id	sid	tid	token	lemma	pos
ejpam-3742	1	1	european	european	PROPN
ejpam-3742	1	2	journal	journal	PROPN
ejpam-3742	1	3	of	of	ADP
ejpam-3742	1	4	pure	pure	ADJ
ejpam-3742	1	5	and	and	CCONJ
ejpam-3742	1	6	applied	apply	VERB
ejpam-3742	1	7	mathematics	mathematic	NOUN
ejpam-3742	1	8	vol	vol	NOUN
ejpam-3742	1	9	.	.	PROPN
ejpam-3742	2	1	13	13	NUM
ejpam-3742	2	2	,	,	PUNCT
ejpam-3742	2	3	no	no	INTJ
ejpam-3742	2	4	.	.	NOUN
ejpam-3742	2	5	3	3	NUM
ejpam-3742	2	6	,	,	PUNCT
ejpam-3742	2	7	2020	2020	NUM
ejpam-3742	2	8	,	,	PUNCT
ejpam-3742	2	9	472	472	NUM
ejpam-3742	2	10	-	-	SYM
ejpam-3742	2	11	482	482	NUM
ejpam-3742	2	12	issn	issn	PROPN
ejpam-3742	2	13	1307	1307	NUM
ejpam-3742	2	14	-	-	SYM
ejpam-3742	2	15	5543	5543	NUM
ejpam-3742	2	16	–	–	PUNCT
ejpam-3742	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3742	2	18	published	publish	VERB
ejpam-3742	2	19	by	by	ADP
ejpam-3742	2	20	new	new	PROPN
ejpam-3742	2	21	york	york	PROPN
ejpam-3742	2	22	business	business	PROPN
ejpam-3742	2	23	global	global	PROPN
ejpam-3742	2	24	adjunction	adjunction	NOUN
ejpam-3742	2	25	and	and	CCONJ
ejpam-3742	2	26	localization	localization	NOUN
ejpam-3742	2	27	in	in	ADP
ejpam-3742	2	28	the	the	DET
ejpam-3742	2	29	category	category	NOUN
ejpam-3742	2	30	a	a	DET
ejpam-3742	2	31	-	-	PUNCT
ejpam-3742	2	32	alg	alg	NOUN
ejpam-3742	2	33	of	of	ADP
ejpam-3742	2	34	a	a	DET
ejpam-3742	2	35	-	-	PUNCT
ejpam-3742	2	36	algebras	algebras	PROPN
ejpam-3742	2	37	moussa	moussa	PROPN
ejpam-3742	2	38	thiaw1,∗	thiaw1,∗	PROPN
ejpam-3742	2	39	,	,	PUNCT
ejpam-3742	2	40	mohamed	mohamed	PROPN
ejpam-3742	2	41	ben	ben	PROPN
ejpam-3742	2	42	faraj	faraj	PROPN
ejpam-3742	2	43	ben	ben	PROPN
ejpam-3742	2	44	maaouia1	maaouia1	PROPN
ejpam-3742	2	45	1	1	NUM
ejpam-3742	2	46	ufr	ufr	NOUN
ejpam-3742	2	47	-	-	PUNCT
ejpam-3742	2	48	sat	sit	VERB
ejpam-3742	2	49	/	/	SYM
ejpam-3742	2	50	gaston	gaston	PROPN
ejpam-3742	2	51	berger	berger	PROPN
ejpam-3742	2	52	,	,	PUNCT
ejpam-3742	2	53	university	university	NOUN
ejpam-3742	2	54	,	,	PUNCT
ejpam-3742	2	55	saint	saint	NOUN
ejpam-3742	2	56	-	-	PUNCT
ejpam-3742	2	57	louis	louis	NOUN
ejpam-3742	2	58	,	,	PUNCT
ejpam-3742	2	59	senegal	senegal	NOUN
ejpam-3742	2	60	in	in	ADP
ejpam-3742	2	61	memory	memory	NOUN
ejpam-3742	2	62	of	of	ADP
ejpam-3742	2	63	the	the	DET
ejpam-3742	2	64	dead	dead	NOUN
ejpam-3742	2	65	of	of	ADP
ejpam-3742	2	66	covid-19	covid-19	PROPN
ejpam-3742	2	67	abstract	abstract	NOUN
ejpam-3742	2	68	.	.	PUNCT
ejpam-3742	3	1	in	in	ADP
ejpam-3742	3	2	our	our	PRON
ejpam-3742	3	3	paper	paper	NOUN
ejpam-3742	3	4	[	[	X
ejpam-3742	3	5	3	3	X
ejpam-3742	3	6	]	]	PUNCT
ejpam-3742	3	7	we	we	PRON
ejpam-3742	3	8	built	build	VERB
ejpam-3742	3	9	the	the	DET
ejpam-3742	3	10	functor	functor	PROPN
ejpam-3742	3	11	êxt	êxt	NOUN
ejpam-3742	3	12	n	n	DET
ejpam-3742	3	13	s−1a(-	s−1a(-	NOUN
ejpam-3742	3	14	,	,	PUNCT
ejpam-3742	3	15	s−1b	s−1b	ADV
ejpam-3742	3	16	)	)	PUNCT
ejpam-3742	3	17	in	in	ADP
ejpam-3742	3	18	the	the	DET
ejpam-3742	3	19	category	category	NOUN
ejpam-3742	3	20	a	a	DET
ejpam-3742	3	21	-	-	PUNCT
ejpam-3742	3	22	alg	alg	PROPN
ejpam-3742	3	23	.	.	PUNCT
ejpam-3742	4	1	the	the	DET
ejpam-3742	4	2	purpuse	purpuse	NOUN
ejpam-3742	4	3	of	of	ADP
ejpam-3742	4	4	this	this	DET
ejpam-3742	4	5	paper	paper	NOUN
ejpam-3742	4	6	is	be	AUX
ejpam-3742	4	7	to	to	PART
ejpam-3742	4	8	show	show	VERB
ejpam-3742	4	9	that	that	SCONJ
ejpam-3742	4	10	if	if	SCONJ
ejpam-3742	4	11	a	a	PRON
ejpam-3742	4	12	is	be	AUX
ejpam-3742	4	13	a	a	DET
ejpam-3742	4	14	ring	ring	NOUN
ejpam-3742	4	15	not	not	PART
ejpam-3742	4	16	necessary	necessary	ADJ
ejpam-3742	4	17	commutative	commutative	ADJ
ejpam-3742	4	18	,	,	PUNCT
ejpam-3742	4	19	s	s	VERB
ejpam-3742	4	20	a	a	DET
ejpam-3742	4	21	central	central	ADJ
ejpam-3742	4	22	multiplicatively	multiplicatively	ADV
ejpam-3742	4	23	closed	close	VERB
ejpam-3742	4	24	subset	subset	NOUN
ejpam-3742	4	25	of	of	ADP
ejpam-3742	4	26	a	a	PRON
ejpam-3742	4	27	and	and	CCONJ
ejpam-3742	4	28	b	b	NOUN
ejpam-3742	4	29	an	an	DET
ejpam-3742	4	30	(	(	PUNCT
ejpam-3742	4	31	a	a	NOUN
ejpam-3742	4	32	-	-	PUNCT
ejpam-3742	4	33	a)-bialgebra	a)-bialgebra	NOUN
ejpam-3742	4	34	,	,	PUNCT
ejpam-3742	4	35	then	then	ADV
ejpam-3742	4	36	tors	tor	NOUN
ejpam-3742	4	37	−1a	−1a	PUNCT
ejpam-3742	4	38	n	n	PROPN
ejpam-3742	4	39	(	(	PUNCT
ejpam-3742	4	40	-	-	INTJ
ejpam-3742	4	41	,	,	PUNCT
ejpam-3742	4	42	s−1b	s−1b	PROPN
ejpam-3742	4	43	)	)	PUNCT
ejpam-3742	4	44	:	:	PUNCT
ejpam-3742	5	1	alg	alg	PROPN
ejpam-3742	5	2	-	-	PUNCT
ejpam-3742	5	3	s−1a	s−1a	PROPN
ejpam-3742	5	4	�	�	PROPN
ejpam-3742	5	5	s−1a	s−1a	NOUN
ejpam-3742	5	6	-	-	PUNCT
ejpam-3742	5	7	modo	modo	NOUN
ejpam-3742	5	8	:	:	PUNCT
ejpam-3742	5	9	êxt	êxt	NOUN
ejpam-3742	5	10	n	n	PRON
ejpam-3742	5	11	s−1a(-	s−1a(-	NOUN
ejpam-3742	5	12	,	,	PUNCT
ejpam-3742	5	13	s−1b)o	s−1b)o	VERB
ejpam-3742	5	14	is	be	AUX
ejpam-3742	5	15	an	an	DET
ejpam-3742	5	16	adjunction	adjunction	NOUN
ejpam-3742	5	17	.	.	PUNCT
ejpam-3742	6	1	2020	2020	NUM
ejpam-3742	6	2	mathematics	mathematic	NOUN
ejpam-3742	6	3	subject	subject	NOUN
ejpam-3742	6	4	classifications	classification	NOUN
ejpam-3742	6	5	:	:	PUNCT
ejpam-3742	6	6	18a25	18a25	NUM
ejpam-3742	6	7	,	,	PUNCT
ejpam-3742	6	8	18a40	18a40	NUM
ejpam-3742	6	9	,	,	PUNCT
ejpam-3742	6	10	18n40	18n40	NUM
ejpam-3742	6	11	,	,	PUNCT
ejpam-3742	6	12	16e35	16e35	NUM
ejpam-3742	6	13	key	key	ADJ
ejpam-3742	6	14	words	word	NOUN
ejpam-3742	6	15	and	and	CCONJ
ejpam-3742	6	16	phrases	phrase	NOUN
ejpam-3742	6	17	:	:	PUNCT
ejpam-3742	6	18	adjunction	adjunction	NOUN
ejpam-3742	6	19	,	,	PUNCT
ejpam-3742	6	20	localization	localization	NOUN
ejpam-3742	6	21	,	,	PUNCT
ejpam-3742	6	22	algebra	algebra	NOUN
ejpam-3742	6	23	,	,	PUNCT
ejpam-3742	6	24	functor	functor	PROPN
ejpam-3742	6	25	1	1	PROPN
ejpam-3742	6	26	.	.	PUNCT
ejpam-3742	6	27	introduction	introduction	NOUN
ejpam-3742	6	28	in	in	ADP
ejpam-3742	6	29	this	this	DET
ejpam-3742	6	30	paper	paper	NOUN
ejpam-3742	6	31	,	,	PUNCT
ejpam-3742	6	32	a	a	PRON
ejpam-3742	6	33	is	be	AUX
ejpam-3742	6	34	assumed	assume	VERB
ejpam-3742	6	35	unitary	unitary	ADJ
ejpam-3742	6	36	,	,	PUNCT
ejpam-3742	6	37	associative	associative	ADJ
ejpam-3742	6	38	and	and	CCONJ
ejpam-3742	6	39	not	not	PART
ejpam-3742	6	40	necessarily	necessarily	ADV
ejpam-3742	6	41	commutative	commutative	ADJ
ejpam-3742	6	42	.	.	PUNCT
ejpam-3742	7	1	a	a	PRON
ejpam-3742	7	2	and	and	CCONJ
ejpam-3742	7	3	b	b	NOUN
ejpam-3742	7	4	are	be	AUX
ejpam-3742	7	5	algebras	algebra	NOUN
ejpam-3742	7	6	assumed	assume	VERB
ejpam-3742	7	7	unitary	unitary	ADJ
ejpam-3742	7	8	,	,	PUNCT
ejpam-3742	7	9	associative	associative	ADJ
ejpam-3742	7	10	and	and	CCONJ
ejpam-3742	7	11	not	not	PART
ejpam-3742	7	12	necessarily	necessarily	ADV
ejpam-3742	7	13	commutative	commutative	ADJ
ejpam-3742	7	14	as	as	ADP
ejpam-3742	7	15	a	a	DET
ejpam-3742	7	16	ring	ring	NOUN
ejpam-3742	7	17	and	and	CCONJ
ejpam-3742	7	18	unital	unital	ADJ
ejpam-3742	7	19	as	as	ADP
ejpam-3742	7	20	an	an	DET
ejpam-3742	7	21	a	a	DET
ejpam-3742	7	22	-	-	PUNCT
ejpam-3742	7	23	module	module	NOUN
ejpam-3742	7	24	.	.	PUNCT
ejpam-3742	8	1	in	in	ADP
ejpam-3742	8	2	general	general	ADJ
ejpam-3742	8	3	,	,	PUNCT
ejpam-3742	8	4	the	the	DET
ejpam-3742	8	5	action	action	NOUN
ejpam-3742	8	6	of	of	ADP
ejpam-3742	8	7	the	the	DET
ejpam-3742	8	8	functor	functor	PROPN
ejpam-3742	8	9	êxt	êxt	NOUN
ejpam-3742	8	10	n	n	PRON
ejpam-3742	8	11	a(-,b	a(-,b	NOUN
ejpam-3742	8	12	)	)	PUNCT
ejpam-3742	8	13	on	on	ADP
ejpam-3742	8	14	an	an	DET
ejpam-3742	8	15	a	a	DET
ejpam-3742	8	16	-	-	PUNCT
ejpam-3742	8	17	module	module	NOUN
ejpam-3742	8	18	m(resp	m(resp	NOUN
ejpam-3742	8	19	.	.	PUNCT
ejpam-3742	9	1	a	a	X
ejpam-3742	9	2	-	-	PUNCT
ejpam-3742	9	3	algebra	algebra	NOUN
ejpam-3742	9	4	a	a	PRON
ejpam-3742	9	5	)	)	PUNCT
ejpam-3742	9	6	is	be	AUX
ejpam-3742	9	7	not	not	PART
ejpam-3742	9	8	an	an	DET
ejpam-3742	9	9	algebra	algebra	NOUN
ejpam-3742	9	10	.	.	PUNCT
ejpam-3742	10	1	in	in	ADP
ejpam-3742	10	2	our	our	PRON
ejpam-3742	10	3	paper	paper	NOUN
ejpam-3742	10	4	[	[	X
ejpam-3742	10	5	3	3	X
ejpam-3742	10	6	]	]	PUNCT
ejpam-3742	10	7	we	we	PRON
ejpam-3742	10	8	built	build	VERB
ejpam-3742	10	9	the	the	DET
ejpam-3742	10	10	functors	functors	PROPN
ejpam-3742	10	11	êxt	êxt	NOUN
ejpam-3742	10	12	n	n	PRON
ejpam-3742	10	13	a(-,b	a(-,b	PROPN
ejpam-3742	10	14	)	)	PUNCT
ejpam-3742	10	15	:	:	PUNCT
ejpam-3742	10	16	alg	alg	PROPN
ejpam-3742	10	17	-	-	PUNCT
ejpam-3742	10	18	a→	a→	NOUN
ejpam-3742	10	19	b	b	NOUN
ejpam-3742	10	20	-	-	PUNCT
ejpam-3742	10	21	alg	alg	PROPN
ejpam-3742	10	22	and	and	CCONJ
ejpam-3742	10	23	s−1	s−1	PROPN
ejpam-3742	10	24	(	(	PUNCT
ejpam-3742	10	25	)	)	PUNCT
ejpam-3742	10	26	:	:	PUNCT
ejpam-3742	10	27	a	a	X
ejpam-3742	10	28	-	-	PUNCT
ejpam-3742	10	29	alg	alg	PROPN
ejpam-3742	10	30	→	→	SYM
ejpam-3742	10	31	s−1(a)-alg	s−1(a)-alg	PROPN
ejpam-3742	10	32	.	.	PUNCT
ejpam-3742	11	1	the	the	DET
ejpam-3742	11	2	notion	notion	NOUN
ejpam-3742	11	3	of	of	ADP
ejpam-3742	11	4	adjunction	adjunction	NOUN
ejpam-3742	11	5	allows	allow	VERB
ejpam-3742	11	6	to	to	PART
ejpam-3742	11	7	see	see	VERB
ejpam-3742	11	8	if	if	SCONJ
ejpam-3742	11	9	two	two	NUM
ejpam-3742	11	10	categories	category	NOUN
ejpam-3742	11	11	are	be	AUX
ejpam-3742	11	12	equivalent	equivalent	ADJ
ejpam-3742	11	13	.	.	PUNCT
ejpam-3742	12	1	this	this	DET
ejpam-3742	12	2	notion	notion	NOUN
ejpam-3742	12	3	of	of	ADP
ejpam-3742	12	4	adjunction	adjunction	NOUN
ejpam-3742	12	5	makes	make	VERB
ejpam-3742	12	6	it	it	PRON
ejpam-3742	12	7	possible	possible	ADJ
ejpam-3742	12	8	to	to	PART
ejpam-3742	12	9	preserve	preserve	VERB
ejpam-3742	12	10	some	some	DET
ejpam-3742	12	11	properties	property	NOUN
ejpam-3742	12	12	from	from	ADP
ejpam-3742	12	13	one	one	NUM
ejpam-3742	12	14	category	category	NOUN
ejpam-3742	12	15	to	to	ADP
ejpam-3742	12	16	another	another	PRON
ejpam-3742	12	17	,	,	PUNCT
ejpam-3742	12	18	such	such	ADJ
ejpam-3742	12	19	as	as	ADP
ejpam-3742	12	20	monomorphisms	monomorphism	NOUN
ejpam-3742	12	21	.	.	PUNCT
ejpam-3742	13	1	the	the	DET
ejpam-3742	13	2	purpose	purpose	NOUN
ejpam-3742	13	3	of	of	ADP
ejpam-3742	13	4	this	this	DET
ejpam-3742	13	5	paper	paper	NOUN
ejpam-3742	13	6	is	be	AUX
ejpam-3742	13	7	to	to	PART
ejpam-3742	13	8	show	show	VERB
ejpam-3742	13	9	that	that	SCONJ
ejpam-3742	13	10	tors	tor	NOUN
ejpam-3742	13	11	−1a	−1a	PUNCT
ejpam-3742	13	12	n	n	PROPN
ejpam-3742	13	13	(	(	PUNCT
ejpam-3742	13	14	-	-	INTJ
ejpam-3742	13	15	,	,	PUNCT
ejpam-3742	13	16	s−1b	s−1b	PROPN
ejpam-3742	13	17	)	)	PUNCT
ejpam-3742	13	18	:	:	PUNCT
ejpam-3742	13	19	alg	alg	PROPN
ejpam-3742	13	20	-	-	PUNCT
ejpam-3742	13	21	s−1a	s−1a	PROPN
ejpam-3742	13	22	→	→	SYM
ejpam-3742	13	23	s−1a	s−1a	NOUN
ejpam-3742	13	24	-	-	PUNCT
ejpam-3742	13	25	modo	modo	NOUN
ejpam-3742	13	26	and	and	CCONJ
ejpam-3742	13	27	êxt	êxt	NOUN
ejpam-3742	13	28	n	n	PRON
ejpam-3742	13	29	s−1a(-	s−1a(-	NOUN
ejpam-3742	13	30	,	,	PUNCT
ejpam-3742	13	31	s−1b)o	s−1b)o	VERB
ejpam-3742	13	32	:	:	PUNCT
ejpam-3742	13	33	s−1a	s−1a	ADJ
ejpam-3742	13	34	-	-	PUNCT
ejpam-3742	13	35	modo	modo	ADJ
ejpam-3742	13	36	→	→	SYM
ejpam-3742	13	37	alg	alg	PROPN
ejpam-3742	13	38	-	-	PUNCT
ejpam-3742	13	39	s−1a	s−1a	PROPN
ejpam-3742	13	40	are	be	AUX
ejpam-3742	13	41	adjoint	adjoint	PROPN
ejpam-3742	13	42	functors	functor	NOUN
ejpam-3742	13	43	,	,	PUNCT
ejpam-3742	13	44	where	where	SCONJ
ejpam-3742	13	45	s	s	NOUN
ejpam-3742	13	46	is	be	AUX
ejpam-3742	13	47	a	a	DET
ejpam-3742	13	48	central	central	ADJ
ejpam-3742	13	49	multiplicatively	multiplicatively	ADV
ejpam-3742	13	50	closed	close	VERB
ejpam-3742	13	51	subset	subset	NOUN
ejpam-3742	13	52	of	of	ADP
ejpam-3742	13	53	a	a	PRON
ejpam-3742	13	54	and	and	CCONJ
ejpam-3742	13	55	b	b	NOUN
ejpam-3742	13	56	a	a	PRON
ejpam-3742	13	57	(	(	PUNCT
ejpam-3742	13	58	a	a	NOUN
ejpam-3742	13	59	-	-	PUNCT
ejpam-3742	13	60	a)-bialgebra	a)-bialgebra	NOUN
ejpam-3742	13	61	but	but	CCONJ
ejpam-3742	13	62	before	before	ADV
ejpam-3742	13	63	,	,	PUNCT
ejpam-3742	13	64	we	we	PRON
ejpam-3742	13	65	show	show	VERB
ejpam-3742	13	66	that	that	SCONJ
ejpam-3742	13	67	the	the	DET
ejpam-3742	13	68	functors	functors	PROPN
ejpam-3742	13	69	⊗a	⊗a	PROPN
ejpam-3742	13	70	s−1(a	s−1(a	PROPN
ejpam-3742	13	71	)	)	PUNCT
ejpam-3742	13	72	:	:	PUNCT
ejpam-3742	13	73	alg	alg	PROPN
ejpam-3742	13	74	-	-	PUNCT
ejpam-3742	13	75	a	a	DET
ejpam-3742	13	76	→	→	SYM
ejpam-3742	13	77	a	a	DET
ejpam-3742	13	78	-	-	PUNCT
ejpam-3742	13	79	modo	modo	NOUN
ejpam-3742	13	80	and	and	CCONJ
ejpam-3742	13	81	homa(-	homa(-	PROPN
ejpam-3742	13	82	,	,	PUNCT
ejpam-3742	13	83	s−1(a	s−1(a	PROPN
ejpam-3742	13	84	)	)	PUNCT
ejpam-3742	13	85	)	)	PUNCT
ejpam-3742	13	86	:	:	PUNCT
ejpam-3742	13	87	a	a	X
ejpam-3742	13	88	-	-	PUNCT
ejpam-3742	13	89	modo	modo	NOUN
ejpam-3742	13	90	→	→	SYM
ejpam-3742	13	91	alg	alg	PROPN
ejpam-3742	13	92	-	-	PUNCT
ejpam-3742	13	93	a	a	PROPN
ejpam-3742	13	94	are	be	AUX
ejpam-3742	13	95	adjoint	adjoint	NOUN
ejpam-3742	13	96	,	,	PUNCT
ejpam-3742	13	97	then	then	ADV
ejpam-3742	13	98	we	we	PRON
ejpam-3742	13	99	show	show	VERB
ejpam-3742	13	100	that	that	SCONJ
ejpam-3742	13	101	the	the	DET
ejpam-3742	13	102	functors	functors	PROPN
ejpam-3742	13	103	s−1	s−1	PROPN
ejpam-3742	13	104	(	(	PUNCT
ejpam-3742	13	105	)	)	PUNCT
ejpam-3742	13	106	:	:	PUNCT
ejpam-3742	13	107	a	a	X
ejpam-3742	13	108	-	-	PUNCT
ejpam-3742	13	109	alg	alg	PROPN
ejpam-3742	13	110	→	→	SYM
ejpam-3742	13	111	s−1(a)-alg	s−1(a)-alg	PROPN
