-1224	227	18	a!)i	a!)i	X
ejpam-1224	227	19	=	=	SYM
ejpam-1224	227	20	a	a	NOUN
ejpam-1224	227	21	!	!	PUNCT
ejpam-1224	228	1	i	i	PRON
ejpam-1224	228	2	.	.	PUNCT
ejpam-1224	229	1	we	we	PRON
ejpam-1224	229	2	can	can	AUX
ejpam-1224	229	3	note	note	VERB
ejpam-1224	229	4	that	that	SCONJ
ejpam-1224	229	5	a	a	DET
ejpam-1224	229	6	!	!	NOUN
ejpam-1224	229	7	1	1	NUM
ejpam-1224	229	8	=	=	SYM
ejpam-1224	229	9	v	v	ADP
ejpam-1224	229	10	∗	∗	NOUN
ejpam-1224	229	11	and	and	CCONJ
ejpam-1224	229	12	a	a	DET
ejpam-1224	229	13	!	!	NOUN
ejpam-1224	229	14	2	2	NUM
ejpam-1224	229	15	=	=	SYM
ejpam-1224	229	16	(	(	PUNCT
ejpam-1224	229	17	v	v	NOUN
ejpam-1224	229	18	∗	∗	ADP
ejpam-1224	229	19	⊗	⊗	PROPN
ejpam-1224	229	20	v	v	ADP
ejpam-1224	229	21	∗)/(r⊥	∗)/(r⊥	PROPN
ejpam-1224	229	22	)	)	PUNCT
ejpam-1224	230	1	=	=	VERB
ejpam-1224	230	2	r∗	r∗	VERB
ejpam-1224	230	3	so	so	CCONJ
ejpam-1224	230	4	(	(	PUNCT
ejpam-1224	230	5	a	a	NOUN
ejpam-1224	230	6	!	!	NOUN
ejpam-1224	230	7	2	2	NUM
ejpam-1224	230	8	)	)	PUNCT
ejpam-1224	230	9	∗	∗	NOUN
ejpam-1224	230	10	=	=	SYM
ejpam-1224	230	11	r.	r.	NOUN
ejpam-1224	230	12	before	before	ADP
ejpam-1224	230	13	defining	define	VERB
ejpam-1224	230	14	the	the	DET
ejpam-1224	230	15	differentials	differential	NOUN
ejpam-1224	230	16	,	,	PUNCT
ejpam-1224	230	17	recall	recall	VERB
ejpam-1224	230	18	the	the	DET
ejpam-1224	230	19	canonical	canonical	ADJ
ejpam-1224	230	20	isomorphism	isomorphism	NOUN
ejpam-1224	230	21	w	w	ADP
ejpam-1224	230	22	∗	∗	NOUN
ejpam-1224	230	23	⊗k	⊗k	X
ejpam-1224	230	24	v	v	NOUN
ejpam-1224	230	25	=	=	SYM
ejpam-1224	230	26	homk(w	homk(w	PROPN
ejpam-1224	230	27	,	,	PUNCT
ejpam-1224	230	28	v	v	NOUN
ejpam-1224	230	29	)	)	PUNCT
ejpam-1224	230	30	defined	define	VERB
ejpam-1224	230	31	by	by	ADP
ejpam-1224	230	32	φ(λ⊗k	φ(λ⊗k	ADJ
ejpam-1224	230	33	v)(w	v)(w	NOUN
ejpam-1224	230	34	)	)	PUNCT
ejpam-1224	230	35	=	=	SYM
ejpam-1224	230	36	λ(w)v	λ(w)v	PROPN
ejpam-1224	230	37	.	.	PUNCT
ejpam-1224	231	1	now	now	ADV
ejpam-1224	231	2	if	if	SCONJ
ejpam-1224	231	3	a=	a=	PROPN
ejpam-1224	231	4	⊕	⊕	PROPN
ejpam-1224	231	5	j∈za	j∈za	PROPN
ejpam-1224	231	6	j	j	PROPN
ejpam-1224	231	7	,	,	PUNCT
ejpam-1224	231	8	then	then	ADV
ejpam-1224	231	9	a⊗k	a⊗k	PROPN
ejpam-1224	231	10	(	(	PUNCT
ejpam-1224	231	11	a	a	PRON
ejpam-1224	231	12	!	!	PUNCT
ejpam-1224	232	1	i	i	NOUN
ejpam-1224	232	2	)	)	PUNCT
ejpam-1224	232	3	∗	∗	NOUN
ejpam-1224	233	1	=	=	SYM
ejpam-1224	233	2	⊕	⊕	PROPN
ejpam-1224	233	3	j∈z	j∈z	NOUN
ejpam-1224	233	4	a	a	DET
ejpam-1224	233	5	j	j	PROPN
ejpam-1224	233	6	⊗k	⊗k	ADJ
ejpam-1224	233	7	(	(	PUNCT
ejpam-1224	233	8	a	a	PRON
ejpam-1224	233	9	!	!	PUNCT
ejpam-1224	234	1	i	i	NOUN
ejpam-1224	234	2	)	)	PUNCT
ejpam-1224	234	3	∗	∗	NOUN
ejpam-1224	234	4	=	=	PUNCT
ejpam-1224	234	5	⊕	⊕	PROPN
ejpam-1224	234	6	j∈z	j∈z	NOUN
ejpam-1224	234	7	homk(a	homk(a	NOUN
ejpam-1224	234	8	!	!	PUNCT
ejpam-1224	235	1	i	i	PRON
ejpam-1224	235	2	,	,	PUNCT
ejpam-1224	235	3	a	a	DET
ejpam-1224	235	4	j	j	NOUN
ejpam-1224	235	5	)	)	PUNCT
ejpam-1224	235	6	.	.	PUNCT
ejpam-1224	236	1	since	since	SCONJ
ejpam-1224	236	2	a	a	PRON
ejpam-1224	236	3	!	!	PUNCT
ejpam-1224	237	1	i	i	PRON
ejpam-1224	237	2	is	be	AUX
ejpam-1224	237	3	finite	finite	ADJ
ejpam-1224	237	4	dimensional	dimensional	ADJ
ejpam-1224	237	5	,	,	PUNCT
ejpam-1224	237	6	we	we	PRON
ejpam-1224	237	7	know	know	VERB
ejpam-1224	237	8	that	that	SCONJ
ejpam-1224	237	9	⊕	⊕	PROPN
ejpam-1224	237	10	j∈z	j∈z	NOUN
ejpam-1224	237	11	homk(a	homk(a	PROPN
ejpam-1224	237	12	!	!	PUNCT
ejpam-1224	238	1	i	i	PRON
ejpam-1224	238	2	,	,	PUNCT
ejpam-1224	238	3	a	a	DET
ejpam-1224	238	4	j	j	NOUN
ejpam-1224	238	5	)	)	PUNCT
ejpam-1224	238	6	=	=	NOUN
ejpam-1224	238	7	homk(a	homk(a	NOUN
ejpam-1224	238	8	!	!	PUNCT
ejpam-1224	239	1	i	i	PRON
ejpam-1224	239	2	,	,	PUNCT
ejpam-1224	239	3	⊕	⊕	PROPN
ejpam-1224	239	4	j∈z	j∈z	VERB
ejpam-1224	239	5	a	a	DET
ejpam-1224	239	6	j	j	NOUN
ejpam-1224	239	7	)	)	PUNCT
ejpam-1224	240	1	=	=	NOUN
ejpam-1224	240	2	homk(a	homk(a	NOUN
ejpam-1224	240	3	!	!	PUNCT
ejpam-1224	241	1	i	i	PRON
ejpam-1224	241	2	,	,	PUNCT
ejpam-1224	241	3	a	a	PRON
ejpam-1224	241	4	)	)	PUNCT
ejpam-1224	241	5	via	via	ADP
ejpam-1224	241	6	the	the	DET
ejpam-1224	241	7	isomorphism	isomorphism	NOUN
ejpam-1224	241	8	a⊗k	a⊗k	PROPN
ejpam-1224	241	9	(	(	PUNCT
ejpam-1224	241	10	a	a	PRON
ejpam-1224	241	11	!	!	PUNCT
ejpam-1224	242	1	i	i	PRON
ejpam-1224	242	2	)	)	PUNCT
ejpam-1224	242	3	∗	∗	NOUN
ejpam-1224	242	4	=	=	SYM
ejpam-1224	242	5	homk(a	homk(a	NOUN
ejpam-1224	242	6	!	!	PUNCT
ejpam-1224	243	1	i	i	PRON
ejpam-1224	243	2	,	,	PUNCT
ejpam-1224	243	3	a	a	PRON
ejpam-1224	243	4	)	)	PUNCT
ejpam-1224	243	5	.	.	PUNCT
ejpam-1224	244	1	the	the	DET
ejpam-1224	244	2	differential	differential	ADJ
ejpam-1224	244	3	δ	δ	PROPN
ejpam-1224	244	4	:	:	PUNCT
ejpam-1224	244	5	a⊗k	a⊗k	PROPN
ejpam-1224	244	6	(	(	PUNCT
ejpam-1224	244	7	a	a	PRON
ejpam-1224	244	8	!	!	PUNCT
ejpam-1224	244	9	i+1	i+1	NUM
ejpam-1224	244	10	)	)	PUNCT
ejpam-1224	244	11	∗	∗	NOUN
ejpam-1224	244	12	→	→	SYM
ejpam-1224	244	13	a⊗k	a⊗k	PROPN
ejpam-1224	244	14	(	(	PUNCT
ejpam-1224	244	15	a	a	PRON
ejpam-1224	244	16	!	!	PUNCT
ejpam-1224	245	1	i	i	PRON
ejpam-1224	245	2	)	)	PUNCT
ejpam-1224	245	3	∗	∗	NOUN
ejpam-1224	245	4	carries	carry	VERB
ejpam-1224	245	5	over	over	ADP
ejpam-1224	245	6	to	to	ADP
ejpam-1224	245	7	a	a	DET
ejpam-1224	245	8	differential	differential	NOUN
ejpam-1224	245	9	d	d	NOUN
ejpam-1224	245	10	:	:	PUNCT
ejpam-1224	245	11	homk(a	homk(a	NOUN
ejpam-1224	245	12	!	!	PUNCT
ejpam-1224	246	1	i+1,a	i+1,a	ADV
ejpam-1224	246	2	)	)	PUNCT
ejpam-1224	246	3	→	→	SYM
ejpam-1224	246	4	homk(a	homk(a	NOUN
ejpam-1224	246	5	!	!	PUNCT
ejpam-1224	247	1	i	i	PRON
ejpam-1224	247	2	,	,	PUNCT
ejpam-1224	247	3	a	a	PRON
ejpam-1224	247	4	)	)	PUNCT
ejpam-1224	247	5	.	.	PUNCT
ejpam-1224	248	1	we	we	PRON
ejpam-1224	248	2	define	define	VERB
ejpam-1224	248	3	d	d	PROPN
ejpam-1224	248	4	as	as	SCONJ
ejpam-1224	248	5	follows	follow	VERB
ejpam-1224	248	6	.	.	PUNCT
ejpam-1224	249	1	let	let	VERB
ejpam-1224	249	2	f	f	PRON
ejpam-1224	249	3	∈	∈	PROPN
ejpam-1224	249	4	homk(a	homk(a	PROPN
ejpam-1224	249	5	!	!	PUNCT
ejpam-1224	250	1	i+1,a	i+1,a	PROPN
ejpam-1224	250	2	)	)	PUNCT
ejpam-1224	250	3	then	then	ADV
ejpam-1224	250	4	d	d	X
ejpam-1224	250	5	f	f	X
ejpam-1224	250	6	∈	∈	PROPN
ejpam-1224	250	7	homk(a	homk(a	NOUN
ejpam-1224	250	8	!	!	PUNCT
ejpam-1224	251	1	i	i	PRON
ejpam-1224	251	2	,	,	PUNCT
ejpam-1224	251	3	a	a	PRON
ejpam-1224	251	4	)	)	PUNCT
ejpam-1224	251	5	is	be	AUX
ejpam-1224	251	6	given	give	VERB
ejpam-1224	251	7	by	by	ADP
ejpam-1224	251	8	d	d	PROPN
ejpam-1224	251	9	f	f	PROPN
ejpam-1224	251	10	(	(	PUNCT
ejpam-1224	251	11	ǎ	ǎ	PROPN
ejpam-1224	251	12	)	)	PUNCT
ejpam-1224	251	13	=	=	PUNCT
ejpam-1224	252	1	∑	∑	PUNCT
ejpam-1224	252	2	α	α	X
ejpam-1224	252	3	f	f	X
ejpam-1224	252	4	(	(	PUNCT
ejpam-1224	252	5	v̌αǎ)vα	v̌αǎ)vα	PROPN
ejpam-1224	252	6	for	for	ADP
ejpam-1224	252	7	ǎ	ǎ	PROPN
ejpam-1224	252	8	∈	∈	PROPN
ejpam-1224	252	9	a	a	PRON
ejpam-1224	252	10	!	!	PUNCT
ejpam-1224	253	1	i	i	PRON
ejpam-1224	253	2	,	,	PUNCT
ejpam-1224	253	3	where	where	SCONJ
ejpam-1224	253	4	�	�	PROPN
ejpam-1224	253	5	vα	vα	VERB
ejpam-1224	253	6	is	be	AUX
ejpam-1224	253	7	any	any	DET
ejpam-1224	253	8	basis	basis	NOUN
ejpam-1224	253	9	of	of	ADP
ejpam-1224	253	10	v	v	NOUN
ejpam-1224	253	11	=	=	SYM
ejpam-1224	253	12	a1	a1	NOUN
ejpam-1224	253	13	,	,	PUNCT
ejpam-1224	253	14	and	and	CCONJ
ejpam-1224	253	15	�	�	PROPN
ejpam-1224	253	16	v̌α	v̌α	PROPN
ejpam-1224	253	17	is	be	AUX
ejpam-1224	253	18	the	the	DET
ejpam-1224	253	19	corresponding	corresponding	ADJ
ejpam-1224	253	20	dual	dual	ADJ
ejpam-1224	253	21	basis	basis	NOUN
ejpam-1224	253	22	of	of	ADP
ejpam-1224	253	23	v	v	NOUN
ejpam-1224	253	24	∗	∗	NOUN
ejpam-1224	253	25	=	=	SYM
ejpam-1224	254	1	a	a	NOUN
ejpam-1224	254	2	!	!	NOUN
ejpam-1224	254	3	1	1	X
ejpam-1224	254	4	.	.	PUNCT
ejpam-1224	255	1	in	in	ADP
ejpam-1224	255	2	fact	fact	NOUN
ejpam-1224	255	3	,	,	PUNCT
ejpam-1224	255	4	this	this	DET
ejpam-1224	255	5	formula	formula	NOUN
ejpam-1224	255	6	for	for	ADP
ejpam-1224	255	7	d	d	PROPN
ejpam-1224	255	8	f	f	PROPN
ejpam-1224	255	9	does	do	AUX
ejpam-1224	255	10	not	not	PART
ejpam-1224	255	11	depend	depend	VERB
ejpam-1224	255	12	on	on	ADP
ejpam-1224	255	13	the	the	DET
ejpam-1224	255	14	choice	choice	NOUN
ejpam-1224	255	15	of	of	ADP
ejpam-1224	255	16	the	the	DET
ejpam-1224	255	17	basis	basis	NOUN
ejpam-1224	255	18	�	�	NOUN
ejpam-1224	255	19	vα	vα	INTJ
ejpam-1224	255	20	.	.	PUNCT
ejpam-1224	256	1	if	if	SCONJ
ejpam-1224	256	2	�	�	PROPN
ejpam-1224	256	3	wα	wα	PROPN
ejpam-1224	256	4	is	be	AUX
ejpam-1224	256	5	another	another	DET
ejpam-1224	256	6	basis	basis	NOUN
ejpam-1224	256	7	for	for	ADP
ejpam-1224	256	8	v	v	NUM
ejpam-1224	256	9	,	,	PUNCT
ejpam-1224	256	10	i.e.	i.e.	X
ejpam-1224	256	11	wα	wα	NOUN
ejpam-1224	256	12	=	=	SYM
ejpam-1224	256	13	σgβαvβ	σgβαvβ	ADJ
ejpam-1224	256	14	,	,	PUNCT
ejpam-1224	256	15	where	where	SCONJ
ejpam-1224	256	16	gβα	gβα	PROPN
ejpam-1224	256	17	is	be	AUX
ejpam-1224	256	18	an	an	DET
ejpam-1224	256	19	invertible	invertible	ADJ
ejpam-1224	256	20	matrix	matrix	NOUN
ejpam-1224	256	21	with	with	ADP
ejpam-1224	256	22	entries	entry	NOUN
ejpam-1224	256	23	in	in	ADP
ejpam-1224	256	24	k	k	PROPN
ejpam-1224	256	25	,	,	PUNCT
ejpam-1224	256	26	then	then	ADV
ejpam-1224	256	27	we	we	PRON
ejpam-1224	256	28	may	may	AUX
ejpam-1224	256	29	also	also	ADV
ejpam-1224	256	30	define	define	VERB
ejpam-1224	256	31	the	the	DET
ejpam-1224	256	32	dual	dual	ADJ
ejpam-1224	256	33	basis	basis	NOUN
ejpam-1224	256	34	of	of	ADP
ejpam-1224	256	35	�	�	PROPN
ejpam-1224	256	36	wα	wα	NOUN
ejpam-1224	256	37	as	as	ADP
ejpam-1224	256	38	�	�	PROPN
ejpam-1224	256	39	w̌α	w̌α	PROPN
ejpam-1224	256	40	=	=	SYM
ejpam-1224	256	41	σhεα	σhεα	PROPN
ejpam-1224	256	42	v̌ε	v̌ε	PROPN
ejpam-1224	256	43	.	.	PUNCT
ejpam-1224	257	1	now	now	ADV
ejpam-1224	257	2	,	,	PUNCT
ejpam-1224	257	3	δαβ	δαβ	NOUN
ejpam-1224	257	4	=	=	NOUN
ejpam-1224	257	5	<	<	X
ejpam-1224	257	6	v̌α	v̌α	NOUN
ejpam-1224	257	7	,	,	PUNCT
ejpam-1224	257	8	vβ	vβ	INTJ
ejpam-1224	257	9	>	>	X
ejpam-1224	257	10	=	=	PROPN
ejpam-1224	257	11	<	<	X
ejpam-1224	257	12	w̌α	w̌α	PROPN
ejpam-1224	257	13	,	,	PUNCT
ejpam-1224	257	14	wβ	wβ	ADP
ejpam-1224	257	15	>	>	PUNCT
ejpam-1224	257	16	=	=	PROPN
ejpam-1224	257	17	<	<	X
ejpam-1224	257	18	w̌α	w̌α	PROPN
ejpam-1224	257	19	,	,	PUNCT
ejpam-1224	257	20	∑	∑	PUNCT
ejpam-1224	257	21	γ	γ	PROPN
ejpam-1224	257	22	gγβ	gγβ	NOUN
ejpam-1224	257	23	vγ	vγ	PROPN
ejpam-1224	257	24	>	>	PUNCT
ejpam-1224	257	25	=	=	PUNCT
ejpam-1224	257	26	∑	∑	PUNCT
ejpam-1224	257	27	γ	γ	PROPN
ejpam-1224	257	28	gγβ	gγβ	PROPN
ejpam-1224	257	29	<	<	X
ejpam-1224	257	30	w̌α	w̌α	PROPN
ejpam-1224	257	31	,	,	PUNCT
ejpam-1224	257	32	vα	vα	ADP
ejpam-1224	257	33	>	>	X
ejpam-1224	257	34	.	.	PUNCT
ejpam-1224	258	1	f.	f.	PROPN
ejpam-1224	258	2	hawwa	hawwa	PROPN
ejpam-1224	258	3	,	,	PUNCT
ejpam-1224	258	4	j.	j.	PROPN
ejpam-1224	258	5	hoffman	hoffman	PROPN
ejpam-1224	258	6	,	,	PUNCT
ejpam-1224	258	7	and	and	CCONJ
ejpam-1224	258	8	h.	h.	PROPN
ejpam-1224	258	9	wang	wang	PROPN
ejpam-1224	258	10	,	,	PUNCT
ejpam-1224	258	11	/	/	SYM
ejpam-1224	258	12	eur	eur	NOUN
ejpam-1224	258	13	.	.	PUNCT
ejpam-1224	259	1	j.	j.	PROPN
ejpam-1224	259	2	pure	pure	PROPN
ejpam-1224	259	3	appl	appl	PROPN
ejpam-1224	259	4	.	.	PROPN
ejpam-1224	259	5	math	math	PROPN
ejpam-1224	259	6	,	,	PUNCT
ejpam-1224	259	7	5	5	NUM
ejpam-1224	259	8	(	(	PUNCT
ejpam-1224	259	9	2012	2012	NUM
ejpam-1224	259	10	)	)	PUNCT
ejpam-1224	259	11	,	,	PUNCT
ejpam-1224	259	12	511	511	NUM
ejpam-1224	259	13	-	-	SYM
ejpam-1224	259	14	539	539	NUM
ejpam-1224	259	15	519	519	NUM
ejpam-1224	259	16	if	if	SCONJ
ejpam-1224	259	17	we	we	PRON
ejpam-1224	259	18	substitute	substitute	VERB
ejpam-1224	259	19	in	in	ADP
ejpam-1224	259	20	for	for	ADP
ejpam-1224	259	21	w̌α	w̌α	PROPN
ejpam-1224	259	22	,	,	PUNCT
ejpam-1224	259	23	we	we	PRON
ejpam-1224	259	24	have	have	VERB
ejpam-1224	259	25	δαβ	δαβ	NOUN
ejpam-1224	259	26	=	=	SYM
ejpam-1224	259	27	∑	∑	PUNCT
ejpam-1224	259	28	γ	γ	PROPN
ejpam-1224	259	29	gγβ	gγβ	PROPN
ejpam-1224	259	30	<	<	X
ejpam-1224	259	31	∑	∑	PUNCT
ejpam-1224	259	32	ε	ε	PROPN
ejpam-1224	259	33	hεα	hεα	PROPN
ejpam-1224	259	34	v̌ε	v̌ε	PROPN
ejpam-1224	259	35	,	,	PUNCT
ejpam-1224	259	36	vγ	vγ	NOUN
ejpam-1224	259	37	>	>	PUNCT
ejpam-1224	259	38	=	=	PUNCT
ejpam-1224	259	39	∑	∑	PUNCT
ejpam-1224	259	40	γ	γ	X
ejpam-1224	259	41	,	,	PUNCT
ejpam-1224	259	42	ε	ε	PROPN
ejpam-1224	259	43	gγβhεα	gγβhεα	PROPN
ejpam-1224	259	44	<	<	X
ejpam-1224	259	45	v̌ε	v̌ε	PROPN
ejpam-1224	259	46	,	,	PUNCT
ejpam-1224	259	47	vγ	vγ	NOUN
ejpam-1224	259	48	>	>	PUNCT
ejpam-1224	259	49	=	=	PUNCT
ejpam-1224	259	50	∑	∑	PUNCT
ejpam-1224	259	51	γ	γ	X
ejpam-1224	259	52	,	,	PUNCT
ejpam-1224	259	53	ε	ε	PROPN
ejpam-1224	259	54	gγβhεαδεγ	gγβhεαδεγ	PROPN
ejpam-1224	259	55	.	.	PUNCT
ejpam-1224	260	1	since	since	SCONJ
ejpam-1224	260	2	δεγ	δεγ	NOUN
ejpam-1224	260	3	vanishes	vanish	VERB
ejpam-1224	260	4	unless	unless	SCONJ
ejpam-1224	260	5	ε=	ε=	ADJ
ejpam-1224	260	6	γ	γ	NOUN
ejpam-1224	260	7	we	we	PRON
ejpam-1224	260	8	may	may	AUX
ejpam-1224	260	9	rewrite	rewrite	VERB
ejpam-1224	260	10	the	the	DET
ejpam-1224	260	11	last	last	ADJ
ejpam-1224	260	12	term	term	NOUN
ejpam-1224	260	13	above	above	ADV
ejpam-1224	260	14	as	as	ADP
ejpam-1224	260	15	δαβ	δαβ	NOUN
ejpam-1224	260	16	=	=	SYM
ejpam-1224	260	17	∑	∑	PUNCT
ejpam-1224	260	18	γ	γ	PROPN
ejpam-1224	260	19	gγβhγα	gγβhγα	NOUN
ejpam-1224	260	20	which	which	PRON
ejpam-1224	260	21	can	can	AUX
ejpam-1224	260	22	be	be	AUX
ejpam-1224	260	23	rewritten	rewrite	VERB
ejpam-1224	260	24	as	as	ADP
ejpam-1224	260	25	δαβ	δαβ	NOUN
ejpam-1224	260	26	=	=	SYM
ejpam-1224	260	27	∑	∑	PUNCT
ejpam-1224	260	28	γ	γ	X
ejpam-1224	260	29	(	(	PUNCT
ejpam-1224	260	30	t	t	PROPN
ejpam-1224	260	31	g)βγhγα	g)βγhγα	PROPN
ejpam-1224	261	1	=	=	PUNCT
ejpam-1224	261	2	(	(	PUNCT
ejpam-1224	261	3	t	t	PROPN
ejpam-1224	261	4	gh)βα	gh)βα	PROPN
ejpam-1224	261	5	.	.	PUNCT
ejpam-1224	262	1	this	this	PRON
ejpam-1224	262	2	shows	show	VERB
ejpam-1224	262	3	that	that	SCONJ
ejpam-1224	262	4	t	t	PROPN
ejpam-1224	262	5	gh=	gh=	VERB
ejpam-1224	262	6	1	1	NUM
ejpam-1224	262	7	,	,	PUNCT
ejpam-1224	262	8	i.e.	i.e.	X
ejpam-1224	262	9	,	,	PUNCT
ejpam-1224	262	10	h=	h=	X
ejpam-1224	262	11	(	(	PUNCT
ejpam-1224	262	12	t	t	NOUN
ejpam-1224	262	13	g)−1	g)−1	NOUN
ejpam-1224	262	14	.	.	PUNCT
ejpam-1224	263	1	so	so	ADV
ejpam-1224	263	2	,	,	PUNCT
ejpam-1224	263	3	if	if	SCONJ
ejpam-1224	263	4	we	we	PRON
ejpam-1224	263	5	have	have	VERB
ejpam-1224	263	6	another	another	DET
ejpam-1224	263	7	basis	basis	NOUN
ejpam-1224	263	8	for	for	ADP
ejpam-1224	263	9	v	v	NOUN
ejpam-1224	263	10	,	,	PUNCT
ejpam-1224	263	11	wα	wα	NOUN
ejpam-1224	263	12	=	=	SYM
ejpam-1224	263	13	∑	∑	PUNCT
ejpam-1224	263	14	β	β	X
ejpam-1224	263	15	gβαvβ	gβαvβ	ADJ
ejpam-1224	263	16	,	,	PUNCT
ejpam-1224	263	17	we	we	PRON
ejpam-1224	263	18	know	know	VERB
ejpam-1224	263	19	that	that	SCONJ
ejpam-1224	263	20	w̌α	w̌α	PROPN
ejpam-1224	263	21	=	=	SYM
ejpam-1224	263	22	∑	∑	PUNCT
ejpam-1224	263	23	γ	γ	X
ejpam-1224	263	24	(	(	PUNCT
ejpam-1224	263	25	t	t	NOUN
ejpam-1224	263	26	g)−1	g)−1	NOUN
ejpam-1224	263	27	γα	γα	ADP
ejpam-1224	263	28	v̌γ	v̌γ	PROPN
ejpam-1224	263	29	and	and	CCONJ
ejpam-1224	263	30	we	we	PRON
ejpam-1224	263	31	would	would	AUX
ejpam-1224	263	32	like	like	VERB
ejpam-1224	263	33	to	to	PART
ejpam-1224	263	34	show	show	VERB
ejpam-1224	263	35	that	that	SCONJ
ejpam-1224	263	36	d	d	PROPN
ejpam-1224	263	37	f	f	X
ejpam-1224	263	38	(	(	PUNCT
ejpam-1224	263	39	ǎ	ǎ	PROPN
ejpam-1224	263	40	)	)	PUNCT
ejpam-1224	263	41	=	=	PUNCT
ejpam-1224	263	42	∑	∑	PUNCT
ejpam-1224	263	43	α	α	X
ejpam-1224	263	44	f	f	X
ejpam-1224	263	45	(	(	PUNCT
ejpam-1224	263	46	v̌αǎ)vα	v̌αǎ)vα	PROPN
ejpam-1224	263	47	=	=	PUNCT
ejpam-1224	263	48	∑	∑	PUNCT
ejpam-1224	263	49	α	α	X
ejpam-1224	263	50	f	f	X
ejpam-1224	263	51	(	(	PUNCT
ejpam-1224	263	52	w̌αǎ)wα	w̌αǎ)wα	X
ejpam-1224	263	53	.	.	PUNCT
ejpam-1224	263	54	observe	observe	VERB
ejpam-1224	263	55	that	that	SCONJ
ejpam-1224	263	56	∑	∑	PROPN
ejpam-1224	263	57	α	α	PROPN
ejpam-1224	263	58	f	f	X
ejpam-1224	263	59	(	(	PUNCT
ejpam-1224	263	60	w̌αǎ)wα	w̌αǎ)wα	X
ejpam-1224	263	61	=	=	PUNCT
ejpam-1224	263	62	∑	∑	PUNCT
ejpam-1224	263	63	α	α	X
ejpam-1224	263	64	f	f	PROPN
ejpam-1224	263	65	(	(	PUNCT
ejpam-1224	263	66	∑	∑	PROPN
ejpam-1224	263	67	γ	γ	X
ejpam-1224	263	68	(	(	PUNCT
ejpam-1224	263	69	t	t	NOUN
ejpam-1224	263	70	g)−1	g)−1	NOUN
ejpam-1224	263	71	γα	γα	ADP
ejpam-1224	263	72	v̌γǎ	v̌γǎ	NOUN
ejpam-1224	263	73	)	)	PUNCT
ejpam-1224	263	74	∑	∑	ADP
ejpam-1224	263	75	β	β	X
ejpam-1224	263	76	gβαvβ	gβαvβ	ADJ
ejpam-1224	263	77	allowing	allow	VERB
ejpam-1224	263	78	us	we	PRON
ejpam-1224	263	79	to	to	PART
ejpam-1224	263	80	simplify	simplify	VERB
ejpam-1224	263	81	to	to	ADP
ejpam-1224	263	82	∑	∑	PROPN
ejpam-1224	263	83	α	α	X
ejpam-1224	263	84	f	f	X
ejpam-1224	263	85	(	(	PUNCT
ejpam-1224	263	86	w̌α	w̌α	PROPN
ejpam-1224	263	87	ǎ)wα	ǎ)wα	PROPN
ejpam-1224	263	88	=	=	PROPN
ejpam-1224	263	89	∑	∑	PUNCT
ejpam-1224	263	90	α	α	X
ejpam-1224	263	91	,	,	PUNCT
ejpam-1224	263	92	β	β	X
ejpam-1224	263	93	,	,	PUNCT
ejpam-1224	263	94	γ	γ	X
ejpam-1224	263	95	(	(	PUNCT
ejpam-1224	263	96	t	t	NOUN
ejpam-1224	263	97	g)−1	g)−1	NOUN
ejpam-1224	263	98	γα	γα	ADP
ejpam-1224	263	99	gβα	gβα	PROPN
ejpam-1224	263	100	f	f	PROPN
ejpam-1224	263	101	(	(	PUNCT
ejpam-1224	263	102	v̌γǎ)v̌β	v̌γǎ)v̌β	PROPN
ejpam-1224	263	103	=	=	SYM
ejpam-1224	263	104	∑	∑	PUNCT
ejpam-1224	263	105	α	α	X
ejpam-1224	263	106	,	,	PUNCT
ejpam-1224	263	107	β	β	X
ejpam-1224	263	108	,	,	PUNCT
ejpam-1224	263	109	γ	γ	X
ejpam-1224	263	110	gβαg−1	gβαg−1	PROPN
ejpam-1224	263	111	αγ	αγ	PROPN
ejpam-1224	263	112	f	f	PROPN
ejpam-1224	263	113	(	(	PUNCT
ejpam-1224	263	114	v̌γǎ)v̌β	v̌γǎ)v̌β	PROPN
ejpam-1224	263	115	.	.	PUNCT
ejpam-1224	264	1	since	since	SCONJ
ejpam-1224	264	2	σgβα(g	σgβα(g	NOUN
ejpam-1224	264	3	−1)αγ	−1)αγ	PROPN
ejpam-1224	264	4	=	=	SYM
ejpam-1224	264	5	δ	δ	PROPN
ejpam-1224	264	6	γ	γ	X
ejpam-1224	264	7	β	β	X
ejpam-1224	264	8	we	we	PRON
ejpam-1224	264	9	may	may	AUX
ejpam-1224	264	10	conclude	conclude	VERB
ejpam-1224	264	11	that	that	SCONJ
ejpam-1224	264	12	∑	∑	PROPN
ejpam-1224	264	13	α	α	PROPN
ejpam-1224	264	14	f	f	X
ejpam-1224	264	15	(	(	PUNCT
ejpam-1224	264	16	w̌αǎ)wα	w̌αǎ)wα	X
ejpam-1224	264	17	=	=	SYM
ejpam-1224	264	18	∑	∑	PUNCT
ejpam-1224	264	19	β	β	X
ejpam-1224	264	20	,	,	PUNCT
ejpam-1224	264	21	γ	γ	X
ejpam-1224	264	22	(	(	PUNCT
ejpam-1224	264	23	∑	∑	PROPN
ejpam-1224	264	24	α	α	DET
ejpam-1224	264	25	gβα(g	gβα(g	PROPN
ejpam-1224	264	26	−1)αγ	−1)αγ	PROPN
ejpam-1224	264	27	)	)	PUNCT
ejpam-1224	264	28	f	f	PROPN
ejpam-1224	264	29	(	(	PUNCT
ejpam-1224	264	30	v̌γǎ)v̌β	v̌γǎ)v̌β	PROPN
ejpam-1224	264	31	=	=	SYM
ejpam-1224	264	32	∑	∑	PUNCT
ejpam-1224	264	33	β	β	X
ejpam-1224	264	34	f	f	X
ejpam-1224	264	35	(	(	PUNCT
ejpam-1224	264	36	v̌γǎ)v̌β	v̌γǎ)v̌β	PROPN
ejpam-1224	264	37	.	.	PUNCT
ejpam-1224	265	1	now	now	ADV
ejpam-1224	265	2	we	we	PRON
ejpam-1224	265	3	will	will	AUX
ejpam-1224	265	4	define	define	VERB
ejpam-1224	265	5	δ	δ	PROPN
ejpam-1224	265	6	so	so	SCONJ
ejpam-1224	265	7	that	that	SCONJ
ejpam-1224	265	8	the	the	DET
ejpam-1224	265	9	following	follow	VERB
ejpam-1224	265	10	commutes	commute	NOUN
ejpam-1224	265	11	:	:	PUNCT
ejpam-1224	265	12	a⊗	a⊗	NOUN
ejpam-1224	265	13	(	(	PUNCT
ejpam-1224	265	14	a	a	X
ejpam-1224	265	15	!	!	PUNCT
ejpam-1224	265	16	i+1	i+1	NUM
ejpam-1224	265	17	)	)	PUNCT
ejpam-1224	265	18	∗	∗	NOUN
ejpam-1224	265	19	δ	δ	NOUN
ejpam-1224	265	20	−−−→	−−−→	ADJ
ejpam-1224	265	21	a⊗	a⊗	NOUN
ejpam-1224	265	22	(	(	PUNCT
ejpam-1224	265	23	a	a	NOUN
ejpam-1224	265	24	!	!	PUNCT
ejpam-1224	266	1	i	i	PRON
ejpam-1224	266	2	)	)	PUNCT
ejpam-1224	266	3	∗	∗	PROPN
ejpam-1224	266	4	φ	φ	PROPN
ejpam-1224	266	5	y	y	PROPN
ejpam-1224	266	6	φ	φ	PROPN
ejpam-1224	266	7	y	y	PROPN
ejpam-1224	266	8	hom(a	hom(a	PROPN
ejpam-1224	266	9	!	!	PUNCT
ejpam-1224	267	1	i+1	i+1	NUM
ejpam-1224	267	2	,	,	PUNCT
ejpam-1224	268	1	a	a	X
ejpam-1224	268	2	)	)	PUNCT
ejpam-1224	268	3	d	d	SYM
ejpam-1224	268	4	−−−→	−−−→	ADJ
ejpam-1224	268	5	hom(a	hom(a	X
ejpam-1224	268	6	!	!	PUNCT
ejpam-1224	269	1	i	i	PRON
ejpam-1224	269	2	,	,	PUNCT
ejpam-1224	269	3	a	a	PRON
ejpam-1224	269	4	)	)	PUNCT
ejpam-1224	269	5	.	.	PUNCT
ejpam-1224	270	1	f.	f.	PROPN
ejpam-1224	270	2	hawwa	hawwa	PROPN
ejpam-1224	270	3	,	,	PUNCT
ejpam-1224	270	4	j.	j.	PROPN
ejpam-1224	270	5	hoffman	hoffman	PROPN
ejpam-1224	270	6	,	,	PUNCT
ejpam-1224	270	7	and	and	CCONJ
ejpam-1224	270	8	h.	h.	PROPN
ejpam-1224	270	9	wang	wang	PROPN
ejpam-1224	270	10	,	,	PUNCT
ejpam-1224	270	11	/	/	SYM
ejpam-1224	270	12	eur	eur	NOUN
ejpam-1224	270	13	.	.	PUNCT
ejpam-1224	271	1	j.	j.	PROPN
ejpam-1224	271	2	pure	pure	PROPN
ejpam-1224	271	3	appl	appl	PROPN
ejpam-1224	271	4	.	.	PROPN
ejpam-1224	271	5	math	math	PROPN
ejpam-1224	271	6	,	,	PUNCT
ejpam-1224	271	7	5	5	NUM
ejpam-1224	271	8	(	(	PUNCT
ejpam-1224	271	9	2012	2012	NUM
ejpam-1224	271	10	)	)	PUNCT
ejpam-1224	271	11	,	,	PUNCT
ejpam-1224	271	12	511	511	NUM
ejpam-1224	271	13	-	-	SYM
ejpam-1224	271	14	539	539	NUM
ejpam-1224	271	15	520	520	NUM
ejpam-1224	271	16	since	since	SCONJ
ejpam-1224	271	17	an	an	DET
ejpam-1224	271	18	element	element	NOUN
ejpam-1224	271	19	of	of	ADP
ejpam-1224	271	20	a⊗	a⊗	NOUN
ejpam-1224	271	21	(	(	PUNCT
ejpam-1224	271	22	a	a	X
ejpam-1224	271	23	!	!	PUNCT
ejpam-1224	271	24	i+1	i+1	NUM
ejpam-1224	271	25	)	)	PUNCT
ejpam-1224	271	26	∗	∗	NOUN
ejpam-1224	271	27	is	be	AUX
ejpam-1224	271	28	a	a	DET
ejpam-1224	271	29	sum	sum	NOUN
ejpam-1224	271	30	of	of	ADP
ejpam-1224	271	31	tensors	tensor	NOUN
ejpam-1224	271	32	a⊗λ	a⊗λ	NOUN
ejpam-1224	271	33	,	,	PUNCT
ejpam-1224	271	34	a	a	DET
ejpam-1224	271	35	∈	∈	PROPN
ejpam-1224	271	36	a	a	PRON
ejpam-1224	271	37	,	,	PUNCT
ejpam-1224	271	38	λ	λ	PROPN
ejpam-1224	271	39	∈	∈	PROPN
ejpam-1224	271	40	(	(	PUNCT
ejpam-1224	271	41	a	a	NOUN
ejpam-1224	271	42	!	!	NOUN
ejpam-1224	271	43	i+1	i+1	NUM
ejpam-1224	271	44	)	)	PUNCT
ejpam-1224	271	45	∗	∗	NOUN
ejpam-1224	271	46	=	=	SYM
ejpam-1224	271	47	homk(a	homk(a	NOUN
ejpam-1224	271	48	!	!	PUNCT
ejpam-1224	272	1	i+1	i+1	ADV
ejpam-1224	272	2	,	,	PUNCT
ejpam-1224	272	3	k	k	X
ejpam-1224	272	4	)	)	PUNCT
ejpam-1224	272	5	it	it	PRON
ejpam-1224	272	6	is	be	AUX
ejpam-1224	272	7	enough	enough	ADJ
ejpam-1224	272	8	to	to	PART
ejpam-1224	272	9	define	define	VERB
ejpam-1224	272	10	δ(a⊗λ	δ(a⊗λ	NOUN
ejpam-1224	272	11	)	)	PUNCT
ejpam-1224	272	12	.	.	PUNCT
ejpam-1224	273	1	set	set	PROPN
ejpam-1224	273	2	δ(a⊗λ	δ(a⊗λ	NOUN
ejpam-1224	273	3	)	)	PUNCT
ejpam-1224	273	4	=	=	PUNCT
ejpam-1224	274	1	∑	∑	PUNCT
ejpam-1224	274	2	α	α	PROPN
ejpam-1224	274	3	avα⊗λα	avα⊗λα	PROPN
ejpam-1224	274	4	,	,	PUNCT
ejpam-1224	274	5	where	where	SCONJ
ejpam-1224	274	6	λα	λα	ADP
ejpam-1224	274	7	=	=	X
ejpam-1224	274	8	λ(v̌α	λ(v̌α	PROPN
ejpam-1224	274	9	·	·	PUNCT
ejpam-1224	274	10	−	−	NUM
ejpam-1224	274	11	)	)	PUNCT
ejpam-1224	274	12	∈	∈	PROPN
ejpam-1224	274	13	(	(	PUNCT
ejpam-1224	274	14	a	a	NOUN
ejpam-1224	274	15	!	!	PUNCT
ejpam-1224	275	1	i	i	PRON
ejpam-1224	275	2	)	)	PUNCT
ejpam-1224	275	3	∗	∗	NOUN
ejpam-1224	275	4	=	=	SYM
ejpam-1224	275	5	homk(a	homk(a	NOUN
ejpam-1224	275	6	!	!	PUNCT
ejpam-1224	276	1	i	i	PRON
ejpam-1224	276	2	,	,	PUNCT
ejpam-1224	276	3	k	k	X
ejpam-1224	276	4	)	)	PUNCT
ejpam-1224	276	5	is	be	AUX
ejpam-1224	276	6	the	the	DET
ejpam-1224	276	7	map	map	NOUN
ejpam-1224	276	8	ǎ	ǎ	PROPN
ejpam-1224	276	9	7→	7→	NUM
ejpam-1224	276	10	λ(v̌αǎ	λ(v̌αǎ	NOUN
ejpam-1224	276	11	)	)	PUNCT
ejpam-1224	276	12	.	.	PUNCT
ejpam-1224	277	1	let	let	VERB
ejpam-1224	277	2	f	f	PROPN
ejpam-1224	277	3	=	=	SYM
ejpam-1224	277	4	φ(a	φ(a	PROPN
ejpam-1224	277	5	⊗	⊗	PROPN
ejpam-1224	277	6	λ	λ	PROPN
ejpam-1224	277	7	)	)	PUNCT
ejpam-1224	277	8	and	and	CCONJ
ejpam-1224	277	9	recall	recall	VERB
ejpam-1224	277	10	that	that	SCONJ
ejpam-1224	277	11	φ(a⊗λ	φ(a⊗λ	NOUN
ejpam-1224	277	12	)	)	PUNCT
ejpam-1224	277	13	(	(	PUNCT
ejpam-1224	277	14	b̌	b̌	PROPN
ejpam-1224	277	15	)	)	PUNCT
ejpam-1224	278	1	=	=	PUNCT
ejpam-1224	278	2	λ	λ	PROPN
ejpam-1224	278	3	(	(	PUNCT
ejpam-1224	278	4	b̌)(a	b̌)(a	PROPN
ejpam-1224	278	5	)	)	PUNCT
ejpam-1224	278	6	giving	give	VERB
ejpam-1224	278	7	us	we	PRON
ejpam-1224	278	8	,	,	PUNCT
ejpam-1224	278	9	dφ(a⊗λ)(ǎ	dφ(a⊗λ)(ǎ	PROPN
ejpam-1224	278	10	)	)	PUNCT
ejpam-1224	278	11	=	=	PUNCT
ejpam-1224	279	1	d	d	X
ejpam-1224	279	2	f	f	X
ejpam-1224	279	3	(	(	PUNCT
ejpam-1224	279	4	ǎ	ǎ	PROPN
ejpam-1224	279	5	)	)	PUNCT
ejpam-1224	279	6	=	=	PUNCT
ejpam-1224	279	7	∑	∑	PUNCT
ejpam-1224	279	8	α	α	X
ejpam-1224	279	9	f	f	X
ejpam-1224	279	10	(	(	PUNCT
ejpam-1224	279	11	v̌αǎ)vα	v̌αǎ)vα	PROPN
ejpam-1224	279	12	=	=	PUNCT
ejpam-1224	279	13	∑	∑	PUNCT
ejpam-1224	279	14	α	α	PROPN
ejpam-1224	279	15	φ(a⊗λ)(v̌αǎ)vα	φ(a⊗λ)(v̌αǎ)vα	PROPN
ejpam-1224	279	16	,	,	PUNCT
ejpam-1224	279	17	so	so	SCONJ
ejpam-1224	279	18	we	we	PRON
ejpam-1224	279	19	have	have	AUX
ejpam-1224	279	20	dφ(a⊗λ)(ǎ	dφ(a⊗λ)(ǎ	VERB
ejpam-1224	279	21	)	)	PUNCT
ejpam-1224	280	1	=	=	PUNCT
ejpam-1224	280	2	∑	∑	PUNCT
ejpam-1224	280	3	α	α	X
ejpam-1224	280	4	φ(a⊗λ)(ǎv̌α)vα	φ(a⊗λ)(ǎv̌α)vα	PUNCT
ejpam-1224	281	1	=	=	PUNCT
ejpam-1224	281	2	∑	∑	PUNCT
ejpam-1224	281	3	α	α	DET
ejpam-1224	281	4	λ(ǎv̌α)avα	λ(ǎv̌α)avα	NOUN
ejpam-1224	281	5	.	.	PUNCT
ejpam-1224	282	1	now	now	ADV
ejpam-1224	282	2	to	to	PART
ejpam-1224	282	3	verify	verify	VERB
ejpam-1224	282	4	that	that	SCONJ
ejpam-1224	282	5	the	the	DET
ejpam-1224	282	6	diagram	diagram	NOUN
ejpam-1224	282	7	commutes	commute	NOUN
ejpam-1224	282	8	,	,	PUNCT
ejpam-1224	282	9	we	we	PRON
ejpam-1224	282	10	must	must	AUX
ejpam-1224	282	11	check	check	VERB
ejpam-1224	282	12	that	that	PRON
ejpam-1224	282	13	dφ(a⊗λ)(ǎ	dφ(a⊗λ)(ǎ	PROPN
ejpam-1224	282	14	)	)	PUNCT
ejpam-1224	282	15	=	=	SYM
ejpam-1224	282	16	φδ(a⊗λ)(ǎ	φδ(a⊗λ)(ǎ	PROPN
ejpam-1224	282	17	)	)	PUNCT
ejpam-1224	282	18	.	.	PUNCT
ejpam-1224	283	1	given	give	VERB
ejpam-1224	283	2	that	that	DET
ejpam-1224	283	3	δ(a⊗λ	δ(a⊗λ	NOUN
ejpam-1224	283	4	)	)	PUNCT
ejpam-1224	283	5	=	=	PUNCT
ejpam-1224	283	6	∑	∑	PUNCT
ejpam-1224	283	7	α	α	X
ejpam-1224	283	8	avα⊗λα	avα⊗λα	NOUN
ejpam-1224	283	9	we	we	PRON
ejpam-1224	283	10	know	know	VERB
ejpam-1224	283	11	the	the	DET
ejpam-1224	283	12	following	following	NOUN
ejpam-1224	283	13	,	,	PUNCT
ejpam-1224	283	14	φδ(a⊗λ)(ǎ	φδ(a⊗λ)(ǎ	PROPN
ejpam-1224	283	15	)	)	PUNCT
ejpam-1224	283	16	=	=	PUNCT
ejpam-1224	284	1	∑	∑	PUNCT
ejpam-1224	284	2	α	α	NOUN
ejpam-1224	284	3	φ(avα	φ(avα	NOUN
ejpam-1224	284	4	⊗λα)(ǎ	⊗λα)(ǎ	PROPN
ejpam-1224	284	5	)	)	PUNCT
ejpam-1224	284	6	=	=	PUNCT
ejpam-1224	285	1	∑	∑	PUNCT
ejpam-1224	285	2	α	α	X
ejpam-1224	285	3	λα(ǎ)avα	λα(ǎ)avα	X
ejpam-1224	285	4	=	=	PUNCT
ejpam-1224	285	5	∑	∑	PUNCT
ejpam-1224	285	6	α	α	NOUN
ejpam-1224	285	7	λ(v̌αǎ)avα	λ(v̌αǎ)avα	NOUN
ejpam-1224	285	8	showing	show	VERB
ejpam-1224	285	9	that	that	SCONJ
ejpam-1224	285	10	the	the	DET
ejpam-1224	285	11	diagram	diagram	NOUN
ejpam-1224	285	12	commutes	commute	NOUN
ejpam-1224	285	13	.	.	PUNCT
ejpam-1224	286	1	now	now	ADV
ejpam-1224	286	2	we	we	PRON
ejpam-1224	286	3	will	will	AUX
ejpam-1224	286	4	need	need	VERB
ejpam-1224	286	5	to	to	PART
ejpam-1224	286	6	show	show	VERB
ejpam-1224	286	7	that	that	PRON
ejpam-1224	286	8	d2	d2	PROPN
ejpam-1224	286	9	=	=	SYM
ejpam-1224	286	10	δ2	δ2	VERB
ejpam-1224	286	11	=	=	NOUN
ejpam-1224	286	12	0	0	NUM
ejpam-1224	286	13	.	.	PUNCT
ejpam-1224	287	1	if	if	SCONJ
ejpam-1224	287	2	we	we	PRON
ejpam-1224	287	3	can	can	AUX
ejpam-1224	287	4	show	show	VERB
ejpam-1224	287	5	that	that	SCONJ
ejpam-1224	287	6	δ2	δ2	VERB
ejpam-1224	287	7	=	=	SYM
ejpam-1224	287	8	0	0	NUM
ejpam-1224	287	9	then	then	ADV
ejpam-1224	287	10	by	by	ADP
ejpam-1224	287	11	duality	duality	NOUN
ejpam-1224	287	12	we	we	PRON
ejpam-1224	287	13	will	will	AUX
ejpam-1224	287	14	know	know	VERB
ejpam-1224	287	15	that	that	DET
ejpam-1224	287	16	d2	d2	PROPN
ejpam-1224	287	17	=	=	SYM
ejpam-1224	287	18	0	0	PROPN
ejpam-1224	287	19	.	.	PUNCT
ejpam-1224	288	1	the	the	DET
ejpam-1224	288	2	map	map	NOUN
ejpam-1224	288	3	δ	δ	PROPN
ejpam-1224	288	4	is	be	AUX
ejpam-1224	288	5	defined	define	VERB
ejpam-1224	288	6	as	as	SCONJ
ejpam-1224	288	7	follows	follow	VERB
ejpam-1224	288	8	δ(a⊗λ	δ(a⊗λ	NOUN
ejpam-1224	288	9	)	)	PUNCT
ejpam-1224	288	10	=	=	PUNCT
ejpam-1224	288	11	∑	∑	PUNCT
ejpam-1224	288	12	α	α	X
ejpam-1224	288	13	avα⊗λ(v̌α	avα⊗λ(v̌α	PROPN
ejpam-1224	288	14	·	·	PUNCT
ejpam-1224	288	15	−	−	NUM
ejpam-1224	288	16	)	)	PUNCT
ejpam-1224	288	17	,	,	PUNCT
ejpam-1224	288	18	where	where	SCONJ
ejpam-1224	288	19	δ	δ	PROPN
ejpam-1224	288	20	:	:	PUNCT
ejpam-1224	288	21	a⊗k	a⊗k	PROPN
ejpam-1224	288	22	(	(	PUNCT
ejpam-1224	288	23	a	a	PRON
ejpam-1224	288	24	!	!	PUNCT
ejpam-1224	288	25	i+1	i+1	NUM
ejpam-1224	288	26	)	)	PUNCT
ejpam-1224	288	27	∗→	∗→	PROPN
ejpam-1224	288	28	a⊗k	a⊗k	PROPN
ejpam-1224	288	29	(	(	PUNCT
ejpam-1224	288	30	a	a	PRON
ejpam-1224	288	31	!	!	PUNCT
ejpam-1224	289	1	i	i	PRON
ejpam-1224	289	2	)	)	PUNCT
ejpam-1224	289	3	∗.	∗.	PROPN
ejpam-1224	289	4	now	now	ADV
ejpam-1224	289	5	define	define	VERB
ejpam-1224	289	6	δ′	δ′	NOUN
ejpam-1224	289	7	:	:	PUNCT
ejpam-1224	289	8	a⊗k	a⊗k	PROPN
ejpam-1224	289	9	(	(	PUNCT
ejpam-1224	289	10	a	a	PROPN
ejpam-1224	289	11	!	!	PUNCT
ejpam-1224	290	1	i	i	PRON
ejpam-1224	290	2	)	)	PUNCT
ejpam-1224	290	3	→	→	SYM
ejpam-1224	290	4	a⊗k	a⊗k	PROPN
ejpam-1224	290	5	(	(	PUNCT
ejpam-1224	290	6	a	a	PRON
ejpam-1224	290	7	!	!	PUNCT
ejpam-1224	290	8	i+1	i+1	NUM
ejpam-1224	290	9	)	)	PUNCT
ejpam-1224	290	10	by	by	ADP
ejpam-1224	290	11	δ′	δ′	PROPN
ejpam-1224	290	12	=	=	SYM
ejpam-1224	291	1	xe	xe	PROPN
ejpam-1224	291	2	where	where	SCONJ
ejpam-1224	291	3	e	e	NOUN
ejpam-1224	291	4	=	=	SYM
ejpam-1224	291	5	∑	∑	PROPN
ejpam-1224	291	6	v̌α	v̌α	PROPN
ejpam-1224	291	7	⊗	⊗	NOUN
ejpam-1224	291	8	vα	vα	INTJ
ejpam-1224	291	9	∈	∈	PROPN
ejpam-1224	291	10	a	a	PRON
ejpam-1224	291	11	!	!	PUNCT
ejpam-1224	292	1	⊗	⊗	PROPN
ejpam-1224	292	2	a.	a.	NOUN
ejpam-1224	293	1	now	now	ADV
ejpam-1224	293	2	we	we	PRON
ejpam-1224	293	3	want	want	VERB
ejpam-1224	293	4	to	to	PART
ejpam-1224	293	5	show	show	VERB
ejpam-1224	293	6	that	that	DET
ejpam-1224	293	7	a⊗	a⊗	NOUN
ejpam-1224	293	8	a	a	X
ejpam-1224	293	9	!	!	PUNCT
ejpam-1224	294	1	i+1	i+1	PRON
ejpam-1224	294	2	=	=	PUNCT
ejpam-1224	295	1	[	[	X
ejpam-1224	295	2	homk(a	homk(a	X
ejpam-1224	295	3	!	!	PUNCT
ejpam-1224	296	1	i+1	i+1	NUM
ejpam-1224	296	2	,	,	PUNCT
ejpam-1224	296	3	a)]∗.	a)]∗.	PROPN
ejpam-1224	296	4	since	since	SCONJ
ejpam-1224	296	5	any	any	DET
ejpam-1224	296	6	k	k	ADJ
ejpam-1224	296	7	-	-	PUNCT
ejpam-1224	296	8	linear	linear	ADJ
ejpam-1224	296	9	map	map	NOUN
ejpam-1224	296	10	can	can	AUX
ejpam-1224	296	11	be	be	AUX
ejpam-1224	296	12	extended	extend	VERB
ejpam-1224	296	13	canonically	canonically	ADV
ejpam-1224	296	14	to	to	ADP
ejpam-1224	296	15	an	an	DET
ejpam-1224	296	16	a	a	DET
ejpam-1224	296	17	-	-	PUNCT
ejpam-1224	296	18	linear	linear	NOUN
ejpam-1224	296	19	map	map	NOUN
ejpam-1224	296	20	,	,	PUNCT
ejpam-1224	296	21	and	and	CCONJ
ejpam-1224	296	22	any	any	DET
ejpam-1224	296	23	a	a	DET
ejpam-1224	296	24	-	-	PUNCT
ejpam-1224	296	25	linear	linear	NOUN
ejpam-1224	296	26	map	map	NOUN
ejpam-1224	296	27	comes	come	VERB
ejpam-1224	296	28	from	from	ADP
ejpam-1224	296	29	a	a	DET
ejpam-1224	296	30	k	k	ADJ
ejpam-1224	296	31	-	-	PUNCT
ejpam-1224	296	32	linear	linear	ADJ
ejpam-1224	296	33	map	map	NOUN
ejpam-1224	296	34	,	,	PUNCT
ejpam-1224	296	35	we	we	PRON
ejpam-1224	296	36	know	know	VERB
ejpam-1224	296	37	that	that	SCONJ
ejpam-1224	296	38	(	(	PUNCT
ejpam-1224	296	39	a	a	X
ejpam-1224	296	40	!	!	PUNCT
ejpam-1224	297	1	i	i	NOUN
ejpam-1224	297	2	)	)	PUNCT
ejpam-1224	297	3	∗⊗	∗⊗	NOUN
ejpam-1224	297	4	a=	a=	NOUN
ejpam-1224	297	5	homa(a	homa(a	PROPN
ejpam-1224	297	6	!	!	PUNCT
ejpam-1224	298	1	i	i	PRON
ejpam-1224	298	2	⊗	⊗	VERB
ejpam-1224	298	3	a	a	PRON
ejpam-1224	298	4	,	,	PUNCT
ejpam-1224	298	5	a	a	NOUN
ejpam-1224	298	6	)	)	PUNCT
ejpam-1224	298	7	=	=	SYM
ejpam-1224	298	8	homk(a	homk(a	NOUN
ejpam-1224	298	9	!	!	PUNCT
ejpam-1224	299	1	i	i	PRON
ejpam-1224	299	2	,	,	PUNCT
ejpam-1224	299	3	a	a	PRON
ejpam-1224	299	4	)	)	PUNCT
ejpam-1224	299	5	.	.	PUNCT
ejpam-1224	300	1	so	so	ADV
ejpam-1224	300	2	a⊗	a⊗	PROPN
ejpam-1224	300	3	a	a	PRON
ejpam-1224	300	4	!	!	PUNCT
ejpam-1224	300	5	i+1	i+1	NUM
ejpam-1224	300	6	and	and	CCONJ
ejpam-1224	300	7	a⊗	a⊗	PROPN
ejpam-1224	300	8	(	(	PUNCT
ejpam-1224	300	9	a	a	X
ejpam-1224	300	10	!	!	PUNCT
ejpam-1224	300	11	i+1	i+1	NUM
ejpam-1224	300	12	)	)	PUNCT
ejpam-1224	300	13	∗	∗	NOUN
ejpam-1224	300	14	are	be	AUX
ejpam-1224	300	15	dual	dual	ADJ
ejpam-1224	300	16	in	in	ADP
ejpam-1224	300	17	the	the	DET
ejpam-1224	300	18	a	a	DET
ejpam-1224	300	19	-	-	PUNCT
ejpam-1224	300	20	linear	linear	NOUN
ejpam-1224	300	21	sense	sense	NOUN
ejpam-1224	300	22	.	.	PUNCT
ejpam-1224	301	1	now	now	ADV
ejpam-1224	301	2	since	since	SCONJ
ejpam-1224	301	3	(	(	PUNCT
ejpam-1224	301	4	δ′)2	δ′)2	NOUN
ejpam-1224	301	5	x	x	PUNCT
ejpam-1224	301	6	=	=	PUNCT
ejpam-1224	301	7	xe2	xe2	PROPN
ejpam-1224	301	8	and	and	CCONJ
ejpam-1224	301	9	assuming	assume	VERB
ejpam-1224	301	10	that	that	SCONJ
ejpam-1224	301	11	e2	e2	PROPN
ejpam-1224	301	12	=	=	PUNCT
ejpam-1224	301	13	0	0	PROPN
ejpam-1224	301	14	that	that	PRON
ejpam-1224	301	15	implies	imply	VERB
ejpam-1224	301	16	that	that	SCONJ
ejpam-1224	301	17	(	(	PUNCT
ejpam-1224	301	18	δ′)2	δ′)2	PROPN
ejpam-1224	301	19	=	=	SYM
ejpam-1224	301	20	0	0	PUNCT
ejpam-1224	301	21	implying	imply	VERB
ejpam-1224	301	22	that	that	SCONJ
ejpam-1224	301	23	δ2	δ2	VERB
ejpam-1224	301	24	=	=	SYM
ejpam-1224	301	25	0	0	NUM
ejpam-1224	301	26	which	which	PRON
ejpam-1224	301	27	,	,	PUNCT
ejpam-1224	301	28	by	by	ADP
ejpam-1224	301	29	duality	duality	NOUN
ejpam-1224	301	30	,	,	PUNCT
ejpam-1224	301	31	tells	tell	VERB
ejpam-1224	301	32	us	we	PRON
ejpam-1224	301	33	that	that	DET
ejpam-1224	301	34	d2	d2	PROPN
ejpam-1224	301	35	=	=	NOUN
ejpam-1224	301	36	0	0	PROPN
ejpam-1224	301	37	.	.	PUNCT
ejpam-1224	301	38	now	now	ADV
ejpam-1224	301	39	to	to	PART
ejpam-1224	301	40	show	show	VERB
ejpam-1224	301	41	that	that	SCONJ
ejpam-1224	301	42	e2	e2	PROPN
ejpam-1224	301	43	=	=	SYM
ejpam-1224	301	44	0	0	NUM
ejpam-1224	301	45	first	first	ADJ
ejpam-1224	301	46	note	note	NOUN
ejpam-1224	301	47	that	that	SCONJ
ejpam-1224	301	48	a	a	DET
ejpam-1224	301	49	!	!	NOUN
ejpam-1224	301	50	2	2	NUM
ejpam-1224	301	51	⊗	⊗	PROPN
ejpam-1224	301	52	a2	a2	PROPN
ejpam-1224	301	53	=	=	PUNCT
ejpam-1224	301	54	(	(	PUNCT
ejpam-1224	301	55	(	(	PUNCT
ejpam-1224	301	56	v	v	NOUN
ejpam-1224	301	57	⊗2)∗/r⊥)⊗	⊗2)∗/r⊥)⊗	PROPN
ejpam-1224	301	58	(	(	PUNCT
ejpam-1224	301	59	v⊗2	v⊗2	NOUN
ejpam-1224	301	60	/	/	SYM
ejpam-1224	301	61	r	r	NOUN
ejpam-1224	301	62	)	)	PUNCT
ejpam-1224	301	63	=	=	SYM
ejpam-1224	301	64	r∗	r∗	PROPN
ejpam-1224	301	65	⊗	⊗	PROPN
ejpam-1224	301	66	(	(	PUNCT
ejpam-1224	301	67	v⊗2	v⊗2	NOUN
ejpam-1224	301	68	/	/	SYM
ejpam-1224	301	69	r	r	NOUN
ejpam-1224	301	70	)	)	PUNCT
ejpam-1224	301	71	=	=	SYM
ejpam-1224	301	72	hom(r	hom(r	PROPN
ejpam-1224	301	73	,	,	PUNCT
ejpam-1224	301	74	v⊗2	v⊗2	NOUN
ejpam-1224	301	75	/	/	SYM
ejpam-1224	301	76	r	r	NOUN
ejpam-1224	301	77	)	)	PUNCT
ejpam-1224	301	78	.	.	PUNCT
ejpam-1224	302	1	now	now	ADV
ejpam-1224	302	2	consider	consider	VERB
ejpam-1224	302	3	the	the	DET
ejpam-1224	302	4	following	follow	VERB
ejpam-1224	302	5	diagram	diagram	NOUN
ejpam-1224	302	6	:	:	PUNCT
ejpam-1224	302	7	(	(	PUNCT
ejpam-1224	302	8	a	a	X
ejpam-1224	302	9	!	!	PUNCT
ejpam-1224	303	1	1⊗	1⊗	NUM
ejpam-1224	303	2	a1)⊗	a1)⊗	NOUN
ejpam-1224	303	3	(	(	PUNCT
ejpam-1224	303	4	a	a	PRON
ejpam-1224	303	5	!	!	NOUN
ejpam-1224	303	6	1	1	NUM
ejpam-1224	303	7	⊗	⊗	PROPN
ejpam-1224	303	8	a1	a1	PROPN
ejpam-1224	303	9	)	)	PUNCT
ejpam-1224	303	10	m	m	VERB
ejpam-1224	303	11	−−−→	−−−→	ADJ
ejpam-1224	303	12	a	a	DET
ejpam-1224	303	13	!	!	NOUN
ejpam-1224	303	14	2	2	NUM
ejpam-1224	303	15	⊗	⊗	PROPN
ejpam-1224	303	16	a2	a2	PROPN
ejpam-1224	303	17	p	p	PROPN
ejpam-1224	303	18	y	y	PROPN
ejpam-1224	303	19	q	q	PUNCT
ejpam-1224	303	20	y	y	NOUN
ejpam-1224	303	21	hom(v⊗2	hom(v⊗2	NUM
ejpam-1224	303	22	,	,	PUNCT
ejpam-1224	303	23	v⊗2	v⊗2	NOUN
ejpam-1224	303	24	)	)	PUNCT
ejpam-1224	303	25	φ	φ	PROPN
ejpam-1224	303	26	−−−→	−−−→	NUM
ejpam-1224	303	27	hom(r	hom(r	PROPN
ejpam-1224	303	28	,	,	PUNCT
ejpam-1224	303	29	v⊗2	v⊗2	NOUN
ejpam-1224	303	30	/	/	SYM
ejpam-1224	303	31	r	r	NOUN
ejpam-1224	303	32	)	)	PUNCT
ejpam-1224	303	33	,	,	PUNCT
ejpam-1224	303	34	f.	f.	PROPN
ejpam-1224	303	35	hawwa	hawwa	PROPN
ejpam-1224	303	36	,	,	PUNCT
ejpam-1224	303	37	j.	j.	PROPN
ejpam-1224	303	38	hoffman	hoffman	PROPN
ejpam-1224	303	39	,	,	PUNCT
ejpam-1224	303	40	and	and	CCONJ
ejpam-1224	303	41	h.	h.	PROPN
ejpam-1224	303	42	wang	wang	PROPN
ejpam-1224	303	43	,	,	PUNCT
ejpam-1224	303	44	/	/	SYM
ejpam-1224	303	45	eur	eur	NOUN
ejpam-1224	303	46	.	.	PUNCT
ejpam-1224	304	1	j.	j.	PROPN
ejpam-1224	304	2	pure	pure	PROPN
ejpam-1224	304	3	appl	appl	PROPN
ejpam-1224	304	4	.	.	PROPN
ejpam-1224	304	5	math	math	PROPN
ejpam-1224	304	6	,	,	PUNCT
ejpam-1224	304	7	5	5	NUM
ejpam-1224	304	8	(	(	PUNCT
ejpam-1224	304	9	2012	2012	NUM
ejpam-1224	304	10	)	)	PUNCT
ejpam-1224	304	11	,	,	PUNCT
ejpam-1224	304	12	511	511	NUM
ejpam-1224	304	13	-	-	SYM
ejpam-1224	304	14	539	539	NUM
ejpam-1224	304	15	521	521	NUM
ejpam-1224	304	16	where	where	SCONJ
ejpam-1224	304	17	m	m	PROPN
ejpam-1224	304	18	is	be	AUX
ejpam-1224	304	19	ring	ring	NOUN
ejpam-1224	304	20	multiplication	multiplication	NOUN
ejpam-1224	304	21	defined	define	VERB
ejpam-1224	304	22	by	by	ADP
ejpam-1224	304	23	m[(ǎ1	m[(ǎ1	PROPN
ejpam-1224	304	24	⊗	⊗	PROPN
ejpam-1224	304	25	a1)⊗	a1)⊗	PROPN
ejpam-1224	304	26	(	(	PUNCT
ejpam-1224	304	27	ǎ2	ǎ2	ADV
ejpam-1224	304	28	⊗	⊗	PROPN
ejpam-1224	304	29	a2	a2	PROPN
ejpam-1224	304	30	)	)	PUNCT
ejpam-1224	304	31	]	]	PUNCT
ejpam-1224	305	1	=	=	PUNCT
ejpam-1224	305	2	ǎ1ǎ2	ǎ1ǎ2	PROPN
ejpam-1224	305	3	⊗	⊗	NOUN
ejpam-1224	305	4	a1a2	a1a2	VERB
ejpam-1224	305	5	with	with	ADP
ejpam-1224	305	6	canonical	canonical	ADJ
ejpam-1224	305	7	isomorphisms	isomorphism	NOUN
ejpam-1224	305	8	p	p	NOUN
ejpam-1224	305	9	and	and	CCONJ
ejpam-1224	305	10	q.	q.	PROPN
ejpam-1224	305	11	now	now	ADV
ejpam-1224	305	12	given	give	VERB
ejpam-1224	305	13	e	e	NOUN
ejpam-1224	305	14	=	=	SYM
ejpam-1224	305	15	∑	∑	PUNCT
ejpam-1224	305	16	v̌α	v̌α	PROPN
ejpam-1224	305	17	⊗	⊗	NOUN
ejpam-1224	306	1	vα	vα	INTJ
ejpam-1224	306	2	∈	∈	PROPN
ejpam-1224	306	3	a	a	PRON
ejpam-1224	306	4	!	!	PUNCT
ejpam-1224	307	1	⊗	⊗	PROPN
ejpam-1224	307	2	a	a	X
ejpam-1224	307	3	,	,	PUNCT
ejpam-1224	307	4	we	we	PRON
ejpam-1224	307	5	know	know	VERB
ejpam-1224	307	6	that	that	SCONJ
ejpam-1224	307	7	e2	e2	PROPN
ejpam-1224	307	8	=	=	PUNCT
ejpam-1224	307	9	(	(	PUNCT
ejpam-1224	307	10	∑	∑	PROPN
ejpam-1224	307	11	v̌α	v̌α	PROPN
ejpam-1224	307	12	⊗	⊗	PROPN
ejpam-1224	307	13	vα	vα	PROPN
ejpam-1224	307	14	)	)	PUNCT
ejpam-1224	307	15	(	(	PUNCT
ejpam-1224	307	16	∑	∑	PROPN
ejpam-1224	307	17	v̌β	v̌β	PROPN
ejpam-1224	307	18	⊗	⊗	PROPN
ejpam-1224	307	19	vβ	vβ	NOUN
ejpam-1224	307	20	)	)	PUNCT
ejpam-1224	307	21	=	=	SYM
ejpam-1224	307	22	∑	∑	PUNCT
ejpam-1224	307	23	α	α	X
ejpam-1224	307	24	,	,	PUNCT
ejpam-1224	307	25	β	β	PROPN
ejpam-1224	307	26	v̌α	v̌α	PROPN
ejpam-1224	307	27	v̌β	v̌β	PROPN
ejpam-1224	307	28	⊗	⊗	PROPN
ejpam-1224	307	29	vαvβ	vαvβ	NOUN
ejpam-1224	307	30	by	by	ADP
ejpam-1224	307	31	definition	definition	NOUN
ejpam-1224	307	32	of	of	ADP
ejpam-1224	307	33	the	the	DET
ejpam-1224	307	34	ring	ring	NOUN
ejpam-1224	307	35	multiplication	multiplication	NOUN
ejpam-1224	307	36	m.	m.	NOUN
ejpam-1224	307	37	we	we	PRON
ejpam-1224	307	38	will	will	AUX
ejpam-1224	307	39	show	show	VERB
ejpam-1224	307	40	that	that	SCONJ
ejpam-1224	307	41	∑	∑	PROPN
ejpam-1224	307	42	α	α	X
ejpam-1224	307	43	,	,	PUNCT
ejpam-1224	307	44	β	β	PROPN
ejpam-1224	307	45	v̌α	v̌α	PROPN
ejpam-1224	307	46	v̌β	v̌β	PROPN
ejpam-1224	307	47	⊗	⊗	PROPN
ejpam-1224	307	48	vαvβ	vαvβ	NOUN
ejpam-1224	307	49	=	=	SYM
ejpam-1224	308	1	0	0	X
ejpam-1224	308	2	.	.	PUNCT
ejpam-1224	308	3	given	give	VERB
ejpam-1224	308	4	f	f	PROPN
ejpam-1224	308	5	∈	∈	PROPN
ejpam-1224	308	6	hom(v⊗2	hom(v⊗2	PROPN
ejpam-1224	308	7	,	,	PUNCT
ejpam-1224	308	8	v⊗2	v⊗2	NOUN
ejpam-1224	308	9	)	)	PUNCT
ejpam-1224	308	10	,	,	PUNCT
ejpam-1224	308	11	then	then	ADV
ejpam-1224	308	12	g	g	PROPN
ejpam-1224	308	13	=	=	SYM
ejpam-1224	308	14	φ	φ	PROPN
ejpam-1224	308	15	(	(	PUNCT
ejpam-1224	308	16	f	f	PROPN
ejpam-1224	308	17	)	)	PUNCT