ejpam-3742	13	112	and	and	CCONJ
ejpam-3742	13	113	⊗a	⊗a	PROPN
ejpam-3742	13	114	s−1(a	s−1(a	PROPN
ejpam-3742	13	115	)	)	PUNCT
ejpam-3742	13	116	:	:	PUNCT
ejpam-3742	13	117	∗corresponding	∗corresponde	VERB
ejpam-3742	13	118	author	author	NOUN
ejpam-3742	13	119	.	.	PUNCT
ejpam-3742	14	1	doi	doi	NOUN
ejpam-3742	14	2	:	:	PUNCT
ejpam-3742	14	3	https://doi.org/10.29020/nybg.ejpam.v13i3.3742	https://doi.org/10.29020/nybg.ejpam.v13i3.3742	PUNCT
ejpam-3742	14	4	email	email	NOUN
ejpam-3742	14	5	addresses	address	VERB
ejpam-3742	14	6	:	:	PUNCT
ejpam-3742	14	7	thiawskr@gmail.com	thiawskr@gmail.com	X
ejpam-3742	14	8	(	(	PUNCT
ejpam-3742	14	9	m.	m.	NOUN
ejpam-3742	14	10	thiaw	thiaw	NOUN
ejpam-3742	14	11	)	)	PUNCT
ejpam-3742	14	12	,	,	PUNCT
ejpam-3742	15	1	mohamed-ben.maaouia@ugb.edu.sn	mohamed-ben.maaouia@ugb.edu.sn	PROPN
ejpam-3742	15	2	,	,	PUNCT
ejpam-3742	15	3	maaouiaalg@hotmail.com	maaouiaalg@hotmail.com	PROPN
ejpam-3742	15	4	(	(	PUNCT
ejpam-3742	15	5	m.	m.	NOUN
ejpam-3742	15	6	maaouia	maaouia	PROPN
ejpam-3742	15	7	)	)	PUNCT
ejpam-3742	15	8	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3742	16	1	472	472	NUM
ejpam-3742	16	2	c	c	AUX
ejpam-3742	16	3	©	©	NOUN
ejpam-3742	16	4	2020	2020	NUM
ejpam-3742	16	5	ejpam	ejpam	VERB
ejpam-3742	16	6	all	all	DET
ejpam-3742	16	7	rights	right	NOUN
ejpam-3742	16	8	reserved	reserve	VERB
ejpam-3742	16	9	.	.	PUNCT
ejpam-3742	17	1	m	m	PROPN
ejpam-3742	17	2	thiaw	thiaw	ADJ
ejpam-3742	17	3	,	,	PUNCT
ejpam-3742	17	4	m	m	AUX
ejpam-3742	17	5	maaouia	maaouia	NOUN
ejpam-3742	17	6	/	/	SYM
ejpam-3742	17	7	eur	eur	NOUN
ejpam-3742	17	8	.	.	PUNCT
ejpam-3742	18	1	j.	j.	PROPN
ejpam-3742	18	2	pure	pure	PROPN
ejpam-3742	18	3	appl	appl	PROPN
ejpam-3742	18	4	.	.	PROPN
ejpam-3742	18	5	math	math	PROPN
ejpam-3742	18	6	,	,	PUNCT
ejpam-3742	18	7	13	13	NUM
ejpam-3742	18	8	(	(	PUNCT
ejpam-3742	18	9	3	3	NUM
ejpam-3742	18	10	)	)	PUNCT
ejpam-3742	18	11	(	(	PUNCT
ejpam-3742	18	12	2020	2020	NUM
ejpam-3742	18	13	)	)	PUNCT
ejpam-3742	18	14	,	,	PUNCT
ejpam-3742	18	15	472	472	NUM
ejpam-3742	18	16	-	-	SYM
ejpam-3742	18	17	482	482	NUM
ejpam-3742	18	18	473	473	NUM
ejpam-3742	18	19	alg	alg	PROPN
ejpam-3742	18	20	-	-	PUNCT
ejpam-3742	18	21	a→	a→	PUNCT
ejpam-3742	18	22	a	a	DET
ejpam-3742	18	23	-	-	PUNCT
ejpam-3742	18	24	modo	modo	NOUN
ejpam-3742	18	25	are	be	AUX
ejpam-3742	18	26	naturally	naturally	ADV
ejpam-3742	18	27	isomorphic	isomorphic	ADJ
ejpam-3742	18	28	and	and	CCONJ
ejpam-3742	18	29	we	we	PRON
ejpam-3742	18	30	deduce	deduce	VERB
ejpam-3742	18	31	that	that	SCONJ
ejpam-3742	18	32	s−1	s−1	PROPN
ejpam-3742	18	33	(	(	PUNCT
ejpam-3742	18	34	)	)	PUNCT
ejpam-3742	18	35	:	:	PUNCT
ejpam-3742	18	36	alg	alg	PROPN
ejpam-3742	18	37	-	-	PUNCT
ejpam-3742	18	38	a	a	DET
ejpam-3742	18	39	�	�	PROPN
ejpam-3742	18	40	a	a	DET
ejpam-3742	18	41	-	-	PUNCT
ejpam-3742	18	42	modo	modo	NOUN
ejpam-3742	18	43	:	:	PUNCT
ejpam-3742	18	44	homa(-	homa(-	NOUN
ejpam-3742	18	45	,	,	PUNCT
ejpam-3742	18	46	s−1(a))o	s−1(a))o	PROPN
ejpam-3742	18	47	is	be	AUX
ejpam-3742	18	48	an	an	DET
ejpam-3742	18	49	adjunction	adjunction	NOUN
ejpam-3742	18	50	.	.	PUNCT
ejpam-3742	19	1	this	this	DET
ejpam-3742	19	2	paper	paper	NOUN
ejpam-3742	19	3	is	be	AUX
ejpam-3742	19	4	divided	divide	VERB
ejpam-3742	19	5	into	into	ADP
ejpam-3742	19	6	three	three	NUM
ejpam-3742	19	7	parts	part	NOUN
ejpam-3742	19	8	.	.	PUNCT
ejpam-3742	20	1	in	in	ADP
ejpam-3742	20	2	the	the	DET
ejpam-3742	20	3	first	first	ADJ
ejpam-3742	20	4	part	part	NOUN
ejpam-3742	20	5	entitled	entitle	VERB
ejpam-3742	20	6	”	"	PUNCT
ejpam-3742	20	7	preliminary	preliminary	ADJ
ejpam-3742	20	8	results	result	NOUN
ejpam-3742	20	9	”	"	PUNCT
ejpam-3742	20	10	we	we	PRON
ejpam-3742	20	11	recall	recall	VERB
ejpam-3742	20	12	some	some	DET
ejpam-3742	20	13	basic	basic	ADJ
ejpam-3742	20	14	results	result	NOUN
ejpam-3742	20	15	.	.	PUNCT
ejpam-3742	21	1	in	in	ADP
ejpam-3742	21	2	the	the	DET
ejpam-3742	21	3	second	second	ADJ
ejpam-3742	21	4	part	part	NOUN
ejpam-3742	21	5	,	,	PUNCT
ejpam-3742	21	6	we	we	PRON
ejpam-3742	21	7	show	show	VERB
ejpam-3742	21	8	that	that	SCONJ
ejpam-3742	21	9	the	the	DET
ejpam-3742	21	10	functors	functors	PROPN
ejpam-3742	21	11	s−1	s−1	PROPN
ejpam-3742	21	12	(	(	PUNCT
ejpam-3742	21	13	)	)	PUNCT
ejpam-3742	21	14	:	:	PUNCT
ejpam-3742	21	15	alg	alg	PROPN
ejpam-3742	21	16	-	-	PUNCT
ejpam-3742	21	17	a	a	DET
ejpam-3742	21	18	→	→	SYM
ejpam-3742	21	19	a	a	DET
ejpam-3742	21	20	-	-	PUNCT
ejpam-3742	21	21	modo	modo	NOUN
ejpam-3742	21	22	and	and	CCONJ
ejpam-3742	21	23	homa(-	homa(-	PROPN
ejpam-3742	21	24	,	,	PUNCT
ejpam-3742	21	25	s−1(a))o	s−1(a))o	NUM
ejpam-3742	21	26	:	:	PUNCT
ejpam-3742	21	27	a	a	DET
ejpam-3742	21	28	-	-	PUNCT
ejpam-3742	21	29	modo	modo	NOUN
ejpam-3742	21	30	→	→	SYM
ejpam-3742	21	31	alg	alg	PROPN
ejpam-3742	21	32	-	-	PUNCT
ejpam-3742	21	33	a	a	PROPN
ejpam-3742	21	34	are	be	AUX
ejpam-3742	21	35	adjoint	adjoint	NOUN
ejpam-3742	21	36	and	and	CCONJ
ejpam-3742	21	37	in	in	ADP
ejpam-3742	21	38	the	the	DET
ejpam-3742	21	39	third	third	ADJ
ejpam-3742	21	40	part	part	NOUN
ejpam-3742	21	41	we	we	PRON
ejpam-3742	21	42	show	show	VERB
ejpam-3742	21	43	the	the	DET
ejpam-3742	21	44	main	main	ADJ
ejpam-3742	21	45	results	result	NOUN
ejpam-3742	21	46	of	of	ADP
ejpam-3742	21	47	this	this	DET
ejpam-3742	21	48	paper	paper	NOUN
ejpam-3742	21	49	(	(	PUNCT
ejpam-3742	21	50	see	see	VERB
ejpam-3742	21	51	theorem	theorem	NOUN
ejpam-3742	21	52	6	6	NUM
ejpam-3742	21	53	)	)	PUNCT
ejpam-3742	21	54	.	.	PUNCT
ejpam-3742	22	1	2	2	X
ejpam-3742	22	2	.	.	X
ejpam-3742	22	3	preliminary	preliminary	ADJ
ejpam-3742	22	4	results	result	NOUN
ejpam-3742	22	5	proposition	proposition	NOUN
ejpam-3742	22	6	1	1	NUM
ejpam-3742	22	7	.	.	PUNCT
ejpam-3742	23	1	let	let	VERB
ejpam-3742	23	2	a	a	PRON
ejpam-3742	23	3	and	and	CCONJ
ejpam-3742	23	4	a	a	DET
ejpam-3742	23	5	be	be	AUX
ejpam-3742	23	6	two	two	NUM
ejpam-3742	23	7	rings	ring	NOUN
ejpam-3742	23	8	,	,	PUNCT
ejpam-3742	23	9	and	and	CCONJ
ejpam-3742	23	10	θ	θ	NOUN
ejpam-3742	23	11	:	:	PUNCT
ejpam-3742	23	12	a	a	DET
ejpam-3742	23	13	−→	−→	NOUN
ejpam-3742	23	14	a	a	PRON
ejpam-3742	23	15	be	be	AUX
ejpam-3742	23	16	a	a	DET
ejpam-3742	23	17	ring	ring	NOUN
ejpam-3742	23	18	morphism	morphism	NOUN
ejpam-3742	23	19	.	.	PUNCT
ejpam-3742	24	1	then	then	ADV
ejpam-3742	24	2	a	a	PRON
ejpam-3742	24	3	has	have	VERB
ejpam-3742	24	4	a	a	DET
ejpam-3742	24	5	structure	structure	NOUN
ejpam-3742	24	6	of	of	ADP
ejpam-3742	24	7	left	left	ADJ
ejpam-3742	24	8	(	(	PUNCT
ejpam-3742	24	9	resp	resp	NOUN
ejpam-3742	24	10	.	.	PUNCT
ejpam-3742	25	1	right	right	ADJ
ejpam-3742	25	2	)	)	PUNCT
ejpam-3742	25	3	a	a	DET
ejpam-3742	25	4	-	-	PUNCT
ejpam-3742	25	5	module	module	NOUN
ejpam-3742	25	6	as	as	ADP
ejpam-3742	25	7	the	the	DET
ejpam-3742	25	8	same	same	ADJ
ejpam-3742	25	9	way	way	NOUN
ejpam-3742	25	10	:	:	PUNCT
ejpam-3742	25	11	•	•	NUM
ejpam-3742	25	12	:	:	PUNCT
ejpam-3742	26	1	a×a	a×a	PROPN
ejpam-3742	26	2	−→	−→	VERB
ejpam-3742	26	3	a	a	DET
ejpam-3742	26	4	(	(	PUNCT
ejpam-3742	26	5	a	a	PRON
ejpam-3742	26	6	,	,	PUNCT
ejpam-3742	26	7	x	x	NOUN
ejpam-3742	26	8	)	)	PUNCT
ejpam-3742	26	9	7−→	7−→	NOUN
ejpam-3742	26	10	a	a	DET
ejpam-3742	26	11	•	•	NOUN
ejpam-3742	26	12	x	x	SYM
ejpam-3742	26	13	=	=	SYM
ejpam-3742	26	14	θ(a)x	θ(a)x	PROPN
ejpam-3742	26	15	(	(	PUNCT
ejpam-3742	26	16	resp	resp	NOUN
ejpam-3742	26	17	.	.	PUNCT
ejpam-3742	27	1	∗	∗	NOUN
ejpam-3742	27	2	:	:	PUNCT
ejpam-3742	27	3	a	a	DET
ejpam-3742	27	4	×a	×a	NOUN
ejpam-3742	27	5	−→	−→	NOUN
ejpam-3742	27	6	a	a	DET
ejpam-3742	27	7	(	(	PUNCT
ejpam-3742	27	8	x	x	NOUN
ejpam-3742	27	9	,	,	PUNCT
ejpam-3742	27	10	a	a	DET
ejpam-3742	27	11	)	)	PUNCT
ejpam-3742	27	12	7−→	7−→	NOUN
ejpam-3742	27	13	x	x	PUNCT
ejpam-3742	27	14	∗	∗	VERB
ejpam-3742	27	15	a	a	PRON
ejpam-3742	27	16	=	=	NOUN
ejpam-3742	27	17	xθ(a	xθ(a	NUM
ejpam-3742	27	18	)	)	PUNCT
ejpam-3742	27	19	)	)	PUNCT
ejpam-3742	28	1	proof	proof	NOUN
ejpam-3742	28	2	.	.	PUNCT
ejpam-3742	29	1	easy	easy	ADJ
ejpam-3742	29	2	.	.	PUNCT
ejpam-3742	30	1	in	in	ADP
ejpam-3742	30	2	all	all	PRON
ejpam-3742	30	3	that	that	PRON
ejpam-3742	30	4	follows	follow	VERB
ejpam-3742	30	5	•	•	NOUN
ejpam-3742	30	6	(	(	PUNCT
ejpam-3742	30	7	resp	resp	NOUN
ejpam-3742	30	8	.	.	PUNCT
ejpam-3742	30	9	∗	∗	NOUN
ejpam-3742	30	10	)	)	PUNCT
ejpam-3742	30	11	designates	designate	VERB
ejpam-3742	30	12	the	the	DET
ejpam-3742	30	13	external	external	ADJ
ejpam-3742	30	14	law	law	NOUN
ejpam-3742	30	15	of	of	ADP
ejpam-3742	30	16	the	the	DET
ejpam-3742	30	17	left	left	NOUN
ejpam-3742	30	18	(	(	PUNCT
ejpam-3742	30	19	resp	resp	NOUN
ejpam-3742	30	20	.	.	PUNCT
ejpam-3742	31	1	right	right	ADJ
ejpam-3742	31	2	)	)	PUNCT
ejpam-3742	31	3	a	a	DET
ejpam-3742	31	4	-	-	PUNCT
ejpam-3742	31	5	module	module	NOUN
ejpam-3742	31	6	a	a	DET
ejpam-3742	31	7	relatively	relatively	ADV
ejpam-3742	31	8	to	to	ADP
ejpam-3742	31	9	θ	θ	PROPN
ejpam-3742	31	10	.	.	PUNCT
ejpam-3742	31	11	definition	definition	NOUN
ejpam-3742	31	12	1	1	NUM
ejpam-3742	31	13	.	.	PUNCT
ejpam-3742	32	1	let	let	VERB
ejpam-3742	32	2	a	a	PRON
ejpam-3742	32	3	and	and	CCONJ
ejpam-3742	32	4	a	a	DET
ejpam-3742	32	5	be	be	AUX
ejpam-3742	32	6	two	two	NUM
ejpam-3742	32	7	rings	ring	NOUN
ejpam-3742	32	8	,	,	PUNCT
ejpam-3742	32	9	and	and	CCONJ
ejpam-3742	32	10	θ	θ	NOUN
ejpam-3742	32	11	:	:	PUNCT
ejpam-3742	32	12	a	a	DET
ejpam-3742	32	13	−→	−→	NOUN
ejpam-3742	32	14	a	a	PRON
ejpam-3742	32	15	be	be	AUX
ejpam-3742	32	16	a	a	DET
ejpam-3742	32	17	ring	ring	NOUN
ejpam-3742	32	18	morphism	morphism	NOUN
ejpam-3742	32	19	.	.	PUNCT
ejpam-3742	33	1	then	then	ADV
ejpam-3742	33	2	(	(	PUNCT
ejpam-3742	33	3	a	a	PRON
ejpam-3742	33	4	,	,	PUNCT
ejpam-3742	33	5	+	+	ADJ
ejpam-3742	33	6	,	,	PUNCT
ejpam-3742	33	7	×	×	NOUN
ejpam-3742	33	8	,	,	PUNCT
ejpam-3742	33	9	•	•	NUM
ejpam-3742	33	10	)	)	PUNCT
ejpam-3742	33	11	(	(	PUNCT
ejpam-3742	33	12	resp	resp	NOUN
ejpam-3742	33	13	.	.	PUNCT
ejpam-3742	34	1	(	(	PUNCT
ejpam-3742	34	2	a	a	DET
ejpam-3742	34	3	,	,	PUNCT
ejpam-3742	34	4	+	+	ADJ
ejpam-3742	34	5	,	,	PUNCT
ejpam-3742	34	6	×	×	NOUN
ejpam-3742	34	7	,	,	PUNCT
ejpam-3742	34	8	∗	∗	NOUN
ejpam-3742	34	9	)	)	PUNCT
ejpam-3742	34	10	)	)	PUNCT
ejpam-3742	34	11	is	be	AUX
ejpam-3742	34	12	called	call	VERB
ejpam-3742	34	13	left	left	ADJ
ejpam-3742	34	14	(	(	PUNCT
ejpam-3742	34	15	resp	resp	NOUN
ejpam-3742	34	16	.	.	PUNCT
ejpam-3742	35	1	right	right	ADJ
ejpam-3742	35	2	)	)	PUNCT
ejpam-3742	35	3	a	a	X
ejpam-3742	35	4	-	-	PUNCT
ejpam-3742	35	5	algebra	algebra	NOUN
ejpam-3742	35	6	relatively	relatively	ADV
ejpam-3742	35	7	to	to	ADP
ejpam-3742	35	8	θ	θ	PROPN
ejpam-3742	35	9	.	.	PUNCT
ejpam-3742	36	1	this	this	DET
ejpam-3742	36	2	definition	definition	NOUN
ejpam-3742	36	3	shows	show	VERB
ejpam-3742	36	4	that	that	SCONJ
ejpam-3742	36	5	to	to	PART
ejpam-3742	36	6	provide	provide	VERB
ejpam-3742	36	7	a	a	PRON
ejpam-3742	36	8	with	with	ADP
ejpam-3742	36	9	a	a	DET
ejpam-3742	36	10	structure	structure	NOUN
ejpam-3742	36	11	of	of	ADP
ejpam-3742	36	12	left	left	ADJ
ejpam-3742	36	13	(	(	PUNCT
ejpam-3742	36	14	resp	resp	NOUN
ejpam-3742	36	15	.	.	PUNCT
ejpam-3742	37	1	right	right	ADJ
ejpam-3742	37	2	)	)	PUNCT
ejpam-3742	37	3	a	a	X
ejpam-3742	37	4	-	-	PUNCT
ejpam-3742	37	5	algebra	algebra	NOUN
ejpam-3742	37	6	it	it	PRON
ejpam-3742	37	7	suffices	suffice	VERB
ejpam-3742	37	8	to	to	PART
ejpam-3742	37	9	have	have	VERB
ejpam-3742	37	10	a	a	DET
ejpam-3742	37	11	ring	ring	NOUN
ejpam-3742	37	12	morphism	morphism	NOUN
ejpam-3742	37	13	of	of	ADP
ejpam-3742	37	14	a	a	PRON
ejpam-3742	37	15	into	into	ADP
ejpam-3742	37	16	a	a	PRON
ejpam-3742	37	17	.	.	PUNCT
ejpam-3742	38	1	definition	definition	NOUN
ejpam-3742	38	2	2	2	NUM
ejpam-3742	38	3	.	.	PUNCT
ejpam-3742	39	1	[	[	X
ejpam-3742	39	2	1	1	X
ejpam-3742	39	3	]	]	PUNCT
ejpam-3742	39	4	let	let	VERB
ejpam-3742	39	5	a	a	PRON
ejpam-3742	39	6	and	and	CCONJ
ejpam-3742	39	7	a	a	DET
ejpam-3742	39	8	be	be	AUX
ejpam-3742	39	9	two	two	NUM
ejpam-3742	39	10	rings	ring	NOUN
ejpam-3742	39	11	,	,	PUNCT
ejpam-3742	39	12	and	and	CCONJ
ejpam-3742	39	13	θ	θ	NOUN
ejpam-3742	39	14	:	:	PUNCT
ejpam-3742	39	15	a	a	DET
ejpam-3742	39	16	−→	−→	NOUN
ejpam-3742	39	17	a	a	PRON
ejpam-3742	39	18	be	be	AUX
ejpam-3742	39	19	a	a	DET
ejpam-3742	39	20	ring	ring	NOUN
ejpam-3742	39	21	morphism	morphism	NOUN
ejpam-3742	39	22	.	.	PUNCT
ejpam-3742	40	1	if	if	SCONJ
ejpam-3742	40	2	im(θ	im(θ	NOUN
ejpam-3742	40	3	)	)	PUNCT
ejpam-3742	40	4	⊆	⊆	NUM
ejpam-3742	40	5	z(a	z(a	NOUN
ejpam-3742	40	6	)	)	PUNCT
ejpam-3742	40	7	,	,	PUNCT
ejpam-3742	40	8	then	then	ADV
ejpam-3742	40	9	a	a	PRON
ejpam-3742	40	10	is	be	AUX
ejpam-3742	40	11	called	call	VERB
ejpam-3742	40	12	an	an	DET
ejpam-3742	40	13	a	a	DET
ejpam-3742	40	14	-	-	PUNCT
ejpam-3742	40	15	algebra	algebra	NOUN
ejpam-3742	40	16	relatively	relatively	ADV
ejpam-3742	40	17	to	to	ADP
ejpam-3742	40	18	θ	θ	PROPN
ejpam-3742	40	19	.	.	PUNCT
ejpam-3742	41	1	definition	definition	NOUN
ejpam-3742	41	2	3	3	X
ejpam-3742	41	3	.	.	PUNCT
ejpam-3742	42	1	let	let	VERB
ejpam-3742	42	2	a	a	PRON
ejpam-3742	42	3	be	be	AUX
ejpam-3742	42	4	a	a	DET
ejpam-3742	42	5	ring	ring	NOUN
ejpam-3742	42	6	,	,	PUNCT
ejpam-3742	42	7	a	a	DET
ejpam-3742	42	8	subset	subset	NOUN
ejpam-3742	42	9	s	s	NOUN
ejpam-3742	42	10	of	of	ADP
ejpam-3742	42	11	a	a	PRON
ejpam-3742	42	12	is	be	AUX
ejpam-3742	42	13	called	call	VERB
ejpam-3742	42	14	multiplicative	multiplicative	ADJ
ejpam-3742	42	15	if	if	SCONJ
ejpam-3742	42	16	1a	1a	PROPN
ejpam-3742	42	17	∈	∈	PROPN
ejpam-3742	42	18	s	s	X
ejpam-3742	42	19	and	and	CCONJ
ejpam-3742	42	20	s	s	VERB
ejpam-3742	42	21	is	be	AUX
ejpam-3742	42	22	stable	stable	ADJ
ejpam-3742	42	23	by	by	ADP
ejpam-3742	42	24	multiplication	multiplication	NOUN
ejpam-3742	42	25	i.e	i.e	PROPN
ejpam-3742	42	26	for	for	ADP
ejpam-3742	42	27	all	all	DET
ejpam-3742	42	28	x	x	NOUN
ejpam-3742	42	29	,	,	PUNCT
ejpam-3742	42	30	t	t	PROPN
ejpam-3742	42	31	∈	∈	PROPN
ejpam-3742	42	32	s	s	PROPN
ejpam-3742	42	33	,	,	PUNCT
ejpam-3742	42	34	xt	xt	PROPN
ejpam-3742	42	35	∈	∈	PROPN
ejpam-3742	42	36	s.	s.	PROPN
ejpam-3742	42	37	definition	definition	NOUN
ejpam-3742	42	38	4	4	X
ejpam-3742	42	39	.	.	PUNCT
ejpam-3742	43	1	let	let	VERB
ejpam-3742	43	2	a	a	PRON
ejpam-3742	43	3	be	be	AUX
ejpam-3742	43	4	a	a	DET
ejpam-3742	43	5	ring	ring	NOUN
ejpam-3742	43	6	and	and	CCONJ
ejpam-3742	43	7	s	s	VERB
ejpam-3742	43	8	a	a	DET
ejpam-3742	43	9	multiplicative	multiplicative	ADJ
ejpam-3742	43	10	subset	subset	NOUN
ejpam-3742	43	11	of	of	ADP
ejpam-3742	43	12	a.	a.	NOUN
ejpam-3742	43	13	we	we	PRON
ejpam-3742	43	14	say	say	VERB
ejpam-3742	43	15	that	that	PRON
ejpam-3742	43	16	s	s	VERB
ejpam-3742	43	17	is	be	AUX
ejpam-3742	43	18	closed	close	VERB
ejpam-3742	43	19	if	if	SCONJ
ejpam-3742	43	20	for	for	ADP
ejpam-3742	43	21	all	all	DET
ejpam-3742	43	22	s	s	NOUN
ejpam-3742	43	23	,	,	PUNCT
ejpam-3742	43	24	s′	s′	ADJ
ejpam-3742	43	25	∈	∈	PROPN
ejpam-3742	43	26	a	a	DET
ejpam-3742	43	27	such	such	ADJ
ejpam-3742	43	28	that	that	SCONJ
ejpam-3742	43	29	ss′	ss′	PROPN
ejpam-3742	43	30	∈	∈	PROPN
ejpam-3742	43	31	s	s	PART
ejpam-3742	43	32	⇒	⇒	NOUN
ejpam-3742	43	33	s	s	PART
ejpam-3742	43	34	∈	∈	NOUN
ejpam-3742	43	35	s	s	NOUN
ejpam-3742	43	36	and	and	CCONJ
ejpam-3742	43	37	s′	s′	ADJ
ejpam-3742	43	38	∈	∈	PROPN
ejpam-3742	43	39	s.	s.	PROPN
ejpam-3742	43	40	definition	definition	NOUN
ejpam-3742	43	41	5	5	NUM
ejpam-3742	43	42	.	.	PUNCT
ejpam-3742	44	1	let	let	VERB
ejpam-3742	44	2	s	s	PRON
ejpam-3742	44	3	be	be	AUX
ejpam-3742	44	4	a	a	DET
ejpam-3742	44	5	multiplicatively	multiplicatively	ADV
ejpam-3742	44	6	closed	close	VERB
ejpam-3742	44	7	subset	subset	NOUN
ejpam-3742	44	8	of	of	ADP
ejpam-3742	44	9	a	a	DET
ejpam-3742	44	10	ring	ring	NOUN
ejpam-3742	44	11	a.	a.	NOUN
ejpam-3742	44	12	we	we	PRON
ejpam-3742	44	13	say	say	VERB
ejpam-3742	44	14	that	that	SCONJ
ejpam-3742	44	15	s	s	AUX
ejpam-3742	44	16	satisfies	satisfy	VERB
ejpam-3742	44	17	the	the	DET
ejpam-3742	44	18	left	left	ADJ
ejpam-3742	44	19	ore	ore	NOUN
ejpam-3742	44	20	conditions	condition	NOUN
ejpam-3742	44	21	if	if	SCONJ
ejpam-3742	44	22	:	:	PUNCT
ejpam-3742	44	23	(	(	PUNCT
ejpam-3742	44	24	i	i	NOUN
ejpam-3742	44	25	)	)	PUNCT
ejpam-3742	44	26	∀a	∀a	VERB
ejpam-3742	44	27	∈	∈	PROPN
ejpam-3742	44	28	a	a	DET
ejpam-3742	44	29	,	,	PUNCT
ejpam-3742	44	30	∀s	∀s	PROPN
ejpam-3742	44	31	∈	∈	PROPN
ejpam-3742	44	32	s	s	PART
ejpam-3742	44	33	∃t	∃t	NOUN
ejpam-3742	44	34	∈	∈	PROPN
ejpam-3742	44	35	s	s	PART
ejpam-3742	44	36	and	and	CCONJ
ejpam-3742	44	37	b	b	PROPN
ejpam-3742	44	38	∈	∈	PROPN
ejpam-3742	44	39	a	a	DET
ejpam-3742	44	40	such	such	ADJ
ejpam-3742	44	41	that	that	PRON
ejpam-3742	44	42	ta	ta	PROPN
ejpam-3742	44	43	=	=	SYM
ejpam-3742	44	44	bs	bs	PROPN
ejpam-3742	44	45	(	(	PUNCT
ejpam-3742	44	46	ii	ii	NOUN
ejpam-3742	44	47	)	)	PUNCT
ejpam-3742	44	48	∀a	∀a	NOUN
ejpam-3742	44	49	∈	∈	PROPN
ejpam-3742	44	50	a	a	DET
ejpam-3742	44	51	,	,	PUNCT
ejpam-3742	44	52	∀	∀	NOUN
ejpam-3742	44	53	s	s	NOUN
ejpam-3742	44	54	∈	∈	NOUN
ejpam-3742	44	55	s	s	VERB
ejpam-3742	44	56	such	such	ADJ
ejpam-3742	44	57	that	that	SCONJ
ejpam-3742	44	58	as	as	ADP
ejpam-3742	44	59	=	=	NOUN
ejpam-3742	44	60	0	0	NUM
ejpam-3742	44	61	,	,	PUNCT
ejpam-3742	44	62	then	then	ADV
ejpam-3742	44	63	it	it	PRON
ejpam-3742	44	64	exist	exist	VERB
ejpam-3742	44	65	t	t	PROPN
ejpam-3742	44	66	∈	∈	PROPN
ejpam-3742	44	67	s	s	VERB
ejpam-3742	44	68	such	such	ADJ
ejpam-3742	44	69	that	that	PRON
ejpam-3742	44	70	ta	ta	AUX
ejpam-3742	44	71	=	=	SYM
ejpam-3742	44	72	0	0	PROPN
ejpam-3742	44	73	.	.	PUNCT
ejpam-3742	44	74	theorem	theorem	NOUN
ejpam-3742	44	75	1	1	NUM
ejpam-3742	44	76	.	.	PUNCT
ejpam-3742	45	1	let	let	VERB
ejpam-3742	45	2	a	a	PRON
ejpam-3742	45	3	be	be	AUX
ejpam-3742	45	4	a	a	DET
ejpam-3742	45	5	ring	ring	NOUN
ejpam-3742	45	6	and	and	CCONJ
ejpam-3742	45	7	s	s	VERB
ejpam-3742	45	8	a	a	DET
ejpam-3742	45	9	multiplicatively	multiplicatively	ADV
ejpam-3742	45	10	closed	close	VERB
ejpam-3742	45	11	subset	subset	NOUN
ejpam-3742	45	12	of	of	ADP
ejpam-3742	45	13	a	a	DET
ejpam-3742	45	14	satisfying	satisfying	NOUN
ejpam-3742	45	15	the	the	DET
ejpam-3742	45	16	left	left	ADJ
ejpam-3742	45	17	ore	ore	NOUN
ejpam-3742	45	18	conditions	condition	NOUN
ejpam-3742	45	19	.	.	PUNCT
ejpam-3742	46	1	the	the	DET
ejpam-3742	46	2	binary	binary	PROPN
ejpam-3742	46	3	relation	relation	NOUN
ejpam-3742	46	4	defined	define	VERB
ejpam-3742	46	5	in	in	ADP
ejpam-3742	46	6	s	s	PROPN
ejpam-3742	46	7	×m	×m	NOUN
ejpam-3742	46	8	by	by	ADP
ejpam-3742	46	9	(	(	PUNCT
ejpam-3742	46	10	s	s	PROPN
ejpam-3742	46	11	,	,	PUNCT
ejpam-3742	46	12	m)r(s′,m′)	m)r(s′,m′)	PROPN
ejpam-3742	46	13	⇐	⇐	ADJ
ejpam-3742	46	14	⇒	⇒	PROPN
ejpam-3742	46	15	∃x	∃x	NOUN
ejpam-3742	46	16	,	,	PUNCT
ejpam-3742	46	17	y	y	PROPN
ejpam-3742	46	18	∈	∈	PROPN
ejpam-3742	46	19	s	s	PART
ejpam-3742	46	20	:	:	PUNCT
ejpam-3742	46	21	{	{	PUNCT
ejpam-3742	46	22	xm	xm	PROPN
ejpam-3742	46	23	=	=	SYM
ejpam-3742	46	24	ym′	ym′	NOUN
ejpam-3742	46	25	xs	xs	PROPN
ejpam-3742	46	26	=	=	PUNCT
ejpam-3742	46	27	ys′	ys′	PROPN
ejpam-3742	46	28	is	be	AUX
ejpam-3742	46	29	an	an	DET
ejpam-3742	46	30	equivalence	equivalence	NOUN
ejpam-3742	46	31	relation	relation	NOUN
ejpam-3742	46	32	.	.	PUNCT
ejpam-3742	47	1	m	m	PROPN
ejpam-3742	47	2	thiaw	thiaw	ADJ
ejpam-3742	47	3	,	,	PUNCT
ejpam-3742	47	4	m	m	AUX
ejpam-3742	47	5	maaouia	maaouia	NOUN
ejpam-3742	47	6	/	/	SYM
ejpam-3742	47	7	eur	eur	NOUN
ejpam-3742	47	8	.	.	PUNCT
ejpam-3742	48	1	j.	j.	PROPN
ejpam-3742	48	2	pure	pure	PROPN
ejpam-3742	48	3	appl	appl	PROPN
ejpam-3742	48	4	.	.	PROPN
ejpam-3742	48	5	math	math	PROPN
ejpam-3742	48	6	,	,	PUNCT
ejpam-3742	48	7	13	13	NUM
ejpam-3742	48	8	(	(	PUNCT
ejpam-3742	48	9	3	3	NUM
ejpam-3742	48	10	)	)	PUNCT
ejpam-3742	48	11	(	(	PUNCT
ejpam-3742	48	12	2020	2020	NUM
ejpam-3742	48	13	)	)	PUNCT
ejpam-3742	48	14	,	,	PUNCT
ejpam-3742	48	15	472	472	NUM
ejpam-3742	48	16	-	-	SYM
ejpam-3742	48	17	482	482	NUM
ejpam-3742	48	18	474	474	NUM
ejpam-3742	48	19	proof	proof	NOUN
ejpam-3742	48	20	.	.	PUNCT
ejpam-3742	49	1	see	see	VERB
ejpam-3742	49	2	[	[	X
ejpam-3742	49	3	4	4	NUM
ejpam-3742	49	4	]	]	PUNCT
ejpam-3742	49	5	,	,	PUNCT
ejpam-3742	49	6	[	[	X
ejpam-3742	49	7	2	2	NUM
ejpam-3742	49	8	]	]	PUNCT
ejpam-3742	49	9	and	and	CCONJ
ejpam-3742	49	10	[	[	X
ejpam-3742	49	11	5	5	NUM
ejpam-3742	49	12	]	]	PUNCT
ejpam-3742	49	13	.	.	PUNCT
ejpam-3742	50	1	theorem	theorem	NOUN
ejpam-3742	50	2	2	2	NUM
ejpam-3742	50	3	.	.	PUNCT
ejpam-3742	51	1	let	let	VERB
ejpam-3742	51	2	a	a	DET
ejpam-3742	51	3	be	be	AUX
ejpam-3742	51	4	a	a	DET
ejpam-3742	51	5	ring	ring	NOUN
ejpam-3742	51	6	not	not	PART
ejpam-3742	51	7	necessary	necessary	ADJ
ejpam-3742	51	8	commutative	commutative	ADJ
ejpam-3742	51	9	and	and	CCONJ
ejpam-3742	51	10	s	s	VERB
ejpam-3742	51	11	a	a	DET
ejpam-3742	51	12	multiplicatively	multiplicatively	ADV
ejpam-3742	51	13	closed	close	VERB
ejpam-3742	51	14	subset	subset	NOUN
ejpam-3742	51	15	of	of	ADP
ejpam-3742	51	16	a	a	DET
ejpam-3742	51	17	satisfying	satisfying	NOUN
ejpam-3742	51	18	the	the	DET
ejpam-3742	51	19	left	left	ADJ
ejpam-3742	51	20	ore	ore	NOUN
ejpam-3742	51	21	condition	condition	NOUN
ejpam-3742	51	22	,	,	PUNCT
ejpam-3742	51	23	then	then	ADV
ejpam-3742	51	24	s−1a	s−1a	PROPN
ejpam-3742	51	25	is	be	AUX
ejpam-3742	51	26	a	a	DET
ejpam-3742	51	27	ring	ring	NOUN
ejpam-3742	51	28	by	by	ADP
ejpam-3742	51	29	the	the	DET
ejpam-3742	51	30	two	two	NUM
ejpam-3742	51	31	following	follow	VERB
ejpam-3742	51	32	operations	operation	NOUN
ejpam-3742	51	33	:	:	PUNCT
ejpam-3742	51	34	•	•	ADP
ejpam-3742	51	35	a	a	DET
ejpam-3742	51	36	t	t	NOUN
ejpam-3742	51	37	+	+	CCONJ
ejpam-3742	51	38	b	b	X
ejpam-3742	51	39	s	s	X
ejpam-3742	51	40	=	=	SYM
ejpam-3742	51	41	xa+yb	xa+yb	PROPN
ejpam-3742	51	42	ys	ys	INTJ
ejpam-3742	51	43	where	where	SCONJ
ejpam-3742	51	44	x	x	X
ejpam-3742	51	45	,	,	PUNCT
ejpam-3742	51	46	y	y	PROPN
ejpam-3742	51	47	∈	∈	PROPN
ejpam-3742	51	48	s	s	PART
ejpam-3742	51	49	:	:	PUNCT
ejpam-3742	51	50	xt	xt	PROPN
ejpam-3742	51	51	=	=	SYM
ejpam-3742	51	52	ys	ys	VERB
ejpam-3742	51	53	•	•	NOUN
ejpam-3742	51	54	a	a	DET
ejpam-3742	51	55	t	t	NOUN
ejpam-3742	51	56	×	×	PROPN
ejpam-3742	51	57	b	b	X
ejpam-3742	51	58	s	s	X
ejpam-3742	51	59	=	=	NOUN
ejpam-3742	51	60	zb	zb	NOUN
ejpam-3742	51	61	wt	wt	INTJ
ejpam-3742	51	62	where	where	SCONJ
ejpam-3742	51	63	(	(	PUNCT
ejpam-3742	51	64	w	w	PROPN
ejpam-3742	51	65	,	,	PUNCT
ejpam-3742	51	66	z	z	NOUN
ejpam-3742	51	67	)	)	PUNCT
ejpam-3742	51	68	∈	∈	PROPN
ejpam-3742	51	69	s	s	PART
ejpam-3742	51	70	×a	×a	NOUN
ejpam-3742	51	71	:	:	PUNCT
ejpam-3742	51	72	wa	wa	PROPN
ejpam-3742	51	73	=	=	SYM
ejpam-3742	51	74	zs	zs	PROPN
ejpam-3742	51	75	.	.	PUNCT
ejpam-3742	51	76	proof	proof	NOUN
ejpam-3742	51	77	.	.	PUNCT
ejpam-3742	52	1	see	see	VERB
ejpam-3742	52	2	[	[	X
ejpam-3742	52	3	4	4	NUM
ejpam-3742	52	4	]	]	PUNCT
ejpam-3742	52	5	.	.	PUNCT
ejpam-3742	53	1	theorem	theorem	NOUN
ejpam-3742	53	2	3	3	X
ejpam-3742	53	3	.	.	PUNCT
ejpam-3742	54	1	let	let	VERB
ejpam-3742	54	2	a	a	DET
ejpam-3742	54	3	be	be	AUX
ejpam-3742	54	4	a	a	DET
ejpam-3742	54	5	left	left	ADJ
ejpam-3742	54	6	(	(	PUNCT
ejpam-3742	54	7	resp	resp	NOUN
ejpam-3742	54	8	.	.	PUNCT
ejpam-3742	55	1	right	right	ADJ
ejpam-3742	55	2	)	)	PUNCT
ejpam-3742	55	3	a	a	X
ejpam-3742	55	4	-	-	PUNCT
ejpam-3742	55	5	algebra	algebra	NOUN
ejpam-3742	55	6	and	and	CCONJ
ejpam-3742	55	7	s	s	VERB
ejpam-3742	55	8	a	a	DET
ejpam-3742	55	9	central	central	ADJ
ejpam-3742	55	10	multiplicatively	multiplicatively	ADV
ejpam-3742	55	11	closed	close	VERB
ejpam-3742	55	12	subset	subset	NOUN
ejpam-3742	55	13	of	of	ADP
ejpam-3742	55	14	a.	a.	NOUN
ejpam-3742	55	15	then	then	ADV
ejpam-3742	55	16	s−1(a	s−1(a	PROPN
ejpam-3742	55	17	)	)	PUNCT
ejpam-3742	56	1	∈	∈	PROPN
ejpam-3742	56	2	ob(s−1a	ob(s−1a	NOUN
ejpam-3742	56	3	-	-	PUNCT
ejpam-3742	56	4	alg	alg	PROPN
ejpam-3742	56	5	)	)	PUNCT
ejpam-3742	56	6	(	(	PUNCT
ejpam-3742	56	7	resp	resp	NOUN
ejpam-3742	56	8	.	.	PUNCT
ejpam-3742	57	1	s−1a	s−1a	PROPN
ejpam-3742	57	2	∈	∈	PROPN
ejpam-3742	57	3	ob(alg	ob(alg	PROPN
ejpam-3742	57	4	-	-	PUNCT
ejpam-3742	57	5	s−1a	s−1a	NOUN
ejpam-3742	57	6	)	)	PUNCT
ejpam-3742	57	7	)	)	PUNCT
ejpam-3742	57	8	.	.	PUNCT
ejpam-3742	58	1	proof	proof	NOUN
ejpam-3742	58	2	.	.	PUNCT
ejpam-3742	59	1	see	see	VERB
ejpam-3742	59	2	[	[	X
ejpam-3742	59	3	3	3	NUM
ejpam-3742	59	4	]	]	PUNCT
ejpam-3742	59	5	.	.	PUNCT
ejpam-3742	60	1	definition	definition	NOUN
ejpam-3742	60	2	6	6	NUM
ejpam-3742	60	3	.	.	PUNCT
ejpam-3742	61	1	let	let	VERB
ejpam-3742	61	2	f	f	X
ejpam-3742	61	3	,	,	PUNCT
ejpam-3742	61	4	g	g	NOUN
ejpam-3742	61	5	:	:	PUNCT
ejpam-3742	61	6	c	c	X
ejpam-3742	61	7	→	→	PUNCT
ejpam-3742	61	8	d	d	X
ejpam-3742	61	9	be	be	AUX
ejpam-3742	61	10	two	two	NUM
ejpam-3742	61	11	covariant	covariant	ADJ
ejpam-3742	61	12	functors	functor	NOUN
ejpam-3742	61	13	.	.	PUNCT
ejpam-3742	62	1	a	a	DET
ejpam-3742	62	2	natural	natural	ADJ
ejpam-3742	62	3	transformation	transformation	NOUN
ejpam-3742	62	4	θ	θ	PROPN
ejpam-3742	62	5	from	from	ADP
ejpam-3742	62	6	f	f	PROPN
ejpam-3742	62	7	to	to	ADP
ejpam-3742	62	8	g	g	PROPN
ejpam-3742	62	9	is	be	AUX
ejpam-3742	62	10	an	an	DET
ejpam-3742	62	11	assignment	assignment	NOUN
ejpam-3742	62	12	to	to	ADP
ejpam-3742	62	13	every	every	DET
ejpam-3742	62	14	object	object	NOUN
ejpam-3742	62	15	x	x	PUNCT
ejpam-3742	62	16	of	of	ADP
ejpam-3742	62	17	c	c	NOUN
ejpam-3742	62	18	of	of	ADP
ejpam-3742	62	19	a	a	DET
ejpam-3742	62	20	morphism	morphism	NOUN
ejpam-3742	62	21	θx	θx	ADP
ejpam-3742	62	22	∈	∈	PROPN
ejpam-3742	62	23	homd(f	homd(f	ADP
ejpam-3742	62	24	(	(	PUNCT
ejpam-3742	62	25	x	x	NOUN
ejpam-3742	62	26	)	)	PUNCT
ejpam-3742	62	27	,	,	PUNCT
ejpam-3742	62	28	g(x	g(x	NOUN
ejpam-3742	62	29	)	)	PUNCT
ejpam-3742	62	30	)	)	PUNCT
ejpam-3742	62	31	such	such	ADJ
ejpam-3742	62	32	that	that	PRON
ejpam-3742	62	33	for	for	ADP
ejpam-3742	62	34	any	any	DET
ejpam-3742	62	35	morphism	morphism	NOUN
ejpam-3742	62	36	f	f	PROPN
ejpam-3742	62	37	∈	∈	PROPN
ejpam-3742	62	38	homc	homc	PROPN
ejpam-3742	62	39	(	(	PUNCT
ejpam-3742	62	40	x	x	X
ejpam-3742	62	41	,	,	PUNCT
ejpam-3742	62	42	y	y	PROPN
ejpam-3742	62	43	)	)	PUNCT
ejpam-3742	62	44	,	,	PUNCT
ejpam-3742	62	45	the	the	DET
ejpam-3742	62	46	following	follow	VERB
ejpam-3742	62	47	diagram	diagram	NOUN
ejpam-3742	62	48	commutes	commute	NOUN
ejpam-3742	62	49	in	in	ADP
ejpam-3742	62	50	d	d	PROPN
ejpam-3742	62	51	f	f	X
ejpam-3742	62	52	(	(	PUNCT
ejpam-3742	62	53	x	x	X
ejpam-3742	62	54	)	)	PUNCT
ejpam-3742	62	55	f	f	PROPN
ejpam-3742	62	56	(	(	PUNCT
ejpam-3742	62	57	f	f	X
ejpam-3742	62	58	)	)	PUNCT
ejpam-3742	62	59	�	�	PROPN
ejpam-3742	62	60	�	�	PROPN
ejpam-3742	62	61	θx	θx	PROPN
ejpam-3742	62	62	//	//	SYM
ejpam-3742	62	63	g(x	g(x	NOUN
ejpam-3742	62	64	)	)	PUNCT
ejpam-3742	62	65	g(f	g(f	PROPN
ejpam-3742	62	66	)	)	PUNCT
ejpam-3742	62	67	⇔	⇔	PROPN