ejpam-1224	308	18	is	be	AUX
ejpam-1224	308	19	the	the	DET
ejpam-1224	308	20	composite	composite	ADJ
ejpam-1224	308	21	r	r	NOUN
ejpam-1224	308	22	,	,	PUNCT
ejpam-1224	308	23	→	→	SYM
ejpam-1224	308	24	v⊗2	v⊗2	NOUN
ejpam-1224	308	25	f	f	X
ejpam-1224	308	26	→	→	SYM
ejpam-1224	308	27	v⊗2→	v⊗2→	ADV
ejpam-1224	308	28	v⊗2	v⊗2	NOUN
ejpam-1224	308	29	/	/	SYM
ejpam-1224	308	30	r.	r.	PROPN
ejpam-1224	308	31	now	now	ADV
ejpam-1224	308	32	we	we	PRON
ejpam-1224	308	33	will	will	AUX
ejpam-1224	308	34	check	check	VERB
ejpam-1224	308	35	that	that	SCONJ
ejpam-1224	308	36	the	the	DET
ejpam-1224	308	37	diagram	diagram	NOUN
ejpam-1224	308	38	commutes	commute	NOUN
ejpam-1224	308	39	.	.	PUNCT
ejpam-1224	309	1	to	to	PART
ejpam-1224	309	2	define	define	VERB
ejpam-1224	309	3	p	p	NOUN
ejpam-1224	309	4	explicitly	explicitly	ADV
ejpam-1224	309	5	first	first	ADJ
ejpam-1224	309	6	recall	recall	NOUN
ejpam-1224	309	7	,	,	PUNCT
ejpam-1224	309	8	(	(	PUNCT
ejpam-1224	309	9	a	a	X
ejpam-1224	309	10	!	!	PUNCT
ejpam-1224	310	1	1⊗	1⊗	NUM
ejpam-1224	310	2	a1)⊗	a1)⊗	NOUN
ejpam-1224	310	3	(	(	PUNCT
ejpam-1224	310	4	a	a	PRON
ejpam-1224	310	5	!	!	NOUN
ejpam-1224	310	6	1	1	NUM
ejpam-1224	310	7	⊗	⊗	PROPN
ejpam-1224	310	8	a1	a1	NOUN
ejpam-1224	310	9	)	)	PUNCT
ejpam-1224	310	10	=	=	PUNCT
ejpam-1224	310	11	(	(	PUNCT
ejpam-1224	310	12	v	v	NOUN
ejpam-1224	310	13	∗	∗	NOUN
ejpam-1224	310	14	⊗	⊗	PROPN
ejpam-1224	310	15	v	v	NOUN
ejpam-1224	310	16	)	)	PUNCT
ejpam-1224	310	17	⊗	⊗	PROPN
ejpam-1224	310	18	(	(	PUNCT
ejpam-1224	310	19	v	v	NOUN
ejpam-1224	310	20	∗	∗	NOUN
ejpam-1224	310	21	⊗	⊗	PROPN
ejpam-1224	310	22	v	v	NOUN
ejpam-1224	310	23	)	)	PUNCT
ejpam-1224	311	1	so	so	ADV
ejpam-1224	311	2	we	we	PRON
ejpam-1224	311	3	know	know	VERB
ejpam-1224	311	4	that	that	SCONJ
ejpam-1224	311	5	p	p	X
ejpam-1224	311	6	:	:	PUNCT
ejpam-1224	311	7	(	(	PUNCT
ejpam-1224	311	8	v	v	NOUN
ejpam-1224	311	9	∗	∗	NOUN
ejpam-1224	311	10	⊗	⊗	PROPN
ejpam-1224	311	11	v	v	NOUN
ejpam-1224	311	12	)	)	PUNCT
ejpam-1224	312	1	⊗	⊗	PROPN
ejpam-1224	312	2	(	(	PUNCT
ejpam-1224	312	3	v	v	NOUN
ejpam-1224	312	4	∗	∗	NOUN
ejpam-1224	312	5	⊗	⊗	PROPN
ejpam-1224	312	6	v	v	NOUN
ejpam-1224	312	7	)	)	PUNCT
ejpam-1224	312	8	→	→	SYM
ejpam-1224	312	9	hom(v⊗2	hom(v⊗2	NUM
ejpam-1224	312	10	,	,	PUNCT
ejpam-1224	312	11	v⊗2	v⊗2	NOUN
ejpam-1224	312	12	)	)	PUNCT
ejpam-1224	312	13	.	.	PUNCT
ejpam-1224	313	1	now	now	ADV
ejpam-1224	313	2	for	for	ADP
ejpam-1224	313	3	(	(	PUNCT
ejpam-1224	313	4	v̌α⊗	v̌α⊗	ADJ
ejpam-1224	313	5	vβ)⊗	vβ)⊗	NOUN
ejpam-1224	313	6	(	(	PUNCT
ejpam-1224	313	7	v̌γ⊗	v̌γ⊗	PROPN
ejpam-1224	313	8	vδ	vδ	NOUN
ejpam-1224	313	9	)	)	PUNCT
ejpam-1224	313	10	∈	∈	PROPN
ejpam-1224	313	11	(	(	PUNCT
ejpam-1224	313	12	v	v	PROPN
ejpam-1224	313	13	∗⊗	∗⊗	PROPN
ejpam-1224	313	14	v	v	NOUN
ejpam-1224	313	15	)	)	PUNCT
ejpam-1224	313	16	⊗	⊗	PROPN
ejpam-1224	313	17	(	(	PUNCT
ejpam-1224	313	18	v	v	PROPN
ejpam-1224	313	19	∗⊗	∗⊗	NOUN
ejpam-1224	313	20	v	v	NOUN
ejpam-1224	313	21	)	)	PUNCT
ejpam-1224	313	22	and	and	CCONJ
ejpam-1224	313	23	(	(	PUNCT
ejpam-1224	313	24	vε	vε	PROPN
ejpam-1224	313	25	⊗	⊗	PROPN
ejpam-1224	313	26	vθ	vθ	PROPN
ejpam-1224	313	27	)	)	PUNCT
ejpam-1224	313	28	∈	∈	PROPN
ejpam-1224	313	29	v⊗2	v⊗2	NOUN
ejpam-1224	313	30	define	define	VERB
ejpam-1224	313	31	p	p	NOUN
ejpam-1224	313	32	as	as	SCONJ
ejpam-1224	313	33	follows	follow	VERB
ejpam-1224	313	34	p((v̌α⊗	p((v̌α⊗	PART
ejpam-1224	313	35	vβ)⊗	vβ)⊗	NOUN
ejpam-1224	313	36	(	(	PUNCT
ejpam-1224	313	37	v̌γ⊗	v̌γ⊗	NOUN
ejpam-1224	313	38	vδ))(vε⊗	vδ))(vε⊗	NOUN
ejpam-1224	313	39	vθ	vθ	NOUN
ejpam-1224	313	40	)	)	PUNCT
ejpam-1224	314	1	=	=	PUNCT
ejpam-1224	314	2	δ	δ	X
ejpam-1224	314	3	α	α	NOUN
ejpam-1224	314	4	εδ	εδ	INTJ
ejpam-1224	314	5	γ	γ	X
ejpam-1224	314	6	θ	θ	PROPN
ejpam-1224	314	7	vβ	vβ	ADP
ejpam-1224	314	8	⊗	⊗	PROPN
ejpam-1224	314	9	vδ	vδ	PROPN
ejpam-1224	314	10	.	.	PROPN
ejpam-1224	314	11	let	let	VERB
ejpam-1224	314	12	us	we	PRON
ejpam-1224	314	13	check	check	VERB
ejpam-1224	314	14	that	that	DET
ejpam-1224	314	15	p(e⊗	p(e⊗	PROPN
ejpam-1224	314	16	e	e	NOUN
ejpam-1224	314	17	)	)	PUNCT
ejpam-1224	314	18	=	=	SYM
ejpam-1224	314	19	i	i	PROPN
ejpam-1224	314	20	d	d	PROPN
ejpam-1224	314	21	∈	∈	PROPN
ejpam-1224	315	1	hom(v⊗2	hom(v⊗2	NUM
ejpam-1224	315	2	,	,	PUNCT
ejpam-1224	315	3	v⊗2	v⊗2	NOUN
ejpam-1224	315	4	)	)	PUNCT
ejpam-1224	315	5	,	,	PUNCT
ejpam-1224	315	6	where	where	SCONJ
ejpam-1224	315	7	e⊗	e⊗	PROPN
ejpam-1224	315	8	e	e	PROPN
ejpam-1224	315	9	=	=	PRON
ejpam-1224	315	10	∑	∑	PROPN
ejpam-1224	315	11	(	(	PUNCT
ejpam-1224	315	12	v̌α⊗	v̌α⊗	PROPN
ejpam-1224	315	13	vα)⊗	vα)⊗	NOUN
ejpam-1224	315	14	∑	∑	PUNCT
ejpam-1224	315	15	(	(	PUNCT
ejpam-1224	315	16	v̌β	v̌β	PROPN
ejpam-1224	315	17	⊗	⊗	NUM
ejpam-1224	315	18	vβ	vβ	NOUN
ejpam-1224	315	19	)	)	PUNCT
ejpam-1224	315	20	.	.	PUNCT
ejpam-1224	316	1	we	we	PRON
ejpam-1224	316	2	evaluate	evaluate	VERB
ejpam-1224	316	3	e⊗	e⊗	PROPN
ejpam-1224	316	4	e	e	PROPN
ejpam-1224	316	5	on	on	ADP
ejpam-1224	316	6	vε	vε	PROPN
ejpam-1224	316	7	⊗	⊗	PROPN
ejpam-1224	316	8	vθ	vθ	INTJ
ejpam-1224	317	1	and	and	CCONJ
ejpam-1224	317	2	we	we	PRON
ejpam-1224	317	3	have	have	VERB
ejpam-1224	317	4	(	(	PUNCT
ejpam-1224	317	5	e⊗	e⊗	PROPN
ejpam-1224	317	6	e)(vε⊗	e)(vε⊗	PROPN
ejpam-1224	317	7	vθ	vθ	VERB
ejpam-1224	317	8	)	)	PUNCT
ejpam-1224	318	1	=	=	PUNCT
ejpam-1224	318	2	∑	∑	PUNCT
ejpam-1224	318	3	α	α	X
ejpam-1224	318	4	,	,	PUNCT
ejpam-1224	318	5	β	β	X
ejpam-1224	318	6	δαεδ	δαεδ	NOUN
ejpam-1224	318	7	β	β	X
ejpam-1224	318	8	θ	θ	PROPN
ejpam-1224	318	9	vα⊗	vα⊗	PROPN
ejpam-1224	318	10	vβ	vβ	ADP
ejpam-1224	318	11	which	which	PRON
ejpam-1224	318	12	will	will	AUX
ejpam-1224	318	13	equal	equal	VERB
ejpam-1224	318	14	zero	zero	NUM
ejpam-1224	318	15	when	when	SCONJ
ejpam-1224	318	16	either	either	PRON
ejpam-1224	318	17	α=	α=	PROPN
ejpam-1224	318	18	ε	ε	PROPN
ejpam-1224	318	19	or	or	CCONJ
ejpam-1224	318	20	β	β	X
ejpam-1224	318	21	=	=	SYM
ejpam-1224	318	22	θ	θ	NOUN
ejpam-1224	318	23	meaning	mean	VERB
ejpam-1224	318	24	that	that	SCONJ
ejpam-1224	318	25	(	(	PUNCT
ejpam-1224	318	26	e⊗	e⊗	PROPN
ejpam-1224	318	27	e)(vε	e)(vε	PROPN
ejpam-1224	318	28	⊗	⊗	PROPN
ejpam-1224	318	29	vθ	vθ	PROPN
ejpam-1224	318	30	)	)	PUNCT
ejpam-1224	318	31	=	=	SYM
ejpam-1224	318	32	(	(	PUNCT
ejpam-1224	318	33	vε⊗	vε⊗	NOUN
ejpam-1224	318	34	vθ	vθ	VERB
ejpam-1224	318	35	)	)	PUNCT
ejpam-1224	318	36	,	,	PUNCT
ejpam-1224	318	37	so	so	CCONJ
ejpam-1224	318	38	e⊗	e⊗	PROPN
ejpam-1224	318	39	e	e	PROPN
ejpam-1224	318	40	is	be	AUX
ejpam-1224	318	41	the	the	DET
ejpam-1224	318	42	identity	identity	NOUN
ejpam-1224	318	43	map	map	NOUN
ejpam-1224	318	44	.	.	PUNCT
ejpam-1224	319	1	the	the	DET
ejpam-1224	319	2	map	map	NOUN
ejpam-1224	319	3	φ	φ	PROPN
ejpam-1224	319	4	clearly	clearly	ADV
ejpam-1224	319	5	takes	take	VERB
ejpam-1224	319	6	i	i	PROPN
ejpam-1224	319	7	d	d	PROPN
ejpam-1224	319	8	∈	∈	PROPN
ejpam-1224	319	9	hom(v⊗2	hom(v⊗2	NUM
ejpam-1224	319	10	,	,	PUNCT
ejpam-1224	319	11	v⊗2	v⊗2	NOUN
ejpam-1224	319	12	)	)	PUNCT
ejpam-1224	319	13	to	to	ADP
ejpam-1224	319	14	the	the	DET
ejpam-1224	319	15	zero	zero	NUM
ejpam-1224	319	16	map	map	NOUN
ejpam-1224	319	17	in	in	ADP
ejpam-1224	319	18	hom(r	hom(r	PROPN
ejpam-1224	319	19	,	,	PUNCT
ejpam-1224	319	20	v⊗2	v⊗2	NOUN
ejpam-1224	319	21	/	/	SYM
ejpam-1224	319	22	r	r	NOUN
ejpam-1224	319	23	)	)	PUNCT
ejpam-1224	319	24	.	.	PUNCT
ejpam-1224	320	1	to	to	PART
ejpam-1224	320	2	define	define	VERB
ejpam-1224	320	3	the	the	DET
ejpam-1224	320	4	isomorphism	isomorphism	NOUN
ejpam-1224	320	5	q	q	NOUN
ejpam-1224	320	6	recall	recall	VERB
ejpam-1224	320	7	that	that	SCONJ
ejpam-1224	320	8	a	a	DET
ejpam-1224	320	9	!	!	NOUN
ejpam-1224	320	10	2	2	NUM
ejpam-1224	320	11	⊗	⊗	PROPN
ejpam-1224	320	12	a2	a2	PROPN
ejpam-1224	320	13	=	=	SYM
ejpam-1224	320	14	(	(	PUNCT
ejpam-1224	320	15	(	(	PUNCT
ejpam-1224	320	16	v	v	ADP
ejpam-1224	320	17	∗)⊗2	∗)⊗2	NOUN
ejpam-1224	320	18	/	/	SYM
ejpam-1224	320	19	r⊥)⊗	r⊥)⊗	NOUN
ejpam-1224	320	20	(	(	PUNCT
ejpam-1224	320	21	v⊗2	v⊗2	NOUN
ejpam-1224	320	22	/	/	SYM
ejpam-1224	320	23	r	r	NOUN
ejpam-1224	320	24	)	)	PUNCT
ejpam-1224	320	25	=	=	SYM
ejpam-1224	321	1	r∗	r∗	PROPN
ejpam-1224	321	2	⊗	⊗	PROPN
ejpam-1224	321	3	(	(	PUNCT
ejpam-1224	321	4	v⊗2	v⊗2	NOUN
ejpam-1224	321	5	/	/	SYM
ejpam-1224	321	6	r	r	NOUN
ejpam-1224	321	7	)	)	PUNCT
ejpam-1224	321	8	.	.	PUNCT
ejpam-1224	322	1	if	if	SCONJ
ejpam-1224	322	2	we	we	PRON
ejpam-1224	322	3	can	can	AUX
ejpam-1224	322	4	show	show	VERB
ejpam-1224	322	5	that	that	SCONJ
ejpam-1224	322	6	the	the	DET
ejpam-1224	322	7	diagram	diagram	NOUN
ejpam-1224	322	8	commutes	commute	NOUN
ejpam-1224	322	9	,	,	PUNCT
ejpam-1224	322	10	that	that	PRON
ejpam-1224	322	11	will	will	AUX
ejpam-1224	322	12	prove	prove	VERB
ejpam-1224	322	13	that	that	DET
ejpam-1224	322	14	q(e2	q(e2	NOUN
ejpam-1224	322	15	)	)	PUNCT
ejpam-1224	322	16	=	=	SYM
ejpam-1224	323	1	0	0	X
ejpam-1224	323	2	.	.	PUNCT
ejpam-1224	324	1	for	for	ADP
ejpam-1224	324	2	an	an	DET
ejpam-1224	324	3	equivalence	equivalence	NOUN
ejpam-1224	324	4	class	class	NOUN
ejpam-1224	324	5	of	of	ADP
ejpam-1224	324	6	elements	element	NOUN
ejpam-1224	324	7	v̌α⊗	v̌α⊗	ADJ
ejpam-1224	324	8	v̌γ⊗	v̌γ⊗	PROPN
ejpam-1224	324	9	vβ	vβ	ADP
ejpam-1224	324	10	⊗	⊗	PROPN
ejpam-1224	324	11	vδ	vδ	X
ejpam-1224	324	12	∈	∈	PROPN
ejpam-1224	324	13	(	(	PUNCT
ejpam-1224	324	14	v	v	ADP
ejpam-1224	324	15	∗)⊗2	∗)⊗2	NOUN
ejpam-1224	324	16	/	/	SYM
ejpam-1224	324	17	r⊥⊗	r⊥⊗	PROPN
ejpam-1224	324	18	(	(	PUNCT
ejpam-1224	324	19	v⊗2	v⊗2	NOUN
ejpam-1224	324	20	/	/	SYM
ejpam-1224	324	21	r	r	NOUN
ejpam-1224	324	22	)	)	PUNCT
ejpam-1224	324	23	and	and	CCONJ
ejpam-1224	324	24	for	for	ADP
ejpam-1224	324	25	an	an	DET
ejpam-1224	324	26	element	element	NOUN
ejpam-1224	324	27	x	x	SYM
ejpam-1224	324	28	∈	∈	NOUN
ejpam-1224	324	29	r	r	NOUN
ejpam-1224	324	30	define	define	NOUN
ejpam-1224	324	31	q	q	NOUN
ejpam-1224	324	32	as	as	SCONJ
ejpam-1224	324	33	follows	follow	VERB
ejpam-1224	324	34	q(v̌α⊗	q(v̌α⊗	PROPN
ejpam-1224	324	35	v̌γ⊗	v̌γ⊗	PROPN
ejpam-1224	324	36	vβ	vβ	ADP
ejpam-1224	324	37	⊗	⊗	PROPN
ejpam-1224	324	38	vδ)(x	vδ)(x	PROPN
ejpam-1224	324	39	)	)	PUNCT
ejpam-1224	325	1	=	=	PUNCT
ejpam-1224	325	2	(	(	PUNCT
ejpam-1224	325	3	v̌α⊗	v̌α⊗	ADJ
ejpam-1224	325	4	v̌γ(x	v̌γ(x	ADJ
ejpam-1224	325	5	)	)	PUNCT
ejpam-1224	325	6	)	)	PUNCT
ejpam-1224	325	7	·	·	PUNCT
ejpam-1224	326	1	vβ	vβ	X
ejpam-1224	326	2	vδ	vδ	NOUN
ejpam-1224	326	3	=	=	SYM
ejpam-1224	326	4	(	(	PUNCT
ejpam-1224	326	5	v̌α⊗	v̌α⊗	ADJ
ejpam-1224	326	6	v̌γ(x	v̌γ(x	ADJ
ejpam-1224	326	7	)	)	PUNCT
ejpam-1224	326	8	)	)	PUNCT
ejpam-1224	326	9	·	·	PUNCT
ejpam-1224	327	1	vβ	vβ	X
ejpam-1224	327	2	⊗	⊗	PROPN
ejpam-1224	327	3	vδ	vδ	PROPN
ejpam-1224	327	4	,	,	PUNCT
ejpam-1224	327	5	f.	f.	PROPN
ejpam-1224	327	6	hawwa	hawwa	PROPN
ejpam-1224	327	7	,	,	PUNCT
ejpam-1224	327	8	j.	j.	PROPN
ejpam-1224	327	9	hoffman	hoffman	PROPN
ejpam-1224	327	10	,	,	PUNCT
ejpam-1224	327	11	and	and	CCONJ
ejpam-1224	327	12	h.	h.	PROPN
ejpam-1224	327	13	wang	wang	PROPN
ejpam-1224	327	14	,	,	PUNCT
ejpam-1224	327	15	/	/	SYM
ejpam-1224	327	16	eur	eur	NOUN
ejpam-1224	327	17	.	.	PUNCT
ejpam-1224	328	1	j.	j.	PROPN
ejpam-1224	328	2	pure	pure	PROPN
ejpam-1224	328	3	appl	appl	PROPN
ejpam-1224	328	4	.	.	PROPN
ejpam-1224	328	5	math	math	PROPN
ejpam-1224	328	6	,	,	PUNCT
ejpam-1224	328	7	5	5	NUM
ejpam-1224	328	8	(	(	PUNCT
ejpam-1224	328	9	2012	2012	NUM
ejpam-1224	328	10	)	)	PUNCT
ejpam-1224	328	11	,	,	PUNCT
ejpam-1224	328	12	511	511	NUM
ejpam-1224	328	13	-	-	SYM
ejpam-1224	328	14	539	539	NUM
ejpam-1224	328	15	522	522	NUM
ejpam-1224	328	16	where	where	SCONJ
ejpam-1224	328	17	v̌α	v̌α	PROPN
ejpam-1224	328	18	⊗	⊗	NOUN
ejpam-1224	328	19	v̌γ	v̌γ	PROPN
ejpam-1224	328	20	∈	∈	PROPN
ejpam-1224	328	21	v	v	ADP
ejpam-1224	328	22	∗	∗	NOUN
ejpam-1224	328	23	⊗	⊗	PROPN
ejpam-1224	328	24	v	v	ADP
ejpam-1224	328	25	∗	∗	NOUN
ejpam-1224	328	26	=	=	SYM
ejpam-1224	328	27	(	(	PUNCT
ejpam-1224	328	28	(	(	PUNCT
ejpam-1224	328	29	v⊗2)∗	v⊗2)∗	NOUN
ejpam-1224	328	30	is	be	AUX
ejpam-1224	328	31	a	a	DET
ejpam-1224	328	32	linear	linear	ADJ
ejpam-1224	328	33	functional	functional	NOUN
ejpam-1224	328	34	.	.	PUNCT
ejpam-1224	329	1	to	to	PART
ejpam-1224	329	2	see	see	VERB
ejpam-1224	329	3	that	that	DET
ejpam-1224	329	4	q	q	NOUN
ejpam-1224	329	5	is	be	AUX
ejpam-1224	329	6	well	well	ADV
ejpam-1224	329	7	defined	define	VERB
ejpam-1224	329	8	,	,	PUNCT
ejpam-1224	329	9	note	note	VERB
ejpam-1224	329	10	that	that	SCONJ
ejpam-1224	329	11	v̌α⊗	v̌α⊗	ADJ
ejpam-1224	329	12	v̌γ	v̌γ	NOUN
ejpam-1224	329	13	is	be	AUX
ejpam-1224	329	14	unique	unique	ADJ
ejpam-1224	329	15	up	up	ADP
ejpam-1224	329	16	to	to	ADP
ejpam-1224	329	17	(	(	PUNCT
ejpam-1224	329	18	v̌α	v̌α	PROPN
ejpam-1224	329	19	⊗	⊗	NOUN
ejpam-1224	329	20	v̌γ(x	v̌γ(x	PROPN
ejpam-1224	329	21	)	)	PUNCT
ejpam-1224	330	1	+	+	CCONJ
ejpam-1224	330	2	ρ	ρ	X
ejpam-1224	330	3	)	)	PUNCT
ejpam-1224	330	4	where	where	SCONJ
ejpam-1224	330	5	ρ	ρ	PROPN
ejpam-1224	330	6	∈	∈	PROPN
ejpam-1224	330	7	r⊥.	r⊥.	NOUN
ejpam-1224	330	8	since	since	SCONJ
ejpam-1224	330	9	ρ	ρ	PROPN
ejpam-1224	330	10	∈	∈	PROPN
ejpam-1224	330	11	r⊥	r⊥	NOUN
ejpam-1224	330	12	,	,	PUNCT
ejpam-1224	330	13	ρ(x	ρ(x	NUM
ejpam-1224	330	14	)	)	PUNCT
ejpam-1224	330	15	=	=	SYM
ejpam-1224	330	16	0	0	NUM
ejpam-1224	331	1	and	and	CCONJ
ejpam-1224	331	2	in	in	ADP
ejpam-1224	331	3	the	the	DET
ejpam-1224	331	4	quotient	quotient	NOUN
ejpam-1224	331	5	(	(	PUNCT
ejpam-1224	331	6	v⊗2	v⊗2	NOUN
ejpam-1224	331	7	/	/	SYM
ejpam-1224	331	8	r	r	NOUN
ejpam-1224	331	9	)	)	PUNCT
ejpam-1224	331	10	so	so	ADV
ejpam-1224	331	11	the	the	DET
ejpam-1224	331	12	map	map	NOUN
ejpam-1224	331	13	q	q	NOUN
ejpam-1224	331	14	is	be	AUX
ejpam-1224	331	15	well	well	ADV
ejpam-1224	331	16	defined	define	VERB
ejpam-1224	331	17	.	.	PUNCT
ejpam-1224	332	1	note	note	VERB
ejpam-1224	332	2	that	that	SCONJ
ejpam-1224	332	3	x	x	SYM
ejpam-1224	332	4	∈	∈	NOUN
ejpam-1224	332	5	r	r	NOUN
ejpam-1224	332	6	is	be	AUX
ejpam-1224	332	7	also	also	ADV
ejpam-1224	332	8	contained	contain	VERB
ejpam-1224	332	9	in	in	ADP
ejpam-1224	332	10	(	(	PUNCT
ejpam-1224	332	11	v⊗2	v⊗2	NOUN
ejpam-1224	332	12	)	)	PUNCT
ejpam-1224	332	13	meaning	mean	VERB
ejpam-1224	332	14	that	that	SCONJ
ejpam-1224	332	15	any	any	DET
ejpam-1224	332	16	linear	linear	ADJ
ejpam-1224	332	17	functional	functional	ADJ
ejpam-1224	332	18	on	on	ADP
ejpam-1224	332	19	v⊗2	v⊗2	NOUN
ejpam-1224	332	20	restricts	restrict	VERB
ejpam-1224	332	21	to	to	PART
ejpam-1224	332	22	r.	r.	VERB
ejpam-1224	332	23	so	so	ADV
ejpam-1224	332	24	to	to	PART
ejpam-1224	332	25	see	see	VERB
ejpam-1224	332	26	that	that	SCONJ
ejpam-1224	332	27	the	the	DET
ejpam-1224	332	28	diagram	diagram	NOUN
ejpam-1224	332	29	commutes	commute	NOUN
ejpam-1224	332	30	,	,	PUNCT
ejpam-1224	332	31	observe	observe	VERB
ejpam-1224	332	32	that	that	SCONJ
ejpam-1224	332	33	φp[(v̌α	φp[(v̌α	PROPN
ejpam-1224	332	34	⊗	⊗	NUM
ejpam-1224	332	35	vβ)⊗	vβ)⊗	NOUN
ejpam-1224	332	36	(	(	PUNCT
ejpam-1224	332	37	v̌γ⊗	v̌γ⊗	NOUN
ejpam-1224	332	38	vδ)](x	vδ)](x	ADJ
ejpam-1224	332	39	)	)	PUNCT
ejpam-1224	332	40	=	=	SYM
ejpam-1224	333	1	[	[	X
ejpam-1224	333	2	(	(	PUNCT
ejpam-1224	333	3	v̌α⊗	v̌α⊗	ADJ
ejpam-1224	333	4	v̌γ)(x	v̌γ)(x	NOUN
ejpam-1224	333	5	)	)	PUNCT
ejpam-1224	333	6	]	]	PUNCT
ejpam-1224	333	7	·	·	PUNCT
ejpam-1224	334	1	vβ	vβ	X
ejpam-1224	334	2	⊗	⊗	PROPN
ejpam-1224	334	3	vδ	vδ	X
ejpam-1224	335	1	=	=	PUNCT
ejpam-1224	336	1	[	[	X
ejpam-1224	336	2	(	(	PUNCT
ejpam-1224	336	3	v̌α⊗	v̌α⊗	ADJ
ejpam-1224	336	4	v̌γ)(x	v̌γ)(x	NOUN
ejpam-1224	336	5	)	)	PUNCT
ejpam-1224	336	6	·	·	PUNCT
ejpam-1224	336	7	(	(	PUNCT
ejpam-1224	336	8	v̌β	v̌β	PROPN
ejpam-1224	336	9	⊗	⊗	PROPN
ejpam-1224	336	10	vδ	vδ	NOUN
ejpam-1224	336	11	)	)	PUNCT
ejpam-1224	336	12	]	]	PUNCT
ejpam-1224	337	1	=	=	SYM
ejpam-1224	337	2	qm[(v̌α⊗	qm[(v̌α⊗	ADJ
ejpam-1224	337	3	vβ)⊗	vβ)⊗	NOUN
ejpam-1224	337	4	(	(	PUNCT
ejpam-1224	337	5	v̌γ⊗	v̌γ⊗	NOUN
ejpam-1224	337	6	vδ)](x	vδ)](x	ADJ
ejpam-1224	337	7	)	)	PUNCT
ejpam-1224	337	8	.	.	PUNCT
ejpam-1224	338	1	we	we	PRON
ejpam-1224	338	2	have	have	AUX
ejpam-1224	338	3	shown	show	VERB
ejpam-1224	338	4	that	that	SCONJ
ejpam-1224	338	5	the	the	DET
ejpam-1224	338	6	diagram	diagram	NOUN
ejpam-1224	338	7	commutes	commute	NOUN
ejpam-1224	338	8	proving	prove	VERB
ejpam-1224	338	9	that	that	DET
ejpam-1224	338	10	q(e2	q(e2	NOUN
ejpam-1224	338	11	)	)	PUNCT
ejpam-1224	338	12	=	=	SYM
ejpam-1224	338	13	0	0	NUM
ejpam-1224	338	14	,	,	PUNCT
ejpam-1224	338	15	so	so	ADV
ejpam-1224	338	16	e2	e2	PROPN
ejpam-1224	338	17	=	=	PUNCT
ejpam-1224	338	18	0	0	PUNCT
ejpam-1224	338	19	since	since	SCONJ
ejpam-1224	338	20	q	q	PROPN
ejpam-1224	338	21	is	be	AUX
ejpam-1224	338	22	an	an	DET
ejpam-1224	338	23	isomorphism	isomorphism	NOUN
ejpam-1224	338	24	.	.	PUNCT
ejpam-1224	339	1	thus	thus	ADV
ejpam-1224	339	2	we	we	PRON
ejpam-1224	339	3	may	may	AUX
ejpam-1224	339	4	define	define	VERB
ejpam-1224	339	5	the	the	DET
ejpam-1224	339	6	koszul	koszul	ADJ
ejpam-1224	339	7	complex	complex	NOUN
ejpam-1224	340	1	k	k	PROPN
ejpam-1224	340	2	i	i	NOUN
ejpam-1224	340	3	=	=	PUNCT
ejpam-1224	340	4	a⊗	a⊗	NOUN
ejpam-1224	340	5	(	(	PUNCT
ejpam-1224	340	6	a	a	NOUN
ejpam-1224	340	7	!	!	PUNCT
ejpam-1224	341	1	i	i	PRON
ejpam-1224	341	2	)	)	PUNCT
ejpam-1224	342	1	∗.	∗.	PROPN
ejpam-1224	342	2	the	the	DET
ejpam-1224	342	3	notation	notation	NOUN
ejpam-1224	342	4	k(a	k(a	PROPN
ejpam-1224	342	5	)	)	PUNCT
ejpam-1224	342	6	will	will	AUX
ejpam-1224	342	7	also	also	ADV
ejpam-1224	342	8	be	be	AUX
ejpam-1224	342	9	used	use	VERB
ejpam-1224	342	10	to	to	PART
ejpam-1224	342	11	indicate	indicate	VERB
ejpam-1224	342	12	the	the	DET
ejpam-1224	342	13	koszul	koszul	ADJ
ejpam-1224	342	14	complex	complex	NOUN
ejpam-1224	342	15	of	of	ADP
ejpam-1224	342	16	a	a	DET
ejpam-1224	342	17	quadratic	quadratic	ADJ
ejpam-1224	342	18	algebra	algebra	NOUN
ejpam-1224	342	19	a.	a.	NOUN
ejpam-1224	342	20	proposition	proposition	NOUN
ejpam-1224	342	21	1	1	NUM
ejpam-1224	342	22	.	.	PUNCT
ejpam-1224	343	1	[	[	X
ejpam-1224	343	2	proposition	proposition	NOUN
ejpam-1224	343	3	2.9.1	2.9.1	NUM
ejpam-1224	343	4	,	,	PUNCT
ejpam-1224	343	5	[	[	X
ejpam-1224	343	6	1	1	NUM
ejpam-1224	343	7	]	]	X
ejpam-1224	343	8	]	]	PUNCT
ejpam-1224	343	9	.	.	PUNCT
ejpam-1224	344	1	let	let	VERB
ejpam-1224	344	2	a	a	PRON
ejpam-1224	344	3	be	be	AUX
ejpam-1224	344	4	a	a	DET
ejpam-1224	344	5	koszul	koszul	ADJ
ejpam-1224	344	6	ring	ring	NOUN
ejpam-1224	344	7	.	.	PUNCT
ejpam-1224	345	1	then	then	ADV
ejpam-1224	345	2	a	a	X
ejpam-1224	345	3	!	!	PUNCT
ejpam-1224	345	4	is	be	AUX
ejpam-1224	345	5	koszul	koszul	ADJ
ejpam-1224	345	6	as	as	ADV
ejpam-1224	345	7	well	well	ADV
ejpam-1224	345	8	.	.	PUNCT
ejpam-1224	346	1	proposition	proposition	NOUN
ejpam-1224	346	2	2	2	NUM
ejpam-1224	346	3	(	(	PUNCT
ejpam-1224	346	4	koszul	koszul	ADJ
ejpam-1224	346	5	algebra	algebra	NOUN
ejpam-1224	346	6	)	)	PUNCT
ejpam-1224	346	7	.	.	PUNCT
ejpam-1224	347	1	let	let	VERB
ejpam-1224	347	2	a	a	PRON
ejpam-1224	347	3	be	be	AUX
ejpam-1224	347	4	a	a	DET
ejpam-1224	347	5	quadratic	quadratic	ADJ
ejpam-1224	347	6	k	k	NOUN
ejpam-1224	347	7	-	-	NOUN
ejpam-1224	347	8	algebra	algebra	NOUN
ejpam-1224	347	9	,	,	PUNCT
ejpam-1224	347	10	then	then	ADV
ejpam-1224	347	11	following	follow	VERB
ejpam-1224	347	12	conditions	condition	NOUN
ejpam-1224	347	13	are	be	AUX
ejpam-1224	347	14	equivalent	equivalent	ADJ
ejpam-1224	347	15	:	:	PUNCT
ejpam-1224	347	16	(	(	PUNCT
ejpam-1224	347	17	a	a	X
ejpam-1224	347	18	)	)	PUNCT
ejpam-1224	347	19	h	h	NOUN
ejpam-1224	347	20	i(k(a))n	i(k(a))n	NOUN
ejpam-1224	347	21	=	=	SYM
ejpam-1224	347	22	0	0	PUNCT
ejpam-1224	348	1	if	if	SCONJ
ejpam-1224	348	2	i	i	PRON
ejpam-1224	348	3	>	>	X
ejpam-1224	348	4	0	0	PUNCT
ejpam-1224	349	1	and	and	CCONJ
ejpam-1224	349	2	if	if	SCONJ
ejpam-1224	349	3	i	i	PRON
ejpam-1224	349	4	=	=	NOUN
ejpam-1224	349	5	0	0	NUM
ejpam-1224	349	6	,	,	PUNCT
ejpam-1224	349	7	n	n	PROPN
ejpam-1224	349	8	6=	6=	PROPN
ejpam-1224	349	9	0	0	NUM
ejpam-1224	349	10	,	,	PUNCT
ejpam-1224	349	11	we	we	PRON
ejpam-1224	349	12	have	have	VERB
ejpam-1224	349	13	h0(k(a))0	h0(k(a))0	PROPN
ejpam-1224	349	14	=	=	SYM
ejpam-1224	349	15	k.	k.	PROPN
ejpam-1224	349	16	(	(	PUNCT
ejpam-1224	349	17	b	b	NOUN
ejpam-1224	349	18	)	)	PUNCT
ejpam-1224	349	19	h	h	NOUN
ejpam-1224	350	1	i	i	PRON
ejpam-1224	350	2	j	j	PROPN
ejpam-1224	350	3	(	(	PUNCT
ejpam-1224	350	4	a	a	PRON
ejpam-1224	350	5	,	,	PUNCT
ejpam-1224	350	6	m	m	NOUN
ejpam-1224	350	7	)	)	PUNCT
ejpam-1224	350	8	,	,	PUNCT
ejpam-1224	350	9	(	(	PUNCT
ejpam-1224	350	10	hochschild	hochschild	ADJ
ejpam-1224	350	11	homology	homology	NOUN
ejpam-1224	350	12	)	)	PUNCT
ejpam-1224	350	13	where	where	SCONJ
ejpam-1224	350	14	a	a	PRON
ejpam-1224	350	15	is	be	AUX
ejpam-1224	350	16	considered	consider	VERB
ejpam-1224	350	17	as	as	ADP
ejpam-1224	350	18	an	an	DET
ejpam-1224	350	19	a	a	DET
ejpam-1224	350	20	-	-	PUNCT
ejpam-1224	350	21	bimodule	bimodule	NOUN
ejpam-1224	350	22	,	,	PUNCT
ejpam-1224	350	23	vanishes	vanish	VERB
ejpam-1224	350	24	for	for	ADP
ejpam-1224	350	25	any	any	DET
ejpam-1224	350	26	z+-graded	z+-graded	ADJ
ejpam-1224	350	27	a	a	DET
ejpam-1224	350	28	-	-	PUNCT
ejpam-1224	350	29	bimodule	bimodule	NOUN
ejpam-1224	350	30	m	m	NOUN
ejpam-1224	351	1	and	and	CCONJ
ejpam-1224	351	2	i	i	PRON
ejpam-1224	351	3	<	<	X
ejpam-1224	351	4	−	−	PROPN
ejpam-1224	352	1	j.	j.	PROPN
ejpam-1224	352	2	(	(	PUNCT
ejpam-1224	352	3	c	c	NOUN
ejpam-1224	352	4	)	)	PUNCT
ejpam-1224	352	5	e	e	NOUN
ejpam-1224	352	6	x	x	SYM
ejpam-1224	352	7	t	t	X
ejpam-1224	352	8	i	i	PRON
ejpam-1224	352	9	j	j	PROPN
ejpam-1224	352	10	(	(	PUNCT
ejpam-1224	352	11	k	k	X
ejpam-1224	352	12	,	,	PUNCT
ejpam-1224	352	13	k	k	NOUN
ejpam-1224	352	14	)	)	PUNCT
ejpam-1224	352	15	=	=	SYM
ejpam-1224	352	16	0	0	NUM
ejpam-1224	352	17	for	for	ADP
ejpam-1224	352	18	all	all	DET
ejpam-1224	352	19	i	i	PRON
ejpam-1224	352	20	6=	6=	PROPN
ejpam-1224	352	21	j	j	PROPN
ejpam-1224	352	22	,	,	PUNCT
ejpam-1224	352	23	where	where	SCONJ
ejpam-1224	352	24	e	e	NOUN
ejpam-1224	352	25	x	x	X
ejpam-1224	352	26	t	t	PROPN
ejpam-1224	352	27	i(k	i(k	PROPN
ejpam-1224	352	28	,	,	PUNCT
ejpam-1224	352	29	k	k	NOUN
ejpam-1224	352	30	)	)	PUNCT
ejpam-1224	352	31	is	be	AUX
ejpam-1224	352	32	taken	take	VERB
ejpam-1224	352	33	in	in	ADP
ejpam-1224	352	34	the	the	DET
ejpam-1224	352	35	category	category	NOUN
ejpam-1224	352	36	of	of	ADP
ejpam-1224	352	37	left	leave	VERB
ejpam-1224	352	38	a	a	DET
ejpam-1224	352	39	-	-	PUNCT
ejpam-1224	352	40	modules	module	NOUN
ejpam-1224	352	41	.	.	PUNCT
ejpam-1224	353	1	(	(	PUNCT
ejpam-1224	353	2	d	d	X
ejpam-1224	353	3	)	)	PUNCT
ejpam-1224	353	4	k•	k•	NOUN
ejpam-1224	353	5	is	be	AUX
ejpam-1224	353	6	a	a	DET
ejpam-1224	353	7	resolution	resolution	NOUN
ejpam-1224	353	8	of	of	ADP
ejpam-1224	353	9	a	a	PRON
ejpam-1224	353	10	in	in	ADP
ejpam-1224	353	11	the	the	DET
ejpam-1224	353	12	category	category	NOUN
ejpam-1224	353	13	of	of	ADP
ejpam-1224	353	14	a	a	DET
ejpam-1224	353	15	-	-	PUNCT
ejpam-1224	353	16	bimodules	bimodule	NOUN
ejpam-1224	353	17	.	.	PUNCT
ejpam-1224	354	1	(	(	PUNCT
ejpam-1224	354	2	e	e	NOUN
ejpam-1224	354	3	)	)	PUNCT
ejpam-1224	354	4	k•	k•	NOUN
ejpam-1224	354	5	⊗a	⊗a	PROPN
ejpam-1224	354	6	k	k	PROPN
ejpam-1224	354	7	is	be	AUX
ejpam-1224	354	8	a	a	DET
ejpam-1224	354	9	resolution	resolution	NOUN
ejpam-1224	354	10	of	of	ADP
ejpam-1224	354	11	k	k	PROPN
ejpam-1224	354	12	in	in	ADP
ejpam-1224	354	13	the	the	DET
ejpam-1224	354	14	category	category	NOUN
ejpam-1224	354	15	of	of	ADP
ejpam-1224	354	16	left	leave	VERB
ejpam-1224	354	17	a	a	DET
ejpam-1224	354	18	-	-	PUNCT
ejpam-1224	354	19	modules	module	NOUN
ejpam-1224	354	20	.	.	PUNCT
ejpam-1224	355	1	(	(	PUNCT
ejpam-1224	355	2	f	f	X
ejpam-1224	355	3	)	)	PUNCT
ejpam-1224	355	4	there	there	PRON
ejpam-1224	355	5	exists	exist	VERB
ejpam-1224	355	6	a	a	DET
ejpam-1224	355	7	free	free	ADJ
ejpam-1224	355	8	resolution	resolution	NOUN
ejpam-1224	355	9	of	of	ADP
ejpam-1224	355	10	k	k	PROPN
ejpam-1224	355	11	such	such	ADJ
ejpam-1224	355	12	that	that	SCONJ
ejpam-1224	355	13	the	the	DET
ejpam-1224	355	14	i’th	i’th	PROPN
ejpam-1224	355	15	syzygies	syzygy	NOUN
ejpam-1224	355	16	are	be	AUX
ejpam-1224	355	17	all	all	PRON
ejpam-1224	355	18	generated	generate	VERB
ejpam-1224	355	19	in	in	ADP
ejpam-1224	355	20	degree	degree	NOUN
ejpam-1224	355	21	i.	i.	NOUN
ejpam-1224	355	22	example	example	NOUN
ejpam-1224	356	1	4	4	X
ejpam-1224	356	2	.	.	PUNCT
ejpam-1224	357	1	let	let	VERB
ejpam-1224	357	2	us	we	PRON
ejpam-1224	357	3	consider	consider	VERB
ejpam-1224	357	4	the	the	DET
ejpam-1224	357	5	special	special	ADJ
ejpam-1224	357	6	case	case	NOUN
ejpam-1224	357	7	where	where	SCONJ
ejpam-1224	357	8	a	a	PRON
ejpam-1224	357	9	is	be	AUX
ejpam-1224	357	10	the	the	DET
ejpam-1224	357	11	symmetric	symmetric	ADJ
ejpam-1224	357	12	algebra	algebra	NOUN
ejpam-1224	357	13	on	on	ADP
ejpam-1224	357	14	v	v	NUM
ejpam-1224	357	15	,	,	PUNCT
ejpam-1224	357	16	s(v	s(v	PROPN
ejpam-1224	357	17	)	)	PUNCT
ejpam-1224	357	18	.	.	PUNCT
ejpam-1224	358	1	the	the	DET
ejpam-1224	358	2	quadratic	quadratic	ADJ
ejpam-1224	358	3	dual	dual	NOUN
ejpam-1224	358	4	a	a	PRON
ejpam-1224	358	5	!	!	PUNCT
ejpam-1224	358	6	will	will	AUX
ejpam-1224	358	7	be	be	AUX
ejpam-1224	358	8	the	the	DET
ejpam-1224	358	9	exterior	exterior	ADJ
ejpam-1224	358	10	algebra	algebra	NOUN
ejpam-1224	358	11	on	on	ADP
ejpam-1224	358	12	v	v	ADP
ejpam-1224	358	13	∗	∗	NOUN
ejpam-1224	358	14	,	,	PUNCT
ejpam-1224	358	15	e(v	e(v	VERB
ejpam-1224	358	16	∗	∗	NOUN
ejpam-1224	358	17	)	)	PUNCT
ejpam-1224	358	18	.	.	PUNCT
ejpam-1224	359	1	therefore	therefore	ADV
ejpam-1224	359	2	we	we	PRON
ejpam-1224	359	3	may	may	AUX
ejpam-1224	359	4	represent	represent	VERB
ejpam-1224	359	5	k(a	k(a	NOUN
ejpam-1224	359	6	)	)	PUNCT
ejpam-1224	359	7	in	in	ADP
ejpam-1224	359	8	the	the	DET
ejpam-1224	359	9	following	following	ADJ
ejpam-1224	359	10	way	way	NOUN
ejpam-1224	359	11	.	.	PUNCT
ejpam-1224	359	12	.	.	PUNCT
ejpam-1224	359	13	.	.	PUNCT
ejpam-1224	360	1	d2−→	d2−→	PROPN
ejpam-1224	360	2	a⊗∧2(v	a⊗∧2(v	VERB
ejpam-1224	360	3	)	)	PUNCT
ejpam-1224	360	4	d1−→	d1−→	PROPN
ejpam-1224	360	5	a⊗	a⊗	NOUN
ejpam-1224	360	6	v	v	ADP
ejpam-1224	360	7	d0−→	d0−→	PROPN
ejpam-1224	360	8	a	a	DET
ejpam-1224	360	9	,	,	PUNCT
ejpam-1224	360	10	where	where	SCONJ
ejpam-1224	360	11	d0	d0	NOUN
ejpam-1224	360	12	:	:	PUNCT
ejpam-1224	360	13	a	a	DET
ejpam-1224	360	14	⊗	⊗	PROPN
ejpam-1224	360	15	v	v	NOUN
ejpam-1224	360	16	→	→	SYM
ejpam-1224	360	17	av	av	NOUN
ejpam-1224	360	18	or	or	CCONJ
ejpam-1224	360	19	more	more	ADV
ejpam-1224	360	20	specifically	specifically	ADV
ejpam-1224	360	21	for	for	ADP
ejpam-1224	360	22	this	this	DET
ejpam-1224	360	23	example	example	NOUN
ejpam-1224	360	24	,	,	PUNCT
ejpam-1224	360	25	d0	d0	NOUN
ejpam-1224	360	26	:	:	PUNCT
ejpam-1224	360	27	p(x	p(x	PROPN
ejpam-1224	360	28	)	)	PUNCT
ejpam-1224	361	1	⊗	⊗	NOUN
ejpam-1224	361	2	x	x	PUNCT
ejpam-1224	361	3	i	i	PRON
ejpam-1224	361	4	→	→	SYM
ejpam-1224	361	5	x	x	X
ejpam-1224	361	6	i	i	PRON
ejpam-1224	361	7	p(x	p(x	PROPN
ejpam-1224	361	8	)	)	PUNCT
ejpam-1224	361	9	with	with	ADP
ejpam-1224	361	10	p(x	p(x	NOUN
ejpam-1224	361	11	)	)	PUNCT
ejpam-1224	361	12	∈	∈	PROPN
ejpam-1224	361	13	s(v	s(v	PROPN
ejpam-1224	361	14	)	)	PUNCT
ejpam-1224	361	15	and	and	CCONJ
ejpam-1224	361	16	x	x	X
ejpam-1224	361	17	i	i	NOUN
ejpam-1224	361	18	∈	∈	PROPN
ejpam-1224	361	19	∧	∧	NOUN
ejpam-1224	361	20	i(v	i(v	PROPN
ejpam-1224	361	21	)	)	PUNCT
ejpam-1224	361	22	.	.	PUNCT
ejpam-1224	362	1	more	more	ADV
ejpam-1224	362	2	generally	generally	ADV
ejpam-1224	362	3	,	,	PUNCT
ejpam-1224	362	4	we	we	PRON
ejpam-1224	362	5	may	may	AUX
ejpam-1224	362	6	define	define	VERB
ejpam-1224	362	7	di	di	NOUN
ejpam-1224	362	8	:	:	PUNCT
ejpam-1224	362	9	a⊗∧p(v	a⊗∧p(v	NOUN
ejpam-1224	362	10	)	)	PUNCT
ejpam-1224	362	11	→	→	SYM
ejpam-1224	362	12	a⊗∧p−1(v	a⊗∧p−1(v	PROPN
ejpam-1224	362	13	)	)	PUNCT
ejpam-1224	362	14	as	as	SCONJ
ejpam-1224	362	15	follows	follow	VERB
ejpam-1224	362	16	,	,	PUNCT
ejpam-1224	362	17	di	di	INTJ
ejpam-1224	362	18	:	:	PUNCT
ejpam-1224	362	19	a⊗	a⊗	PROPN
ejpam-1224	362	20	vi1	vi1	INTJ
ejpam-1224	362	21	∧	∧	PROPN
ejpam-1224	362	22	vi2	vi2	PROPN
ejpam-1224	362	23	∧	∧	PROPN
ejpam-1224	362	24	·	·	PUNCT
ejpam-1224	362	25	·	·	PUNCT
ejpam-1224	362	26	·	·	PUNCT
ejpam-1224	363	1	∧	∧	NOUN
ejpam-1224	363	2	vip	vip	NOUN
ejpam-1224	363	3	→	→	SYM
ejpam-1224	363	4	σavi	σavi	PROPN
ejpam-1224	363	5	j	j	PROPN
ejpam-1224	363	6	(	(	PUNCT
ejpam-1224	363	7	−1	−1	NOUN
ejpam-1224	363	8	)	)	PUNCT
ejpam-1224	363	9	j−1vi1	j−1vi1	PROPN
ejpam-1224	364	1	∧	∧	PROPN
ejpam-1224	364	2	·	·	PUNCT
ejpam-1224	364	3	·	·	PUNCT
ejpam-1224	364	4	·	·	PUNCT
ejpam-1224	365	1	∧	∧	NOUN
ejpam-1224	365	2	bvi	bvi	NOUN
ejpam-1224	365	3	j	j	PROPN
ejpam-1224	365	4	∧	∧	PROPN
ejpam-1224	365	5	·	·	PUNCT
ejpam-1224	365	6	·	·	PUNCT
ejpam-1224	365	7	·	·	PUNCT
ejpam-1224	366	1	∧	∧	NOUN
ejpam-1224	366	2	vip	vip	NOUN
ejpam-1224	366	3	.	.	PUNCT
ejpam-1224	367	1	note	note	VERB
ejpam-1224	367	2	that	that	SCONJ
ejpam-1224	367	3	the	the	DET
ejpam-1224	367	4	koszul	koszul	ADJ
ejpam-1224	367	5	complex	complex	NOUN
ejpam-1224	367	6	is	be	AUX
ejpam-1224	367	7	graded	grade	VERB
ejpam-1224	367	8	by	by	ADP
ejpam-1224	367	9	tensor	tensor	NOUN
ejpam-1224	367	10	degree	degree	NOUN
ejpam-1224	367	11	since	since	SCONJ
ejpam-1224	367	12	a	a	PRON
ejpam-1224	367	13	and	and	CCONJ
ejpam-1224	367	14	a	a	PRON
ejpam-1224	367	15	!	!	NOUN
ejpam-1224	367	16	are	be	AUX
ejpam-1224	367	17	both	both	PRON
ejpam-1224	367	18	graded	grade	VERB
ejpam-1224	367	19	.	.	PUNCT
ejpam-1224	368	1	for	for	ADP
ejpam-1224	368	2	a	a	DET
ejpam-1224	368	3	⊗	⊗	PROPN
ejpam-1224	368	4	v	v	NUM
ejpam-1224	368	5	∈	∈	PROPN
ejpam-1224	368	6	(	(	PUNCT
ejpam-1224	368	7	a⊗	a⊗	NOUN
ejpam-1224	368	8	v	v	NOUN
ejpam-1224	368	9	)	)	PUNCT
ejpam-1224	368	10	n	n	CCONJ
ejpam-1224	368	11	,	,	PUNCT
ejpam-1224	368	12	deg(a	deg(a	PROPN
ejpam-1224	368	13	)	)	PUNCT
ejpam-1224	368	14	=	=	SYM
ejpam-1224	368	15	n	n	CCONJ
ejpam-1224	368	16	−	−	NUM
ejpam-1224	368	17	1	1	NUM
ejpam-1224	368	18	and	and	CCONJ
ejpam-1224	368	19	deg(v	deg(v	PROPN
ejpam-1224	368	20	)	)	PUNCT
ejpam-1224	368	21	=	=	SYM
ejpam-1224	368	22	1	1	NUM
ejpam-1224	368	23	so	so	ADV
ejpam-1224	368	24	deg(a	deg(a	PROPN
ejpam-1224	368	25	⊗	⊗	PROPN
ejpam-1224	368	26	v	v	NOUN
ejpam-1224	368	27	)	)	PUNCT
ejpam-1224	368	28	=	=	VERB
ejpam-1224	368	29	n.	n.	NOUN
ejpam-1224	368	30	also	also	ADV
ejpam-1224	368	31	note	note	VERB
ejpam-1224	368	32	that	that	SCONJ
ejpam-1224	368	33	h	h	NOUN
ejpam-1224	368	34	i(k∗)n	i(k∗)n	NOUN
ejpam-1224	368	35	=	=	SYM
ejpam-1224	368	36	0	0	PROPN
ejpam-1224	368	37	for	for	ADP
ejpam-1224	368	38	all	all	DET
ejpam-1224	368	39	i	i	PRON
ejpam-1224	368	40	>	>	X
ejpam-1224	368	41	0	0	PUNCT
ejpam-1224	369	1	and	and	CCONJ
ejpam-1224	369	2	for	for	ADP
ejpam-1224	369	3	i	i	PRON
ejpam-1224	369	4	=	=	NOUN
ejpam-1224	369	5	0	0	NUM
ejpam-1224	369	6	with	with	ADP
ejpam-1224	369	7	n	n	PROPN
ejpam-1224	369	8	6=	6=	NUM
ejpam-1224	369	9	0	0	NUM
ejpam-1224	369	10	.	.	PUNCT
ejpam-1224	370	1	the	the	DET
ejpam-1224	370	2	only	only	ADJ
ejpam-1224	370	3	nontrivial	nontrivial	ADJ
ejpam-1224	370	4	homology	homology	NOUN
ejpam-1224	370	5	group	group	NOUN
ejpam-1224	370	6	is	be	AUX
ejpam-1224	370	7	h0(k∗)0	h0(k∗)0	PROPN
ejpam-1224	370	8	=	=	SYM
ejpam-1224	370	9	k.	k.	PROPN
ejpam-1224	370	10	f.	f.	PROPN
ejpam-1224	370	11	hawwa	hawwa	PROPN
ejpam-1224	370	12	,	,	PUNCT
ejpam-1224	370	13	j.	j.	PROPN
ejpam-1224	370	14	hoffman	hoffman	PROPN
ejpam-1224	370	15	,	,	PUNCT
ejpam-1224	370	16	and	and	CCONJ
ejpam-1224	370	17	h.	h.	PROPN
ejpam-1224	370	18	wang	wang	PROPN
ejpam-1224	370	19	,	,	PUNCT
ejpam-1224	370	20	/	/	SYM
ejpam-1224	370	21	eur	eur	NOUN
ejpam-1224	370	22	.	.	PUNCT
ejpam-1224	371	1	j.	j.	PROPN
ejpam-1224	371	2	pure	pure	PROPN
ejpam-1224	371	3	appl	appl	PROPN
ejpam-1224	371	4	.	.	PROPN
ejpam-1224	371	5	math	math	PROPN
ejpam-1224	371	6	,	,	PUNCT
ejpam-1224	371	7	5	5	NUM
ejpam-1224	371	8	(	(	PUNCT
ejpam-1224	371	9	2012	2012	NUM
ejpam-1224	371	10	)	)	PUNCT
ejpam-1224	371	11	,	,	PUNCT
ejpam-1224	371	12	511	511	NUM
ejpam-1224	371	13	-	-	SYM
ejpam-1224	371	14	539	539	NUM
ejpam-1224	371	15	523	523	NUM
ejpam-1224	371	16	5	5	NUM
ejpam-1224	371	17	.	.	PUNCT
ejpam-1224	372	1	duality	duality	NOUN
ejpam-1224	372	2	let	let	VERB
ejpam-1224	372	3	u	u	PRON
ejpam-1224	372	4	=	=	PROPN
ejpam-1224	372	5	t	t	PROPN
ejpam-1224	372	6	(	(	PUNCT
ejpam-1224	372	7	v	v	NOUN
ejpam-1224	372	8	)	)	PUNCT
ejpam-1224	372	9	/	/	SYM
ejpam-1224	372	10	<	<	X
ejpam-1224	372	11	p	p	X
ejpam-1224	372	12	>	>	X
ejpam-1224	372	13	be	be	AUX
ejpam-1224	372	14	a	a	DET
ejpam-1224	372	15	λ	λ	NOUN
ejpam-1224	372	16	-	-	PUNCT
ejpam-1224	372	17	graded	grade	VERB
ejpam-1224	372	18	filtered	filter	VERB
ejpam-1224	372	19	quadratic	quadratic	ADJ
ejpam-1224	372	20	algebra	algebra	NOUN
ejpam-1224	372	21	.	.	PUNCT
ejpam-1224	373	1	let	let	VERB
ejpam-1224	373	2	a	a	DET
ejpam-1224	373	3	=	=	X
ejpam-1224	373	4	t	t	PROPN
ejpam-1224	373	5	(	(	PUNCT
ejpam-1224	373	6	v	v	NOUN
ejpam-1224	373	7	)	)	PUNCT
ejpam-1224	373	8	/	/	SYM
ejpam-1224	373	9	<	<	X
ejpam-1224	373	10	r	r	NOUN
ejpam-1224	373	11	>	>	PUNCT
ejpam-1224	373	12	,	,	PUNCT
ejpam-1224	373	13	where	where	SCONJ
ejpam-1224	373	14	r=	r=	ADJ
ejpam-1224	373	15	β(p	β(p	PROPN
ejpam-1224	373	16	)	)	PUNCT
ejpam-1224	373	17	as	as	ADP
ejpam-1224	373	18	in	in	ADP
ejpam-1224	373	19	section	section	NOUN
ejpam-1224	373	20	2	2	NUM
ejpam-1224	373	21	.	.	PUNCT
ejpam-1224	374	1	we	we	PRON
ejpam-1224	374	2	define	define	VERB
ejpam-1224	374	3	a	a	DET
ejpam-1224	374	4	dual	dual	ADJ
ejpam-1224	374	5	λ	λ	NOUN
ejpam-1224	374	6	-	-	PUNCT
ejpam-1224	374	7	graded	grade	VERB
ejpam-1224	374	8	curved	curved	ADJ
ejpam-1224	374	9	differential	differential	NOUN
ejpam-1224	374	10	graded	grade	VERB
ejpam-1224	374	11	algebra	algebra	NOUN
ejpam-1224	374	12	(	(	PUNCT
ejpam-1224	374	13	a	a	PROPN
ejpam-1224	374	14	!	!	PUNCT
ejpam-1224	374	15	,	,	PUNCT
ejpam-1224	374	16	d	d	X
ejpam-1224	374	17	,	,	PUNCT
ejpam-1224	374	18	c	c	NOUN
ejpam-1224	374	19	)	)	PUNCT
ejpam-1224	374	20	as	as	SCONJ
ejpam-1224	374	21	follows	follow	VERB
ejpam-1224	374	22	:	:	PUNCT
ejpam-1224	374	23	a	a	X
ejpam-1224	374	24	!	!	PUNCT
ejpam-1224	375	1	=	=	SYM
ejpam-1224	375	2	t	t	PROPN
ejpam-1224	375	3	(	(	PUNCT
ejpam-1224	375	4	v	v	NOUN
ejpam-1224	375	5	∗)/r⊥	∗)/r⊥	PROPN
ejpam-1224	375	6	,	,	PUNCT
ejpam-1224	375	7	α	α	X
ejpam-1224	375	8	:	:	PUNCT
ejpam-1224	375	9	r	r	NOUN
ejpam-1224	375	10	p−1	p−1	PROPN
ejpam-1224	375	11	2−−−→	2−−−→	NUM
ejpam-1224	375	12	p	p	X
ejpam-1224	375	13	p1−−−→	p1−−−→	PROPN
ejpam-1224	375	14	v	v	PROPN
ejpam-1224	375	15	,	,	PUNCT
ejpam-1224	375	16	β	β	X
ejpam-1224	375	17	:	:	PUNCT
ejpam-1224	375	18	r	r	NOUN
ejpam-1224	375	19	p−1	p−1	PROPN
ejpam-1224	375	20	2−−−→	2−−−→	NUM
ejpam-1224	375	21	p	p	NOUN
ejpam-1224	375	22	p0−−−→	p0−−−→	PROPN
ejpam-1224	375	23	k	k	PROPN
ejpam-1224	375	24	,	,	PUNCT
ejpam-1224	375	25	with	with	ADP
ejpam-1224	375	26	a	a	PRON
ejpam-1224	375	27	!	!	NOUN
ejpam-1224	375	28	1	1	NUM
ejpam-1224	375	29	=	=	SYM
ejpam-1224	375	30	v	v	NUM
ejpam-1224	375	31	∗	∗	NOUN
ejpam-1224	375	32	,	,	PUNCT
ejpam-1224	375	33	d	d	NOUN
ejpam-1224	375	34	=	=	PUNCT
ejpam-1224	375	35	α∗	α∗	NOUN
ejpam-1224	375	36	,	,	PUNCT
ejpam-1224	375	37	and	and	CCONJ
ejpam-1224	375	38	c	c	NOUN
ejpam-1224	375	39	=	=	SYM
ejpam-1224	375	40	β∗(1	β∗(1	NOUN
ejpam-1224	375	41	)	)	PUNCT
ejpam-1224	375	42	.	.	PUNCT
ejpam-1224	376	1	theorem	theorem	NOUN
ejpam-1224	376	2	1	1	NUM
ejpam-1224	376	3	.	.	PUNCT
ejpam-1224	376	4	assume	assume	VERB
ejpam-1224	376	5	a	a	PRON
ejpam-1224	376	6	is	be	AUX
ejpam-1224	376	7	koszul	koszul	ADJ
ejpam-1224	376	8	.	.	PUNCT
ejpam-1224	377	1	then	then	ADV
ejpam-1224	377	2	u	u	NOUN
ejpam-1224	377	3	is	be	AUX
ejpam-1224	377	4	of	of	ADP
ejpam-1224	377	5	pbw	pbw	NOUN
ejpam-1224	377	6	-	-	PUNCT
ejpam-1224	377	7	type	type	NOUN
ejpam-1224	377	8	if	if	SCONJ
ejpam-1224	378	1	and	and	CCONJ
ejpam-1224	378	2	only	only	ADV
ejpam-1224	378	3	if	if	SCONJ
ejpam-1224	378	4	the	the	DET
ejpam-1224	378	5	map	map	NOUN
ejpam-1224	378	6	α∗	α∗	VERB
ejpam-1224	378	7	extends	extend	VERB
ejpam-1224	378	8	to	to	ADP
ejpam-1224	378	9	an	an	DET
ejpam-1224	378	10	antiderivation	antiderivation	NOUN
ejpam-1224	378	11	d	d	NOUN
ejpam-1224	378	12	on	on	ADP
ejpam-1224	378	13	a	a	PRON
ejpam-1224	378	14	!	!	PUNCT
ejpam-1224	379	1	such	such	ADJ
ejpam-1224	379	2	that	that	PRON
ejpam-1224	379	3	,	,	PUNCT
ejpam-1224	379	4	letting	let	VERB
ejpam-1224	379	5	c	c	NOUN
ejpam-1224	379	6	=	=	SYM
ejpam-1224	379	7	β∗(1	β∗(1	NOUN
ejpam-1224	379	8	)	)	PUNCT
ejpam-1224	379	9	,	,	PUNCT
ejpam-1224	379	10	(	(	PUNCT
ejpam-1224	379	11	a	a	X
ejpam-1224	379	12	!	!	PUNCT
ejpam-1224	379	13	,	,	PUNCT
ejpam-1224	379	14	d	d	X
ejpam-1224	379	15	,	,	PUNCT
ejpam-1224	379	16	c	c	X
ejpam-1224	379	17	)	)	PUNCT
ejpam-1224	379	18	is	be	AUX
ejpam-1224	379	19	a	a	DET
ejpam-1224	379	20	curved	curved	ADJ
ejpam-1224	379	21	differential	differential	NOUN
ejpam-1224	379	22	graded	grade	VERB
ejpam-1224	379	23	algebra	algebra	NOUN
ejpam-1224	379	24	.	.	PUNCT
ejpam-1224	380	1	in	in	ADP
ejpam-1224	380	2	particular	particular	ADJ
ejpam-1224	380	3	,	,	PUNCT
ejpam-1224	380	4	when	when	SCONJ
ejpam-1224	380	5	c	c	NOUN
ejpam-1224	380	6	=	=	SYM
ejpam-1224	380	7	0	0	PROPN
ejpam-1224	380	8	,	,	PUNCT
ejpam-1224	380	9	giving	give	VERB
ejpam-1224	380	10	a	a	PRON
ejpam-1224	380	11	!	!	PUNCT
ejpam-1224	381	1	the	the	DET
ejpam-1224	381	2	structure	structure	NOUN
ejpam-1224	381	3	of	of	ADP
ejpam-1224	381	4	a	a	DET
ejpam-1224	381	5	differential	differential	NOUN
ejpam-1224	381	6	graded	grade	VERB
ejpam-1224	381	7	algebra	algebra	NOUN
ejpam-1224	381	8	is	be	AUX
ejpam-1224	381	9	equivalent	equivalent	ADJ
ejpam-1224	381	10	to	to	ADP
ejpam-1224	381	11	giving	give	VERB
ejpam-1224	381	12	a	a	DET
ejpam-1224	381	13	subspace	subspace	NOUN
ejpam-1224	381	14	p	p	PROPN
ejpam-1224	381	15	⊂	⊂	PROPN
ejpam-1224	381	16	v	v	PROPN
ejpam-1224	381	17	⊕	⊕	PROPN
ejpam-1224	381	18	(	(	PUNCT
ejpam-1224	381	19	v	v	NOUN
ejpam-1224	381	20	⊗	⊗	PROPN
ejpam-1224	381	21	v	v	NOUN
ejpam-1224	381	22	)	)	PUNCT
ejpam-1224	381	23	with	with	ADP
ejpam-1224	381	24	p2(p	p2(p	NOUN
ejpam-1224	381	25	)	)	PUNCT
ejpam-1224	382	1	=	=	SYM
ejpam-1224	382	2	r	r	NOUN
ejpam-1224	382	3	such	such	ADJ
ejpam-1224	382	4	that	that	DET
ejpam-1224	382	5	gru	gru	NOUN
ejpam-1224	382	6	=	=	SYM
ejpam-1224	382	7	a.	a.	NOUN
ejpam-1224	382	8	theorem	theorem	NOUN
ejpam-1224	382	9	2	2	X
ejpam-1224	382	10	.	.	X
ejpam-1224	382	11	assume	assume	VERB
ejpam-1224	382	12	a	a	PRON
ejpam-1224	382	13	is	be	AUX
ejpam-1224	382	14	koszul	koszul	ADJ
ejpam-1224	382	15	.	.	PUNCT
ejpam-1224	383	1	then	then	ADV
ejpam-1224	383	2	u	u	NOUN
ejpam-1224	383	3	is	be	AUX
ejpam-1224	383	4	of	of	ADP
ejpam-1224	383	5	pbw	pbw	NOUN
ejpam-1224	383	6	-	-	PUNCT
ejpam-1224	383	7	type	type	NOUN
ejpam-1224	383	8	if	if	SCONJ
ejpam-1224	383	9	and	and	CCONJ
ejpam-1224	383	10	only	only	ADV
ejpam-1224	383	11	if	if	SCONJ
ejpam-1224	383	12	1	1	NUM
ejpam-1224	383	13	.	.	PUNCT
ejpam-1224	383	14	im(α⊗	im(α⊗	X
ejpam-1224	384	1	i	i	PROPN
ejpam-1224	384	2	d	d	NOUN
ejpam-1224	384	3	−	−	PROPN
ejpam-1224	385	1	i	i	PROPN
ejpam-1224	385	2	d	d	PROPN
ejpam-1224	385	3	⊗α	⊗α	NOUN
ejpam-1224	385	4	)	)	PUNCT
ejpam-1224	386	1	⊆	⊆	NUM
ejpam-1224	386	2	r⊆	r⊆	NOUN
ejpam-1224	386	3	v	v	ADP
ejpam-1224	386	4	⊗	⊗	NUM
ejpam-1224	386	5	v	v	NOUN
ejpam-1224	386	6	(	(	PUNCT
ejpam-1224	386	7	this	this	DET
ejpam-1224	386	8	map	map	NOUN
ejpam-1224	386	9	is	be	AUX
ejpam-1224	386	10	defined	define	VERB
ejpam-1224	386	11	on	on	ADP
ejpam-1224	386	12	(	(	PUNCT
ejpam-1224	386	13	r⊗	r⊗	NOUN
ejpam-1224	386	14	v	v	NOUN
ejpam-1224	386	15	)	)	PUNCT
ejpam-1224	386	16	∩	∩	NOUN
ejpam-1224	386	17	(	(	PUNCT
ejpam-1224	386	18	v	v	NOUN
ejpam-1224	386	19	⊗	⊗	PROPN
ejpam-1224	386	20	r	r	NOUN
ejpam-1224	386	21	)	)	PUNCT
ejpam-1224	386	22	)	)	PUNCT
ejpam-1224	386	23	.	.	PUNCT
ejpam-1224	387	1	2	2	X
ejpam-1224	387	2	.	.	X
ejpam-1224	387	3	α	α	X
ejpam-1224	387	4	◦	◦	NOUN
ejpam-1224	387	5	(	(	PUNCT
ejpam-1224	387	6	α⊗	α⊗	X
ejpam-1224	388	1	i	i	PROPN
ejpam-1224	388	2	d	d	PROPN
ejpam-1224	388	3	−	−	PROPN
ejpam-1224	389	1	i	i	PROPN
ejpam-1224	389	2	d	d	PROPN
ejpam-1224	389	3	⊗α	⊗α	NOUN
ejpam-1224	389	4	)	)	PUNCT
ejpam-1224	390	1	=	=	PUNCT
ejpam-1224	391	1	β	β	X
ejpam-1224	391	2	⊗	⊗	PROPN
ejpam-1224	392	1	i	i	PROPN
ejpam-1224	392	2	d	d	PROPN
ejpam-1224	392	3	−	−	PROPN
ejpam-1224	393	1	i	i	PROPN
ejpam-1224	393	2	d	d	PROPN