ejpam-3742	62	68	g(f)	g(f)	PROPN
ejpam-3742	62	69	◦	◦	NOUN
ejpam-3742	62	70	θx	θx	NOUN
ejpam-3742	62	71	=	=	NOUN
ejpam-3742	62	72	θy	θy	NOUN
ejpam-3742	62	73	◦	◦	NOUN
ejpam-3742	62	74	f	f	X
ejpam-3742	62	75	(	(	PUNCT
ejpam-3742	62	76	f	f	NOUN
ejpam-3742	62	77	)	)	PUNCT
ejpam-3742	62	78	.	.	PUNCT
ejpam-3742	63	1	�	�	PROPN
ejpam-3742	63	2	�	�	PROPN
ejpam-3742	63	3	f	f	PROPN
ejpam-3742	63	4	(	(	PUNCT
ejpam-3742	63	5	y	y	PROPN
ejpam-3742	63	6	)	)	PUNCT
ejpam-3742	63	7	θy	θy	PROPN
ejpam-3742	63	8	//	//	NUM
ejpam-3742	63	9	g(y	g(y	PROPN
ejpam-3742	63	10	)	)	PUNCT
ejpam-3742	63	11	if	if	SCONJ
ejpam-3742	63	12	θx	θx	X
ejpam-3742	63	13	is	be	AUX
ejpam-3742	63	14	an	an	DET
ejpam-3742	63	15	isomorphism	isomorphism	NOUN
ejpam-3742	63	16	for	for	ADP
ejpam-3742	63	17	any	any	DET
ejpam-3742	63	18	object	object	NOUN
ejpam-3742	63	19	x	x	PUNCT
ejpam-3742	63	20	of	of	ADP
ejpam-3742	63	21	c	c	NOUN
ejpam-3742	63	22	,	,	PUNCT
ejpam-3742	63	23	then	then	ADV
ejpam-3742	63	24	θ	θ	PROPN
ejpam-3742	63	25	is	be	AUX
ejpam-3742	63	26	called	call	VERB
ejpam-3742	63	27	functorial	functorial	NOUN
ejpam-3742	63	28	isomorphism	isomorphism	NOUN
ejpam-3742	63	29	.	.	PUNCT
ejpam-3742	64	1	notation	notation	NOUN
ejpam-3742	64	2	:	:	PUNCT
ejpam-3742	64	3	we	we	PRON
ejpam-3742	64	4	note	note	VERB
ejpam-3742	64	5	by	by	ADP
ejpam-3742	64	6	f	f	PROPN
ejpam-3742	64	7	∼=	∼=	PROPN
ejpam-3742	64	8	g	g	NOUN
ejpam-3742	64	9	,	,	PUNCT
ejpam-3742	64	10	if	if	SCONJ
ejpam-3742	64	11	there	there	PRON
ejpam-3742	64	12	is	be	VERB
ejpam-3742	64	13	a	a	DET
ejpam-3742	64	14	functorial	functorial	NOUN
ejpam-3742	64	15	isomorphism	isomorphism	NOUN
ejpam-3742	64	16	θ	θ	NOUN
ejpam-3742	64	17	:	:	PUNCT
ejpam-3742	65	1	f	f	X
ejpam-3742	65	2	→	→	SYM
ejpam-3742	65	3	g.	g.	PROPN
ejpam-3742	65	4	definition	definition	NOUN
ejpam-3742	65	5	7	7	NUM
ejpam-3742	65	6	.	.	PUNCT
ejpam-3742	66	1	a	a	DET
ejpam-3742	66	2	pair	pair	NOUN
ejpam-3742	66	3	of	of	ADP
ejpam-3742	66	4	functors	functors	PROPN
ejpam-3742	66	5	f	f	PROPN
ejpam-3742	66	6	:	:	PUNCT
ejpam-3742	67	1	c	c	PROPN
ejpam-3742	67	2	�	�	PROPN
ejpam-3742	68	1	d	d	NOUN
ejpam-3742	68	2	:	:	PUNCT
ejpam-3742	68	3	g	g	PROPN
ejpam-3742	68	4	is	be	AUX
ejpam-3742	68	5	an	an	DET
ejpam-3742	68	6	adjunction	adjunction	NOUN
ejpam-3742	68	7	if	if	SCONJ
ejpam-3742	68	8	we	we	PRON
ejpam-3742	68	9	have	have	VERB
ejpam-3742	68	10	for	for	ADP
ejpam-3742	68	11	any	any	DET
ejpam-3742	68	12	(	(	PUNCT
ejpam-3742	68	13	x	x	NOUN
ejpam-3742	68	14	,	,	PUNCT
ejpam-3742	68	15	y	y	PROPN
ejpam-3742	68	16	)	)	PUNCT
ejpam-3742	68	17	∈	∈	PROPN
ejpam-3742	68	18	ob(c	ob(c	NUM
ejpam-3742	68	19	)	)	PUNCT
ejpam-3742	69	1	×ob(d	×ob(d	NOUN
ejpam-3742	69	2	)	)	PUNCT
ejpam-3742	69	3	a	a	DET
ejpam-3742	69	4	bijection	bijection	NOUN
ejpam-3742	69	5	φx	φx	NOUN
ejpam-3742	69	6	,	,	PUNCT
ejpam-3742	69	7	y	y	PROPN
ejpam-3742	69	8	:	:	PUNCT
ejpam-3742	69	9	homd(fx	homd(fx	PROPN
ejpam-3742	69	10	,	,	PUNCT
ejpam-3742	69	11	y	y	PROPN
ejpam-3742	69	12	)	)	PUNCT
ejpam-3742	69	13	−→	−→	NOUN
ejpam-3742	69	14	homc	homc	NOUN
ejpam-3742	69	15	(	(	PUNCT
ejpam-3742	69	16	x	x	X
ejpam-3742	69	17	,	,	PUNCT
ejpam-3742	69	18	gy	gy	PROPN
ejpam-3742	69	19	)	)	PUNCT
ejpam-3742	69	20	such	such	ADJ
ejpam-3742	69	21	that	that	SCONJ
ejpam-3742	69	22	the	the	DET
ejpam-3742	69	23	following	follow	VERB
ejpam-3742	69	24	two	two	NUM
ejpam-3742	69	25	squares	square	NOUN
ejpam-3742	69	26	are	be	AUX
ejpam-3742	69	27	commutative	commutative	ADJ
ejpam-3742	69	28	:	:	PUNCT
ejpam-3742	69	29	homd(fx	homd(fx	PROPN
ejpam-3742	69	30	′	′	PROPN
ejpam-3742	69	31	,	,	PUNCT
ejpam-3742	69	32	y	y	PROPN
ejpam-3742	69	33	)	)	PUNCT
ejpam-3742	69	34	φx′,y	φx′,y	NOUN
ejpam-3742	69	35	//	//	SYM
ejpam-3742	69	36	(	(	PUNCT
ejpam-3742	69	37	ff)∗	ff)∗	PROPN
ejpam-3742	69	38	�	�	PROPN
ejpam-3742	69	39	�	�	PROPN
ejpam-3742	69	40	homc	homc	PROPN
ejpam-3742	69	41	(	(	PUNCT
ejpam-3742	69	42	x	x	SYM
ejpam-3742	69	43	′	′	NUM
ejpam-3742	69	44	,	,	PUNCT
ejpam-3742	69	45	gy	gy	NOUN
ejpam-3742	69	46	)	)	PUNCT
ejpam-3742	69	47	f∗	f∗	NOUN
ejpam-3742	69	48	and	and	CCONJ
ejpam-3742	69	49	�	�	PROPN
ejpam-3742	69	50	�	�	PROPN
ejpam-3742	69	51	homd(fx	homd(fx	PROPN
ejpam-3742	69	52	,	,	PUNCT
ejpam-3742	69	53	y	y	PROPN
ejpam-3742	69	54	)	)	PUNCT
ejpam-3742	69	55	φx	φx	PROPN
ejpam-3742	69	56	,	,	PUNCT
ejpam-3742	69	57	y	y	PROPN
ejpam-3742	69	58	//	//	PROPN
ejpam-3742	69	59	homc	homc	PROPN
ejpam-3742	69	60	(	(	PUNCT
ejpam-3742	69	61	x	x	X
ejpam-3742	69	62	,	,	PUNCT
ejpam-3742	69	63	gy	gy	NOUN
ejpam-3742	69	64	)	)	PUNCT
ejpam-3742	69	65	homd(fx	homd(fx	PROPN
ejpam-3742	69	66	,	,	PUNCT
ejpam-3742	69	67	y	y	PROPN
ejpam-3742	69	68	)	)	PUNCT
ejpam-3742	70	1	φx	φx	PROPN
ejpam-3742	70	2	,	,	PUNCT
ejpam-3742	70	3	y	y	PROPN
ejpam-3742	70	4	//	//	X
ejpam-3742	70	5	g∗	g∗	PROPN
ejpam-3742	70	6	�	�	PROPN
ejpam-3742	70	7	�	�	PROPN
ejpam-3742	70	8	homc	homc	PROPN
ejpam-3742	70	9	(	(	PUNCT
ejpam-3742	70	10	x	x	X
ejpam-3742	70	11	,	,	PUNCT
ejpam-3742	70	12	gy	gy	NOUN
ejpam-3742	70	13	)	)	PUNCT
ejpam-3742	70	14	(	(	PUNCT
ejpam-3742	70	15	gg)∗	gg)∗	PROPN
ejpam-3742	70	16	�	�	PROPN
ejpam-3742	70	17	�	�	PROPN
ejpam-3742	70	18	homd(fx	homd(fx	PROPN
ejpam-3742	70	19	,	,	PUNCT
ejpam-3742	70	20	y	y	PROPN
ejpam-3742	70	21	′	′	NUM
ejpam-3742	70	22	)	)	PUNCT
ejpam-3742	70	23	φx	φx	PROPN
ejpam-3742	70	24	,	,	PUNCT
ejpam-3742	70	25	y	y	PROPN
ejpam-3742	70	26	′	′	PROPN
ejpam-3742	70	27	//	//	X
ejpam-3742	70	28	homc	homc	PROPN
ejpam-3742	70	29	(	(	PUNCT
ejpam-3742	70	30	x	x	X
ejpam-3742	70	31	,	,	PUNCT
ejpam-3742	70	32	gy	gy	NOUN
ejpam-3742	70	33	′	′	NOUN
ejpam-3742	70	34	)	)	PUNCT
ejpam-3742	71	1	where	where	SCONJ
ejpam-3742	71	2	f	f	X
ejpam-3742	71	3	:	:	PUNCT
ejpam-3742	71	4	x	x	PUNCT
ejpam-3742	71	5	−→	−→	NOUN
ejpam-3742	71	6	x	x	PUNCT
ejpam-3742	71	7	′	′	NOUN
ejpam-3742	71	8	and	and	CCONJ
ejpam-3742	71	9	g	g	NOUN
ejpam-3742	71	10	:	:	PUNCT
ejpam-3742	71	11	y	y	PROPN
ejpam-3742	71	12	−→	−→	NOUN
ejpam-3742	71	13	y	y	PROPN
ejpam-3742	71	14	′	′	NOUN
ejpam-3742	71	15	are	be	AUX
ejpam-3742	71	16	morphisms	morphism	NOUN
ejpam-3742	71	17	.	.	PUNCT
ejpam-3742	72	1	m	m	PROPN
ejpam-3742	72	2	thiaw	thiaw	NOUN
ejpam-3742	72	3	,	,	PUNCT
ejpam-3742	72	4	m	m	AUX
ejpam-3742	72	5	maaouia	maaouia	NOUN
ejpam-3742	72	6	/	/	SYM
ejpam-3742	72	7	eur	eur	NOUN
ejpam-3742	72	8	.	.	PUNCT
ejpam-3742	73	1	j.	j.	PROPN
ejpam-3742	73	2	pure	pure	PROPN
ejpam-3742	73	3	appl	appl	PROPN
ejpam-3742	73	4	.	.	PROPN
ejpam-3742	73	5	math	math	PROPN
ejpam-3742	73	6	,	,	PUNCT
ejpam-3742	73	7	13	13	NUM
ejpam-3742	73	8	(	(	PUNCT
ejpam-3742	73	9	3	3	NUM
ejpam-3742	73	10	)	)	PUNCT
ejpam-3742	73	11	(	(	PUNCT
ejpam-3742	73	12	2020	2020	NUM
ejpam-3742	73	13	)	)	PUNCT
ejpam-3742	73	14	,	,	PUNCT
ejpam-3742	73	15	472	472	NUM
ejpam-3742	73	16	-	-	SYM
ejpam-3742	73	17	482	482	NUM
ejpam-3742	73	18	475	475	NUM
ejpam-3742	73	19	proposition	proposition	NOUN
ejpam-3742	73	20	2	2	NUM
ejpam-3742	73	21	.	.	PUNCT
ejpam-3742	74	1	if	if	SCONJ
ejpam-3742	74	2	f	f	PROPN
ejpam-3742	74	3	:	:	PUNCT
ejpam-3742	74	4	c	c	AUX
ejpam-3742	74	5	−→	−→	NOUN
ejpam-3742	74	6	d	d	NOUN
ejpam-3742	74	7	has	have	VERB
ejpam-3742	74	8	two	two	NUM
ejpam-3742	74	9	right	right	ADJ
ejpam-3742	74	10	(	(	PUNCT
ejpam-3742	74	11	resp	resp	NOUN
ejpam-3742	74	12	.	.	PUNCT
ejpam-3742	75	1	left	left	ADJ
ejpam-3742	75	2	)	)	PUNCT
ejpam-3742	75	3	adjoint	adjoint	PROPN
ejpam-3742	75	4	g	g	NOUN
ejpam-3742	75	5	and	and	CCONJ
ejpam-3742	75	6	h	h	NOUN
ejpam-3742	75	7	,	,	PUNCT
ejpam-3742	75	8	then	then	ADV
ejpam-3742	75	9	g	g	PROPN
ejpam-3742	75	10	and	and	CCONJ
ejpam-3742	75	11	h	h	NOUN
ejpam-3742	75	12	are	be	AUX
ejpam-3742	75	13	naturally	naturally	ADV
ejpam-3742	75	14	isomorphic	isomorphic	ADJ
ejpam-3742	75	15	.	.	PUNCT
ejpam-3742	76	1	reciprocally	reciprocally	PROPN
ejpam-3742	76	2	,	,	PUNCT
ejpam-3742	76	3	if	if	SCONJ
ejpam-3742	76	4	f	f	PROPN
ejpam-3742	76	5	is	be	AUX
ejpam-3742	76	6	left	leave	VERB
ejpam-3742	76	7	(	(	PUNCT
ejpam-3742	76	8	resp	resp	NOUN
ejpam-3742	76	9	.	.	PUNCT
ejpam-3742	77	1	right	right	ADJ
ejpam-3742	77	2	)	)	PUNCT
ejpam-3742	77	3	adjoint	adjoint	VERB
ejpam-3742	77	4	to	to	ADP
ejpam-3742	77	5	g	g	NOUN
ejpam-3742	77	6	,	,	PUNCT
ejpam-3742	77	7	and	and	CCONJ
ejpam-3742	77	8	g	g	NOUN
ejpam-3742	77	9	is	be	AUX
ejpam-3742	77	10	naturally	naturally	ADV
ejpam-3742	77	11	isomorphic	isomorphic	ADJ
ejpam-3742	77	12	to	to	ADP
ejpam-3742	77	13	h	h	NOUN
ejpam-3742	77	14	,	,	PUNCT
ejpam-3742	77	15	then	then	ADV
ejpam-3742	77	16	f	f	PROPN
ejpam-3742	77	17	is	be	AUX
ejpam-3742	77	18	also	also	ADV
ejpam-3742	77	19	a	a	DET
ejpam-3742	77	20	left	left	ADJ
ejpam-3742	77	21	adjoint	adjoint	NOUN
ejpam-3742	77	22	to	to	ADP
ejpam-3742	77	23	h.	h.	PROPN
ejpam-3742	77	24	proposition	proposition	PROPN
ejpam-3742	77	25	3	3	X
ejpam-3742	77	26	.	.	PUNCT
ejpam-3742	77	27	suppose	suppose	VERB
ejpam-3742	77	28	ki	ki	PROPN
ejpam-3742	77	29	is	be	AUX
ejpam-3742	77	30	the	the	DET
ejpam-3742	77	31	i	i	PROPN
ejpam-3742	77	32	-	-	PUNCT
ejpam-3742	77	33	th	th	X
ejpam-3742	77	34	syzygy	syzygy	NOUN
ejpam-3742	77	35	of	of	ADP
ejpam-3742	77	36	some	some	DET
ejpam-3742	77	37	projective	projective	ADJ
ejpam-3742	77	38	resolution	resolution	NOUN
ejpam-3742	77	39	of	of	ADP
ejpam-3742	77	40	b.	b.	PROPN
ejpam-3742	77	41	then	then	ADV
ejpam-3742	77	42	torn+1(-,b	torn+1(-,b	ADV
ejpam-3742	77	43	)	)	PUNCT
ejpam-3742	77	44	and	and	CCONJ
ejpam-3742	77	45	torn−i(-,ki	torn−i(-,ki	NOUN
ejpam-3742	77	46	)	)	PUNCT
ejpam-3742	77	47	are	be	AUX
ejpam-3742	77	48	naturally	naturally	ADV
ejpam-3742	77	49	isomorphic	isomorphic	ADJ
ejpam-3742	77	50	functors	functor	NOUN
ejpam-3742	77	51	;	;	PUNCT
ejpam-3742	77	52	also	also	ADV
ejpam-3742	77	53	êxt	êxt	NOUN
ejpam-3742	77	54	n+1	n+1	PROPN
ejpam-3742	77	55	(	(	PUNCT
ejpam-3742	77	56	-,b	-,b	ADJ
ejpam-3742	77	57	)	)	PUNCT
ejpam-3742	77	58	and	and	CCONJ
ejpam-3742	77	59	êxt	êxt	NOUN
ejpam-3742	77	60	n−i	n−i	NOUN
ejpam-3742	77	61	(	(	PUNCT
ejpam-3742	77	62	-,ki	-,ki	NOUN
ejpam-3742	77	63	)	)	PUNCT
ejpam-3742	77	64	are	be	AUX
ejpam-3742	77	65	naturally	naturally	ADV
ejpam-3742	77	66	isomorphic	isomorphic	ADJ
ejpam-3742	77	67	functors	functor	NOUN
ejpam-3742	77	68	.	.	PUNCT
ejpam-3742	78	1	proof	proof	NOUN
ejpam-3742	78	2	.	.	PUNCT
ejpam-3742	79	1	see	see	VERB
ejpam-3742	79	2	[	[	X
ejpam-3742	79	3	6	6	NUM
ejpam-3742	79	4	,	,	PUNCT
ejpam-3742	79	5	chap	chap	NOUN
ejpam-3742	79	6	.	.	PUNCT
ejpam-3742	80	1	10	10	NUM
ejpam-3742	80	2	]	]	PUNCT
ejpam-3742	80	3	and	and	CCONJ
ejpam-3742	80	4	[	[	X
ejpam-3742	80	5	7	7	NUM
ejpam-3742	80	6	,	,	PUNCT
ejpam-3742	80	7	chap	chap	NOUN
ejpam-3742	80	8	.	.	PUNCT
ejpam-3742	81	1	5	5	NUM
ejpam-3742	81	2	]	]	PUNCT
ejpam-3742	81	3	.	.	PUNCT
ejpam-3742	82	1	3	3	X
ejpam-3742	82	2	.	.	X
ejpam-3742	82	3	the	the	DET
ejpam-3742	82	4	adjunction	adjunction	NOUN
ejpam-3742	82	5	of	of	ADP
ejpam-3742	82	6	the	the	DET
ejpam-3742	82	7	functors	functors	PROPN
ejpam-3742	82	8	s−1	s−1	PROPN
ejpam-3742	82	9	(	(	PUNCT
ejpam-3742	82	10	)	)	PUNCT
ejpam-3742	82	11	and	and	CCONJ
ejpam-3742	82	12	homa(-,b	homa(-,b	X
ejpam-3742	82	13	)	)	PUNCT
ejpam-3742	82	14	in	in	ADP
ejpam-3742	82	15	the	the	DET
ejpam-3742	82	16	category	category	NOUN
ejpam-3742	82	17	of	of	ADP
ejpam-3742	82	18	a	a	DET
ejpam-3742	82	19	-	-	PUNCT
ejpam-3742	82	20	alg	alg	NOUN
ejpam-3742	82	21	theorem	theorem	VERB
ejpam-3742	82	22	4	4	NUM
ejpam-3742	82	23	.	.	PUNCT
ejpam-3742	83	1	let	let	VERB
ejpam-3742	83	2	a	a	PRON
ejpam-3742	83	3	be	be	AUX
ejpam-3742	83	4	a	a	DET
ejpam-3742	83	5	ring	ring	NOUN
ejpam-3742	83	6	and	and	CCONJ
ejpam-3742	83	7	s	s	VERB
ejpam-3742	83	8	a	a	DET
ejpam-3742	83	9	central	central	ADJ
ejpam-3742	83	10	multiplicatively	multiplicatively	ADV
ejpam-3742	83	11	closed	close	VERB
ejpam-3742	83	12	subset	subset	NOUN
ejpam-3742	83	13	of	of	ADP
ejpam-3742	83	14	a.	a.	NOUN
ejpam-3742	83	15	then	then	ADV
ejpam-3742	83	16	the	the	DET
ejpam-3742	83	17	functors	functors	PROPN
ejpam-3742	83	18	s−1	s−1	PROPN
ejpam-3742	83	19	(	(	PUNCT
ejpam-3742	83	20	)	)	PUNCT
ejpam-3742	83	21	and	and	CCONJ
ejpam-3742	83	22	-⊗a	-⊗a	PROPN
ejpam-3742	83	23	s−1(a	s−1(a	PROPN
ejpam-3742	83	24	)	)	PUNCT
ejpam-3742	83	25	are	be	AUX
ejpam-3742	83	26	naturally	naturally	ADV
ejpam-3742	83	27	isomorphic	isomorphic	ADJ
ejpam-3742	83	28	(	(	PUNCT
ejpam-3742	83	29	s−1	s−1	PROPN
ejpam-3742	83	30	(	(	PUNCT
ejpam-3742	83	31	)	)	PUNCT
ejpam-3742	83	32	∼=	∼=	PROPN
ejpam-3742	83	33	-⊗a	-⊗a	PUNCT
ejpam-3742	83	34	s−1(a	s−1(a	PROPN
ejpam-3742	83	35	)	)	PUNCT
ejpam-3742	83	36	)	)	PUNCT
ejpam-3742	83	37	.	.	PUNCT
ejpam-3742	84	1	proof	proof	NOUN
ejpam-3742	84	2	.	.	PUNCT
ejpam-3742	85	1	let	let	VERB
ejpam-3742	85	2	θ	θ	NOUN
ejpam-3742	85	3	:	:	PUNCT
ejpam-3742	85	4	s−1()→	s−1()→	PROPN
ejpam-3742	85	5	-⊗a	-⊗a	PROPN
ejpam-3742	85	6	s−1(a	s−1(a	PROPN
ejpam-3742	85	7	)	)	PUNCT
ejpam-3742	85	8	.	.	PUNCT
ejpam-3742	86	1	∗	∗	NOUN
ejpam-3742	86	2	show	show	VERB
ejpam-3742	86	3	that	that	SCONJ
ejpam-3742	86	4	θ	θ	PROPN
ejpam-3742	86	5	is	be	AUX
ejpam-3742	86	6	a	a	DET
ejpam-3742	86	7	natural	natural	ADJ
ejpam-3742	86	8	transformation	transformation	NOUN
ejpam-3742	86	9	.	.	PUNCT
ejpam-3742	87	1	let	let	VERB
ejpam-3742	87	2	a	a	DET
ejpam-3742	87	3	∈	∈	PROPN
ejpam-3742	87	4	ob(a	ob(a	NOUN
ejpam-3742	87	5	-	-	PUNCT
ejpam-3742	87	6	alg	alg	PROPN
ejpam-3742	87	7	)	)	PUNCT
ejpam-3742	87	8	.	.	PUNCT
ejpam-3742	88	1	consider	consider	VERB