ejpam-1224	393	3	⊗	⊗	PROPN
ejpam-1224	393	4	β	β	X
ejpam-1224	393	5	.	.	PUNCT
ejpam-1224	394	1	3	3	X
ejpam-1224	394	2	.	.	X
ejpam-1224	394	3	β	β	X
ejpam-1224	394	4	◦	◦	NOUN
ejpam-1224	394	5	(	(	PUNCT
ejpam-1224	394	6	α⊗	α⊗	X
ejpam-1224	394	7	i	i	PROPN
ejpam-1224	395	1	d	d	PROPN
ejpam-1224	395	2	−	−	PROPN
ejpam-1224	396	1	i	i	PROPN
ejpam-1224	396	2	d	d	PROPN
ejpam-1224	396	3	⊗α	⊗α	NOUN
ejpam-1224	396	4	)	)	PUNCT
ejpam-1224	397	1	=	=	SYM
ejpam-1224	397	2	0	0	X
ejpam-1224	397	3	.	.	PUNCT
ejpam-1224	398	1	these	these	DET
ejpam-1224	398	2	two	two	NUM
ejpam-1224	398	3	theorems	theorem	NOUN
ejpam-1224	398	4	amount	amount	NOUN
ejpam-1224	398	5	to	to	ADP
ejpam-1224	398	6	giving	give	VERB
ejpam-1224	398	7	a	a	PRON
ejpam-1224	398	8	!	!	PUNCT
ejpam-1224	399	1	the	the	DET
ejpam-1224	399	2	structure	structure	NOUN
ejpam-1224	399	3	of	of	ADP
ejpam-1224	399	4	a	a	DET
ejpam-1224	399	5	cdga	cdga	NOUN
ejpam-1224	399	6	.	.	PUNCT
ejpam-1224	400	1	the	the	DET
ejpam-1224	400	2	following	follow	VERB
ejpam-1224	400	3	lemma	lemma	PROPN
ejpam-1224	400	4	will	will	AUX
ejpam-1224	400	5	be	be	AUX
ejpam-1224	400	6	made	make	VERB
ejpam-1224	400	7	use	use	NOUN
ejpam-1224	400	8	of	of	ADP
ejpam-1224	400	9	in	in	ADP
ejpam-1224	400	10	section	section	NOUN
ejpam-1224	400	11	6	6	NUM
ejpam-1224	400	12	.	.	PUNCT
ejpam-1224	401	1	lemma	lemma	PROPN
ejpam-1224	401	2	1	1	NUM
ejpam-1224	401	3	.	.	PUNCT
ejpam-1224	402	1	the	the	DET
ejpam-1224	402	2	element	element	NOUN
ejpam-1224	402	3	in	in	ADP
ejpam-1224	402	4	u	u	PROPN
ejpam-1224	402	5	⊗k	⊗k	NOUN
ejpam-1224	402	6	a	a	PRON
ejpam-1224	402	7	!	!	PUNCT
ejpam-1224	403	1	∑	∑	PROPN
ejpam-1224	403	2	xαxβ	xαxβ	PROPN
ejpam-1224	403	3	⊗	⊗	PROPN
ejpam-1224	403	4	x̌β	x̌β	PROPN
ejpam-1224	404	1	x̌α+	x̌α+	PROPN
ejpam-1224	404	2	∑	∑	PROPN
ejpam-1224	404	3	xα⊗	xα⊗	PROPN
ejpam-1224	404	4	d	d	PROPN
ejpam-1224	404	5	(	(	PUNCT
ejpam-1224	404	6	x̌α	x̌α	NOUN
ejpam-1224	404	7	)	)	PUNCT
ejpam-1224	405	1	+	+	NUM
ejpam-1224	406	1	1⊗	1⊗	NUM
ejpam-1224	406	2	c	c	NOUN
ejpam-1224	406	3	(	(	PUNCT
ejpam-1224	406	4	1	1	NUM
ejpam-1224	406	5	)	)	PUNCT
ejpam-1224	406	6	and	and	CCONJ
ejpam-1224	406	7	the	the	DET
ejpam-1224	406	8	element	element	NOUN
ejpam-1224	406	9	in	in	ADP
ejpam-1224	406	10	a!⊗k	a!⊗k	PROPN
ejpam-1224	406	11	u	u	PROPN
ejpam-1224	406	12	∑	∑	PROPN
ejpam-1224	406	13	x̌β	x̌β	PROPN
ejpam-1224	406	14	x̌α⊗	x̌α⊗	ADJ
ejpam-1224	406	15	xαxβ	xαxβ	NOUN
ejpam-1224	406	16	+	+	CCONJ
ejpam-1224	406	17	d	d	X
ejpam-1224	406	18	(	(	PUNCT
ejpam-1224	406	19	x̌α)⊗	x̌α)⊗	PROPN
ejpam-1224	406	20	xα+	xα+	PROPN
ejpam-1224	406	21	c	c	PROPN
ejpam-1224	407	1	⊗	⊗	PROPN
ejpam-1224	407	2	1	1	NUM
ejpam-1224	407	3	are	be	AUX
ejpam-1224	407	4	both	both	PRON
ejpam-1224	407	5	zero	zero	NUM
ejpam-1224	407	6	.	.	PUNCT
ejpam-1224	408	1	proof	proof	NOUN
ejpam-1224	408	2	.	.	PUNCT
ejpam-1224	409	1	consider	consider	VERB
ejpam-1224	409	2	the	the	DET
ejpam-1224	409	3	pairing	pairing	NOUN
ejpam-1224	409	4	(	(	PUNCT
ejpam-1224	409	5	u	u	NOUN
ejpam-1224	409	6	⊗	⊗	PROPN
ejpam-1224	409	7	a	a	NOUN
ejpam-1224	409	8	!	!	PUNCT
ejpam-1224	410	1	2)⊗	2)⊗	NUM
ejpam-1224	410	2	(	(	PUNCT
ejpam-1224	410	3	a	a	NOUN
ejpam-1224	410	4	!	!	NOUN
ejpam-1224	410	5	2	2	X
ejpam-1224	410	6	)	)	PUNCT
ejpam-1224	410	7	∗→	∗→	ADJ
ejpam-1224	410	8	u	u	NOUN
ejpam-1224	410	9	.	.	PUNCT
ejpam-1224	411	1	denoting	denote	VERB
ejpam-1224	411	2	the	the	DET
ejpam-1224	411	3	element	element	NOUN
ejpam-1224	411	4	in	in	ADP
ejpam-1224	411	5	(	(	PUNCT
ejpam-1224	411	6	1	1	NUM
ejpam-1224	411	7	)	)	PUNCT
ejpam-1224	411	8	as	as	ADP
ejpam-1224	411	9	m	m	PROPN
ejpam-1224	411	10	,	,	PUNCT
ejpam-1224	411	11	we	we	PRON
ejpam-1224	411	12	show	show	VERB
ejpam-1224	411	13	that	that	SCONJ
ejpam-1224	411	14	〈	〈	NOUN
ejpam-1224	411	15	m,−	m,−	PROPN
ejpam-1224	411	16	〉	〉	NOUN
ejpam-1224	411	17	:	:	PUNCT
ejpam-1224	411	18	(	(	PUNCT
ejpam-1224	411	19	a	a	X
ejpam-1224	411	20	!	!	NOUN
ejpam-1224	411	21	2	2	X
ejpam-1224	411	22	)	)	PUNCT
ejpam-1224	411	23	∗→	∗→	NOUN
ejpam-1224	411	24	u	u	NOUN
ejpam-1224	411	25	is	be	AUX
ejpam-1224	411	26	zero	zero	NUM
ejpam-1224	411	27	.	.	PUNCT
ejpam-1224	412	1	note	note	VERB
ejpam-1224	412	2	that	that	SCONJ
ejpam-1224	412	3	〈	〈	PROPN
ejpam-1224	412	4	m	m	PROPN
ejpam-1224	412	5	,	,	PUNCT
ejpam-1224	412	6	r	r	NOUN
ejpam-1224	412	7	〉	〉	NOUN
ejpam-1224	412	8	=	=	SYM
ejpam-1224	412	9	∑¬	∑¬	PROPN
ejpam-1224	412	10	xαxβ	xαxβ	PROPN
ejpam-1224	413	1	⊗	⊗	PROPN
ejpam-1224	413	2	x̌β	x̌β	PROPN
ejpam-1224	413	3	x̌α	x̌α	PROPN
ejpam-1224	413	4	,	,	PUNCT
ejpam-1224	413	5	r	r	PROPN
ejpam-1224	413	6	¶	¶	PROPN
ejpam-1224	413	7	+	+	CCONJ
ejpam-1224	413	8	∑	∑	PROPN
ejpam-1224	413	9	xα⊗	xα⊗	PROPN
ejpam-1224	413	10	d	d	PROPN
ejpam-1224	413	11	(	(	PUNCT
ejpam-1224	413	12	x̌α	x̌α	NOUN
ejpam-1224	413	13	)	)	PUNCT
ejpam-1224	413	14	,	,	PUNCT
ejpam-1224	413	15	r	r	NOUN
ejpam-1224	413	16	�	�	PROPN
ejpam-1224	413	17	+	+	CCONJ
ejpam-1224	413	18	〈	〈	PROPN
ejpam-1224	413	19	1⊗	1⊗	PROPN
ejpam-1224	413	20	c	c	NOUN
ejpam-1224	413	21	,	,	PUNCT
ejpam-1224	413	22	r	r	NOUN
ejpam-1224	413	23	〉	〉	NOUN
ejpam-1224	413	24	.	.	PUNCT
ejpam-1224	414	1	also	also	ADV
ejpam-1224	414	2	note	note	VERB
ejpam-1224	414	3	that	that	SCONJ
ejpam-1224	414	4	for	for	ADP
ejpam-1224	414	5	an	an	DET
ejpam-1224	414	6	element	element	NOUN
ejpam-1224	414	7	r	r	NOUN
ejpam-1224	414	8	in	in	ADP
ejpam-1224	414	9	r=	r=	ADJ
ejpam-1224	414	10	(	(	PUNCT
ejpam-1224	414	11	a	a	NOUN
ejpam-1224	414	12	!	!	NOUN
ejpam-1224	414	13	2	2	NUM
ejpam-1224	414	14	)	)	PUNCT
ejpam-1224	414	15	∗	∗	NOUN
ejpam-1224	414	16	we	we	PRON
ejpam-1224	414	17	have	have	VERB
ejpam-1224	414	18	∑	∑	ADV
ejpam-1224	414	19	xαxβ	xαxβ	NOUN
ejpam-1224	414	20	¬	¬	PROPN
ejpam-1224	414	21	x̌β	x̌β	PROPN
ejpam-1224	414	22	x̌α	x̌α	PROPN
ejpam-1224	414	23	,	,	PUNCT
ejpam-1224	414	24	r	r	NOUN
ejpam-1224	414	25	¶	¶	NOUN
ejpam-1224	414	26	=	=	SYM
ejpam-1224	415	1	r	r	NOUN
ejpam-1224	415	2	,	,	PUNCT
ejpam-1224	415	3	∑	∑	PROPN
ejpam-1224	415	4	xα	xα	PROPN
ejpam-1224	415	5	d	d	X
ejpam-1224	415	6	(	(	PUNCT
ejpam-1224	415	7	x̌α	x̌α	NOUN
ejpam-1224	415	8	)	)	PUNCT
ejpam-1224	415	9	,	,	PUNCT
ejpam-1224	415	10	r	r	NOUN
ejpam-1224	415	11	�	�	PROPN
ejpam-1224	415	12	=	=	SYM
ejpam-1224	415	13	α(r	α(r	PROPN
ejpam-1224	415	14	)	)	PUNCT
ejpam-1224	415	15	,	,	PUNCT
ejpam-1224	415	16	〈	〈	PROPN
ejpam-1224	415	17	c	c	X
ejpam-1224	415	18	,	,	PUNCT
ejpam-1224	415	19	r	r	NOUN
ejpam-1224	415	20	〉	〉	NOUN
ejpam-1224	415	21	=	=	SYM
ejpam-1224	415	22	β(r	β(r	NOUN
ejpam-1224	415	23	)	)	PUNCT
ejpam-1224	415	24	,	,	PUNCT
ejpam-1224	415	25	and	and	CCONJ
ejpam-1224	415	26	since	since	SCONJ
ejpam-1224	415	27	r	r	NOUN
ejpam-1224	415	28	+	+	NOUN
ejpam-1224	415	29	α(r	α(r	NOUN
ejpam-1224	415	30	)	)	PUNCT
ejpam-1224	415	31	+	+	CCONJ
ejpam-1224	416	1	β(r	β(r	NOUN
ejpam-1224	416	2	)	)	PUNCT
ejpam-1224	416	3	=	=	SYM
ejpam-1224	416	4	0	0	NUM
ejpam-1224	416	5	in	in	ADP
ejpam-1224	416	6	u	u	PROPN
ejpam-1224	416	7	,	,	PUNCT
ejpam-1224	416	8	the	the	DET
ejpam-1224	416	9	lemma	lemma	PROPN
ejpam-1224	416	10	is	be	AUX
ejpam-1224	416	11	proven	prove	VERB
ejpam-1224	416	12	.	.	PUNCT
ejpam-1224	417	1	f.	f.	PROPN
ejpam-1224	417	2	hawwa	hawwa	PROPN
ejpam-1224	417	3	,	,	PUNCT
ejpam-1224	417	4	j.	j.	PROPN
ejpam-1224	417	5	hoffman	hoffman	PROPN
ejpam-1224	417	6	,	,	PUNCT
ejpam-1224	417	7	and	and	CCONJ
ejpam-1224	417	8	h.	h.	PROPN
ejpam-1224	417	9	wang	wang	PROPN
ejpam-1224	417	10	,	,	PUNCT
ejpam-1224	417	11	/	/	SYM
ejpam-1224	417	12	eur	eur	NOUN
ejpam-1224	417	13	.	.	PUNCT
ejpam-1224	418	1	j.	j.	PROPN
ejpam-1224	418	2	pure	pure	PROPN
ejpam-1224	418	3	appl	appl	PROPN
ejpam-1224	418	4	.	.	PROPN
ejpam-1224	418	5	math	math	PROPN
ejpam-1224	418	6	,	,	PUNCT
ejpam-1224	418	7	5	5	NUM
ejpam-1224	418	8	(	(	PUNCT
ejpam-1224	418	9	2012	2012	NUM
ejpam-1224	418	10	)	)	PUNCT
ejpam-1224	418	11	,	,	PUNCT
ejpam-1224	418	12	511	511	NUM
ejpam-1224	418	13	-	-	SYM
ejpam-1224	418	14	539	539	NUM
ejpam-1224	418	15	524	524	NUM
ejpam-1224	418	16	example	example	NOUN
ejpam-1224	418	17	5	5	NUM
ejpam-1224	418	18	.	.	PUNCT
ejpam-1224	419	1	we	we	PRON
ejpam-1224	419	2	may	may	AUX
ejpam-1224	419	3	first	first	ADV
ejpam-1224	419	4	consider	consider	VERB
ejpam-1224	419	5	the	the	DET
ejpam-1224	419	6	case	case	NOUN
ejpam-1224	419	7	where	where	SCONJ
ejpam-1224	419	8	u	u	NOUN
ejpam-1224	419	9	=	=	NOUN
ejpam-1224	419	10	a	a	PRON
ejpam-1224	419	11	is	be	AUX
ejpam-1224	419	12	a	a	DET
ejpam-1224	419	13	λ	λ	NOUN
ejpam-1224	419	14	-	-	PUNCT
ejpam-1224	419	15	graded	grade	VERB
ejpam-1224	419	16	filtered	filter	VERB
ejpam-1224	419	17	algebra	algebra	NOUN
ejpam-1224	419	18	.	.	PUNCT
ejpam-1224	420	1	the	the	DET
ejpam-1224	420	2	dual	dual	ADJ
ejpam-1224	420	3	will	will	AUX
ejpam-1224	420	4	be	be	AUX
ejpam-1224	420	5	the	the	DET
ejpam-1224	420	6	cdga	cdga	NOUN
ejpam-1224	420	7	(	(	PUNCT
ejpam-1224	420	8	a	a	PROPN
ejpam-1224	420	9	!	!	PUNCT
ejpam-1224	420	10	,	,	PUNCT
ejpam-1224	421	1	d	d	X
ejpam-1224	421	2	=	=	SYM
ejpam-1224	421	3	0	0	NUM
ejpam-1224	421	4	,	,	PUNCT
ejpam-1224	421	5	c	c	NOUN
ejpam-1224	421	6	=	=	SYM
ejpam-1224	421	7	0	0	NUM
ejpam-1224	421	8	)	)	PUNCT
ejpam-1224	421	9	.	.	PUNCT
ejpam-1224	422	1	example	example	NOUN
ejpam-1224	423	1	6	6	NUM
ejpam-1224	423	2	.	.	PUNCT
ejpam-1224	423	3	let	let	VERB
ejpam-1224	423	4	u	u	NOUN
ejpam-1224	423	5	=	=	VERB
ejpam-1224	423	6	ug	ug	PART
ejpam-1224	423	7	be	be	AUX
ejpam-1224	423	8	the	the	DET
ejpam-1224	423	9	universal	universal	ADJ
ejpam-1224	423	10	enveloping	enveloping	NOUN
ejpam-1224	423	11	algebra	algebra	NOUN
ejpam-1224	423	12	of	of	ADP
ejpam-1224	423	13	a	a	DET
ejpam-1224	423	14	lie	lie	NOUN
ejpam-1224	423	15	algebra	algebra	NOUN
ejpam-1224	424	1	g.	g.	PROPN
ejpam-1224	424	2	then	then	ADV
ejpam-1224	424	3	the	the	DET
ejpam-1224	424	4	dual	dual	ADJ
ejpam-1224	424	5	(	(	PUNCT
ejpam-1224	424	6	a	a	NOUN
ejpam-1224	424	7	!	!	PUNCT
ejpam-1224	424	8	,	,	PUNCT
ejpam-1224	425	1	d	d	X
ejpam-1224	425	2	,	,	PUNCT
ejpam-1224	425	3	c	c	NOUN
ejpam-1224	425	4	=	=	SYM
ejpam-1224	425	5	0	0	NUM
ejpam-1224	425	6	)	)	PUNCT
ejpam-1224	425	7	is	be	AUX
ejpam-1224	425	8	the	the	DET
ejpam-1224	425	9	chevalley	chevalley	PROPN
ejpam-1224	425	10	-	-	PUNCT
ejpam-1224	425	11	eilenberg	eilenberg	NOUN
ejpam-1224	425	12	complex	complex	NOUN
ejpam-1224	425	13	of	of	ADP
ejpam-1224	425	14	the	the	DET
ejpam-1224	425	15	lie	lie	NOUN
ejpam-1224	425	16	algebra	algebra	PROPN
ejpam-1224	425	17	g.	g.	PROPN
ejpam-1224	425	18	example	example	NOUN
ejpam-1224	426	1	7	7	X
ejpam-1224	426	2	.	.	PUNCT
ejpam-1224	426	3	the	the	DET
ejpam-1224	426	4	symmetric	symmetric	ADJ
ejpam-1224	426	5	algebra	algebra	NOUN
ejpam-1224	426	6	on	on	ADP
ejpam-1224	426	7	v	v	NUM
ejpam-1224	426	8	,	,	PUNCT
ejpam-1224	426	9	s(v	s(v	PROPN
ejpam-1224	426	10	)	)	PUNCT
ejpam-1224	426	11	,	,	PUNCT
ejpam-1224	426	12	is	be	AUX
ejpam-1224	426	13	defined	define	VERB
ejpam-1224	426	14	by	by	ADP
ejpam-1224	426	15	r	r	NOUN
ejpam-1224	426	16	=	=	SYM
ejpam-1224	426	17	(	(	PUNCT
ejpam-1224	426	18	x	x	PROPN
ejpam-1224	426	19	⊗	⊗	PROPN
ejpam-1224	426	20	y	y	PROPN
ejpam-1224	426	21	−	−	PROPN
ejpam-1224	426	22	y	y	PROPN
ejpam-1224	426	23	⊗	⊗	PROPN
ejpam-1224	426	24	x)x	x)x	PUNCT
ejpam-1224	426	25	,	,	PUNCT
ejpam-1224	426	26	y∈v	y∈v	NOUN
ejpam-1224	426	27	.	.	PUNCT
ejpam-1224	427	1	the	the	DET
ejpam-1224	427	2	quadratic	quadratic	ADJ
ejpam-1224	427	3	dual	dual	ADJ
ejpam-1224	427	4	algebra	algebra	NOUN
ejpam-1224	427	5	of	of	ADP
ejpam-1224	427	6	s(v	s(v	PROPN
ejpam-1224	427	7	)	)	PUNCT
ejpam-1224	427	8	is	be	AUX
ejpam-1224	427	9	the	the	DET
ejpam-1224	427	10	exterior	exterior	ADJ
ejpam-1224	427	11	algebra	algebra	NOUN
ejpam-1224	427	12	e(v	e(v	VERB
ejpam-1224	427	13	∗	∗	NOUN
ejpam-1224	427	14	)	)	PUNCT
ejpam-1224	427	15	defined	define	VERB
ejpam-1224	427	16	by	by	ADP
ejpam-1224	427	17	the	the	DET
ejpam-1224	427	18	relations	relation	NOUN
ejpam-1224	427	19	(	(	PUNCT
ejpam-1224	427	20	x⊗	x⊗	PROPN
ejpam-1224	427	21	x)x∈v∗	x)x∈v∗	PUNCT
ejpam-1224	428	1	in	in	ADP
ejpam-1224	428	2	v	v	NUM
ejpam-1224	428	3	∗	∗	NOUN
ejpam-1224	428	4	⊗	⊗	PROPN
ejpam-1224	428	5	v	v	ADP
ejpam-1224	428	6	∗.	∗.	PROPN
ejpam-1224	428	7	example	example	NOUN
ejpam-1224	428	8	8	8	NUM
ejpam-1224	428	9	.	.	PUNCT
ejpam-1224	428	10	continuing	continue	VERB
ejpam-1224	428	11	example	example	NOUN
ejpam-1224	428	12	3	3	NUM
ejpam-1224	428	13	,	,	PUNCT
ejpam-1224	428	14	we	we	PRON
ejpam-1224	428	15	can	can	AUX
ejpam-1224	428	16	show	show	VERB
ejpam-1224	428	17	explicitly	explicitly	ADV
ejpam-1224	428	18	that	that	SCONJ
ejpam-1224	428	19	theorems	theorem	VERB
ejpam-1224	428	20	1	1	NUM
ejpam-1224	428	21	and	and	CCONJ
ejpam-1224	428	22	2	2	NUM
ejpam-1224	428	23	amount	amount	NOUN
ejpam-1224	428	24	to	to	ADP
ejpam-1224	428	25	giving	give	VERB
ejpam-1224	428	26	a	a	PRON
ejpam-1224	428	27	!	!	PUNCT
ejpam-1224	429	1	the	the	DET
ejpam-1224	429	2	structure	structure	NOUN
ejpam-1224	429	3	of	of	ADP
ejpam-1224	429	4	a	a	DET
ejpam-1224	429	5	cdga	cdga	NOUN
ejpam-1224	429	6	.	.	PUNCT
ejpam-1224	430	1	we	we	PRON
ejpam-1224	430	2	have	have	VERB
ejpam-1224	430	3	the	the	DET
ejpam-1224	430	4	following	follow	VERB
ejpam-1224	430	5	algebra	algebra	NOUN
ejpam-1224	430	6	u	u	NOUN
ejpam-1224	430	7	=	=	PROPN
ejpam-1224	430	8	k[x]/(x2−	k[x]/(x2−	PROPN
ejpam-1224	430	9	(	(	PUNCT
ejpam-1224	430	10	a−	a−	PROPN
ejpam-1224	430	11	b)x	b)x	X
ejpam-1224	430	12	+	+	CCONJ
ejpam-1224	430	13	ab	ab	X
ejpam-1224	430	14	)	)	PUNCT
ejpam-1224	430	15	=	=	SYM
ejpam-1224	430	16	k[x]/(x	k[x]/(x	NOUN
ejpam-1224	430	17	−	−	NOUN
ejpam-1224	430	18	a)⊕	a)⊕	VERB
ejpam-1224	430	19	k[x]/(x	k[x]/(x	NOUN
ejpam-1224	430	20	−	−	PROPN
ejpam-1224	430	21	b	b	NOUN
ejpam-1224	430	22	)	)	PUNCT
ejpam-1224	430	23	.	.	PUNCT
ejpam-1224	431	1	given	give	VERB
ejpam-1224	431	2	u	u	NOUN
ejpam-1224	431	3	,	,	PUNCT
ejpam-1224	431	4	we	we	PRON
ejpam-1224	431	5	know	know	VERB
ejpam-1224	431	6	that	that	SCONJ
ejpam-1224	431	7	a	a	PRON
ejpam-1224	431	8	!	!	PUNCT
ejpam-1224	432	1	=	=	SYM
ejpam-1224	432	2	k[ξ	k[ξ	X
ejpam-1224	432	3	]	]	PUNCT
ejpam-1224	432	4	assuming	assume	VERB
ejpam-1224	432	5	<	<	X
ejpam-1224	432	6	x	x	X
ejpam-1224	432	7	,	,	PUNCT
ejpam-1224	432	8	ξ	ξ	X
ejpam-1224	432	9	>	>	PUNCT
ejpam-1224	432	10	=	=	PROPN
ejpam-1224	432	11	1	1	X
ejpam-1224	432	12	.	.	PUNCT
ejpam-1224	433	1	by	by	ADP
ejpam-1224	433	2	definition	definition	NOUN
ejpam-1224	433	3	we	we	PRON
ejpam-1224	433	4	know	know	VERB
ejpam-1224	433	5	α(x2	α(x2	NOUN
ejpam-1224	433	6	)	)	PUNCT
ejpam-1224	434	1	=	=	SYM
ejpam-1224	434	2	−(a+	−(a+	NOUN
ejpam-1224	434	3	b)x	b)x	NOUN
ejpam-1224	434	4	and	and	CCONJ
ejpam-1224	434	5	β(x2	β(x2	NOUN
ejpam-1224	434	6	)	)	PUNCT
ejpam-1224	435	1	=	=	SYM
ejpam-1224	435	2	ab	ab	PROPN
ejpam-1224	435	3	,	,	PUNCT
ejpam-1224	435	4	so	so	ADV
ejpam-1224	435	5	now	now	ADV
ejpam-1224	435	6	to	to	PART
ejpam-1224	435	7	calculate	calculate	VERB
ejpam-1224	435	8	the	the	DET
ejpam-1224	435	9	differential	differential	NOUN
ejpam-1224	435	10	we	we	PRON
ejpam-1224	435	11	have	have	VERB
ejpam-1224	435	12	<	<	X
ejpam-1224	435	13	α∗(ξ	α∗(ξ	PROPN
ejpam-1224	435	14	)	)	PUNCT
ejpam-1224	435	15	,	,	PUNCT
ejpam-1224	436	1	x2	x2	X
ejpam-1224	436	2	>	>	PUNCT
ejpam-1224	436	3	=	=	X
ejpam-1224	436	4	<	<	X
ejpam-1224	436	5	ξ	ξ	PROPN
ejpam-1224	436	6	,	,	PUNCT
ejpam-1224	436	7	α(x2)>=	α(x2)>=	NUM
ejpam-1224	436	8	<	<	X
ejpam-1224	436	9	ξ,−(a+	ξ,−(a+	NOUN
ejpam-1224	436	10	b)x	b)x	X
ejpam-1224	436	11	>	>	PUNCT
ejpam-1224	436	12	=	=	PUNCT
ejpam-1224	437	1	−(a+	−(a+	NUM
ejpam-1224	437	2	b	b	NOUN
ejpam-1224	437	3	)	)	PUNCT
ejpam-1224	437	4	.	.	PUNCT
ejpam-1224	438	1	this	this	PRON
ejpam-1224	438	2	tells	tell	VERB
ejpam-1224	438	3	us	we	PRON
ejpam-1224	438	4	that	that	SCONJ
ejpam-1224	438	5	α∗(ξ	α∗(ξ	NOUN
ejpam-1224	438	6	)	)	PUNCT
ejpam-1224	438	7	is	be	AUX
ejpam-1224	438	8	the	the	DET
ejpam-1224	438	9	element	element	NOUN
ejpam-1224	438	10	of	of	ADP
ejpam-1224	438	11	a	a	DET
ejpam-1224	438	12	!	!	NOUN
ejpam-1224	438	13	2	2	NUM
ejpam-1224	438	14	for	for	ADP
ejpam-1224	438	15	which	which	PRON
ejpam-1224	438	16	<	<	X
ejpam-1224	438	17	α∗(ξ	α∗(ξ	PROPN
ejpam-1224	438	18	)	)	PUNCT
ejpam-1224	438	19	,	,	PUNCT
ejpam-1224	439	1	x2	x2	PROPN
ejpam-1224	439	2	>	>	PUNCT
ejpam-1224	439	3	=	=	PROPN
ejpam-1224	440	1	−(a+	−(a+	NUM
ejpam-1224	440	2	b	b	NOUN
ejpam-1224	440	3	)	)	PUNCT
ejpam-1224	440	4	,	,	PUNCT
ejpam-1224	440	5	so	so	ADV
ejpam-1224	440	6	α∗(ξ	α∗(ξ	PROPN
ejpam-1224	440	7	)	)	PUNCT
ejpam-1224	441	1	=	=	SYM
ejpam-1224	441	2	ξ2	ξ2	NOUN
ejpam-1224	441	3	.	.	PUNCT
ejpam-1224	442	1	this	this	PRON
ejpam-1224	442	2	tells	tell	VERB
ejpam-1224	442	3	us	we	PRON
ejpam-1224	442	4	that	that	DET
ejpam-1224	442	5	dξ=	dξ=	PROPN
ejpam-1224	442	6	−(a+	−(a+	NOUN
ejpam-1224	442	7	b)ξ2	b)ξ2	PROPN
ejpam-1224	442	8	.	.	PUNCT
ejpam-1224	443	1	now	now	ADV
ejpam-1224	443	2	let	let	VERB
ejpam-1224	443	3	us	we	PRON
ejpam-1224	443	4	calculate	calculate	VERB
ejpam-1224	443	5	d(ξ2	d(ξ2	NOUN
ejpam-1224	443	6	)	)	PUNCT
ejpam-1224	443	7	.	.	PUNCT
ejpam-1224	444	1	we	we	PRON
ejpam-1224	444	2	have	have	VERB
ejpam-1224	444	3	d(ξ2	d(ξ2	NOUN
ejpam-1224	444	4	)	)	PUNCT
ejpam-1224	445	1	=	=	PUNCT
ejpam-1224	445	2	dξ	dξ	PROPN
ejpam-1224	445	3	·	·	PUNCT
ejpam-1224	445	4	ξ−	ξ−	NOUN
ejpam-1224	445	5	ξ	ξ	PROPN
ejpam-1224	445	6	·	·	PUNCT
ejpam-1224	445	7	dξ=	dξ=	PROPN
ejpam-1224	445	8	−(a+	−(a+	NOUN
ejpam-1224	445	9	b)ξ2	b)ξ2	PROPN
ejpam-1224	445	10	·	·	PUNCT
ejpam-1224	445	11	ξ+	ξ+	X
ejpam-1224	445	12	ξ	ξ	X
ejpam-1224	445	13	·	·	PUNCT
ejpam-1224	445	14	(	(	PUNCT
ejpam-1224	445	15	a+	a+	PUNCT
ejpam-1224	445	16	b)ξ2	b)ξ2	PROPN
ejpam-1224	445	17	=	=	SYM
ejpam-1224	445	18	0	0	PROPN
ejpam-1224	445	19	.	.	PUNCT
ejpam-1224	446	1	therefore	therefore	ADV
ejpam-1224	446	2	we	we	PRON
ejpam-1224	446	3	have	have	VERB
ejpam-1224	446	4	the	the	DET
ejpam-1224	446	5	differential	differential	NOUN
ejpam-1224	446	6	d(ξn	d(ξn	NOUN
ejpam-1224	446	7	)	)	PUNCT
ejpam-1224	446	8	=	=	SYM
ejpam-1224	446	9	(	(	PUNCT
ejpam-1224	446	10	−(a+	−(a+	NUM
ejpam-1224	446	11	b)ξn+1	b)ξn+1	NOUN
ejpam-1224	446	12	if	if	SCONJ
ejpam-1224	446	13	n	n	NOUN
ejpam-1224	446	14	is	be	AUX
ejpam-1224	446	15	odd	odd	ADJ
ejpam-1224	446	16	0	0	NUM
ejpam-1224	446	17	if	if	SCONJ
ejpam-1224	446	18	n	n	NOUN
ejpam-1224	446	19	is	be	AUX
ejpam-1224	446	20	even	even	ADV
ejpam-1224	446	21	.	.	PUNCT
ejpam-1224	447	1	it	it	PRON
ejpam-1224	447	2	is	be	AUX
ejpam-1224	447	3	easy	easy	ADJ
ejpam-1224	447	4	to	to	PART
ejpam-1224	447	5	see	see	VERB
ejpam-1224	447	6	that	that	DET
ejpam-1224	447	7	d2	d2	PROPN
ejpam-1224	447	8	=	=	SYM
ejpam-1224	447	9	0	0	NUM
ejpam-1224	447	10	.	.	NOUN
ejpam-1224	447	11	6	6	NUM
ejpam-1224	447	12	.	.	X
ejpam-1224	448	1	the	the	DET
ejpam-1224	448	2	duality	duality	NOUN
ejpam-1224	448	3	functors	functor	VERB
ejpam-1224	448	4	f	f	PROPN
ejpam-1224	448	5	and	and	CCONJ
ejpam-1224	448	6	g	g	PROPN
ejpam-1224	448	7	we	we	PRON
ejpam-1224	448	8	let	let	VERB
ejpam-1224	448	9	u	u	PRON
ejpam-1224	448	10	be	be	AUX
ejpam-1224	448	11	a	a	DET
ejpam-1224	448	12	λ	λ	NOUN
ejpam-1224	448	13	-	-	PUNCT
ejpam-1224	448	14	graded	grade	VERB
ejpam-1224	448	15	filtered	filter	VERB
ejpam-1224	448	16	quadratic	quadratic	ADJ
ejpam-1224	448	17	algebra	algebra	NOUN
ejpam-1224	448	18	such	such	ADJ
ejpam-1224	448	19	that	that	SCONJ
ejpam-1224	448	20	a	a	DET
ejpam-1224	448	21	=	=	NOUN
ejpam-1224	448	22	gr(u	gr(u	X
ejpam-1224	448	23	)	)	PUNCT
ejpam-1224	448	24	is	be	AUX
ejpam-1224	448	25	koszul	koszul	ADJ
ejpam-1224	448	26	,	,	PUNCT
ejpam-1224	448	27	and	and	CCONJ
ejpam-1224	448	28	we	we	PRON
ejpam-1224	448	29	let	let	VERB
ejpam-1224	448	30	(	(	PUNCT
ejpam-1224	448	31	a	a	X
ejpam-1224	448	32	!	!	PUNCT
ejpam-1224	448	33	,	,	PUNCT
ejpam-1224	448	34	d	d	X
ejpam-1224	448	35	,	,	PUNCT
ejpam-1224	448	36	c	c	AUX
ejpam-1224	448	37	)	)	PUNCT
ejpam-1224	448	38	be	be	AUX
ejpam-1224	448	39	the	the	DET
ejpam-1224	448	40	dual	dual	ADJ
ejpam-1224	448	41	cdga	cdga	NOUN
ejpam-1224	448	42	.	.	PUNCT
ejpam-1224	449	1	let	let	VERB
ejpam-1224	449	2	t	t	NOUN
ejpam-1224	449	3	=	=	SYM
ejpam-1224	449	4	u	u	PROPN
ejpam-1224	449	5	⊗	⊗	PROPN
ejpam-1224	449	6	a	a	X
ejpam-1224	449	7	!	!	PUNCT
ejpam-1224	449	8	.	.	PUNCT
ejpam-1224	450	1	this	this	PRON
ejpam-1224	450	2	is	be	AUX
ejpam-1224	450	3	a	a	DET
ejpam-1224	450	4	u	u	NOUN
ejpam-1224	450	5	−	−	PROPN
ejpam-1224	450	6	a	a	PROPN
ejpam-1224	450	7	!	!	PUNCT
ejpam-1224	450	8	bimodule	bimodule	NOUN
ejpam-1224	451	1	and	and	CCONJ
ejpam-1224	451	2	we	we	PRON
ejpam-1224	451	3	give	give	VERB
ejpam-1224	451	4	it	it	PRON
ejpam-1224	451	5	the	the	DET
ejpam-1224	451	6	grading	grading	NOUN
ejpam-1224	451	7	of	of	ADP
ejpam-1224	451	8	a	a	PRON
ejpam-1224	451	9	!	!	PUNCT
ejpam-1224	451	10	.	.	PUNCT
ejpam-1224	452	1	let	let	VERB
ejpam-1224	452	2	d	d	PRON
ejpam-1224	452	3	be	be	AUX
ejpam-1224	452	4	the	the	DET
ejpam-1224	452	5	endomorphism	endomorphism	NOUN
ejpam-1224	452	6	defined	define	VERB
ejpam-1224	452	7	by	by	ADP
ejpam-1224	452	8	u⊗	u⊗	NOUN
ejpam-1224	452	9	a	a	DET
ejpam-1224	452	10	7−→	7−→	PROPN
ejpam-1224	452	11	∑	∑	PROPN
ejpam-1224	452	12	uxα⊗	uxα⊗	PROPN
ejpam-1224	452	13	x̌αa+	x̌αa+	PROPN
ejpam-1224	452	14	u⊗	u⊗	PROPN
ejpam-1224	452	15	d(a	d(a	PROPN
ejpam-1224	452	16	)	)	PUNCT
ejpam-1224	452	17	where	where	SCONJ
ejpam-1224	452	18	xα	xα	PRON
ejpam-1224	452	19	is	be	AUX
ejpam-1224	452	20	a	a	DET
ejpam-1224	452	21	basis	basis	NOUN
ejpam-1224	452	22	for	for	ADP
ejpam-1224	452	23	v	v	NOUN
ejpam-1224	452	24	and	and	CCONJ
ejpam-1224	452	25	x̌α	x̌α	PROPN
ejpam-1224	452	26	is	be	AUX
ejpam-1224	452	27	the	the	DET
ejpam-1224	452	28	dual	dual	ADJ
ejpam-1224	452	29	basis	basis	NOUN
ejpam-1224	452	30	for	for	ADP
ejpam-1224	452	31	v	v	ADP
ejpam-1224	452	32	∗.	∗.	PROPN
ejpam-1224	452	33	this	this	DET
ejpam-1224	452	34	definition	definition	NOUN
ejpam-1224	452	35	is	be	AUX
ejpam-1224	452	36	independent	independent	ADJ
ejpam-1224	452	37	of	of	ADP
ejpam-1224	452	38	the	the	DET
ejpam-1224	452	39	choice	choice	NOUN
ejpam-1224	452	40	of	of	ADP
ejpam-1224	452	41	this	this	DET
ejpam-1224	452	42	basis	basis	NOUN
ejpam-1224	452	43	and	and	CCONJ
ejpam-1224	452	44	one	one	PRON
ejpam-1224	452	45	can	can	AUX
ejpam-1224	452	46	check	check	VERB
ejpam-1224	452	47	that	that	SCONJ
ejpam-1224	452	48	this	this	PRON
ejpam-1224	452	49	gives	give	VERB
ejpam-1224	452	50	u	u	PRON
ejpam-1224	452	51	⊗	⊗	PROPN
ejpam-1224	452	52	a	a	NOUN
ejpam-1224	452	53	!	!	PUNCT
ejpam-1224	453	1	the	the	DET
ejpam-1224	453	2	structure	structure	NOUN
ejpam-1224	453	3	of	of	ADP
ejpam-1224	453	4	a	a	DET
ejpam-1224	453	5	right	right	ADJ
ejpam-1224	453	6	cgd	cgd	PROPN
ejpam-1224	453	7	module	module	NOUN
ejpam-1224	453	8	over	over	ADP
ejpam-1224	453	9	(	(	PUNCT
ejpam-1224	453	10	a	a	NOUN
ejpam-1224	453	11	!	!	PUNCT
ejpam-1224	453	12	,	,	PUNCT
ejpam-1224	453	13	d	d	X
ejpam-1224	453	14	,	,	PUNCT
ejpam-1224	453	15	c	c	NOUN
ejpam-1224	453	16	)	)	PUNCT
ejpam-1224	453	17	.	.	PUNCT
ejpam-1224	454	1	f.	f.	PROPN
ejpam-1224	454	2	hawwa	hawwa	PROPN
ejpam-1224	454	3	,	,	PUNCT
ejpam-1224	454	4	j.	j.	PROPN
ejpam-1224	454	5	hoffman	hoffman	PROPN
ejpam-1224	454	6	,	,	PUNCT
ejpam-1224	454	7	and	and	CCONJ
ejpam-1224	454	8	h.	h.	PROPN
ejpam-1224	454	9	wang	wang	PROPN
ejpam-1224	454	10	,	,	PUNCT
ejpam-1224	454	11	/	/	SYM
ejpam-1224	454	12	eur	eur	NOUN
ejpam-1224	454	13	.	.	PUNCT
ejpam-1224	455	1	j.	j.	PROPN
ejpam-1224	455	2	pure	pure	PROPN
ejpam-1224	455	3	appl	appl	PROPN
ejpam-1224	455	4	.	.	PROPN
ejpam-1224	455	5	math	math	PROPN
ejpam-1224	455	6	,	,	PUNCT
ejpam-1224	455	7	5	5	NUM
ejpam-1224	455	8	(	(	PUNCT
ejpam-1224	455	9	2012	2012	NUM
ejpam-1224	455	10	)	)	PUNCT
ejpam-1224	455	11	,	,	PUNCT
ejpam-1224	455	12	511	511	NUM
ejpam-1224	455	13	-	-	SYM
ejpam-1224	455	14	539	539	NUM
ejpam-1224	455	15	525	525	NUM
ejpam-1224	455	16	lemma	lemma	PROPN
ejpam-1224	455	17	2	2	NUM
ejpam-1224	455	18	.	.	X
ejpam-1224	456	1	for	for	ADP
ejpam-1224	456	2	t	t	NOUN
ejpam-1224	456	3	=	=	SYM
ejpam-1224	456	4	u	u	PROPN
ejpam-1224	456	5	⊗	⊗	PROPN
ejpam-1224	456	6	a	a	PROPN
ejpam-1224	456	7	!	!	PUNCT
ejpam-1224	457	1	a	a	DET
ejpam-1224	457	2	λ	λ	NOUN
ejpam-1224	457	3	-	-	PUNCT
ejpam-1224	457	4	graded	grade	VERB
ejpam-1224	457	5	(	(	PUNCT
ejpam-1224	457	6	u	u	NOUN
ejpam-1224	457	7	,	,	PUNCT
ejpam-1224	457	8	a!)-bimodule	a!)-bimodule	PROPN
ejpam-1224	457	9	,	,	PUNCT
ejpam-1224	457	10	t	t	PROPN
ejpam-1224	457	11	is	be	AUX
ejpam-1224	457	12	a	a	DET
ejpam-1224	457	13	right	right	NOUN
ejpam-1224	457	14	a!-cdgm	a!-cdgm	PRON
ejpam-1224	457	15	.	.	PUNCT
ejpam-1224	458	1	proof	proof	NOUN
ejpam-1224	458	2	.	.	PUNCT
ejpam-1224	459	1	it	it	PRON
ejpam-1224	459	2	is	be	AUX
ejpam-1224	459	3	clear	clear	ADJ
ejpam-1224	459	4	that	that	SCONJ
ejpam-1224	459	5	t	t	PROPN
ejpam-1224	459	6	is	be	AUX
ejpam-1224	459	7	a	a	DET
ejpam-1224	459	8	λ	λ	NOUN
ejpam-1224	459	9	-	-	PUNCT
ejpam-1224	459	10	graded	grade	VERB
ejpam-1224	459	11	(	(	PUNCT
ejpam-1224	459	12	u	u	NOUN
ejpam-1224	459	13	,	,	PUNCT
ejpam-1224	459	14	a!)-bimodule	a!)-bimodule	NOUN
ejpam-1224	459	15	.	.	PUNCT
ejpam-1224	460	1	we	we	PRON
ejpam-1224	460	2	only	only	ADV
ejpam-1224	460	3	need	need	VERB
ejpam-1224	460	4	to	to	PART
ejpam-1224	460	5	check	check	VERB
ejpam-1224	460	6	that	that	PRON
ejpam-1224	460	7	d2(u⊗	d2(u⊗	VERB
ejpam-1224	460	8	a	a	PRON
ejpam-1224	460	9	)	)	PUNCT
ejpam-1224	460	10	=	=	SYM
ejpam-1224	460	11	−u⊗	−u⊗	PROPN
ejpam-1224	460	12	ac	ac	PROPN
ejpam-1224	460	13	.	.	PUNCT
ejpam-1224	461	1	we	we	PRON
ejpam-1224	461	2	define	define	VERB
ejpam-1224	461	3	d	d	NOUN
ejpam-1224	461	4	as	as	SCONJ
ejpam-1224	461	5	follows	follow	VERB
ejpam-1224	461	6	d(u⊗	d(u⊗	PROPN
ejpam-1224	461	7	a	a	PRON
ejpam-1224	461	8	)	)	PUNCT
ejpam-1224	461	9	=	=	PUNCT
ejpam-1224	462	1	∑	∑	PROPN
ejpam-1224	462	2	uxα⊗	uxα⊗	PROPN
ejpam-1224	462	3	x̌αa+	x̌αa+	PROPN
ejpam-1224	462	4	u⊗	u⊗	PROPN
ejpam-1224	462	5	d(a	d(a	PROPN
ejpam-1224	462	6	)	)	PUNCT
ejpam-1224	462	7	.	.	PUNCT
ejpam-1224	463	1	we	we	PRON
ejpam-1224	463	2	have	have	AUX
ejpam-1224	463	3	d2(u⊗	d2(u⊗	VERB
ejpam-1224	463	4	a	a	PRON
ejpam-1224	463	5	)	)	PUNCT
ejpam-1224	463	6	=	=	SYM
ejpam-1224	464	1	∑	∑	PUNCT
ejpam-1224	464	2	uxαxβ	uxαxβ	PROPN
ejpam-1224	464	3	⊗	⊗	PROPN
ejpam-1224	464	4	x̌β	x̌β	PROPN
ejpam-1224	464	5	x̌αa+	x̌αa+	PUNCT
ejpam-1224	464	6	∑	∑	X
ejpam-1224	464	7	uxα⊗	uxα⊗	PROPN
ejpam-1224	464	8	x̌αd(a)+	x̌αd(a)+	NOUN
ejpam-1224	464	9	∑	∑	PROPN
ejpam-1224	464	10	uxα⊗	uxα⊗	PROPN
ejpam-1224	464	11	d	d	PROPN
ejpam-1224	464	12	(	(	PUNCT
ejpam-1224	464	13	x̌αa	x̌αa	PROPN
ejpam-1224	464	14	)	)	PUNCT
ejpam-1224	464	15	+	+	CCONJ
ejpam-1224	464	16	u⊗	u⊗	PROPN
ejpam-1224	464	17	d2(a	d2(a	NOUN
ejpam-1224	464	18	)	)	PUNCT
ejpam-1224	464	19	=	=	PUNCT
ejpam-1224	464	20	∑	∑	PUNCT
ejpam-1224	464	21	uxαxβ	uxαxβ	PROPN
ejpam-1224	464	22	⊗	⊗	PROPN
ejpam-1224	464	23	x̌β	x̌β	PROPN
ejpam-1224	464	24	x̌αa+	x̌αa+	PUNCT
ejpam-1224	465	1	∑	∑	PROPN
ejpam-1224	466	1	uxα⊗	uxα⊗	PROPN
ejpam-1224	466	2	d	d	X
ejpam-1224	466	3	(	(	PUNCT
ejpam-1224	466	4	x̌α)a+	x̌α)a+	PROPN
ejpam-1224	466	5	u⊗	u⊗	PROPN
ejpam-1224	466	6	ca−	ca−	SYM
ejpam-1224	466	7	u⊗	u⊗	NOUN
ejpam-1224	466	8	ac	ac	PROPN
ejpam-1224	466	9	=	=	SYM
ejpam-1224	466	10	−u⊗	−u⊗	PROPN
ejpam-1224	466	11	ac	ac	PROPN
ejpam-1224	466	12	.	.	PUNCT
ejpam-1224	467	1	the	the	DET
ejpam-1224	467	2	minus	minus	PROPN
ejpam-1224	467	3	sign	sign	NOUN
ejpam-1224	467	4	is	be	AUX
ejpam-1224	467	5	as	as	SCONJ
ejpam-1224	467	6	we	we	PRON
ejpam-1224	467	7	would	would	AUX
ejpam-1224	467	8	expect	expect	VERB
ejpam-1224	467	9	since	since	SCONJ
ejpam-1224	467	10	t	t	PROPN
ejpam-1224	467	11	is	be	AUX
ejpam-1224	467	12	a	a	DET
ejpam-1224	467	13	right	right	ADJ
ejpam-1224	467	14	a!-module	a!-module	NOUN
ejpam-1224	467	15	.	.	PUNCT
ejpam-1224	468	1	the	the	DET
ejpam-1224	468	2	pair	pair	NOUN
ejpam-1224	468	3	of	of	ADP
ejpam-1224	468	4	adjoint	adjoint	PROPN
ejpam-1224	468	5	functors	functors	PROPN
ejpam-1224	468	6	f	f	X
ejpam-1224	468	7	:	:	PUNCT
ejpam-1224	468	8	comλ(a	comλ(a	INTJ
ejpam-1224	468	9	!	!	PUNCT
ejpam-1224	468	10	,	,	PUNCT
ejpam-1224	469	1	d	d	X
ejpam-1224	469	2	,	,	PUNCT
ejpam-1224	469	3	c	c	NOUN
ejpam-1224	469	4	)	)	PUNCT
ejpam-1224	469	5	⇆	⇆	PROPN
ejpam-1224	469	6	comλ(u	comλ(u	NOUN
ejpam-1224	469	7	)	)	PUNCT
ejpam-1224	469	8	:	:	PUNCT
ejpam-1224	470	1	g	g	PROPN
ejpam-1224	470	2	is	be	AUX
ejpam-1224	470	3	given	give	VERB
ejpam-1224	470	4	by	by	ADP
ejpam-1224	470	5	f(n	f(n	PROPN
ejpam-1224	470	6	)	)	PUNCT
ejpam-1224	471	1	=	=	SYM
ejpam-1224	471	2	t	t	NOUN
ejpam-1224	471	3	⊗a	⊗a	NOUN
ejpam-1224	471	4	!	!	PUNCT
ejpam-1224	472	1	n	n	X
ejpam-1224	472	2	,	,	PUNCT
ejpam-1224	472	3	g(m	g(m	NUM
ejpam-1224	472	4	)	)	PUNCT
ejpam-1224	472	5	=	=	SYM
ejpam-1224	472	6	homu(t	homu(t	PROPN
ejpam-1224	472	7	,	,	PUNCT
ejpam-1224	472	8	m	m	PROPN
ejpam-1224	472	9	)	)	PUNCT
ejpam-1224	472	10	.	.	PUNCT
ejpam-1224	473	1	explicitly	explicitly	ADV
ejpam-1224	473	2	,	,	PUNCT
ejpam-1224	473	3	we	we	PRON
ejpam-1224	473	4	have	have	VERB
ejpam-1224	473	5	f(n	f(n	PROPN
ejpam-1224	473	6	)	)	PUNCT
ejpam-1224	474	1	p	p	X
ejpam-1224	474	2	λ	λ	X
ejpam-1224	474	3	=	=	PROPN
ejpam-1224	474	4	⊕	⊕	PROPN
ejpam-1224	474	5	µ+ν	µ+ν	NOUN
ejpam-1224	474	6	=	=	SYM
ejpam-1224	474	7	λ	λ	X
ejpam-1224	474	8	uµ	uµ	NOUN
ejpam-1224	474	9	⊗k	⊗k	ADJ
ejpam-1224	474	10	n	n	CCONJ
ejpam-1224	474	11	p	p	NOUN
ejpam-1224	474	12	ν	ν	NOUN
ejpam-1224	474	13	with	with	ADP
ejpam-1224	474	14	d(u⊗	d(u⊗	PROPN
ejpam-1224	474	15	n	n	CCONJ
ejpam-1224	474	16	)	)	PUNCT
ejpam-1224	475	1	=	=	PUNCT
ejpam-1224	475	2	∑	∑	PUNCT
ejpam-1224	475	3	α	α	PROPN
ejpam-1224	475	4	uxα⊗	uxα⊗	PROPN
ejpam-1224	475	5	x̌αn+	x̌αn+	PROPN
ejpam-1224	476	1	u⊗	u⊗	PROPN
ejpam-1224	476	2	dn	dn	PROPN
ejpam-1224	476	3	(	(	PUNCT
ejpam-1224	476	4	n	n	CCONJ
ejpam-1224	476	5	)	)	PUNCT
ejpam-1224	476	6	.	.	PUNCT
ejpam-1224	477	1	(	(	PUNCT
ejpam-1224	477	2	2	2	X
ejpam-1224	477	3	)	)	PUNCT
ejpam-1224	477	4	since	since	SCONJ
ejpam-1224	477	5	degλ	degλ	ADJ
ejpam-1224	477	6	(	(	PUNCT
ejpam-1224	477	7	x̌α	x̌α	NOUN
ejpam-1224	477	8	)	)	PUNCT
ejpam-1224	477	9	=	=	PUNCT
ejpam-1224	477	10	−degλ(xα	−degλ(xα	NOUN
ejpam-1224	477	11	)	)	PUNCT
ejpam-1224	477	12	one	one	PRON
ejpam-1224	477	13	can	can	AUX
ejpam-1224	477	14	show	show	VERB
ejpam-1224	477	15	that	that	SCONJ
ejpam-1224	477	16	d	d	PROPN
ejpam-1224	477	17	preserves	preserve	VERB
ejpam-1224	477	18	the	the	DET
ejpam-1224	477	19	λ	λ	NOUN
ejpam-1224	477	20	-	-	PUNCT
ejpam-1224	477	21	grading	grade	VERB
ejpam-1224	477	22	.	.	PUNCT
ejpam-1224	478	1	since	since	SCONJ
ejpam-1224	478	2	axα	axα	NOUN
ejpam-1224	478	3	∈	∈	PROPN
ejpam-1224	478	4	uµ+deg(xα	uµ+deg(xα	VERB
ejpam-1224	478	5	)	)	PUNCT
ejpam-1224	478	6	and	and	CCONJ
ejpam-1224	478	7	x̌αn	x̌αn	PROPN
ejpam-1224	478	8	∈	∈	PROPN
ejpam-1224	478	9	n	n	CCONJ
ejpam-1224	478	10	p+1	p+1	PROPN
ejpam-1224	478	11	ν−deg(xα	ν−deg(xα	PROPN
ejpam-1224	478	12	)	)	PUNCT
ejpam-1224	478	13	,	,	PUNCT
ejpam-1224	478	14	the	the	DET
ejpam-1224	478	15	sum	sum	NOUN
ejpam-1224	478	16	µ+	µ+	VERB
ejpam-1224	478	17	ν	ν	NOUN
ejpam-1224	478	18	=	=	SYM
ejpam-1224	478	19	λ	λ	PROPN
ejpam-1224	478	20	remains	remain	VERB
ejpam-1224	478	21	unchanged	unchanged	ADJ
ejpam-1224	478	22	in	in	ADP
ejpam-1224	478	23	the	the	DET
ejpam-1224	478	24	tensor	tensor	NOUN
ejpam-1224	478	25	.	.	PUNCT
ejpam-1224	479	1	the	the	DET
ejpam-1224	479	2	map	map	NOUN
ejpam-1224	479	3	d	d	NOUN
ejpam-1224	479	4	is	be	AUX
ejpam-1224	479	5	also	also	ADV
ejpam-1224	479	6	u	u	NOUN
ejpam-1224	479	7	-	-	NOUN
ejpam-1224	479	8	linear	linear	ADJ
ejpam-1224	479	9	,	,	PUNCT
ejpam-1224	479	10	this	this	PRON
ejpam-1224	479	11	can	can	AUX
ejpam-1224	479	12	easily	easily	ADV
ejpam-1224	479	13	be	be	AUX
ejpam-1224	479	14	seen	see	VERB
ejpam-1224	479	15	since	since	SCONJ
ejpam-1224	479	16	d(u1u⊗	d(u1u⊗	NOUN
ejpam-1224	479	17	n	n	CCONJ
ejpam-1224	479	18	)	)	PUNCT
ejpam-1224	479	19	=	=	PUNCT
ejpam-1224	480	1	∑	∑	PUNCT
ejpam-1224	480	2	u1uxα⊗	u1uxα⊗	PROPN
ejpam-1224	480	3	xαn+	xαn+	PROPN
ejpam-1224	480	4	u1u⊗	u1u⊗	PROPN
ejpam-1224	480	5	dn	dn	PROPN
ejpam-1224	480	6	(	(	PUNCT
ejpam-1224	480	7	n	n	CCONJ
ejpam-1224	480	8	)	)	PUNCT
ejpam-1224	480	9	=	=	SYM
ejpam-1224	480	10	u1	u1	PROPN
ejpam-1224	480	11	∑	∑	PROPN
ejpam-1224	480	12	uxα⊗	uxα⊗	PROPN
ejpam-1224	480	13	xαn+	xαn+	PROPN
ejpam-1224	480	14	u⊗	u⊗	PROPN
ejpam-1224	480	15	dn	dn	PROPN
ejpam-1224	480	16	(	(	PUNCT
ejpam-1224	480	17	n	n	CCONJ
ejpam-1224	480	18	)	)	PUNCT
ejpam-1224	480	19	=	=	SYM
ejpam-1224	480	20	u1d(u⊗	u1d(u⊗	PROPN
ejpam-1224	480	21	n	n	CCONJ
ejpam-1224	480	22	)	)	PUNCT
ejpam-1224	480	23	.	.	PUNCT
ejpam-1224	481	1	lemma	lemma	PROPN
ejpam-1224	481	2	3	3	X
ejpam-1224	481	3	.	.	PUNCT
ejpam-1224	481	4	d2	d2	PROPN
ejpam-1224	481	5	=	=	NOUN
ejpam-1224	481	6	0	0	NUM
ejpam-1224	481	7	in	in	ADP
ejpam-1224	481	8	equation	equation	NOUN
ejpam-1224	481	9	(	(	PUNCT
ejpam-1224	481	10	2	2	NUM
ejpam-1224	481	11	)	)	PUNCT
ejpam-1224	481	12	and	and	CCONJ
ejpam-1224	481	13	if	if	SCONJ
ejpam-1224	481	14	n	n	PRON
ejpam-1224	481	15	is	be	AUX
ejpam-1224	481	16	in	in	ADP
ejpam-1224	481	17	comλ(a	comλ(a	PROPN
ejpam-1224	481	18	!	!	PUNCT
ejpam-1224	481	19	,	,	PUNCT
ejpam-1224	482	1	d	d	X
ejpam-1224	482	2	,	,	PUNCT
ejpam-1224	482	3	c	c	PROPN
ejpam-1224	482	4	)	)	PUNCT
ejpam-1224	482	5	then	then	ADV
ejpam-1224	482	6	f(n	f(n	PROPN
ejpam-1224	482	7	)	)	PUNCT
ejpam-1224	482	8	is	be	AUX
ejpam-1224	482	9	in	in	ADP
ejpam-1224	482	10	comλ(u	comλ(u	NOUN
ejpam-1224	482	11	)	)	PUNCT
ejpam-1224	482	12	.	.	PUNCT
ejpam-1224	483	1	proof	proof	NOUN
ejpam-1224	483	2	.	.	PUNCT
ejpam-1224	484	1	all	all	PRON
ejpam-1224	484	2	of	of	ADP
ejpam-1224	484	3	the	the	DET
ejpam-1224	484	4	axioms	axiom	NOUN
ejpam-1224	484	5	necessary	necessary	ADJ
ejpam-1224	484	6	to	to	PART
ejpam-1224	484	7	show	show	VERB
ejpam-1224	484	8	that	that	SCONJ
ejpam-1224	484	9	f(n	f(n	PROPN
ejpam-1224	484	10	)	)	PUNCT
ejpam-1224	484	11	∈	∈	PROPN
ejpam-1224	484	12	comλ(u	comλ(u	NOUN
ejpam-1224	484	13	)	)	PUNCT
ejpam-1224	484	14	are	be	AUX
ejpam-1224	484	15	obvious	obvious	ADJ
ejpam-1224	484	16	except	except	SCONJ
ejpam-1224	484	17	for	for	ADP
ejpam-1224	484	18	that	that	DET
ejpam-1224	484	19	d2	d2	NOUN
ejpam-1224	484	20	=	=	SYM
ejpam-1224	484	21	0	0	NUM
ejpam-1224	484	22	,	,	PUNCT
ejpam-1224	484	23	so	so	ADV
ejpam-1224	484	24	let	let	VERB
ejpam-1224	484	25	us	we	PRON
ejpam-1224	484	26	verify	verify	VERB
ejpam-1224	484	27	this	this	PRON
ejpam-1224	484	28	.	.	PUNCT
ejpam-1224	485	1	for	for	ADP
ejpam-1224	485	2	u⊗	u⊗	NOUN
ejpam-1224	485	3	n	n	PROPN
ejpam-1224	485	4	∈	∈	PROPN
ejpam-1224	485	5	f(n	f(n	PROPN
ejpam-1224	485	6	)	)	PUNCT
ejpam-1224	485	7	we	we	PRON
ejpam-1224	485	8	have	have	VERB
ejpam-1224	485	9	d2(a⊗	d2(a⊗	PROPN
ejpam-1224	485	10	n	n	CCONJ
ejpam-1224	485	11	)	)	PUNCT
ejpam-1224	485	12	=	=	SYM
ejpam-1224	485	13	∑	∑	PUNCT
ejpam-1224	485	14	α	α	PROPN
ejpam-1224	485	15	(	(	PUNCT
ejpam-1224	485	16	∑	∑	PROPN
ejpam-1224	485	17	β	β	X
ejpam-1224	485	18	axαxβ	axαxβ	NOUN
ejpam-1224	485	19	⊗	⊗	PROPN
ejpam-1224	485	20	x̌β	x̌β	PROPN
ejpam-1224	485	21	x̌αn+	x̌αn+	PROPN
ejpam-1224	486	1	axα⊗	axα⊗	NOUN
ejpam-1224	486	2	dn	dn	PROPN
ejpam-1224	486	3	(	(	PUNCT
ejpam-1224	486	4	x̌αn))+	x̌αn))+	ADP
ejpam-1224	486	5	∑	∑	PUNCT
ejpam-1224	486	6	γ	γ	PROPN
ejpam-1224	486	7	axγ⊗	axγ⊗	PROPN
ejpam-1224	486	8	x̌γdn	x̌γdn	PUNCT
ejpam-1224	486	9	(	(	PUNCT
ejpam-1224	486	10	n	n	CCONJ
ejpam-1224	486	11	)	)	PUNCT
ejpam-1224	486	12	+	+	CCONJ
ejpam-1224	486	13	a⊗	a⊗	PROPN
ejpam-1224	486	14	d2	d2	PROPN
ejpam-1224	486	15	n	n	CCONJ
ejpam-1224	486	16	(	(	PUNCT
ejpam-1224	486	17	n	n	CCONJ
ejpam-1224	486	18	)	)	PUNCT
ejpam-1224	486	19	.	.	PUNCT
ejpam-1224	487	1	f.	f.	PROPN
ejpam-1224	487	2	hawwa	hawwa	PROPN
ejpam-1224	487	3	,	,	PUNCT
ejpam-1224	487	4	j.	j.	PROPN
ejpam-1224	487	5	hoffman	hoffman	PROPN
ejpam-1224	487	6	,	,	PUNCT
ejpam-1224	487	7	and	and	CCONJ
ejpam-1224	487	8	h.	h.	PROPN
ejpam-1224	487	9	wang	wang	PROPN
ejpam-1224	487	10	,	,	PUNCT
ejpam-1224	487	11	/	/	SYM
ejpam-1224	487	12	eur	eur	NOUN
ejpam-1224	487	13	.	.	PUNCT
ejpam-1224	488	1	j.	j.	PROPN
ejpam-1224	488	2	pure	pure	PROPN
ejpam-1224	488	3	appl	appl	PROPN
ejpam-1224	488	4	.	.	PROPN
ejpam-1224	488	5	math	math	PROPN
ejpam-1224	488	6	,	,	PUNCT
ejpam-1224	488	7	5	5	NUM
ejpam-1224	488	8	(	(	PUNCT
ejpam-1224	488	9	2012	2012	NUM
ejpam-1224	488	10	)	)	PUNCT
ejpam-1224	488	11	,	,	PUNCT
ejpam-1224	488	12	511	511	NUM
ejpam-1224	488	13	-	-	SYM
ejpam-1224	488	14	539	539	NUM
ejpam-1224	488	15	526	526	NUM
ejpam-1224	488	16	the	the	DET
ejpam-1224	488	17	term	term	NOUN
ejpam-1224	488	18	∑	∑	PUNCT
ejpam-1224	488	19	α	α	PROPN
ejpam-1224	488	20	axα⊗	axα⊗	NOUN
ejpam-1224	488	21	dn	dn	NOUN
ejpam-1224	488	22	(	(	PUNCT
ejpam-1224	488	23	x̌αn	x̌αn	PROPN
ejpam-1224	488	24	)	)	PUNCT
ejpam-1224	488	25	may	may	AUX
ejpam-1224	488	26	be	be	AUX
ejpam-1224	488	27	rewritten	rewrite	VERB
ejpam-1224	488	28	as	as	ADP
ejpam-1224	488	29	∑	∑	PROPN
ejpam-1224	488	30	α	α	NOUN
ejpam-1224	488	31	axα⊗	axα⊗	PROPN
ejpam-1224	488	32	d	d	PROPN
ejpam-1224	488	33	(	(	PUNCT
ejpam-1224	488	34	x̌α)n−	x̌α)n−	PROPN
ejpam-1224	488	35	axα⊗	axα⊗	PROPN
ejpam-1224	488	36	x̌αdn	x̌αdn	PUNCT
ejpam-1224	488	37	(	(	PUNCT
ejpam-1224	488	38	n	n	CCONJ
ejpam-1224	488	39	)	)	PUNCT
ejpam-1224	488	40	which	which	PRON
ejpam-1224	488	41	allows	allow	VERB
ejpam-1224	488	42	us	we	PRON
ejpam-1224	488	43	to	to	PART
ejpam-1224	488	44	simplify	simplify	VERB
ejpam-1224	488	45	and	and	CCONJ
ejpam-1224	488	46	apply	apply	VERB
ejpam-1224	488	47	lemma	lemma	PROPN
ejpam-1224	488	48	1	1	NUM
ejpam-1224	488	49	as	as	SCONJ
ejpam-1224	488	50	follows	follow	VERB
ejpam-1224	488	51	,	,	PUNCT
ejpam-1224	488	52	d2(a⊗	d2(a⊗	PROPN
ejpam-1224	488	53	n	n	CCONJ
ejpam-1224	488	54	)	)	PUNCT
ejpam-1224	488	55	=	=	SYM
ejpam-1224	488	56	∑	∑	PUNCT
ejpam-1224	488	57	α	α	PROPN
ejpam-1224	488	58	(	(	PUNCT
ejpam-1224	488	59	∑	∑	PROPN
ejpam-1224	488	60	β	β	X
ejpam-1224	488	61	axαxβ	axαxβ	NOUN
ejpam-1224	488	62	⊗	⊗	PROPN
ejpam-1224	488	63	x̌β	x̌β	PROPN
ejpam-1224	488	64	x̌αn+	x̌αn+	PUNCT
ejpam-1224	489	1	axα+	axα+	PROPN
ejpam-1224	490	1	d	d	PROPN
ejpam-1224	490	2	(	(	PUNCT
ejpam-1224	490	3	x̌α)n	x̌α)n	NUM
ejpam-1224	490	4	)	)	PUNCT
ejpam-1224	491	1	+	+	CCONJ
ejpam-1224	491	2	a⊗	a⊗	NOUN
ejpam-1224	491	3	cn	cn	PROPN
ejpam-1224	492	1	=	=	NOUN
ejpam-1224	492	2	a	a	PROPN
ejpam-1224	492	3	(	(	PUNCT
ejpam-1224	492	4	∑	∑	PROPN
ejpam-1224	492	5	α	α	PROPN
ejpam-1224	492	6	(	(	PUNCT
ejpam-1224	492	7	∑	∑	PROPN
ejpam-1224	492	8	β	β	X
ejpam-1224	492	9	xαxβ	xαxβ	PROPN
ejpam-1224	492	10	⊗	⊗	PROPN
ejpam-1224	492	11	x̌β	x̌β	PROPN
ejpam-1224	493	1	x̌α+	x̌α+	PROPN
ejpam-1224	493	2	xα+	xα+	PROPN
ejpam-1224	494	1	d	d	PROPN
ejpam-1224	494	2	(	(	PUNCT
ejpam-1224	494	3	x̌α	x̌α	NOUN
ejpam-1224	494	4	)	)	PUNCT
ejpam-1224	494	5	)	)	PUNCT
ejpam-1224	495	1	+	+	PUNCT
ejpam-1224	496	1	1⊗	1⊗	NUM
ejpam-1224	496	2	c)n	c)n	NOUN
ejpam-1224	496	3	=	=	PUNCT
ejpam-1224	497	1	0	0	X
ejpam-1224	497	2	.	.	PUNCT
ejpam-1224	498	1	next	next	ADJ
ejpam-1224	498	2	,	,	PUNCT
ejpam-1224	498	3	g(m	g(m	NUM
ejpam-1224	498	4	)	)	PUNCT
ejpam-1224	499	1	=	=	SYM
ejpam-1224	499	2	homu(t	homu(t	PROPN
ejpam-1224	499	3	,	,	PUNCT
ejpam-1224	499	4	m	m	NOUN
ejpam-1224	499	5	)	)	PUNCT
ejpam-1224	499	6	=	=	SYM
ejpam-1224	500	1	homk(a	homk(a	NOUN
ejpam-1224	500	2	!	!	PUNCT
ejpam-1224	500	3	,	,	PUNCT
ejpam-1224	500	4	m	m	VERB
ejpam-1224	500	5	)	)	PUNCT
ejpam-1224	500	6	has	have	VERB
ejpam-1224	500	7	the	the	DET
ejpam-1224	500	8	structure	structure	NOUN
ejpam-1224	500	9	of	of	ADP
ejpam-1224	500	10	a	a	DET
ejpam-1224	500	11	graded	grade	VERB
ejpam-1224	500	12	a!-module	a!-module	NOUN
ejpam-1224	500	13	,	,	PUNCT
ejpam-1224	500	14	defined	define	VERB
ejpam-1224	500	15	as	as	ADP
ejpam-1224	500	16	(	(	PUNCT
ejpam-1224	500	17	a	a	DET
ejpam-1224	500	18	·	·	PUNCT
ejpam-1224	500	19	f	f	X
ejpam-1224	500	20	)	)	PUNCT
ejpam-1224	500	21	(	(	PUNCT
ejpam-1224	500	22	b	b	X
ejpam-1224	500	23	)	)	PUNCT
ejpam-1224	500	24	=	=	SYM
ejpam-1224	500	25	(	(	PUNCT
ejpam-1224	500	26	−1)q(p+r	−1)q(p+r	NOUN
ejpam-1224	500	27	)	)	PUNCT
ejpam-1224	500	28	f	f	PROPN
ejpam-1224	501	1	(	(	PUNCT
ejpam-1224	501	2	ba	ba	PROPN
ejpam-1224	501	3	)	)	PUNCT
ejpam-1224	501	4	,	,	PUNCT
ejpam-1224	501	5	a	a	DET
ejpam-1224	501	6	∈	∈	PROPN
ejpam-1224	501	7	(	(	PUNCT
ejpam-1224	501	8	a!)q	a!)q	NOUN
ejpam-1224	501	9	,	,	PUNCT
ejpam-1224	501	10	b	b	X
ejpam-1224	501	11	∈	∈	PROPN
ejpam-1224	501	12	(	(	PUNCT
ejpam-1224	501	13	a!)r	a!)r	NOUN