ejpam-3742	88	2	θa	θa	PRON
ejpam-3742	88	3	:	:	PUNCT
ejpam-3742	88	4	a	a	DET
ejpam-3742	88	5	×	×	PROPN
ejpam-3742	88	6	s−1(a	s−1(a	PROPN
ejpam-3742	88	7	)	)	PUNCT
ejpam-3742	89	1	−→	−→	NOUN
ejpam-3742	89	2	s−1(a	s−1(a	PROPN
ejpam-3742	89	3	)	)	PUNCT
ejpam-3742	90	1	(	(	PUNCT
ejpam-3742	90	2	x	x	X
ejpam-3742	90	3	,	,	PUNCT
ejpam-3742	90	4	a	a	DET
ejpam-3742	90	5	s	s	NOUN
ejpam-3742	90	6	)	)	PUNCT
ejpam-3742	90	7	7−→	7−→	NOUN
ejpam-3742	90	8	a	a	PRON
ejpam-3742	90	9	·	·	PUNCT
ejpam-3742	90	10	x	x	SYM
ejpam-3742	90	11	s	s	VERB
ejpam-3742	90	12	we	we	PRON
ejpam-3742	90	13	have	have	VERB
ejpam-3742	90	14	θa	θa	NUM
ejpam-3742	90	15	which	which	PRON
ejpam-3742	90	16	is	be	AUX
ejpam-3742	90	17	a	a	DET
ejpam-3742	90	18	-	-	PUNCT
ejpam-3742	90	19	bilinear	bilinear	NOUN
ejpam-3742	90	20	,	,	PUNCT
ejpam-3742	90	21	so	so	ADV
ejpam-3742	90	22	by	by	ADP
ejpam-3742	90	23	the	the	DET
ejpam-3742	90	24	universal	universal	ADJ
ejpam-3742	90	25	property	property	NOUN
ejpam-3742	90	26	of	of	ADP
ejpam-3742	90	27	tensor	tensor	NOUN
ejpam-3742	90	28	product	product	NOUN
ejpam-3742	90	29	,	,	PUNCT
ejpam-3742	90	30	there	there	PRON
ejpam-3742	90	31	exist	exist	VERB
ejpam-3742	90	32	a	a	DET
ejpam-3742	90	33	morphism	morphism	NOUN
ejpam-3742	90	34	of	of	ADP
ejpam-3742	90	35	groups	group	NOUN
ejpam-3742	91	1	θa	θa	NUM
ejpam-3742	91	2	:	:	PUNCT
ejpam-3742	91	3	a	a	DET
ejpam-3742	91	4	⊗	⊗	PROPN
ejpam-3742	91	5	s−1(a	s−1(a	PROPN
ejpam-3742	91	6	)	)	PUNCT
ejpam-3742	92	1	−→	−→	NOUN
ejpam-3742	92	2	s−1(a	s−1(a	PROPN
ejpam-3742	92	3	)	)	PUNCT
ejpam-3742	92	4	defined	define	VERB
ejpam-3742	92	5	by	by	ADP
ejpam-3742	92	6	θa	θa	PRON
ejpam-3742	92	7	(	(	PUNCT
ejpam-3742	92	8	xi	xi	PROPN
ejpam-3742	92	9	⊗	⊗	PROPN
ejpam-3742	92	10	∑	∑	PROPN
ejpam-3742	92	11	ai	ai	VERB
ejpam-3742	92	12	si	si	NOUN
ejpam-3742	92	13	)	)	PUNCT
ejpam-3742	93	1	=	=	PUNCT
ejpam-3742	93	2	∑	∑	ADV
ejpam-3742	93	3	ai	ai	VERB
ejpam-3742	93	4	·	·	PUNCT
ejpam-3742	93	5	xi	xi	X
ejpam-3742	93	6	si	si	PROPN
ejpam-3742	93	7	.	.	PUNCT
ejpam-3742	94	1	let	let	VERB
ejpam-3742	94	2	f	f	PRON
ejpam-3742	94	3	∈	∈	PROPN
ejpam-3742	94	4	homa	homa	NOUN
ejpam-3742	94	5	-	-	PUNCT
ejpam-3742	94	6	alg(a	alg(a	PROPN
ejpam-3742	94	7	,	,	PUNCT
ejpam-3742	94	8	a	a	DET
ejpam-3742	94	9	′	′	NOUN
ejpam-3742	94	10	)	)	PUNCT
ejpam-3742	94	11	,	,	PUNCT
ejpam-3742	94	12	show	show	VERB
ejpam-3742	94	13	that	that	SCONJ
ejpam-3742	94	14	the	the	DET
ejpam-3742	94	15	following	follow	VERB
ejpam-3742	94	16	diagram	diagram	NOUN
ejpam-3742	94	17	is	be	AUX
ejpam-3742	94	18	commutative	commutative	ADJ
ejpam-3742	94	19	a	a	DET
ejpam-3742	94	20	⊗	⊗	PROPN
ejpam-3742	94	21	s−1(a	s−1(a	PROPN
ejpam-3742	94	22	)	)	PUNCT
ejpam-3742	95	1	f⊗1s−1(a	f⊗1s−1(a	PROPN
ejpam-3742	95	2	)	)	PUNCT
ejpam-3742	95	3	�	�	PROPN
ejpam-3742	95	4	�	�	PROPN
ejpam-3742	95	5	θa	θa	NUM
ejpam-3742	95	6	//	//	NUM
ejpam-3742	95	7	s−1(a	s−1(a	PROPN
ejpam-3742	95	8	)	)	PUNCT
ejpam-3742	95	9	s−1(f	s−1(f	PROPN
ejpam-3742	95	10	)	)	PUNCT
ejpam-3742	96	1	⇔	⇔	PROPN
ejpam-3742	96	2	s−1(f)	s−1(f)	PROPN
ejpam-3742	96	3	◦	◦	NOUN
ejpam-3742	96	4	θa	θa	NOUN
ejpam-3742	96	5	=	=	NOUN
ejpam-3742	96	6	θa	θa	NUM
ejpam-3742	96	7	′	′	NOUN
ejpam-3742	96	8	◦	◦	NOUN
ejpam-3742	96	9	(f⊗1s−1(a	(f⊗1s−1(a	NOUN
ejpam-3742	96	10	)	)	PUNCT
ejpam-3742	96	11	)	)	PUNCT
ejpam-3742	96	12	.	.	PUNCT
ejpam-3742	97	1	�	�	PROPN
ejpam-3742	97	2	�	�	PROPN
ejpam-3742	97	3	a	a	DET
ejpam-3742	97	4	′	′	NUM
ejpam-3742	97	5	⊗	⊗	NUM
ejpam-3742	97	6	s−1(a	s−1(a	PROPN
ejpam-3742	97	7	)	)	PUNCT
ejpam-3742	97	8	θa	θa	NUM
ejpam-3742	97	9	′	′	NUM
ejpam-3742	97	10	//	//	SYM
ejpam-3742	97	11	s−1(a	s−1(a	PROPN
ejpam-3742	97	12	′	′	NUM
ejpam-3742	97	13	)	)	PUNCT
ejpam-3742	97	14	let	let	VERB
ejpam-3742	97	15	xi	xi	PROPN
ejpam-3742	97	16	⊗	⊗	PROPN
ejpam-3742	97	17	∑	∑	VERB
ejpam-3742	97	18	ai	ai	VERB
ejpam-3742	97	19	si	si	PROPN
ejpam-3742	97	20	∈	∈	PROPN
ejpam-3742	97	21	a	a	DET
ejpam-3742	97	22	⊗	⊗	PROPN
ejpam-3742	97	23	s−1(a	s−1(a	PROPN
ejpam-3742	97	24	)	)	PUNCT
ejpam-3742	97	25	.	.	PUNCT
ejpam-3742	98	1	on	on	ADP
ejpam-3742	98	2	the	the	DET
ejpam-3742	98	3	one	one	NUM
ejpam-3742	98	4	hand	hand	NOUN
ejpam-3742	98	5	we	we	PRON
ejpam-3742	98	6	have	have	VERB
ejpam-3742	98	7	,	,	PUNCT
ejpam-3742	98	8	θa	θa	NUM
ejpam-3742	98	9	′	′	NOUN
ejpam-3742	98	10	◦	◦	NOUN
ejpam-3742	98	11	f	f	PROPN
ejpam-3742	98	12	⊗	⊗	PROPN
ejpam-3742	98	13	1s−1(a)(xi	1s−1(a)(xi	PROPN
ejpam-3742	99	1	⊗	⊗	NOUN
ejpam-3742	99	2	∑	∑	PROPN
ejpam-3742	99	3	ai	ai	INTJ
ejpam-3742	99	4	si	si	NOUN
ejpam-3742	99	5	)	)	PUNCT
ejpam-3742	100	1	=	=	SYM
ejpam-3742	100	2	θa	θa	NUM
ejpam-3742	100	3	′(f(xi)⊗	′(f(xi)⊗	VERB
ejpam-3742	100	4	∑	∑	VERB
ejpam-3742	100	5	ai	ai	VERB
ejpam-3742	100	6	si	si	NOUN
ejpam-3742	100	7	)	)	PUNCT
ejpam-3742	101	1	=	=	PUNCT
ejpam-3742	101	2	∑	∑	PUNCT
ejpam-3742	101	3	ai	ai	VERB
ejpam-3742	101	4	·	·	SYM
ejpam-3742	101	5	f(xi	f(xi	NUM
ejpam-3742	101	6	)	)	PUNCT
ejpam-3742	101	7	si	si	X
ejpam-3742	101	8	.	.	PUNCT
ejpam-3742	102	1	on	on	ADP
ejpam-3742	102	2	the	the	DET
ejpam-3742	102	3	other	other	ADJ
ejpam-3742	102	4	hand	hand	NOUN
ejpam-3742	102	5	m	m	NOUN
ejpam-3742	102	6	thiaw	thiaw	NOUN
ejpam-3742	102	7	,	,	PUNCT
ejpam-3742	102	8	m	m	AUX
ejpam-3742	102	9	maaouia	maaouia	NOUN
ejpam-3742	102	10	/	/	SYM
ejpam-3742	102	11	eur	eur	NOUN
ejpam-3742	102	12	.	.	PUNCT
ejpam-3742	103	1	j.	j.	PROPN
ejpam-3742	103	2	pure	pure	PROPN
ejpam-3742	103	3	appl	appl	PROPN
ejpam-3742	103	4	.	.	PROPN
ejpam-3742	103	5	math	math	PROPN
ejpam-3742	103	6	,	,	PUNCT
ejpam-3742	103	7	13	13	NUM
ejpam-3742	103	8	(	(	PUNCT
ejpam-3742	103	9	3	3	NUM
ejpam-3742	103	10	)	)	PUNCT
ejpam-3742	103	11	(	(	PUNCT
ejpam-3742	103	12	2020	2020	NUM
ejpam-3742	103	13	)	)	PUNCT
ejpam-3742	103	14	,	,	PUNCT
ejpam-3742	103	15	472	472	NUM
ejpam-3742	103	16	-	-	SYM
ejpam-3742	103	17	482	482	NUM
ejpam-3742	103	18	476	476	NUM
ejpam-3742	103	19	s−1(f	s−1(f	PROPN
ejpam-3742	103	20	)	)	PUNCT
ejpam-3742	103	21	◦	◦	NOUN
ejpam-3742	103	22	θa	θa	NUM
ejpam-3742	103	23	(	(	PUNCT
ejpam-3742	103	24	xi	xi	PROPN
ejpam-3742	103	25	⊗	⊗	PROPN
ejpam-3742	103	26	∑	∑	PROPN
ejpam-3742	103	27	ai	ai	VERB
ejpam-3742	103	28	si	si	PROPN
ejpam-3742	103	29	)	)	PUNCT
ejpam-3742	103	30	=	=	SYM
ejpam-3742	103	31	s−1(f	s−1(f	PROPN
ejpam-3742	103	32	)	)	PUNCT
ejpam-3742	103	33	(	(	PUNCT
ejpam-3742	103	34	∑	∑	ADV
ejpam-3742	103	35	ai	ai	VERB
ejpam-3742	103	36	·	·	PUNCT
ejpam-3742	103	37	xi	xi	X
ejpam-3742	103	38	si	si	X
ejpam-3742	103	39	)	)	PUNCT
ejpam-3742	103	40	=	=	SYM
ejpam-3742	103	41	∑	∑	PUNCT
ejpam-3742	103	42	s−1(f	s−1(f	PROPN
ejpam-3742	103	43	)	)	PUNCT
ejpam-3742	103	44	(	(	PUNCT
ejpam-3742	103	45	ai	ai	PROPN
ejpam-3742	103	46	·	·	PUNCT
ejpam-3742	103	47	xi	xi	X
ejpam-3742	103	48	si	si	X
ejpam-3742	103	49	)	)	PUNCT
ejpam-3742	104	1	=	=	PUNCT
ejpam-3742	104	2	∑	∑	PUNCT
ejpam-3742	104	3	ai	ai	VERB
ejpam-3742	104	4	·	·	SYM
ejpam-3742	104	5	f(xi	f(xi	NUM
ejpam-3742	104	6	)	)	PUNCT
ejpam-3742	104	7	si	si	X
ejpam-3742	104	8	.	.	PUNCT
ejpam-3742	105	1	so	so	ADV
ejpam-3742	105	2	we	we	PRON
ejpam-3742	105	3	have	have	VERB
ejpam-3742	105	4	,	,	PUNCT
ejpam-3742	105	5	s−1(f	s−1(f	PROPN
ejpam-3742	105	6	)	)	PUNCT
ejpam-3742	105	7	◦	◦	NOUN
ejpam-3742	105	8	θa	θa	NUM
ejpam-3742	105	9	=	=	SYM
ejpam-3742	105	10	θa	θa	NUM
ejpam-3742	105	11	′	′	NOUN
ejpam-3742	106	1	◦	◦	NOUN
ejpam-3742	106	2	(	(	PUNCT
ejpam-3742	106	3	f	f	PROPN
ejpam-3742	106	4	⊗	⊗	PROPN
ejpam-3742	106	5	1s−1(a	1s−1(a	NUM
ejpam-3742	106	6	)	)	PUNCT
ejpam-3742	106	7	)	)	PUNCT
ejpam-3742	107	1	and	and	CCONJ
ejpam-3742	107	2	therefore	therefore	ADV
ejpam-3742	107	3	θ	θ	PROPN
ejpam-3742	107	4	is	be	AUX
ejpam-3742	107	5	a	a	DET
ejpam-3742	107	6	natural	natural	ADJ
ejpam-3742	107	7	transformation	transformation	NOUN
ejpam-3742	107	8	.	.	PUNCT
ejpam-3742	108	1	∗	∗	NOUN
ejpam-3742	108	2	show	show	VERB
ejpam-3742	108	3	that	that	SCONJ
ejpam-3742	108	4	for	for	ADP
ejpam-3742	108	5	any	any	DET
ejpam-3742	108	6	a	a	DET
ejpam-3742	108	7	∈	∈	PROPN
ejpam-3742	108	8	ob(a	ob(a	NOUN
ejpam-3742	108	9	-	-	SYM
ejpam-3742	108	10	alg	alg	PROPN
ejpam-3742	108	11	)	)	PUNCT
ejpam-3742	108	12	,	,	PUNCT
ejpam-3742	108	13	θa	θa	NUM
ejpam-3742	108	14	is	be	AUX
ejpam-3742	108	15	bijective	bijective	ADJ
ejpam-3742	108	16	.	.	PUNCT
ejpam-3742	109	1	•	•	INTJ
ejpam-3742	109	2	let	let	VERB
ejpam-3742	109	3	x	x	NOUN
ejpam-3742	109	4	s	s	VERB
ejpam-3742	109	5	∈	∈	PROPN
ejpam-3742	109	6	s−1(a	s−1(a	PROPN
ejpam-3742	109	7	)	)	PUNCT
ejpam-3742	109	8	.	.	PUNCT
ejpam-3742	110	1	we	we	PRON
ejpam-3742	110	2	have	have	VERB
ejpam-3742	110	3	θa	θa	NUM
ejpam-3742	110	4	(	(	PUNCT
ejpam-3742	110	5	x⊗	x⊗	PROPN
ejpam-3742	110	6	1	1	NUM
ejpam-3742	110	7	s	s	PART
ejpam-3742	110	8	)	)	PUNCT
ejpam-3742	110	9	=	=	PUNCT
ejpam-3742	111	1	x	x	SYM
ejpam-3742	111	2	s	s	PART
ejpam-3742	111	3	⇒	⇒	NOUN
ejpam-3742	111	4	θa	θa	NUM
ejpam-3742	111	5	is	be	AUX
ejpam-3742	111	6	surjective	surjective	ADJ
ejpam-3742	111	7	.	.	PUNCT
ejpam-3742	112	1	•	•	NUM
ejpam-3742	112	2	let	let	VERB
ejpam-3742	112	3	xi	xi	PROPN
ejpam-3742	112	4	⊗	⊗	PROPN
ejpam-3742	112	5	∑	∑	VERB
ejpam-3742	112	6	ai	ai	VERB
ejpam-3742	112	7	si	si	PROPN
ejpam-3742	112	8	∈	∈	PROPN
ejpam-3742	112	9	a	a	DET
ejpam-3742	112	10	⊗	⊗	PROPN
ejpam-3742	112	11	s−1(a	s−1(a	PROPN
ejpam-3742	112	12	)	)	PUNCT
ejpam-3742	112	13	.	.	PUNCT
ejpam-3742	113	1	we	we	PRON
ejpam-3742	113	2	have	have	VERB
ejpam-3742	113	3	∑	∑	PROPN
ejpam-3742	113	4	xi	xi	PROPN
ejpam-3742	113	5	⊗	⊗	PROPN
ejpam-3742	113	6	ai	ai	VERB
ejpam-3742	113	7	si	si	PROPN
ejpam-3742	113	8	=	=	PUNCT
ejpam-3742	113	9	∑	∑	PROPN
ejpam-3742	113	10	(	(	PUNCT
ejpam-3742	113	11	∏	∏	X
ejpam-3742	113	12	si)siaixi	si)siaixi	VERB
ejpam-3742	113	13	⊗	⊗	PROPN
ejpam-3742	113	14	1∏	1∏	NUM
ejpam-3742	113	15	si	si	X
ejpam-3742	113	16	.	.	PUNCT
ejpam-3742	114	1	pose	pose	PROPN
ejpam-3742	114	2	s	s	PART
ejpam-3742	114	3	=	=	SYM
ejpam-3742	114	4	∏	∏	X
ejpam-3742	114	5	si	si	X
ejpam-3742	114	6	and	and	CCONJ
ejpam-3742	114	7	zi	zi	NOUN
ejpam-3742	114	8	=	=	PUNCT
ejpam-3742	114	9	s−1si	s−1si	PROPN
ejpam-3742	115	1	∈	∈	PROPN
ejpam-3742	115	2	s.	s.	PROPN
ejpam-3742	116	1	so	so	SCONJ
ejpam-3742	116	2	we	we	PRON
ejpam-3742	116	3	have	have	VERB
ejpam-3742	116	4	∑	∑	PROPN
ejpam-3742	116	5	xi	xi	PROPN
ejpam-3742	116	6	⊗	⊗	PROPN
ejpam-3742	116	7	ai	ai	VERB
ejpam-3742	116	8	si	si	PROPN
ejpam-3742	116	9	=	=	PUNCT
ejpam-3742	116	10	∑	∑	PROPN
ejpam-3742	116	11	ziaixi	ziaixi	PROPN
ejpam-3742	116	12	⊗	⊗	PROPN
ejpam-3742	116	13	1	1	NUM
ejpam-3742	116	14	s	s	NOUN
ejpam-3742	116	15	=	=	PUNCT
ejpam-3742	116	16	(	(	PUNCT
ejpam-3742	116	17	∑	∑	PROPN
ejpam-3742	116	18	ziaixi)⊗	ziaixi)⊗	NOUN
ejpam-3742	116	19	1	1	NUM
ejpam-3742	116	20	s	s	PART
ejpam-3742	116	21	.	.	PUNCT
ejpam-3742	117	1	so	so	ADV
ejpam-3742	117	2	the	the	DET
ejpam-3742	117	3	elements	element	NOUN
ejpam-3742	117	4	of	of	ADP
ejpam-3742	117	5	s−1(a)⊗a	s−1(a)⊗a	NOUN
ejpam-3742	117	6	are	be	AUX
ejpam-3742	117	7	written	write	VERB
ejpam-3742	117	8	in	in	ADP
ejpam-3742	117	9	the	the	DET
ejpam-3742	117	10	form	form	NOUN
ejpam-3742	117	11	1	1	NUM
ejpam-3742	117	12	s	s	PART
ejpam-3742	117	13	⊗	⊗	PROPN
ejpam-3742	117	14	y	y	PROPN
ejpam-3742	117	15	,	,	PUNCT
ejpam-3742	117	16	where	where	SCONJ
ejpam-3742	117	17	y	y	PROPN
ejpam-3742	117	18	∈	∈	PROPN
ejpam-3742	117	19	a	a	PRON
ejpam-3742	117	20	and	and	CCONJ
ejpam-3742	117	21	s	s	PROPN
ejpam-3742	117	22	∈	∈	PROPN
ejpam-3742	117	23	s.	s.	PROPN
ejpam-3742	117	24	let	let	VERB
ejpam-3742	117	25	1	1	NUM
ejpam-3742	117	26	s	s	VERB
ejpam-3742	117	27	⊗	⊗	NUM
ejpam-3742	117	28	y	y	PROPN
ejpam-3742	117	29	∈	∈	PROPN
ejpam-3742	117	30	kerθa	kerθa	NOUN
ejpam-3742	117	31	⇔	⇔	X
ejpam-3742	117	32	θa	θa	PROPN
ejpam-3742	117	33	(	(	PUNCT
ejpam-3742	117	34	1	1	NUM
ejpam-3742	117	35	s	s	NOUN
ejpam-3742	117	36	⊗	⊗	PROPN
ejpam-3742	117	37	y	y	PROPN
ejpam-3742	117	38	)	)	PUNCT
ejpam-3742	118	1	=	=	SYM
ejpam-3742	118	2	0s−1a	0s−1a	PROPN
ejpam-3742	118	3	⇒	⇒	VERB
ejpam-3742	118	4	y	y	PROPN
ejpam-3742	118	5	s	s	PROPN
ejpam-3742	118	6	=	=	X
ejpam-3742	118	7	0a	0a	PROPN
ejpam-3742	118	8	1	1	NUM
ejpam-3742	118	9	⇒	⇒	PROPN
ejpam-3742	118	10	∃	∃	PROPN
ejpam-3742	118	11	s1	s1	PROPN
ejpam-3742	118	12	,	,	PUNCT
ejpam-3742	118	13	s2	s2	NOUN
ejpam-3742	118	14	∈	∈	PROPN
ejpam-3742	118	15	s	s	VERB
ejpam-3742	119	1	such	such	ADJ
ejpam-3742	119	2	that	that	SCONJ
ejpam-3742	119	3	{	{	PUNCT
ejpam-3742	119	4	s1y	s1y	NOUN
ejpam-3742	119	5	=	=	NOUN
ejpam-3742	119	6	0	0	NUM
ejpam-3742	119	7	s1s	s1s	PROPN
ejpam-3742	119	8	=	=	NOUN
ejpam-3742	119	9	s2	s2	NOUN
ejpam-3742	119	10	so	so	ADV
ejpam-3742	119	11	1	1	NUM
ejpam-3742	119	12	s	s	VERB
ejpam-3742	119	13	⊗	⊗	NUM
ejpam-3742	119	14	y	y	PROPN
ejpam-3742	119	15	=	=	SYM
ejpam-3742	119	16	1	1	NUM
ejpam-3742	119	17	ss1	ss1	PROPN
ejpam-3742	119	18	⊗	⊗	PROPN
ejpam-3742	119	19	s1y	s1y	PROPN
ejpam-3742	119	20	=	=	SYM
ejpam-3742	119	21	1	1	NUM
ejpam-3742	119	22	ss1	ss1	NOUN
ejpam-3742	119	23	⊗	⊗	NOUN
ejpam-3742	119	24	0	0	PUNCT
ejpam-3742	120	1	=	=	SYM
ejpam-3742	120	2	0	0	NUM
ejpam-3742	120	3	⇒	⇒	NOUN
ejpam-3742	120	4	kerθa	kerθa	NOUN
ejpam-3742	120	5	=	=	SYM
ejpam-3742	120	6	{	{	PUNCT
ejpam-3742	120	7	0s−1a	0s−1a	NOUN
ejpam-3742	120	8	}	}	PUNCT
ejpam-3742	120	9	⇒	⇒	NOUN
ejpam-3742	120	10	θa	θa	PRON
ejpam-3742	120	11	is	be	AUX
ejpam-3742	120	12	injective	injective	ADJ
ejpam-3742	120	13	.	.	PUNCT
ejpam-3742	121	1	so	so	ADV
ejpam-3742	121	2	θa	θa	NOUN
ejpam-3742	121	3	is	be	AUX
ejpam-3742	121	4	bijective	bijective	ADJ
ejpam-3742	121	5	.	.	PUNCT
ejpam-3742	122	1	therefore	therefore	ADV
ejpam-3742	122	2	s−1	s−1	PROPN
ejpam-3742	122	3	(	(	PUNCT
ejpam-3742	122	4	)	)	PUNCT
ejpam-3742	122	5	∼=	∼=	PROPN
ejpam-3742	122	6	-⊗a	-⊗a	PUNCT
ejpam-3742	122	7	s−1(a	s−1(a	PROPN
ejpam-3742	122	8	)	)	PUNCT
ejpam-3742	122	9	.	.	PUNCT
ejpam-3742	123	1	theorem	theorem	NOUN
ejpam-3742	123	2	5	5	NUM
ejpam-3742	123	3	.	.	PUNCT
ejpam-3742	124	1	let	let	VERB
ejpam-3742	124	2	a	a	PRON
ejpam-3742	124	3	be	be	AUX
ejpam-3742	124	4	a	a	DET
ejpam-3742	124	5	ring	ring	NOUN
ejpam-3742	124	6	and	and	CCONJ
ejpam-3742	124	7	s	s	VERB
ejpam-3742	124	8	a	a	DET
ejpam-3742	124	9	central	central	ADJ
ejpam-3742	124	10	multiplicatively	multiplicatively	ADV
ejpam-3742	124	11	closed	close	VERB
ejpam-3742	124	12	subset	subset	NOUN
ejpam-3742	124	13	of	of	ADP
ejpam-3742	124	14	a.	a.	NOUN
ejpam-3742	124	15	then	then	ADV
ejpam-3742	124	16	-⊗a	-⊗a	PROPN
ejpam-3742	124	17	s−1(a	s−1(a	PROPN
ejpam-3742	124	18	)	)	PUNCT
ejpam-3742	124	19	:	:	PUNCT
ejpam-3742	124	20	alg	alg	PROPN
ejpam-3742	124	21	-	-	PUNCT
ejpam-3742	124	22	a	a	DET
ejpam-3742	124	23	�	�	PROPN
ejpam-3742	124	24	a	a	DET
ejpam-3742	124	25	-	-	PUNCT
ejpam-3742	124	26	modo	modo	NOUN
ejpam-3742	124	27	:	:	PUNCT
ejpam-3742	124	28	homa(-	homa(-	NOUN
ejpam-3742	124	29	,	,	PUNCT
ejpam-3742	124	30	s−1(a))o	s−1(a))o	PROPN
ejpam-3742	124	31	is	be	AUX
ejpam-3742	124	32	an	an	DET
ejpam-3742	124	33	adjunction	adjunction	NOUN
ejpam-3742	124	34	.	.	PUNCT
ejpam-3742	125	1	proof	proof	NOUN
ejpam-3742	125	2	.	.	PUNCT
ejpam-3742	126	1	∗	∗	NOUN
ejpam-3742	126	2	let	let	VERB
ejpam-3742	126	3	a	a	DET
ejpam-3742	126	4	∈	∈	PROPN
ejpam-3742	126	5	ob(alg	ob(alg	NOUN
ejpam-3742	126	6	-	-	PUNCT
ejpam-3742	126	7	a	a	NOUN
ejpam-3742	126	8	)	)	PUNCT
ejpam-3742	126	9	,	,	PUNCT
ejpam-3742	126	10	r	r	NOUN
ejpam-3742	126	11	∈	∈	PROPN
ejpam-3742	126	12	ob(a	ob(a	NOUN
ejpam-3742	126	13	-	-	PUNCT
ejpam-3742	126	14	modo	modo	NOUN
ejpam-3742	126	15	)	)	PUNCT
ejpam-3742	126	16	.	.	PUNCT
ejpam-3742	127	1	let	let	VERB
ejpam-3742	127	2	ϕa	ϕa	VERB
ejpam-3742	127	3	,	,	PUNCT
ejpam-3742	127	4	r	r	NOUN
ejpam-3742	127	5	:	:	PUNCT
ejpam-3742	127	6	homa	homa	NOUN
ejpam-3742	127	7	-	-	PUNCT
ejpam-3742	127	8	modo(a	modo(a	PROPN
ejpam-3742	127	9	⊗a	⊗a	VERB
ejpam-3742	127	10	s−1(a),r	s−1(a),r	NOUN
ejpam-3742	127	11	)	)	PUNCT
ejpam-3742	127	12	−→	−→	ADJ
ejpam-3742	127	13	homalg	homalg	PROPN
ejpam-3742	127	14	-	-	PUNCT
ejpam-3742	127	15	a(a	a(a	PROPN
ejpam-3742	127	16	,	,	PUNCT
ejpam-3742	127	17	homa(r	homa(r	PROPN
ejpam-3742	127	18	,	,	PUNCT
ejpam-3742	127	19	s−1(a))o	s−1(a))o	NUM
ejpam-3742	127	20	)	)	PUNCT
ejpam-3742	128	1	f	f	PROPN
ejpam-3742	128	2	7−→	7−→	PROPN
ejpam-3742	128	3	ϕa	ϕa	NOUN
ejpam-3742	128	4	,	,	PUNCT
ejpam-3742	128	5	r(f	r(f	PROPN
ejpam-3742	128	6	)	)	PUNCT
ejpam-3742	128	7	:	:	PUNCT
ejpam-3742	128	8	a	a	DET
ejpam-3742	128	9	−→	−→	ADJ
ejpam-3742	128	10	homa(s−1(a),r	homa(s−1(a),r	NOUN
ejpam-3742	128	11	)	)	PUNCT
ejpam-3742	128	12	x	x	SYM
ejpam-3742	129	1	7−→	7−→	NOUN
ejpam-3742	129	2	ϕa	ϕa	NOUN
ejpam-3742	129	3	,	,	PUNCT
ejpam-3742	129	4	r(f)(x	r(f)(x	PROPN
ejpam-3742	129	5	)	)	PUNCT
ejpam-3742	129	6	:	:	PUNCT
ejpam-3742	129	7	s−1(a	s−1(a	PROPN
ejpam-3742	129	8	)	)	PUNCT
ejpam-3742	130	1	−→	−→	NOUN
ejpam-3742	130	2	r	r	NOUN
ejpam-3742	130	3	y	y	PROPN
ejpam-3742	130	4	s	s	PART
ejpam-3742	130	5	7−→	7−→	NOUN
ejpam-3742	130	6	f(x⊗	f(x⊗	NOUN
ejpam-3742	130	7	y	y	PROPN
ejpam-3742	130	8	s	s	PROPN
ejpam-3742	130	9	)	)	PUNCT
ejpam-3742	130	10	.	.	PUNCT
ejpam-3742	131	1	m	m	PROPN
ejpam-3742	131	2	thiaw	thiaw	ADJ
ejpam-3742	131	3	,	,	PUNCT
ejpam-3742	131	4	m	m	AUX
ejpam-3742	131	5	maaouia	maaouia	NOUN
ejpam-3742	131	6	/	/	SYM
ejpam-3742	131	7	eur	eur	NOUN
ejpam-3742	131	8	.	.	PUNCT
ejpam-3742	132	1	j.	j.	PROPN
ejpam-3742	132	2	pure	pure	PROPN
ejpam-3742	132	3	appl	appl	PROPN
ejpam-3742	132	4	.	.	PROPN
ejpam-3742	132	5	math	math	PROPN
ejpam-3742	132	6	,	,	PUNCT
ejpam-3742	132	7	13	13	NUM
ejpam-3742	132	8	(	(	PUNCT
ejpam-3742	132	9	3	3	NUM
ejpam-3742	132	10	)	)	PUNCT
ejpam-3742	132	11	(	(	PUNCT
ejpam-3742	132	12	2020	2020	NUM
ejpam-3742	132	13	)	)	PUNCT
ejpam-3742	132	14	,	,	PUNCT
ejpam-3742	132	15	472	472	NUM
ejpam-3742	132	16	-	-	SYM
ejpam-3742	132	17	482	482	NUM
ejpam-3742	132	18	477	477	NUM
ejpam-3742	132	19	it	it	PRON
ejpam-3742	132	20	is	be	AUX
ejpam-3742	132	21	clear	clear	ADJ
ejpam-3742	132	22	that	that	SCONJ
ejpam-3742	132	23	ϕa	ϕa	INTJ
ejpam-3742	132	24	,	,	PUNCT
ejpam-3742	132	25	r	r	NOUN
ejpam-3742	132	26	is	be	AUX
ejpam-3742	132	27	well	well	ADV
ejpam-3742	132	28	defined	define	VERB
ejpam-3742	132	29	.	.	PUNCT
ejpam-3742	133	1	consider	consider	VERB
ejpam-3742	133	2	the	the	DET
ejpam-3742	133	3	map	map	NOUN
ejpam-3742	133	4	,	,	PUNCT
ejpam-3742	133	5	ψ	ψ	X
ejpam-3742	133	6	:	:	PUNCT
ejpam-3742	133	7	homalg	homalg	PROPN
ejpam-3742	133	8	-	-	PUNCT
ejpam-3742	133	9	a(a	a(a	PROPN
ejpam-3742	133	10	,	,	PUNCT
ejpam-3742	133	11	homa(r	homa(r	PROPN
ejpam-3742	133	12	,	,	PUNCT
ejpam-3742	133	13	s−1(a))o	s−1(a))o	NUM
ejpam-3742	133	14	)	)	PUNCT
ejpam-3742	133	15	−→	−→	NOUN
ejpam-3742	133	16	homa	homa	NOUN
ejpam-3742	133	17	-	-	PUNCT
ejpam-3742	133	18	modo(a	modo(a	PROPN
ejpam-3742	133	19	⊗a	⊗a	VERB
ejpam-3742	133	20	s−1(a),r	s−1(a),r	NOUN
ejpam-3742	133	21	)	)	PUNCT
ejpam-3742	133	22	g	g	PROPN
ejpam-3742	133	23	7−→	7−→	PROPN
ejpam-3742	133	24	ψ(g	ψ(g	PROPN
ejpam-3742	133	25	)	)	PUNCT
ejpam-3742	133	26	:	:	PUNCT
ejpam-3742	133	27	a	a	DET
ejpam-3742	133	28	⊗a	⊗a	NOUN
ejpam-3742	133	29	s−1(a	s−1(a	PROPN
ejpam-3742	133	30	)	)	PUNCT
ejpam-3742	134	1	−→	−→	NOUN
ejpam-3742	134	2	r	r	NOUN
ejpam-3742	134	3	x⊗	x⊗	VERB
ejpam-3742	134	4	y	y	PROPN
ejpam-3742	134	5	s	s	PROPN
ejpam-3742	134	6	7−→	7−→	PROPN
ejpam-3742	134	7	ψ(g)(x⊗	ψ(g)(x⊗	PROPN
ejpam-3742	134	8	y	y	PROPN
ejpam-3742	134	9	s	s	PART
ejpam-3742	134	10	)	)	PUNCT
ejpam-3742	134	11	=	=	SYM
ejpam-3742	134	12	g(x	g(x	NOUN
ejpam-3742	134	13	)	)	PUNCT
ejpam-3742	134	14	(	(	PUNCT
ejpam-3742	134	15	y	y	PROPN
ejpam-3742	134	16	s	s	PROPN
ejpam-3742	134	17	)	)	PUNCT
ejpam-3742	134	18	.	.	PUNCT
ejpam-3742	135	1	let	let	VERB
ejpam-3742	135	2	g	g	PROPN
ejpam-3742	135	3	∈	∈	PROPN
ejpam-3742	135	4	homalg	homalg	PROPN
ejpam-3742	135	5	-	-	PUNCT
ejpam-3742	135	6	a(a	a(a	PROPN
ejpam-3742	135	7	,	,	PUNCT
ejpam-3742	135	8	homa(r	homa(r	PROPN
ejpam-3742	135	9	,	,	PUNCT
ejpam-3742	135	10	s−1(a))o	s−1(a))o	NUM
ejpam-3742	135	11	)	)	PUNCT
ejpam-3742	135	12	,	,	PUNCT
ejpam-3742	135	13	x	x	PUNCT
ejpam-3742	135	14	∈	∈	PROPN
ejpam-3742	135	15	a	a	PRON
ejpam-3742	135	16	,	,	PUNCT
ejpam-3742	135	17	y	y	PROPN
ejpam-3742	135	18	s	s	PROPN
ejpam-3742	135	19	∈	∈	PROPN
ejpam-3742	135	20	s−1(a	s−1(a	PROPN
ejpam-3742	135	21	)	)	PUNCT
ejpam-3742	135	22	,	,	PUNCT
ejpam-3742	135	23	we	we	PRON
ejpam-3742	135	24	have	have	VERB
ejpam-3742	135	25	ϕa	ϕa	NOUN
ejpam-3742	135	26	,	,	PUNCT
ejpam-3742	135	27	r	r	NOUN
ejpam-3742	135	28	◦	◦	NOUN
ejpam-3742	135	29	ψ(g)(x⊗	ψ(g)(x⊗	PROPN
ejpam-3742	135	30	y	y	PROPN
ejpam-3742	135	31	s	s	PART
ejpam-3742	135	32	)	)	PUNCT
ejpam-3742	136	1	=	=	SYM
ejpam-3742	136	2	ϕa	ϕa	NOUN
ejpam-3742	136	3	,	,	PUNCT
ejpam-3742	136	4	r(ψ(g)(x⊗	r(ψ(g)(x⊗	NOUN
ejpam-3742	136	5	y	y	NOUN
ejpam-3742	136	6	s	s	PART
ejpam-3742	136	7	)	)	PUNCT
ejpam-3742	136	8	)	)	PUNCT
ejpam-3742	137	1	=	=	SYM
ejpam-3742	137	2	ϕa	ϕa	PROPN
ejpam-3742	137	3	,	,	PUNCT
ejpam-3742	137	4	r(g(x	r(g(x	PROPN
ejpam-3742	137	5	)	)	PUNCT
ejpam-3742	137	6	(	(	PUNCT
ejpam-3742	137	7	y	y	PROPN
ejpam-3742	137	8	s	s	PROPN
ejpam-3742	137	9	)	)	PUNCT
ejpam-3742	137	10	)	)	PUNCT
ejpam-3742	138	1	=	=	SYM
ejpam-3742	138	2	g(x⊗	g(x⊗	PROPN
ejpam-3742	138	3	y	y	PROPN
ejpam-3742	138	4	s	s	PROPN
ejpam-3742	138	5	)	)	PUNCT
ejpam-3742	138	6	.	.	PUNCT
ejpam-3742	139	1	hence	hence	ADV
ejpam-3742	139	2	ϕa	ϕa	INTJ
ejpam-3742	139	3	,	,	PUNCT
ejpam-3742	139	4	r	r	NOUN
ejpam-3742	139	5	◦	◦	NOUN
ejpam-3742	139	6	ψ(g	ψ(g	NOUN
ejpam-3742	139	7	)	)	PUNCT
ejpam-3742	139	8	=	=	SYM
ejpam-3742	139	9	g	g	NOUN
ejpam-3742	139	10	,	,	PUNCT
ejpam-3742	139	11	∀	∀	X
ejpam-3742	139	12	g	g	PROPN
ejpam-3742	139	13	∈	∈	PROPN
ejpam-3742	139	14	homalg	homalg	PROPN
ejpam-3742	139	15	-	-	PUNCT
ejpam-3742	139	16	a(a	a(a	PROPN
ejpam-3742	139	17	,	,	PUNCT
ejpam-3742	139	18	homa(r	homa(r	PROPN
ejpam-3742	139	19	,	,	PUNCT
ejpam-3742	139	20	s−1(a))o	s−1(a))o	NUM
ejpam-3742	139	21	)	)	PUNCT
ejpam-3742	139	22	.	.	PUNCT
ejpam-3742	140	1	so	so	ADV
ejpam-3742	140	2	ϕa	ϕa	PROPN
ejpam-3742	140	3	,	,	PUNCT
ejpam-3742	140	4	r	r	NOUN
ejpam-3742	140	5	◦	◦	NOUN
ejpam-3742	140	6	ψ	ψ	X
ejpam-3742	140	7	=	=	PROPN
ejpam-3742	140	8	1homalg	1homalg	PROPN
ejpam-3742	140	9	-	-	PUNCT
ejpam-3742	140	10	a(a	a(a	PROPN
ejpam-3742	140	11	,	,	PUNCT
ejpam-3742	140	12	homa(r	homa(r	PROPN
ejpam-3742	140	13	,	,	PUNCT
ejpam-3742	140	14	s−1(a))o	s−1(a))o	NUM
ejpam-3742	140	15	)	)	PUNCT
ejpam-3742	140	16	.	.	PUNCT
ejpam-3742	141	1	similarly	similarly	ADV
ejpam-3742	141	2	,	,	PUNCT
ejpam-3742	141	3	we	we	PRON
ejpam-3742	141	4	show	show	VERB
ejpam-3742	141	5	that	that	SCONJ
ejpam-3742	141	6	ψ	ψ	X
ejpam-3742	141	7	◦	◦	NOUN
ejpam-3742	141	8	ϕa	ϕa	ADP
ejpam-3742	141	9	,	,	PUNCT
ejpam-3742	141	10	r	r	NOUN
ejpam-3742	141	11	=	=	SYM
ejpam-3742	141	12	1homalg	1homalg	PROPN
ejpam-3742	141	13	-	-	PUNCT
ejpam-3742	141	14	a(a⊗s−1(a),r	a(a⊗s−1(a),r	PROPN
ejpam-3742	141	15	)	)	PUNCT
ejpam-3742	141	16	.	.	PUNCT
ejpam-3742	142	1	so	so	ADV
ejpam-3742	142	2	ϕa	ϕa	PROPN
ejpam-3742	142	3	,	,	PUNCT
ejpam-3742	142	4	r	r	NOUN
ejpam-3742	142	5	is	be	AUX
ejpam-3742	142	6	an	an	DET
ejpam-3742	142	7	isomorphism	isomorphism	NOUN
ejpam-3742	142	8	of	of	ADP
ejpam-3742	142	9	left	left	ADJ
ejpam-3742	142	10	a	a	DET
ejpam-3742	142	11	-	-	PUNCT
ejpam-3742	142	12	algebras	algebras	NOUN
ejpam-3742	142	13	.	.	PUNCT
ejpam-3742	143	1	∗	∗	NOUN
ejpam-3742	143	2	it	it	PRON
ejpam-3742	143	3	remains	remain	VERB
ejpam-3742	143	4	to	to	PART
ejpam-3742	143	5	show	show	VERB
ejpam-3742	143	6	that	that	SCONJ
ejpam-3742	143	7	ϕa	ϕa	NOUN
ejpam-3742	143	8	,	,	PUNCT
ejpam-3742	143	9	r	r	NOUN
ejpam-3742	143	10	is	be	AUX
ejpam-3742	143	11	natural	natural	ADJ
ejpam-3742	143	12	in	in	ADP
ejpam-3742	143	13	a	a	PRON
ejpam-3742	143	14	and	and	CCONJ
ejpam-3742	143	15	in	in	ADP
ejpam-3742	143	16	r.	r.	PROPN
ejpam-3742	143	17	let	let	VERB
ejpam-3742	143	18	f	f	PROPN
ejpam-3742	143	19	:	:	PUNCT
ejpam-3742	143	20	a	a	DET
ejpam-3742	143	21	−→	−→	NOUN
ejpam-3742	143	22	a	a	DET
ejpam-3742	143	23	′	′	NOUN
ejpam-3742	143	24	and	and	CCONJ
ejpam-3742	143	25	g	g	NOUN
ejpam-3742	143	26	:	:	PUNCT
ejpam-3742	143	27	r	r	NOUN
ejpam-3742	143	28	−→	−→	NOUN
ejpam-3742	143	29	r′	r′	NOUN
ejpam-3742	143	30	be	be	AUX
ejpam-3742	143	31	two	two	NUM
ejpam-3742	143	32	morphisms	morphism	NOUN
ejpam-3742	143	33	of	of	ADP
ejpam-3742	143	34	left	leave	VERB
ejpam-3742	143	35	a	a	DET
ejpam-3742	143	36	-	-	PUNCT
ejpam-3742	143	37	algebras	algebras	X
ejpam-3742	143	38	.	.	PUNCT
ejpam-3742	144	1	pose	pose	VERB
ejpam-3742	144	2	f	f	PROPN
ejpam-3742	144	3	=	=	PUNCT
ejpam-3742	144	4	-⊗a	-⊗a	PROPN
ejpam-3742	144	5	s−1(a	s−1(a	PROPN
ejpam-3742	144	6	)	)	PUNCT
ejpam-3742	144	7	and	and	CCONJ
ejpam-3742	144	8	g	g	PROPN
ejpam-3742	144	9	=	=	SYM
ejpam-3742	144	10	homa(-	homa(-	PROPN
ejpam-3742	144	11	,	,	PUNCT
ejpam-3742	144	12	s−1(a))o	s−1(a))o	NUM
ejpam-3742	144	13	.	.	PUNCT
ejpam-3742	145	1	we	we	PRON
ejpam-3742	145	2	have	have	VERB
ejpam-3742	145	3	f∗	f∗	NOUN
ejpam-3742	145	4	◦	◦	NOUN
ejpam-3742	145	5	ϕa	ϕa	ADP
ejpam-3742	145	6	′,r(h)(x	′,r(h)(x	NOUN
ejpam-3742	145	7	)	)	PUNCT
ejpam-3742	145	8	(	(	PUNCT
ejpam-3742	145	9	y	y	NOUN
ejpam-3742	145	10	s	s	PROPN
ejpam-3742	145	11	)	)	PUNCT
ejpam-3742	145	12	=	=	SYM
ejpam-3742	145	13	ϕa	ϕa	PROPN
ejpam-3742	145	14	′,r(h	′,r(h	NOUN
ejpam-3742	145	15	)	)	PUNCT
ejpam-3742	145	16	◦	◦	VERB
ejpam-3742	145	17	f(x	f(x	PROPN
ejpam-3742	145	18	)	)	PUNCT
ejpam-3742	146	1	(	(	PUNCT
ejpam-3742	146	2	y	y	NOUN
ejpam-3742	146	3	s	s	PROPN
ejpam-3742	146	4	)	)	PUNCT
ejpam-3742	146	5	=	=	SYM
ejpam-3742	146	6	ϕa	ϕa	PROPN
ejpam-3742	146	7	′,r(h)(f(x	′,r(h)(f(x	PROPN
ejpam-3742	146	8	)	)	PUNCT
ejpam-3742	146	9	)	)	PUNCT
ejpam-3742	147	1	(	(	PUNCT
ejpam-3742	147	2	y	y	NOUN
ejpam-3742	147	3	s	s	PROPN
ejpam-3742	147	4	)	)	PUNCT
ejpam-3742	148	1	=	=	SYM
ejpam-3742	148	2	h(f(x)⊗	h(f(x)⊗	PROPN
ejpam-3742	148	3	y	y	PROPN
ejpam-3742	148	4	s	s	PROPN
ejpam-3742	148	5	)	)	PUNCT
ejpam-3742	148	6	.	.	PUNCT
ejpam-3742	149	1	on	on	ADP
ejpam-3742	149	2	the	the	DET
ejpam-3742	149	3	other	other	ADJ
ejpam-3742	149	4	hand	hand	NOUN
ejpam-3742	149	5	we	we	PRON
ejpam-3742	149	6	have	have	VERB
ejpam-3742	149	7	:	:	PUNCT
ejpam-3742	149	8	ϕa	ϕa	INTJ
ejpam-3742	149	9	,	,	PUNCT
ejpam-3742	149	10	r	r	NOUN
ejpam-3742	149	11	◦	◦	NOUN
ejpam-3742	149	12	(	(	PUNCT
ejpam-3742	149	13	ff)∗(h)(x	ff)∗(h)(x	PROPN
ejpam-3742	149	14	)	)	PUNCT
ejpam-3742	149	15	(	(	PUNCT
ejpam-3742	149	16	y	y	PROPN
ejpam-3742	149	17	s	s	PROPN
ejpam-3742	149	18	)	)	PUNCT
ejpam-3742	149	19	=	=	SYM
ejpam-3742	149	20	(	(	PUNCT
ejpam-3742	149	21	ff)∗(h)(x⊗	ff)∗(h)(x⊗	X
ejpam-3742	149	22	y	y	PROPN
ejpam-3742	149	23	s	s	PROPN
ejpam-3742	149	24	)	)	PUNCT
ejpam-3742	149	25	=	=	PUNCT
ejpam-3742	150	1	h(ff)(x⊗	h(ff)(x⊗	PROPN
ejpam-3742	150	2	y	y	PROPN
ejpam-3742	150	3	s	s	PART
ejpam-3742	150	4	)	)	PUNCT