ejpam-1224	501	14	,	,	PUNCT
ejpam-1224	501	15	f	f	PROPN
ejpam-1224	501	16	∈	∈	PROPN
ejpam-1224	502	1	hom	hom	X
ejpam-1224	503	1	p	p	PROPN
ejpam-1224	503	2	k	k	PROPN
ejpam-1224	503	3	(	(	PUNCT
ejpam-1224	503	4	a	a	PROPN
ejpam-1224	503	5	!	!	PROPN
ejpam-1224	503	6	,	,	PUNCT
ejpam-1224	503	7	m	m	PROPN
ejpam-1224	503	8	)	)	PUNCT
ejpam-1224	503	9	.	.	PUNCT
ejpam-1224	504	1	one	one	PRON
ejpam-1224	504	2	can	can	AUX
ejpam-1224	504	3	verify	verify	VERB
ejpam-1224	504	4	that	that	DET
ejpam-1224	504	5	a1	a1	NOUN
ejpam-1224	504	6	·	·	PUNCT
ejpam-1224	504	7	(	(	PUNCT
ejpam-1224	504	8	a2	a2	PROPN
ejpam-1224	504	9	·	·	PUNCT
ejpam-1224	504	10	f	f	X
ejpam-1224	504	11	)	)	PUNCT
ejpam-1224	505	1	=	=	SYM
ejpam-1224	505	2	(	(	PUNCT
ejpam-1224	505	3	a1a2	a1a2	PROPN
ejpam-1224	505	4	)	)	PUNCT
ejpam-1224	505	5	·	·	PUNCT
ejpam-1224	506	1	f	f	X
ejpam-1224	506	2	.	.	PUNCT
ejpam-1224	507	1	also	also	ADV
ejpam-1224	507	2	it	it	PRON
ejpam-1224	507	3	carries	carry	VERB
ejpam-1224	507	4	an	an	DET
ejpam-1224	507	5	internal	internal	ADJ
ejpam-1224	507	6	λ	λ	NOUN
ejpam-1224	507	7	-	-	PUNCT
ejpam-1224	507	8	grading	grade	VERB
ejpam-1224	507	9	:	:	PUNCT
ejpam-1224	507	10	g(m	g(m	ADJ
ejpam-1224	507	11	)	)	PUNCT
ejpam-1224	507	12	p	p	NOUN
ejpam-1224	507	13	λ	λ	X
ejpam-1224	507	14	=	=	SYM
ejpam-1224	507	15	∏	∏	PROPN
ejpam-1224	507	16	r≥0	r≥0	PROPN
ejpam-1224	507	17	∏	∏	PROPN
ejpam-1224	507	18	µ	µ	PROPN
ejpam-1224	507	19	homk((a	homk((a	NUM
ejpam-1224	507	20	!	!	PUNCT
ejpam-1224	507	21	)	)	PUNCT
ejpam-1224	507	22	rµ	rµ	VERB
ejpam-1224	507	23	,	,	PUNCT
ejpam-1224	507	24	m	m	PROPN
ejpam-1224	507	25	p+r	p+r	NOUN
ejpam-1224	507	26	λ+µ	λ+µ	X
ejpam-1224	507	27	)	)	PUNCT
ejpam-1224	507	28	with	with	ADP
ejpam-1224	507	29	d	d	PROPN
ejpam-1224	507	30	is	be	AUX
ejpam-1224	507	31	given	give	VERB
ejpam-1224	507	32	by	by	ADP
ejpam-1224	507	33	d	d	PROPN
ejpam-1224	507	34	(	(	PUNCT
ejpam-1224	507	35	f	f	PROPN
ejpam-1224	507	36	)	)	PUNCT
ejpam-1224	507	37	(	(	PUNCT
ejpam-1224	507	38	a	a	X
ejpam-1224	507	39	)	)	PUNCT
ejpam-1224	507	40	=	=	SYM
ejpam-1224	507	41	(	(	PUNCT
ejpam-1224	507	42	−1)|	−1)|	NOUN
ejpam-1224	507	43	f	f	PROPN
ejpam-1224	507	44	|+1	|+1	PROPN
ejpam-1224	508	1	∑	∑	PROPN
ejpam-1224	508	2	xα	xα	PROPN
ejpam-1224	508	3	f	f	PROPN
ejpam-1224	508	4	(	(	PUNCT
ejpam-1224	508	5	x̌αa	x̌αa	PROPN
ejpam-1224	508	6	)	)	PUNCT
ejpam-1224	509	1	+	+	CCONJ
ejpam-1224	509	2	(	(	PUNCT
ejpam-1224	509	3	−1)|	−1)|	PROPN
ejpam-1224	509	4	f	f	PROPN
ejpam-1224	509	5	|+1	|+1	PROPN
ejpam-1224	509	6	f	f	PROPN
ejpam-1224	509	7	(	(	PUNCT
ejpam-1224	509	8	da!(a	da!(a	PROPN
ejpam-1224	509	9	)	)	PUNCT
ejpam-1224	509	10	)	)	PUNCT
ejpam-1224	510	1	+	+	CCONJ
ejpam-1224	510	2	dm	dm	X
ejpam-1224	510	3	(	(	PUNCT
ejpam-1224	510	4	f	f	X
ejpam-1224	510	5	(	(	PUNCT
ejpam-1224	510	6	a	a	NOUN
ejpam-1224	510	7	)	)	PUNCT
ejpam-1224	510	8	)	)	PUNCT
ejpam-1224	510	9	)	)	PUNCT
ejpam-1224	510	10	.	.	PUNCT
ejpam-1224	511	1	(	(	PUNCT
ejpam-1224	511	2	3	3	X
ejpam-1224	511	3	)	)	PUNCT
ejpam-1224	511	4	note	note	NOUN
ejpam-1224	511	5	that	that	SCONJ
ejpam-1224	511	6	our	our	PRON
ejpam-1224	511	7	sign	sign	NOUN
ejpam-1224	511	8	conventions	convention	NOUN
ejpam-1224	511	9	differ	differ	VERB
ejpam-1224	511	10	from	from	ADP
ejpam-1224	511	11	that	that	PRON
ejpam-1224	511	12	in	in	ADP
ejpam-1224	511	13	[	[	X
ejpam-1224	511	14	3	3	NUM
ejpam-1224	511	15	]	]	PUNCT
ejpam-1224	511	16	.	.	PUNCT
ejpam-1224	512	1	example	example	NOUN
ejpam-1224	512	2	9	9	NUM
ejpam-1224	512	3	.	.	PUNCT
ejpam-1224	512	4	continuing	continue	VERB
ejpam-1224	512	5	example	example	NOUN
ejpam-1224	512	6	3	3	NUM
ejpam-1224	512	7	the	the	DET
ejpam-1224	512	8	algebra	algebra	NOUN
ejpam-1224	512	9	u	u	NOUN
ejpam-1224	512	10	has	have	VERB
ejpam-1224	512	11	two	two	NUM
ejpam-1224	512	12	simple	simple	ADJ
ejpam-1224	512	13	modules	module	NOUN
ejpam-1224	512	14	of	of	ADP
ejpam-1224	512	15	dimension	dimension	NOUN
ejpam-1224	512	16	1	1	NUM
ejpam-1224	512	17	over	over	ADP
ejpam-1224	512	18	k	k	PROPN
ejpam-1224	512	19	namely	namely	ADV
ejpam-1224	512	20	ka	ka	PROPN
ejpam-1224	512	21	=	=	SYM
ejpam-1224	512	22	k[x]/(x	k[x]/(x	PROPN
ejpam-1224	512	23	−	−	PROPN
ejpam-1224	512	24	a	a	NOUN
ejpam-1224	512	25	)	)	PUNCT
ejpam-1224	512	26	and	and	CCONJ
ejpam-1224	512	27	kb	kb	PROPN
ejpam-1224	512	28	=	=	SYM
ejpam-1224	512	29	k[x]/(x	k[x]/(x	PROPN
ejpam-1224	512	30	−	−	PROPN
ejpam-1224	512	31	b	b	NOUN
ejpam-1224	512	32	)	)	PUNCT
ejpam-1224	512	33	.	.	PUNCT
ejpam-1224	513	1	by	by	ADP
ejpam-1224	513	2	definition	definition	NOUN
ejpam-1224	513	3	,	,	PUNCT
ejpam-1224	513	4	the	the	DET
ejpam-1224	513	5	cdg	cdg	NOUN
ejpam-1224	513	6	-	-	PUNCT
ejpam-1224	513	7	module	module	NOUN
ejpam-1224	513	8	g(ka	g(ka	NOUN
ejpam-1224	513	9	)	)	PUNCT
ejpam-1224	513	10	p	p	NOUN
ejpam-1224	513	11	=	=	SYM
ejpam-1224	513	12	∏	∏	PROPN
ejpam-1224	513	13	r≥0	r≥0	PROPN
ejpam-1224	513	14	hom(a	hom(a	PROPN
ejpam-1224	513	15	!	!	PUNCT
ejpam-1224	514	1	r	r	NOUN
ejpam-1224	514	2	,	,	PUNCT
ejpam-1224	514	3	k	k	PROPN
ejpam-1224	514	4	p+r	p+r	PROPN
ejpam-1224	514	5	a	a	PRON
ejpam-1224	514	6	)	)	PUNCT
ejpam-1224	514	7	.	.	PUNCT
ejpam-1224	515	1	note	note	VERB
ejpam-1224	515	2	that	that	SCONJ
ejpam-1224	515	3	k	k	PROPN
ejpam-1224	515	4	p+r	p+r	PROPN
ejpam-1224	515	5	a	a	PRON
ejpam-1224	515	6	is	be	AUX
ejpam-1224	515	7	nonzero	nonzero	NOUN
ejpam-1224	515	8	only	only	ADV
ejpam-1224	515	9	if	if	SCONJ
ejpam-1224	515	10	p	p	X
ejpam-1224	515	11	=	=	SYM
ejpam-1224	515	12	−r	−r	PROPN
ejpam-1224	515	13	.	.	PUNCT
ejpam-1224	516	1	now	now	ADV
ejpam-1224	516	2	since	since	SCONJ
ejpam-1224	516	3	hom(a	hom(a	PROPN
ejpam-1224	516	4	!	!	PUNCT
ejpam-1224	517	1	r	r	NOUN
ejpam-1224	517	2	,	,	PUNCT
ejpam-1224	517	3	ka	ka	PROPN
ejpam-1224	517	4	)	)	PUNCT
ejpam-1224	517	5	=	=	SYM
ejpam-1224	518	1	(	(	PUNCT
ejpam-1224	518	2	x	x	SYM
ejpam-1224	518	3	r	r	X
ejpam-1224	518	4	)	)	PUNCT
ejpam-1224	518	5	we	we	PRON
ejpam-1224	518	6	can	can	AUX
ejpam-1224	518	7	check	check	VERB
ejpam-1224	518	8	that	that	PRON
ejpam-1224	518	9	for	for	ADP
ejpam-1224	518	10	the	the	DET
ejpam-1224	518	11	cdg	cdg	NOUN
ejpam-1224	518	12	-	-	PUNCT
ejpam-1224	518	13	module	module	NOUN
ejpam-1224	518	14	g(ka	g(ka	NOUN
ejpam-1224	518	15	)	)	PUNCT
ejpam-1224	518	16	we	we	PRON
ejpam-1224	518	17	have	have	VERB
ejpam-1224	518	18	·	·	PUNCT
ejpam-1224	518	19	·	·	PUNCT
ejpam-1224	518	20	·	·	PUNCT
ejpam-1224	518	21	(	(	PUNCT
ejpam-1224	518	22	x3	x3	ADJ
ejpam-1224	518	23	)	)	PUNCT
ejpam-1224	518	24	aξ	aξ	INTJ
ejpam-1224	518	25	→	→	SYM
ejpam-1224	518	26	(	(	PUNCT
ejpam-1224	518	27	x2	x2	PROPN
ejpam-1224	518	28	)	)	PUNCT
ejpam-1224	518	29	bξ	bξ	PROPN
ejpam-1224	518	30	→	→	X
ejpam-1224	518	31	(	(	PUNCT
ejpam-1224	518	32	x	x	X
ejpam-1224	518	33	)	)	PUNCT
ejpam-1224	518	34	aξ	aξ	INTJ
ejpam-1224	518	35	→	→	SYM
ejpam-1224	518	36	(	(	PUNCT
ejpam-1224	518	37	1)→	1)→	NUM
ejpam-1224	518	38	(	(	PUNCT
ejpam-1224	518	39	0)→	0)→	NUM
ejpam-1224	518	40	·	·	PUNCT
ejpam-1224	518	41	·	·	PUNCT
ejpam-1224	518	42	·	·	PUNCT
ejpam-1224	518	43	.	.	PUNCT
ejpam-1224	519	1	the	the	DET
ejpam-1224	519	2	module	module	NOUN
ejpam-1224	519	3	multiplication	multiplication	NOUN
ejpam-1224	519	4	for	for	ADP
ejpam-1224	519	5	v	v	NOUN
ejpam-1224	519	6	∈	∈	PROPN
ejpam-1224	519	7	ka	ka	PROPN
ejpam-1224	519	8	is	be	AUX
ejpam-1224	519	9	defined	define	VERB
ejpam-1224	519	10	as	as	ADP
ejpam-1224	519	11	x	x	X
ejpam-1224	519	12	·	·	PUNCT
ejpam-1224	519	13	v	v	X
ejpam-1224	519	14	=	=	SYM
ejpam-1224	519	15	av	av	PROPN
ejpam-1224	519	16	.	.	PUNCT
ejpam-1224	520	1	now	now	ADV
ejpam-1224	520	2	let	let	VERB
ejpam-1224	520	3	us	we	PRON
ejpam-1224	520	4	consider	consider	VERB
ejpam-1224	520	5	fg(ka	fg(ka	NOUN
ejpam-1224	520	6	)	)	PUNCT
ejpam-1224	520	7	which	which	PRON
ejpam-1224	520	8	has	have	VERB
ejpam-1224	520	9	the	the	DET
ejpam-1224	520	10	form	form	NOUN
ejpam-1224	520	11	·	·	PUNCT
ejpam-1224	520	12	·	·	PUNCT
ejpam-1224	520	13	·	·	PUNCT
ejpam-1224	521	1	→	→	PUNCT
ejpam-1224	521	2	u	u	X
ejpam-1224	521	3	⊗	⊗	PROPN
ejpam-1224	521	4	(	(	PUNCT
ejpam-1224	521	5	a	a	NOUN
ejpam-1224	521	6	!	!	PUNCT
ejpam-1224	521	7	p	p	X
ejpam-1224	521	8	)	)	PUNCT
ejpam-1224	521	9	∗⊗	∗⊗	PROPN
ejpam-1224	521	10	ka→	ka→	NOUN
ejpam-1224	521	11	u	u	NOUN
ejpam-1224	521	12	⊗	⊗	PROPN
ejpam-1224	521	13	(	(	PUNCT
ejpam-1224	521	14	a	a	PROPN
ejpam-1224	521	15	!	!	PUNCT
ejpam-1224	522	1	p−1	p−1	NOUN
ejpam-1224	522	2	)	)	PUNCT
ejpam-1224	522	3	∗	∗	PROPN
ejpam-1224	522	4	⊗	⊗	PROPN
ejpam-1224	522	5	ka→	ka→	NOUN
ejpam-1224	522	6	·	·	PUNCT
ejpam-1224	522	7	·	·	PUNCT
ejpam-1224	522	8	·	·	PUNCT
ejpam-1224	522	9	.	.	PUNCT
ejpam-1224	523	1	the	the	DET
ejpam-1224	523	2	differential	differential	NOUN
ejpam-1224	523	3	for	for	ADP
ejpam-1224	523	4	fg(ka	fg(ka	NOUN
ejpam-1224	523	5	)	)	PUNCT
ejpam-1224	523	6	is	be	AUX
ejpam-1224	523	7	given	give	VERB
ejpam-1224	523	8	by	by	ADP
ejpam-1224	523	9	d(u⊗	d(u⊗	PROPN
ejpam-1224	523	10	ξ̇p	ξ̇p	PROPN
ejpam-1224	523	11	⊗	⊗	PROPN
ejpam-1224	523	12	1	1	NUM
ejpam-1224	523	13	)	)	PUNCT
ejpam-1224	523	14	=	=	SYM
ejpam-1224	523	15	ux	ux	PROPN
ejpam-1224	523	16	⊗	⊗	PROPN
ejpam-1224	523	17	ξ̇p−1	ξ̇p−1	PROPN
ejpam-1224	523	18	⊗	⊗	PROPN
ejpam-1224	523	19	1	1	NUM
ejpam-1224	523	20	+	+	CCONJ
ejpam-1224	523	21	(	(	PUNCT
ejpam-1224	523	22	−1)p+1(u⊗	−1)p+1(u⊗	ADJ
ejpam-1224	523	23	ξ̇p−1	ξ̇p−1	NOUN
ejpam-1224	523	24	⊗	⊗	PROPN
ejpam-1224	523	25	a+	a+	PUNCT
ejpam-1224	523	26	u⊗	u⊗	PROPN
ejpam-1224	523	27	d(ξ̇p)⊗	d(ξ̇p)⊗	PROPN
ejpam-1224	523	28	1	1	NUM
ejpam-1224	523	29	)	)	PUNCT
ejpam-1224	523	30	.	.	PUNCT
ejpam-1224	524	1	it	it	PRON
ejpam-1224	524	2	is	be	AUX
ejpam-1224	524	3	easy	easy	ADJ
ejpam-1224	524	4	to	to	PART
ejpam-1224	524	5	check	check	VERB
ejpam-1224	524	6	that	that	DET
ejpam-1224	524	7	d2	d2	PROPN
ejpam-1224	524	8	=	=	SYM
ejpam-1224	524	9	0	0	PROPN
ejpam-1224	524	10	and	and	CCONJ
ejpam-1224	524	11	the	the	DET
ejpam-1224	524	12	complex	complex	ADJ
ejpam-1224	524	13	fg(ka	fg(ka	NOUN
ejpam-1224	524	14	)	)	PUNCT
ejpam-1224	524	15	will	will	AUX
ejpam-1224	524	16	be	be	AUX
ejpam-1224	524	17	quasi	quasi	ADJ
ejpam-1224	524	18	-	-	ADJ
ejpam-1224	524	19	isomorphic	isomorphic	ADJ
ejpam-1224	524	20	to	to	AUX
ejpam-1224	524	21	ka	ka	X
ejpam-1224	524	22	by	by	ADP
ejpam-1224	524	23	proposition	proposition	NOUN
ejpam-1224	524	24	4	4	NUM
ejpam-1224	524	25	.	.	PUNCT
ejpam-1224	525	1	f.	f.	PROPN
ejpam-1224	525	2	hawwa	hawwa	PROPN
ejpam-1224	525	3	,	,	PUNCT
ejpam-1224	525	4	j.	j.	PROPN
ejpam-1224	525	5	hoffman	hoffman	PROPN
ejpam-1224	525	6	,	,	PUNCT
ejpam-1224	525	7	and	and	CCONJ
ejpam-1224	525	8	h.	h.	PROPN
ejpam-1224	525	9	wang	wang	PROPN
ejpam-1224	525	10	,	,	PUNCT
ejpam-1224	525	11	/	/	SYM
ejpam-1224	525	12	eur	eur	NOUN
ejpam-1224	525	13	.	.	PUNCT
ejpam-1224	526	1	j.	j.	PROPN
ejpam-1224	526	2	pure	pure	PROPN
ejpam-1224	526	3	appl	appl	PROPN
ejpam-1224	526	4	.	.	PROPN
ejpam-1224	526	5	math	math	PROPN
ejpam-1224	526	6	,	,	PUNCT
ejpam-1224	526	7	5	5	NUM
ejpam-1224	526	8	(	(	PUNCT
ejpam-1224	526	9	2012	2012	NUM
ejpam-1224	526	10	)	)	PUNCT
ejpam-1224	526	11	,	,	PUNCT
ejpam-1224	526	12	511	511	NUM
ejpam-1224	526	13	-	-	SYM
ejpam-1224	526	14	539	539	NUM
ejpam-1224	526	15	527	527	NUM
ejpam-1224	527	1	lemma	lemma	PROPN
ejpam-1224	527	2	4	4	X
ejpam-1224	527	3	.	.	PUNCT
ejpam-1224	527	4	d2	d2	PROPN
ejpam-1224	527	5	=	=	SYM
ejpam-1224	527	6	c	c	PROPN
ejpam-1224	527	7	in	in	ADP
ejpam-1224	527	8	equation	equation	NOUN
ejpam-1224	527	9	(	(	PUNCT
ejpam-1224	527	10	3	3	NUM
ejpam-1224	527	11	)	)	PUNCT
ejpam-1224	527	12	and	and	CCONJ
ejpam-1224	527	13	if	if	SCONJ
ejpam-1224	527	14	m	m	NOUN
ejpam-1224	527	15	is	be	AUX
ejpam-1224	527	16	in	in	ADP
ejpam-1224	527	17	comλ(u	comλ(u	NOUN
ejpam-1224	527	18	)	)	PUNCT
ejpam-1224	527	19	then	then	ADV
ejpam-1224	527	20	g(m	g(m	VERB
ejpam-1224	527	21	)	)	PUNCT
ejpam-1224	527	22	is	be	AUX
ejpam-1224	527	23	in	in	ADP
ejpam-1224	527	24	comλ(a	comλ(a	PROPN
ejpam-1224	527	25	!	!	PUNCT
ejpam-1224	527	26	,	,	PUNCT
ejpam-1224	528	1	d	d	X
ejpam-1224	528	2	,	,	PUNCT
ejpam-1224	528	3	c	c	NOUN
ejpam-1224	528	4	)	)	PUNCT
ejpam-1224	528	5	.	.	PUNCT
ejpam-1224	529	1	proof	proof	NOUN
ejpam-1224	529	2	.	.	PUNCT
ejpam-1224	530	1	to	to	PART
ejpam-1224	530	2	verify	verify	VERB
ejpam-1224	530	3	that	that	DET
ejpam-1224	530	4	d2	d2	PROPN
ejpam-1224	530	5	(	(	PUNCT
ejpam-1224	530	6	f	f	PROPN
ejpam-1224	530	7	)	)	PUNCT
ejpam-1224	531	1	=	=	PUNCT
ejpam-1224	532	1	c	c	NOUN
ejpam-1224	532	2	f	f	NOUN
ejpam-1224	533	1	we	we	PRON
ejpam-1224	533	2	have	have	VERB
ejpam-1224	533	3	d(d	d(d	PROPN
ejpam-1224	533	4	(	(	PUNCT
ejpam-1224	533	5	f	f	PROPN
ejpam-1224	533	6	)	)	PUNCT
ejpam-1224	533	7	(	(	PUNCT
ejpam-1224	533	8	a	a	NOUN
ejpam-1224	533	9	)	)	PUNCT
ejpam-1224	533	10	)	)	PUNCT
ejpam-1224	533	11	=	=	SYM
ejpam-1224	534	1	d[(−1)|	d[(−1)|	NUM
ejpam-1224	534	2	f	f	PROPN
ejpam-1224	534	3	|+1	|+1	NOUN
ejpam-1224	534	4	∑	∑	PROPN
ejpam-1224	534	5	xα	xα	PROPN
ejpam-1224	534	6	f	f	PROPN
ejpam-1224	534	7	(	(	PUNCT
ejpam-1224	534	8	x̌αa	x̌αa	PROPN
ejpam-1224	534	9	)	)	PUNCT
ejpam-1224	534	10	]	]	PUNCT
ejpam-1224	535	1	+	+	CCONJ
ejpam-1224	535	2	d[(−1)|	d[(−1)|	NUM
ejpam-1224	535	3	f	f	NOUN
ejpam-1224	535	4	|+1	|+1	SYM
ejpam-1224	535	5	f	f	PROPN
ejpam-1224	535	6	(	(	PUNCT
ejpam-1224	535	7	da!(a	da!(a	PROPN
ejpam-1224	535	8	)	)	PUNCT
ejpam-1224	535	9	)	)	PUNCT
ejpam-1224	535	10	]	]	PUNCT
ejpam-1224	536	1	+	+	CCONJ
ejpam-1224	536	2	d[dm	d[dm	PROPN
ejpam-1224	536	3	(	(	PUNCT
ejpam-1224	536	4	f	f	X
ejpam-1224	536	5	(	(	PUNCT
ejpam-1224	536	6	a	a	NOUN
ejpam-1224	536	7	)	)	PUNCT
ejpam-1224	536	8	)	)	PUNCT
ejpam-1224	536	9	]	]	PUNCT
ejpam-1224	536	10	.	.	PUNCT
ejpam-1224	537	1	let	let	VERB
ejpam-1224	537	2	us	we	PRON
ejpam-1224	537	3	examine	examine	VERB
ejpam-1224	537	4	the	the	DET
ejpam-1224	537	5	first	first	ADJ
ejpam-1224	537	6	term	term	NOUN
ejpam-1224	537	7	of	of	ADP
ejpam-1224	537	8	this	this	DET
ejpam-1224	537	9	differential	differential	NOUN
ejpam-1224	537	10	.	.	PUNCT
ejpam-1224	538	1	let	let	VERB
ejpam-1224	538	2	g(a	g(a	PROPN
ejpam-1224	538	3	)	)	PUNCT
ejpam-1224	539	1	=	=	PUNCT
ejpam-1224	540	1	(	(	PUNCT
ejpam-1224	540	2	−1)|	−1)|	NOUN
ejpam-1224	540	3	f	f	PROPN
ejpam-1224	540	4	|+1	|+1	PROPN
ejpam-1224	540	5	∑	∑	PROPN
ejpam-1224	540	6	xα	xα	PROPN
ejpam-1224	540	7	f	f	PROPN
ejpam-1224	540	8	(	(	PUNCT
ejpam-1224	540	9	x̌αa	x̌αa	PROPN
ejpam-1224	540	10	)	)	PUNCT
ejpam-1224	541	1	and	and	CCONJ
ejpam-1224	541	2	let	let	VERB
ejpam-1224	541	3	�	�	PROPN
ejpam-1224	541	4	�	�	PROPN
ejpam-1224	541	5	f	f	PROPN
ejpam-1224	541	6	�	�	PROPN
ejpam-1224	541	7	�	�	PROPN
ejpam-1224	542	1	=	=	PUNCT
ejpam-1224	542	2	p	p	NOUN
ejpam-1224	543	1	so	so	ADV
ejpam-1224	543	2	we	we	PRON
ejpam-1224	543	3	have	have	VERB
ejpam-1224	543	4	d(g)(a	d(g)(a	NOUN
ejpam-1224	543	5	)	)	PUNCT
ejpam-1224	543	6	=	=	VERB
ejpam-1224	544	1	(	(	PUNCT
ejpam-1224	544	2	−1)p+2	−1)p+2	VERB
ejpam-1224	544	3	∑	∑	PUNCT
ejpam-1224	544	4	β	β	PROPN
ejpam-1224	544	5	xβ	xβ	PROPN
ejpam-1224	544	6	g	g	PROPN
ejpam-1224	544	7	(	(	PUNCT
ejpam-1224	544	8	x̌βa	x̌βa	PROPN
ejpam-1224	544	9	)	)	PUNCT
ejpam-1224	545	1	+	+	CCONJ
ejpam-1224	545	2	(	(	PUNCT
ejpam-1224	545	3	−1)p+2g(da!(a	−1)p+2g(da!(a	PROPN
ejpam-1224	545	4	)	)	PUNCT
ejpam-1224	545	5	)	)	PUNCT
ejpam-1224	546	1	+	+	CCONJ
ejpam-1224	546	2	dm	dm	X
ejpam-1224	546	3	(	(	PUNCT
ejpam-1224	546	4	g(a	g(a	PROPN
ejpam-1224	546	5	)	)	PUNCT
ejpam-1224	546	6	)	)	PUNCT
ejpam-1224	546	7	which	which	PRON
ejpam-1224	546	8	can	can	AUX
ejpam-1224	546	9	be	be	AUX
ejpam-1224	546	10	rewritten	rewrite	VERB
ejpam-1224	546	11	as	as	ADP
ejpam-1224	546	12	d(g)(a	d(g)(a	NOUN
ejpam-1224	546	13	)	)	PUNCT
ejpam-1224	546	14	=	=	SYM
ejpam-1224	547	1	−	−	PROPN
ejpam-1224	547	2	∑	∑	PUNCT
ejpam-1224	547	3	β	β	PROPN
ejpam-1224	547	4	,	,	PUNCT
ejpam-1224	547	5	α	α	PROPN
ejpam-1224	548	1	xβ	xβ	PROPN
ejpam-1224	548	2	xα	xα	PROPN
ejpam-1224	549	1	f	f	X
ejpam-1224	549	2	(	(	PUNCT
ejpam-1224	549	3	x̌α	x̌α	PROPN
ejpam-1224	549	4	x̌βa)−	x̌βa)−	PROPN
ejpam-1224	549	5	∑	∑	PUNCT
ejpam-1224	549	6	γ	γ	X
ejpam-1224	549	7	xγ	xγ	PROPN
ejpam-1224	549	8	f	f	PROPN
ejpam-1224	549	9	(	(	PUNCT
ejpam-1224	549	10	x̌γda!(a))+	x̌γda!(a))+	X
ejpam-1224	549	11	(	(	PUNCT
ejpam-1224	549	12	−1)p+1	−1)p+1	NOUN
ejpam-1224	549	13	∑	∑	PUNCT
ejpam-1224	549	14	δ	δ	PROPN
ejpam-1224	549	15	dm	dm	PROPN
ejpam-1224	549	16	(	(	PUNCT
ejpam-1224	549	17	xδ	xδ	PROPN
ejpam-1224	549	18	f	f	PROPN
ejpam-1224	549	19	(	(	PUNCT
ejpam-1224	549	20	x̌δa	x̌δa	PROPN
ejpam-1224	549	21	)	)	PUNCT
ejpam-1224	549	22	)	)	PUNCT
ejpam-1224	549	23	.	.	PUNCT
ejpam-1224	550	1	now	now	ADV
ejpam-1224	550	2	recall	recall	VERB
ejpam-1224	550	3	from	from	ADP
ejpam-1224	550	4	lemma	lemma	PROPN
ejpam-1224	550	5	1	1	NUM
ejpam-1224	550	6	that	that	SCONJ
ejpam-1224	550	7	∑	∑	PUNCT
ejpam-1224	550	8	α	α	X
ejpam-1224	550	9	,	,	PUNCT
ejpam-1224	550	10	β	β	PROPN
ejpam-1224	550	11	xαxβ	xαxβ	PROPN
ejpam-1224	551	1	⊗	⊗	PROPN
ejpam-1224	551	2	x̌β	x̌β	PROPN
ejpam-1224	552	1	x̌α+	x̌α+	PROPN
ejpam-1224	552	2	∑	∑	PROPN
ejpam-1224	552	3	xα⊗	xα⊗	PROPN
ejpam-1224	552	4	d	d	PROPN
ejpam-1224	552	5	(	(	PUNCT
ejpam-1224	552	6	x̌α	x̌α	NOUN
ejpam-1224	552	7	)	)	PUNCT
ejpam-1224	553	1	+	+	PUNCT
ejpam-1224	554	1	1⊗	1⊗	NUM
ejpam-1224	554	2	c	c	NOUN
ejpam-1224	554	3	=	=	SYM
ejpam-1224	554	4	0	0	NUM
ejpam-1224	554	5	(	(	PUNCT
ejpam-1224	554	6	4	4	NUM
ejpam-1224	554	7	)	)	PUNCT
ejpam-1224	554	8	and	and	CCONJ
ejpam-1224	554	9	since	since	SCONJ
ejpam-1224	554	10	we	we	PRON
ejpam-1224	554	11	know	know	VERB
ejpam-1224	554	12	da	da	VERB
ejpam-1224	554	13	!	!	PUNCT
ejpam-1224	554	14	(	(	PUNCT
ejpam-1224	554	15	x̌γa	x̌γa	PROPN
ejpam-1224	554	16	)	)	PUNCT
ejpam-1224	554	17	=	=	SYM
ejpam-1224	555	1	da	da	NOUN
ejpam-1224	555	2	!	!	PUNCT
ejpam-1224	555	3	(	(	PUNCT
ejpam-1224	555	4	x̌γ)a−	x̌γ)a−	PROPN
ejpam-1224	555	5	x̌γda!(a	x̌γda!(a	PROPN
ejpam-1224	555	6	)	)	PUNCT
ejpam-1224	555	7	we	we	PRON
ejpam-1224	555	8	have	have	VERB
ejpam-1224	555	9	∑	∑	PROPN
ejpam-1224	555	10	xγ	xγ	PROPN
ejpam-1224	555	11	f	f	PROPN
ejpam-1224	555	12	(	(	PUNCT
ejpam-1224	555	13	x̌γda!(a	x̌γda!(a	PROPN
ejpam-1224	555	14	)	)	PUNCT
ejpam-1224	555	15	)	)	PUNCT
ejpam-1224	556	1	=	=	PUNCT
ejpam-1224	556	2	∑	∑	PUNCT
ejpam-1224	556	3	xγ	xγ	PROPN
ejpam-1224	557	1	f	f	PROPN
ejpam-1224	557	2	(	(	PUNCT
ejpam-1224	557	3	da	da	X
ejpam-1224	557	4	!	!	PUNCT
ejpam-1224	557	5	(	(	PUNCT
ejpam-1224	557	6	x̌γ)a)−	x̌γ)a)−	VERB
ejpam-1224	557	7	∑	∑	PROPN
ejpam-1224	557	8	xγ	xγ	PROPN
ejpam-1224	557	9	f	f	PROPN
ejpam-1224	557	10	(	(	PUNCT
ejpam-1224	557	11	da	da	X
ejpam-1224	557	12	!	!	PUNCT
ejpam-1224	557	13	(	(	PUNCT
ejpam-1224	557	14	x̌γa	x̌γa	PROPN
ejpam-1224	557	15	)	)	PUNCT
ejpam-1224	557	16	)	)	PUNCT
ejpam-1224	557	17	.	.	PUNCT
ejpam-1224	558	1	so	so	ADV
ejpam-1224	558	2	we	we	PRON
ejpam-1224	558	3	may	may	AUX
ejpam-1224	558	4	rewrite	rewrite	VERB
ejpam-1224	558	5	d(g)(a	d(g)(a	NOUN
ejpam-1224	558	6	)	)	PUNCT
ejpam-1224	558	7	as	as	ADP
ejpam-1224	558	8	d(g)(a	d(g)(a	NOUN
ejpam-1224	558	9	)	)	PUNCT
ejpam-1224	559	1	=	=	SYM
ejpam-1224	559	2	f	f	PROPN
ejpam-1224	559	3	(	(	PUNCT
ejpam-1224	559	4	ca	ca	NOUN
ejpam-1224	559	5	)	)	PUNCT
ejpam-1224	560	1	+	+	CCONJ
ejpam-1224	560	2	∑	∑	PUNCT
ejpam-1224	560	3	γ	γ	X
ejpam-1224	560	4	xγ	xγ	PROPN
ejpam-1224	560	5	f	f	PROPN
ejpam-1224	560	6	(	(	PUNCT
ejpam-1224	560	7	da	da	X
ejpam-1224	560	8	!	!	PUNCT
ejpam-1224	560	9	(	(	PUNCT
ejpam-1224	560	10	x̌γa	x̌γa	PROPN
ejpam-1224	560	11	)	)	PUNCT
ejpam-1224	560	12	)	)	PUNCT
ejpam-1224	561	1	+	+	CCONJ
ejpam-1224	561	2	(	(	PUNCT
ejpam-1224	561	3	−1)p+1	−1)p+1	NOUN
ejpam-1224	561	4	dm	dm	PROPN
ejpam-1224	561	5	(	(	PUNCT
ejpam-1224	561	6	∑	∑	PROPN
ejpam-1224	561	7	δ	δ	PROPN
ejpam-1224	561	8	xδ	xδ	PROPN
ejpam-1224	561	9	f	f	PROPN
ejpam-1224	561	10	(	(	PUNCT
ejpam-1224	561	11	x̌δa	x̌δa	PROPN
ejpam-1224	561	12	)	)	PUNCT
ejpam-1224	561	13	)	)	PUNCT
ejpam-1224	561	14	.	.	PUNCT
ejpam-1224	562	1	now	now	ADV
ejpam-1224	562	2	let	let	VERB
ejpam-1224	562	3	us	we	PRON
ejpam-1224	562	4	examine	examine	VERB
ejpam-1224	562	5	the	the	DET
ejpam-1224	562	6	second	second	ADJ
ejpam-1224	562	7	term	term	NOUN
ejpam-1224	562	8	of	of	ADP
ejpam-1224	562	9	d(d	d(d	PROPN
ejpam-1224	562	10	(	(	PUNCT
ejpam-1224	562	11	f	f	PROPN
ejpam-1224	562	12	)	)	PUNCT
ejpam-1224	562	13	(	(	PUNCT
ejpam-1224	562	14	a	a	NOUN
ejpam-1224	562	15	)	)	PUNCT
ejpam-1224	562	16	)	)	PUNCT
ejpam-1224	562	17	.	.	PUNCT
ejpam-1224	563	1	let	let	VERB
ejpam-1224	563	2	h(a	h(a	PROPN
ejpam-1224	563	3	)	)	PUNCT
ejpam-1224	564	1	=	=	PRON
ejpam-1224	564	2	(	(	PUNCT
ejpam-1224	564	3	−1)p+1	−1)p+1	NOUN
ejpam-1224	564	4	f	f	X
ejpam-1224	564	5	(	(	PUNCT
ejpam-1224	564	6	da!(a	da!(a	PROPN
ejpam-1224	564	7	)	)	PUNCT
ejpam-1224	564	8	)	)	PUNCT
ejpam-1224	565	1	so	so	ADV
ejpam-1224	565	2	we	we	PRON
ejpam-1224	565	3	have	have	VERB
ejpam-1224	565	4	dh(a	dh(a	ADV
ejpam-1224	565	5	)	)	PUNCT
ejpam-1224	565	6	=	=	PUNCT
ejpam-1224	566	1	(	(	PUNCT
ejpam-1224	566	2	−1)p+2	−1)p+2	VERB
ejpam-1224	566	3	∑	∑	PUNCT
ejpam-1224	566	4	xαh	xαh	PROPN
ejpam-1224	566	5	(	(	PUNCT
ejpam-1224	566	6	x̌αa	x̌αa	PROPN
ejpam-1224	566	7	)	)	PUNCT
ejpam-1224	566	8	+	+	CCONJ
ejpam-1224	566	9	(	(	PUNCT
ejpam-1224	566	10	−1)p+2h(da!(a	−1)p+2h(da!(a	PROPN
ejpam-1224	566	11	)	)	PUNCT
ejpam-1224	566	12	)	)	PUNCT
ejpam-1224	567	1	+	+	CCONJ
ejpam-1224	567	2	dm	dm	X
ejpam-1224	567	3	(	(	PUNCT
ejpam-1224	567	4	h(a	h(a	PROPN
ejpam-1224	567	5	)	)	PUNCT
ejpam-1224	567	6	)	)	PUNCT
ejpam-1224	568	1	=	=	PUNCT
ejpam-1224	569	1	−	−	PROPN
ejpam-1224	569	2	∑	∑	INTJ
ejpam-1224	569	3	xα	xα	PROPN
ejpam-1224	569	4	f	f	PROPN
ejpam-1224	569	5	(	(	PUNCT
ejpam-1224	569	6	da	da	X
ejpam-1224	569	7	!	!	PUNCT
ejpam-1224	569	8	(	(	PUNCT
ejpam-1224	569	9	x̌αa))−	x̌αa))−	PROPN
ejpam-1224	569	10	f	f	PROPN
ejpam-1224	569	11	(	(	PUNCT
ejpam-1224	569	12	da!(da!(a)))+	da!(da!(a)))+	PROPN
ejpam-1224	569	13	(	(	PUNCT
ejpam-1224	569	14	−1)p+1	−1)p+1	NOUN
ejpam-1224	569	15	dm	dm	PROPN
ejpam-1224	569	16	(	(	PUNCT
ejpam-1224	569	17	f	f	X
ejpam-1224	569	18	(	(	PUNCT
ejpam-1224	569	19	da!(a	da!(a	PROPN
ejpam-1224	569	20	)	)	PUNCT
ejpam-1224	569	21	)	)	PUNCT
ejpam-1224	569	22	)	)	PUNCT
ejpam-1224	570	1	=	=	PUNCT
ejpam-1224	571	1	−	−	PROPN
ejpam-1224	571	2	∑	∑	INTJ
ejpam-1224	571	3	xα	xα	PROPN
ejpam-1224	571	4	f	f	PROPN
ejpam-1224	571	5	(	(	PUNCT
ejpam-1224	571	6	da	da	X
ejpam-1224	571	7	!	!	PUNCT
ejpam-1224	571	8	(	(	PUNCT
ejpam-1224	571	9	x̌αa	x̌αa	PROPN
ejpam-1224	571	10	)	)	PUNCT
ejpam-1224	571	11	)	)	PUNCT
ejpam-1224	572	1	+	+	CCONJ
ejpam-1224	572	2	(	(	PUNCT
ejpam-1224	572	3	−1)p+1	−1)p+1	NOUN
ejpam-1224	572	4	dm	dm	PROPN
ejpam-1224	572	5	(	(	PUNCT
ejpam-1224	572	6	f	f	X
ejpam-1224	572	7	(	(	PUNCT
ejpam-1224	572	8	da!(a)))−	da!(a)))−	PROPN
ejpam-1224	572	9	f	f	PROPN
ejpam-1224	572	10	(	(	PUNCT
ejpam-1224	572	11	ca	ca	NOUN
ejpam-1224	572	12	)	)	PUNCT
ejpam-1224	573	1	+	+	NUM
ejpam-1224	573	2	f	f	X
ejpam-1224	573	3	(	(	PUNCT
ejpam-1224	573	4	ac	ac	PROPN
ejpam-1224	573	5	)	)	PUNCT
ejpam-1224	573	6	.	.	PUNCT
ejpam-1224	574	1	for	for	ADP
ejpam-1224	574	2	the	the	DET
ejpam-1224	574	3	third	third	ADJ
ejpam-1224	574	4	term	term	NOUN
ejpam-1224	574	5	of	of	ADP
ejpam-1224	574	6	d(d	d(d	PROPN
ejpam-1224	574	7	(	(	PUNCT
ejpam-1224	574	8	f	f	PROPN
ejpam-1224	574	9	)	)	PUNCT
ejpam-1224	574	10	(	(	PUNCT
ejpam-1224	574	11	a	a	NOUN
ejpam-1224	574	12	)	)	PUNCT
ejpam-1224	574	13	)	)	PUNCT
ejpam-1224	574	14	,	,	PUNCT
ejpam-1224	574	15	let	let	VERB
ejpam-1224	574	16	k(a	k(a	NOUN
ejpam-1224	574	17	)	)	PUNCT
ejpam-1224	575	1	=	=	SYM
ejpam-1224	575	2	dm	dm	INTJ
ejpam-1224	575	3	(	(	PUNCT
ejpam-1224	575	4	f	f	X
ejpam-1224	575	5	(	(	PUNCT
ejpam-1224	575	6	a	a	NOUN
ejpam-1224	575	7	)	)	PUNCT
ejpam-1224	575	8	)	)	PUNCT
ejpam-1224	575	9	.	.	PUNCT
ejpam-1224	576	1	so	so	ADV
ejpam-1224	576	2	we	we	PRON
ejpam-1224	576	3	have	have	VERB
ejpam-1224	576	4	dk(a	dk(a	NOUN
ejpam-1224	576	5	)	)	PUNCT
ejpam-1224	576	6	=	=	PUNCT
ejpam-1224	577	1	(	(	PUNCT
ejpam-1224	577	2	−1)p+2	−1)p+2	VERB
ejpam-1224	577	3	∑	∑	PROPN
ejpam-1224	577	4	xαk	xαk	PROPN
ejpam-1224	577	5	(	(	PUNCT
ejpam-1224	577	6	x̌αa	x̌αa	PROPN
ejpam-1224	577	7	)	)	PUNCT
ejpam-1224	577	8	+	+	CCONJ
ejpam-1224	577	9	(	(	PUNCT
ejpam-1224	577	10	−1)p+2k(da!(a))+	−1)p+2k(da!(a))+	NUM
ejpam-1224	577	11	dm	dm	PROPN
ejpam-1224	577	12	(	(	PUNCT
ejpam-1224	577	13	k(a	k(a	PROPN
ejpam-1224	577	14	)	)	PUNCT
ejpam-1224	577	15	)	)	PUNCT
ejpam-1224	577	16	=	=	PUNCT
ejpam-1224	578	1	(	(	PUNCT
ejpam-1224	578	2	−1)p+2	−1)p+2	VERB
ejpam-1224	578	3	∑	∑	PUNCT
ejpam-1224	578	4	xαdm	xαdm	PROPN
ejpam-1224	578	5	(	(	PUNCT
ejpam-1224	578	6	f	f	PROPN
ejpam-1224	578	7	(	(	PUNCT
ejpam-1224	578	8	x̌αa	x̌αa	PROPN
ejpam-1224	578	9	)	)	PUNCT
ejpam-1224	578	10	)	)	PUNCT
ejpam-1224	579	1	+	+	CCONJ
ejpam-1224	579	2	(	(	PUNCT
ejpam-1224	579	3	−1)p+2	−1)p+2	VERB
ejpam-1224	579	4	dm	dm	X
ejpam-1224	579	5	(	(	PUNCT
ejpam-1224	579	6	f	f	X
ejpam-1224	579	7	(	(	PUNCT
ejpam-1224	579	8	da!(a)))+	da!(a)))+	PROPN
ejpam-1224	579	9	dm	dm	PROPN
ejpam-1224	579	10	(	(	PUNCT
ejpam-1224	579	11	dm	dm	PROPN
ejpam-1224	579	12	(	(	PUNCT
ejpam-1224	579	13	f	f	X
ejpam-1224	579	14	(	(	PUNCT
ejpam-1224	579	15	a	a	NOUN
ejpam-1224	579	16	)	)	PUNCT
ejpam-1224	579	17	)	)	PUNCT
ejpam-1224	579	18	)	)	PUNCT
ejpam-1224	579	19	=	=	PUNCT
ejpam-1224	579	20	(	(	PUNCT
ejpam-1224	579	21	−1)p+2	−1)p+2	VERB
ejpam-1224	579	22	∑	∑	PUNCT
ejpam-1224	579	23	xαdm	xαdm	PROPN
ejpam-1224	579	24	(	(	PUNCT
ejpam-1224	579	25	f	f	PROPN
ejpam-1224	579	26	(	(	PUNCT
ejpam-1224	579	27	x̌αa	x̌αa	PROPN
ejpam-1224	579	28	)	)	PUNCT
ejpam-1224	579	29	)	)	PUNCT
ejpam-1224	580	1	+	+	CCONJ
ejpam-1224	580	2	(	(	PUNCT
ejpam-1224	580	3	−1)p+2	−1)p+2	VERB
ejpam-1224	580	4	dm	dm	X
ejpam-1224	580	5	(	(	PUNCT
ejpam-1224	580	6	f	f	X
ejpam-1224	580	7	(	(	PUNCT
ejpam-1224	580	8	da!(a	da!(a	PROPN
ejpam-1224	580	9	)	)	PUNCT
ejpam-1224	580	10	)	)	PUNCT
ejpam-1224	580	11	)	)	PUNCT
ejpam-1224	580	12	.	.	PUNCT
ejpam-1224	581	1	f.	f.	PROPN
ejpam-1224	581	2	hawwa	hawwa	PROPN
ejpam-1224	581	3	,	,	PUNCT
ejpam-1224	581	4	j.	j.	PROPN
ejpam-1224	581	5	hoffman	hoffman	PROPN
ejpam-1224	581	6	,	,	PUNCT
ejpam-1224	581	7	and	and	CCONJ
ejpam-1224	581	8	h.	h.	PROPN
ejpam-1224	581	9	wang	wang	PROPN
ejpam-1224	581	10	,	,	PUNCT
ejpam-1224	581	11	/	/	SYM
ejpam-1224	581	12	eur	eur	NOUN
ejpam-1224	581	13	.	.	PUNCT
ejpam-1224	582	1	j.	j.	PROPN
ejpam-1224	582	2	pure	pure	PROPN
ejpam-1224	582	3	appl	appl	PROPN
ejpam-1224	582	4	.	.	PROPN
ejpam-1224	582	5	math	math	PROPN
ejpam-1224	582	6	,	,	PUNCT
ejpam-1224	582	7	5	5	NUM
ejpam-1224	582	8	(	(	PUNCT
ejpam-1224	582	9	2012	2012	NUM
ejpam-1224	582	10	)	)	PUNCT
ejpam-1224	582	11	,	,	PUNCT
ejpam-1224	582	12	511	511	NUM
ejpam-1224	582	13	-	-	SYM
ejpam-1224	582	14	539	539	NUM
ejpam-1224	582	15	528	528	NUM
ejpam-1224	582	16	note	note	NOUN
ejpam-1224	582	17	that	that	SCONJ
ejpam-1224	582	18	since	since	SCONJ
ejpam-1224	582	19	dm	dm	PROPN
ejpam-1224	582	20	is	be	AUX
ejpam-1224	582	21	u	u	NOUN
ejpam-1224	582	22	-	-	NOUN
ejpam-1224	582	23	linear	linear	ADJ
ejpam-1224	582	24	we	we	PRON
ejpam-1224	582	25	have	have	VERB
ejpam-1224	582	26	d	d	NOUN
ejpam-1224	582	27	(	(	PUNCT
ejpam-1224	582	28	∑	∑	PROPN
ejpam-1224	582	29	xδ	xδ	PROPN
ejpam-1224	582	30	f	f	PROPN
ejpam-1224	582	31	(	(	PUNCT
ejpam-1224	582	32	x̌δa	x̌δa	PROPN
ejpam-1224	582	33	)	)	PUNCT
ejpam-1224	582	34	)	)	PUNCT
ejpam-1224	582	35	=	=	PUNCT
ejpam-1224	583	1	∑	∑	PUNCT
ejpam-1224	583	2	xδd	xδd	PROPN
ejpam-1224	583	3	(	(	PUNCT
ejpam-1224	583	4	f	f	PROPN
ejpam-1224	583	5	(	(	PUNCT
ejpam-1224	583	6	x̌δa	x̌δa	PROPN
ejpam-1224	583	7	)	)	PUNCT
ejpam-1224	583	8	)	)	PUNCT
ejpam-1224	583	9	.	.	PUNCT
ejpam-1224	584	1	now	now	ADV
ejpam-1224	584	2	we	we	PRON
ejpam-1224	584	3	can	can	AUX
ejpam-1224	584	4	list	list	VERB
ejpam-1224	584	5	all	all	DET
ejpam-1224	584	6	remaining	remain	VERB
ejpam-1224	584	7	terms	term	NOUN
ejpam-1224	584	8	of	of	ADP
ejpam-1224	584	9	the	the	DET
ejpam-1224	584	10	differential	differential	ADJ
ejpam-1224	584	11	d2	d2	PROPN
ejpam-1224	584	12	(	(	PUNCT
ejpam-1224	584	13	f	f	PROPN
ejpam-1224	584	14	)	)	PUNCT
ejpam-1224	584	15	(	(	PUNCT
ejpam-1224	584	16	a	a	NOUN
ejpam-1224	584	17	)	)	PUNCT
ejpam-1224	584	18	as	as	ADP
ejpam-1224	584	19	so	so	PROPN
ejpam-1224	584	20	d2	d2	PROPN
ejpam-1224	584	21	(	(	PUNCT
ejpam-1224	584	22	f	f	PROPN
ejpam-1224	584	23	)	)	PUNCT
ejpam-1224	584	24	(	(	PUNCT
ejpam-1224	584	25	a	a	X
ejpam-1224	584	26	)	)	PUNCT
ejpam-1224	584	27	=	=	SYM
ejpam-1224	584	28	f	f	PROPN
ejpam-1224	584	29	(	(	PUNCT
ejpam-1224	584	30	ca	ca	NOUN
ejpam-1224	584	31	)	)	PUNCT
ejpam-1224	585	1	+	+	CCONJ
ejpam-1224	585	2	∑	∑	PUNCT
ejpam-1224	585	3	γ	γ	X
ejpam-1224	585	4	xγ	xγ	PROPN
ejpam-1224	585	5	f	f	PROPN
ejpam-1224	585	6	(	(	PUNCT
ejpam-1224	585	7	da	da	X
ejpam-1224	585	8	!	!	PUNCT
ejpam-1224	585	9	(	(	PUNCT
ejpam-1224	585	10	x̌γa	x̌γa	PROPN
ejpam-1224	585	11	)	)	PUNCT
ejpam-1224	585	12	)	)	PUNCT
ejpam-1224	586	1	+	+	CCONJ
ejpam-1224	586	2	(	(	PUNCT
ejpam-1224	586	3	−1)p+1	−1)p+1	NOUN
ejpam-1224	586	4	dm	dm	PROPN
ejpam-1224	586	5	(	(	PUNCT
ejpam-1224	586	6	∑	∑	PROPN
ejpam-1224	586	7	δ	δ	PROPN
ejpam-1224	586	8	xδ	xδ	PROPN
ejpam-1224	586	9	f	f	PROPN
ejpam-1224	586	10	(	(	PUNCT
ejpam-1224	586	11	x̌δa	x̌δa	PROPN
ejpam-1224	586	12	)	)	PUNCT
ejpam-1224	586	13	)	)	PUNCT
ejpam-1224	587	1	−	−	PROPN
ejpam-1224	588	1	∑	∑	PUNCT
ejpam-1224	588	2	xα	xα	PROPN
ejpam-1224	588	3	f	f	PROPN
ejpam-1224	588	4	(	(	PUNCT
ejpam-1224	588	5	da	da	X
ejpam-1224	588	6	!	!	PUNCT
ejpam-1224	588	7	(	(	PUNCT
ejpam-1224	588	8	x̌αa	x̌αa	PROPN
ejpam-1224	588	9	)	)	PUNCT
ejpam-1224	588	10	)	)	PUNCT
ejpam-1224	589	1	+	+	CCONJ
ejpam-1224	589	2	(	(	PUNCT
ejpam-1224	589	3	−1)p+1	−1)p+1	NOUN
ejpam-1224	589	4	dm	dm	PROPN
ejpam-1224	589	5	(	(	PUNCT
ejpam-1224	589	6	f	f	X
ejpam-1224	589	7	(	(	PUNCT
ejpam-1224	589	8	da!(a)))−	da!(a)))−	PROPN
ejpam-1224	589	9	f	f	PROPN
ejpam-1224	589	10	(	(	PUNCT
ejpam-1224	589	11	ca	ca	NOUN
ejpam-1224	589	12	)	)	PUNCT
ejpam-1224	590	1	+	+	NUM
ejpam-1224	590	2	f	f	X
ejpam-1224	590	3	(	(	PUNCT
ejpam-1224	590	4	ac	ac	PROPN
ejpam-1224	590	5	)	)	PUNCT
ejpam-1224	590	6	+	+	CCONJ
ejpam-1224	590	7	(	(	PUNCT
ejpam-1224	590	8	−1)p+1	−1)p+1	NOUN
ejpam-1224	590	9	∑	∑	PUNCT
ejpam-1224	590	10	xαdm	xαdm	PROPN
ejpam-1224	590	11	(	(	PUNCT
ejpam-1224	590	12	f	f	PROPN
ejpam-1224	590	13	(	(	PUNCT
ejpam-1224	590	14	x̌αa	x̌αa	PROPN
ejpam-1224	590	15	)	)	PUNCT
ejpam-1224	590	16	)	)	PUNCT
ejpam-1224	591	1	+	+	CCONJ
ejpam-1224	591	2	(	(	PUNCT
ejpam-1224	591	3	−1)p+2	−1)p+2	VERB
ejpam-1224	591	4	dm	dm	X
ejpam-1224	591	5	(	(	PUNCT
ejpam-1224	591	6	f	f	X
ejpam-1224	591	7	(	(	PUNCT
ejpam-1224	591	8	da!(a	da!(a	PROPN
ejpam-1224	591	9	)	)	PUNCT
ejpam-1224	591	10	)	)	PUNCT
ejpam-1224	591	11	)	)	PUNCT
ejpam-1224	592	1	=	=	SYM
ejpam-1224	592	2	f	f	PROPN
ejpam-1224	592	3	(	(	PUNCT
ejpam-1224	592	4	ac	ac	PROPN
ejpam-1224	592	5	)	)	PUNCT
ejpam-1224	592	6	=	=	SYM
ejpam-1224	592	7	(	(	PUNCT
ejpam-1224	592	8	c	c	X
ejpam-1224	592	9	·	·	PUNCT
ejpam-1224	592	10	f	f	X
ejpam-1224	592	11	)	)	PUNCT
ejpam-1224	592	12	(	(	PUNCT
ejpam-1224	592	13	a	a	NOUN
ejpam-1224	592	14	)	)	PUNCT
ejpam-1224	592	15	.	.	PUNCT
ejpam-1224	593	1	we	we	PRON
ejpam-1224	593	2	will	will	AUX
ejpam-1224	593	3	now	now	ADV
ejpam-1224	593	4	check	check	VERB
ejpam-1224	593	5	that	that	SCONJ
ejpam-1224	593	6	d(a	d(a	PROPN
ejpam-1224	593	7	·	·	PUNCT
ejpam-1224	593	8	f	f	X
ejpam-1224	593	9	)	)	PUNCT
ejpam-1224	594	1	=	=	PUNCT
ejpam-1224	594	2	da	da	X
ejpam-1224	594	3	·	·	PUNCT
ejpam-1224	594	4	f	f	X
ejpam-1224	595	1	+	+	CCONJ
ejpam-1224	595	2	(	(	PUNCT
ejpam-1224	595	3	−1)|a|a	−1)|a|a	NOUN
ejpam-1224	595	4	·	·	PUNCT
ejpam-1224	595	5	d	d	NOUN
ejpam-1224	595	6	f	f	X
ejpam-1224	595	7	.	.	PUNCT
ejpam-1224	596	1	let	let	VERB
ejpam-1224	596	2	�	�	PROPN
ejpam-1224	596	3	�	�	PROPN
ejpam-1224	596	4	f	f	PROPN
ejpam-1224	596	5	�	�	PROPN
ejpam-1224	596	6	�	�	PROPN
ejpam-1224	596	7	=	=	SYM
ejpam-1224	596	8	p	p	PROPN
ejpam-1224	596	9	,	,	PUNCT
ejpam-1224	596	10	|a|	|a|	PROPN
ejpam-1224	596	11	=	=	SYM
ejpam-1224	596	12	q	q	PROPN
ejpam-1224	596	13	,	,	PUNCT
ejpam-1224	596	14	and	and	CCONJ
ejpam-1224	596	15	|b|	|b|	PROPN
ejpam-1224	597	1	=	=	PUNCT
ejpam-1224	597	2	r.	r.	PROPN
ejpam-1224	598	1	so	so	ADV
ejpam-1224	598	2	we	we	PRON
ejpam-1224	598	3	have	have	VERB
ejpam-1224	598	4	d(a	d(a	PROPN
ejpam-1224	598	5	·	·	PUNCT
ejpam-1224	598	6	f	f	X
ejpam-1224	598	7	)	)	PUNCT
ejpam-1224	598	8	(	(	PUNCT
ejpam-1224	598	9	b	b	X
ejpam-1224	598	10	)	)	PUNCT
ejpam-1224	598	11	=	=	SYM
ejpam-1224	598	12	(	(	PUNCT
ejpam-1224	598	13	−1)p+q+1	−1)p+q+1	PROPN
ejpam-1224	598	14	∑	∑	PROPN
ejpam-1224	598	15	xα(a	xα(a	X
ejpam-1224	598	16	·	·	PUNCT
ejpam-1224	598	17	f	f	X
ejpam-1224	598	18	)	)	PUNCT
ejpam-1224	598	19	(	(	PUNCT
ejpam-1224	598	20	x̌αb	x̌αb	X
ejpam-1224	598	21	)	)	PUNCT
ejpam-1224	598	22	+	+	CCONJ
ejpam-1224	598	23	(	(	PUNCT
ejpam-1224	598	24	−1)p+q+1(a	−1)p+q+1(a	ADP
ejpam-1224	598	25	·	·	PUNCT
ejpam-1224	598	26	f	f	X
ejpam-1224	598	27	)	)	PUNCT
ejpam-1224	598	28	(	(	PUNCT
ejpam-1224	598	29	d(b))+	d(b))+	VERB
ejpam-1224	598	30	d(a	d(a	PROPN
ejpam-1224	598	31	·	·	PUNCT
ejpam-1224	598	32	f	f	X
ejpam-1224	598	33	)	)	PUNCT
ejpam-1224	598	34	(	(	PUNCT
ejpam-1224	598	35	b	b	X
ejpam-1224	598	36	)	)	PUNCT
ejpam-1224	598	37	which	which	PRON
ejpam-1224	598	38	may	may	AUX
ejpam-1224	598	39	be	be	AUX
ejpam-1224	598	40	rewritten	rewrite	VERB
ejpam-1224	598	41	as	as	ADP
ejpam-1224	598	42	d(a	d(a	PROPN
ejpam-1224	598	43	·	·	SYM
ejpam-1224	598	44	f	f	NOUN
ejpam-1224	598	45	)	)	PUNCT
ejpam-1224	598	46	(	(	PUNCT
ejpam-1224	598	47	b	b	X
ejpam-1224	598	48	)	)	PUNCT
ejpam-1224	598	49	=	=	SYM
ejpam-1224	598	50	(	(	PUNCT
ejpam-1224	598	51	−1)qp+qr+p+1	−1)qp+qr+p+1	NOUN
ejpam-1224	598	52	∑	∑	PUNCT
ejpam-1224	598	53	xα	xα	PROPN
ejpam-1224	598	54	f	f	PROPN
ejpam-1224	598	55	(	(	PUNCT
ejpam-1224	598	56	(	(	PUNCT
ejpam-1224	598	57	x̌αba))+(−1)qp+qr+p+1	x̌αba))+(−1)qp+qr+p+1	PUNCT
ejpam-1224	598	58	f	f	X
ejpam-1224	598	59	(	(	PUNCT
ejpam-1224	598	60	(	(	PUNCT
ejpam-1224	598	61	d(b)a))+(−1)qp+qrd	d(b)a))+(−1)qp+qrd	X
ejpam-1224	598	62	(	(	PUNCT
ejpam-1224	598	63	f	f	PROPN
ejpam-1224	598	64	(	(	PUNCT
ejpam-1224	598	65	ba	ba	PROPN
ejpam-1224	598	66	)	)	PUNCT
ejpam-1224	598	67	)	)	PUNCT
ejpam-1224	598	68	.	.	PUNCT
ejpam-1224	599	1	recalling	recall	VERB
ejpam-1224	599	2	that	that	SCONJ
ejpam-1224	599	3	f	f	PROPN
ejpam-1224	599	4	(	(	PUNCT
ejpam-1224	599	5	d(b)a	d(b)a	PROPN
ejpam-1224	599	6	)	)	PUNCT
ejpam-1224	600	1	=	=	SYM
ejpam-1224	600	2	f	f	PROPN
ejpam-1224	600	3	(	(	PUNCT
ejpam-1224	600	4	d(ba))+	d(ba))+	PROPN
ejpam-1224	600	5	(	(	PUNCT
ejpam-1224	600	6	−1)r+1	−1)r+1	PROPN
ejpam-1224	600	7	f	f	X
ejpam-1224	600	8	(	(	PUNCT
ejpam-1224	600	9	b(da	b(da	NOUN
ejpam-1224	600	10	)	)	PUNCT
ejpam-1224	600	11	)	)	PUNCT
ejpam-1224	600	12	,	,	PUNCT
ejpam-1224	600	13	we	we	PRON
ejpam-1224	600	14	have	have	VERB
ejpam-1224	600	15	d(a	d(a	PROPN
ejpam-1224	600	16	·	·	PUNCT
ejpam-1224	600	17	f	f	X
ejpam-1224	600	18	)	)	PUNCT
ejpam-1224	600	19	(	(	PUNCT
ejpam-1224	600	20	b	b	X
ejpam-1224	600	21	)	)	PUNCT
ejpam-1224	600	22	=(	=(	ADJ
ejpam-1224	600	23	−1)qp+qr+p+1	−1)qp+qr+p+1	NOUN
ejpam-1224	600	24	∑	∑	PUNCT
ejpam-1224	600	25	xα	xα	PROPN
ejpam-1224	600	26	f	f	PROPN
ejpam-1224	600	27	(	(	PUNCT
ejpam-1224	600	28	(	(	PUNCT
ejpam-1224	600	29	x̌αba	x̌αba	PROPN
ejpam-1224	600	30	)	)	PUNCT
ejpam-1224	600	31	)	)	PUNCT
ejpam-1224	601	1	+	+	CCONJ
ejpam-1224	601	2	(	(	PUNCT
ejpam-1224	601	3	−1)qp+qr+p+1	−1)qp+qr+p+1	INTJ
ejpam-1224	601	4	f	f	X
ejpam-1224	601	5	(	(	PUNCT
ejpam-1224	601	6	d(ba	d(ba	NUM
ejpam-1224	601	7	)	)	PUNCT
ejpam-1224	601	8	)	)	PUNCT
ejpam-1224	602	1	+	+	CCONJ
ejpam-1224	602	2	(	(	PUNCT
ejpam-1224	602	3	−1)qp+qr+p+r	−1)qp+qr+p+r	PROPN
ejpam-1224	602	4	f	f	X
ejpam-1224	602	5	(	(	PUNCT
ejpam-1224	602	6	b(da))+	b(da))+	NOUN
ejpam-1224	602	7	(	(	PUNCT
ejpam-1224	602	8	−1)qp+qrd	−1)qp+qrd	X
ejpam-1224	602	9	(	(	PUNCT
ejpam-1224	602	10	f	f	PROPN
ejpam-1224	602	11	(	(	PUNCT
ejpam-1224	602	12	ba	ba	PROPN
ejpam-1224	602	13	)	)	PUNCT
ejpam-1224	602	14	)	)	PUNCT
ejpam-1224	602	15	.	.	PUNCT
ejpam-1224	603	1	let	let	VERB
ejpam-1224	603	2	us	we	PRON
ejpam-1224	603	3	now	now	ADV
ejpam-1224	603	4	calculate	calculate	VERB
ejpam-1224	603	5	(	(	PUNCT
ejpam-1224	603	6	da	da	NOUN
ejpam-1224	603	7	·	·	PUNCT
ejpam-1224	603	8	f	f	X
ejpam-1224	603	9	)	)	PUNCT
ejpam-1224	604	1	(	(	PUNCT
ejpam-1224	604	2	b)+	b)+	PROPN
ejpam-1224	604	3	(	(	PUNCT
ejpam-1224	604	4	−1)qa	−1)qa	NOUN
ejpam-1224	604	5	·	·	PUNCT
ejpam-1224	604	6	d	d	X
ejpam-1224	604	7	(	(	PUNCT
ejpam-1224	604	8	f	f	X
ejpam-1224	604	9	(	(	PUNCT
ejpam-1224	604	10	b	b	NOUN
ejpam-1224	604	11	)	)	PUNCT
ejpam-1224	604	12	)	)	PUNCT
ejpam-1224	604	13	.	.	PUNCT
ejpam-1224	605	1	for	for	ADP
ejpam-1224	605	2	the	the	DET
ejpam-1224	605	3	first	first	ADJ
ejpam-1224	605	4	term	term	NOUN
ejpam-1224	605	5	,	,	PUNCT
ejpam-1224	605	6	we	we	PRON
ejpam-1224	605	7	have	have	VERB
ejpam-1224	605	8	(	(	PUNCT
ejpam-1224	605	9	da	da	X
ejpam-1224	605	10	·	·	PUNCT
ejpam-1224	605	11	f	f	X
ejpam-1224	605	12	)	)	PUNCT
ejpam-1224	605	13	(	(	PUNCT
ejpam-1224	605	14	b	b	X
ejpam-1224	605	15	)	)	PUNCT
ejpam-1224	605	16	=	=	SYM
ejpam-1224	606	1	(	(	PUNCT
ejpam-1224	606	2	−1)qp+qr+p+r	−1)qp+qr+p+r	NOUN
ejpam-1224	606	3	f	f	X
ejpam-1224	606	4	(	(	PUNCT
ejpam-1224	606	5	b(da	b(da	NOUN
ejpam-1224	606	6	)	)	PUNCT
ejpam-1224	606	7	)	)	PUNCT
ejpam-1224	606	8	and	and	CCONJ
ejpam-1224	606	9	for	for	ADP
ejpam-1224	606	10	the	the	DET
ejpam-1224	606	11	second	second	ADJ
ejpam-1224	606	12	term	term	NOUN
ejpam-1224	606	13	,	,	PUNCT
ejpam-1224	606	14	we	we	PRON
ejpam-1224	606	15	have	have	VERB
ejpam-1224	606	16	(	(	PUNCT
ejpam-1224	606	17	−1)q(a·d	−1)q(a·d	PROPN
ejpam-1224	606	18	f	f	PROPN
ejpam-1224	606	19	)	)	PUNCT
ejpam-1224	606	20	(	(	PUNCT
ejpam-1224	606	21	b	b	X
ejpam-1224	606	22	)	)	PUNCT
ejpam-1224	606	23	=	=	SYM
ejpam-1224	606	24	(	(	PUNCT
ejpam-1224	606	25	−1)qp+qr+p+1	−1)qp+qr+p+1	NOUN
ejpam-1224	606	26	∑	∑	PUNCT
ejpam-1224	606	27	xα	xα	PROPN
ejpam-1224	606	28	f	f	PROPN
ejpam-1224	606	29	(	(	PUNCT
ejpam-1224	606	30	(	(	PUNCT
ejpam-1224	606	31	x̌αba))+(−1)qp+qr+p+1	x̌αba))+(−1)qp+qr+p+1	PUNCT
ejpam-1224	606	32	f	f	PROPN
ejpam-1224	606	33	(	(	PUNCT
ejpam-1224	606	34	d(ba))+(−1)qp+qrd	d(ba))+(−1)qp+qrd	PROPN
ejpam-1224	606	35	(	(	PUNCT
ejpam-1224	606	36	f	f	PROPN
ejpam-1224	606	37	(	(	PUNCT
ejpam-1224	606	38	ba	ba	PROPN
ejpam-1224	606	39	)	)	PUNCT
ejpam-1224	606	40	)	)	PUNCT
ejpam-1224	606	41	which	which	PRON
ejpam-1224	606	42	proves	prove	VERB
ejpam-1224	606	43	that	that	SCONJ
ejpam-1224	606	44	d(a	d(a	PROPN
ejpam-1224	606	45	·	·	PUNCT
ejpam-1224	606	46	f	f	X
ejpam-1224	606	47	)	)	PUNCT
ejpam-1224	607	1	=	=	PUNCT
ejpam-1224	607	2	da	da	X
ejpam-1224	607	3	·	·	PUNCT
ejpam-1224	607	4	f	f	X
ejpam-1224	608	1	+	+	CCONJ
ejpam-1224	608	2	(	(	PUNCT
ejpam-1224	608	3	−1)|a|a	−1)|a|a	NOUN
ejpam-1224	608	4	·	·	PUNCT
ejpam-1224	608	5	d	d	NOUN
ejpam-1224	608	6	f	f	PROPN
ejpam-1224	608	7	.	.	PUNCT
ejpam-1224	609	1	these	these	PRON
ejpam-1224	609	2	define	define	VERB
ejpam-1224	609	3	a	a	DET
ejpam-1224	609	4	structure	structure	NOUN
ejpam-1224	609	5	of	of	ADP
ejpam-1224	609	6	a	a	DET
ejpam-1224	609	7	cdgm	cdgm	NOUN
ejpam-1224	609	8	over	over	ADP
ejpam-1224	609	9	the	the	DET
ejpam-1224	609	10	cdga	cdga	NOUN
ejpam-1224	609	11	(	(	PUNCT
ejpam-1224	609	12	a	a	PROPN
ejpam-1224	609	13	!	!	PUNCT
ejpam-1224	609	14	,	,	PUNCT
ejpam-1224	609	15	d	d	X
ejpam-1224	609	16	,	,	PUNCT
ejpam-1224	609	17	c	c	NOUN
ejpam-1224	609	18	)	)	PUNCT
ejpam-1224	609	19	.	.	PUNCT
ejpam-1224	610	1	more	more	ADV
ejpam-1224	610	2	explicitly	explicitly	ADV
ejpam-1224	610	3	(	(	PUNCT
ejpam-1224	610	4	a!)pµ×	a!)pµ×	NOUN
ejpam-1224	610	5	g(m)qν	g(m)qν	X
ejpam-1224	610	6	→	→	SYM
ejpam-1224	610	7	g(m	g(m	PROPN
ejpam-1224	610	8	)	)	PUNCT
ejpam-1224	610	9	p+q	p+q	X
ejpam-1224	610	10	µ+ν	µ+ν	X
ejpam-1224	610	11	.	.	PUNCT
ejpam-1224	611	1	note	note	VERB
ejpam-1224	611	2	that	that	SCONJ
ejpam-1224	611	3	when	when	SCONJ
ejpam-1224	611	4	a	a	PRON
ejpam-1224	611	5	!	!	PUNCT
ejpam-1224	612	1	=	=	SYM
ejpam-1224	612	2	e(v	e(v	NOUN
ejpam-1224	612	3	∗	∗	NOUN
ejpam-1224	612	4	)	)	PUNCT
ejpam-1224	612	5	with	with	ADP
ejpam-1224	612	6	dim	dim	ADJ
ejpam-1224	612	7	v	v	ADP
ejpam-1224	612	8	<	<	X
ejpam-1224	612	9	∞	∞	PROPN
ejpam-1224	612	10	,	,	PUNCT
ejpam-1224	612	11	the	the	DET
ejpam-1224	612	12	above	above	ADJ
ejpam-1224	612	13	direct	direct	ADJ
ejpam-1224	612	14	products	product	NOUN
ejpam-1224	612	15	are	be	AUX
ejpam-1224	612	16	direct	direct	ADJ
ejpam-1224	612	17	sums	sum	NOUN
ejpam-1224	612	18	since	since	SCONJ
ejpam-1224	612	19	dim	dim	VERB
ejpam-1224	612	20	a	a	PRON
ejpam-1224	612	21	!	!	PUNCT
ejpam-1224	613	1	<	<	X
ejpam-1224	613	2	∞.	∞.	PROPN
ejpam-1224	613	3	f.	f.	PROPN
ejpam-1224	613	4	hawwa	hawwa	PROPN
ejpam-1224	613	5	,	,	PUNCT
ejpam-1224	613	6	j.	j.	PROPN
ejpam-1224	613	7	hoffman	hoffman	PROPN
ejpam-1224	613	8	,	,	PUNCT
ejpam-1224	613	9	and	and	CCONJ
ejpam-1224	613	10	h.	h.	PROPN
ejpam-1224	613	11	wang	wang	PROPN
ejpam-1224	613	12	,	,	PUNCT
ejpam-1224	613	13	/	/	SYM
ejpam-1224	613	14	eur	eur	NOUN
ejpam-1224	613	15	.	.	PUNCT
ejpam-1224	614	1	j.	j.	PROPN
ejpam-1224	614	2	pure	pure	PROPN
ejpam-1224	614	3	appl	appl	PROPN
ejpam-1224	614	4	.	.	PROPN
ejpam-1224	614	5	math	math	PROPN
ejpam-1224	614	6	,	,	PUNCT
ejpam-1224	614	7	5	5	NUM
ejpam-1224	614	8	(	(	PUNCT
ejpam-1224	614	9	2012	2012	NUM
ejpam-1224	614	10	)	)	PUNCT
ejpam-1224	614	11	,	,	PUNCT
ejpam-1224	614	12	511	511	NUM
ejpam-1224	614	13	-	-	SYM
ejpam-1224	614	14	539	539	NUM
ejpam-1224	614	15	529	529	NUM
ejpam-1224	614	16	proposition	proposition	NOUN
ejpam-1224	614	17	3	3	NUM
ejpam-1224	614	18	.	.	PUNCT
ejpam-1224	615	1	we	we	PRON
ejpam-1224	615	2	have	have	VERB
ejpam-1224	615	3	:	:	PUNCT
ejpam-1224	615	4	1	1	X
ejpam-1224	615	5	.	.	X
ejpam-1224	616	1	for	for	ADP
ejpam-1224	616	2	n	n	PRON
ejpam-1224	616	3	in	in	ADP
ejpam-1224	616	4	comλ(a	comλ(a	PROPN
ejpam-1224	616	5	!	!	PUNCT
ejpam-1224	616	6	,	,	PUNCT
ejpam-1224	616	7	d	d	X
ejpam-1224	616	8	)	)	PUNCT
ejpam-1224	616	9	and	and	CCONJ
ejpam-1224	616	10	m	m	PROPN
ejpam-1224	616	11	in	in	ADP
ejpam-1224	616	12	comλ(u	comλ(u	NOUN
ejpam-1224	616	13	)	)	PUNCT
ejpam-1224	616	14	there	there	PRON
ejpam-1224	616	15	is	be	VERB
ejpam-1224	616	16	a	a	DET
ejpam-1224	616	17	canonical	canonical	ADJ
ejpam-1224	616	18	isomorphism	isomorphism	NOUN
ejpam-1224	616	19	of	of	ADP
ejpam-1224	616	20	differential	differential	NOUN
ejpam-1224	616	21	graded	grade	VERB
ejpam-1224	616	22	λ	λ	NOUN
ejpam-1224	616	23	-	-	PUNCT
ejpam-1224	616	24	graded	grade	VERB
ejpam-1224	616	25	vector	vector	NOUN
ejpam-1224	616	26	spaces	space	NOUN
ejpam-1224	616	27	homu(f(n	homu(f(n	NOUN
ejpam-1224	616	28	)	)	PUNCT
ejpam-1224	616	29	,	,	PUNCT
ejpam-1224	616	30	m	m	NOUN
ejpam-1224	616	31	)	)	PUNCT
ejpam-1224	617	1	=	=	SYM
ejpam-1224	617	2	homa!(n	homa!(n	NOUN
ejpam-1224	617	3	,	,	PUNCT
ejpam-1224	617	4	g(m	g(m	PROPN
ejpam-1224	617	5	)	)	PUNCT
ejpam-1224	617	6	)	)	PUNCT
ejpam-1224	617	7	.	.	PUNCT
ejpam-1224	618	1	2	2	X
ejpam-1224	618	2	.	.	X
ejpam-1224	618	3	the	the	DET
ejpam-1224	618	4	functors	functors	PROPN
ejpam-1224	618	5	f	f	PROPN
ejpam-1224	618	6	and	and	CCONJ
ejpam-1224	618	7	g	g	PROPN
ejpam-1224	618	8	are	be	AUX
ejpam-1224	618	9	adjoint	adjoint	NOUN
ejpam-1224	618	10	,	,	PUNCT
ejpam-1224	618	11	i.e.	i.e.	X
ejpam-1224	618	12	,	,	PUNCT
ejpam-1224	618	13	homcomλ(u	homcomλ(u	PROPN
ejpam-1224	618	14	)	)	PUNCT
ejpam-1224	618	15	(	(	PUNCT
ejpam-1224	618	16	f(n	f(n	PROPN
ejpam-1224	618	17	)	)	PUNCT
ejpam-1224	618	18	,	,	PUNCT
ejpam-1224	618	19	m	m	NOUN
ejpam-1224	618	20	)	)	PUNCT
ejpam-1224	619	1	=	=	SYM
ejpam-1224	619	2	homcomλ(a	homcomλ(a	NOUN
ejpam-1224	619	3	!	!	PUNCT
ejpam-1224	619	4	,	,	PUNCT
ejpam-1224	619	5	d)(n	d)(n	X
ejpam-1224	619	6	,	,	PUNCT
ejpam-1224	619	7	g(m	g(m	NUM
ejpam-1224	619	8	)	)	PUNCT
ejpam-1224	619	9	)	)	PUNCT
ejpam-1224	619	10	.	.	PUNCT
ejpam-1224	620	1	3	3	X
ejpam-1224	620	2	.	.	X
ejpam-1224	620	3	the	the	DET
ejpam-1224	620	4	functors	functors	PROPN
ejpam-1224	620	5	f	f	PROPN
ejpam-1224	620	6	and	and	CCONJ
ejpam-1224	620	7	g	g	PROPN
ejpam-1224	620	8	are	be	AUX
ejpam-1224	620	9	exact	exact	ADJ
ejpam-1224	620	10	.	.	PUNCT
ejpam-1224	621	1	proof	proof	NOUN
ejpam-1224	621	2	.	.	PUNCT
ejpam-1224	622	1	since	since	SCONJ
ejpam-1224	622	2	f(n	f(n	PROPN
ejpam-1224	622	3	)	)	PUNCT
ejpam-1224	622	4	=	=	SYM
ejpam-1224	622	5	t	t	NOUN
ejpam-1224	622	6	⊗a	⊗a	NOUN
ejpam-1224	622	7	!	!	PUNCT
ejpam-1224	623	1	n	n	PROPN
ejpam-1224	623	2	and	and	CCONJ
ejpam-1224	623	3	g(m	g(m	ADJ
ejpam-1224	623	4	)	)	PUNCT
ejpam-1224	623	5	=	=	SYM
ejpam-1224	623	6	homu(t	homu(t	PROPN
ejpam-1224	623	7	,	,	PUNCT
ejpam-1224	623	8	m	m	PROPN
ejpam-1224	623	9	)	)	PUNCT
ejpam-1224	623	10	,	,	PUNCT
ejpam-1224	623	11	the	the	DET
ejpam-1224	623	12	first	first	ADJ
ejpam-1224	623	13	statement	statement	NOUN
ejpam-1224	623	14	follows	follow	VERB
ejpam-1224	623	15	directly	directly	ADV
ejpam-1224	623	16	from	from	ADP
ejpam-1224	623	17	the	the	DET
ejpam-1224	623	18	adjointness	adjointness	NOUN
ejpam-1224	623	19	of	of	ADP
ejpam-1224	623	20	hom	hom	NOUN
ejpam-1224	623	21	and	and	CCONJ
ejpam-1224	623	22	tensor	tensor	NOUN
ejpam-1224	623	23	product	product	NOUN
ejpam-1224	623	24	.	.	PUNCT
ejpam-1224	624	1	explicitly	explicitly	ADV
ejpam-1224	624	2	both	both	DET
ejpam-1224	624	3	complexes	complex	NOUN
ejpam-1224	624	4	have	have	VERB
ejpam-1224	624	5	(	(	PUNCT
ejpam-1224	624	6	p	p	X
ejpam-1224	624	7	,	,	PUNCT
ejpam-1224	624	8	λ)’th	λ)’th	NOUN
ejpam-1224	624	9	term	term	NOUN
ejpam-1224	624	10	equal	equal	ADJ
ejpam-1224	624	11	to	to	ADP
ejpam-1224	624	12	∏	∏	PROPN
ejpam-1224	624	13	r∈z	r∈z	NOUN
ejpam-1224	624	14	∏	∏	PROPN
ejpam-1224	624	15	µ	µ	PRON
ejpam-1224	624	16	homk(n	homk(n	ADP
ejpam-1224	624	17	r	r	NOUN
ejpam-1224	624	18	µ	µ	X
ejpam-1224	624	19	,	,	PUNCT
ejpam-1224	624	20	m	m	VERB
ejpam-1224	624	21	p+r	p+r	NOUN
ejpam-1224	624	22	λ+µ	λ+µ	X
ejpam-1224	624	23	)	)	PUNCT
ejpam-1224	624	24	with	with	ADP
ejpam-1224	624	25	differential	differential	NOUN
ejpam-1224	624	26	d	d	NOUN
ejpam-1224	624	27	given	give	VERB
ejpam-1224	624	28	as	as	SCONJ
ejpam-1224	624	29	follows	follow	VERB
ejpam-1224	624	30	for	for	ADP
ejpam-1224	624	31	f	f	PROPN
ejpam-1224	624	32	∈	∈	PROPN
ejpam-1224	624	33	∏	∏	PROPN
ejpam-1224	624	34	r∈zhomk(n	r∈zhomk(n	SYM
ejpam-1224	624	35	r	r	NOUN
ejpam-1224	624	36	,	,	PUNCT
ejpam-1224	624	37	m	m	PROPN
ejpam-1224	624	38	p+r	p+r	NUM
ejpam-1224	624	39	)	)	PUNCT
ejpam-1224	624	40	and	and	CCONJ
ejpam-1224	624	41	n	n	PRON
ejpam-1224	624	42	∈	∈	PROPN
ejpam-1224	624	43	n	n	PRON
ejpam-1224	624	44	r	r	NOUN
ejpam-1224	624	45	,	,	PUNCT
ejpam-1224	624	46	d	d	X
ejpam-1224	624	47	(	(	PUNCT
ejpam-1224	624	48	f	f	NOUN
ejpam-1224	624	49	)	)	PUNCT
ejpam-1224	624	50	(	(	PUNCT
ejpam-1224	624	51	n	n	CCONJ
ejpam-1224	624	52	)	)	PUNCT
ejpam-1224	624	53	=	=	SYM
ejpam-1224	625	1	(	(	PUNCT
ejpam-1224	625	2	−1)rdm	−1)rdm	NOUN
ejpam-1224	625	3	f	f	PROPN
ejpam-1224	625	4	(	(	PUNCT
ejpam-1224	625	5	n)+	n)+	PROPN
ejpam-1224	625	6	(	(	PUNCT
ejpam-1224	625	7	−1)r+1	−1)r+1	INTJ
ejpam-1224	625	8	f	f	X
ejpam-1224	625	9	dn	dn	PROPN
ejpam-1224	625	10	(	(	PUNCT
ejpam-1224	625	11	n)+	n)+	PROPN
ejpam-1224	625	12	(	(	PUNCT
ejpam-1224	625	13	−1)r+1	−1)r+1	INTJ
ejpam-1224	625	14	∑	∑	PROPN
ejpam-1224	625	15	α	α	NOUN
ejpam-1224	625	16	xα	xα	PROPN
ejpam-1224	625	17	f	f	PROPN
ejpam-1224	625	18	(	(	PUNCT
ejpam-1224	625	19	x̌αn	x̌αn	PROPN
ejpam-1224	625	20	)	)	PUNCT
ejpam-1224	625	21	.	.	PUNCT
ejpam-1224	626	1	to	to	PART
ejpam-1224	626	2	see	see	VERB
ejpam-1224	626	3	that	that	SCONJ
ejpam-1224	626	4	the	the	DET
ejpam-1224	626	5	functors	functors	PROPN
ejpam-1224	626	6	f	f	PROPN
ejpam-1224	626	7	and	and	CCONJ
ejpam-1224	626	8	g	g	PROPN
ejpam-1224	626	9	are	be	AUX
ejpam-1224	626	10	adjoint	adjoint	NOUN
ejpam-1224	626	11	we	we	PRON
ejpam-1224	626	12	note	note	VERB
ejpam-1224	626	13	that	that	SCONJ
ejpam-1224	626	14	the	the	DET
ejpam-1224	626	15	two	two	NUM
ejpam-1224	626	16	sides	side	NOUN
ejpam-1224	626	17	are	be	AUX
ejpam-1224	626	18	the	the	DET
ejpam-1224	626	19	cycles	cycle	NOUN
ejpam-1224	626	20	of	of	ADP
ejpam-1224	626	21	degree	degree	NOUN
ejpam-1224	626	22	0	0	NUM
ejpam-1224	626	23	in	in	ADP
ejpam-1224	626	24	the	the	DET
ejpam-1224	626	25	complexes	complex	NOUN
ejpam-1224	626	26	described	describe	VERB
ejpam-1224	626	27	in	in	ADP
ejpam-1224	626	28	the	the	DET
ejpam-1224	626	29	first	first	ADJ
ejpam-1224	626	30	statement	statement	NOUN
ejpam-1224	626	31	.	.	PUNCT
ejpam-1224	627	1	the	the	DET
ejpam-1224	627	2	functor	functor	PROPN
ejpam-1224	627	3	f	f	PROPN
ejpam-1224	627	4	is	be	AUX
ejpam-1224	627	5	exact	exact	ADJ
ejpam-1224	627	6	since	since	SCONJ
ejpam-1224	627	7	as	as	ADP
ejpam-1224	627	8	a	a	DET
ejpam-1224	627	9	module	module	NOUN
ejpam-1224	627	10	,	,	PUNCT
ejpam-1224	627	11	f(n	f(n	PROPN
ejpam-1224	627	12	)	)	PUNCT
ejpam-1224	628	1	=	=	SYM
ejpam-1224	628	2	t	t	NOUN
ejpam-1224	628	3	⊗a	⊗a	NOUN
ejpam-1224	628	4	!	!	PUNCT
ejpam-1224	629	1	n	n	PRON
ejpam-1224	629	2	=	=	SYM
ejpam-1224	629	3	u	u	NOUN
ejpam-1224	629	4	⊗k	⊗k	ADJ
ejpam-1224	629	5	n	n	CCONJ
ejpam-1224	630	1	and	and	CCONJ
ejpam-1224	630	2	k	k	PROPN
ejpam-1224	630	3	is	be	AUX
ejpam-1224	630	4	a	a	DET
ejpam-1224	630	5	field	field	NOUN
ejpam-1224	630	6	.	.	PUNCT
ejpam-1224	631	1	for	for	ADP
ejpam-1224	631	2	the	the	DET
ejpam-1224	631	3	same	same	ADJ
ejpam-1224	631	4	reason	reason	NOUN
ejpam-1224	631	5	,	,	PUNCT
ejpam-1224	631	6	the	the	DET
ejpam-1224	631	7	functor	functor	PROPN
ejpam-1224	631	8	g	g	PROPN
ejpam-1224	631	9	is	be	AUX
ejpam-1224	631	10	exact	exact	ADJ
ejpam-1224	631	11	since	since	SCONJ
ejpam-1224	631	12	g(m	g(m	NOUN
ejpam-1224	631	13	)	)	PUNCT
ejpam-1224	632	1	=	=	SYM
ejpam-1224	632	2	homu(t	homu(t	PROPN
ejpam-1224	632	3	,	,	PUNCT
ejpam-1224	632	4	m	m	NOUN
ejpam-1224	632	5	)	)	PUNCT
ejpam-1224	632	6	=	=	SYM
ejpam-1224	633	1	homk(a	homk(a	NOUN
ejpam-1224	633	2	!	!	PUNCT
ejpam-1224	633	3	,	,	PUNCT
ejpam-1224	633	4	m	m	PROPN
ejpam-1224	633	5	)	)	PUNCT
ejpam-1224	633	6	.	.	PUNCT
ejpam-1224	634	1	lemma	lemma	PROPN
ejpam-1224	634	2	5	5	X
ejpam-1224	634	3	.	.	PUNCT
ejpam-1224	635	1	let	let	VERB
ejpam-1224	635	2	m	m	PRON
ejpam-1224	635	3	be	be	AUX
ejpam-1224	635	4	a	a	DET
ejpam-1224	635	5	u	u	NOUN
ejpam-1224	635	6	-	-	NOUN
ejpam-1224	635	7	module	module	NOUN
ejpam-1224	635	8	considered	consider	VERB
ejpam-1224	635	9	as	as	ADP
ejpam-1224	635	10	a	a	DET
ejpam-1224	635	11	complex	complex	NOUN
ejpam-1224	635	12	situated	situate	VERB
ejpam-1224	635	13	in	in	ADP
ejpam-1224	635	14	degree	degree	NOUN
ejpam-1224	635	15	0	0	NUM
ejpam-1224	635	16	.	.	PUNCT
ejpam-1224	636	1	then	then	ADV
ejpam-1224	636	2	fg(m)→	fg(m)→	VERB
ejpam-1224	636	3	m	m	NOUN
ejpam-1224	636	4	is	be	AUX
ejpam-1224	636	5	a	a	DET
ejpam-1224	636	6	quasi	quasi	NOUN
ejpam-1224	636	7	-	-	NOUN
ejpam-1224	636	8	isomorphism	isomorphism	NOUN
ejpam-1224	636	9	.	.	PUNCT
ejpam-1224	637	1	note	note	NOUN
ejpam-1224	637	2	that	that	SCONJ
ejpam-1224	637	3	fg(m	fg(m	NOUN
ejpam-1224	637	4	)	)	PUNCT
ejpam-1224	637	5	is	be	AUX
ejpam-1224	637	6	the	the	DET
ejpam-1224	637	7	complex	complex	ADJ
ejpam-1224	637	8	·	·	PUNCT
ejpam-1224	637	9	·	·	PUNCT
ejpam-1224	637	10	·	·	PUNCT
ejpam-1224	638	1	→	→	PUNCT
ejpam-1224	638	2	u	u	X
ejpam-1224	638	3	⊗	⊗	PROPN
ejpam-1224	638	4	(	(	PUNCT
ejpam-1224	638	5	a	a	NOUN
ejpam-1224	638	6	!	!	PUNCT
ejpam-1224	639	1	p	p	X
ejpam-1224	639	2	)	)	PUNCT
ejpam-1224	639	3	∗	∗	NOUN
ejpam-1224	639	4	⊗m	⊗m	NOUN
ejpam-1224	639	5	→	→	SYM
ejpam-1224	639	6	u	u	NOUN
ejpam-1224	639	7	⊗	⊗	PROPN
ejpam-1224	639	8	(	(	PUNCT
ejpam-1224	639	9	a	a	PROPN
ejpam-1224	639	10	!	!	PUNCT
ejpam-1224	639	11	p−1	p−1	NOUN
ejpam-1224	639	12	)	)	PUNCT
ejpam-1224	639	13	∗	∗	NOUN
ejpam-1224	639	14	⊗m	⊗m	NOUN
ejpam-1224	639	15	→	→	SYM
ejpam-1224	639	16	·	·	PUNCT
ejpam-1224	639	17	·	·	PUNCT
ejpam-1224	639	18	·	·	PUNCT
ejpam-1224	640	1	→	→	PUNCT
ejpam-1224	640	2	u	u	NOUN
ejpam-1224	640	3	⊗m	⊗m	NOUN
ejpam-1224	640	4	and	and	CCONJ
ejpam-1224	640	5	the	the	DET
ejpam-1224	640	6	differential	differential	NOUN
ejpam-1224	640	7	is	be	AUX
ejpam-1224	640	8	given	give	VERB
ejpam-1224	640	9	by	by	ADP
ejpam-1224	640	10	d(u⊗	d(u⊗	PROPN
ejpam-1224	640	11	a∗	a∗	PROPN
ejpam-1224	640	12	⊗m	⊗m	PROPN
ejpam-1224	640	13	)	)	PUNCT
ejpam-1224	641	1	=	=	PUNCT
ejpam-1224	641	2	∑	∑	PUNCT
ejpam-1224	641	3	uxα⊗	uxα⊗	PROPN
ejpam-1224	641	4	x̌αa∗	x̌αa∗	NOUN
ejpam-1224	641	5	⊗m±	⊗m±	PROPN
ejpam-1224	641	6	∑	∑	PUNCT
ejpam-1224	641	7	u⊗	u⊗	VERB
ejpam-1224	641	8	a∗	a∗	PROPN
ejpam-1224	641	9	x̌α⊗	x̌α⊗	PROPN
ejpam-1224	641	10	xαm±	xαm±	PROPN
ejpam-1224	641	11	u⊗	u⊗	PROPN
ejpam-1224	641	12	d∗(a∗)⊗m	d∗(a∗)⊗m	PROPN
ejpam-1224	641	13	.	.	PUNCT
ejpam-1224	642	1	proof	proof	NOUN
ejpam-1224	642	2	.	.	PUNCT
ejpam-1224	643	1	proof	proof	NOUN
ejpam-1224	643	2	is	be	AUX
ejpam-1224	643	3	from	from	ADP
ejpam-1224	643	4	[	[	X
ejpam-1224	643	5	3	3	NUM
ejpam-1224	643	6	]	]	PUNCT
ejpam-1224	643	7	.	.	PUNCT
ejpam-1224	644	1	the	the	DET
ejpam-1224	644	2	complex	complex	ADJ
ejpam-1224	644	3	fg(m	fg(m	NOUN
ejpam-1224	644	4	)	)	PUNCT
ejpam-1224	644	5	has	have	VERB
ejpam-1224	644	6	a	a	DET
ejpam-1224	644	7	filtration	filtration	NOUN
ejpam-1224	644	8	fig(m	fig(m	NOUN
ejpam-1224	644	9	)	)	PUNCT
ejpam-1224	644	10	defined	define	VERB
ejpam-1224	644	11	as	as	ADP
ejpam-1224	644	12	·	·	PUNCT
ejpam-1224	644	13	·	·	PUNCT
ejpam-1224	644	14	·	·	PUNCT
ejpam-1224	645	1	→	→	SYM
ejpam-1224	645	2	fi−2u	fi−2u	PROPN
ejpam-1224	645	3	⊗	⊗	NOUN
ejpam-1224	645	4	(	(	PUNCT
ejpam-1224	645	5	a	a	NOUN
ejpam-1224	645	6	!	!	NOUN
ejpam-1224	645	7	2	2	NUM
ejpam-1224	645	8	)	)	PUNCT
ejpam-1224	645	9	∗	∗	NOUN
ejpam-1224	645	10	⊗m	⊗m	NOUN
ejpam-1224	645	11	→	→	PUNCT
ejpam-1224	645	12	fi−1u	fi−1u	ADJ
ejpam-1224	645	13	⊗	⊗	PROPN
ejpam-1224	645	14	(	(	PUNCT
ejpam-1224	645	15	a	a	NOUN
ejpam-1224	645	16	!	!	NOUN
ejpam-1224	645	17	1	1	NUM
ejpam-1224	645	18	)	)	PUNCT
ejpam-1224	645	19	∗⊗m	∗⊗m	NOUN
ejpam-1224	645	20	→	→	SYM
ejpam-1224	645	21	fiu	fiu	PROPN
ejpam-1224	645	22	⊗m	⊗m	PROPN
ejpam-1224	645	23	.	.	PUNCT
ejpam-1224	646	1	we	we	PRON
ejpam-1224	646	2	claim	claim	VERB
ejpam-1224	646	3	that	that	SCONJ
ejpam-1224	646	4	for	for	ADP
ejpam-1224	646	5	i	i	PRON
ejpam-1224	646	6	≥	≥	NOUN
ejpam-1224	646	7	0	0	NUM
ejpam-1224	646	8	,	,	PUNCT
ejpam-1224	646	9	we	we	PRON
ejpam-1224	646	10	have	have	VERB
ejpam-1224	646	11	hp(fig(m	hp(fig(m	VERB
ejpam-1224	646	12	)	)	PUNCT
ejpam-1224	646	13	)	)	PUNCT
ejpam-1224	647	1	=	=	PUNCT
ejpam-1224	647	2	m	m	VERB
ejpam-1224	647	3	for	for	ADP
ejpam-1224	647	4	p	p	NOUN
ejpam-1224	647	5	=	=	SYM
ejpam-1224	647	6	0	0	NUM
ejpam-1224	647	7	and	and	CCONJ
ejpam-1224	647	8	zero	zero	NUM
ejpam-1224	647	9	otherwise	otherwise	ADV
ejpam-1224	647	10	.	.	PUNCT
ejpam-1224	648	1	this	this	PRON
ejpam-1224	648	2	follows	follow	VERB
ejpam-1224	648	3	by	by	ADP
ejpam-1224	648	4	induction	induction	NOUN
ejpam-1224	648	5	from	from	ADP
ejpam-1224	648	6	the	the	DET
ejpam-1224	648	7	exact	exact	ADJ
ejpam-1224	648	8	sequence	sequence	NOUN
ejpam-1224	648	9	0→	0→	PROPN
ejpam-1224	648	10	fi−1g(m)→	fi−1g(m)→	VERB
ejpam-1224	648	11	fig(m)→	fig(m)→	NOUN
ejpam-1224	648	12	fig(m)/fi−1g(m)→	fig(m)/fi−1g(m)→	NOUN
ejpam-1224	648	13	0	0	NUM
ejpam-1224	648	14	f.	f.	PROPN
ejpam-1224	648	15	hawwa	hawwa	PROPN
ejpam-1224	648	16	,	,	PUNCT
ejpam-1224	648	17	j.	j.	PROPN
ejpam-1224	648	18	hoffman	hoffman	PROPN
ejpam-1224	648	19	,	,	PUNCT
ejpam-1224	648	20	and	and	CCONJ
ejpam-1224	648	21	h.	h.	PROPN
ejpam-1224	648	22	wang	wang	PROPN
ejpam-1224	648	23	,	,	PUNCT
ejpam-1224	648	24	/	/	SYM
ejpam-1224	648	25	eur	eur	NOUN
ejpam-1224	648	26	.	.	PUNCT
ejpam-1224	649	1	j.	j.	PROPN
ejpam-1224	649	2	pure	pure	PROPN
ejpam-1224	649	3	appl	appl	PROPN
ejpam-1224	649	4	.	.	PROPN
ejpam-1224	649	5	math	math	PROPN
ejpam-1224	649	6	,	,	PUNCT
ejpam-1224	649	7	5	5	NUM
ejpam-1224	649	8	(	(	PUNCT
ejpam-1224	649	9	2012	2012	NUM
ejpam-1224	649	10	)	)	PUNCT
ejpam-1224	649	11	,	,	PUNCT
ejpam-1224	649	12	511	511	NUM
ejpam-1224	649	13	-	-	SYM
ejpam-1224	649	14	539	539	NUM
ejpam-1224	649	15	530	530	NUM
ejpam-1224	649	16	by	by	ADP
ejpam-1224	649	17	noting	note	VERB
ejpam-1224	649	18	that	that	SCONJ
ejpam-1224	649	19	the	the	DET
ejpam-1224	649	20	term	term	NOUN
ejpam-1224	649	21	figm	figm	NOUN
ejpam-1224	649	22	/	/	SYM
ejpam-1224	649	23	fi−1g(m	fi−1g(m	VERB
ejpam-1224	649	24	)	)	PUNCT
ejpam-1224	649	25	is	be	AUX
ejpam-1224	649	26	a	a	DET
ejpam-1224	649	27	homogeneous	homogeneous	ADJ
ejpam-1224	649	28	part	part	NOUN
ejpam-1224	649	29	of	of	ADP
ejpam-1224	649	30	the	the	DET
ejpam-1224	649	31	koszul	koszul	ADJ
ejpam-1224	649	32	complex	complex	NOUN
ejpam-1224	649	33	for	for	ADP
ejpam-1224	649	34	a	a	PRON
ejpam-1224	649	35	and	and	CCONJ
ejpam-1224	649	36	a	a	PRON
ejpam-1224	649	37	!	!	PROPN
ejpam-1224	649	38	tensored	tensore	VERB
ejpam-1224	649	39	with	with	ADP
ejpam-1224	649	40	m	m	PROPN
ejpam-1224	649	41	(	(	PUNCT
ejpam-1224	649	42	over	over	ADP
ejpam-1224	649	43	k	k	NOUN
ejpam-1224	649	44	)	)	PUNCT
ejpam-1224	649	45	i.e.	i.e.	X
ejpam-1224	649	46	a0	a0	PROPN
ejpam-1224	649	47	⊗	⊗	PROPN
ejpam-1224	649	48	(	(	PUNCT
ejpam-1224	649	49	a	a	PROPN
ejpam-1224	649	50	!	!	PUNCT
ejpam-1224	650	1	i	i	NOUN
ejpam-1224	650	2	)	)	PUNCT
ejpam-1224	650	3	∗⊗m	∗⊗m	PROPN
ejpam-1224	650	4	→	→	SYM
ejpam-1224	650	5	·	·	PUNCT
ejpam-1224	650	6	·	·	PUNCT
ejpam-1224	650	7	·	·	PUNCT
ejpam-1224	651	1	→	→	PUNCT
ejpam-1224	651	2	ai	ai	INTJ
ejpam-1224	651	3	⊗	⊗	PROPN
ejpam-1224	651	4	(	(	PUNCT
ejpam-1224	651	5	a	a	PRON
ejpam-1224	651	6	!	!	NOUN
ejpam-1224	651	7	0	0	NUM
ejpam-1224	651	8	)	)	PUNCT
ejpam-1224	651	9	∗⊗m	∗⊗m	NOUN
ejpam-1224	651	10	with	with	ADP
ejpam-1224	651	11	differential	differential	ADJ
ejpam-1224	651	12	d(u⊗	d(u⊗	PROPN
ejpam-1224	651	13	a∗	a∗	PROPN
ejpam-1224	651	14	⊗m	⊗m	PROPN
ejpam-1224	651	15	)	)	PUNCT
ejpam-1224	652	1	=	=	PUNCT
ejpam-1224	652	2	∑	∑	PUNCT
ejpam-1224	652	3	uxα⊗	uxα⊗	PROPN
ejpam-1224	652	4	a∗	a∗	PROPN
ejpam-1224	652	5	x̌α⊗m	x̌α⊗m	PROPN
ejpam-1224	652	6	.	.	PUNCT
ejpam-1224	653	1	we	we	PRON
ejpam-1224	653	2	want	want	VERB
ejpam-1224	653	3	to	to	PART
ejpam-1224	653	4	show	show	VERB
ejpam-1224	653	5	that	that	SCONJ
ejpam-1224	653	6	fig(m)→	fig(m)→	NOUN
ejpam-1224	653	7	m	m	NOUN
ejpam-1224	653	8	is	be	AUX
ejpam-1224	653	9	a	a	DET
ejpam-1224	653	10	quasi	quasi	NOUN
ejpam-1224	653	11	-	-	NOUN
ejpam-1224	653	12	isomorphism	isomorphism	ADJ
ejpam-1224	653	13	,	,	PUNCT
ejpam-1224	653	14	that	that	ADV
ejpam-1224	653	15	is	is	ADV
ejpam-1224	653	16	,	,	PUNCT
ejpam-1224	653	17	hp(fig(m	hp(fig(m	PROPN
ejpam-1224	653	18	)	)	PUNCT
ejpam-1224	653	19	)	)	PUNCT
ejpam-1224	654	1	=	=	SYM
ejpam-1224	654	2	0	0	NUM
ejpam-1224	655	1	for	for	ADP
ejpam-1224	655	2	all	all	DET
ejpam-1224	655	3	i	i	PRON
ejpam-1224	655	4	and	and	CCONJ
ejpam-1224	655	5	with	with	ADP
ejpam-1224	655	6	p	p	X
ejpam-1224	655	7	<	<	X
ejpam-1224	655	8	0	0	NUM
ejpam-1224	655	9	,	,	PUNCT
ejpam-1224	655	10	and	and	CCONJ
ejpam-1224	655	11	h0(fig(m	h0(fig(m	ADJ
ejpam-1224	655	12	)	)	PUNCT
ejpam-1224	655	13	)	)	PUNCT
ejpam-1224	656	1	=	=	PUNCT
ejpam-1224	656	2	m	m	VERB
ejpam-1224	656	3	for	for	ADP
ejpam-1224	656	4	all	all	DET
ejpam-1224	656	5	i.	i.	NOUN
ejpam-1224	656	6	we	we	PRON
ejpam-1224	656	7	know	know	VERB
ejpam-1224	656	8	that	that	PRON
ejpam-1224	656	9	fg(m	fg(m	NOUN
ejpam-1224	656	10	)	)	PUNCT
ejpam-1224	657	1	=	=	SYM
ejpam-1224	657	2	lim	lim	PROPN
ejpam-1224	657	3	−→	−→	NOUN
ejpam-1224	657	4	fi	fi	NOUN
ejpam-1224	657	5	g(m	g(m	ADJ
ejpam-1224	657	6	)	)	PUNCT
ejpam-1224	657	7	so	so	ADV
ejpam-1224	657	8	therefore	therefore	ADV
ejpam-1224	657	9	hp(fg(m	hp(fg(m	ADJ
ejpam-1224	657	10	)	)	PUNCT
ejpam-1224	657	11	)	)	PUNCT
ejpam-1224	658	1	=	=	PUNCT
ejpam-1224	658	2	hp(lim	hp(lim	NOUN
ejpam-1224	658	3	−→	−→	NOUN
ejpam-1224	658	4	fig(m	fig(m	NOUN
ejpam-1224	658	5	)	)	PUNCT
ejpam-1224	658	6	)	)	PUNCT
ejpam-1224	659	1	=	=	SYM
ejpam-1224	659	2	lim	lim	PROPN
ejpam-1224	659	3	−→	−→	NOUN
ejpam-1224	659	4	hp(fig(m	hp(fig(m	PROPN
ejpam-1224	659	5	)	)	PUNCT
ejpam-1224	659	6	)	)	PUNCT
ejpam-1224	659	7	and	and	CCONJ
ejpam-1224	659	8	thus	thus	ADV
ejpam-1224	659	9	fg(m)→	fg(m)→	VERB
ejpam-1224	659	10	m	m	NOUN
ejpam-1224	659	11	is	be	AUX
ejpam-1224	659	12	a	a	DET
ejpam-1224	659	13	quasi	quasi	NOUN
ejpam-1224	659	14	-	-	NOUN
ejpam-1224	659	15	isomorphism	isomorphism	NOUN
ejpam-1224	659	16	provided	provide	VERB
ejpam-1224	659	17	that	that	DET
ejpam-1224	659	18	fig(m)→	fig(m)→	NOUN
ejpam-1224	659	19	m	m	NOUN
ejpam-1224	659	20	is	be	AUX
ejpam-1224	659	21	for	for	ADP
ejpam-1224	659	22	all	all	DET
ejpam-1224	659	23	i.	i.	NOUN
ejpam-1224	659	24	now	now	ADV
ejpam-1224	659	25	we	we	PRON
ejpam-1224	659	26	will	will	AUX
ejpam-1224	659	27	prove	prove	VERB
ejpam-1224	659	28	by	by	ADP
ejpam-1224	659	29	induction	induction	NOUN
ejpam-1224	659	30	that	that	PRON
ejpam-1224	659	31	hp(fig(m	hp(fig(m	VERB
ejpam-1224	659	32	)	)	PUNCT
ejpam-1224	659	33	)	)	PUNCT
ejpam-1224	660	1	=	=	SYM
ejpam-1224	660	2	0	0	NUM
ejpam-1224	661	1	for	for	ADP
ejpam-1224	661	2	all	all	DET
ejpam-1224	661	3	p	p	X
ejpam-1224	661	4	<	<	X
ejpam-1224	661	5	0	0	PROPN
ejpam-1224	661	6	and	and	CCONJ
ejpam-1224	661	7	h0(fig(m	h0(fig(m	ADJ
ejpam-1224	661	8	)	)	PUNCT
ejpam-1224	661	9	)	)	PUNCT
ejpam-1224	662	1	=	=	PUNCT
ejpam-1224	662	2	m	m	VERB
ejpam-1224	662	3	for	for	ADP
ejpam-1224	662	4	all	all	DET
ejpam-1224	662	5	i.	i.	NOUN
ejpam-1224	662	6	the	the	DET
ejpam-1224	662	7	case	case	NOUN
ejpam-1224	662	8	when	when	SCONJ
ejpam-1224	662	9	i	i	PRON
ejpam-1224	662	10	=	=	SYM
ejpam-1224	662	11	0	0	NUM
ejpam-1224	662	12	is	be	AUX
ejpam-1224	662	13	trivial	trivial	ADJ
ejpam-1224	662	14	since	since	SCONJ
ejpam-1224	662	15	f0g(m	f0g(m	VERB
ejpam-1224	662	16	)	)	PUNCT
ejpam-1224	662	17	=	=	NOUN
ejpam-1224	662	18	m	m	VERB
ejpam-1224	662	19	.	.	PUNCT
ejpam-1224	663	1	now	now	ADV
ejpam-1224	663	2	assume	assume	VERB
ejpam-1224	663	3	i	i	PRON
ejpam-1224	663	4	>	>	X
ejpam-1224	663	5	0	0	PUNCT
ejpam-1224	663	6	and	and	CCONJ
ejpam-1224	663	7	consider	consider	VERB
ejpam-1224	663	8	the	the	DET
ejpam-1224	663	9	following	following	ADJ
ejpam-1224	663	10	commutative	commutative	ADJ
ejpam-1224	663	11	diagram	diagram	NOUN
ejpam-1224	663	12	of	of	ADP
ejpam-1224	663	13	exact	exact	ADJ
ejpam-1224	663	14	sequences	sequence	NOUN
ejpam-1224	663	15	,	,	PUNCT
ejpam-1224	663	16	0	0	NUM
ejpam-1224	663	17	−−−→	−−−→	NUM
ejpam-1224	663	18	fig(m	fig(m	PROPN
ejpam-1224	663	19	)	)	PUNCT
ejpam-1224	663	20	−−−→	−−−→	NOUN
ejpam-1224	663	21	fi+1g(m	fi+1g(m	ADJ
ejpam-1224	663	22	)	)	PUNCT
ejpam-1224	663	23	−−−→	−−−→	NUM
ejpam-1224	663	24	fi+1g(m)/fig(m	fi+1g(m)/fig(m	PROPN
ejpam-1224	663	25	)	)	PUNCT
ejpam-1224	663	26	−−−→	−−−→	NOUN
ejpam-1224	663	27	0y	0y	PUNCT
ejpam-1224	664	1	α	α	PRON
ejpam-1224	664	2	y	y	NOUN
ejpam-1224	664	3	β	β	PROPN
ejpam-1224	664	4	y	y	PROPN
ejpam-1224	664	5	γ	γ	PROPN
ejpam-1224	664	6	y	y	PROPN
ejpam-1224	664	7	y	y	PROPN
ejpam-1224	664	8	0	0	NUM
ejpam-1224	664	9	−−−→	−−−→	NUM
ejpam-1224	664	10	m	m	PROPN
ejpam-1224	664	11	−−−→	−−−→	ADJ
ejpam-1224	664	12	m	m	PROPN
ejpam-1224	664	13	−−−→	−−−→	ADJ
ejpam-1224	664	14	0	0	NUM
ejpam-1224	664	15	−−−→	−−−→	NUM
ejpam-1224	664	16	0	0	NUM
ejpam-1224	664	17	.	.	PUNCT
ejpam-1224	665	1	the	the	DET
ejpam-1224	665	2	map	map	NOUN
ejpam-1224	665	3	α	α	NOUN
ejpam-1224	665	4	is	be	AUX
ejpam-1224	665	5	a	a	DET
ejpam-1224	665	6	quasi	quasi	NOUN
ejpam-1224	665	7	-	-	NOUN
ejpam-1224	665	8	isomorphism	isomorphism	NOUN
ejpam-1224	665	9	by	by	ADP
ejpam-1224	665	10	the	the	DET
ejpam-1224	665	11	induction	induction	NOUN
ejpam-1224	665	12	hypothesis	hypothesis	NOUN
ejpam-1224	665	13	and	and	CCONJ
ejpam-1224	665	14	the	the	DET
ejpam-1224	665	15	map	map	NOUN
ejpam-1224	665	16	γ	γ	NOUN
ejpam-1224	665	17	is	be	AUX
ejpam-1224	665	18	a	a	DET
ejpam-1224	665	19	quasiisomorphism	quasiisomorphism	NOUN
ejpam-1224	665	20	since	since	SCONJ
ejpam-1224	665	21	a	a	PRON
ejpam-1224	665	22	is	be	AUX
ejpam-1224	665	23	a	a	DET
ejpam-1224	665	24	koszul	koszul	ADJ
ejpam-1224	665	25	algebra	algebra	NOUN
ejpam-1224	665	26	.	.	PUNCT
ejpam-1224	666	1	now	now	ADV
ejpam-1224	666	2	by	by	ADP
ejpam-1224	666	3	applying	apply	VERB
ejpam-1224	666	4	the	the	DET
ejpam-1224	666	5	5	5	NUM
ejpam-1224	666	6	-	-	PUNCT
ejpam-1224	666	7	lemma	lemma	NOUN
ejpam-1224	666	8	we	we	PRON
ejpam-1224	666	9	know	know	VERB
ejpam-1224	666	10	that	that	SCONJ
ejpam-1224	666	11	the	the	DET
ejpam-1224	666	12	map	map	NOUN
ejpam-1224	666	13	β	β	NOUN
ejpam-1224	666	14	is	be	AUX
ejpam-1224	666	15	also	also	ADV
ejpam-1224	666	16	a	a	DET
ejpam-1224	666	17	quasi	quasi	NOUN
ejpam-1224	666	18	-	-	NOUN
ejpam-1224	666	19	isomorphism	isomorphism	NOUN
ejpam-1224	666	20	.	.	PUNCT
ejpam-1224	667	1	we	we	PRON
ejpam-1224	667	2	know	know	VERB
ejpam-1224	667	3	that	that	DET
ejpam-1224	667	4	fg(m	fg(m	NOUN
ejpam-1224	667	5	)	)	PUNCT
ejpam-1224	667	6	is	be	AUX
ejpam-1224	667	7	lim	lim	PROPN
ejpam-1224	667	8	−→	−→	PROPN
ejpam-1224	667	9	fig(m	fig(m	PROPN
ejpam-1224	667	10	)	)	PUNCT
ejpam-1224	667	11	and	and	CCONJ
ejpam-1224	667	12	since	since	SCONJ
ejpam-1224	667	13	taking	take	VERB
ejpam-1224	667	14	the	the	DET
ejpam-1224	667	15	filtered	filter	VERB
ejpam-1224	667	16	direct	direct	ADJ
ejpam-1224	667	17	limit	limit	NOUN
ejpam-1224	667	18	is	be	AUX
ejpam-1224	667	19	an	an	DET
ejpam-1224	667	20	exact	exact	ADJ
ejpam-1224	667	21	functor	functor	NOUN
ejpam-1224	667	22	it	it	PRON
ejpam-1224	667	23	commutes	commute	VERB
ejpam-1224	667	24	with	with	ADP
ejpam-1224	667	25	cohomology	cohomology	NOUN
ejpam-1224	667	26	so	so	SCONJ
ejpam-1224	667	27	we	we	PRON
ejpam-1224	667	28	get	get	VERB
ejpam-1224	667	29	the	the	DET
ejpam-1224	667	30	lemma	lemma	PROPN
ejpam-1224	667	31	.	.	PUNCT
ejpam-1224	668	1	corollary	corollary	ADJ
ejpam-1224	668	2	1	1	NUM
ejpam-1224	668	3	.	.	PUNCT
ejpam-1224	669	1	for	for	ADP
ejpam-1224	669	2	m•	m•	NOUN
ejpam-1224	669	3	a	a	DET
ejpam-1224	669	4	bounded	bounded	ADJ
ejpam-1224	669	5	complex	complex	NOUN
ejpam-1224	669	6	indexed	index	VERB
ejpam-1224	669	7	as	as	SCONJ
ejpam-1224	669	8	follows	follow	VERB
ejpam-1224	669	9	0→	0→	PROPN
ejpam-1224	669	10	m	m	NOUN
ejpam-1224	669	11	b	b	PROPN
ejpam-1224	669	12	→	→	SYM
ejpam-1224	669	13	m	m	NOUN
ejpam-1224	669	14	b+1→	b+1→	NOUN
ejpam-1224	669	15	·	·	PUNCT
ejpam-1224	669	16	·	·	PUNCT
ejpam-1224	669	17	·	·	PUNCT
ejpam-1224	669	18	→	→	PUNCT
ejpam-1224	669	19	m	m	VERB
ejpam-1224	669	20	t−1→	t−1→	NUM
ejpam-1224	669	21	m	m	NOUN
ejpam-1224	669	22	t	t	NOUN
ejpam-1224	669	23	→	→	SYM
ejpam-1224	669	24	0	0	PROPN
ejpam-1224	669	25	.	.	PUNCT
ejpam-1224	669	26	hp(fig(m	hp(fig(m	VERB
ejpam-1224	669	27	•	•	NUM
ejpam-1224	669	28	)	)	PUNCT
ejpam-1224	669	29	)	)	PUNCT
ejpam-1224	670	1	=	=	SYM
ejpam-1224	670	2	0	0	NUM
ejpam-1224	670	3	for	for	ADP
ejpam-1224	670	4	all	all	DET
ejpam-1224	670	5	i	i	PRON
ejpam-1224	670	6	and	and	CCONJ
ejpam-1224	670	7	for	for	ADP
ejpam-1224	670	8	p	p	X
ejpam-1224	670	9	<	<	X
ejpam-1224	670	10	b.	b.	PROPN
ejpam-1224	670	11	proposition	proposition	NOUN
ejpam-1224	670	12	4	4	NUM
ejpam-1224	670	13	.	.	PUNCT
ejpam-1224	671	1	assuming	assume	VERB
ejpam-1224	671	2	that	that	SCONJ
ejpam-1224	671	3	a	a	PRON
ejpam-1224	671	4	and	and	CCONJ
ejpam-1224	671	5	a	a	PRON
ejpam-1224	671	6	!	!	NOUN
ejpam-1224	671	7	are	be	AUX
ejpam-1224	671	8	koszul	koszul	ADJ
ejpam-1224	671	9	,	,	PUNCT
ejpam-1224	671	10	the	the	DET
ejpam-1224	671	11	natural	natural	ADJ
ejpam-1224	671	12	morphisms	morphism	NOUN
ejpam-1224	671	13	coming	come	VERB
ejpam-1224	671	14	from	from	ADP
ejpam-1224	671	15	the	the	DET
ejpam-1224	671	16	adjunction	adjunction	NOUN
ejpam-1224	671	17	fg(m)→	fg(m)→	NOUN
ejpam-1224	671	18	m	m	NOUN
ejpam-1224	671	19	,	,	PUNCT
ejpam-1224	671	20	n	n	PROPN
ejpam-1224	671	21	→	→	PUNCT
ejpam-1224	671	22	gf(n	gf(n	X
ejpam-1224	671	23	)	)	PUNCT
ejpam-1224	671	24	are	be	AUX
ejpam-1224	671	25	quasi	quasi	NOUN
ejpam-1224	671	26	-	-	NOUN
ejpam-1224	671	27	isomorphisms	isomorphisms	X
ejpam-1224	671	28	.	.	PUNCT
ejpam-1224	672	1	proof	proof	NOUN
ejpam-1224	672	2	.	.	PUNCT
ejpam-1224	673	1	assume	assume	VERB
ejpam-1224	673	2	m	m	PROPN
ejpam-1224	673	3	is	be	AUX
ejpam-1224	673	4	bounded	bound	VERB
ejpam-1224	673	5	and	and	CCONJ
ejpam-1224	673	6	indexed	index	VERB
ejpam-1224	673	7	as	as	SCONJ
ejpam-1224	673	8	follows	follow	VERB
ejpam-1224	673	9	0→	0→	PROPN
ejpam-1224	673	10	m	m	NOUN
ejpam-1224	673	11	b	b	PROPN
ejpam-1224	673	12	→	→	SYM
ejpam-1224	673	13	m	m	NOUN
ejpam-1224	673	14	b+1→	b+1→	NOUN
ejpam-1224	673	15	·	·	PUNCT
ejpam-1224	673	16	·	·	PUNCT
ejpam-1224	673	17	·	·	PUNCT
ejpam-1224	674	1	→	→	PUNCT
ejpam-1224	674	2	m	m	VERB
ejpam-1224	675	1	t−1→	t−1→	NUM
ejpam-1224	675	2	m	m	NOUN
ejpam-1224	675	3	t	t	NOUN
ejpam-1224	675	4	→	→	SYM
ejpam-1224	675	5	0	0	X
ejpam-1224	675	6	.	.	PUNCT
ejpam-1224	676	1	let	let	VERB
ejpam-1224	676	2	σ	σ	PRON
ejpam-1224	676	3	>	>	X
ejpam-1224	676	4	bm	bm	PROPN
ejpam-1224	676	5	be	be	VERB
ejpam-1224	676	6	the	the	DET
ejpam-1224	676	7	truncation	truncation	NOUN
ejpam-1224	676	8	m	m	VERB
ejpam-1224	676	9	b+1	b+1	NOUN
ejpam-1224	676	10	→	→	SYM
ejpam-1224	676	11	m	m	PROPN
ejpam-1224	676	12	b+2	b+2	ADJ
ejpam-1224	676	13	→	→	X
ejpam-1224	676	14	·	·	PUNCT
ejpam-1224	676	15	·	·	PUNCT
ejpam-1224	676	16	·	·	PUNCT
ejpam-1224	677	1	and	and	CCONJ
ejpam-1224	677	2	so	so	ADV
ejpam-1224	677	3	m	m	PROPN
ejpam-1224	677	4	b[−b	b[−b	PROPN
ejpam-1224	677	5	]	]	PUNCT
ejpam-1224	677	6	will	will	AUX
ejpam-1224	677	7	just	just	ADV
ejpam-1224	677	8	be	be	AUX
ejpam-1224	677	9	a	a	DET
ejpam-1224	677	10	module	module	NOUN
ejpam-1224	677	11	considered	consider	VERB
ejpam-1224	677	12	as	as	ADP
ejpam-1224	677	13	a	a	DET
ejpam-1224	677	14	one	one	NUM
ejpam-1224	677	15	term	term	NOUN
ejpam-1224	677	16	complex	complex	NOUN
ejpam-1224	677	17	.	.	PUNCT
ejpam-1224	678	1	we	we	PRON
ejpam-1224	678	2	may	may	AUX
ejpam-1224	678	3	now	now	ADV
ejpam-1224	678	4	form	form	VERB
ejpam-1224	678	5	the	the	DET
ejpam-1224	678	6	following	follow	VERB
ejpam-1224	678	7	short	short	ADJ
ejpam-1224	678	8	exact	exact	ADJ
ejpam-1224	678	9	sequence	sequence	NOUN
ejpam-1224	678	10	0→	0→	PROPN
ejpam-1224	678	11	σ	σ	PROPN
ejpam-1224	678	12	>	>	PROPN
ejpam-1224	678	13	b	b	PROPN
ejpam-1224	678	14	m	m	PROPN
ejpam-1224	678	15	→	→	PROPN
ejpam-1224	678	16	m	m	PROPN
ejpam-1224	678	17	→	→	SYM
ejpam-1224	678	18	m	m	NOUN
ejpam-1224	678	19	b[−b]→	b[−b]→	PROPN
ejpam-1224	678	20	0	0	NUM
ejpam-1224	678	21	.	.	PUNCT
ejpam-1224	679	1	f.	f.	PROPN
ejpam-1224	679	2	hawwa	hawwa	PROPN
ejpam-1224	679	3	,	,	PUNCT
ejpam-1224	679	4	j.	j.	PROPN
ejpam-1224	679	5	hoffman	hoffman	PROPN
ejpam-1224	679	6	,	,	PUNCT
ejpam-1224	679	7	and	and	CCONJ
ejpam-1224	679	8	h.	h.	PROPN
ejpam-1224	679	9	wang	wang	PROPN
ejpam-1224	679	10	,	,	PUNCT
ejpam-1224	679	11	/	/	SYM
ejpam-1224	679	12	eur	eur	NOUN
ejpam-1224	679	13	.	.	PUNCT
ejpam-1224	680	1	j.	j.	PROPN
ejpam-1224	680	2	pure	pure	PROPN
ejpam-1224	680	3	appl	appl	PROPN
ejpam-1224	680	4	.	.	PROPN
ejpam-1224	680	5	math	math	PROPN
ejpam-1224	680	6	,	,	PUNCT
ejpam-1224	680	7	5	5	NUM
ejpam-1224	680	8	(	(	PUNCT
ejpam-1224	680	9	2012	2012	NUM
ejpam-1224	680	10	)	)	PUNCT
ejpam-1224	680	11	,	,	PUNCT
ejpam-1224	680	12	511	511	NUM
ejpam-1224	680	13	-	-	SYM
ejpam-1224	680	14	539	539	NUM
ejpam-1224	680	15	531	531	NUM
ejpam-1224	680	16	consider	consider	VERB
ejpam-1224	680	17	the	the	DET
ejpam-1224	680	18	following	following	ADJ
ejpam-1224	680	19	commutative	commutative	ADJ
ejpam-1224	680	20	diagram	diagram	NOUN
ejpam-1224	680	21	of	of	ADP
ejpam-1224	680	22	exact	exact	ADJ
ejpam-1224	680	23	sequences	sequence	NOUN
ejpam-1224	680	24	0	0	SYM
ejpam-1224	680	25	−−−→	−−−→	NUM
ejpam-1224	680	26	fg(σ	fg(σ	NUM
ejpam-1224	680	27	>	>	X
ejpam-1224	680	28	bm	bm	PROPN
ejpam-1224	680	29	)	)	PUNCT
ejpam-1224	680	30	)	)	PUNCT
ejpam-1224	681	1	−−−→	−−−→	VERB
ejpam-1224	681	2	fg(m	fg(m	NOUN
ejpam-1224	681	3	)	)	PUNCT
ejpam-1224	681	4	−−−→	−−−→	NUM
ejpam-1224	681	5	fg(m	fg(m	X
ejpam-1224	681	6	b[−b	b[−b	PROPN
ejpam-1224	681	7	]	]	PUNCT
ejpam-1224	681	8	)	)	PUNCT
ejpam-1224	682	1	−−−→	−−−→	NOUN
ejpam-1224	682	2	0y	0y	NUM
ejpam-1224	683	1	α	α	PRON
ejpam-1224	683	2	y	y	NOUN
ejpam-1224	683	3	β	β	PROPN
ejpam-1224	683	4	y	y	PROPN
ejpam-1224	683	5	γ	γ	PROPN
ejpam-1224	683	6	y	y	PROPN
ejpam-1224	683	7	y	y	PROPN
ejpam-1224	683	8	0	0	NUM
ejpam-1224	683	9	−−−→	−−−→	PROPN
ejpam-1224	683	10	σ	σ	PROPN
ejpam-1224	683	11	>	>	X
ejpam-1224	683	12	bm	bm	PROPN
ejpam-1224	683	13	−−−→	−−−→	PROPN
ejpam-1224	683	14	m	m	PROPN
ejpam-1224	683	15	−−−→	−−−→	ADJ
ejpam-1224	683	16	m	m	PROPN
ejpam-1224	683	17	b[−b	b[−b	PROPN
ejpam-1224	683	18	]	]	PUNCT
ejpam-1224	684	1	−−−→	−−−→	NUM
ejpam-1224	684	2	0	0	NUM
ejpam-1224	684	3	.	.	PUNCT
ejpam-1224	685	1	the	the	DET
ejpam-1224	685	2	map	map	NOUN
ejpam-1224	685	3	α	α	NOUN
ejpam-1224	685	4	is	be	AUX
ejpam-1224	685	5	a	a	DET
ejpam-1224	685	6	quasi	quasi	NOUN
ejpam-1224	685	7	-	-	NOUN
ejpam-1224	685	8	isomorphism	isomorphism	NOUN
ejpam-1224	685	9	by	by	ADP
ejpam-1224	685	10	induction	induction	NOUN
ejpam-1224	685	11	on	on	ADP
ejpam-1224	685	12	the	the	DET
ejpam-1224	685	13	length	length	NOUN
ejpam-1224	685	14	of	of	ADP
ejpam-1224	685	15	the	the	DET
ejpam-1224	685	16	truncation	truncation	NOUN
ejpam-1224	685	17	,	,	PUNCT
ejpam-1224	685	18	the	the	DET
ejpam-1224	685	19	map	map	NOUN
ejpam-1224	685	20	γ	γ	NOUN
ejpam-1224	685	21	is	be	AUX
ejpam-1224	685	22	a	a	DET
ejpam-1224	685	23	quasi	quasi	NOUN
ejpam-1224	685	24	-	-	NOUN
ejpam-1224	685	25	isomorphism	isomorphism	NOUN
ejpam-1224	685	26	by	by	ADP
ejpam-1224	685	27	lemma	lemma	PROPN
ejpam-1224	685	28	5	5	NUM
ejpam-1224	685	29	so	so	ADV
ejpam-1224	685	30	by	by	ADP
ejpam-1224	685	31	the	the	DET
ejpam-1224	685	32	5	5	NUM
ejpam-1224	685	33	-	-	PUNCT
ejpam-1224	685	34	lemma	lemma	NOUN
ejpam-1224	685	35	we	we	PRON
ejpam-1224	685	36	know	know	VERB
ejpam-1224	685	37	that	that	SCONJ
ejpam-1224	685	38	the	the	DET
ejpam-1224	685	39	map	map	NOUN
ejpam-1224	685	40	β	β	NOUN
ejpam-1224	685	41	is	be	AUX
ejpam-1224	685	42	also	also	ADV
ejpam-1224	685	43	a	a	DET
ejpam-1224	685	44	quasi	quasi	NOUN
ejpam-1224	685	45	-	-	NOUN
ejpam-1224	685	46	isomorphism	isomorphism	NOUN
ejpam-1224	685	47	.	.	PUNCT
ejpam-1224	686	1	now	now	ADV
ejpam-1224	686	2	let	let	VERB
ejpam-1224	686	3	us	we	PRON
ejpam-1224	686	4	assume	assume	VERB
ejpam-1224	686	5	that	that	SCONJ
ejpam-1224	686	6	the	the	DET
ejpam-1224	686	7	complex	complex	NOUN
ejpam-1224	686	8	m	m	VERB
ejpam-1224	686	9	is	be	AUX
ejpam-1224	686	10	bounded	bound	VERB
ejpam-1224	686	11	above	above	ADP
ejpam-1224	686	12	so	so	ADV
ejpam-1224	686	13	m	m	ADV
ejpam-1224	686	14	=	=	NOUN
ejpam-1224	686	15	lim	lim	PROPN
ejpam-1224	686	16	−→	−→	NOUN
ejpam-1224	686	17	σ≥pm	σ≥pm	VERB
ejpam-1224	686	18	where	where	SCONJ
ejpam-1224	686	19	the	the	DET
ejpam-1224	686	20	σ≥pm	σ≥pm	NOUN
ejpam-1224	686	21	are	be	AUX
ejpam-1224	686	22	bounded	bound	VERB
ejpam-1224	686	23	.	.	PUNCT
ejpam-1224	687	1	since	since	SCONJ
ejpam-1224	687	2	we	we	PRON
ejpam-1224	687	3	know	know	VERB
ejpam-1224	687	4	that	that	SCONJ
ejpam-1224	687	5	g(m	g(m	VERB
ejpam-1224	687	6	)	)	PUNCT
ejpam-1224	687	7	p	p	NOUN
ejpam-1224	687	8	λ	λ	X
ejpam-1224	687	9	=	=	SYM
ejpam-1224	687	10	∏	∏	PROPN
ejpam-1224	687	11	r≥0	r≥0	PROPN
ejpam-1224	687	12	∏	∏	PROPN
ejpam-1224	687	13	µ	µ	PROPN
ejpam-1224	687	14	homk((a	homk((a	NUM
ejpam-1224	687	15	!	!	PUNCT
ejpam-1224	687	16	)	)	PUNCT
ejpam-1224	687	17	rµ	rµ	VERB
ejpam-1224	687	18	,	,	PUNCT
ejpam-1224	687	19	m	m	PROPN
ejpam-1224	687	20	p+r	p+r	NOUN
ejpam-1224	687	21	λ+µ	λ+µ	X
ejpam-1224	687	22	)	)	PUNCT
ejpam-1224	688	1	we	we	PRON
ejpam-1224	688	2	can	can	AUX
ejpam-1224	688	3	now	now	ADV
ejpam-1224	688	4	show	show	VERB
ejpam-1224	688	5	that	that	SCONJ
ejpam-1224	688	6	g	g	PROPN
ejpam-1224	688	7	commutes	commute	NOUN
ejpam-1224	688	8	with	with	ADP
ejpam-1224	688	9	direct	direct	ADJ
ejpam-1224	688	10	limit	limit	NOUN
ejpam-1224	688	11	.	.	PUNCT
ejpam-1224	689	1	we	we	PRON
ejpam-1224	689	2	know	know	VERB
ejpam-1224	689	3	that	that	SCONJ
ejpam-1224	689	4	m	m	VERB
ejpam-1224	690	1	=	=	VERB
ejpam-1224	690	2	lim	lim	PROPN
ejpam-1224	690	3	−→	−→	NOUN
ejpam-1224	690	4	σ≤sm	σ≤sm	NOUN
ejpam-1224	690	5	and	and	CCONJ
ejpam-1224	690	6	even	even	ADV
ejpam-1224	690	7	[	[	X
ejpam-1224	690	8	m]l	m]l	X
ejpam-1224	691	1	=	=	PUNCT
ejpam-1224	692	1	[	[	X
ejpam-1224	692	2	lim	lim	NOUN
ejpam-1224	692	3	−→	−→	PROPN
ejpam-1224	692	4	σ≤sm]l	σ≤sm]l	PROPN
ejpam-1224	692	5	.	.	PUNCT
ejpam-1224	693	1	now	now	ADV
ejpam-1224	693	2	note	note	VERB
ejpam-1224	693	3	that	that	SCONJ
ejpam-1224	694	1	[	[	X
ejpam-1224	694	2	lim	lim	NOUN
ejpam-1224	694	3	−→	−→	NOUN
ejpam-1224	694	4	σ≤sm]l	σ≤sm]l	PROPN
ejpam-1224	694	5	=	=	SYM
ejpam-1224	694	6	0	0	PUNCT
ejpam-1224	695	1	if	if	SCONJ
ejpam-1224	695	2	l	l	NOUN
ejpam-1224	695	3	<	<	X
ejpam-1224	695	4	s	s	X
ejpam-1224	695	5	and	and	CCONJ
ejpam-1224	695	6	equals	equal	VERB
ejpam-1224	695	7	m	m	VERB
ejpam-1224	695	8	l	l	NOUN
ejpam-1224	695	9	if	if	SCONJ
ejpam-1224	695	10	l	l	PROPN
ejpam-1224	695	11	≥	≥	AUX
ejpam-1224	695	12	s.	s.	PROPN
ejpam-1224	695	13	since	since	SCONJ
ejpam-1224	695	14	m	m	PROPN
ejpam-1224	695	15	is	be	AUX
ejpam-1224	695	16	bounded	bound	VERB
ejpam-1224	695	17	above	above	ADV
ejpam-1224	695	18	,	,	PUNCT
ejpam-1224	695	19	we	we	PRON
ejpam-1224	695	20	know	know	VERB
ejpam-1224	695	21	that	that	SCONJ
ejpam-1224	695	22	m	m	VERB
ejpam-1224	695	23	l	l	NOUN
ejpam-1224	695	24	=	=	PUNCT
ejpam-1224	695	25	0	0	NUM
ejpam-1224	695	26	for	for	ADP
ejpam-1224	695	27	l	l	NOUN
ejpam-1224	695	28	>	>	PUNCT
ejpam-1224	695	29	>	>	X
ejpam-1224	695	30	0	0	NUM
ejpam-1224	695	31	which	which	PRON
ejpam-1224	695	32	tells	tell	VERB
ejpam-1224	695	33	us	we	PRON
ejpam-1224	695	34	that	that	SCONJ
ejpam-1224	695	35	there	there	PRON
ejpam-1224	695	36	exists	exist	VERB
ejpam-1224	695	37	an	an	DET
ejpam-1224	695	38	s0	s0	NOUN
ejpam-1224	695	39	such	such	ADJ
ejpam-1224	695	40	that	that	PRON
ejpam-1224	695	41	for	for	ADP
ejpam-1224	695	42	all	all	DET
ejpam-1224	695	43	s	s	PART
ejpam-1224	695	44	≥	≥	NOUN
ejpam-1224	695	45	s0	s0	NOUN
ejpam-1224	695	46	we	we	PRON
ejpam-1224	695	47	have	have	VERB
ejpam-1224	695	48	(	(	PUNCT
ejpam-1224	695	49	σ≤sm)p+r	σ≤sm)p+r	NOUN
ejpam-1224	695	50	=	=	SYM
ejpam-1224	695	51	m	m	VERB
ejpam-1224	695	52	p+r	p+r	NOUN
ejpam-1224	695	53	for	for	ADP
ejpam-1224	695	54	all	all	DET
ejpam-1224	695	55	p	p	NOUN
ejpam-1224	695	56	and	and	CCONJ
ejpam-1224	695	57	r	r	NOUN
ejpam-1224	695	58	≥	≥	NOUN
ejpam-1224	695	59	0	0	NUM
ejpam-1224	695	60	.	.	PUNCT
ejpam-1224	696	1	therefore	therefore	ADV
ejpam-1224	696	2	g(lim	g(lim	PROPN
ejpam-1224	696	3	−→	−→	NOUN
ejpam-1224	696	4	σ≥pm	σ≥pm	NOUN
ejpam-1224	696	5	)	)	PUNCT
ejpam-1224	696	6	=	=	SYM
ejpam-1224	696	7	g(m	g(m	VERB
ejpam-1224	696	8	)	)	PUNCT
ejpam-1224	696	9	.	.	PUNCT
ejpam-1224	697	1	since	since	SCONJ
ejpam-1224	697	2	f	f	PROPN
ejpam-1224	697	3	is	be	AUX
ejpam-1224	697	4	a	a	DET
ejpam-1224	697	5	left	left	ADJ
ejpam-1224	697	6	adjoint	adjoint	NOUN
ejpam-1224	697	7	it	it	PRON
ejpam-1224	697	8	also	also	ADV
ejpam-1224	697	9	commutes	commute	VERB
ejpam-1224	697	10	with	with	ADP
ejpam-1224	697	11	the	the	DET
ejpam-1224	697	12	direct	direct	ADJ
ejpam-1224	697	13	limit	limit	NOUN
ejpam-1224	697	14	so	so	SCONJ
ejpam-1224	697	15	we	we	PRON
ejpam-1224	697	16	have	have	VERB
ejpam-1224	697	17	that	that	DET
ejpam-1224	697	18	fg(m	fg(m	VERB
ejpam-1224	697	19	)	)	PUNCT
ejpam-1224	697	20	=	=	SYM
ejpam-1224	698	1	fg(lim	fg(lim	PROPN
ejpam-1224	698	2	−→	−→	NOUN
ejpam-1224	698	3	σ≥pm	σ≥pm	NOUN
ejpam-1224	698	4	)	)	PUNCT
ejpam-1224	699	1	=	=	SYM
ejpam-1224	699	2	lim	lim	PROPN
ejpam-1224	699	3	−→	−→	NOUN
ejpam-1224	699	4	fg(σ≥p	fg(σ≥p	ADJ
ejpam-1224	699	5	m)→	m)→	NOUN
ejpam-1224	699	6	lim	lim	NOUN
ejpam-1224	699	7	−→	−→	NOUN
ejpam-1224	699	8	σ≥p	σ≥p	ADV
ejpam-1224	699	9	m	m	VERB
ejpam-1224	699	10	=	=	NOUN
ejpam-1224	699	11	m	m	VERB
ejpam-1224	699	12	is	be	AUX
ejpam-1224	699	13	a	a	DET
ejpam-1224	699	14	quasi	quasi	NOUN
ejpam-1224	699	15	-	-	NOUN
ejpam-1224	699	16	isomorphism	isomorphism	NOUN
ejpam-1224	699	17	since	since	SCONJ
ejpam-1224	699	18	lim	lim	PROPN
ejpam-1224	699	19	−→	−→	NOUN
ejpam-1224	699	20	is	be	AUX
ejpam-1224	699	21	exact	exact	ADJ
ejpam-1224	699	22	in	in	ADP
ejpam-1224	699	23	the	the	DET
ejpam-1224	699	24	category	category	NOUN
ejpam-1224	699	25	of	of	ADP
ejpam-1224	699	26	vector	vector	NOUN
ejpam-1224	699	27	spaces	space	NOUN
ejpam-1224	699	28	.	.	PUNCT
ejpam-1224	700	1	next	next	ADV
ejpam-1224	700	2	suppose	suppose	VERB
ejpam-1224	700	3	that	that	SCONJ
ejpam-1224	700	4	m	m	PROPN
ejpam-1224	700	5	is	be	AUX
ejpam-1224	700	6	bounded	bound	VERB
ejpam-1224	700	7	below	below	ADP
ejpam-1224	700	8	e.g.	e.g.	ADV