ejpam-3742	150	5	=	=	SYM
ejpam-3742	150	6	h(f	h(f	PROPN
ejpam-3742	150	7	⊗	⊗	NOUN
ejpam-3742	150	8	1s−1(a))(x⊗	1s−1(a))(x⊗	NUM
ejpam-3742	150	9	y	y	NOUN
ejpam-3742	150	10	s	s	PART
ejpam-3742	150	11	)	)	PUNCT
ejpam-3742	151	1	=	=	SYM
ejpam-3742	151	2	h(f(x)⊗	h(f(x)⊗	PROPN
ejpam-3742	151	3	y	y	PROPN
ejpam-3742	151	4	s	s	PROPN
ejpam-3742	151	5	)	)	PUNCT
ejpam-3742	151	6	.	.	PUNCT
ejpam-3742	152	1	so	so	ADV
ejpam-3742	152	2	f∗	f∗	PROPN
ejpam-3742	152	3	◦	◦	NOUN
ejpam-3742	152	4	ϕa	ϕa	ADP
ejpam-3742	152	5	′,r(h)(x	′,r(h)(x	NOUN
ejpam-3742	152	6	)	)	PUNCT
ejpam-3742	152	7	(	(	PUNCT
ejpam-3742	152	8	y	y	NOUN
ejpam-3742	152	9	s	s	PROPN
ejpam-3742	152	10	)	)	PUNCT
ejpam-3742	153	1	=	=	SYM
ejpam-3742	153	2	ϕa	ϕa	NOUN
ejpam-3742	153	3	,	,	PUNCT
ejpam-3742	153	4	r	r	NOUN
ejpam-3742	153	5	◦	◦	NOUN
ejpam-3742	153	6	(	(	PUNCT
ejpam-3742	153	7	ff)∗(h)(x	ff)∗(h)(x	PROPN
ejpam-3742	153	8	)	)	PUNCT
ejpam-3742	153	9	(	(	PUNCT
ejpam-3742	153	10	y	y	PROPN
ejpam-3742	153	11	s	s	PROPN
ejpam-3742	153	12	)	)	PUNCT
ejpam-3742	153	13	,	,	PUNCT
ejpam-3742	153	14	∀	∀	NUM
ejpam-3742	153	15	h	h	NOUN
ejpam-3742	153	16	∈	∈	NOUN
ejpam-3742	153	17	homa(a	homa(a	NOUN
ejpam-3742	153	18	⊗	⊗	NOUN
ejpam-3742	153	19	s−1(a),r	s−1(a),r	PROPN
ejpam-3742	153	20	)	)	PUNCT
ejpam-3742	153	21	,	,	PUNCT
ejpam-3742	153	22	x	x	PUNCT
ejpam-3742	153	23	∈	∈	PROPN
ejpam-3742	153	24	a	a	PRON
ejpam-3742	153	25	and	and	CCONJ
ejpam-3742	153	26	y	y	PROPN
ejpam-3742	153	27	s	s	PROPN
ejpam-3742	153	28	∈	∈	PROPN
ejpam-3742	153	29	s−1(a	s−1(a	PROPN
ejpam-3742	153	30	)	)	PUNCT
ejpam-3742	153	31	.	.	PUNCT
ejpam-3742	154	1	so	so	ADV
ejpam-3742	154	2	f∗	f∗	PROPN
ejpam-3742	154	3	◦	◦	NOUN
ejpam-3742	154	4	ϕa	ϕa	ADP
ejpam-3742	154	5	′,r	′,r	NOUN
ejpam-3742	154	6	=	=	PUNCT
ejpam-3742	154	7	ϕa	ϕa	NOUN
ejpam-3742	154	8	,	,	PUNCT
ejpam-3742	154	9	r	r	NOUN
ejpam-3742	154	10	◦	◦	NOUN
ejpam-3742	154	11	(	(	PUNCT
ejpam-3742	154	12	ff)∗	ff)∗	PROPN
ejpam-3742	154	13	⇒	⇒	NOUN
ejpam-3742	154	14	ϕa	ϕa	NUM
ejpam-3742	154	15	,	,	PUNCT
ejpam-3742	154	16	r	r	NOUN
ejpam-3742	154	17	is	be	AUX
ejpam-3742	154	18	natural	natural	ADJ
ejpam-3742	154	19	in	in	ADP
ejpam-3742	154	20	a	a	PRON
ejpam-3742	154	21	.	.	PUNCT
ejpam-3742	155	1	we	we	PRON
ejpam-3742	155	2	show	show	VERB
ejpam-3742	155	3	in	in	ADP
ejpam-3742	155	4	the	the	DET
ejpam-3742	155	5	same	same	ADJ
ejpam-3742	155	6	way	way	NOUN
ejpam-3742	155	7	that	that	PRON
ejpam-3742	155	8	ϕa	ϕa	INTJ
ejpam-3742	155	9	,	,	PUNCT
ejpam-3742	155	10	r	r	NOUN
ejpam-3742	155	11	is	be	AUX
ejpam-3742	155	12	natural	natural	ADJ
ejpam-3742	155	13	in	in	ADP
ejpam-3742	155	14	r.	r.	PROPN
ejpam-3742	155	15	therefore	therefore	ADV
ejpam-3742	155	16	the	the	DET
ejpam-3742	155	17	functors	functors	PROPN
ejpam-3742	155	18	-⊗a	-⊗a	PUNCT
ejpam-3742	155	19	s−1(a	s−1(a	PROPN
ejpam-3742	155	20	)	)	PUNCT
ejpam-3742	155	21	and	and	CCONJ
ejpam-3742	155	22	homa(-	homa(-	PROPN
ejpam-3742	155	23	,	,	PUNCT
ejpam-3742	155	24	s−1(a))o	s−1(a))o	PROPN
ejpam-3742	155	25	are	be	AUX
ejpam-3742	155	26	adjoint	adjoint	NOUN
ejpam-3742	155	27	.	.	PUNCT
ejpam-3742	156	1	m	m	PROPN
ejpam-3742	156	2	thiaw	thiaw	NOUN
ejpam-3742	156	3	,	,	PUNCT
ejpam-3742	156	4	m	m	AUX
ejpam-3742	156	5	maaouia	maaouia	NOUN
ejpam-3742	156	6	/	/	SYM
ejpam-3742	156	7	eur	eur	NOUN
ejpam-3742	156	8	.	.	PUNCT
ejpam-3742	157	1	j.	j.	PROPN
ejpam-3742	157	2	pure	pure	PROPN
ejpam-3742	157	3	appl	appl	PROPN
ejpam-3742	157	4	.	.	PROPN
ejpam-3742	157	5	math	math	PROPN
ejpam-3742	157	6	,	,	PUNCT
ejpam-3742	157	7	13	13	NUM
ejpam-3742	157	8	(	(	PUNCT
ejpam-3742	157	9	3	3	NUM
ejpam-3742	157	10	)	)	PUNCT
ejpam-3742	157	11	(	(	PUNCT
ejpam-3742	157	12	2020	2020	NUM
ejpam-3742	157	13	)	)	PUNCT
ejpam-3742	157	14	,	,	PUNCT
ejpam-3742	157	15	472	472	NUM
ejpam-3742	157	16	-	-	SYM
ejpam-3742	157	17	482	482	NUM
ejpam-3742	157	18	478	478	NUM
ejpam-3742	157	19	corollary	corollary	ADJ
ejpam-3742	157	20	1	1	NUM
ejpam-3742	157	21	.	.	PUNCT
ejpam-3742	158	1	let	let	VERB
ejpam-3742	158	2	a	a	PRON
ejpam-3742	158	3	be	be	AUX
ejpam-3742	158	4	a	a	DET
ejpam-3742	158	5	ring	ring	NOUN
ejpam-3742	158	6	and	and	CCONJ
ejpam-3742	158	7	s	s	VERB
ejpam-3742	158	8	a	a	DET
ejpam-3742	158	9	central	central	ADJ
ejpam-3742	158	10	multiplicatively	multiplicatively	ADV
ejpam-3742	158	11	closed	close	VERB
ejpam-3742	158	12	subset	subset	NOUN
ejpam-3742	158	13	of	of	ADP
ejpam-3742	158	14	a.	a.	NOUN
ejpam-3742	158	15	then	then	ADV
ejpam-3742	158	16	s−1	s−1	PROPN
ejpam-3742	158	17	(	(	PUNCT
ejpam-3742	158	18	)	)	PUNCT
ejpam-3742	158	19	:	:	PUNCT
ejpam-3742	158	20	alg	alg	PROPN
ejpam-3742	158	21	-	-	PUNCT
ejpam-3742	158	22	a	a	DET
ejpam-3742	158	23	�	�	PROPN
ejpam-3742	158	24	a	a	DET
ejpam-3742	158	25	-	-	PUNCT
ejpam-3742	158	26	modo	modo	NOUN
ejpam-3742	158	27	:	:	PUNCT
ejpam-3742	158	28	homa(-	homa(-	NOUN
ejpam-3742	158	29	,	,	PUNCT
ejpam-3742	158	30	s−1(a))o	s−1(a))o	PROPN
ejpam-3742	158	31	is	be	AUX
ejpam-3742	158	32	an	an	DET
ejpam-3742	158	33	adjunction	adjunction	NOUN
ejpam-3742	158	34	.	.	PUNCT
ejpam-3742	159	1	proof	proof	NOUN
ejpam-3742	159	2	.	.	PUNCT
ejpam-3742	160	1	by	by	ADP
ejpam-3742	160	2	the	the	DET
ejpam-3742	160	3	theorem	theorem	NOUN
ejpam-3742	160	4	4	4	NUM
ejpam-3742	160	5	,	,	PUNCT
ejpam-3742	160	6	we	we	PRON
ejpam-3742	160	7	have	have	AUX
ejpam-3742	160	8	-⊗a	-⊗a	PROPN
ejpam-3742	160	9	s−1(a	s−1(a	PROPN
ejpam-3742	160	10	)	)	PUNCT
ejpam-3742	160	11	is	be	AUX
ejpam-3742	160	12	a	a	DET
ejpam-3742	160	13	left	left	ADJ
ejpam-3742	160	14	adjoint	adjoint	NOUN
ejpam-3742	160	15	to	to	ADP
ejpam-3742	160	16	homa(-	homa(-	PROPN
ejpam-3742	160	17	,	,	PUNCT
ejpam-3742	160	18	s−1(a))o	s−1(a))o	NOUN
ejpam-3742	160	19	and	and	CCONJ
ejpam-3742	160	20	by	by	ADP
ejpam-3742	160	21	the	the	DET
ejpam-3742	160	22	theorem	theorem	ADJ
ejpam-3742	160	23	4	4	NUM
ejpam-3742	160	24	s−1	s−1	PROPN
ejpam-3742	160	25	(	(	PUNCT
ejpam-3742	160	26	)	)	PUNCT
ejpam-3742	160	27	is	be	AUX
ejpam-3742	160	28	isomorphic	isomorphic	ADJ
ejpam-3742	160	29	to	to	ADP
ejpam-3742	160	30	homa(-	homa(-	PROPN
ejpam-3742	160	31	,	,	PUNCT
ejpam-3742	160	32	s−1(a))o	s−1(a))o	NOUN
ejpam-3742	160	33	,	,	PUNCT
ejpam-3742	160	34	so	so	SCONJ
ejpam-3742	160	35	the	the	DET
ejpam-3742	160	36	fonctor	fonctor	NOUN
ejpam-3742	160	37	s−1	s−1	PROPN
ejpam-3742	160	38	(	(	PUNCT
ejpam-3742	160	39	)	)	PUNCT
ejpam-3742	160	40	is	be	AUX
ejpam-3742	160	41	a	a	DET
ejpam-3742	160	42	left	left	ADJ
ejpam-3742	160	43	adjoint	adjoint	NOUN
ejpam-3742	160	44	to	to	ADP
ejpam-3742	160	45	homa(-	homa(-	PROPN
ejpam-3742	160	46	,	,	PUNCT
ejpam-3742	160	47	s−1(a))o	s−1(a))o	NUM
ejpam-3742	160	48	.	.	PUNCT
ejpam-3742	161	1	corollary	corollary	ADJ
ejpam-3742	161	2	2	2	NUM
ejpam-3742	161	3	.	.	PUNCT
ejpam-3742	162	1	let	let	VERB
ejpam-3742	162	2	a	a	PRON
ejpam-3742	162	3	be	be	AUX
ejpam-3742	162	4	a	a	DET
ejpam-3742	162	5	duo	duo	NOUN
ejpam-3742	162	6	ring	ring	NOUN
ejpam-3742	162	7	,	,	PUNCT
ejpam-3742	162	8	p	p	X
ejpam-3742	162	9	a	a	DET
ejpam-3742	162	10	prime	prime	ADJ
ejpam-3742	162	11	ideal	ideal	NOUN
ejpam-3742	162	12	of	of	ADP
ejpam-3742	162	13	a	a	PRON
ejpam-3742	162	14	and	and	CCONJ
ejpam-3742	162	15	s	s	NOUN
ejpam-3742	162	16	=	=	PUNCT
ejpam-3742	162	17	(	(	PUNCT
ejpam-3742	162	18	a	a	NOUN
ejpam-3742	162	19	-	-	PUNCT
ejpam-3742	162	20	p	p	NOUN
ejpam-3742	162	21	)	)	PUNCT
ejpam-3742	162	22	∩	∩	ADJ
ejpam-3742	162	23	z(a	z(a	NOUN
ejpam-3742	162	24	)	)	PUNCT
ejpam-3742	162	25	.	.	PUNCT
ejpam-3742	163	1	then	then	ADV
ejpam-3742	163	2	s−1	s−1	PROPN
ejpam-3742	163	3	(	(	PUNCT
ejpam-3742	163	4	)	)	PUNCT
ejpam-3742	163	5	:	:	PUNCT
ejpam-3742	163	6	alg	alg	PROPN
ejpam-3742	163	7	-	-	PUNCT
ejpam-3742	163	8	a	a	DET
ejpam-3742	163	9	�	�	PROPN
ejpam-3742	163	10	a	a	DET
ejpam-3742	163	11	-	-	PUNCT
ejpam-3742	163	12	modo	modo	NOUN
ejpam-3742	163	13	:	:	PUNCT
ejpam-3742	163	14	homa(-	homa(-	NOUN
ejpam-3742	163	15	,	,	PUNCT
ejpam-3742	163	16	s−1(a))o	s−1(a))o	PROPN
ejpam-3742	163	17	is	be	AUX
ejpam-3742	163	18	an	an	DET
ejpam-3742	163	19	adjunction	adjunction	NOUN
ejpam-3742	163	20	.	.	PUNCT
ejpam-3742	164	1	proof	proof	NOUN
ejpam-3742	164	2	.	.	PUNCT
ejpam-3742	165	1	since	since	SCONJ
ejpam-3742	165	2	a	a	PRON
ejpam-3742	165	3	is	be	AUX
ejpam-3742	165	4	a	a	DET
ejpam-3742	165	5	duo	duo	NOUN
ejpam-3742	165	6	ring	ring	NOUN
ejpam-3742	165	7	,	,	PUNCT
ejpam-3742	165	8	then	then	ADV
ejpam-3742	165	9	a	a	X
ejpam-3742	165	10	-	-	PUNCT
ejpam-3742	165	11	p	p	NOUN
ejpam-3742	165	12	is	be	AUX
ejpam-3742	165	13	a	a	DET
ejpam-3742	165	14	multiplicatively	multiplicatively	ADV
ejpam-3742	165	15	closed	close	VERB
ejpam-3742	165	16	subset	subset	NOUN
ejpam-3742	165	17	of	of	ADP
ejpam-3742	165	18	a	a	PRON
ejpam-3742	165	19	,	,	PUNCT
ejpam-3742	165	20	so	so	NOUN
ejpam-3742	165	21	s	s	PART
ejpam-3742	165	22	=	=	PUNCT
ejpam-3742	165	23	(	(	PUNCT
ejpam-3742	165	24	a	a	NOUN
ejpam-3742	165	25	-	-	PUNCT
ejpam-3742	165	26	p	p	NOUN
ejpam-3742	165	27	)	)	PUNCT
ejpam-3742	165	28	∩	∩	ADJ
ejpam-3742	165	29	z(a	z(a	NOUN
ejpam-3742	165	30	)	)	PUNCT
ejpam-3742	165	31	is	be	AUX
ejpam-3742	165	32	a	a	DET
ejpam-3742	165	33	central	central	ADJ
ejpam-3742	165	34	multiplicatively	multiplicatively	ADV
ejpam-3742	165	35	closed	close	VERB
ejpam-3742	165	36	subset	subset	NOUN
ejpam-3742	165	37	of	of	ADP
ejpam-3742	165	38	a.	a.	NOUN
ejpam-3742	165	39	so	so	ADV
ejpam-3742	165	40	by	by	ADP
ejpam-3742	165	41	the	the	DET
ejpam-3742	165	42	corollary	corollary	ADJ
ejpam-3742	165	43	1	1	NUM
ejpam-3742	165	44	s−1	s−1	PROPN
ejpam-3742	165	45	(	(	PUNCT
ejpam-3742	165	46	)	)	PUNCT
ejpam-3742	165	47	is	be	AUX
ejpam-3742	165	48	a	a	DET
ejpam-3742	165	49	left	left	ADJ
ejpam-3742	165	50	adjoint	adjoint	NOUN
ejpam-3742	165	51	to	to	ADP
ejpam-3742	165	52	homa(-	homa(-	PROPN
ejpam-3742	165	53	,	,	PUNCT
ejpam-3742	165	54	s−1(a))o	s−1(a))o	NUM
ejpam-3742	165	55	.	.	PUNCT
ejpam-3742	166	1	corollary	corollary	ADJ
ejpam-3742	166	2	3	3	X
ejpam-3742	166	3	.	.	PUNCT
ejpam-3742	167	1	let	let	VERB
ejpam-3742	167	2	a	a	PRON
ejpam-3742	167	3	be	be	AUX
ejpam-3742	167	4	a	a	DET
ejpam-3742	167	5	duo	duo	NOUN
ejpam-3742	167	6	ring	ring	NOUN
ejpam-3742	167	7	,	,	PUNCT
ejpam-3742	167	8	p	p	X
ejpam-3742	167	9	a	a	DET
ejpam-3742	167	10	prime	prime	ADJ
ejpam-3742	167	11	ideal	ideal	NOUN
ejpam-3742	167	12	of	of	ADP
ejpam-3742	167	13	a	a	PRON
ejpam-3742	167	14	,	,	PUNCT
ejpam-3742	167	15	sr	sr	PROPN
ejpam-3742	167	16	the	the	DET
ejpam-3742	167	17	set	set	NOUN
ejpam-3742	167	18	of	of	ADP
ejpam-3742	167	19	regular	regular	ADJ
ejpam-3742	167	20	elements	element	NOUN
ejpam-3742	167	21	of	of	ADP
ejpam-3742	167	22	a	a	DET
ejpam-3742	167	23	-	-	PUNCT
ejpam-3742	167	24	p	p	NOUN
ejpam-3742	167	25	and	and	CCONJ
ejpam-3742	167	26	s	s	PART
ejpam-3742	167	27	=	=	PROPN
ejpam-3742	167	28	sr	sr	PROPN
ejpam-3742	167	29	∩	∩	NOUN
ejpam-3742	167	30	z(a	z(a	NOUN
ejpam-3742	167	31	)	)	PUNCT
ejpam-3742	167	32	.	.	PUNCT
ejpam-3742	168	1	then	then	ADV
ejpam-3742	168	2	s−1	s−1	PROPN
ejpam-3742	168	3	(	(	PUNCT
ejpam-3742	168	4	)	)	PUNCT
ejpam-3742	168	5	:	:	PUNCT
ejpam-3742	168	6	alg	alg	PROPN
ejpam-3742	168	7	-	-	PUNCT
ejpam-3742	168	8	a	a	DET
ejpam-3742	168	9	�	�	PROPN
ejpam-3742	168	10	a	a	DET
ejpam-3742	168	11	-	-	PUNCT
ejpam-3742	168	12	modo	modo	NOUN
ejpam-3742	168	13	:	:	PUNCT
ejpam-3742	168	14	homa(-	homa(-	NOUN
ejpam-3742	168	15	,	,	PUNCT
ejpam-3742	168	16	s−1(a))o	s−1(a))o	PROPN
ejpam-3742	168	17	is	be	AUX
ejpam-3742	168	18	an	an	DET
ejpam-3742	168	19	adjunction	adjunction	NOUN
ejpam-3742	168	20	.	.	PUNCT
ejpam-3742	169	1	proof	proof	NOUN
ejpam-3742	169	2	.	.	PUNCT
ejpam-3742	170	1	since	since	SCONJ
ejpam-3742	170	2	a	a	PRON
ejpam-3742	170	3	is	be	AUX
ejpam-3742	170	4	a	a	DET
ejpam-3742	170	5	duo	duo	NOUN
ejpam-3742	170	6	ring	ring	NOUN
ejpam-3742	170	7	,	,	PUNCT
ejpam-3742	170	8	then	then	ADV
ejpam-3742	170	9	the	the	DET
ejpam-3742	170	10	set	set	NOUN
ejpam-3742	170	11	of	of	ADP
ejpam-3742	170	12	regular	regular	ADJ
ejpam-3742	170	13	elements	element	NOUN
ejpam-3742	170	14	,	,	PUNCT
ejpam-3742	170	15	sr	sr	PROPN
ejpam-3742	170	16	,	,	PUNCT
ejpam-3742	170	17	of	of	ADP
ejpam-3742	170	18	a	a	DET
ejpam-3742	170	19	-	-	PUNCT
ejpam-3742	170	20	p	p	NOUN
ejpam-3742	170	21	is	be	AUX
ejpam-3742	170	22	a	a	DET
ejpam-3742	170	23	multiplicatively	multiplicatively	ADV
ejpam-3742	170	24	closed	close	VERB
ejpam-3742	170	25	subset	subset	NOUN
ejpam-3742	170	26	of	of	ADP
ejpam-3742	170	27	a	a	DET
ejpam-3742	170	28	,	,	PUNCT
ejpam-3742	170	29	so	so	PROPN
ejpam-3742	170	30	s	s	PART
ejpam-3742	170	31	=	=	PROPN
ejpam-3742	170	32	sr	sr	PROPN
ejpam-3742	170	33	∩z(a	∩z(a	PROPN
ejpam-3742	170	34	)	)	PUNCT
ejpam-3742	170	35	is	be	AUX
ejpam-3742	170	36	a	a	DET
ejpam-3742	170	37	central	central	ADJ
ejpam-3742	170	38	multiplicatively	multiplicatively	ADV
ejpam-3742	170	39	closed	close	VERB
ejpam-3742	170	40	subset	subset	NOUN
ejpam-3742	170	41	of	of	ADP
ejpam-3742	170	42	a.	a.	NOUN
ejpam-3742	170	43	so	so	ADV
ejpam-3742	170	44	by	by	ADP
ejpam-3742	170	45	the	the	DET
ejpam-3742	170	46	corollary	corollary	ADJ
ejpam-3742	170	47	1	1	NUM
ejpam-3742	170	48	s−1	s−1	PROPN
ejpam-3742	170	49	(	(	PUNCT
ejpam-3742	170	50	)	)	PUNCT
ejpam-3742	170	51	is	be	AUX
ejpam-3742	170	52	a	a	DET
ejpam-3742	170	53	left	left	ADJ
ejpam-3742	170	54	adjoint	adjoint	NOUN
ejpam-3742	170	55	to	to	ADP
ejpam-3742	170	56	homa(-	homa(-	PROPN
ejpam-3742	170	57	,	,	PUNCT