ejpam-1224	700	9	m	m	PROPN
ejpam-1224	700	10	=	=	SYM
ejpam-1224	700	11	σ	σ	PROPN
ejpam-1224	700	12	>	>	PROPN
ejpam-1224	700	13	b	b	PROPN
ejpam-1224	700	14	m	m	VERB
ejpam-1224	700	15	and	and	CCONJ
ejpam-1224	700	16	indexed	index	VERB
ejpam-1224	700	17	as	as	SCONJ
ejpam-1224	700	18	follows	follow	VERB
ejpam-1224	700	19	0→	0→	PROPN
ejpam-1224	700	20	m	m	NOUN
ejpam-1224	700	21	b	b	PROPN
ejpam-1224	700	22	→	→	SYM
ejpam-1224	700	23	m	m	NOUN
ejpam-1224	700	24	b+1→	b+1→	NOUN
ejpam-1224	700	25	·	·	PUNCT
ejpam-1224	700	26	·	·	PUNCT
ejpam-1224	700	27	·	·	PUNCT
ejpam-1224	700	28	.	.	PUNCT
ejpam-1224	701	1	we	we	PRON
ejpam-1224	701	2	know	know	VERB
ejpam-1224	701	3	by	by	ADP
ejpam-1224	701	4	lemma	lemma	PROPN
ejpam-1224	701	5	5	5	NUM
ejpam-1224	701	6	that	that	PRON
ejpam-1224	701	7	for	for	ADP
ejpam-1224	701	8	a	a	DET
ejpam-1224	701	9	module	module	NOUN
ejpam-1224	701	10	m	m	NOUN
ejpam-1224	701	11	over	over	ADP
ejpam-1224	701	12	u	u	PROPN
ejpam-1224	701	13	,	,	PUNCT
ejpam-1224	701	14	fig(m	fig(m	PROPN
ejpam-1224	701	15	)	)	PUNCT
ejpam-1224	701	16	is	be	AUX
ejpam-1224	701	17	exact	exact	ADJ
ejpam-1224	701	18	in	in	ADP
ejpam-1224	701	19	cohomological	cohomological	ADJ
ejpam-1224	701	20	degrees	degree	NOUN
ejpam-1224	701	21	<	<	X
ejpam-1224	701	22	0	0	NUM
ejpam-1224	701	23	.	.	PUNCT
ejpam-1224	702	1	first	first	ADV
ejpam-1224	702	2	we	we	PRON
ejpam-1224	702	3	must	must	AUX
ejpam-1224	702	4	define	define	VERB
ejpam-1224	702	5	the	the	DET
ejpam-1224	702	6	filtration	filtration	NOUN
ejpam-1224	702	7	fig(m	fig(m	NOUN
ejpam-1224	702	8	)	)	PUNCT
ejpam-1224	702	9	for	for	ADP
ejpam-1224	702	10	when	when	SCONJ
ejpam-1224	702	11	m	m	PROPN
ejpam-1224	702	12	is	be	AUX
ejpam-1224	702	13	a	a	DET
ejpam-1224	702	14	bounded	bounded	ADJ
ejpam-1224	702	15	complex	complex	NOUN
ejpam-1224	702	16	,	,	PUNCT
ejpam-1224	702	17	not	not	PART
ejpam-1224	702	18	just	just	ADV
ejpam-1224	702	19	a	a	DET
ejpam-1224	702	20	module	module	NOUN
ejpam-1224	702	21	.	.	PUNCT
ejpam-1224	703	1	let	let	VERB
ejpam-1224	704	1	[	[	X
ejpam-1224	704	2	fi	fi	NOUN
ejpam-1224	704	3	g(m	g(m	VERB
ejpam-1224	704	4	)	)	PUNCT
ejpam-1224	704	5	]	]	PUNCT
ejpam-1224	705	1	a	a	PRON
ejpam-1224	705	2	=	=	SYM
ejpam-1224	705	3	fi+au	fi+au	NOUN
ejpam-1224	705	4	⊗	⊗	PROPN
ejpam-1224	705	5	∏	∏	PROPN
ejpam-1224	705	6	p≥0	p≥0	PROPN
ejpam-1224	705	7	hom(a	hom(a	PROPN
ejpam-1224	705	8	!	!	PUNCT
ejpam-1224	706	1	p	p	X
ejpam-1224	706	2	,	,	PUNCT
ejpam-1224	706	3	m	m	PROPN
ejpam-1224	706	4	p+a	p+a	NOUN
ejpam-1224	706	5	)	)	PUNCT
ejpam-1224	706	6	.	.	PUNCT
ejpam-1224	707	1	if	if	SCONJ
ejpam-1224	707	2	m	m	NOUN
ejpam-1224	707	3	is	be	AUX
ejpam-1224	707	4	bounded	bound	VERB
ejpam-1224	707	5	above	above	ADV
ejpam-1224	707	6	,	,	PUNCT
ejpam-1224	707	7	in	in	ADP
ejpam-1224	707	8	particular	particular	ADJ
ejpam-1224	707	9	bounded	bound	VERB
ejpam-1224	707	10	,	,	PUNCT
ejpam-1224	707	11	then	then	ADV
ejpam-1224	707	12	gr	gr	INTJ
ejpam-1224	707	13	f	f	X
ejpam-1224	708	1	i	i	PRON
ejpam-1224	708	2	fg(m	fg(m	VERB
ejpam-1224	708	3	)	)	PUNCT
ejpam-1224	709	1	=	=	SYM
ejpam-1224	709	2	⊕	⊕	PROPN
ejpam-1224	709	3	p≥0	p≥0	NOUN
ejpam-1224	709	4	ai+a	ai+a	PROPN
ejpam-1224	709	5	⊗	⊗	PROPN
ejpam-1224	709	6	(	(	PUNCT
ejpam-1224	709	7	a	a	NOUN
ejpam-1224	709	8	!	!	PUNCT
ejpam-1224	710	1	p	p	X
ejpam-1224	710	2	)	)	PUNCT
ejpam-1224	710	3	∗⊗m	∗⊗m	PROPN
ejpam-1224	710	4	p+a	p+a	PROPN
ejpam-1224	710	5	.	.	PUNCT
ejpam-1224	711	1	let	let	VERB
ejpam-1224	711	2	m	m	PRON
ejpam-1224	711	3	be	be	AUX
ejpam-1224	711	4	a	a	DET
ejpam-1224	711	5	complex	complex	NOUN
ejpam-1224	711	6	bounded	bound	VERB
ejpam-1224	711	7	below	below	ADP
ejpam-1224	711	8	i.e.	i.e.	X
ejpam-1224	711	9	m•	m•	X
ejpam-1224	711	10	=	=	SYM
ejpam-1224	711	11	0	0	PROPN
ejpam-1224	712	1	for	for	ADP
ejpam-1224	712	2	i	i	PRON
ejpam-1224	712	3	<	<	X
ejpam-1224	712	4	b.	b.	PROPN
ejpam-1224	712	5	we	we	PRON
ejpam-1224	712	6	want	want	VERB
ejpam-1224	712	7	to	to	PART
ejpam-1224	712	8	show	show	VERB
ejpam-1224	712	9	that	that	SCONJ
ejpam-1224	712	10	fg(m)→	fg(m)→	NOUN
ejpam-1224	712	11	m	m	VERB
ejpam-1224	712	12	is	be	AUX
ejpam-1224	712	13	a	a	DET
ejpam-1224	712	14	quasi	quasi	NOUN
ejpam-1224	712	15	-	-	NOUN
ejpam-1224	712	16	isomorphism	isomorphism	NOUN
ejpam-1224	712	17	in	in	ADP
ejpam-1224	712	18	degrees	degree	NOUN
ejpam-1224	712	19	<	<	X
ejpam-1224	712	20	b.	b.	PROPN
ejpam-1224	713	1	also	also	ADV
ejpam-1224	713	2	we	we	PRON
ejpam-1224	713	3	know	know	VERB
ejpam-1224	713	4	that	that	SCONJ
ejpam-1224	713	5	h	h	NOUN
ejpam-1224	713	6	i(m	i(m	NOUN
ejpam-1224	713	7	)	)	PUNCT
ejpam-1224	713	8	=	=	SYM
ejpam-1224	713	9	0	0	NUM
ejpam-1224	714	1	for	for	ADP
ejpam-1224	714	2	i	i	PRON
ejpam-1224	714	3	<	<	X
ejpam-1224	714	4	b.	b.	PROPN
ejpam-1224	714	5	since	since	SCONJ
ejpam-1224	714	6	we	we	PROPN
ejpam-1224	714	7	f.	f.	PROPN
ejpam-1224	714	8	hawwa	hawwa	PROPN
ejpam-1224	714	9	,	,	PUNCT
ejpam-1224	714	10	j.	j.	PROPN
ejpam-1224	714	11	hoffman	hoffman	PROPN
ejpam-1224	714	12	,	,	PUNCT
ejpam-1224	714	13	and	and	CCONJ
ejpam-1224	714	14	h.	h.	PROPN
ejpam-1224	714	15	wang	wang	PROPN
ejpam-1224	714	16	,	,	PUNCT
ejpam-1224	714	17	/	/	SYM
ejpam-1224	714	18	eur	eur	NOUN
ejpam-1224	714	19	.	.	PUNCT
ejpam-1224	715	1	j.	j.	PROPN
ejpam-1224	715	2	pure	pure	PROPN
ejpam-1224	715	3	appl	appl	PROPN
ejpam-1224	715	4	.	.	PROPN
ejpam-1224	715	5	math	math	PROPN
ejpam-1224	715	6	,	,	PUNCT
ejpam-1224	715	7	5	5	NUM
ejpam-1224	715	8	(	(	PUNCT
ejpam-1224	715	9	2012	2012	NUM
ejpam-1224	715	10	)	)	PUNCT
ejpam-1224	715	11	,	,	PUNCT
ejpam-1224	715	12	511	511	NUM
ejpam-1224	715	13	-	-	SYM
ejpam-1224	715	14	539	539	NUM
ejpam-1224	715	15	532	532	NUM
ejpam-1224	715	16	know	know	NOUN
ejpam-1224	715	17	that	that	SCONJ
ejpam-1224	715	18	fg(m	fg(m	VERB
ejpam-1224	715	19	)	)	PUNCT
ejpam-1224	716	1	=	=	SYM
ejpam-1224	716	2	lim	lim	PROPN
ejpam-1224	716	3	−→	−→	PROPN
ejpam-1224	716	4	fig(m	fig(m	PROPN
ejpam-1224	716	5	)	)	PUNCT
ejpam-1224	717	1	and	and	CCONJ
ejpam-1224	717	2	since	since	SCONJ
ejpam-1224	717	3	we	we	PRON
ejpam-1224	717	4	know	know	VERB
ejpam-1224	717	5	that	that	SCONJ
ejpam-1224	717	6	taking	take	VERB
ejpam-1224	717	7	cohomology	cohomology	NOUN
ejpam-1224	717	8	commutes	commute	NOUN
ejpam-1224	717	9	with	with	ADP
ejpam-1224	717	10	taking	take	VERB
ejpam-1224	717	11	direct	direct	ADJ
ejpam-1224	717	12	limits	limit	NOUN
ejpam-1224	717	13	,	,	PUNCT
ejpam-1224	717	14	it	it	PRON
ejpam-1224	717	15	suffices	suffice	VERB
ejpam-1224	717	16	to	to	PART
ejpam-1224	717	17	show	show	VERB
ejpam-1224	717	18	that	that	SCONJ
ejpam-1224	717	19	h	h	NOUN
ejpam-1224	717	20	i(fνg(m	i(fνg(m	VERB
ejpam-1224	717	21	)	)	PUNCT
ejpam-1224	717	22	)	)	PUNCT
ejpam-1224	718	1	=	=	SYM
ejpam-1224	718	2	0	0	PUNCT
ejpam-1224	719	1	for	for	ADP
ejpam-1224	719	2	i	i	PRON
ejpam-1224	719	3	<	<	X
ejpam-1224	719	4	b	b	PROPN
ejpam-1224	719	5	and	and	CCONJ
ejpam-1224	719	6	for	for	ADP
ejpam-1224	719	7	all	all	DET
ejpam-1224	719	8	ν	ν	NOUN
ejpam-1224	719	9	>	>	PUNCT
ejpam-1224	719	10	>	>	X
ejpam-1224	719	11	0	0	NUM
ejpam-1224	719	12	which	which	PRON
ejpam-1224	719	13	amounts	amount	VERB
ejpam-1224	719	14	to	to	ADP
ejpam-1224	719	15	showing	show	VERB
ejpam-1224	719	16	that	that	SCONJ
ejpam-1224	719	17	h	h	PROPN
ejpam-1224	719	18	i(fg(m	i(fg(m	VERB
ejpam-1224	719	19	)	)	PUNCT
ejpam-1224	719	20	)	)	PUNCT
ejpam-1224	720	1	=	=	SYM
ejpam-1224	720	2	0	0	PUNCT
ejpam-1224	721	1	for	for	ADP
ejpam-1224	721	2	i	i	PRON
ejpam-1224	721	3	<	<	X
ejpam-1224	721	4	b.	b.	PROPN
ejpam-1224	721	5	by	by	ADP
ejpam-1224	721	6	our	our	PRON
ejpam-1224	721	7	proof	proof	NOUN
ejpam-1224	721	8	of	of	ADP
ejpam-1224	721	9	lemma	lemma	PROPN
ejpam-1224	721	10	5	5	NUM
ejpam-1224	721	11	we	we	PRON
ejpam-1224	721	12	know	know	VERB
ejpam-1224	721	13	that	that	SCONJ
ejpam-1224	721	14	h	h	NOUN
ejpam-1224	721	15	i(fνg(m	i(fνg(m	VERB
ejpam-1224	721	16	)	)	PUNCT
ejpam-1224	721	17	)	)	PUNCT
ejpam-1224	722	1	=	=	SYM
ejpam-1224	722	2	0	0	PUNCT
ejpam-1224	723	1	for	for	ADP
ejpam-1224	723	2	i	i	PRON
ejpam-1224	723	3	<	<	X
ejpam-1224	723	4	b	b	PROPN
ejpam-1224	723	5	and	and	CCONJ
ejpam-1224	723	6	for	for	ADP
ejpam-1224	723	7	all	all	DET
ejpam-1224	723	8	ν	ν	NOUN
ejpam-1224	723	9	>	>	X
ejpam-1224	723	10	>	>	X
ejpam-1224	723	11	0	0	PUNCT
ejpam-1224	723	12	is	be	AUX
ejpam-1224	723	13	true	true	ADJ
ejpam-1224	723	14	for	for	ADP
ejpam-1224	723	15	the	the	DET
ejpam-1224	723	16	case	case	NOUN
ejpam-1224	723	17	where	where	SCONJ
ejpam-1224	723	18	m	m	PRON
ejpam-1224	723	19	is	be	AUX
ejpam-1224	723	20	a	a	DET
ejpam-1224	723	21	module	module	NOUN
ejpam-1224	723	22	considered	consider	VERB
ejpam-1224	723	23	as	as	ADP
ejpam-1224	723	24	a	a	DET
ejpam-1224	723	25	one	one	NUM
ejpam-1224	723	26	term	term	NOUN
ejpam-1224	723	27	complex	complex	NOUN
ejpam-1224	723	28	situated	situate	VERB
ejpam-1224	723	29	in	in	ADP
ejpam-1224	723	30	deg	deg	PROPN
ejpam-1224	723	31	b.	b.	PROPN
ejpam-1224	723	32	now	now	ADV
ejpam-1224	723	33	if	if	SCONJ
ejpam-1224	723	34	we	we	PRON
ejpam-1224	723	35	allow	allow	VERB
ejpam-1224	723	36	for	for	SCONJ
ejpam-1224	723	37	m	m	NOUN
ejpam-1224	723	38	to	to	PART
ejpam-1224	723	39	be	be	AUX
ejpam-1224	723	40	a	a	DET
ejpam-1224	723	41	bounded	bounded	ADJ
ejpam-1224	723	42	complex	complex	NOUN
ejpam-1224	723	43	,	,	PUNCT
ejpam-1224	723	44	again	again	ADV
ejpam-1224	723	45	by	by	ADP
ejpam-1224	723	46	our	our	PRON
ejpam-1224	723	47	proof	proof	NOUN
ejpam-1224	723	48	of	of	ADP
ejpam-1224	723	49	lemma	lemma	PROPN
ejpam-1224	723	50	5	5	NUM
ejpam-1224	723	51	we	we	PRON
ejpam-1224	723	52	can	can	AUX
ejpam-1224	723	53	induct	induct	VERB
ejpam-1224	723	54	on	on	ADP
ejpam-1224	723	55	the	the	DET
ejpam-1224	723	56	length	length	NOUN
ejpam-1224	723	57	of	of	ADP
ejpam-1224	723	58	the	the	DET
ejpam-1224	723	59	complex	complex	ADJ
ejpam-1224	723	60	and	and	CCONJ
ejpam-1224	723	61	again	again	ADV
ejpam-1224	723	62	show	show	VERB
ejpam-1224	723	63	our	our	PRON
ejpam-1224	723	64	intended	intended	ADJ
ejpam-1224	723	65	result	result	NOUN
ejpam-1224	723	66	.	.	PUNCT
ejpam-1224	724	1	now	now	ADV
ejpam-1224	724	2	let	let	VERB
ejpam-1224	724	3	m	m	NOUN
ejpam-1224	724	4	=	=	SYM
ejpam-1224	724	5	lim	lim	PROPN
ejpam-1224	724	6	←−	←−	PROPN
ejpam-1224	724	7	σ≤pm	σ≤pm	PROPN
ejpam-1224	724	8	and	and	CCONJ
ejpam-1224	724	9	note	note	VERB
ejpam-1224	724	10	that	that	SCONJ
ejpam-1224	724	11	each	each	DET
ejpam-1224	724	12	σ≤pm	σ≤pm	PROPN
ejpam-1224	724	13	is	be	AUX
ejpam-1224	724	14	bounded	bound	VERB
ejpam-1224	724	15	since	since	SCONJ
ejpam-1224	724	16	m	m	PROPN
ejpam-1224	724	17	is	be	AUX
ejpam-1224	724	18	bounded	bound	VERB
ejpam-1224	724	19	below	below	ADV
ejpam-1224	724	20	.	.	PUNCT
ejpam-1224	725	1	we	we	PRON
ejpam-1224	725	2	know	know	VERB
ejpam-1224	725	3	that	that	PRON
ejpam-1224	725	4	fνg(m	fνg(m	VERB
ejpam-1224	725	5	)	)	PUNCT
ejpam-1224	725	6	=	=	SYM
ejpam-1224	725	7	fνg(lim	fνg(lim	NOUN
ejpam-1224	725	8	←−	←−	NUM
ejpam-1224	725	9	σ≤p	σ≤p	NOUN
ejpam-1224	725	10	m	m	NOUN
ejpam-1224	725	11	)	)	PUNCT
ejpam-1224	726	1	=	=	SYM
ejpam-1224	726	2	fν	fν	NOUN
ejpam-1224	726	3	(	(	PUNCT
ejpam-1224	726	4	lim←−	lim←−	PROPN
ejpam-1224	726	5	g(σ≤p	g(σ≤p	ADJ
ejpam-1224	726	6	m	m	NOUN
ejpam-1224	726	7	)	)	PUNCT
ejpam-1224	726	8	)	)	PUNCT
ejpam-1224	727	1	=	=	SYM
ejpam-1224	727	2	lim	lim	PROPN
ejpam-1224	727	3	←−	←−	PROPN
ejpam-1224	727	4	(	(	PUNCT
ejpam-1224	727	5	fνg(σ≤p	fνg(σ≤p	PROPN
ejpam-1224	727	6	m	m	PROPN
ejpam-1224	727	7	)	)	PUNCT
ejpam-1224	727	8	)	)	PUNCT
ejpam-1224	727	9	.	.	PUNCT
ejpam-1224	728	1	the	the	DET
ejpam-1224	728	2	first	first	ADJ
ejpam-1224	728	3	equality	equality	NOUN
ejpam-1224	728	4	is	be	AUX
ejpam-1224	728	5	easy	easy	ADJ
ejpam-1224	728	6	to	to	PART
ejpam-1224	728	7	see	see	VERB
ejpam-1224	728	8	since	since	SCONJ
ejpam-1224	728	9	m	m	PROPN
ejpam-1224	728	10	=	=	NOUN
ejpam-1224	728	11	lim	lim	PROPN
ejpam-1224	728	12	←−	←−	PROPN
ejpam-1224	728	13	σ≤pm	σ≤pm	PROPN
ejpam-1224	728	14	,	,	PUNCT
ejpam-1224	728	15	the	the	DET
ejpam-1224	728	16	second	second	ADJ
ejpam-1224	728	17	equality	equality	NOUN
ejpam-1224	728	18	follows	follow	VERB
ejpam-1224	728	19	from	from	ADP
ejpam-1224	728	20	the	the	DET
ejpam-1224	728	21	fact	fact	NOUN
ejpam-1224	728	22	that	that	SCONJ
ejpam-1224	728	23	g	g	PROPN
ejpam-1224	728	24	is	be	AUX
ejpam-1224	728	25	a	a	DET
ejpam-1224	728	26	right	right	ADJ
ejpam-1224	728	27	adjoint	adjoint	NOUN
ejpam-1224	728	28	and	and	CCONJ
ejpam-1224	728	29	the	the	DET
ejpam-1224	728	30	third	third	ADJ
ejpam-1224	728	31	equality	equality	NOUN
ejpam-1224	728	32	follows	follow	VERB
ejpam-1224	728	33	from	from	ADP
ejpam-1224	728	34	the	the	DET
ejpam-1224	728	35	fact	fact	NOUN
ejpam-1224	728	36	that	that	SCONJ
ejpam-1224	728	37	each	each	DET
ejpam-1224	728	38	fνg(m	fνg(m	VERB
ejpam-1224	728	39	)	)	PUNCT
ejpam-1224	728	40	is	be	AUX
ejpam-1224	728	41	finite	finite	ADJ
ejpam-1224	728	42	dimensional	dimensional	ADJ
ejpam-1224	728	43	,	,	PUNCT
ejpam-1224	728	44	and	and	CCONJ
ejpam-1224	728	45	therefore	therefore	ADV
ejpam-1224	728	46	commutes	commute	NOUN
ejpam-1224	728	47	with	with	ADP
ejpam-1224	728	48	inverse	inverse	NOUN
ejpam-1224	728	49	limit	limit	NOUN
ejpam-1224	728	50	.	.	PUNCT
ejpam-1224	729	1	now	now	ADV
ejpam-1224	729	2	we	we	PRON
ejpam-1224	729	3	would	would	AUX
ejpam-1224	729	4	like	like	VERB
ejpam-1224	729	5	to	to	PART
ejpam-1224	729	6	show	show	VERB
ejpam-1224	729	7	that	that	SCONJ
ejpam-1224	729	8	even	even	ADV
ejpam-1224	729	9	though	though	SCONJ
ejpam-1224	729	10	inverse	inverse	NOUN
ejpam-1224	729	11	limit	limit	NOUN
ejpam-1224	729	12	does	do	AUX
ejpam-1224	729	13	not	not	PART
ejpam-1224	729	14	usually	usually	ADV
ejpam-1224	729	15	commute	commute	VERB
ejpam-1224	729	16	with	with	ADP
ejpam-1224	729	17	cohomology	cohomology	NOUN
ejpam-1224	729	18	,	,	PUNCT
ejpam-1224	729	19	in	in	ADP
ejpam-1224	729	20	our	our	PRON
ejpam-1224	729	21	case	case	NOUN
ejpam-1224	729	22	we	we	PRON
ejpam-1224	729	23	do	do	AUX
ejpam-1224	729	24	have	have	VERB
ejpam-1224	729	25	h	h	NOUN
ejpam-1224	729	26	i(lim	i(lim	PROPN
ejpam-1224	729	27	←−	←−	PROPN
ejpam-1224	729	28	fνg(σ≤p	fνg(σ≤p	PROPN
ejpam-1224	729	29	m	m	NOUN
ejpam-1224	729	30	)	)	PUNCT
ejpam-1224	729	31	)	)	PUNCT
ejpam-1224	730	1	=	=	SYM
ejpam-1224	730	2	lim	lim	PROPN
ejpam-1224	730	3	←−	←−	PROPN
ejpam-1224	730	4	h	h	PROPN
ejpam-1224	730	5	i(fνg(σ≤pm	i(fνg(σ≤pm	NOUN
ejpam-1224	730	6	)	)	PUNCT
ejpam-1224	730	7	)	)	PUNCT
ejpam-1224	730	8	.	.	PUNCT
ejpam-1224	731	1	this	this	DET
ejpam-1224	731	2	equality	equality	NOUN
ejpam-1224	731	3	follows	follow	VERB
ejpam-1224	731	4	from	from	ADP
ejpam-1224	731	5	the	the	DET
ejpam-1224	731	6	fact	fact	NOUN
ejpam-1224	731	7	that	that	SCONJ
ejpam-1224	731	8	each	each	DET
ejpam-1224	731	9	fνg(σ≤pm	fνg(σ≤pm	NOUN
ejpam-1224	731	10	)	)	PUNCT
ejpam-1224	731	11	and	and	CCONJ
ejpam-1224	731	12	h	h	NOUN
ejpam-1224	731	13	i(fνg(σ≤pm	i(fνg(σ≤pm	NOUN
ejpam-1224	731	14	)	)	PUNCT
ejpam-1224	731	15	)	)	PUNCT
ejpam-1224	731	16	satisfy	satisfy	VERB
ejpam-1224	731	17	the	the	DET
ejpam-1224	731	18	mittag	mittag	ADJ
ejpam-1224	731	19	-	-	PUNCT
ejpam-1224	731	20	leffler	leffler	NOUN
ejpam-1224	731	21	condition	condition	NOUN
ejpam-1224	731	22	(	(	PUNCT
ejpam-1224	731	23	see	see	VERB
ejpam-1224	731	24	proposition	proposition	NOUN
ejpam-1224	731	25	5	5	NUM
ejpam-1224	731	26	)	)	PUNCT
ejpam-1224	731	27	.	.	PUNCT
ejpam-1224	732	1	we	we	PRON
ejpam-1224	732	2	also	also	ADV
ejpam-1224	732	3	know	know	VERB
ejpam-1224	732	4	that	that	SCONJ
ejpam-1224	732	5	for	for	ADP
ejpam-1224	732	6	i	i	PRON
ejpam-1224	732	7	<	<	X
ejpam-1224	732	8	b	b	X
ejpam-1224	732	9	the	the	DET
ejpam-1224	732	10	following	follow	VERB
ejpam-1224	732	11	is	be	AUX
ejpam-1224	732	12	true	true	ADJ
ejpam-1224	732	13	,	,	PUNCT
ejpam-1224	732	14	h	h	NOUN
ejpam-1224	732	15	i(lim	i(lim	PROPN
ejpam-1224	732	16	←−	←−	PROPN
ejpam-1224	732	17	σ≤p	σ≤p	NOUN
ejpam-1224	732	18	m	m	NOUN
ejpam-1224	732	19	)	)	PUNCT
ejpam-1224	733	1	=	=	SYM
ejpam-1224	733	2	lim	lim	PROPN
ejpam-1224	733	3	←−	←−	PROPN
ejpam-1224	733	4	h	h	NOUN
ejpam-1224	733	5	i(σ≤pm	i(σ≤pm	NOUN
ejpam-1224	733	6	)	)	PUNCT
ejpam-1224	733	7	,	,	PUNCT
ejpam-1224	733	8	since	since	SCONJ
ejpam-1224	733	9	m	m	PROPN
ejpam-1224	733	10	=	=	SYM
ejpam-1224	733	11	0	0	NUM
ejpam-1224	733	12	for	for	ADP
ejpam-1224	733	13	i	i	PRON
ejpam-1224	733	14	<	<	X
ejpam-1224	733	15	b	b	NOUN
ejpam-1224	734	1	and	and	CCONJ
ejpam-1224	734	2	we	we	PRON
ejpam-1224	734	3	know	know	VERB
ejpam-1224	734	4	by	by	ADP
ejpam-1224	734	5	our	our	PRON
ejpam-1224	734	6	proof	proof	NOUN
ejpam-1224	734	7	of	of	ADP
ejpam-1224	734	8	lemma	lemma	PROPN
ejpam-1224	734	9	5	5	NUM
ejpam-1224	734	10	that	that	SCONJ
ejpam-1224	734	11	since	since	SCONJ
ejpam-1224	734	12	each	each	DET
ejpam-1224	734	13	σ≤p	σ≤p	NOUN
ejpam-1224	734	14	m	m	VERB
ejpam-1224	734	15	is	be	AUX
ejpam-1224	734	16	bounded	bound	VERB
ejpam-1224	734	17	we	we	PRON
ejpam-1224	734	18	have	have	VERB
ejpam-1224	734	19	lim	lim	PROPN
ejpam-1224	734	20	←−	←−	PROPN
ejpam-1224	734	21	h	h	PROPN
ejpam-1224	734	22	i(fνg(σ≤pm	i(fνg(σ≤pm	NOUN
ejpam-1224	734	23	)	)	PUNCT
ejpam-1224	734	24	)	)	PUNCT
ejpam-1224	735	1	=	=	SYM
ejpam-1224	735	2	lim	lim	PROPN
ejpam-1224	735	3	←−	←−	PROPN
ejpam-1224	735	4	h	h	NOUN
ejpam-1224	735	5	i(σ≤pm	i(σ≤pm	NOUN
ejpam-1224	735	6	)	)	PUNCT
ejpam-1224	735	7	,	,	PUNCT
ejpam-1224	735	8	proving	prove	VERB
ejpam-1224	735	9	that	that	SCONJ
ejpam-1224	735	10	h	h	NOUN
ejpam-1224	735	11	i(fνg(m	i(fνg(m	VERB
ejpam-1224	735	12	)	)	PUNCT
ejpam-1224	735	13	)	)	PUNCT
ejpam-1224	736	1	=	=	SYM
ejpam-1224	736	2	0	0	PUNCT
ejpam-1224	737	1	for	for	ADP
ejpam-1224	737	2	i	i	PRON
ejpam-1224	737	3	<	<	X
ejpam-1224	737	4	b	b	PROPN
ejpam-1224	737	5	and	and	CCONJ
ejpam-1224	737	6	for	for	ADP
ejpam-1224	737	7	all	all	DET
ejpam-1224	737	8	ν	ν	NOUN
ejpam-1224	737	9	>	>	X
ejpam-1224	737	10	>	>	X
ejpam-1224	737	11	0	0	X
ejpam-1224	737	12	.	.	PUNCT
ejpam-1224	738	1	now	now	ADV
ejpam-1224	738	2	let	let	VERB
ejpam-1224	738	3	m	m	PRON
ejpam-1224	738	4	be	be	AUX
ejpam-1224	738	5	an	an	DET
ejpam-1224	738	6	arbitrary	arbitrary	ADJ
ejpam-1224	738	7	complex	complex	NOUN
ejpam-1224	738	8	.	.	PUNCT
ejpam-1224	739	1	consider	consider	VERB
ejpam-1224	739	2	the	the	DET
ejpam-1224	739	3	following	follow	VERB
ejpam-1224	739	4	diagram	diagram	NOUN
ejpam-1224	739	5	0	0	NUM
ejpam-1224	739	6	−−−→	−−−→	NUM
ejpam-1224	739	7	fg(σ	fg(σ	NOUN
ejpam-1224	739	8	>	>	X
ejpam-1224	739	9	p)m	p)m	X
ejpam-1224	739	10	−−−→	−−−→	NUM
ejpam-1224	739	11	fg(m	fg(m	NOUN
ejpam-1224	739	12	)	)	PUNCT
ejpam-1224	739	13	−−−→	−−−→	PROPN
ejpam-1224	740	1	fg(σ≤p	fg(σ≤p	NUM
ejpam-1224	740	2	m	m	NOUN
ejpam-1224	740	3	)	)	PUNCT
ejpam-1224	740	4	−−−→	−−−→	NOUN
ejpam-1224	740	5	0y	0y	PUNCT
ejpam-1224	741	1	α	α	PRON
ejpam-1224	741	2	y	y	NOUN
ejpam-1224	741	3	β	β	PROPN
ejpam-1224	741	4	y	y	PROPN
ejpam-1224	741	5	γ	γ	PROPN
ejpam-1224	741	6	y	y	PROPN
ejpam-1224	741	7	y	y	PROPN
ejpam-1224	741	8	0	0	NUM
ejpam-1224	741	9	−−−→	−−−→	NUM
ejpam-1224	741	10	σ	σ	PROPN
ejpam-1224	741	11	>	>	PROPN
ejpam-1224	741	12	pm	pm	PROPN
ejpam-1224	741	13	−−−→	−−−→	NUM
ejpam-1224	741	14	m	m	PROPN
ejpam-1224	741	15	−−−→	−−−→	ADJ
ejpam-1224	741	16	σ≤p	σ≤p	NOUN
ejpam-1224	741	17	m	m	VERB
ejpam-1224	741	18	−−−→	−−−→	NOUN
ejpam-1224	741	19	0	0	NUM
ejpam-1224	741	20	and	and	CCONJ
ejpam-1224	741	21	the	the	DET
ejpam-1224	741	22	resulting	result	VERB
ejpam-1224	741	23	cohomology	cohomology	NOUN
ejpam-1224	741	24	diagram	diagram	NOUN
ejpam-1224	741	25	:	:	PUNCT
ejpam-1224	741	26	h	h	NOUN
ejpam-1224	741	27	i(fg(σ	i(fg(σ	PROPN
ejpam-1224	741	28	>	>	X
ejpam-1224	741	29	p	p	NOUN
ejpam-1224	741	30	m	m	NOUN
ejpam-1224	741	31	)	)	PUNCT
ejpam-1224	741	32	)	)	PUNCT
ejpam-1224	742	1	−−−→	−−−→	NUM
ejpam-1224	742	2	h	h	NOUN
ejpam-1224	742	3	i(fg(m	i(fg(m	VERB
ejpam-1224	742	4	)	)	PUNCT
ejpam-1224	742	5	)	)	PUNCT
ejpam-1224	743	1	−−−→	−−−→	VERB
ejpam-1224	743	2	h	h	NOUN
ejpam-1224	743	3	i(fg(σ≤p(m	i(fg(σ≤p(m	NOUN
ejpam-1224	743	4	)	)	PUNCT
ejpam-1224	743	5	)	)	PUNCT
ejpam-1224	744	1	−−−→	−−−→	PROPN
ejpam-1224	744	2	h	h	NOUN
ejpam-1224	744	3	i+1(fg(σ	i+1(fg(σ	VERB
ejpam-1224	744	4	>	>	X
ejpam-1224	744	5	p	p	X
ejpam-1224	745	1	m))yα	m))yα	VERB
ejpam-1224	745	2	yβ	yβ	PROPN
ejpam-1224	745	3	yγ	yγ	PUNCT
ejpam-1224	745	4	yα′	yα′	ADJ
ejpam-1224	745	5	h	h	PROPN
ejpam-1224	745	6	i(σ	i(σ	PROPN
ejpam-1224	745	7	>	>	X
ejpam-1224	745	8	pm	pm	NOUN
ejpam-1224	745	9	)	)	PUNCT
ejpam-1224	745	10	−−−→	−−−→	ADJ
ejpam-1224	745	11	h	h	NOUN
ejpam-1224	745	12	i(m	i(m	NOUN
ejpam-1224	745	13	)	)	PUNCT
ejpam-1224	745	14	−−−→	−−−→	PROPN
ejpam-1224	745	15	h	h	NOUN
ejpam-1224	745	16	i(σ≤pm	i(σ≤pm	NOUN
ejpam-1224	745	17	)	)	PUNCT
ejpam-1224	745	18	−−−→	−−−→	PROPN
ejpam-1224	745	19	h	h	NOUN
ejpam-1224	745	20	i+1(σ	i+1(σ	PROPN
ejpam-1224	745	21	>	>	X
ejpam-1224	745	22	pm	pm	PROPN
ejpam-1224	745	23	)	)	PUNCT
ejpam-1224	745	24	.	.	PUNCT
ejpam-1224	746	1	we	we	PRON
ejpam-1224	746	2	know	know	VERB
ejpam-1224	746	3	that	that	SCONJ
ejpam-1224	746	4	the	the	DET
ejpam-1224	746	5	map	map	NOUN
ejpam-1224	746	6	γ	γ	NOUN
ejpam-1224	746	7	is	be	AUX
ejpam-1224	746	8	an	an	DET
ejpam-1224	746	9	isomorphism	isomorphism	NOUN
ejpam-1224	746	10	in	in	ADP
ejpam-1224	746	11	all	all	DET
ejpam-1224	746	12	degrees	degree	NOUN
ejpam-1224	746	13	i	i	PRON
ejpam-1224	746	14	since	since	SCONJ
ejpam-1224	746	15	σ≤p	σ≤p	NOUN
ejpam-1224	746	16	m	m	VERB
ejpam-1224	746	17	is	be	AUX
ejpam-1224	746	18	bounded	bound	VERB
ejpam-1224	746	19	above	above	ADV
ejpam-1224	746	20	.	.	PUNCT
ejpam-1224	747	1	we	we	PRON
ejpam-1224	747	2	have	have	AUX
ejpam-1224	747	3	also	also	ADV
ejpam-1224	747	4	shown	show	VERB
ejpam-1224	747	5	that	that	SCONJ
ejpam-1224	747	6	α	α	PRON
ejpam-1224	747	7	is	be	AUX
ejpam-1224	747	8	an	an	DET
ejpam-1224	747	9	isomorphism	isomorphism	NOUN
ejpam-1224	747	10	in	in	ADP
ejpam-1224	747	11	degrees	degree	NOUN
ejpam-1224	747	12	i	i	NOUN
ejpam-1224	747	13	≤	≤	NOUN
ejpam-1224	747	14	p	p	NOUN
ejpam-1224	747	15	since	since	SCONJ
ejpam-1224	747	16	σ	σ	PROPN
ejpam-1224	747	17	>	>	X
ejpam-1224	747	18	p	p	X
ejpam-1224	747	19	m	m	VERB
ejpam-1224	747	20	is	be	AUX
ejpam-1224	747	21	bounded	bound	VERB
ejpam-1224	747	22	below	below	ADV
ejpam-1224	747	23	.	.	PUNCT
ejpam-1224	748	1	similarly	similarly	ADV
ejpam-1224	748	2	,	,	PUNCT
ejpam-1224	748	3	α′	α′	NUM
ejpam-1224	748	4	is	be	AUX
ejpam-1224	748	5	an	an	DET
ejpam-1224	748	6	isomorphism	isomorphism	NOUN
ejpam-1224	748	7	in	in	ADP
ejpam-1224	748	8	degrees	degree	NOUN
ejpam-1224	748	9	i	i	NOUN
ejpam-1224	748	10	+	+	CCONJ
ejpam-1224	748	11	1	1	NUM
ejpam-1224	748	12	≤	≤	NUM
ejpam-1224	748	13	p.	p.	NOUN
ejpam-1224	748	14	the	the	DET
ejpam-1224	748	15	5	5	NUM
ejpam-1224	748	16	-	-	PUNCT
ejpam-1224	748	17	lemma	lemma	PROPN
ejpam-1224	748	18	now	now	ADV
ejpam-1224	748	19	shows	show	VERB
ejpam-1224	748	20	that	that	SCONJ
ejpam-1224	748	21	β	β	PROPN
ejpam-1224	748	22	is	be	AUX
ejpam-1224	748	23	an	an	DET
ejpam-1224	748	24	f.	f.	PROPN
ejpam-1224	748	25	hawwa	hawwa	PROPN
ejpam-1224	748	26	,	,	PUNCT
ejpam-1224	748	27	j.	j.	PROPN
ejpam-1224	748	28	hoffman	hoffman	PROPN
ejpam-1224	748	29	,	,	PUNCT
ejpam-1224	748	30	and	and	CCONJ
ejpam-1224	748	31	h.	h.	PROPN
ejpam-1224	748	32	wang	wang	PROPN
ejpam-1224	748	33	,	,	PUNCT
ejpam-1224	748	34	/	/	SYM
ejpam-1224	748	35	eur	eur	NOUN
ejpam-1224	748	36	.	.	PUNCT
ejpam-1224	749	1	j.	j.	PROPN
ejpam-1224	749	2	pure	pure	PROPN
ejpam-1224	749	3	appl	appl	PROPN
ejpam-1224	749	4	.	.	PROPN
ejpam-1224	749	5	math	math	PROPN
ejpam-1224	749	6	,	,	PUNCT
ejpam-1224	749	7	5	5	NUM
ejpam-1224	749	8	(	(	PUNCT
ejpam-1224	749	9	2012	2012	NUM
ejpam-1224	749	10	)	)	PUNCT
ejpam-1224	749	11	,	,	PUNCT
ejpam-1224	749	12	511	511	NUM
ejpam-1224	749	13	-	-	SYM
ejpam-1224	749	14	539	539	NUM
ejpam-1224	749	15	533	533	NUM
ejpam-1224	749	16	isomorphism	isomorphism	NOUN
ejpam-1224	749	17	in	in	ADP
ejpam-1224	749	18	degrees	degree	NOUN
ejpam-1224	749	19	i	i	NOUN
ejpam-1224	749	20	≤	≤	NUM
ejpam-1224	749	21	p−	p−	NOUN
ejpam-1224	749	22	1	1	NUM
ejpam-1224	749	23	.	.	PUNCT
ejpam-1224	750	1	since	since	SCONJ
ejpam-1224	750	2	p	p	NOUN
ejpam-1224	750	3	is	be	AUX
ejpam-1224	750	4	arbitrary	arbitrary	ADJ
ejpam-1224	750	5	,	,	PUNCT
ejpam-1224	750	6	β	β	X
ejpam-1224	750	7	is	be	AUX
ejpam-1224	750	8	an	an	DET
ejpam-1224	750	9	isomorphism	isomorphism	NOUN
ejpam-1224	750	10	in	in	ADP
ejpam-1224	750	11	all	all	DET
ejpam-1224	750	12	degrees	degree	NOUN
ejpam-1224	750	13	i.	i.	NOUN
ejpam-1224	750	14	we	we	PRON
ejpam-1224	750	15	now	now	ADV
ejpam-1224	750	16	would	would	AUX
ejpam-1224	750	17	like	like	VERB
ejpam-1224	750	18	to	to	PART
ejpam-1224	750	19	show	show	VERB
ejpam-1224	750	20	that	that	SCONJ
ejpam-1224	750	21	n	n	NOUN
ejpam-1224	750	22	→	→	SYM
ejpam-1224	750	23	gf(n	gf(n	X
ejpam-1224	750	24	)	)	PUNCT
ejpam-1224	750	25	is	be	AUX
ejpam-1224	750	26	a	a	DET
ejpam-1224	750	27	quasi	quasi	NOUN
ejpam-1224	750	28	-	-	NOUN
ejpam-1224	750	29	isomorphism	isomorphism	NOUN
ejpam-1224	750	30	.	.	PUNCT
ejpam-1224	751	1	the	the	DET
ejpam-1224	751	2	complex	complex	NOUN
ejpam-1224	751	3	gf(k	gf(k	VERB
ejpam-1224	751	4	)	)	PUNCT
ejpam-1224	751	5	is	be	AUX
ejpam-1224	751	6	the	the	DET
ejpam-1224	751	7	complex	complex	ADJ
ejpam-1224	751	8	·	·	PUNCT
ejpam-1224	751	9	·	·	PUNCT
ejpam-1224	751	10	·	·	PUNCT
ejpam-1224	752	1	→	→	PUNCT
ejpam-1224	752	2	(	(	PUNCT
ejpam-1224	752	3	a	a	NOUN
ejpam-1224	752	4	!	!	PUNCT
ejpam-1224	752	5	p	p	X
ejpam-1224	752	6	)	)	PUNCT
ejpam-1224	752	7	∗⊗	∗⊗	NOUN
ejpam-1224	752	8	u	u	NOUN
ejpam-1224	752	9	→	→	PUNCT
ejpam-1224	752	10	(	(	PUNCT
ejpam-1224	752	11	a	a	X
ejpam-1224	752	12	!	!	PUNCT
ejpam-1224	752	13	p−1	p−1	NOUN
ejpam-1224	752	14	)	)	PUNCT
ejpam-1224	752	15	∗⊗	∗⊗	NOUN
ejpam-1224	752	16	u	u	NOUN
ejpam-1224	752	17	→	→	SYM
ejpam-1224	752	18	·	·	PUNCT
ejpam-1224	752	19	·	·	PUNCT
ejpam-1224	752	20	·	·	PUNCT
ejpam-1224	753	1	→	→	SYM
ejpam-1224	753	2	u	u	PROPN
ejpam-1224	753	3	.	.	PUNCT
ejpam-1224	754	1	by	by	ADP
ejpam-1224	754	2	the	the	DET
ejpam-1224	754	3	same	same	ADJ
ejpam-1224	754	4	argument	argument	NOUN
ejpam-1224	754	5	as	as	ADP
ejpam-1224	754	6	in	in	ADP
ejpam-1224	754	7	the	the	DET
ejpam-1224	754	8	proof	proof	NOUN
ejpam-1224	754	9	of	of	ADP
ejpam-1224	754	10	lemma	lemma	PROPN
ejpam-1224	754	11	5	5	NUM
ejpam-1224	754	12	the	the	DET
ejpam-1224	754	13	map	map	NOUN
ejpam-1224	754	14	k→	k→	ADJ
ejpam-1224	754	15	gf(k	gf(k	X
ejpam-1224	754	16	)	)	PUNCT
ejpam-1224	754	17	is	be	AUX
ejpam-1224	754	18	a	a	DET
ejpam-1224	754	19	quasi	quasi	NOUN
ejpam-1224	754	20	-	-	NOUN
ejpam-1224	754	21	isomorphism	isomorphism	NOUN
ejpam-1224	754	22	.	.	PUNCT
ejpam-1224	755	1	so	so	ADV
ejpam-1224	755	2	if	if	SCONJ
ejpam-1224	755	3	n	n	PRON
ejpam-1224	755	4	=	=	SYM
ejpam-1224	755	5	n0	n0	NOUN
ejpam-1224	755	6	we	we	PRON
ejpam-1224	755	7	have	have	VERB
ejpam-1224	755	8	gf(n	gf(n	X
ejpam-1224	755	9	)	)	PUNCT
ejpam-1224	756	1	=	=	PRON
ejpam-1224	756	2	gf(k)⊗k	gf(k)⊗k	PROPN
ejpam-1224	756	3	n	n	PROPN
ejpam-1224	756	4	and	and	CCONJ
ejpam-1224	756	5	so	so	ADV
ejpam-1224	756	6	n	n	ADV
ejpam-1224	756	7	→	→	PUNCT
ejpam-1224	756	8	gf(n	gf(n	X
ejpam-1224	756	9	)	)	PUNCT
ejpam-1224	756	10	is	be	AUX
ejpam-1224	756	11	also	also	ADV
ejpam-1224	756	12	a	a	DET
ejpam-1224	756	13	quasi	quasi	NOUN
ejpam-1224	756	14	-	-	NOUN
ejpam-1224	756	15	isomorphism	isomorphism	NOUN
ejpam-1224	756	16	.	.	PUNCT
ejpam-1224	757	1	by	by	ADP
ejpam-1224	757	2	induction	induction	NOUN
ejpam-1224	757	3	on	on	ADP
ejpam-1224	757	4	the	the	DET
ejpam-1224	757	5	length	length	NOUN
ejpam-1224	757	6	of	of	ADP
ejpam-1224	757	7	the	the	DET
ejpam-1224	757	8	truncations	truncation	NOUN
ejpam-1224	757	9	,	,	PUNCT
ejpam-1224	757	10	we	we	PRON
ejpam-1224	757	11	know	know	VERB
ejpam-1224	757	12	that	that	SCONJ
ejpam-1224	757	13	n	n	NOUN
ejpam-1224	757	14	→	→	SYM
ejpam-1224	757	15	gf(n	gf(n	X
ejpam-1224	757	16	)	)	PUNCT
ejpam-1224	757	17	is	be	AUX
ejpam-1224	757	18	a	a	DET
ejpam-1224	757	19	quasiisomorphism	quasiisomorphism	NOUN
ejpam-1224	757	20	for	for	ADP
ejpam-1224	757	21	bounded	bounded	ADJ
ejpam-1224	757	22	n	n	X
ejpam-1224	757	23	.	.	PUNCT
ejpam-1224	758	1	now	now	ADV
ejpam-1224	758	2	let	let	VERB
ejpam-1224	758	3	n	n	PRON
ejpam-1224	758	4	be	be	AUX
ejpam-1224	758	5	bounded	bound	VERB
ejpam-1224	758	6	above	above	ADV
ejpam-1224	758	7	.	.	PUNCT
ejpam-1224	759	1	we	we	PRON
ejpam-1224	759	2	know	know	VERB
ejpam-1224	759	3	that	that	SCONJ
ejpam-1224	759	4	n	n	PROPN
ejpam-1224	759	5	=	=	SYM
ejpam-1224	759	6	lim	lim	PROPN
ejpam-1224	759	7	−→	−→	PROPN
ejpam-1224	759	8	σ	σ	PROPN
ejpam-1224	759	9	>	>	X
ejpam-1224	759	10	pn	pn	PROPN
ejpam-1224	759	11	for	for	ADP
ejpam-1224	759	12	p→−∞	p→−∞	NOUN
ejpam-1224	759	13	and	and	CCONJ
ejpam-1224	759	14	we	we	PRON
ejpam-1224	759	15	also	also	ADV
ejpam-1224	759	16	know	know	VERB
ejpam-1224	759	17	that	that	SCONJ
ejpam-1224	759	18	for	for	ADP
ejpam-1224	759	19	n	n	CCONJ
ejpam-1224	759	20	bounded	bound	VERB
ejpam-1224	759	21	above	above	ADV
ejpam-1224	759	22	,	,	PUNCT
ejpam-1224	759	23	σ	σ	PROPN
ejpam-1224	759	24	>	>	X
ejpam-1224	759	25	pn	pn	PROPN
ejpam-1224	759	26	→	→	SYM
ejpam-1224	759	27	gf(σ	gf(σ	PROPN
ejpam-1224	759	28	>	>	X
ejpam-1224	759	29	pn	pn	X
ejpam-1224	759	30	)	)	PUNCT
ejpam-1224	759	31	is	be	AUX
ejpam-1224	759	32	a	a	DET
ejpam-1224	759	33	quasi	quasi	NOUN
ejpam-1224	759	34	-	-	NOUN
ejpam-1224	759	35	isomorphism	isomorphism	NOUN
ejpam-1224	759	36	for	for	ADP
ejpam-1224	759	37	all	all	DET
ejpam-1224	759	38	p	p	NOUN
ejpam-1224	759	39	since	since	SCONJ
ejpam-1224	759	40	each	each	DET
ejpam-1224	759	41	σ	σ	PROPN
ejpam-1224	759	42	>	>	X
ejpam-1224	759	43	pn	pn	PROPN
ejpam-1224	759	44	is	be	AUX
ejpam-1224	759	45	bounded	bound	VERB
ejpam-1224	759	46	.	.	PUNCT
ejpam-1224	760	1	since	since	SCONJ
ejpam-1224	760	2	we	we	PRON
ejpam-1224	760	3	know	know	VERB
ejpam-1224	760	4	that	that	SCONJ
ejpam-1224	760	5	direct	direct	ADJ
ejpam-1224	760	6	limit	limit	NOUN
ejpam-1224	760	7	commutes	commute	VERB
ejpam-1224	760	8	with	with	ADP
ejpam-1224	760	9	taking	take	VERB
ejpam-1224	760	10	cohomology	cohomology	NOUN
ejpam-1224	760	11	,	,	PUNCT
ejpam-1224	760	12	we	we	PRON
ejpam-1224	760	13	would	would	AUX
ejpam-1224	760	14	like	like	VERB
ejpam-1224	760	15	to	to	PART
ejpam-1224	760	16	show	show	VERB
ejpam-1224	760	17	that	that	SCONJ
ejpam-1224	760	18	gf(lim	gf(lim	NOUN
ejpam-1224	760	19	−→	−→	NOUN
ejpam-1224	760	20	σ	σ	PROPN
ejpam-1224	760	21	>	>	X
ejpam-1224	760	22	pn	pn	PROPN
ejpam-1224	760	23	)	)	PUNCT
ejpam-1224	760	24	=	=	PROPN
ejpam-1224	761	1	g	g	PROPN
ejpam-1224	761	2	lim	lim	PROPN
ejpam-1224	761	3	−→	−→	PROPN
ejpam-1224	761	4	f(σ	f(σ	PROPN
ejpam-1224	761	5	>	>	X
ejpam-1224	761	6	pn	pn	PROPN
ejpam-1224	761	7	)	)	PUNCT
ejpam-1224	762	1	=	=	VERB
ejpam-1224	762	2	lim	lim	PROPN
ejpam-1224	762	3	−→	−→	PROPN
ejpam-1224	762	4	gf(σ	gf(σ	NOUN
ejpam-1224	762	5	>	>	X
ejpam-1224	762	6	pn	pn	NOUN
ejpam-1224	762	7	)	)	PUNCT
ejpam-1224	762	8	.	.	PUNCT
ejpam-1224	763	1	the	the	DET
ejpam-1224	763	2	first	first	ADJ
ejpam-1224	763	3	equality	equality	NOUN
ejpam-1224	763	4	is	be	AUX
ejpam-1224	763	5	clear	clear	ADJ
ejpam-1224	763	6	since	since	SCONJ
ejpam-1224	763	7	f	f	PROPN
ejpam-1224	763	8	is	be	AUX
ejpam-1224	763	9	a	a	DET
ejpam-1224	763	10	left	left	ADJ
ejpam-1224	763	11	adjoint	adjoint	NOUN
ejpam-1224	763	12	but	but	CCONJ
ejpam-1224	763	13	it	it	PRON
ejpam-1224	763	14	remains	remain	VERB
ejpam-1224	763	15	to	to	PART
ejpam-1224	763	16	show	show	VERB
ejpam-1224	763	17	that	that	SCONJ
ejpam-1224	763	18	g	g	PROPN
ejpam-1224	763	19	commutes	commute	NOUN
ejpam-1224	763	20	with	with	ADP
ejpam-1224	763	21	direct	direct	ADJ
ejpam-1224	763	22	limit	limit	NOUN
ejpam-1224	763	23	.	.	PUNCT
ejpam-1224	764	1	we	we	PRON
ejpam-1224	764	2	know	know	VERB
ejpam-1224	764	3	gf(σ	gf(σ	NOUN
ejpam-1224	764	4	>	>	X
ejpam-1224	764	5	pn)i	pn)i	PROPN
ejpam-1224	764	6	=	=	SYM
ejpam-1224	764	7	∏	∏	PROPN
ejpam-1224	764	8	r≥0	r≥0	PROPN
ejpam-1224	764	9	homk((a	homk((a	NUM
ejpam-1224	764	10	!	!	PUNCT
ejpam-1224	764	11	)	)	PUNCT
ejpam-1224	765	1	r	r	NOUN
ejpam-1224	765	2	,	,	PUNCT
ejpam-1224	765	3	f(σ	f(σ	PROPN
ejpam-1224	765	4	>	>	X
ejpam-1224	765	5	pn)i+r	pn)i+r	PROPN
ejpam-1224	765	6	)	)	PUNCT
ejpam-1224	765	7	and	and	CCONJ
ejpam-1224	765	8	since	since	SCONJ
ejpam-1224	765	9	p−	p−	NOUN
ejpam-1224	765	10	i	i	NOUN
ejpam-1224	765	11	+	+	CCONJ
ejpam-1224	765	12	1≤	1≤	NUM
ejpam-1224	765	13	r	r	NOUN
ejpam-1224	765	14	≤	≤	PUNCT
ejpam-1224	766	1	t	t	NOUN
ejpam-1224	766	2	−	−	PROPN
ejpam-1224	767	1	i	i	PRON
ejpam-1224	767	2	we	we	PRON
ejpam-1224	767	3	have	have	VERB
ejpam-1224	767	4	gf(σ	gf(σ	NOUN
ejpam-1224	767	5	>	>	X
ejpam-1224	767	6	pn)i	pn)i	PROPN
ejpam-1224	767	7	=	=	SYM
ejpam-1224	767	8	t−i⊕	t−i⊕	PROPN
ejpam-1224	767	9	r	r	NOUN
ejpam-1224	767	10	=	=	SYM
ejpam-1224	767	11	p−i+1	p−i+1	NOUN
ejpam-1224	767	12	homk((a	homk((a	NOUN
ejpam-1224	767	13	!	!	PUNCT
ejpam-1224	767	14	)	)	PUNCT
ejpam-1224	768	1	r	r	NOUN
ejpam-1224	768	2	,	,	PUNCT
ejpam-1224	768	3	f(σ	f(σ	PROPN
ejpam-1224	768	4	>	>	X
ejpam-1224	768	5	pn)i+r	pn)i+r	PROPN
ejpam-1224	768	6	)	)	PUNCT
ejpam-1224	768	7	.	.	PUNCT
ejpam-1224	769	1	if	if	SCONJ
ejpam-1224	769	2	we	we	PRON
ejpam-1224	769	3	take	take	VERB
ejpam-1224	769	4	the	the	DET
ejpam-1224	769	5	direct	direct	ADJ
ejpam-1224	769	6	limit	limit	NOUN
ejpam-1224	769	7	of	of	ADP
ejpam-1224	769	8	both	both	DET
ejpam-1224	769	9	sides	side	NOUN
ejpam-1224	769	10	as	as	ADP
ejpam-1224	769	11	p→−∞	p→−∞	NOUN
ejpam-1224	769	12	we	we	PRON
ejpam-1224	769	13	have	have	VERB
ejpam-1224	769	14	lim	lim	NOUN
ejpam-1224	769	15	−→	−→	PROPN
ejpam-1224	769	16	gf(σ	gf(σ	NOUN
ejpam-1224	769	17	>	>	X
ejpam-1224	769	18	pn)i	pn)i	PROPN
ejpam-1224	769	19	=	=	SYM
ejpam-1224	769	20	t−i⊕	t−i⊕	PROPN
ejpam-1224	769	21	0	0	NUM
ejpam-1224	769	22	homk((a	homk((a	NUM
ejpam-1224	769	23	!	!	PUNCT
ejpam-1224	769	24	)	)	PUNCT
ejpam-1224	770	1	r	r	NOUN
ejpam-1224	770	2	,	,	PUNCT
ejpam-1224	770	3	f(σ	f(σ	PROPN
ejpam-1224	770	4	>	>	X
ejpam-1224	770	5	pn)i+r	pn)i+r	PROPN
ejpam-1224	770	6	)	)	PUNCT
ejpam-1224	770	7	which	which	PRON
ejpam-1224	770	8	we	we	PRON
ejpam-1224	770	9	would	would	AUX
ejpam-1224	770	10	like	like	VERB
ejpam-1224	770	11	to	to	PART
ejpam-1224	770	12	have	have	VERB
ejpam-1224	770	13	equal	equal	ADJ
ejpam-1224	770	14	to	to	ADP
ejpam-1224	770	15	g	g	PROPN
ejpam-1224	770	16	lim	lim	PROPN
ejpam-1224	770	17	−→	−→	PROPN
ejpam-1224	770	18	f(σ	f(σ	PROPN
ejpam-1224	770	19	>	>	X
ejpam-1224	770	20	pn	pn	PROPN
ejpam-1224	770	21	)	)	PUNCT
ejpam-1224	770	22	.	.	PUNCT
ejpam-1224	771	1	we	we	PRON
ejpam-1224	771	2	know	know	VERB
ejpam-1224	771	3	g	g	PROPN
ejpam-1224	771	4	lim	lim	PROPN
ejpam-1224	771	5	−→	−→	PROPN
ejpam-1224	771	6	f(σ	f(σ	PROPN
ejpam-1224	771	7	>	>	X
ejpam-1224	771	8	pn	pn	PROPN
ejpam-1224	771	9	)	)	PUNCT
ejpam-1224	771	10	=	=	SYM
ejpam-1224	771	11	∏	∏	PROPN
ejpam-1224	771	12	r≥0	r≥0	PROPN
ejpam-1224	771	13	homk((a	homk((a	NUM
ejpam-1224	771	14	!	!	PUNCT
ejpam-1224	771	15	)	)	PUNCT
ejpam-1224	772	1	r	r	NOUN
ejpam-1224	772	2	,	,	PUNCT
ejpam-1224	773	1	[	[	X
ejpam-1224	773	2	lim	lim	NOUN
ejpam-1224	773	3	−→	−→	PROPN
ejpam-1224	773	4	f(σ	f(σ	PROPN
ejpam-1224	773	5	>	>	X
ejpam-1224	773	6	pn)]i+r	pn)]i+r	PROPN
ejpam-1224	773	7	)	)	PUNCT
ejpam-1224	773	8	=	=	SYM
ejpam-1224	773	9	∏	∏	PROPN
ejpam-1224	773	10	r≥0	r≥0	PROPN
ejpam-1224	773	11	homk((a	homk((a	NUM
ejpam-1224	773	12	!	!	PUNCT
ejpam-1224	773	13	)	)	PUNCT
ejpam-1224	774	1	r	r	NOUN
ejpam-1224	774	2	,	,	PUNCT
ejpam-1224	774	3	lim	lim	PROPN
ejpam-1224	774	4	−→	−→	PROPN
ejpam-1224	774	5	u	u	PROPN
ejpam-1224	774	6	⊗	⊗	PROPN
ejpam-1224	774	7	(	(	PUNCT
ejpam-1224	774	8	σ	σ	PROPN
ejpam-1224	774	9	>	>	X
ejpam-1224	774	10	pn)i+r	pn)i+r	PROPN
ejpam-1224	774	11	)	)	PUNCT
ejpam-1224	774	12	=	=	SYM
ejpam-1224	774	13	∏	∏	PROPN
ejpam-1224	774	14	r≥0	r≥0	NOUN
ejpam-1224	774	15	lim	lim	NOUN
ejpam-1224	774	16	−→	−→	NOUN
ejpam-1224	774	17	homk((a	homk((a	NUM
ejpam-1224	774	18	!	!	PUNCT
ejpam-1224	774	19	)	)	PUNCT
ejpam-1224	775	1	r	r	NOUN
ejpam-1224	775	2	,	,	PUNCT
ejpam-1224	775	3	u	u	NOUN
ejpam-1224	775	4	⊗	⊗	PROPN
ejpam-1224	775	5	(	(	PUNCT
ejpam-1224	775	6	σ	σ	PROPN
ejpam-1224	775	7	>	>	X
ejpam-1224	775	8	pn)i+r	pn)i+r	PROPN
ejpam-1224	775	9	)	)	PUNCT
ejpam-1224	775	10	.	.	PUNCT
ejpam-1224	776	1	f.	f.	PROPN
ejpam-1224	776	2	hawwa	hawwa	PROPN
ejpam-1224	776	3	,	,	PUNCT
ejpam-1224	776	4	j.	j.	PROPN
ejpam-1224	776	5	hoffman	hoffman	PROPN
ejpam-1224	776	6	,	,	PUNCT
ejpam-1224	776	7	and	and	CCONJ
ejpam-1224	776	8	h.	h.	PROPN
ejpam-1224	776	9	wang	wang	PROPN
ejpam-1224	776	10	,	,	PUNCT
ejpam-1224	776	11	/	/	SYM
ejpam-1224	776	12	eur	eur	NOUN
ejpam-1224	776	13	.	.	PUNCT
ejpam-1224	777	1	j.	j.	PROPN
ejpam-1224	777	2	pure	pure	PROPN
ejpam-1224	777	3	appl	appl	PROPN
ejpam-1224	777	4	.	.	PROPN
ejpam-1224	777	5	math	math	PROPN
ejpam-1224	777	6	,	,	PUNCT
ejpam-1224	777	7	5	5	NUM
ejpam-1224	777	8	(	(	PUNCT
ejpam-1224	777	9	2012	2012	NUM
ejpam-1224	777	10	)	)	PUNCT
ejpam-1224	777	11	,	,	PUNCT
ejpam-1224	777	12	511	511	NUM
ejpam-1224	777	13	-	-	SYM
ejpam-1224	777	14	539	539	NUM
ejpam-1224	777	15	534	534	NUM
ejpam-1224	777	16	the	the	DET
ejpam-1224	777	17	third	third	ADJ
ejpam-1224	777	18	equality	equality	NOUN
ejpam-1224	777	19	is	be	AUX
ejpam-1224	777	20	due	due	ADJ
ejpam-1224	777	21	to	to	ADP
ejpam-1224	777	22	the	the	DET
ejpam-1224	777	23	fact	fact	NOUN
ejpam-1224	777	24	that	that	SCONJ
ejpam-1224	777	25	each	each	PRON
ejpam-1224	777	26	(	(	PUNCT
ejpam-1224	777	27	a!)r	a!)r	NOUN
ejpam-1224	777	28	is	be	AUX
ejpam-1224	777	29	finite	finite	ADJ
ejpam-1224	777	30	dimensional	dimensional	ADJ
ejpam-1224	777	31	and	and	CCONJ
ejpam-1224	777	32	since	since	SCONJ
ejpam-1224	777	33	we	we	PRON
ejpam-1224	777	34	know	know	VERB
ejpam-1224	777	35	that	that	SCONJ
ejpam-1224	777	36	r	r	NOUN
ejpam-1224	777	37	is	be	AUX
ejpam-1224	777	38	bounded	bound	VERB
ejpam-1224	777	39	,	,	PUNCT
ejpam-1224	777	40	i.e.	i.e.	X
ejpam-1224	777	41	,	,	PUNCT
ejpam-1224	778	1	p−	p−	INTJ
ejpam-1224	778	2	i	i	NOUN
ejpam-1224	778	3	+	+	CCONJ
ejpam-1224	778	4	1≤	1≤	NUM
ejpam-1224	778	5	r	r	NOUN
ejpam-1224	778	6	≤	≤	PUNCT
ejpam-1224	779	1	t	t	NOUN
ejpam-1224	779	2	−	−	PROPN
ejpam-1224	780	1	i	i	PRON
ejpam-1224	780	2	we	we	PRON
ejpam-1224	780	3	have	have	VERB
ejpam-1224	780	4	for	for	ADP
ejpam-1224	780	5	p→−∞	p→−∞	NOUN
ejpam-1224	780	6	g	g	PROPN
ejpam-1224	780	7	lim	lim	PROPN
ejpam-1224	780	8	−→	−→	PROPN
ejpam-1224	780	9	f(σ	f(σ	PROPN
ejpam-1224	780	10	>	>	X
ejpam-1224	780	11	pn	pn	PROPN
ejpam-1224	780	12	)	)	PUNCT
ejpam-1224	781	1	=	=	VERB
ejpam-1224	781	2	lim	lim	PROPN
ejpam-1224	781	3	−→	−→	PROPN
ejpam-1224	781	4	t−i⊕	t−i⊕	PROPN
ejpam-1224	781	5	r=0	r=0	PROPN
ejpam-1224	781	6	homk((a	homk((a	NUM
ejpam-1224	781	7	!	!	PUNCT
ejpam-1224	781	8	)	)	PUNCT
ejpam-1224	782	1	r	r	NOUN
ejpam-1224	782	2	,	,	PUNCT
ejpam-1224	782	3	f(σ	f(σ	PROPN
ejpam-1224	782	4	>	>	X
ejpam-1224	782	5	pn)i+r	pn)i+r	PROPN
ejpam-1224	782	6	)	)	PUNCT
ejpam-1224	782	7	which	which	PRON
ejpam-1224	782	8	eventually	eventually	ADV
ejpam-1224	782	9	stabilizes	stabilize	VERB
ejpam-1224	782	10	in	in	ADP
ejpam-1224	782	11	this	this	DET
ejpam-1224	782	12	range	range	NOUN
ejpam-1224	782	13	of	of	ADP
ejpam-1224	782	14	r	r	NOUN
ejpam-1224	782	15	giving	give	VERB
ejpam-1224	782	16	us	we	PRON
ejpam-1224	782	17	g	g	PROPN
ejpam-1224	782	18	lim	lim	PROPN
ejpam-1224	782	19	−→	−→	PROPN
ejpam-1224	782	20	f(σ	f(σ	PROPN
ejpam-1224	782	21	>	>	X
ejpam-1224	782	22	pn	pn	PROPN
ejpam-1224	782	23	)	)	PUNCT
ejpam-1224	783	1	=	=	VERB
ejpam-1224	783	2	lim	lim	PROPN
ejpam-1224	783	3	−→	−→	PROPN
ejpam-1224	783	4	gf(σ	gf(σ	NOUN
ejpam-1224	783	5	>	>	X
ejpam-1224	783	6	pn	pn	NOUN
ejpam-1224	783	7	)	)	PUNCT
ejpam-1224	783	8	showing	show	VERB
ejpam-1224	783	9	that	that	SCONJ
ejpam-1224	783	10	g	g	PROPN
ejpam-1224	783	11	can	can	AUX
ejpam-1224	783	12	commute	commute	VERB
ejpam-1224	783	13	with	with	ADP
ejpam-1224	783	14	direct	direct	ADJ
ejpam-1224	783	15	limit	limit	NOUN
ejpam-1224	783	16	and	and	CCONJ
ejpam-1224	783	17	showing	show	VERB
ejpam-1224	783	18	that	that	PRON
ejpam-1224	783	19	for	for	ADP
ejpam-1224	783	20	n	n	CCONJ
ejpam-1224	783	21	bounded	bound	VERB
ejpam-1224	783	22	above	above	ADV
ejpam-1224	783	23	,	,	PUNCT
ejpam-1224	783	24	we	we	PRON
ejpam-1224	783	25	have	have	VERB
ejpam-1224	783	26	n	n	NOUN
ejpam-1224	783	27	→	→	SYM
ejpam-1224	783	28	gf(n	gf(n	X
ejpam-1224	783	29	)	)	PUNCT
ejpam-1224	783	30	is	be	AUX
ejpam-1224	783	31	a	a	DET
ejpam-1224	783	32	quasi	quasi	NOUN
ejpam-1224	783	33	-	-	NOUN
ejpam-1224	783	34	isomorphism	isomorphism	NOUN
ejpam-1224	783	35	.	.	PUNCT
ejpam-1224	784	1	now	now	ADV
ejpam-1224	784	2	let	let	VERB
ejpam-1224	784	3	n	n	PRON
ejpam-1224	784	4	be	be	AUX
ejpam-1224	784	5	arbitrary	arbitrary	ADJ
ejpam-1224	784	6	.	.	PUNCT
ejpam-1224	785	1	we	we	PRON
ejpam-1224	785	2	know	know	VERB
ejpam-1224	785	3	for	for	ADP
ejpam-1224	785	4	p→∞	p→∞	PRON
ejpam-1224	785	5	,	,	PUNCT
ejpam-1224	785	6	lim	lim	PROPN
ejpam-1224	785	7	←−	←−	PROPN
ejpam-1224	785	8	σ≤pn	σ≤pn	X
ejpam-1224	785	9	=	=	SYM
ejpam-1224	785	10	n	n	NOUN
ejpam-1224	785	11	and	and	CCONJ
ejpam-1224	785	12	we	we	PRON
ejpam-1224	785	13	know	know	VERB
ejpam-1224	785	14	that	that	SCONJ
ejpam-1224	785	15	each	each	DET
ejpam-1224	785	16	σ≤pn	σ≤pn	NOUN
ejpam-1224	785	17	is	be	AUX
ejpam-1224	785	18	bounded	bound	VERB
ejpam-1224	785	19	above	above	ADP
ejpam-1224	785	20	so	so	ADV
ejpam-1224	785	21	for	for	ADP
ejpam-1224	785	22	all	all	DET
ejpam-1224	785	23	p	p	X
ejpam-1224	785	24	we	we	PRON
ejpam-1224	785	25	know	know	VERB
ejpam-1224	785	26	that	that	SCONJ
ejpam-1224	785	27	σ≤pn	σ≤pn	X
ejpam-1224	785	28	→	→	SYM
ejpam-1224	785	29	gf(σ≤pn	gf(σ≤pn	NOUN
ejpam-1224	785	30	)	)	PUNCT
ejpam-1224	785	31	is	be	AUX
ejpam-1224	785	32	a	a	DET
ejpam-1224	785	33	quasi	quasi	NOUN
ejpam-1224	785	34	-	-	NOUN
ejpam-1224	785	35	isomorphism	isomorphism	NOUN
ejpam-1224	785	36	.	.	PUNCT
ejpam-1224	786	1	by	by	ADP
ejpam-1224	786	2	lemma	lemma	PROPN
ejpam-1224	786	3	7	7	NUM
ejpam-1224	786	4	we	we	PRON
ejpam-1224	786	5	know	know	VERB
ejpam-1224	786	6	lim	lim	PROPN
ejpam-1224	786	7	←−	←−	PROPN
ejpam-1224	786	8	σ≤pn	σ≤pn	PROPN
ejpam-1224	786	9	=	=	SYM
ejpam-1224	786	10	lim	lim	PROPN
ejpam-1224	786	11	←−	←−	PUNCT
ejpam-1224	786	12	gf(σ≤pn	gf(σ≤pn	PROPN
ejpam-1224	786	13	)	)	PUNCT
ejpam-1224	786	14	and	and	CCONJ
ejpam-1224	786	15	we	we	PRON
ejpam-1224	786	16	also	also	ADV
ejpam-1224	786	17	know	know	VERB
ejpam-1224	786	18	that	that	SCONJ
ejpam-1224	786	19	lim	lim	PROPN
ejpam-1224	786	20	←−	←−	PUNCT
ejpam-1224	786	21	gf(σ≤pn	gf(σ≤pn	PROPN
ejpam-1224	786	22	)	)	PUNCT
ejpam-1224	786	23	=	=	SYM
ejpam-1224	786	24	g	g	PROPN
ejpam-1224	786	25	lim	lim	PROPN
ejpam-1224	786	26	←−	←−	PROPN
ejpam-1224	786	27	f(σ≤pn	f(σ≤pn	PROPN
ejpam-1224	786	28	)	)	PUNCT
ejpam-1224	786	29	since	since	SCONJ
ejpam-1224	786	30	g	g	PROPN
ejpam-1224	786	31	is	be	AUX
ejpam-1224	786	32	a	a	DET
ejpam-1224	786	33	right	right	ADJ
ejpam-1224	786	34	adjoint	adjoint	NOUN
ejpam-1224	786	35	.	.	PUNCT
ejpam-1224	787	1	it	it	PRON
ejpam-1224	787	2	remains	remain	VERB
ejpam-1224	787	3	to	to	PART
ejpam-1224	787	4	show	show	VERB
ejpam-1224	787	5	that	that	SCONJ
ejpam-1224	787	6	f	f	PROPN
ejpam-1224	787	7	can	can	AUX
ejpam-1224	787	8	commute	commute	VERB
ejpam-1224	787	9	with	with	ADP
ejpam-1224	787	10	inverse	inverse	NOUN
ejpam-1224	787	11	limit	limit	NOUN
ejpam-1224	787	12	.	.	PUNCT
ejpam-1224	788	1	we	we	PRON
ejpam-1224	788	2	know	know	VERB
ejpam-1224	788	3	that	that	PRON
ejpam-1224	788	4	f(n)i	f(n)i	NOUN
ejpam-1224	788	5	=	=	SYM
ejpam-1224	788	6	u	u	NOUN
ejpam-1224	788	7	⊗	⊗	PROPN
ejpam-1224	789	1	n	n	PROPN
ejpam-1224	789	2	i	i	PRON
ejpam-1224	789	3	by	by	ADP
ejpam-1224	789	4	definition	definition	NOUN
ejpam-1224	790	1	and	and	CCONJ
ejpam-1224	790	2	we	we	PRON
ejpam-1224	790	3	know	know	VERB
ejpam-1224	790	4	that	that	SCONJ
ejpam-1224	790	5	for	for	ADP
ejpam-1224	790	6	a	a	DET
ejpam-1224	790	7	fixed	fix	VERB
ejpam-1224	790	8	i	i	PROPN
ejpam-1224	790	9	and	and	CCONJ
ejpam-1224	790	10	for	for	ADP
ejpam-1224	790	11	p→∞	p→∞	ADV
ejpam-1224	790	12	we	we	PRON
ejpam-1224	790	13	have	have	VERB
ejpam-1224	790	14	lim	lim	PROPN
ejpam-1224	790	15	←−	←−	PROPN
ejpam-1224	790	16	f(σ≤pn)i	f(σ≤pn)i	PROPN
ejpam-1224	790	17	=	=	SYM
ejpam-1224	790	18	lim	lim	PROPN
ejpam-1224	790	19	←−	←−	PROPN
ejpam-1224	790	20	u	u	PROPN
ejpam-1224	790	21	⊗	⊗	PROPN
ejpam-1224	790	22	(	(	PUNCT
ejpam-1224	790	23	σ≤pn)i	σ≤pn)i	PROPN
ejpam-1224	790	24	and	and	CCONJ
ejpam-1224	790	25	since	since	SCONJ
ejpam-1224	790	26	p	p	PRON
ejpam-1224	790	27	will	will	AUX
ejpam-1224	790	28	become	become	VERB
ejpam-1224	790	29	greater	great	ADJ
ejpam-1224	790	30	that	that	SCONJ
ejpam-1224	790	31	i	i	PRON
ejpam-1224	790	32	after	after	ADP
ejpam-1224	790	33	finitely	finitely	ADV
ejpam-1224	790	34	many	many	ADJ
ejpam-1224	790	35	steps	step	NOUN
ejpam-1224	790	36	,	,	PUNCT
ejpam-1224	790	37	both	both	DET
ejpam-1224	790	38	sides	side	NOUN
ejpam-1224	790	39	will	will	AUX
ejpam-1224	790	40	equal	equal	VERB
ejpam-1224	790	41	u	u	PRON
ejpam-1224	790	42	⊗	⊗	PROPN
ejpam-1224	790	43	n	n	CCONJ
ejpam-1224	791	1	i	i	PRON
ejpam-1224	791	2	showing	show	VERB
ejpam-1224	791	3	our	our	PRON
ejpam-1224	791	4	intended	intend	VERB
ejpam-1224	791	5	equality	equality	NOUN
ejpam-1224	791	6	and	and	CCONJ
ejpam-1224	791	7	thus	thus	ADV
ejpam-1224	791	8	proving	prove	VERB
ejpam-1224	791	9	that	that	SCONJ
ejpam-1224	791	10	for	for	ADP
ejpam-1224	791	11	arbitrary	arbitrary	ADJ
ejpam-1224	791	12	n	n	NOUN
ejpam-1224	791	13	,	,	PUNCT
ejpam-1224	791	14	n	n	CCONJ
ejpam-1224	791	15	→	→	PUNCT
ejpam-1224	791	16	gf(n	gf(n	X
ejpam-1224	791	17	)	)	PUNCT
ejpam-1224	791	18	is	be	AUX
ejpam-1224	791	19	a	a	DET
ejpam-1224	791	20	quasiisomorphism	quasiisomorphism	NOUN
ejpam-1224	791	21	.	.	PUNCT
ejpam-1224	792	1	proposition	proposition	NOUN
ejpam-1224	792	2	5	5	NUM
ejpam-1224	792	3	.	.	PUNCT
ejpam-1224	793	1	let	let	VERB
ejpam-1224	793	2	k∗p	k∗p	PRON
ejpam-1224	793	3	be	be	AUX
ejpam-1224	793	4	a	a	DET
ejpam-1224	793	5	projective	projective	ADJ
ejpam-1224	793	6	system	system	NOUN
ejpam-1224	793	7	of	of	ADP
ejpam-1224	793	8	complexes	complex	NOUN
ejpam-1224	793	9	of	of	ADP
ejpam-1224	793	10	modules	module	NOUN
ejpam-1224	793	11	over	over	ADP
ejpam-1224	793	12	a	a	DET
ejpam-1224	793	13	ring	ring	NOUN
ejpam-1224	793	14	r	r	NOUN
ejpam-1224	793	15	:	:	PUNCT
ejpam-1224	793	16	.	.	PUNCT
ejpam-1224	793	17	.	.	PUNCT
ejpam-1224	794	1	.→	.→	PUNCT
ejpam-1224	795	1	k∗p+1→	k∗p+1→	PROPN
ejpam-1224	795	2	k∗p	k∗p	PROPN
ejpam-1224	795	3	→	→	PUNCT
ejpam-1224	795	4	.	.	PUNCT
ejpam-1224	795	5	.	.	PUNCT
ejpam-1224	796	1	..	..	PUNCT
ejpam-1224	796	2	suppose	suppose	VERB
ejpam-1224	796	3	that	that	SCONJ
ejpam-1224	796	4	k∗p	k∗p	PROPN
ejpam-1224	796	5	satisfies	satisfy	VERB
ejpam-1224	796	6	the	the	DET
ejpam-1224	796	7	mittag	mittag	ADJ
ejpam-1224	796	8	-	-	PUNCT
ejpam-1224	796	9	leffler	leffler	NOUN
ejpam-1224	796	10	condition	condition	NOUN
ejpam-1224	796	11	(	(	PUNCT
ejpam-1224	796	12	ml	ml	NOUN
ejpam-1224	796	13	)	)	PUNCT
ejpam-1224	796	14	and	and	CCONJ
ejpam-1224	796	15	that	that	SCONJ
ejpam-1224	796	16	each	each	DET
ejpam-1224	796	17	ha(k∗p	ha(k∗p	NOUN
ejpam-1224	796	18	)	)	PUNCT
ejpam-1224	796	19	satisfies	satisfy	VERB
ejpam-1224	796	20	the	the	DET
ejpam-1224	796	21	ml	ml	NOUN
ejpam-1224	796	22	condition	condition	NOUN
ejpam-1224	796	23	,	,	PUNCT
ejpam-1224	796	24	for	for	ADP
ejpam-1224	796	25	instance	instance	NOUN
ejpam-1224	796	26	if	if	SCONJ
ejpam-1224	796	27	it	it	PRON
ejpam-1224	796	28	satisfies	satisfy	VERB
ejpam-1224	796	29	the	the	DET
ejpam-1224	796	30	descending	descend	VERB
ejpam-1224	796	31	chain	chain	NOUN
ejpam-1224	796	32	condition	condition	NOUN
ejpam-1224	796	33	(	(	PUNCT
ejpam-1224	796	34	dcc	dcc	PROPN
ejpam-1224	796	35	)	)	PUNCT
ejpam-1224	796	36	,	,	PUNCT
ejpam-1224	796	37	(	(	PUNCT
ejpam-1224	796	38	eg	eg	NOUN
ejpam-1224	796	39	.	.	PUNCT
ejpam-1224	796	40	,	,	PUNCT
ejpam-1224	796	41	if	if	SCONJ
ejpam-1224	796	42	each	each	PRON
ejpam-1224	796	43	is	be	AUX
ejpam-1224	796	44	a	a	DET
ejpam-1224	796	45	finite	finite	ADJ
ejpam-1224	796	46	dimensional	dimensional	ADJ
ejpam-1224	796	47	vector	vector	NOUN
ejpam-1224	796	48	space	space	NOUN
ejpam-1224	796	49	over	over	ADP
ejpam-1224	796	50	the	the	DET
ejpam-1224	796	51	field	field	NOUN
ejpam-1224	796	52	r=	r=	ADJ
ejpam-1224	796	53	k	k	NOUN
ejpam-1224	796	54	)	)	PUNCT
ejpam-1224	796	55	.	.	PUNCT
ejpam-1224	797	1	then	then	ADV
ejpam-1224	797	2	(	(	PUNCT
ejpam-1224	797	3	lim	lim	PROPN
ejpam-1224	797	4	←−	←−	PROPN
ejpam-1224	797	5	p	p	PROPN
ejpam-1224	797	6	)	)	PUNCT
ejpam-1224	797	7	ha(k∗p	ha(k∗p	NUM
ejpam-1224	797	8	)	)	PUNCT
ejpam-1224	797	9	=	=	PUNCT
ejpam-1224	798	1	ha(lim	ha(lim	PROPN
ejpam-1224	798	2	←−	←−	PROPN
ejpam-1224	798	3	p	p	PROPN
ejpam-1224	798	4	k∗p	k∗p	PROPN
ejpam-1224	798	5	)	)	PUNCT
ejpam-1224	798	6	.	.	PUNCT
ejpam-1224	799	1	f.	f.	PROPN
ejpam-1224	799	2	hawwa	hawwa	PROPN
ejpam-1224	799	3	,	,	PUNCT
ejpam-1224	799	4	j.	j.	PROPN
ejpam-1224	799	5	hoffman	hoffman	PROPN
ejpam-1224	799	6	,	,	PUNCT
ejpam-1224	799	7	and	and	CCONJ
ejpam-1224	799	8	h.	h.	PROPN
ejpam-1224	799	9	wang	wang	PROPN
ejpam-1224	799	10	,	,	PUNCT
ejpam-1224	799	11	/	/	SYM
ejpam-1224	799	12	eur	eur	NOUN
ejpam-1224	799	13	.	.	PUNCT
ejpam-1224	800	1	j.	j.	PROPN
ejpam-1224	800	2	pure	pure	PROPN
ejpam-1224	800	3	appl	appl	PROPN
ejpam-1224	800	4	.	.	PROPN
ejpam-1224	800	5	math	math	PROPN
ejpam-1224	800	6	,	,	PUNCT
ejpam-1224	800	7	5	5	NUM
ejpam-1224	800	8	(	(	PUNCT
ejpam-1224	800	9	2012	2012	NUM
ejpam-1224	800	10	)	)	PUNCT
ejpam-1224	800	11	,	,	PUNCT
ejpam-1224	800	12	511	511	NUM
ejpam-1224	800	13	-	-	SYM
ejpam-1224	800	14	539	539	NUM
ejpam-1224	800	15	535	535	NUM
ejpam-1224	800	16	lemma	lemma	PROPN
ejpam-1224	800	17	6	6	NUM
ejpam-1224	800	18	.	.	PUNCT
ejpam-1224	801	1	for	for	ADP
ejpam-1224	801	2	all	all	DET
ejpam-1224	801	3	sufficiently	sufficiently	ADV
ejpam-1224	801	4	large	large	ADJ
ejpam-1224	801	5	i	i	PROPN
ejpam-1224	801	6	,	,	PUNCT
ejpam-1224	801	7	the	the	DET
ejpam-1224	801	8	projective	projective	ADJ
ejpam-1224	801	9	systems	system	NOUN
ejpam-1224	801	10	p→	p→	VERB
ejpam-1224	801	11	fig(σ	fig(σ	NOUN
ejpam-1224	801	12	≤pm	≤pm	NOUN
ejpam-1224	801	13	)	)	PUNCT
ejpam-1224	801	14	and	and	CCONJ
ejpam-1224	801	15	p→	p→	VERB
ejpam-1224	801	16	ha(fig(σ	ha(fig(σ	NOUN
ejpam-1224	801	17	≤p	≤p	PROPN
ejpam-1224	801	18	m	m	PROPN
ejpam-1224	801	19	)	)	PUNCT
ejpam-1224	801	20	)	)	PUNCT
ejpam-1224	801	21	satisfy	satisfy	VERB
ejpam-1224	801	22	the	the	DET
ejpam-1224	801	23	ml	ml	NOUN
ejpam-1224	801	24	condition	condition	NOUN
ejpam-1224	801	25	when	when	SCONJ
ejpam-1224	801	26	m	m	PROPN
ejpam-1224	801	27	is	be	AUX
ejpam-1224	801	28	bounded	bound	VERB
ejpam-1224	801	29	below	below	ADV
ejpam-1224	801	30	,	,	PUNCT
ejpam-1224	801	31	therefore	therefore	ADV
ejpam-1224	801	32	lim	lim	PROPN
ejpam-1224	801	33	←−	←−	PROPN
ejpam-1224	801	34	p	p	NOUN
ejpam-1224	801	35	ha(fig(σ	ha(fig(σ	NOUN
ejpam-1224	801	36	≤pm	≤pm	NOUN
ejpam-1224	801	37	)	)	PUNCT
ejpam-1224	801	38	)	)	PUNCT
ejpam-1224	802	1	=	=	SYM
ejpam-1224	802	2	ha(fig(m	ha(fig(m	ADJ
ejpam-1224	802	3	)	)	PUNCT
ejpam-1224	802	4	)	)	PUNCT
ejpam-1224	803	1	=	=	PUNCT
ejpam-1224	803	2	ha(lim	ha(lim	PROPN
ejpam-1224	803	3	←−	←−	PROPN
ejpam-1224	803	4	p	p	NOUN
ejpam-1224	803	5	fig(σ	fig(σ	ADJ
ejpam-1224	803	6	≤p	≤p	NOUN
ejpam-1224	803	7	m	m	NOUN
ejpam-1224	803	8	)	)	PUNCT
ejpam-1224	803	9	)	)	PUNCT
ejpam-1224	803	10	.	.	PUNCT
ejpam-1224	804	1	proof	proof	NOUN
ejpam-1224	804	2	.	.	PUNCT
ejpam-1224	805	1	since	since	SCONJ
ejpam-1224	805	2	m	m	PROPN
ejpam-1224	805	3	is	be	AUX
ejpam-1224	805	4	bounded	bound	VERB
ejpam-1224	805	5	below	below	ADV
ejpam-1224	805	6	we	we	PRON
ejpam-1224	805	7	know	know	VERB
ejpam-1224	805	8	that	that	SCONJ
ejpam-1224	805	9	σ≤p	σ≤p	NOUN
ejpam-1224	805	10	m	m	VERB
ejpam-1224	805	11	is	be	AUX
ejpam-1224	805	12	a	a	DET
ejpam-1224	805	13	bounded	bounded	ADJ
ejpam-1224	805	14	complex	complex	NOUN
ejpam-1224	805	15	.	.	PUNCT
ejpam-1224	806	1	by	by	ADP
ejpam-1224	806	2	choosing	choose	VERB
ejpam-1224	806	3	i	i	PRON
ejpam-1224	806	4	large	large	ADJ
ejpam-1224	806	5	enough	enough	ADV
ejpam-1224	806	6	we	we	PRON
ejpam-1224	806	7	know	know	VERB
ejpam-1224	806	8	that	that	SCONJ
ejpam-1224	806	9	fig(σ	fig(σ	ADJ
ejpam-1224	806	10	≤p)m	≤p)m	NOUN
ejpam-1224	806	11	→	→	SYM
ejpam-1224	806	12	σ≤p	σ≤p	NOUN
ejpam-1224	806	13	m	m	NOUN
ejpam-1224	806	14	is	be	AUX
ejpam-1224	806	15	a	a	DET
ejpam-1224	806	16	quasi	quasi	NOUN
ejpam-1224	806	17	-	-	NOUN
ejpam-1224	806	18	isomorphism	isomorphism	NOUN
ejpam-1224	806	19	.	.	PUNCT
ejpam-1224	807	1	note	note	VERB
ejpam-1224	807	2	that	that	SCONJ
ejpam-1224	807	3	the	the	DET
ejpam-1224	807	4	i	i	PROPN
ejpam-1224	807	5	that	that	PRON
ejpam-1224	807	6	works	work	VERB
ejpam-1224	807	7	depends	depend	VERB
ejpam-1224	807	8	only	only	ADV
ejpam-1224	807	9	on	on	ADP
ejpam-1224	807	10	the	the	DET
ejpam-1224	807	11	lower	low	ADJ
ejpam-1224	807	12	bound	bind	VERB
ejpam-1224	807	13	of	of	ADP
ejpam-1224	807	14	the	the	DET
ejpam-1224	807	15	complex	complex	ADJ
ejpam-1224	807	16	σ≤pm	σ≤pm	NOUN
ejpam-1224	807	17	and	and	CCONJ
ejpam-1224	807	18	this	this	PRON
ejpam-1224	807	19	is	be	AUX
ejpam-1224	807	20	the	the	DET
ejpam-1224	807	21	same	same	ADJ
ejpam-1224	807	22	for	for	ADP
ejpam-1224	807	23	all	all	DET
ejpam-1224	807	24	p	p	NOUN
ejpam-1224	807	25	,	,	PUNCT
ejpam-1224	807	26	so	so	ADV
ejpam-1224	807	27	let	let	VERB
ejpam-1224	807	28	us	we	PRON
ejpam-1224	807	29	fix	fix	VERB
ejpam-1224	807	30	an	an	DET
ejpam-1224	807	31	i.	i.	NOUN
ejpam-1224	807	32	thus	thus	ADV
ejpam-1224	807	33	p→	p→	VERB
ejpam-1224	807	34	ha(fig(σ	ha(fig(σ	NOUN
ejpam-1224	807	35	≤pm	≤pm	NOUN
ejpam-1224	807	36	)	)	PUNCT
ejpam-1224	807	37	)	)	PUNCT
ejpam-1224	807	38	is	be	AUX
ejpam-1224	807	39	ml	ml	NOUN
ejpam-1224	807	40	since	since	SCONJ
ejpam-1224	807	41	for	for	ADP
ejpam-1224	807	42	large	large	ADJ
ejpam-1224	807	43	p	p	NOUN
ejpam-1224	807	44	(	(	PUNCT
ejpam-1224	807	45	in	in	ADP
ejpam-1224	807	46	fact	fact	NOUN
ejpam-1224	807	47	p	p	X
ejpam-1224	807	48	>	>	X
ejpam-1224	807	49	a	a	PROPN
ejpam-1224	807	50	)	)	PUNCT
ejpam-1224	807	51	,	,	PUNCT
ejpam-1224	807	52	these	these	DET
ejpam-1224	807	53	values	value	NOUN
ejpam-1224	807	54	are	be	AUX
ejpam-1224	807	55	constant	constant	ADJ
ejpam-1224	807	56	and	and	CCONJ
ejpam-1224	807	57	equal	equal	ADJ
ejpam-1224	807	58	to	to	ADP
ejpam-1224	807	59	ha(m	ha(m	NUM
ejpam-1224	807	60	)	)	PUNCT
ejpam-1224	807	61	.	.	PUNCT
ejpam-1224	808	1	for	for	SCONJ
ejpam-1224	808	2	fig(σ	fig(σ	ADJ
ejpam-1224	808	3	≤p)m	≤p)m	NOUN
ejpam-1224	808	4	note	note	VERB
ejpam-1224	808	5	that	that	SCONJ
ejpam-1224	808	6	in	in	ADP
ejpam-1224	808	7	any	any	DET
ejpam-1224	808	8	degree	degree	NOUN
ejpam-1224	808	9	,	,	PUNCT
ejpam-1224	808	10	the	the	DET
ejpam-1224	808	11	transition	transition	NOUN
ejpam-1224	808	12	maps	map	NOUN
ejpam-1224	808	13	fi	fi	NOUN
ejpam-1224	808	14	g(σ	g(σ	PROPN
ejpam-1224	808	15	≤p+1	≤p+1	NOUN
ejpam-1224	808	16	m	m	NOUN
ejpam-1224	808	17	)	)	PUNCT
ejpam-1224	808	18	j	j	PROPN
ejpam-1224	809	1	=	=	X
ejpam-1224	809	2	ui+	ui+	PROPN
ejpam-1224	809	3	j	j	PROPN
ejpam-1224	809	4	⊗	⊗	PROPN
ejpam-1224	809	5	p+1−	p+1−	PROPN
ejpam-1224	809	6	j∏	j∏	PROPN
ejpam-1224	809	7	r=0	r=0	PROPN
ejpam-1224	809	8	hom((a!)r	hom((a!)r	PROPN
ejpam-1224	809	9	,	,	PUNCT
ejpam-1224	809	10	m	m	PROPN
ejpam-1224	809	11	j+r	j+r	NUM
ejpam-1224	809	12	)	)	PUNCT
ejpam-1224	810	1	→	→	SYM
ejpam-1224	810	2	fig(σ	fig(σ	ADJ
ejpam-1224	810	3	≤p	≤p	NOUN
ejpam-1224	810	4	m	m	NOUN
ejpam-1224	810	5	)	)	PUNCT
ejpam-1224	810	6	j	j	PROPN
ejpam-1224	810	7	induced	induce	VERB
ejpam-1224	810	8	by	by	ADP
ejpam-1224	810	9	the	the	DET
ejpam-1224	810	10	natural	natural	ADJ
ejpam-1224	810	11	projection	projection	NOUN
ejpam-1224	810	12	p+1−	p+1−	PROPN
ejpam-1224	810	13	j∏	j∏	PROPN
ejpam-1224	810	14	r=0	r=0	PROPN
ejpam-1224	810	15	hom((a!)r	hom((a!)r	PROPN
ejpam-1224	810	16	,	,	PUNCT
ejpam-1224	810	17	m	m	PROPN
ejpam-1224	810	18	j+r	j+r	NUM
ejpam-1224	810	19	)	)	PUNCT
ejpam-1224	811	1	→	→	SYM
ejpam-1224	811	2	p−	p−	X
ejpam-1224	811	3	j∏	j∏	PROPN
ejpam-1224	811	4	r=0	r=0	PROPN
ejpam-1224	811	5	hom((a!)r	hom((a!)r	PROPN
ejpam-1224	811	6	,	,	PUNCT
ejpam-1224	811	7	m	m	PROPN
ejpam-1224	811	8	j+r	j+r	X
ejpam-1224	811	9	)	)	PUNCT
ejpam-1224	811	10	are	be	AUX
ejpam-1224	811	11	surjective	surjective	ADJ
ejpam-1224	811	12	,	,	PUNCT
ejpam-1224	811	13	hence	hence	ADV
ejpam-1224	811	14	we	we	PRON
ejpam-1224	811	15	have	have	VERB
ejpam-1224	811	16	the	the	DET
ejpam-1224	811	17	ml	ml	NOUN
ejpam-1224	811	18	condition	condition	NOUN
ejpam-1224	811	19	satisfied	satisfied	ADJ
ejpam-1224	811	20	.	.	PUNCT
ejpam-1224	812	1	lemma	lemma	PROPN
ejpam-1224	812	2	7	7	NUM
ejpam-1224	812	3	.	.	PUNCT
ejpam-1224	813	1	for	for	ADP
ejpam-1224	813	2	all	all	DET
ejpam-1224	813	3	sufficiently	sufficiently	ADV
ejpam-1224	813	4	large	large	ADJ
ejpam-1224	813	5	i	i	PROPN
ejpam-1224	813	6	,	,	PUNCT
ejpam-1224	813	7	the	the	DET
ejpam-1224	813	8	projective	projective	PROPN
ejpam-1224	813	9	systems	system	NOUN
ejpam-1224	813	10	p→	p→	VERB
ejpam-1224	813	11	gf(σ≤pn	gf(σ≤pn	PROPN
ejpam-1224	813	12	)	)	PUNCT
ejpam-1224	813	13	and	and	CCONJ
ejpam-1224	813	14	p→	p→	VERB
ejpam-1224	813	15	ha(gf(σ≤pn	ha(gf(σ≤pn	PROPN
ejpam-1224	813	16	)	)	PUNCT
ejpam-1224	813	17	)	)	PUNCT
ejpam-1224	813	18	satisfy	satisfy	VERB
ejpam-1224	813	19	the	the	DET
ejpam-1224	813	20	ml	ml	NOUN
ejpam-1224	813	21	condition	condition	NOUN
ejpam-1224	813	22	for	for	ADP
ejpam-1224	813	23	any	any	DET
ejpam-1224	813	24	n	n	CCONJ
ejpam-1224	813	25	,	,	PUNCT
ejpam-1224	813	26	therefore	therefore	ADV
ejpam-1224	813	27	lim	lim	PROPN
ejpam-1224	813	28	←−	←−	PROPN
ejpam-1224	813	29	p	p	PROPN
ejpam-1224	813	30	ha(gf(σ≤pn	ha(gf(σ≤pn	PROPN
ejpam-1224	813	31	)	)	PUNCT
ejpam-1224	813	32	)	)	PUNCT
ejpam-1224	814	1	=	=	SYM
ejpam-1224	814	2	ha(gf(n	ha(gf(n	X
ejpam-1224	814	3	)	)	PUNCT
ejpam-1224	814	4	)	)	PUNCT
ejpam-1224	815	1	=	=	PUNCT
ejpam-1224	815	2	ha(lim	ha(lim	PROPN
ejpam-1224	815	3	←−	←−	PROPN
ejpam-1224	815	4	p	p	PROPN
ejpam-1224	815	5	gf(σ≤pn	gf(σ≤pn	PROPN
ejpam-1224	815	6	)	)	PUNCT
ejpam-1224	815	7	)	)	PUNCT
ejpam-1224	815	8	.	.	PUNCT
ejpam-1224	816	1	proof	proof	NOUN
ejpam-1224	816	2	.	.	PUNCT
ejpam-1224	817	1	the	the	DET
ejpam-1224	817	2	second	second	NOUN
ejpam-1224	817	3	of	of	ADP
ejpam-1224	817	4	the	the	DET
ejpam-1224	817	5	two	two	NUM
ejpam-1224	817	6	projective	projective	ADJ
ejpam-1224	817	7	systems	system	NOUN
ejpam-1224	817	8	clearly	clearly	ADV
ejpam-1224	817	9	satisfies	satisfy	VERB
ejpam-1224	817	10	the	the	DET
ejpam-1224	817	11	ml	ml	NOUN
ejpam-1224	817	12	condition	condition	NOUN
ejpam-1224	817	13	since	since	SCONJ
ejpam-1224	817	14	ha(gf(σ≤pn	ha(gf(σ≤pn	NOUN
ejpam-1224	817	15	)	)	PUNCT
ejpam-1224	817	16	)	)	PUNCT
ejpam-1224	818	1	=	=	PUNCT
ejpam-1224	818	2	ha(σ≤pn	ha(σ≤pn	NOUN
ejpam-1224	818	3	)	)	PUNCT
ejpam-1224	818	4	and	and	CCONJ
ejpam-1224	818	5	since	since	SCONJ
ejpam-1224	818	6	each	each	DET
ejpam-1224	818	7	σ≤pn	σ≤pn	NOUN
ejpam-1224	818	8	is	be	AUX
ejpam-1224	818	9	bounded	bound	VERB
ejpam-1224	818	10	above	above	ADV
ejpam-1224	818	11	,	,	PUNCT
ejpam-1224	818	12	and	and	CCONJ
ejpam-1224	818	13	since	since	SCONJ
ejpam-1224	818	14	for	for	ADP
ejpam-1224	818	15	all	all	PRON
ejpam-1224	818	16	i	i	PRON
ejpam-1224	818	17	the	the	DET
ejpam-1224	818	18	projective	projective	ADJ
ejpam-1224	818	19	system	system	NOUN
ejpam-1224	818	20	is	be	AUX
ejpam-1224	818	21	constant	constant	ADJ
ejpam-1224	818	22	for	for	ADP
ejpam-1224	818	23	large	large	ADJ
ejpam-1224	818	24	values	value	NOUN
ejpam-1224	818	25	of	of	ADP
ejpam-1224	818	26	p	p	NOUN
ejpam-1224	818	27	and	and	CCONJ
ejpam-1224	818	28	it	it	PRON
ejpam-1224	818	29	equals	equal	VERB
ejpam-1224	818	30	ha(n	ha(n	NOUN
ejpam-1224	818	31	)	)	PUNCT
ejpam-1224	818	32	.	.	PUNCT
ejpam-1224	819	1	now	now	ADV
ejpam-1224	819	2	to	to	PART
ejpam-1224	819	3	show	show	VERB
ejpam-1224	819	4	that	that	SCONJ
ejpam-1224	819	5	the	the	DET
ejpam-1224	819	6	first	first	ADJ
ejpam-1224	819	7	system	system	NOUN
ejpam-1224	819	8	satisfies	satisfy	VERB
ejpam-1224	819	9	the	the	DET
ejpam-1224	819	10	ml	ml	NOUN
ejpam-1224	819	11	condition	condition	NOUN
ejpam-1224	819	12	observe	observe	VERB
ejpam-1224	819	13	that	that	SCONJ
ejpam-1224	819	14	(	(	PUNCT
ejpam-1224	819	15	gfσ≤pn	gfσ≤pn	PROPN
ejpam-1224	819	16	)	)	PUNCT
ejpam-1224	819	17	j	j	PROPN
ejpam-1224	819	18	=	=	SYM
ejpam-1224	819	19	∏	∏	PROPN
ejpam-1224	819	20	r≥0	r≥0	PROPN
ejpam-1224	819	21	hom((a!)r	hom((a!)r	PROPN
ejpam-1224	819	22	,	,	PUNCT
ejpam-1224	819	23	u	u	PROPN
ejpam-1224	819	24	⊗	⊗	PROPN
ejpam-1224	819	25	(	(	PUNCT
ejpam-1224	819	26	σ≤pn	σ≤pn	X
ejpam-1224	819	27	)	)	PUNCT
ejpam-1224	819	28	j+r	j+r	NUM
ejpam-1224	819	29	)	)	PUNCT
ejpam-1224	819	30	and	and	CCONJ
ejpam-1224	819	31	since	since	SCONJ
ejpam-1224	819	32	σ≤pn	σ≤pn	NOUN
ejpam-1224	819	33	equals	equal	VERB
ejpam-1224	819	34	n	n	PRON
ejpam-1224	819	35	j+r	j+r	NUM
ejpam-1224	819	36	when	when	SCONJ
ejpam-1224	819	37	j+	j+	NUM
ejpam-1224	819	38	r	r	NOUN
ejpam-1224	819	39	≤	≤	ADJ
ejpam-1224	819	40	p	p	NOUN
ejpam-1224	819	41	and	and	CCONJ
ejpam-1224	819	42	zero	zero	NUM
ejpam-1224	819	43	otherwise	otherwise	ADV
ejpam-1224	819	44	we	we	PRON
ejpam-1224	819	45	have	have	VERB
ejpam-1224	819	46	(	(	PUNCT
ejpam-1224	819	47	gfσ≤pn	gfσ≤pn	PROPN
ejpam-1224	819	48	)	)	PUNCT
ejpam-1224	819	49	j	j	NOUN
ejpam-1224	820	1	=	=	PUNCT
ejpam-1224	821	1	p−	p−	PROPN
ejpam-1224	821	2	j∏	j∏	PROPN
ejpam-1224	821	3	r≥0	r≥0	PROPN
ejpam-1224	821	4	hom((a!)r	hom((a!)r	PROPN
ejpam-1224	821	5	,	,	PUNCT
ejpam-1224	821	6	u	u	NOUN
ejpam-1224	821	7	⊗	⊗	PROPN
ejpam-1224	821	8	n	n	PRON
ejpam-1224	821	9	j+r	j+r	PROPN
ejpam-1224	821	10	)	)	PUNCT
ejpam-1224	822	1	f.	f.	PROPN
ejpam-1224	822	2	hawwa	hawwa	PROPN
ejpam-1224	822	3	,	,	PUNCT
ejpam-1224	822	4	j.	j.	PROPN
ejpam-1224	822	5	hoffman	hoffman	PROPN
ejpam-1224	822	6	,	,	PUNCT
ejpam-1224	822	7	and	and	CCONJ
ejpam-1224	822	8	h.	h.	PROPN
ejpam-1224	822	9	wang	wang	PROPN
ejpam-1224	822	10	,	,	PUNCT
ejpam-1224	822	11	/	/	SYM
ejpam-1224	822	12	eur	eur	NOUN
ejpam-1224	822	13	.	.	PUNCT
ejpam-1224	823	1	j.	j.	PROPN
ejpam-1224	823	2	pure	pure	PROPN
ejpam-1224	823	3	appl	appl	PROPN
ejpam-1224	823	4	.	.	PROPN
ejpam-1224	823	5	math	math	PROPN
ejpam-1224	823	6	,	,	PUNCT
ejpam-1224	823	7	5	5	NUM
ejpam-1224	823	8	(	(	PUNCT
ejpam-1224	823	9	2012	2012	NUM
ejpam-1224	823	10	)	)	PUNCT
ejpam-1224	823	11	,	,	PUNCT
ejpam-1224	823	12	511	511	NUM
ejpam-1224	823	13	-	-	SYM
ejpam-1224	823	14	539	539	NUM
ejpam-1224	823	15	536	536	NUM
ejpam-1224	823	16	so	so	SCONJ
ejpam-1224	823	17	the	the	DET
ejpam-1224	823	18	natural	natural	ADJ
ejpam-1224	823	19	projection	projection	NOUN
ejpam-1224	823	20	p−	p−	NOUN
ejpam-1224	823	21	j∏	j∏	PROPN
ejpam-1224	823	22	r≥0	r≥0	PROPN
ejpam-1224	823	23	hom((a!)r	hom((a!)r	PROPN
ejpam-1224	823	24	,	,	PUNCT
ejpam-1224	823	25	u	u	PROPN
ejpam-1224	823	26	⊗	⊗	PROPN
ejpam-1224	823	27	n	n	PROPN
ejpam-1224	823	28	j+r)→	j+r)→	PROPN
ejpam-1224	823	29	p−	p−	NOUN
ejpam-1224	823	30	j−1∏	j−1∏	PROPN
ejpam-1224	823	31	r≥0	r≥0	PROPN
ejpam-1224	823	32	hom((a!)r	hom((a!)r	PROPN
ejpam-1224	823	33	,	,	PUNCT
ejpam-1224	823	34	u	u	NOUN
ejpam-1224	823	35	⊗n	⊗n	PROPN
ejpam-1224	823	36	j+r	j+r	X
ejpam-1224	823	37	)	)	PUNCT
ejpam-1224	823	38	is	be	AUX
ejpam-1224	823	39	clearly	clearly	ADV
ejpam-1224	823	40	surjective	surjective	ADJ
ejpam-1224	823	41	thus	thus	ADV
ejpam-1224	823	42	showing	show	VERB
ejpam-1224	823	43	that	that	SCONJ
ejpam-1224	823	44	the	the	DET
ejpam-1224	823	45	ml	ml	NOUN
ejpam-1224	823	46	condition	condition	NOUN
ejpam-1224	823	47	is	be	AUX
ejpam-1224	823	48	satisfied	satisfied	ADJ
ejpam-1224	823	49	.	.	PUNCT
ejpam-1224	824	1	7	7	X
ejpam-1224	824	2	.	.	NUM
ejpam-1224	824	3	equivalences	equivalence	NOUN
ejpam-1224	824	4	of	of	ADP
ejpam-1224	824	5	categories	category	NOUN
ejpam-1224	824	6	let	let	VERB
ejpam-1224	824	7	kλ(a	kλ(a	NOUN
ejpam-1224	824	8	!	!	PUNCT
ejpam-1224	824	9	,	,	PUNCT
ejpam-1224	825	1	d	d	X
ejpam-1224	825	2	,	,	PUNCT
ejpam-1224	825	3	c	c	AUX
ejpam-1224	825	4	)	)	PUNCT
ejpam-1224	825	5	be	be	AUX
ejpam-1224	825	6	the	the	DET
ejpam-1224	825	7	category	category	NOUN
ejpam-1224	825	8	comλ(a	comλ(a	ADV
ejpam-1224	825	9	!	!	PUNCT
ejpam-1224	825	10	,	,	PUNCT
ejpam-1224	826	1	d	d	X
ejpam-1224	826	2	,	,	PUNCT
ejpam-1224	826	3	c	c	NOUN
ejpam-1224	826	4	)	)	PUNCT
ejpam-1224	826	5	with	with	ADP
ejpam-1224	826	6	morphisms	morphism	NOUN
ejpam-1224	826	7	being	be	AUX
ejpam-1224	826	8	chain	chain	NOUN
ejpam-1224	826	9	homotopy	homotopy	NOUN
ejpam-1224	826	10	equivalence	equivalence	NOUN
ejpam-1224	826	11	classes	class	NOUN
ejpam-1224	826	12	of	of	ADP
ejpam-1224	826	13	maps	map	NOUN
ejpam-1224	826	14	.	.	PUNCT
ejpam-1224	827	1	similarly	similarly	ADV
ejpam-1224	827	2	we	we	PRON
ejpam-1224	827	3	may	may	AUX
ejpam-1224	827	4	define	define	VERB
ejpam-1224	827	5	the	the	DET
ejpam-1224	827	6	category	category	NOUN
ejpam-1224	827	7	kλ(u	kλ(u	NUM
ejpam-1224	827	8	)	)	PUNCT
ejpam-1224	827	9	.	.	PUNCT
ejpam-1224	828	1	definition	definition	NOUN
ejpam-1224	828	2	7	7	NUM
ejpam-1224	828	3	.	.	PUNCT
ejpam-1224	829	1	the	the	DET
ejpam-1224	829	2	null	null	ADJ
ejpam-1224	829	3	system	system	NOUN
ejpam-1224	829	4	,	,	PUNCT
ejpam-1224	829	5	n	n	CCONJ
ejpam-1224	829	6	,	,	PUNCT
ejpam-1224	829	7	of	of	ADP
ejpam-1224	829	8	kλ(a	kλ(a	NOUN
ejpam-1224	829	9	!	!	PUNCT
ejpam-1224	829	10	,	,	PUNCT
ejpam-1224	830	1	d	d	X
ejpam-1224	830	2	,	,	PUNCT
ejpam-1224	830	3	c	c	X
ejpam-1224	830	4	)	)	PUNCT
ejpam-1224	830	5	is	be	AUX
ejpam-1224	830	6	defined	define	VERB
ejpam-1224	830	7	to	to	PART
ejpam-1224	830	8	be	be	AUX
ejpam-1224	830	9	all	all	PRON
ejpam-1224	830	10	of	of	ADP
ejpam-1224	830	11	the	the	DET
ejpam-1224	830	12	complexes	complex	NOUN
ejpam-1224	830	13	,	,	PUNCT
ejpam-1224	830	14	x	x	INTJ
ejpam-1224	830	15	,	,	PUNCT
ejpam-1224	830	16	such	such	ADJ
ejpam-1224	830	17	that	that	SCONJ
ejpam-1224	830	18	f(x	f(x	PROPN
ejpam-1224	830	19	)	)	PUNCT
ejpam-1224	830	20	is	be	AUX
ejpam-1224	830	21	acyclic	acyclic	ADJ
ejpam-1224	830	22	.	.	PUNCT
ejpam-1224	831	1	the	the	DET
ejpam-1224	831	2	null	null	ADJ
ejpam-1224	831	3	system	system	NOUN
ejpam-1224	831	4	,	,	PUNCT
ejpam-1224	831	5	n	n	CCONJ
ejpam-1224	831	6	,	,	PUNCT
ejpam-1224	831	7	of	of	ADP
ejpam-1224	831	8	kλ(u	kλ(u	NUM
ejpam-1224	831	9	)	)	PUNCT
ejpam-1224	831	10	is	be	AUX
ejpam-1224	831	11	defined	define	VERB
ejpam-1224	831	12	to	to	PART
ejpam-1224	831	13	be	be	AUX
ejpam-1224	831	14	all	all	PRON
ejpam-1224	831	15	of	of	ADP
ejpam-1224	831	16	the	the	DET
ejpam-1224	831	17	complexes	complex	NOUN
ejpam-1224	831	18	,	,	PUNCT
ejpam-1224	831	19	y	y	PROPN
ejpam-1224	831	20	,	,	PUNCT
ejpam-1224	831	21	such	such	ADJ
ejpam-1224	831	22	that	that	PRON
ejpam-1224	831	23	g(y	g(y	NOUN
ejpam-1224	831	24	)	)	PUNCT
ejpam-1224	831	25	is	be	AUX
ejpam-1224	831	26	acyclic	acyclic	ADJ
ejpam-1224	831	27	.	.	PUNCT
ejpam-1224	832	1	we	we	PRON
ejpam-1224	832	2	define	define	VERB
ejpam-1224	832	3	dλ(a	dλ(a	NOUN
ejpam-1224	832	4	!	!	PUNCT
ejpam-1224	832	5	,	,	PUNCT
ejpam-1224	833	1	d	d	X
ejpam-1224	833	2	,	,	PUNCT
ejpam-1224	833	3	c	c	NOUN
ejpam-1224	833	4	)	)	PUNCT
ejpam-1224	833	5	to	to	PART
ejpam-1224	833	6	be	be	AUX
ejpam-1224	833	7	the	the	DET
ejpam-1224	833	8	category	category	NOUN
ejpam-1224	833	9	kλ(a	kλ(a	X
ejpam-1224	833	10	!	!	PUNCT
ejpam-1224	833	11	,	,	PUNCT
ejpam-1224	834	1	d	d	X
ejpam-1224	834	2	,	,	PUNCT
ejpam-1224	834	3	c)/n	c)/n	PROPN
ejpam-1224	834	4	where	where	SCONJ
ejpam-1224	834	5	n	n	X
ejpam-1224	834	6	is	be	AUX
ejpam-1224	834	7	the	the	DET
ejpam-1224	834	8	null	null	ADJ
ejpam-1224	834	9	system	system	NOUN
ejpam-1224	834	10	of	of	ADP
ejpam-1224	834	11	kλ(a	kλ(a	NOUN
ejpam-1224	834	12	!	!	PUNCT
ejpam-1224	834	13	,	,	PUNCT
ejpam-1224	835	1	d	d	X
ejpam-1224	835	2	,	,	PUNCT
ejpam-1224	835	3	c	c	NOUN
ejpam-1224	835	4	)	)	PUNCT
ejpam-1224	835	5	.	.	PUNCT
ejpam-1224	836	1	we	we	PRON
ejpam-1224	836	2	also	also	ADV
ejpam-1224	836	3	define	define	VERB
ejpam-1224	836	4	dλ(u	dλ(u	NOUN
ejpam-1224	836	5	)	)	PUNCT
ejpam-1224	836	6	to	to	PART
ejpam-1224	836	7	be	be	AUX
ejpam-1224	836	8	the	the	DET
ejpam-1224	836	9	category	category	NOUN
ejpam-1224	836	10	kλ(u)/n	kλ(u)/n	VERB
ejpam-1224	836	11	where	where	SCONJ
ejpam-1224	836	12	n	n	PRON
ejpam-1224	836	13	is	be	AUX
ejpam-1224	836	14	the	the	DET
ejpam-1224	836	15	null	null	ADJ
ejpam-1224	836	16	system	system	NOUN
ejpam-1224	836	17	of	of	ADP
ejpam-1224	836	18	kλ(u	kλ(u	NOUN
ejpam-1224	836	19	)	)	PUNCT
ejpam-1224	836	20	.	.	PUNCT
ejpam-1224	837	1	theorem	theorem	ADJ
ejpam-1224	837	2	3	3	NUM
ejpam-1224	837	3	(	(	PUNCT
ejpam-1224	837	4	the	the	DET
ejpam-1224	837	5	main	main	ADJ
ejpam-1224	837	6	result	result	NOUN
ejpam-1224	837	7	)	)	PUNCT
ejpam-1224	837	8	.	.	PUNCT
ejpam-1224	838	1	the	the	DET
ejpam-1224	838	2	adjunction	adjunction	NOUN
ejpam-1224	838	3	f	f	PROPN
ejpam-1224	838	4	and	and	CCONJ
ejpam-1224	838	5	g	g	PROPN
ejpam-1224	838	6	given	give	VERB
ejpam-1224	838	7	in	in	ADP
ejpam-1224	838	8	proposition	proposition	NOUN
ejpam-1224	838	9	3	3	NUM
ejpam-1224	838	10	induces	induce	VERB
ejpam-1224	838	11	an	an	DET
ejpam-1224	838	12	equivalence	equivalence	NOUN
ejpam-1224	838	13	of	of	ADP
ejpam-1224	838	14	categories	category	NOUN
ejpam-1224	838	15	between	between	ADP
ejpam-1224	838	16	the	the	DET
ejpam-1224	838	17	quotient	quotient	NOUN
ejpam-1224	838	18	categories	category	NOUN
ejpam-1224	838	19	dλ(a	dλ(a	PRON
ejpam-1224	838	20	!	!	PUNCT
ejpam-1224	838	21	,	,	PUNCT
ejpam-1224	839	1	d	d	X
ejpam-1224	839	2	,	,	PUNCT
ejpam-1224	839	3	c	c	NOUN
ejpam-1224	839	4	)	)	PUNCT
ejpam-1224	839	5	and	and	CCONJ
ejpam-1224	839	6	dλ(u	dλ(u	NUM
ejpam-1224	839	7	)	)	PUNCT
ejpam-1224	839	8	.	.	PUNCT
ejpam-1224	840	1	proof	proof	NOUN
ejpam-1224	840	2	.	.	PUNCT
ejpam-1224	841	1	the	the	DET
ejpam-1224	841	2	proof	proof	NOUN
ejpam-1224	841	3	of	of	ADP
ejpam-1224	841	4	this	this	PRON
ejpam-1224	841	5	is	be	AUX
ejpam-1224	841	6	exactly	exactly	ADV
ejpam-1224	841	7	the	the	DET
ejpam-1224	841	8	same	same	ADJ
ejpam-1224	841	9	as	as	ADP
ejpam-1224	841	10	in	in	ADP
ejpam-1224	841	11	[	[	X
ejpam-1224	841	12	3	3	NUM
ejpam-1224	841	13	]	]	PUNCT
ejpam-1224	841	14	.	.	PUNCT
ejpam-1224	842	1	8	8	X
ejpam-1224	842	2	.	.	X
ejpam-1224	842	3	relating	relate	VERB
ejpam-1224	842	4	floystad	floystad	NOUN
ejpam-1224	842	5	’s	’s	PART
ejpam-1224	842	6	duality	duality	NOUN
ejpam-1224	842	7	to	to	ADP
ejpam-1224	842	8	the	the	DET
ejpam-1224	842	9	classical	classical	ADJ
ejpam-1224	842	10	koszul	koszul	ADJ
ejpam-1224	842	11	duality	duality	NOUN
ejpam-1224	842	12	classical	classical	ADJ
ejpam-1224	842	13	koszul	koszul	ADJ
ejpam-1224	842	14	duality	duality	NOUN
ejpam-1224	842	15	concerns	concern	VERB
ejpam-1224	842	16	the	the	DET
ejpam-1224	842	17	pair	pair	NOUN
ejpam-1224	842	18	of	of	ADP
ejpam-1224	842	19	positively	positively	ADV
ejpam-1224	842	20	graded	grade	VERB
ejpam-1224	842	21	algebras	algebras	PROPN
ejpam-1224	842	22	a	a	PRON
ejpam-1224	842	23	and	and	CCONJ
ejpam-1224	842	24	a	a	PRON
ejpam-1224	842	25	!	!	PUNCT
ejpam-1224	842	26	.	.	PUNCT
ejpam-1224	843	1	floystad	floystad	PROPN
ejpam-1224	843	2	’s	’s	PART
ejpam-1224	843	3	version	version	NOUN
ejpam-1224	843	4	of	of	ADP
ejpam-1224	843	5	koszul	koszul	ADJ
ejpam-1224	843	6	duality	duality	NOUN
ejpam-1224	843	7	considers	consider	VERB
ejpam-1224	843	8	the	the	DET
ejpam-1224	843	9	case	case	NOUN
ejpam-1224	843	10	where	where	SCONJ
ejpam-1224	843	11	u	u	NOUN
ejpam-1224	843	12	=	=	NOUN
ejpam-1224	843	13	a	a	PRON
ejpam-1224	843	14	for	for	ADP
ejpam-1224	843	15	a	a	DET
ejpam-1224	843	16	filtered	filter	VERB
ejpam-1224	843	17	algebra	algebra	NOUN
ejpam-1224	843	18	u	u	NOUN
ejpam-1224	843	19	,	,	PUNCT
ejpam-1224	843	20	meaning	mean	VERB
ejpam-1224	843	21	that	that	SCONJ
ejpam-1224	843	22	the	the	DET
ejpam-1224	843	23	filtration	filtration	NOUN
ejpam-1224	843	24	arises	arise	VERB
ejpam-1224	843	25	from	from	ADP
ejpam-1224	843	26	a	a	DET
ejpam-1224	843	27	grading	grading	NOUN
ejpam-1224	843	28	of	of	ADP
ejpam-1224	843	29	a.	a.	NOUN
ejpam-1224	843	30	the	the	DET
ejpam-1224	843	31	case	case	NOUN
ejpam-1224	843	32	which	which	PRON
ejpam-1224	843	33	is	be	AUX
ejpam-1224	843	34	of	of	ADP
ejpam-1224	843	35	interest	interest	NOUN
ejpam-1224	843	36	to	to	ADP
ejpam-1224	843	37	us	we	PRON
ejpam-1224	843	38	is	be	AUX
ejpam-1224	843	39	represented	represent	VERB
ejpam-1224	843	40	in	in	ADP
ejpam-1224	843	41	the	the	DET
ejpam-1224	843	42	following	following	ADJ
ejpam-1224	843	43	commutative	commutative	ADJ
ejpam-1224	843	44	diagram	diagram	NOUN
ejpam-1224	843	45	gb	gb	ADP
ejpam-1224	843	46	:	:	PUNCT
ejpam-1224	843	47	c(b	c(b	PROPN
ejpam-1224	843	48	!	!	PUNCT
ejpam-1224	843	49	)	)	PUNCT
ejpam-1224	844	1	←−	←−	VERB
ejpam-1224	844	2	−−−→	−−−→	NOUN
ejpam-1224	844	3	c(b	c(b	PROPN
ejpam-1224	844	4	)	)	PUNCT
ejpam-1224	844	5	:	:	PUNCT
ejpam-1224	845	1	fb	fb	INTJ
ejpam-1224	845	2	i	i	PRON
ejpam-1224	845	3	y	y	VERB
ejpam-1224	845	4	j	j	PROPN
ejpam-1224	845	5	y	y	PROPN
ejpam-1224	845	6	g̃	g̃	PROPN
ejpam-1224	845	7	:	:	PUNCT
ejpam-1224	845	8	cz(a	cz(a	X
ejpam-1224	845	9	)	)	PUNCT
ejpam-1224	845	10	←−	←−	VERB
ejpam-1224	845	11	−−−→	−−−→	PROPN
ejpam-1224	845	12	cz(a	cz(a	NOUN
ejpam-1224	845	13	!	!	PUNCT
ejpam-1224	846	1	•	•	X
ejpam-1224	846	2	)	)	PUNCT
ejpam-1224	846	3	:	:	PUNCT
ejpam-1224	847	1	f̃	f̃	PROPN
ejpam-1224	847	2	φ	φ	PROPN
ejpam-1224	847	3	↑	↑	PROPN
ejpam-1224	847	4	↓	↓	PROPN
ejpam-1224	848	1	ψ	ψ	ADP
ejpam-1224	848	2	g	g	NOUN
ejpam-1224	848	3	:	:	PUNCT
ejpam-1224	848	4	comz(u	comz(u	NOUN
ejpam-1224	848	5	=	=	PUNCT
ejpam-1224	848	6	a	a	X
ejpam-1224	848	7	)	)	PUNCT
ejpam-1224	848	8	←−	←−	ADJ
ejpam-1224	848	9	−−−→	−−−→	ADJ
ejpam-1224	848	10	comz(a	comz(a	NOUN
ejpam-1224	848	11	!	!	PUNCT
ejpam-1224	848	12	,	,	PUNCT
ejpam-1224	849	1	d	d	X
ejpam-1224	849	2	=	=	SYM
ejpam-1224	849	3	0	0	NUM
ejpam-1224	849	4	,	,	PUNCT
ejpam-1224	849	5	c	c	NOUN
ejpam-1224	849	6	=	=	SYM
ejpam-1224	849	7	0	0	NUM
ejpam-1224	849	8	)	)	PUNCT
ejpam-1224	849	9	:	:	PUNCT
ejpam-1224	850	1	f.	f.	PROPN
ejpam-1224	850	2	in	in	ADP
ejpam-1224	850	3	this	this	DET
ejpam-1224	850	4	commutative	commutative	ADJ
ejpam-1224	850	5	diagram	diagram	NOUN
ejpam-1224	850	6	b	b	PROPN
ejpam-1224	850	7	=	=	PUNCT
ejpam-1224	850	8	a	a	PROPN
ejpam-1224	850	9	!	!	PROPN
ejpam-1224	850	10	,	,	PUNCT
ejpam-1224	850	11	cz(a	cz(a	NOUN
ejpam-1224	850	12	)	)	PUNCT
ejpam-1224	850	13	is	be	AUX
ejpam-1224	850	14	the	the	DET
ejpam-1224	850	15	category	category	NOUN
ejpam-1224	850	16	of	of	ADP
ejpam-1224	850	17	chain	chain	NOUN
ejpam-1224	850	18	complexes	complex	NOUN
ejpam-1224	850	19	of	of	ADP
ejpam-1224	850	20	graded	grade	VERB
ejpam-1224	850	21	left	leave	VERB
ejpam-1224	850	22	a	a	DET
ejpam-1224	850	23	-	-	PUNCT
ejpam-1224	850	24	modules	module	NOUN
ejpam-1224	850	25	and	and	CCONJ
ejpam-1224	850	26	cz(a	cz(a	NOUN
ejpam-1224	850	27	!	!	PUNCT
ejpam-1224	851	1	•	•	X
ejpam-1224	851	2	)	)	PUNCT
ejpam-1224	851	3	is	be	AUX
ejpam-1224	851	4	the	the	DET
ejpam-1224	851	5	category	category	NOUN
ejpam-1224	851	6	of	of	ADP
ejpam-1224	851	7	chain	chain	NOUN
ejpam-1224	851	8	complexes	complex	NOUN
ejpam-1224	851	9	of	of	ADP
ejpam-1224	851	10	graded	grade	VERB
ejpam-1224	851	11	left	leave	VERB
ejpam-1224	851	12	a!-modules	a!-module	NOUN
ejpam-1224	851	13	.	.	PUNCT
ejpam-1224	852	1	the	the	DET
ejpam-1224	852	2	functors	functors	PROPN
ejpam-1224	852	3	fb	fb	INTJ
ejpam-1224	852	4	and	and	CCONJ
ejpam-1224	852	5	gb	gb	PRON
ejpam-1224	852	6	are	be	AUX
ejpam-1224	852	7	the	the	DET
ejpam-1224	852	8	functors	functor	NOUN
ejpam-1224	852	9	from	from	ADP
ejpam-1224	852	10	[	[	X
ejpam-1224	852	11	1	1	NUM
ejpam-1224	852	12	]	]	PUNCT
ejpam-1224	852	13	given	give	VERB
ejpam-1224	852	14	by	by	ADP
ejpam-1224	852	15	(	(	PUNCT
ejpam-1224	852	16	fb	fb	INTJ
ejpam-1224	852	17	m)pq	m)pq	PROPN
ejpam-1224	852	18	=	=	PROPN
ejpam-1224	852	19	⊕	⊕	PROPN
ejpam-1224	852	20	p	p	NOUN
ejpam-1224	852	21	=	=	PROPN
ejpam-1224	852	22	i+	i+	NOUN
ejpam-1224	852	23	j	j	NOUN
ejpam-1224	852	24	q	q	NOUN
ejpam-1224	852	25	=	=	VERB
ejpam-1224	852	26	l−	l−	NOUN
ejpam-1224	852	27	j	j	PROPN
ejpam-1224	852	28	b	b	X
ejpam-1224	852	29	!	!	PUNCT
ejpam-1224	853	1	l	l	PROPN
ejpam-1224	853	2	⊗m	⊗m	NOUN
ejpam-1224	854	1	i	i	PRON
ejpam-1224	854	2	j	j	PROPN
ejpam-1224	854	3	,	,	PUNCT
ejpam-1224	854	4	(	(	PUNCT
ejpam-1224	854	5	gbn)pq	gbn)pq	NOUN
ejpam-1224	854	6	=	=	PROPN
ejpam-1224	854	7	⊕	⊕	PROPN
ejpam-1224	855	1	p	p	NOUN
ejpam-1224	855	2	=	=	PROPN
ejpam-1224	855	3	i+	i+	NOUN
ejpam-1224	855	4	j	j	NOUN
ejpam-1224	855	5	q	q	NOUN
ejpam-1224	855	6	=	=	VERB
ejpam-1224	855	7	l−	l−	NOUN
ejpam-1224	855	8	j	j	PROPN
ejpam-1224	855	9	homk(b−l	homk(b−l	PROPN
ejpam-1224	855	10	,	,	PUNCT
ejpam-1224	855	11	n	n	CCONJ
ejpam-1224	855	12	i	i	PRON
ejpam-1224	855	13	j	j	PROPN
ejpam-1224	855	14	)	)	PUNCT
ejpam-1224	855	15	.	.	PUNCT
ejpam-1224	856	1	f.	f.	PROPN
ejpam-1224	856	2	hawwa	hawwa	PROPN
ejpam-1224	856	3	,	,	PUNCT
ejpam-1224	856	4	j.	j.	PROPN
ejpam-1224	856	5	hoffman	hoffman	PROPN
ejpam-1224	856	6	,	,	PUNCT
ejpam-1224	856	7	and	and	CCONJ
ejpam-1224	856	8	h.	h.	PROPN
ejpam-1224	856	9	wang	wang	PROPN
ejpam-1224	856	10	,	,	PUNCT
ejpam-1224	856	11	/	/	SYM
ejpam-1224	856	12	eur	eur	NOUN
ejpam-1224	856	13	.	.	PUNCT
ejpam-1224	857	1	j.	j.	PROPN
ejpam-1224	857	2	pure	pure	PROPN
ejpam-1224	857	3	appl	appl	PROPN
ejpam-1224	857	4	.	.	PROPN
ejpam-1224	857	5	math	math	PROPN
ejpam-1224	857	6	,	,	PUNCT
ejpam-1224	857	7	5	5	NUM
ejpam-1224	857	8	(	(	PUNCT
ejpam-1224	857	9	2012	2012	NUM
ejpam-1224	857	10	)	)	PUNCT
ejpam-1224	857	11	,	,	PUNCT
ejpam-1224	857	12	511	511	NUM
ejpam-1224	857	13	-	-	SYM
ejpam-1224	857	14	539	539	NUM
ejpam-1224	857	15	537	537	NUM
ejpam-1224	857	16	the	the	DET
ejpam-1224	857	17	functors	functors	PROPN
ejpam-1224	857	18	f̃	f̃	PROPN
ejpam-1224	857	19	and	and	CCONJ
ejpam-1224	857	20	g̃	g̃	PROPN
ejpam-1224	857	21	have	have	AUX
ejpam-1224	857	22	been	be	AUX
ejpam-1224	857	23	constructed	construct	VERB
ejpam-1224	857	24	such	such	ADJ
ejpam-1224	857	25	that	that	SCONJ
ejpam-1224	857	26	f̃	f̃	PROPN
ejpam-1224	857	27	=	=	SYM
ejpam-1224	857	28	fψ	fψ	PROPN
ejpam-1224	857	29	and	and	CCONJ
ejpam-1224	857	30	g̃	g̃	PROPN
ejpam-1224	857	31	=	=	SYM
ejpam-1224	857	32	gφ	gφ	NOUN
ejpam-1224	857	33	making	make	VERB
ejpam-1224	857	34	the	the	DET
ejpam-1224	857	35	lower	low	ADJ
ejpam-1224	857	36	half	half	NOUN
ejpam-1224	857	37	of	of	ADP
ejpam-1224	857	38	the	the	DET
ejpam-1224	857	39	diagram	diagram	NOUN
ejpam-1224	857	40	commute	commute	NOUN
ejpam-1224	857	41	.	.	PUNCT
ejpam-1224	858	1	we	we	PRON
ejpam-1224	858	2	would	would	AUX
ejpam-1224	858	3	like	like	VERB
ejpam-1224	858	4	to	to	PART
ejpam-1224	858	5	relate	relate	VERB
ejpam-1224	858	6	the	the	DET
ejpam-1224	858	7	following	following	NOUN
ejpam-1224	858	8	ψ	ψ	X
ejpam-1224	858	9	:	:	PUNCT
ejpam-1224	858	10	cz(a	cz(a	X
ejpam-1224	858	11	!	!	PUNCT
ejpam-1224	859	1	•	•	X
ejpam-1224	859	2	)	)	PUNCT
ejpam-1224	859	3	⇆	⇆	ADP
ejpam-1224	859	4	comz(a	comz(a	NOUN
ejpam-1224	859	5	!	!	PUNCT
ejpam-1224	859	6	,	,	PUNCT
ejpam-1224	860	1	d	d	X
ejpam-1224	860	2	=	=	SYM
ejpam-1224	860	3	0	0	NUM
ejpam-1224	860	4	,	,	PUNCT
ejpam-1224	860	5	c	c	NOUN
ejpam-1224	860	6	=	=	SYM
ejpam-1224	860	7	0	0	NUM
ejpam-1224	860	8	)	)	PUNCT
ejpam-1224	860	9	:	:	PUNCT
ejpam-1224	860	10	φ	φ	VERB
ejpam-1224	860	11	by	by	ADP
ejpam-1224	860	12	defining	define	VERB
ejpam-1224	860	13	φ	φ	PROPN
ejpam-1224	860	14	and	and	CCONJ
ejpam-1224	860	15	ψ	ψ	X
ejpam-1224	860	16	such	such	ADJ
ejpam-1224	860	17	that	that	SCONJ
ejpam-1224	860	18	they	they	PRON
ejpam-1224	860	19	are	be	AUX
ejpam-1224	860	20	well	well	ADV
ejpam-1224	860	21	defined	define	VERB
ejpam-1224	860	22	,	,	PUNCT
ejpam-1224	860	23	inverses	inverse	NOUN
ejpam-1224	860	24	of	of	ADP
ejpam-1224	860	25	each	each	DET
ejpam-1224	860	26	other	other	ADJ
ejpam-1224	860	27	,	,	PUNCT
ejpam-1224	860	28	and	and	CCONJ
ejpam-1224	860	29	make	make	VERB
ejpam-1224	860	30	the	the	DET
ejpam-1224	860	31	diagram	diagram	NOUN
ejpam-1224	860	32	commute	commute	NOUN
ejpam-1224	860	33	.	.	PUNCT
ejpam-1224	861	1	now	now	ADV
ejpam-1224	861	2	note	note	VERB
ejpam-1224	861	3	the	the	DET
ejpam-1224	861	4	a	a	NOUN
ejpam-1224	861	5	!	!	NOUN
ejpam-1224	861	6	•	•	NOUN
ejpam-1224	861	7	on	on	ADP
ejpam-1224	861	8	the	the	DET
ejpam-1224	861	9	left	left	ADJ
ejpam-1224	861	10	hand	hand	NOUN
ejpam-1224	861	11	side	side	NOUN
ejpam-1224	861	12	is	be	AUX
ejpam-1224	861	13	a	a	DET
ejpam-1224	861	14	ring	ring	NOUN
ejpam-1224	861	15	while	while	SCONJ
ejpam-1224	861	16	the	the	DET
ejpam-1224	861	17	a	a	X
ejpam-1224	861	18	!	!	PUNCT
ejpam-1224	862	1	on	on	ADP
ejpam-1224	862	2	the	the	DET
ejpam-1224	862	3	right	right	ADJ
ejpam-1224	862	4	hand	hand	NOUN
ejpam-1224	862	5	side	side	NOUN
ejpam-1224	862	6	will	will	AUX
ejpam-1224	862	7	be	be	AUX
ejpam-1224	862	8	regarded	regard	VERB
ejpam-1224	862	9	as	as	ADP
ejpam-1224	862	10	a	a	DET
ejpam-1224	862	11	cdga	cdga	NOUN
ejpam-1224	862	12	with	with	ADP
ejpam-1224	862	13	d	d	PROPN
ejpam-1224	862	14	=	=	SYM
ejpam-1224	862	15	c	c	NOUN
ejpam-1224	862	16	=	=	SYM
ejpam-1224	862	17	0	0	PROPN
ejpam-1224	862	18	.	.	PUNCT
ejpam-1224	863	1	namely	namely	ADV
ejpam-1224	863	2	we	we	PRON
ejpam-1224	863	3	define	define	VERB
ejpam-1224	863	4	(	(	PUNCT
ejpam-1224	863	5	ψa	ψa	NOUN
ejpam-1224	863	6	!	!	NOUN
ejpam-1224	863	7	•	•	NUM
ejpam-1224	863	8	)	)	PUNCT
ejpam-1224	863	9	=	=	SYM
ejpam-1224	863	10	(	(	PUNCT
ejpam-1224	863	11	a	a	PRON
ejpam-1224	863	12	!	!	PUNCT
ejpam-1224	863	13	,	,	PUNCT
ejpam-1224	864	1	d	d	X
ejpam-1224	864	2	=	=	SYM
ejpam-1224	864	3	0	0	NUM
ejpam-1224	864	4	,	,	PUNCT
ejpam-1224	864	5	c	c	NOUN
ejpam-1224	864	6	=	=	SYM
ejpam-1224	864	7	0	0	NUM
ejpam-1224	864	8	)	)	PUNCT
ejpam-1224	864	9	as	as	ADP
ejpam-1224	864	10	the	the	DET
ejpam-1224	864	11	z	z	NOUN
ejpam-1224	864	12	-	-	PUNCT
ejpam-1224	864	13	graded	grade	VERB
ejpam-1224	864	14	cdga	cdga	NOUN
ejpam-1224	864	15	by	by	ADP
ejpam-1224	864	16	the	the	DET
ejpam-1224	864	17	rule	rule	NOUN
ejpam-1224	864	18	,	,	PUNCT
ejpam-1224	864	19	(	(	PUNCT
ejpam-1224	864	20	ψa!)ij	ψa!)ij	NOUN
ejpam-1224	864	21	=	=	SYM
ejpam-1224	864	22	(	(	PUNCT
ejpam-1224	864	23	0	0	NUM
ejpam-1224	864	24	if	if	SCONJ
ejpam-1224	864	25	i	i	PRON
ejpam-1224	864	26	+	+	X
ejpam-1224	864	27	j	j	PROPN
ejpam-1224	864	28	6=	6=	ADP
ejpam-1224	864	29	0	0	SYM
ejpam-1224	865	1	a	a	PRON
ejpam-1224	865	2	!	!	PUNCT
ejpam-1224	866	1	i	i	PRON
ejpam-1224	866	2	if	if	SCONJ
ejpam-1224	866	3	−	−	PROPN
ejpam-1224	866	4	j	j	NOUN
ejpam-1224	867	1	=	=	VERB
ejpam-1224	867	2	i	i	PRON
ejpam-1224	867	3	≥	≥	VERB
ejpam-1224	867	4	0	0	NUM
ejpam-1224	867	5	.	.	PUNCT
ejpam-1224	868	1	for	for	ADP
ejpam-1224	868	2	any	any	DET
ejpam-1224	868	3	complex	complex	ADJ
ejpam-1224	868	4	(	(	PUNCT
ejpam-1224	868	5	m	m	PROPN
ejpam-1224	868	6	,	,	PUNCT
ejpam-1224	868	7	dm	dm	PROPN
ejpam-1224	868	8	)	)	PUNCT
ejpam-1224	868	9	∈	∈	PROPN
ejpam-1224	868	10	cz(a	cz(a	X
ejpam-1224	868	11	!	!	PUNCT
ejpam-1224	869	1	i	i	PRON
ejpam-1224	869	2	)	)	PUNCT
ejpam-1224	870	1	we	we	PRON
ejpam-1224	870	2	define	define	VERB
ejpam-1224	870	3	a	a	DET
ejpam-1224	870	4	cdg	cdg	NOUN
ejpam-1224	870	5	-	-	PUNCT
ejpam-1224	870	6	a!-module	a!-module	PROPN
ejpam-1224	870	7	(	(	PUNCT
ejpam-1224	870	8	ψm	ψm	NOUN
ejpam-1224	870	9	)	)	PUNCT
ejpam-1224	870	10	=	=	SYM
ejpam-1224	870	11	(	(	PUNCT
ejpam-1224	870	12	n	n	X
ejpam-1224	870	13	,	,	PUNCT
ejpam-1224	870	14	dn	dn	PROPN
ejpam-1224	870	15	)	)	PUNCT
ejpam-1224	870	16	by	by	ADP
ejpam-1224	870	17	the	the	DET
ejpam-1224	870	18	rule	rule	NOUN
ejpam-1224	870	19	(	(	PUNCT
ejpam-1224	870	20	ψm)i	ψm)i	PROPN
ejpam-1224	870	21	j	j	NOUN
ejpam-1224	871	1	=	=	SYM
ejpam-1224	872	1	n	n	PROPN
ejpam-1224	873	1	i	i	PRON
ejpam-1224	873	2	j	j	PROPN
ejpam-1224	874	1	=	=	VERB
ejpam-1224	874	2	m	m	VERB
ejpam-1224	874	3	i+	i+	VERB
ejpam-1224	875	1	j	j	PROPN
ejpam-1224	875	2	−	−	PROPN
ejpam-1224	875	3	j	j	PROPN
ejpam-1224	875	4	with	with	ADP
ejpam-1224	875	5	differential	differential	NOUN
ejpam-1224	875	6	dn	dn	PROPN
ejpam-1224	875	7	(	(	PUNCT
ejpam-1224	875	8	x	x	X
ejpam-1224	875	9	)	)	PUNCT
ejpam-1224	875	10	=	=	SYM
ejpam-1224	875	11	(	(	PUNCT
ejpam-1224	875	12	−1)sdm	−1)sdm	NOUN
ejpam-1224	875	13	(	(	PUNCT
ejpam-1224	875	14	x	x	NOUN
ejpam-1224	875	15	)	)	PUNCT
ejpam-1224	875	16	for	for	ADP
ejpam-1224	875	17	x	x	SYM
ejpam-1224	875	18	∈	∈	PROPN
ejpam-1224	875	19	n	n	PROPN
ejpam-1224	875	20	s.	s.	PROPN
ejpam-1224	875	21	one	one	NUM
ejpam-1224	875	22	must	must	AUX
ejpam-1224	875	23	now	now	ADV
ejpam-1224	875	24	check	check	VERB
ejpam-1224	875	25	all	all	DET
ejpam-1224	875	26	the	the	DET
ejpam-1224	875	27	necessary	necessary	ADJ
ejpam-1224	875	28	axioms	axiom	NOUN
ejpam-1224	875	29	to	to	PART
ejpam-1224	875	30	show	show	VERB
ejpam-1224	875	31	that	that	SCONJ
ejpam-1224	875	32	ψ(m	ψ(m	PROPN
ejpam-1224	875	33	,	,	PUNCT
ejpam-1224	875	34	dm	dm	PROPN
ejpam-1224	875	35	)	)	PUNCT
ejpam-1224	875	36	=	=	SYM
ejpam-1224	875	37	(	(	PUNCT
ejpam-1224	875	38	n	n	CCONJ
ejpam-1224	875	39	,	,	PUNCT
ejpam-1224	875	40	dn	dn	PROPN
ejpam-1224	875	41	)	)	PUNCT
ejpam-1224	875	42	is	be	AUX
ejpam-1224	875	43	an	an	DET
ejpam-1224	875	44	element	element	NOUN
ejpam-1224	875	45	of	of	ADP
ejpam-1224	875	46	comz(a	comz(a	NOUN
ejpam-1224	875	47	!	!	PUNCT
ejpam-1224	875	48	,	,	PUNCT
ejpam-1224	876	1	d	d	X
ejpam-1224	876	2	=	=	SYM
ejpam-1224	876	3	0	0	NUM
ejpam-1224	876	4	,	,	PUNCT
ejpam-1224	876	5	c	c	NOUN
ejpam-1224	876	6	=	=	SYM
ejpam-1224	876	7	0	0	NUM
ejpam-1224	876	8	)	)	PUNCT
ejpam-1224	876	9	for	for	ADP
ejpam-1224	876	10	(	(	PUNCT
ejpam-1224	876	11	m	m	PROPN
ejpam-1224	876	12	,	,	PUNCT
ejpam-1224	876	13	dm	dm	PROPN
ejpam-1224	876	14	)	)	PUNCT
ejpam-1224	876	15	∈	∈	PROPN
ejpam-1224	876	16	cz(a	cz(a	X
ejpam-1224	876	17	!	!	PUNCT
ejpam-1224	877	1	•	•	NUM
ejpam-1224	877	2	)	)	PUNCT
ejpam-1224	877	3	.	.	PUNCT
ejpam-1224	878	1	clearly	clearly	ADV
ejpam-1224	878	2	d2	d2	VERB
ejpam-1224	878	3	n	n	NOUN
ejpam-1224	878	4	=	=	SYM
ejpam-1224	878	5	0	0	PUNCT
ejpam-1224	878	6	since	since	SCONJ
ejpam-1224	878	7	we	we	PRON
ejpam-1224	878	8	know	know	VERB
ejpam-1224	878	9	that	that	SCONJ
ejpam-1224	878	10	d2	d2	PROPN
ejpam-1224	878	11	m	m	PROPN
ejpam-1224	878	12	=	=	NOUN
ejpam-1224	878	13	0	0	X
ejpam-1224	878	14	.	.	PUNCT
ejpam-1224	879	1	we	we	PRON
ejpam-1224	879	2	also	also	ADV
ejpam-1224	879	3	need	need	VERB
ejpam-1224	879	4	to	to	PART
ejpam-1224	879	5	check	check	VERB
ejpam-1224	879	6	a!-linearity	a!-linearity	NOUN
ejpam-1224	879	7	of	of	ADP
ejpam-1224	879	8	dn	dn	NOUN
ejpam-1224	879	9	meaning	mean	VERB
ejpam-1224	879	10	that	that	SCONJ
ejpam-1224	879	11	for	for	ADP
ejpam-1224	879	12	x	x	SYM
ejpam-1224	879	13	∈	∈	PROPN
ejpam-1224	879	14	n	n	NOUN
ejpam-1224	879	15	s	s	NOUN
ejpam-1224	879	16	and	and	CCONJ
ejpam-1224	879	17	α	α	NOUN
ejpam-1224	879	18	∈	∈	PROPN
ejpam-1224	879	19	(	(	PUNCT
ejpam-1224	879	20	a!)k−k	a!)k−k	ADV
ejpam-1224	879	21	we	we	PRON
ejpam-1224	879	22	have	have	VERB
ejpam-1224	879	23	dn	dn	INTJ
ejpam-1224	879	24	(	(	PUNCT
ejpam-1224	879	25	αx	αx	NOUN
ejpam-1224	879	26	)	)	PUNCT
ejpam-1224	879	27	=	=	SYM
ejpam-1224	879	28	(	(	PUNCT
ejpam-1224	879	29	−1)sαdn	−1)sαdn	NOUN
ejpam-1224	879	30	(	(	PUNCT
ejpam-1224	879	31	x	x	NOUN
ejpam-1224	879	32	)	)	PUNCT
ejpam-1224	879	33	.	.	PUNCT
ejpam-1224	880	1	this	this	PRON
ejpam-1224	880	2	is	be	AUX
ejpam-1224	880	3	clearly	clearly	ADV
ejpam-1224	880	4	true	true	ADJ
ejpam-1224	880	5	since	since	SCONJ
ejpam-1224	880	6	both	both	DET
ejpam-1224	880	7	sides	side	NOUN
ejpam-1224	880	8	equal	equal	ADJ
ejpam-1224	880	9	(	(	PUNCT
ejpam-1224	880	10	−1)s+kαdm	−1)s+kαdm	PROPN
ejpam-1224	880	11	(	(	PUNCT
ejpam-1224	880	12	x	x	NOUN
ejpam-1224	880	13	)	)	PUNCT
ejpam-1224	880	14	.	.	PUNCT
ejpam-1224	881	1	this	this	PRON
ejpam-1224	881	2	also	also	ADV
ejpam-1224	881	3	verifies	verify	VERB
ejpam-1224	881	4	that	that	PRON
ejpam-1224	881	5	dn	dn	PROPN
ejpam-1224	881	6	(	(	PUNCT
ejpam-1224	881	7	αx	αx	NOUN
ejpam-1224	881	8	)	)	PUNCT
ejpam-1224	881	9	=	=	SYM
ejpam-1224	881	10	da!(α)(x)+	da!(α)(x)+	X
ejpam-1224	881	11	(	(	PUNCT
ejpam-1224	881	12	−1)deg(α)αdn	−1)deg(α)αdn	X
ejpam-1224	881	13	(	(	PUNCT
ejpam-1224	881	14	x	x	X
ejpam-1224	881	15	)	)	PUNCT
ejpam-1224	881	16	since	since	SCONJ
ejpam-1224	881	17	da!(α)(x	da!(α)(x	NOUN
ejpam-1224	881	18	)	)	PUNCT
ejpam-1224	881	19	=	=	SYM
ejpam-1224	882	1	0	0	X
ejpam-1224	882	2	.	.	PUNCT
ejpam-1224	883	1	now	now	ADV
ejpam-1224	883	2	we	we	PRON
ejpam-1224	883	3	need	need	VERB
ejpam-1224	883	4	to	to	PART
ejpam-1224	883	5	check	check	VERB
ejpam-1224	883	6	the	the	DET
ejpam-1224	883	7	module	module	NOUN
ejpam-1224	883	8	structure	structure	NOUN
ejpam-1224	883	9	of	of	ADP
ejpam-1224	883	10	(	(	PUNCT
ejpam-1224	883	11	n	n	X
ejpam-1224	883	12	,	,	PUNCT
ejpam-1224	883	13	dn	dn	PROPN
ejpam-1224	883	14	)	)	PUNCT
ejpam-1224	883	15	.	.	PUNCT
ejpam-1224	884	1	we	we	PRON
ejpam-1224	884	2	know	know	VERB
ejpam-1224	884	3	that	that	SCONJ
ejpam-1224	884	4	a	a	PRON
ejpam-1224	884	5	!	!	PUNCT
ejpam-1224	885	1	p	p	NOUN
ejpam-1224	885	2	×m	×m	NOUN
ejpam-1224	885	3	r+s	r+s	PROPN
ejpam-1224	885	4	−s	−s	NOUN
ejpam-1224	885	5	⊂	⊂	X
ejpam-1224	885	6	m	m	VERB
ejpam-1224	885	7	r+s	r+s	PROPN
ejpam-1224	885	8	p−s	p−s	NOUN
ejpam-1224	885	9	and	and	CCONJ
ejpam-1224	885	10	under	under	ADP
ejpam-1224	885	11	ψ	ψ	NOUN
ejpam-1224	885	12	this	this	DET
ejpam-1224	885	13	corresponds	correspond	NOUN
ejpam-1224	885	14	to	to	ADP
ejpam-1224	885	15	(	(	PUNCT
ejpam-1224	885	16	a	a	X
ejpam-1224	885	17	!	!	PUNCT
ejpam-1224	885	18	)	)	PUNCT
ejpam-1224	886	1	p	p	X
ejpam-1224	886	2	−p	−p	ADJ
ejpam-1224	886	3	×	×	NOUN
ejpam-1224	886	4	n	n	PRON
ejpam-1224	886	5	r	r	NOUN
ejpam-1224	886	6	s	s	X
ejpam-1224	886	7	⊂	⊂	PROPN
ejpam-1224	886	8	n	n	PRON
ejpam-1224	886	9	p+r	p+r	X
ejpam-1224	886	10	−p+s	−p+	NOUN
ejpam-1224	887	1	and	and	CCONJ
ejpam-1224	887	2	we	we	PRON
ejpam-1224	887	3	know	know	VERB
ejpam-1224	887	4	this	this	PRON
ejpam-1224	887	5	is	be	AUX
ejpam-1224	887	6	true	true	ADJ
ejpam-1224	887	7	by	by	ADP
ejpam-1224	887	8	our	our	PRON
ejpam-1224	887	9	definition	definition	NOUN
ejpam-1224	887	10	of	of	ADP
ejpam-1224	887	11	ψ	ψ	NOUN
ejpam-1224	887	12	verifying	verify	VERB
ejpam-1224	887	13	that	that	SCONJ
ejpam-1224	887	14	ψ(m	ψ(m	NOUN
ejpam-1224	887	15	)	)	PUNCT
ejpam-1224	887	16	is	be	AUX
ejpam-1224	887	17	an	an	DET
ejpam-1224	887	18	a!-module	a!-module	NOUN
ejpam-1224	887	19	.	.	PUNCT
ejpam-1224	888	1	now	now	ADV
ejpam-1224	888	2	we	we	PRON
ejpam-1224	888	3	’d	’d	AUX
ejpam-1224	888	4	like	like	VERB
ejpam-1224	888	5	to	to	PART
ejpam-1224	888	6	check	check	VERB
ejpam-1224	888	7	that	that	SCONJ
ejpam-1224	888	8	φ(n	φ(n	PROPN
ejpam-1224	888	9	,	,	PUNCT
ejpam-1224	888	10	dn	dn	NOUN
ejpam-1224	888	11	)	)	PUNCT
ejpam-1224	888	12	=	=	PUNCT
ejpam-1224	889	1	(	(	PUNCT
ejpam-1224	889	2	m	m	PROPN
ejpam-1224	889	3	,	,	PUNCT
ejpam-1224	889	4	dm	dm	PROPN
ejpam-1224	889	5	)	)	PUNCT
ejpam-1224	889	6	for	for	ADP
ejpam-1224	889	7	(	(	PUNCT
ejpam-1224	889	8	m	m	PROPN
ejpam-1224	889	9	,	,	PUNCT
ejpam-1224	889	10	dm	dm	PROPN
ejpam-1224	889	11	)	)	PUNCT
ejpam-1224	889	12	∈	∈	PROPN
ejpam-1224	889	13	cz(a	cz(a	X
ejpam-1224	889	14	!	!	PUNCT
ejpam-1224	890	1	•	•	NUM
ejpam-1224	890	2	)	)	PUNCT
ejpam-1224	890	3	.	.	PUNCT
ejpam-1224	891	1	now	now	ADV
ejpam-1224	891	2	let	let	VERB
ejpam-1224	891	3	us	we	PRON
ejpam-1224	891	4	define	define	VERB
ejpam-1224	891	5	φ	φ	PROPN
ejpam-1224	891	6	such	such	ADJ
ejpam-1224	891	7	that	that	DET
ejpam-1224	891	8	φ(a	φ(a	PROPN
ejpam-1224	891	9	!	!	PUNCT
ejpam-1224	891	10	,	,	PUNCT
ejpam-1224	892	1	d	d	X
ejpam-1224	892	2	=	=	SYM
ejpam-1224	892	3	0	0	NUM
ejpam-1224	892	4	,	,	PUNCT
ejpam-1224	892	5	c	c	NOUN
ejpam-1224	892	6	=	=	SYM
ejpam-1224	892	7	0	0	NUM
ejpam-1224	892	8	)	)	PUNCT
ejpam-1224	892	9	=	=	SYM
ejpam-1224	892	10	a	a	PRON
ejpam-1224	892	11	!	!	PUNCT
ejpam-1224	892	12	•.	•.	NOUN
ejpam-1224	892	13	namely	namely	ADV
ejpam-1224	892	14	we	we	PRON
ejpam-1224	892	15	define	define	VERB
ejpam-1224	892	16	φ(a	φ(a	ADJ
ejpam-1224	892	17	!	!	PUNCT
ejpam-1224	892	18	,	,	PUNCT
ejpam-1224	893	1	d	d	X
ejpam-1224	893	2	=	=	SYM
ejpam-1224	893	3	0	0	NUM
ejpam-1224	893	4	,	,	PUNCT
ejpam-1224	893	5	c	c	NOUN
ejpam-1224	893	6	=	=	SYM
ejpam-1224	893	7	0	0	NUM
ejpam-1224	893	8	)	)	PUNCT
ejpam-1224	893	9	as	as	ADP
ejpam-1224	893	10	the	the	DET
ejpam-1224	893	11	chain	chain	NOUN
ejpam-1224	893	12	complex	complex	NOUN
ejpam-1224	893	13	of	of	ADP
ejpam-1224	893	14	graded	grade	VERB
ejpam-1224	893	15	left	leave	VERB
ejpam-1224	893	16	a!-modules	a!-module	NOUN
ejpam-1224	893	17	by	by	ADP
ejpam-1224	893	18	the	the	DET
ejpam-1224	893	19	rule	rule	NOUN
ejpam-1224	893	20	φ(a	φ(a	PROPN
ejpam-1224	893	21	!	!	PUNCT
ejpam-1224	893	22	,	,	PUNCT
ejpam-1224	894	1	d	d	X
ejpam-1224	894	2	=	=	SYM
ejpam-1224	894	3	0	0	NUM
ejpam-1224	894	4	,	,	PUNCT
ejpam-1224	894	5	c	c	X
ejpam-1224	894	6	=	=	SYM
ejpam-1224	895	1	0)i−	0)i−	NUM
ejpam-1224	895	2	j	j	NOUN
ejpam-1224	895	3	=	=	PRON
ejpam-1224	895	4	(	(	PUNCT
ejpam-1224	895	5	a	a	NOUN
ejpam-1224	895	6	!	!	NOUN
ejpam-1224	895	7	•	•	NUM
ejpam-1224	895	8	)	)	PUNCT
ejpam-1224	895	9	j	j	NOUN
ejpam-1224	896	1	and	and	CCONJ
ejpam-1224	896	2	we	we	PRON
ejpam-1224	896	3	will	will	AUX
ejpam-1224	896	4	define	define	VERB
ejpam-1224	896	5	an	an	DET
ejpam-1224	896	6	a!-module	a!-module	NOUN
ejpam-1224	896	7	by	by	ADP
ejpam-1224	896	8	the	the	DET
ejpam-1224	896	9	rule	rule	NOUN
ejpam-1224	896	10	(	(	PUNCT
ejpam-1224	896	11	φn)ij	φn)ij	X
ejpam-1224	896	12	=	=	VERB
ejpam-1224	896	13	m	m	VERB
ejpam-1224	896	14	i	i	PRON
ejpam-1224	896	15	j	j	NOUN
ejpam-1224	896	16	=	=	SYM
ejpam-1224	897	1	n	n	PROPN
ejpam-1224	897	2	i+	i+	NUM
ejpam-1224	898	1	j	j	PROPN
ejpam-1224	898	2	−	−	PROPN
ejpam-1224	898	3	j	j	PROPN
ejpam-1224	898	4	with	with	ADP
ejpam-1224	898	5	differential	differential	NOUN
ejpam-1224	898	6	dm	dm	X
ejpam-1224	898	7	(	(	PUNCT
ejpam-1224	898	8	x	x	NOUN
ejpam-1224	898	9	)	)	PUNCT
ejpam-1224	898	10	=	=	SYM
ejpam-1224	898	11	(	(	PUNCT
ejpam-1224	898	12	−1)i+	−1)i+	NOUN
ejpam-1224	898	13	jdn	jdn	PROPN
ejpam-1224	898	14	(	(	PUNCT
ejpam-1224	898	15	x	x	NOUN
ejpam-1224	898	16	)	)	PUNCT
ejpam-1224	898	17	for	for	ADP
ejpam-1224	898	18	x	x	PROPN
ejpam-1224	898	19	∈	∈	PROPN
ejpam-1224	898	20	m	m	VERB
ejpam-1224	898	21	i	i	NOUN
ejpam-1224	898	22	j	j	PROPN
ejpam-1224	898	23	.	.	PUNCT
ejpam-1224	899	1	clearly	clearly	ADV
ejpam-1224	899	2	d2	d2	VERB
ejpam-1224	899	3	m	m	PROPN
ejpam-1224	899	4	=	=	NOUN
ejpam-1224	899	5	0	0	PUNCT
ejpam-1224	900	1	since	since	SCONJ
ejpam-1224	900	2	dn	dn	PROPN
ejpam-1224	900	3	=	=	NOUN
ejpam-1224	900	4	0	0	X
ejpam-1224	900	5	.	.	PUNCT
ejpam-1224	900	6	we	we	PRON
ejpam-1224	900	7	also	also	ADV
ejpam-1224	900	8	must	must	AUX
ejpam-1224	900	9	show	show	VERB
ejpam-1224	900	10	that	that	SCONJ
ejpam-1224	900	11	dm	dm	PROPN
ejpam-1224	900	12	(	(	PUNCT
ejpam-1224	900	13	αx	αx	NOUN
ejpam-1224	900	14	)	)	PUNCT
ejpam-1224	900	15	=	=	SYM
ejpam-1224	900	16	αdm	αdm	NOUN
ejpam-1224	900	17	(	(	PUNCT
ejpam-1224	900	18	x	x	NOUN
ejpam-1224	900	19	)	)	PUNCT
ejpam-1224	900	20	and	and	CCONJ
ejpam-1224	900	21	this	this	PRON
ejpam-1224	900	22	is	be	AUX
ejpam-1224	900	23	clear	clear	ADJ
ejpam-1224	900	24	since	since	SCONJ
ejpam-1224	900	25	dm	dm	PROPN
ejpam-1224	900	26	(	(	PUNCT
ejpam-1224	900	27	αx	αx	NOUN
ejpam-1224	900	28	)	)	PUNCT
ejpam-1224	900	29	=	=	SYM
ejpam-1224	900	30	(	(	PUNCT
ejpam-1224	900	31	−1)i+	−1)i+	PROPN
ejpam-1224	900	32	jα(dn	jα(dn	PROPN
ejpam-1224	900	33	(	(	PUNCT
ejpam-1224	900	34	x	x	NOUN
ejpam-1224	900	35	)	)	PUNCT
ejpam-1224	900	36	)	)	PUNCT
ejpam-1224	901	1	=	=	SYM
ejpam-1224	901	2	α(dm	α(dm	NUM
ejpam-1224	901	3	(	(	PUNCT
ejpam-1224	901	4	x	x	NOUN
ejpam-1224	901	5	)	)	PUNCT
ejpam-1224	901	6	)	)	PUNCT
ejpam-1224	901	7	.	.	PUNCT
ejpam-1224	902	1	f.	f.	PROPN
ejpam-1224	902	2	hawwa	hawwa	PROPN
ejpam-1224	902	3	,	,	PUNCT
ejpam-1224	902	4	j.	j.	PROPN
ejpam-1224	902	5	hoffman	hoffman	PROPN
ejpam-1224	902	6	,	,	PUNCT
ejpam-1224	902	7	and	and	CCONJ
ejpam-1224	902	8	h.	h.	PROPN
ejpam-1224	902	9	wang	wang	PROPN
ejpam-1224	902	10	,	,	PUNCT
ejpam-1224	902	11	/	/	SYM
ejpam-1224	902	12	eur	eur	NOUN
ejpam-1224	902	13	.	.	PUNCT
ejpam-1224	903	1	j.	j.	PROPN
ejpam-1224	903	2	pure	pure	PROPN
ejpam-1224	903	3	appl	appl	PROPN
ejpam-1224	903	4	.	.	PROPN
ejpam-1224	903	5	math	math	PROPN
ejpam-1224	903	6	,	,	PUNCT
ejpam-1224	903	7	5	5	NUM
ejpam-1224	903	8	(	(	PUNCT
ejpam-1224	903	9	2012	2012	NUM
ejpam-1224	903	10	)	)	PUNCT
ejpam-1224	903	11	,	,	PUNCT
ejpam-1224	903	12	511	511	NUM
ejpam-1224	903	13	-	-	SYM
ejpam-1224	903	14	539	539	NUM
ejpam-1224	903	15	538	538	NUM
ejpam-1224	903	16	finally	finally	ADV
ejpam-1224	903	17	it	it	PRON
ejpam-1224	903	18	remains	remain	VERB
ejpam-1224	903	19	to	to	PART
ejpam-1224	903	20	show	show	VERB
ejpam-1224	903	21	that	that	SCONJ
ejpam-1224	903	22	a	a	PRON
ejpam-1224	903	23	!	!	PUNCT
ejpam-1224	904	1	r	r	NOUN
ejpam-1224	904	2	×m	×m	NOUN
ejpam-1224	905	1	i	i	PRON
ejpam-1224	905	2	j	j	PROPN
ejpam-1224	906	1	⊂	⊂	NOUN
ejpam-1224	906	2	m	m	VERB
ejpam-1224	906	3	i	i	PRON
ejpam-1224	906	4	j+r	j+r	VERB
ejpam-1224	906	5	which	which	PRON
ejpam-1224	906	6	,	,	PUNCT
ejpam-1224	906	7	under	under	ADP
ejpam-1224	906	8	φ	φ	NUM
ejpam-1224	906	9	,	,	PUNCT
ejpam-1224	906	10	corresponds	correspond	VERB
ejpam-1224	906	11	to	to	ADP
ejpam-1224	906	12	(	(	PUNCT
ejpam-1224	906	13	a!)r−r	a!)r−r	ADJ
ejpam-1224	906	14	⊗	⊗	PROPN
ejpam-1224	906	15	n	n	PROPN
ejpam-1224	906	16	i+	i+	NOUN
ejpam-1224	906	17	j	j	NOUN
ejpam-1224	907	1	−	−	PROPN
ejpam-1224	907	2	j	j	PROPN
ejpam-1224	907	3	⊂	⊂	PROPN
ejpam-1224	907	4	n	n	CCONJ
ejpam-1224	907	5	i+	i+	NOUN
ejpam-1224	907	6	j+r	j+r	NUM
ejpam-1224	907	7	−	−	PROPN
ejpam-1224	907	8	j−r	j−r	NOUN
ejpam-1224	907	9	which	which	PRON
ejpam-1224	907	10	we	we	PRON
ejpam-1224	907	11	know	know	VERB
ejpam-1224	907	12	is	be	AUX
ejpam-1224	907	13	true	true	ADJ
ejpam-1224	907	14	by	by	ADP
ejpam-1224	907	15	our	our	PRON
ejpam-1224	907	16	definition	definition	NOUN
ejpam-1224	907	17	of	of	ADP
ejpam-1224	907	18	φ	φ	PROPN
ejpam-1224	907	19	thus	thus	ADV
ejpam-1224	907	20	completing	complete	VERB
ejpam-1224	907	21	our	our	PRON
ejpam-1224	907	22	verification	verification	NOUN
ejpam-1224	907	23	that	that	DET
ejpam-1224	907	24	φ(a	φ(a	PROPN
ejpam-1224	907	25	!	!	PUNCT
ejpam-1224	907	26	,	,	PUNCT
ejpam-1224	908	1	d	d	X
ejpam-1224	908	2	=	=	SYM
ejpam-1224	908	3	0	0	NUM
ejpam-1224	908	4	,	,	PUNCT
ejpam-1224	908	5	c	c	NOUN
ejpam-1224	908	6	=	=	SYM
ejpam-1224	908	7	0	0	NUM
ejpam-1224	908	8	)	)	PUNCT
ejpam-1224	908	9	=	=	SYM
ejpam-1224	908	10	a	a	PRON
ejpam-1224	908	11	!	!	PUNCT
ejpam-1224	908	12	•.	•.	NOUN
ejpam-1224	908	13	now	now	ADV
ejpam-1224	908	14	we	we	PRON
ejpam-1224	908	15	need	need	VERB
ejpam-1224	908	16	to	to	PART
ejpam-1224	908	17	verify	verify	VERB
ejpam-1224	908	18	that	that	SCONJ
ejpam-1224	908	19	the	the	DET
ejpam-1224	908	20	diagram	diagram	NOUN
ejpam-1224	908	21	commutes	commute	NOUN
ejpam-1224	908	22	.	.	PUNCT
ejpam-1224	909	1	the	the	DET
ejpam-1224	909	2	lower	low	ADJ
ejpam-1224	909	3	half	half	NOUN
ejpam-1224	909	4	of	of	ADP
ejpam-1224	909	5	the	the	DET
ejpam-1224	909	6	diagram	diagram	NOUN
ejpam-1224	909	7	commutes	commute	NOUN
ejpam-1224	909	8	by	by	ADP
ejpam-1224	909	9	definition	definition	NOUN
ejpam-1224	909	10	of	of	ADP
ejpam-1224	909	11	f̃	f̃	PROPN
ejpam-1224	909	12	and	and	CCONJ
ejpam-1224	909	13	g̃.	g̃.	PROPN
ejpam-1224	909	14	more	more	ADV
ejpam-1224	909	15	explicitly	explicitly	ADV
ejpam-1224	909	16	,	,	PUNCT
ejpam-1224	909	17	f̃	f̃	PROPN
ejpam-1224	909	18	=	=	PUNCT
ejpam-1224	909	19	fψ	fψ	PROPN
ejpam-1224	909	20	and	and	CCONJ
ejpam-1224	909	21	g̃	g̃	PROPN
ejpam-1224	909	22	=	=	SYM
ejpam-1224	909	23	gφ	gφ	PROPN
ejpam-1224	909	24	by	by	ADP
ejpam-1224	909	25	definition	definition	NOUN
ejpam-1224	909	26	.	.	PUNCT
ejpam-1224	910	1	what	what	PRON
ejpam-1224	910	2	remains	remain	VERB
ejpam-1224	910	3	is	be	AUX
ejpam-1224	910	4	to	to	PART
ejpam-1224	910	5	verify	verify	VERB
ejpam-1224	910	6	that	that	PRON
ejpam-1224	910	7	fψ(m	fψ(m	PUNCT
ejpam-1224	910	8	,	,	PUNCT
ejpam-1224	910	9	dm	dm	X
ejpam-1224	910	10	)	)	PUNCT
ejpam-1224	911	1	p	p	X
ejpam-1224	911	2	q	q	NOUN
ejpam-1224	912	1	=	=	PUNCT
ejpam-1224	912	2	(	(	PUNCT
ejpam-1224	912	3	fb	fb	INTJ
ejpam-1224	912	4	m)pq	m)pq	PROPN
ejpam-1224	912	5	and	and	CCONJ
ejpam-1224	912	6	φg(n	φg(n	NOUN
ejpam-1224	912	7	,	,	PUNCT
ejpam-1224	912	8	dn	dn	PROPN
ejpam-1224	912	9	)	)	PUNCT
ejpam-1224	912	10	p	p	X
ejpam-1224	912	11	q	q	NOUN
ejpam-1224	913	1	=	=	PUNCT
ejpam-1224	913	2	(	(	PUNCT
ejpam-1224	913	3	gbn)pq	gbn)pq	PROPN
ejpam-1224	913	4	.	.	PUNCT
ejpam-1224	914	1	we	we	PRON
ejpam-1224	914	2	know	know	VERB
ejpam-1224	914	3	that	that	PRON
ejpam-1224	914	4	fψ(m	fψ(m	PUNCT
ejpam-1224	914	5	,	,	PUNCT
ejpam-1224	914	6	dm	dm	X
ejpam-1224	914	7	)	)	PUNCT
ejpam-1224	914	8	p	p	X
ejpam-1224	914	9	q	q	NOUN
ejpam-1224	914	10	=	=	PUNCT
ejpam-1224	914	11	⊕	⊕	PROPN
ejpam-1224	914	12	r+s	r+s	PROPN
ejpam-1224	914	13	=	=	SYM
ejpam-1224	914	14	q	q	NOUN
ejpam-1224	914	15	ar	ar	NOUN
ejpam-1224	914	16	⊗ψ(m	⊗ψ(m	NOUN
ejpam-1224	914	17	)	)	PUNCT
ejpam-1224	915	1	p	p	X
ejpam-1224	915	2	s	s	PART
ejpam-1224	915	3	=	=	PROPN
ejpam-1224	915	4	⊕	⊕	PROPN
ejpam-1224	915	5	r+s	r+s	PROPN
ejpam-1224	915	6	=	=	PROPN
ejpam-1224	915	7	q	q	NOUN
ejpam-1224	915	8	b	b	NOUN
ejpam-1224	915	9	!	!	PUNCT
ejpam-1224	916	1	r	r	NOUN
ejpam-1224	916	2	⊗m	⊗m	NOUN
ejpam-1224	916	3	p+s	p+s	NUM
ejpam-1224	916	4	−s	−s	NOUN
ejpam-1224	917	1	and	and	CCONJ
ejpam-1224	917	2	we	we	PRON
ejpam-1224	917	3	also	also	ADV
ejpam-1224	917	4	know	know	VERB
ejpam-1224	917	5	that	that	SCONJ
ejpam-1224	917	6	(	(	PUNCT
ejpam-1224	917	7	fbm)pq	fbm)pq	ADJ
ejpam-1224	917	8	=	=	SYM
ejpam-1224	917	9	⊕	⊕	PROPN
ejpam-1224	917	10	p	p	NOUN
ejpam-1224	917	11	=	=	PROPN
ejpam-1224	917	12	i+	i+	NOUN
ejpam-1224	917	13	j	j	NOUN
ejpam-1224	917	14	q	q	NOUN
ejpam-1224	918	1	=	=	VERB
ejpam-1224	918	2	l−	l−	NOUN
ejpam-1224	918	3	j	j	PROPN
ejpam-1224	918	4	b	b	X
ejpam-1224	918	5	!	!	PUNCT
ejpam-1224	919	1	l	l	PROPN
ejpam-1224	919	2	⊗m	⊗m	NOUN
ejpam-1224	920	1	i	i	PRON
ejpam-1224	920	2	j	j	PROPN
ejpam-1224	921	1	so	so	ADV
ejpam-1224	921	2	fψ(m	fψ(m	PUNCT
ejpam-1224	921	3	,	,	PUNCT
ejpam-1224	921	4	dm	dm	X
ejpam-1224	921	5	)	)	PUNCT
ejpam-1224	922	1	p	p	X
ejpam-1224	922	2	q	q	NOUN
ejpam-1224	922	3	=	=	PUNCT
ejpam-1224	922	4	(	(	PUNCT
ejpam-1224	922	5	fbm	fbm	NOUN
ejpam-1224	922	6	)	)	PUNCT
ejpam-1224	922	7	p	p	NOUN
ejpam-1224	922	8	q	q	NOUN
ejpam-1224	922	9	as	as	ADV
ejpam-1224	922	10	long	long	ADV
ejpam-1224	922	11	as	as	SCONJ
ejpam-1224	922	12	i	i	PRON
ejpam-1224	922	13	=	=	PROPN
ejpam-1224	922	14	p	p	PROPN
ejpam-1224	923	1	+	+	X
ejpam-1224	923	2	s	s	PROPN
ejpam-1224	923	3	,	,	PUNCT
ejpam-1224	923	4	j	j	NOUN
ejpam-1224	923	5	=	=	PUNCT
ejpam-1224	923	6	−s	−s	PROPN
ejpam-1224	923	7	,	,	PUNCT
ejpam-1224	923	8	and	and	CCONJ
ejpam-1224	924	1	l	l	NOUN
ejpam-1224	924	2	=	=	PUNCT
ejpam-1224	924	3	r	r	NOUN
ejpam-1224	924	4	which	which	PRON
ejpam-1224	924	5	are	be	AUX
ejpam-1224	924	6	all	all	ADV
ejpam-1224	924	7	clearly	clearly	ADV
ejpam-1224	924	8	true	true	ADJ
ejpam-1224	924	9	since	since	SCONJ
ejpam-1224	924	10	we	we	PRON
ejpam-1224	924	11	know	know	VERB
ejpam-1224	925	1	that	that	SCONJ
ejpam-1224	925	2	p	p	PROPN
ejpam-1224	925	3	=	=	X
ejpam-1224	925	4	i+	i+	X
ejpam-1224	925	5	j	j	PROPN
ejpam-1224	925	6	,	,	PUNCT
ejpam-1224	925	7	q	q	PROPN
ejpam-1224	925	8	=	=	PUNCT
ejpam-1224	925	9	l	l	NOUN
ejpam-1224	926	1	−	−	X
ejpam-1224	926	2	j	j	PROPN
ejpam-1224	926	3	and	and	CCONJ
ejpam-1224	926	4	r	r	PROPN
ejpam-1224	926	5	+	+	SYM
ejpam-1224	926	6	s	s	PART
ejpam-1224	926	7	=	=	NOUN
ejpam-1224	926	8	q.	q.	NOUN
ejpam-1224	926	9	we	we	PRON
ejpam-1224	926	10	also	also	ADV
ejpam-1224	926	11	must	must	AUX
ejpam-1224	926	12	check	check	VERB
ejpam-1224	926	13	that	that	SCONJ
ejpam-1224	926	14	the	the	DET
ejpam-1224	926	15	differential	differential	NOUN
ejpam-1224	926	16	on	on	ADP
ejpam-1224	926	17	fψ(m	fψ(m	PUNCT
ejpam-1224	926	18	,	,	PUNCT
ejpam-1224	926	19	dm	dm	PROPN
ejpam-1224	926	20	)	)	PUNCT
ejpam-1224	926	21	p	p	X
ejpam-1224	926	22	q	q	PROPN
ejpam-1224	926	23	matches	match	VERB
ejpam-1224	926	24	the	the	DET
ejpam-1224	926	25	differential	differential	NOUN
ejpam-1224	926	26	on	on	ADP
ejpam-1224	926	27	(	(	PUNCT
ejpam-1224	926	28	fb	fb	INTJ
ejpam-1224	926	29	m	m	PROPN
ejpam-1224	926	30	)	)	PUNCT
ejpam-1224	926	31	p	p	X
ejpam-1224	926	32	q	q	NOUN
ejpam-1224	926	33	.	.	PUNCT
ejpam-1224	927	1	for	for	SCONJ
ejpam-1224	927	2	x	x	PROPN
ejpam-1224	927	3	∈	∈	PROPN
ejpam-1224	927	4	n	n	NOUN
ejpam-1224	927	5	s	s	VERB
ejpam-1224	927	6	we	we	PRON
ejpam-1224	927	7	have	have	VERB
ejpam-1224	927	8	the	the	DET
ejpam-1224	927	9	differential	differential	NOUN
ejpam-1224	927	10	on	on	ADP
ejpam-1224	927	11	fψ(m	fψ(m	PUNCT
ejpam-1224	927	12	,	,	PUNCT
ejpam-1224	927	13	dm	dm	PROPN
ejpam-1224	927	14	)	)	PUNCT
ejpam-1224	927	15	is	be	AUX
ejpam-1224	927	16	given	give	VERB
ejpam-1224	927	17	by	by	ADP
ejpam-1224	927	18	df	df	PROPN
ejpam-1224	927	19	(	(	PUNCT
ejpam-1224	927	20	a⊗	a⊗	NOUN
ejpam-1224	927	21	n	n	CCONJ
ejpam-1224	927	22	)	)	PUNCT
ejpam-1224	928	1	=	=	SYM
ejpam-1224	928	2	σaxα⊗	σaxα⊗	PROPN
ejpam-1224	928	3	x̌αn+	x̌αn+	PROPN
ejpam-1224	928	4	a⊗	a⊗	PROPN
ejpam-1224	928	5	dn	dn	PROPN
ejpam-1224	928	6	(	(	PUNCT
ejpam-1224	928	7	n	n	CCONJ
ejpam-1224	928	8	)	)	PUNCT
ejpam-1224	928	9	=	=	SYM
ejpam-1224	929	1	σaxα⊗	σaxα⊗	PROPN
ejpam-1224	929	2	x̌αn+	x̌αn+	PUNCT
ejpam-1224	930	1	(	(	PUNCT
ejpam-1224	930	2	−1)sa⊗	−1)sa⊗	NOUN
ejpam-1224	930	3	dm	dm	X
ejpam-1224	930	4	(	(	PUNCT
ejpam-1224	930	5	n	n	CCONJ
ejpam-1224	930	6	)	)	PUNCT
ejpam-1224	930	7	.	.	PUNCT
ejpam-1224	931	1	the	the	DET
ejpam-1224	931	2	differential	differential	NOUN
ejpam-1224	931	3	for	for	ADP
ejpam-1224	931	4	fb(m	fb(m	NOUN
ejpam-1224	931	5	,	,	PUNCT
ejpam-1224	931	6	dm	dm	PROPN
ejpam-1224	931	7	)	)	PUNCT
ejpam-1224	931	8	with	with	ADP
ejpam-1224	931	9	a⊗m	a⊗m	PROPN
ejpam-1224	931	10	∈	∈	PROPN
ejpam-1224	931	11	b	b	X
ejpam-1224	931	12	!	!	PUNCT
ejpam-1224	932	1	m	m	PROPN
ejpam-1224	932	2	⊗m	⊗m	NOUN
ejpam-1224	933	1	i	i	PRON
ejpam-1224	933	2	j	j	PROPN
ejpam-1224	933	3	is	be	AUX
ejpam-1224	933	4	given	give	VERB
ejpam-1224	933	5	by	by	ADP
ejpam-1224	933	6	dfb	dfb	PROPN
ejpam-1224	933	7	(	(	PUNCT
ejpam-1224	933	8	a⊗	a⊗	NOUN
ejpam-1224	933	9	n	n	CCONJ
ejpam-1224	933	10	)	)	PUNCT
ejpam-1224	933	11	=	=	PUNCT
ejpam-1224	933	12	(	(	PUNCT
ejpam-1224	933	13	−1)i+	−1)i+	NOUN
ejpam-1224	933	14	jσav̌α⊗	jσav̌α⊗	ADV
ejpam-1224	934	1	vαm+	vαm+	PROPN
ejpam-1224	934	2	a⊗	a⊗	PROPN
ejpam-1224	934	3	dm	dm	PROPN
ejpam-1224	934	4	(	(	PUNCT
ejpam-1224	934	5	n	n	CCONJ
ejpam-1224	934	6	)	)	PUNCT
ejpam-1224	934	7	.	.	PUNCT
ejpam-1224	935	1	since	since	SCONJ
ejpam-1224	935	2	i+	i+	NUM
ejpam-1224	935	3	j	j	PROPN
ejpam-1224	935	4	=	=	SYM
ejpam-1224	935	5	s	s	VERB
ejpam-1224	935	6	we	we	PRON
ejpam-1224	935	7	see	see	VERB
ejpam-1224	935	8	that	that	SCONJ
ejpam-1224	935	9	df	df	PROPN
ejpam-1224	935	10	and	and	CCONJ
ejpam-1224	935	11	dfb	dfb	PROPN
ejpam-1224	935	12	differ	differ	VERB
ejpam-1224	935	13	by	by	ADP
ejpam-1224	935	14	a	a	DET
ejpam-1224	935	15	sign	sign	NOUN
ejpam-1224	935	16	:	:	PUNCT
ejpam-1224	935	17	df	df	PROPN
ejpam-1224	935	18	(	(	PUNCT
ejpam-1224	935	19	a⊗	a⊗	NOUN
ejpam-1224	935	20	n	n	CCONJ
ejpam-1224	935	21	)	)	PUNCT
ejpam-1224	936	1	=	=	SYM
ejpam-1224	936	2	(	(	PUNCT
ejpam-1224	936	3	−1)i+	−1)i+	NOUN
ejpam-1224	936	4	jdfb	jdfb	NOUN
ejpam-1224	936	5	(	(	PUNCT
ejpam-1224	936	6	a⊗	a⊗	NOUN
ejpam-1224	936	7	n	n	CCONJ
ejpam-1224	936	8	)	)	PUNCT
ejpam-1224	936	9	.	.	PUNCT
ejpam-1224	937	1	let	let	VERB
ejpam-1224	937	2	us	we	PRON
ejpam-1224	937	3	check	check	VERB
ejpam-1224	937	4	that	that	PRON
ejpam-1224	937	5	gb	gb	ADP
ejpam-1224	937	6	=	=	NOUN
ejpam-1224	937	7	φg	φg	VERB
ejpam-1224	937	8	.	.	PUNCT
ejpam-1224	938	1	we	we	PRON
ejpam-1224	938	2	know	know	VERB
ejpam-1224	938	3	that	that	SCONJ
ejpam-1224	938	4	the	the	DET
ejpam-1224	938	5	following	follow	VERB
ejpam-1224	938	6	expression	expression	NOUN
ejpam-1224	938	7	(	(	PUNCT
ejpam-1224	938	8	gbn)pq	gbn)pq	NOUN
ejpam-1224	938	9	=	=	PROPN
ejpam-1224	938	10	⊕	⊕	PROPN
ejpam-1224	938	11	p	p	NOUN
ejpam-1224	938	12	=	=	PROPN
ejpam-1224	938	13	i+	i+	NOUN
ejpam-1224	938	14	j	j	NOUN
ejpam-1224	938	15	q	q	NOUN
ejpam-1224	938	16	=	=	VERB
ejpam-1224	938	17	l−	l−	NOUN
ejpam-1224	938	18	j	j	PROPN
ejpam-1224	938	19	homk(b−l	homk(b−l	PROPN
ejpam-1224	938	20	,	,	PUNCT
ejpam-1224	938	21	n	n	CCONJ
ejpam-1224	938	22	i	i	PRON
ejpam-1224	938	23	j	j	PROPN
ejpam-1224	938	24	)	)	PUNCT
ejpam-1224	938	25	will	will	AUX
ejpam-1224	938	26	be	be	AUX
ejpam-1224	938	27	equal	equal	ADJ
ejpam-1224	938	28	to	to	ADP
ejpam-1224	938	29	φg(n	φg(n	NOUN
ejpam-1224	938	30	,	,	PUNCT
ejpam-1224	938	31	dn	dn	PROPN
ejpam-1224	938	32	)	)	PUNCT
ejpam-1224	938	33	p	p	X
ejpam-1224	938	34	q	q	PROPN
ejpam-1224	938	35	=	=	SYM
ejpam-1224	938	36	g(n	g(n	PROPN
ejpam-1224	938	37	,	,	PUNCT
ejpam-1224	938	38	dn	dn	PROPN
ejpam-1224	938	39	)	)	PUNCT
ejpam-1224	938	40	p+q	p+q	NOUN
ejpam-1224	938	41	−q	−q	NOUN
ejpam-1224	938	42	=	=	PUNCT
ejpam-1224	938	43	⊕	⊕	PROPN
ejpam-1224	938	44	r≥0	r≥0	NOUN
ejpam-1224	938	45	homk(br	homk(br	PROPN
ejpam-1224	938	46	,	,	PUNCT
ejpam-1224	938	47	n	n	CCONJ
ejpam-1224	938	48	p+q+r	p+q+r	NOUN
ejpam-1224	938	49	−q−r	−q−r	PROPN
ejpam-1224	938	50	)	)	PUNCT
ejpam-1224	938	51	references	reference	VERB
ejpam-1224	938	52	539	539	NUM
ejpam-1224	938	53	only	only	ADV
ejpam-1224	938	54	if	if	SCONJ
ejpam-1224	938	55	r	r	NOUN
ejpam-1224	938	56	=	=	SYM
ejpam-1224	938	57	−l	−l	NOUN
ejpam-1224	938	58	,	,	PUNCT
ejpam-1224	938	59	j	j	NOUN
ejpam-1224	938	60	=	=	PUNCT
ejpam-1224	938	61	−q−	−q−	NOUN
ejpam-1224	938	62	r	r	NOUN
ejpam-1224	938	63	,	,	PUNCT
ejpam-1224	938	64	and	and	CCONJ
ejpam-1224	938	65	i	i	PRON
ejpam-1224	938	66	=	=	PROPN
ejpam-1224	938	67	p+q+	p+q+	NUM
ejpam-1224	938	68	r.	r.	NOUN
ejpam-1224	938	69	these	these	DET
ejpam-1224	938	70	identities	identity	NOUN
ejpam-1224	938	71	follow	follow	VERB
ejpam-1224	938	72	immediately	immediately	ADV
ejpam-1224	938	73	by	by	ADP
ejpam-1224	938	74	definition	definition	NOUN
ejpam-1224	938	75	of	of	ADP
ejpam-1224	938	76	p	p	NOUN
ejpam-1224	938	77	and	and	CCONJ
ejpam-1224	938	78	q	q	NOUN
ejpam-1224	938	79	proving	prove	VERB
ejpam-1224	938	80	that	that	SCONJ
ejpam-1224	938	81	gb	gb	ADP
ejpam-1224	938	82	=	=	VERB
ejpam-1224	938	83	φg	φg	VERB
ejpam-1224	938	84	.	.	PUNCT
ejpam-1224	938	85	to	to	PART
ejpam-1224	938	86	verify	verify	VERB
ejpam-1224	938	87	that	that	SCONJ
ejpam-1224	938	88	the	the	DET
ejpam-1224	938	89	differentials	differential	NOUN
ejpam-1224	938	90	agree	agree	VERB
ejpam-1224	938	91	consider	consider	VERB
ejpam-1224	938	92	the	the	DET
ejpam-1224	938	93	total	total	ADJ
ejpam-1224	938	94	differential	differential	NOUN
ejpam-1224	938	95	on	on	ADP
ejpam-1224	938	96	(	(	PUNCT
ejpam-1224	938	97	gbn)i	gbn)i	NOUN
ejpam-1224	938	98	l	l	NOUN
ejpam-1224	938	99	,	,	PUNCT
ejpam-1224	938	100	for	for	ADP
ejpam-1224	938	101	b	b	PROPN
ejpam-1224	938	102	∈	∈	PROPN
ejpam-1224	938	103	b	b	X
ejpam-1224	938	104	=	=	PUNCT
ejpam-1224	938	105	a	a	PRON
ejpam-1224	938	106	!	!	PUNCT
ejpam-1224	938	107	given	give	VERB
ejpam-1224	938	108	by	by	ADP
ejpam-1224	938	109	(	(	PUNCT
ejpam-1224	938	110	dgb	dgb	PROPN
ejpam-1224	938	111	f	f	PROPN
ejpam-1224	938	112	)	)	PUNCT
ejpam-1224	938	113	(	(	PUNCT
ejpam-1224	938	114	b	b	X
ejpam-1224	938	115	)	)	PUNCT
ejpam-1224	938	116	=	=	SYM
ejpam-1224	939	1	(	(	PUNCT
ejpam-1224	939	2	−1)iσv̌α	−1)iσv̌α	INTJ
ejpam-1224	939	3	f	f	PROPN
ejpam-1224	939	4	(	(	PUNCT
ejpam-1224	939	5	vαa	vαa	NOUN
ejpam-1224	939	6	)	)	PUNCT
ejpam-1224	940	1	+	+	CCONJ
ejpam-1224	940	2	dn	dn	PROPN
ejpam-1224	940	3	(	(	PUNCT
ejpam-1224	940	4	f	f	PROPN
ejpam-1224	940	5	(	(	PUNCT
ejpam-1224	940	6	b	b	NOUN
ejpam-1224	940	7	)	)	PUNCT
ejpam-1224	940	8	)	)	PUNCT
ejpam-1224	940	9	and	and	CCONJ
ejpam-1224	940	10	the	the	DET
ejpam-1224	940	11	differential	differential	NOUN
ejpam-1224	940	12	on	on	ADP
ejpam-1224	940	13	φg(n	φg(n	NOUN
ejpam-1224	940	14	,	,	PUNCT
ejpam-1224	940	15	dn	dn	PROPN
ejpam-1224	940	16	)	)	PUNCT
ejpam-1224	941	1	p	p	X
ejpam-1224	941	2	q	q	NOUN
ejpam-1224	941	3	=	=	SYM
ejpam-1224	941	4	homk((a	homk((a	NOUN
ejpam-1224	941	5	!	!	PUNCT
ejpam-1224	941	6	)	)	PUNCT
ejpam-1224	941	7	r−r	r−r	VERB
ejpam-1224	941	8	,	,	PUNCT
ejpam-1224	941	9	n	n	CCONJ
ejpam-1224	941	10	p+q+r	p+q+r	NOUN
ejpam-1224	941	11	−q−r	−q−r	PROPN
ejpam-1224	941	12	)	)	PUNCT
ejpam-1224	941	13	for	for	ADP
ejpam-1224	941	14	a	a	DET
ejpam-1224	941	15	∈	∈	PROPN
ejpam-1224	941	16	a	a	PRON
ejpam-1224	941	17	!	!	PUNCT
ejpam-1224	941	18	which	which	PRON
ejpam-1224	941	19	is	be	AUX
ejpam-1224	941	20	given	give	VERB
ejpam-1224	941	21	by	by	ADP
ejpam-1224	941	22	(	(	PUNCT
ejpam-1224	941	23	dg	dg	PROPN
ejpam-1224	941	24	f	f	PROPN
ejpam-1224	941	25	)	)	PUNCT
ejpam-1224	941	26	(	(	PUNCT
ejpam-1224	941	27	a	a	X
ejpam-1224	941	28	)	)	PUNCT
ejpam-1224	941	29	=	=	SYM
ejpam-1224	942	1	(	(	PUNCT
ejpam-1224	942	2	−1)|	−1)|	NOUN
ejpam-1224	942	3	f	f	PROPN
ejpam-1224	942	4	|+1σxα	|+1σxα	PROPN
ejpam-1224	942	5	f	f	PROPN
ejpam-1224	942	6	(	(	PUNCT
ejpam-1224	942	7	x̌αa	x̌αa	PROPN
ejpam-1224	942	8	)	)	PUNCT
ejpam-1224	943	1	+	+	CCONJ
ejpam-1224	943	2	(	(	PUNCT
ejpam-1224	943	3	−1)|	−1)|	PROPN
ejpam-1224	943	4	f	f	PROPN
ejpam-1224	943	5	|+1	|+1	PROPN
ejpam-1224	943	6	f	f	PROPN
ejpam-1224	943	7	(	(	PUNCT
ejpam-1224	943	8	da!(a	da!(a	PROPN
ejpam-1224	943	9	)	)	PUNCT
ejpam-1224	943	10	)	)	PUNCT
ejpam-1224	944	1	+	+	CCONJ
ejpam-1224	944	2	dn	dn	X
ejpam-1224	944	3	(	(	PUNCT
ejpam-1224	944	4	f	f	PROPN
ejpam-1224	944	5	(	(	PUNCT
ejpam-1224	944	6	a	a	NOUN
ejpam-1224	944	7	)	)	PUNCT
ejpam-1224	944	8	)	)	PUNCT
ejpam-1224	944	9	.	.	PUNCT
ejpam-1224	945	1	=	=	PUNCT
ejpam-1224	945	2	(	(	PUNCT
ejpam-1224	945	3	−1)p+q+1σxα	−1)p+q+1σxα	X
ejpam-1224	945	4	f	f	X
ejpam-1224	945	5	(	(	PUNCT
ejpam-1224	945	6	x̌αa	x̌αa	PROPN
ejpam-1224	945	7	)	)	PUNCT
ejpam-1224	945	8	+	+	CCONJ
ejpam-1224	945	9	(	(	PUNCT
ejpam-1224	945	10	−1)p+q+1dn	−1)p+q+1dn	PROPN
ejpam-1224	945	11	(	(	PUNCT
ejpam-1224	945	12	f	f	X
ejpam-1224	945	13	(	(	PUNCT
ejpam-1224	945	14	a	a	NOUN
ejpam-1224	945	15	)	)	PUNCT
ejpam-1224	945	16	)	)	PUNCT
ejpam-1224	945	17	=	=	SYM
ejpam-1224	945	18	(	(	PUNCT
ejpam-1224	945	19	−1)r+1σxα	−1)r+1σxα	X
ejpam-1224	945	20	f	f	PROPN
ejpam-1224	945	21	(	(	PUNCT
ejpam-1224	945	22	x̌αa	x̌αa	PROPN
ejpam-1224	945	23	)	)	PUNCT
ejpam-1224	945	24	+	+	CCONJ
ejpam-1224	945	25	dn	dn	PROPN
ejpam-1224	945	26	(	(	PUNCT
ejpam-1224	945	27	f	f	PROPN
ejpam-1224	945	28	(	(	PUNCT
ejpam-1224	945	29	a	a	NOUN
ejpam-1224	945	30	)	)	PUNCT
ejpam-1224	945	31	)	)	PUNCT
ejpam-1224	946	1	we	we	PRON
ejpam-1224	946	2	can	can	AUX
ejpam-1224	946	3	see	see	VERB
ejpam-1224	946	4	that	that	SCONJ
ejpam-1224	946	5	the	the	DET
ejpam-1224	946	6	two	two	NUM
ejpam-1224	946	7	differentials	differential	NOUN
ejpam-1224	946	8	,	,	PUNCT
ejpam-1224	946	9	dgb	dgb	PROPN
ejpam-1224	946	10	and	and	CCONJ
ejpam-1224	946	11	dg	dg	PROPN
ejpam-1224	946	12	,	,	PUNCT
ejpam-1224	946	13	only	only	ADV
ejpam-1224	946	14	differ	differ	VERB
ejpam-1224	946	15	by	by	ADP
ejpam-1224	946	16	a	a	DET
ejpam-1224	946	17	sign	sign	NOUN
ejpam-1224	946	18	.	.	PUNCT
ejpam-1224	947	1	references	reference	NOUN
ejpam-1224	947	2	[	[	X
ejpam-1224	947	3	1	1	NUM
ejpam-1224	947	4	]	]	PUNCT
ejpam-1224	947	5	a.	a.	NOUN
ejpam-1224	947	6	beilinson	beilinson	PROPN
ejpam-1224	947	7	,	,	PUNCT
ejpam-1224	947	8	v.	v.	ADP
ejpam-1224	947	9	ginzburg	ginzburg	NOUN
ejpam-1224	947	10	,	,	PUNCT
ejpam-1224	947	11	and	and	CCONJ
ejpam-1224	947	12	w.	w.	PROPN
ejpam-1224	947	13	soergel	soergel	PROPN
ejpam-1224	947	14	.	.	PUNCT
ejpam-1224	948	1	koszul	koszul	ADJ
ejpam-1224	948	2	duality	duality	NOUN
ejpam-1224	948	3	patterns	pattern	NOUN
ejpam-1224	948	4	in	in	ADP
ejpam-1224	948	5	representation	representation	NOUN
ejpam-1224	948	6	theory	theory	NOUN
ejpam-1224	948	7	,	,	PUNCT
ejpam-1224	948	8	journal	journal	NOUN
ejpam-1224	948	9	of	of	ADP
ejpam-1224	948	10	the	the	DET
ejpam-1224	948	11	american	american	PROPN
ejpam-1224	948	12	mathematical	mathematical	PROPN
ejpam-1224	948	13	society	society	NOUN
ejpam-1224	948	14	.	.	PUNCT
ejpam-1224	949	1	9	9	NUM
ejpam-1224	949	2	)	)	PUNCT
ejpam-1224	949	3	,	,	PUNCT
ejpam-1224	949	4	no.2	no.2	PROPN
ejpam-1224	949	5	473	473	NUM
ejpam-1224	949	6	-	-	SYM
ejpam-1224	949	7	527	527	NUM
ejpam-1224	949	8	.	.	PUNCT
ejpam-1224	949	9	1996	1996	NUM
ejpam-1224	949	10	.	.	PUNCT
ejpam-1224	950	1	[	[	X
ejpam-1224	950	2	2	2	NUM
ejpam-1224	950	3	]	]	X
ejpam-1224	950	4	i.	i.	PROPN
ejpam-1224	950	5	bernstein	bernstein	PROPN
ejpam-1224	950	6	,	,	PUNCT
ejpam-1224	950	7	i.	i.	PROPN
ejpam-1224	950	8	gelfand	gelfand	PROPN
ejpam-1224	950	9	,	,	PUNCT
ejpam-1224	950	10	and	and	CCONJ
ejpam-1224	950	11	s.	s.	PROPN
ejpam-1224	950	12	gelfand	gelfand	PROPN
ejpam-1224	950	13	.	.	PUNCT
ejpam-1224	951	1	algebraic	algebraic	ADJ
ejpam-1224	951	2	bundles	bundle	NOUN
ejpam-1224	951	3	over	over	ADP
ejpam-1224	951	4	pn	pn	NOUN
ejpam-1224	951	5	and	and	CCONJ
ejpam-1224	951	6	problems	problem	NOUN
ejpam-1224	951	7	of	of	ADP
ejpam-1224	951	8	linear	linear	PROPN
ejpam-1224	951	9	algebra	algebra	PROPN
ejpam-1224	951	10	,	,	PUNCT
ejpam-1224	951	11	funktsional’nyi	funktsional’nyi	PROPN
ejpam-1224	951	12	analiz	analiz	NOUN
ejpam-1224	951	13	i	i	PRON
ejpam-1224	951	14	ego	ego	VERB
ejpam-1224	951	15	prilozheniya	prilozheniya	NOUN
ejpam-1224	951	16	12	12	NUM
ejpam-1224	951	17	)	)	PUNCT
ejpam-1224	951	18	;	;	PUNCT
ejpam-1224	951	19	english	english	ADJ
ejpam-1224	951	20	translation	translation	NOUN
ejpam-1224	951	21	in	in	ADP
ejpam-1224	951	22	functional	functional	ADJ
ejpam-1224	951	23	analysis	analysis	NOUN
ejpam-1224	951	24	and	and	CCONJ
ejpam-1224	951	25	its	its	PRON
ejpam-1224	951	26	applications	application	NOUN
ejpam-1224	951	27	12	12	NUM
ejpam-1224	951	28	,	,	PUNCT
ejpam-1224	951	29	212	212	NUM
ejpam-1224	951	30	-	-	SYM
ejpam-1224	951	31	214	214	NUM
ejpam-1224	951	32	.	.	PUNCT
ejpam-1224	952	1	1978	1978	NUM
ejpam-1224	952	2	.	.	PUNCT
ejpam-1224	953	1	[	[	X
ejpam-1224	953	2	3	3	X
ejpam-1224	953	3	]	]	X
ejpam-1224	953	4	g.	g.	PROPN
ejpam-1224	953	5	floystad	floystad	PROPN
ejpam-1224	953	6	.	.	PUNCT
ejpam-1224	954	1	koszul	koszul	ADJ
ejpam-1224	954	2	duality	duality	NOUN
ejpam-1224	954	3	and	and	CCONJ
ejpam-1224	954	4	equivalences	equivalence	NOUN
ejpam-1224	954	5	of	of	ADP
ejpam-1224	954	6	categories	category	NOUN
ejpam-1224	954	7	,	,	PUNCT
ejpam-1224	954	8	transactions	transaction	NOUN
ejpam-1224	954	9	of	of	ADP
ejpam-1224	954	10	the	the	DET
ejpam-1224	954	11	american	american	PROPN
ejpam-1224	954	12	mathematical	mathematical	PROPN
ejpam-1224	954	13	society	society	NOUN
ejpam-1224	954	14	.	.	PUNCT
ejpam-1224	955	1	358	358	NUM
ejpam-1224	955	2	,	,	PUNCT
ejpam-1224	955	3	p.	p.	NOUN
ejpam-1224	955	4	2373	2373	NUM
ejpam-1224	955	5	-	-	SYM
ejpam-1224	955	6	2398	2398	NUM
ejpam-1224	955	7	.	.	PUNCT
ejpam-1224	956	1	2006	2006	NUM
ejpam-1224	956	2	.	.	PUNCT
ejpam-1224	957	1	[	[	X
ejpam-1224	957	2	4	4	NUM
ejpam-1224	957	3	]	]	ADJ
ejpam-1224	957	4	m.	m.	NOUN
ejpam-1224	957	5	kapranov	kapranov	NOUN
ejpam-1224	957	6	.	.	PUNCT
ejpam-1224	958	1	on	on	ADP
ejpam-1224	958	2	the	the	DET
ejpam-1224	958	3	derived	derive	VERB
ejpam-1224	958	4	categories	category	NOUN
ejpam-1224	958	5	of	of	ADP
ejpam-1224	958	6	coherent	coherent	ADJ
ejpam-1224	958	7	sheaves	sheaf	NOUN
ejpam-1224	958	8	on	on	ADP
ejpam-1224	958	9	some	some	DET
ejpam-1224	958	10	homogeneous	homogeneous	ADJ
ejpam-1224	958	11	spaces	space	NOUN
ejpam-1224	958	12	,	,	PUNCT
ejpam-1224	958	13	inventions	invention	NOUN
ejpam-1224	958	14	mathematicae	mathematicae	VERB
ejpam-1224	958	15	.	.	PUNCT
ejpam-1224	959	1	92	92	NUM
ejpam-1224	959	2	,	,	PUNCT
ejpam-1224	959	3	479	479	NUM
ejpam-1224	959	4	-	-	SYM
ejpam-1224	959	5	508	508	NUM
ejpam-1224	959	6	.	.	PUNCT
ejpam-1224	959	7	1988	1988	NUM
ejpam-1224	959	8	.	.	PUNCT
ejpam-1224	960	1	[	[	X
ejpam-1224	960	2	5	5	NUM
ejpam-1224	960	3	]	]	PUNCT
ejpam-1224	960	4	a.	a.	NOUN
ejpam-1224	960	5	polishchuk	polishchuk	NOUN
ejpam-1224	960	6	and	and	CCONJ
ejpam-1224	960	7	l.	l.	PROPN
ejpam-1224	960	8	positselski	positselski	PROPN
ejpam-1224	960	9	.	.	PUNCT
ejpam-1224	961	1	quadratic	quadratic	ADJ
ejpam-1224	961	2	algebras	algebra	NOUN
ejpam-1224	961	3	,	,	PUNCT
ejpam-1224	961	4	university	university	NOUN
ejpam-1224	961	5	lecture	lecture	NOUN
ejpam-1224	961	6	series,37	series,37	NOUN
ejpam-1224	961	7	.	.	PUNCT
ejpam-1224	962	1	american	american	PROPN
ejpam-1224	962	2	mathematical	mathematical	PROPN
ejpam-1224	962	3	society	society	NOUN
ejpam-1224	962	4	,	,	PUNCT
ejpam-1224	962	5	providence	providence	NOUN
ejpam-1224	962	6	,	,	PUNCT
ejpam-1224	962	7	ri	ri	NOUN
ejpam-1224	962	8	,	,	PUNCT
ejpam-1224	962	9	2005	2005	NUM
ejpam-1224	962	10	.	.	PUNCT