ejpam-3742	170	58	s−1(a))o	s−1(a))o	NUM
ejpam-3742	170	59	.	.	PUNCT
ejpam-3742	171	1	proposition	proposition	NOUN
ejpam-3742	171	2	4	4	NUM
ejpam-3742	171	3	.	.	PUNCT
ejpam-3742	171	4	let	let	VERB
ejpam-3742	171	5	a	a	PRON
ejpam-3742	171	6	be	be	AUX
ejpam-3742	171	7	a	a	DET
ejpam-3742	171	8	ring	ring	NOUN
ejpam-3742	171	9	,	,	PUNCT
ejpam-3742	171	10	b	b	PROPN
ejpam-3742	171	11	a	a	DET
ejpam-3742	171	12	(	(	PUNCT
ejpam-3742	171	13	a	a	NOUN
ejpam-3742	171	14	-	-	PUNCT
ejpam-3742	171	15	a)-bialgebra	a)-bialgebra	NOUN
ejpam-3742	171	16	and	and	CCONJ
ejpam-3742	171	17	s	s	VERB
ejpam-3742	171	18	a	a	DET
ejpam-3742	171	19	central	central	ADJ
ejpam-3742	171	20	multiplicatively	multiplicatively	ADV
ejpam-3742	171	21	closed	close	VERB
ejpam-3742	171	22	subset	subset	NOUN
ejpam-3742	171	23	of	of	ADP
ejpam-3742	171	24	a.	a.	NOUN
ejpam-3742	171	25	then	then	ADV
ejpam-3742	171	26	-⊗a	-⊗a	PROPN
ejpam-3742	171	27	s−1(b	s−1(b	PROPN
ejpam-3742	171	28	)	)	PUNCT
ejpam-3742	171	29	:	:	PUNCT
ejpam-3742	171	30	alg	alg	PROPN
ejpam-3742	171	31	-	-	PUNCT
ejpam-3742	171	32	s−1a	s−1a	PROPN
ejpam-3742	171	33	�	�	PROPN
ejpam-3742	171	34	s−1a	s−1a	NOUN
ejpam-3742	171	35	-	-	PUNCT
ejpam-3742	171	36	modo	modo	NOUN
ejpam-3742	171	37	:	:	PUNCT
ejpam-3742	171	38	homa(-	homa(-	NOUN
ejpam-3742	171	39	,	,	PUNCT
ejpam-3742	171	40	s−1(b))o	s−1(b))o	PROPN
ejpam-3742	171	41	is	be	AUX
ejpam-3742	171	42	an	an	DET
ejpam-3742	171	43	adjunction	adjunction	NOUN
ejpam-3742	171	44	.	.	PUNCT
ejpam-3742	172	1	proof	proof	NOUN
ejpam-3742	172	2	.	.	PUNCT
ejpam-3742	173	1	the	the	DET
ejpam-3742	173	2	proof	proof	NOUN
ejpam-3742	173	3	is	be	AUX
ejpam-3742	173	4	similar	similar	ADJ
ejpam-3742	173	5	to	to	ADP
ejpam-3742	173	6	that	that	PRON
ejpam-3742	173	7	of	of	ADP
ejpam-3742	173	8	the	the	DET
ejpam-3742	173	9	previous	previous	ADJ
ejpam-3742	173	10	theorem	theorem	NOUN
ejpam-3742	173	11	.	.	PROPN
ejpam-3742	174	1	m	m	PROPN
ejpam-3742	174	2	thiaw	thiaw	NOUN
ejpam-3742	174	3	,	,	PUNCT
ejpam-3742	174	4	m	m	AUX
ejpam-3742	174	5	maaouia	maaouia	NOUN
ejpam-3742	174	6	/	/	SYM
ejpam-3742	174	7	eur	eur	NOUN
ejpam-3742	174	8	.	.	PUNCT
ejpam-3742	175	1	j.	j.	PROPN
ejpam-3742	175	2	pure	pure	PROPN
ejpam-3742	175	3	appl	appl	PROPN
ejpam-3742	175	4	.	.	PROPN
ejpam-3742	175	5	math	math	PROPN
ejpam-3742	175	6	,	,	PUNCT
ejpam-3742	175	7	13	13	NUM
ejpam-3742	175	8	(	(	PUNCT
ejpam-3742	175	9	3	3	NUM
ejpam-3742	175	10	)	)	PUNCT
ejpam-3742	175	11	(	(	PUNCT
ejpam-3742	175	12	2020	2020	NUM
ejpam-3742	175	13	)	)	PUNCT
ejpam-3742	175	14	,	,	PUNCT
ejpam-3742	175	15	472	472	NUM
ejpam-3742	175	16	-	-	SYM
ejpam-3742	175	17	482	482	NUM
ejpam-3742	175	18	479	479	NUM
ejpam-3742	175	19	4	4	NUM
ejpam-3742	175	20	.	.	PUNCT
ejpam-3742	176	1	the	the	DET
ejpam-3742	176	2	adjunction	adjunction	NOUN
ejpam-3742	176	3	of	of	ADP
ejpam-3742	176	4	the	the	DET
ejpam-3742	176	5	functors	functor	NOUN
ejpam-3742	176	6	êxt	êxt	NOUN
ejpam-3742	176	7	n	n	DET
ejpam-3742	176	8	s−1a(-	s−1a(-	NOUN
ejpam-3742	176	9	,	,	PUNCT
ejpam-3742	176	10	s	s	X
ejpam-3742	176	11	−1b	−1b	PROPN
ejpam-3742	176	12	)	)	PUNCT
ejpam-3742	176	13	and	and	CCONJ
ejpam-3742	176	14	tors	tor	NOUN
ejpam-3742	176	15	−1a	−1a	PUNCT
ejpam-3742	176	16	n	n	PROPN
ejpam-3742	176	17	(	(	PUNCT
ejpam-3742	176	18	-	-	INTJ
ejpam-3742	176	19	,	,	PUNCT
ejpam-3742	176	20	s−1b	s−1b	NOUN
ejpam-3742	176	21	)	)	PUNCT
ejpam-3742	176	22	in	in	ADP
ejpam-3742	176	23	the	the	DET
ejpam-3742	176	24	category	category	NOUN
ejpam-3742	176	25	a	a	DET
ejpam-3742	176	26	-	-	PUNCT
ejpam-3742	176	27	alg	alg	NOUN
ejpam-3742	176	28	proposition	proposition	NOUN
ejpam-3742	176	29	5	5	NUM
ejpam-3742	176	30	.	.	PUNCT
ejpam-3742	177	1	let	let	VERB
ejpam-3742	177	2	b	b	X
ejpam-3742	177	3	be	be	AUX
ejpam-3742	177	4	a	a	DET
ejpam-3742	177	5	(	(	PUNCT
ejpam-3742	177	6	b	b	X
ejpam-3742	177	7	-	-	PUNCT
ejpam-3742	177	8	a)-bialgebra.then	a)-bialgebra.then	VERB
ejpam-3742	177	9	the	the	DET
ejpam-3742	177	10	correspondence	correspondence	NOUN
ejpam-3742	177	11	êxt	êxt	NOUN
ejpam-3742	177	12	n	n	PROPN
ejpam-3742	177	13	b(-,b	b(-,b	PROPN
ejpam-3742	177	14	)	)	PUNCT
ejpam-3742	177	15	:	:	PUNCT
ejpam-3742	178	1	b	b	X
ejpam-3742	178	2	-	-	PUNCT
ejpam-3742	178	3	mod	mod	ADJ
ejpam-3742	178	4	−→	−→	PROPN
ejpam-3742	178	5	alg	alg	PROPN
ejpam-3742	178	6	-	-	PUNCT
ejpam-3742	178	7	a	a	PROPN
ejpam-3742	178	8	(	(	PUNCT
ejpam-3742	178	9	i	i	NOUN
ejpam-3742	178	10	)	)	PUNCT
ejpam-3742	178	11	which	which	PRON
ejpam-3742	178	12	has	have	VERB
ejpam-3742	178	13	any	any	DET
ejpam-3742	178	14	left	left	ADJ
ejpam-3742	178	15	b	b	NOUN
ejpam-3742	178	16	-	-	PUNCT
ejpam-3742	178	17	module	module	NOUN
ejpam-3742	178	18	m	m	NOUN
ejpam-3742	178	19	,	,	PUNCT
ejpam-3742	178	20	we	we	PRON
ejpam-3742	178	21	associate	associate	VERB
ejpam-3742	178	22	the	the	DET
ejpam-3742	178	23	right	right	ADJ
ejpam-3742	178	24	a	a	DET
ejpam-3742	178	25	-	-	PUNCT
ejpam-3742	178	26	algebra	algebra	NOUN
ejpam-3742	178	27	êxt	êxt	NOUN
ejpam-3742	178	28	n	n	PRON
ejpam-3742	178	29	b(m	b(m	PROPN
ejpam-3742	178	30	,	,	PUNCT
ejpam-3742	178	31	b	b	NOUN
ejpam-3742	178	32	)	)	PUNCT
ejpam-3742	178	33	,	,	PUNCT
ejpam-3742	178	34	(	(	PUNCT
ejpam-3742	178	35	ii	ii	NOUN
ejpam-3742	178	36	)	)	PUNCT
ejpam-3742	178	37	which	which	PRON
ejpam-3742	178	38	has	have	VERB
ejpam-3742	178	39	any	any	DET
ejpam-3742	178	40	morphism	morphism	NOUN
ejpam-3742	178	41	of	of	ADP
ejpam-3742	178	42	left	left	ADJ
ejpam-3742	178	43	b	b	NOUN
ejpam-3742	178	44	-	-	PUNCT
ejpam-3742	178	45	modules	module	NOUN
ejpam-3742	178	46	f	f	NOUN
ejpam-3742	178	47	:	:	PUNCT
ejpam-3742	178	48	m	m	VERB
ejpam-3742	178	49	−→m	−→m	NOUN
ejpam-3742	178	50	′	′	NUM
ejpam-3742	178	51	,	,	PUNCT
ejpam-3742	178	52	we	we	PRON
ejpam-3742	178	53	associate	associate	VERB
ejpam-3742	178	54	êxt	êxt	NOUN
ejpam-3742	178	55	n	n	PROPN
ejpam-3742	178	56	b(f	b(f	PROPN
ejpam-3742	178	57	,	,	PUNCT
ejpam-3742	178	58	b	b	PROPN
ejpam-3742	178	59	)	)	PUNCT
ejpam-3742	178	60	:	:	PUNCT
ejpam-3742	178	61	êxt	êxt	NOUN
ejpam-3742	178	62	n	n	PRON
ejpam-3742	178	63	b(m	b(m	PROPN
ejpam-3742	178	64	′,b)→	′,b)→	ADJ
ejpam-3742	178	65	êxt	êxt	NOUN
ejpam-3742	178	66	n	n	PRON
ejpam-3742	178	67	b(m	b(m	PROPN
ejpam-3742	178	68	,	,	PUNCT
ejpam-3742	178	69	b	b	NOUN
ejpam-3742	178	70	)	)	PUNCT
ejpam-3742	178	71	is	be	AUX
ejpam-3742	178	72	a	a	DET
ejpam-3742	178	73	contravariant	contravariant	ADJ
ejpam-3742	178	74	functor	functor	NOUN
ejpam-3742	178	75	.	.	PUNCT
ejpam-3742	179	1	proof	proof	NOUN
ejpam-3742	179	2	.	.	PUNCT
ejpam-3742	180	1	∗	∗	NOUN
ejpam-3742	180	2	we	we	PRON
ejpam-3742	180	3	have	have	VERB
ejpam-3742	180	4	m	m	PROPN
ejpam-3742	180	5	∈	∈	NOUN
ejpam-3742	180	6	ob(b	ob(b	NOUN
ejpam-3742	180	7	-	-	PUNCT
ejpam-3742	180	8	mod	mod	NOUN
ejpam-3742	180	9	)	)	PUNCT
ejpam-3742	180	10	⇒	⇒	VERB
ejpam-3742	180	11	êxt	êxt	NOUN
ejpam-3742	180	12	n	n	PRON
ejpam-3742	180	13	b(m	b(m	PROPN
ejpam-3742	180	14	,	,	PUNCT
ejpam-3742	180	15	b	b	NOUN
ejpam-3742	180	16	)	)	PUNCT
ejpam-3742	180	17	∈	∈	PROPN
ejpam-3742	180	18	ob(alg	ob(alg	NOUN
ejpam-3742	180	19	-	-	PUNCT
ejpam-3742	180	20	a	a	NOUN
ejpam-3742	180	21	)	)	PUNCT
ejpam-3742	180	22	(	(	PUNCT
ejpam-3742	180	23	see	see	VERB
ejpam-3742	180	24	[	[	X
ejpam-3742	180	25	3	3	NUM
ejpam-3742	180	26	]	]	NUM
ejpam-3742	180	27	)	)	PUNCT
ejpam-3742	180	28	,	,	PUNCT
ejpam-3742	180	29	so	so	CCONJ
ejpam-3742	180	30	the	the	DET
ejpam-3742	180	31	action	action	NOUN
ejpam-3742	180	32	of	of	ADP
ejpam-3742	180	33	êxt	êxt	NOUN
ejpam-3742	180	34	n	n	PROPN
ejpam-3742	180	35	b(-,b	b(-,b	NOUN
ejpam-3742	180	36	)	)	PUNCT
ejpam-3742	180	37	on	on	ADP
ejpam-3742	180	38	the	the	DET
ejpam-3742	180	39	objects	object	NOUN
ejpam-3742	180	40	of	of	ADP
ejpam-3742	180	41	alg	alg	PROPN
ejpam-3742	180	42	-	-	PUNCT
ejpam-3742	180	43	a	a	DET
ejpam-3742	180	44	makes	make	VERB
ejpam-3742	180	45	sense	sense	NOUN
ejpam-3742	180	46	.	.	PUNCT
ejpam-3742	181	1	∗	∗	NOUN
ejpam-3742	181	2	let	let	VERB
ejpam-3742	181	3	f	f	PROPN
ejpam-3742	181	4	:	:	PUNCT
ejpam-3742	181	5	m	m	VERB
ejpam-3742	181	6	→	→	SYM
ejpam-3742	181	7	m	m	AUX
ejpam-3742	181	8	′	′	NUM
ejpam-3742	181	9	be	be	VERB
ejpam-3742	181	10	a	a	DET
ejpam-3742	181	11	morphism	morphism	NOUN
ejpam-3742	181	12	of	of	ADP
ejpam-3742	181	13	left	left	ADJ
ejpam-3742	181	14	b	b	NOUN
ejpam-3742	181	15	-	-	PUNCT
ejpam-3742	181	16	modules	module	NOUN
ejpam-3742	181	17	.	.	PUNCT
ejpam-3742	182	1	by	by	ADP
ejpam-3742	182	2	the	the	DET
ejpam-3742	182	3	comparison	comparison	NOUN
ejpam-3742	182	4	theorem	theorem	VERB
ejpam-3742	182	5	we	we	PRON
ejpam-3742	182	6	have	have	VERB
ejpam-3742	182	7	the	the	DET
ejpam-3742	182	8	following	follow	VERB
ejpam-3742	182	9	commutative	commutative	ADJ
ejpam-3742	182	10	diagram	diagram	NOUN
ejpam-3742	182	11	pm	pm	NOUN
ejpam-3742	182	12	:	:	PUNCT
ejpam-3742	182	13	.	.	PUNCT
ejpam-3742	182	14	.	.	PUNCT
ejpam-3742	182	15	.	.	PUNCT
ejpam-3742	183	1	//	//	PUNCT
ejpam-3742	184	1	f̃	f̃	PROPN
ejpam-3742	184	2	�	�	PROPN
ejpam-3742	184	3	�	�	PROPN
ejpam-3742	184	4	pn	pn	PROPN
ejpam-3742	184	5	//	//	PROPN
ejpam-3742	184	6	f̃n	f̃n	X
ejpam-3742	184	7	�	�	PROPN
ejpam-3742	184	8	�	�	PROPN
ejpam-3742	184	9	pn−1	pn−1	PROPN
ejpam-3742	184	10	·	·	PUNCT
ejpam-3742	184	11	·	·	PUNCT
ejpam-3742	184	12	·	·	PUNCT
ejpam-3742	184	13	//	//	SYM
ejpam-3742	184	14	˜fn−1	˜fn−1	PROPN
ejpam-3742	184	15	�	�	PROPN
ejpam-3742	184	16	�	�	PROPN
ejpam-3742	184	17	p0	p0	PROPN
ejpam-3742	184	18	//	//	SYM
ejpam-3742	184	19	f̃0	f̃0	PROPN
ejpam-3742	184	20	�	�	PROPN
ejpam-3742	184	21	�	�	PROPN
ejpam-3742	184	22	a	a	DET
ejpam-3742	184	23	//	//	X
ejpam-3742	184	24	f	f	PROPN
ejpam-3742	184	25	�	�	PROPN
ejpam-3742	184	26	�	�	PROPN
ejpam-3742	184	27	0	0	NUM
ejpam-3742	184	28	pm	pm	NOUN
ejpam-3742	184	29	′	′	NUM
ejpam-3742	184	30	:	:	PUNCT
ejpam-3742	184	31	.	.	PUNCT
ejpam-3742	184	32	.	.	PUNCT
ejpam-3742	184	33	.	.	PUNCT
ejpam-3742	185	1	//	//	PUNCT
ejpam-3742	186	1	p	p	PROPN
ejpam-3742	186	2	′n	′n	PROPN
ejpam-3742	186	3	//	//	PUNCT
ejpam-3742	186	4	p	p	DET
ejpam-3742	186	5	′n−1	′n−1	PROPN
ejpam-3742	186	6	·	·	PUNCT
ejpam-3742	186	7	·	·	PUNCT
ejpam-3742	186	8	·	·	PUNCT
ejpam-3742	187	1	//	//	PUNCT
ejpam-3742	187	2	p	p	NOUN
ejpam-3742	187	3	′0	′0	PROPN
ejpam-3742	187	4	//	//	SYM
ejpam-3742	187	5	b	b	PROPN
ejpam-3742	187	6	//	//	X
ejpam-3742	187	7	0	0	NUM
ejpam-3742	187	8	by	by	ADP
ejpam-3742	187	9	applying	apply	VERB
ejpam-3742	187	10	the	the	DET
ejpam-3742	187	11	contravariant	contravariant	ADJ
ejpam-3742	187	12	functor	functor	PROPN
ejpam-3742	187	13	homb(-,b	homb(-,b	NOUN
ejpam-3742	187	14	)	)	PUNCT
ejpam-3742	187	15	we	we	PRON
ejpam-3742	187	16	have	have	VERB
ejpam-3742	187	17	homb(pm	homb(pm	NOUN
ejpam-3742	187	18	,	,	PUNCT
ejpam-3742	187	19	b	b	NOUN
ejpam-3742	187	20	)	)	PUNCT
ejpam-3742	187	21	:	:	PUNCT
ejpam-3742	187	22	0	0	NUM
ejpam-3742	187	23	//	//	X
ejpam-3742	187	24	homb(f̃	homb(f̃	PROPN
ejpam-3742	187	25	,	,	PUNCT
ejpam-3742	187	26	b	b	X
ejpam-3742	187	27	)	)	PUNCT
ejpam-3742	187	28	�	�	NOUN
ejpam-3742	187	29	�	�	NOUN
ejpam-3742	187	30	homb(m	homb(m	NOUN
ejpam-3742	187	31	,	,	PUNCT
ejpam-3742	187	32	b	b	NOUN
ejpam-3742	187	33	)	)	PUNCT
ejpam-3742	187	34	//	//	NOUN
ejpam-3742	188	1	homb(f	homb(f	PROPN
ejpam-3742	188	2	,	,	PUNCT
ejpam-3742	188	3	b	b	NOUN
ejpam-3742	188	4	)	)	PUNCT
ejpam-3742	188	5	�	�	PROPN
ejpam-3742	188	6	�	�	PROPN
ejpam-3742	188	7	homb(p0,b	homb(p0,b	NOUN
ejpam-3742	188	8	)	)	PUNCT
ejpam-3742	188	9	·	·	PUNCT
ejpam-3742	188	10	·	·	PUNCT
ejpam-3742	188	11	·	·	PUNCT
ejpam-3742	188	12	homb(f̃0,b	homb(f̃0,b	VERB
ejpam-3742	188	13	)	)	PUNCT
ejpam-3742	188	14	�	�	PROPN
ejpam-3742	188	15	�	�	PROPN
ejpam-3742	188	16	homb(pm	homb(pm	PROPN
ejpam-3742	188	17	′	′	NUM
ejpam-3742	188	18	,	,	PUNCT
ejpam-3742	188	19	b	b	X
ejpam-3742	188	20	)	)	PUNCT
ejpam-3742	188	21	:	:	PUNCT
ejpam-3742	189	1	0	0	NUM
ejpam-3742	189	2	//	//	PUNCT
ejpam-3742	189	3	homb(m	homb(m	ADV
ejpam-3742	189	4	′,b	′,b	NUM
ejpam-3742	189	5	)	)	PUNCT
ejpam-3742	189	6	//	//	PUNCT
ejpam-3742	190	1	homb(p	homb(p	PROPN
ejpam-3742	190	2	′0,b	′0,b	PROPN
ejpam-3742	190	3	)	)	PUNCT
ejpam-3742	190	4	·	·	PUNCT
ejpam-3742	190	5	·	·	PUNCT
ejpam-3742	190	6	·	·	PUNCT
ejpam-3742	191	1	so	so	ADV
ejpam-3742	191	2	homb(f̃	homb(f̃	NOUN
ejpam-3742	191	3	,	,	PUNCT
ejpam-3742	191	4	b	b	NOUN
ejpam-3742	191	5	)	)	PUNCT
ejpam-3742	191	6	:	:	PUNCT
ejpam-3742	191	7	homb(pm	homb(pm	VERB
ejpam-3742	191	8	,	,	PUNCT
ejpam-3742	191	9	b	b	NOUN
ejpam-3742	191	10	)	)	PUNCT
ejpam-3742	191	11	−→	−→	NOUN
ejpam-3742	191	12	homb(pm	homb(pm	NOUN
ejpam-3742	191	13	′	′	PRON
ejpam-3742	191	14	,	,	PUNCT
ejpam-3742	191	15	b	b	X
ejpam-3742	191	16	)	)	PUNCT
ejpam-3742	191	17	is	be	AUX
ejpam-3742	191	18	a	a	DET
ejpam-3742	191	19	morphism	morphism	NOUN
ejpam-3742	191	20	of	of	ADP
ejpam-3742	191	21	chain	chain	NOUN
ejpam-3742	191	22	complex	complex	NOUN
ejpam-3742	191	23	.	.	PUNCT
ejpam-3742	192	1	we	we	PRON
ejpam-3742	192	2	have	have	VERB
ejpam-3742	192	3	hn(homb(f̃	hn(homb(f̃	NOUN
ejpam-3742	192	4	,	,	PUNCT
ejpam-3742	192	5	b	b	NOUN
ejpam-3742	192	6	)	)	PUNCT
ejpam-3742	192	7	)	)	PUNCT
ejpam-3742	192	8	:	:	PUNCT
ejpam-3742	193	1	hn(homb(pm	hn(homb(pm	INTJ
ejpam-3742	193	2	,	,	PUNCT
ejpam-3742	193	3	b	b	NOUN
ejpam-3742	193	4	)	)	PUNCT
ejpam-3742	193	5	)	)	PUNCT
ejpam-3742	194	1	−→	−→	NOUN
ejpam-3742	194	2	hn(homb(pm	hn(homb(pm	NOUN
ejpam-3742	194	3	′	′	X
ejpam-3742	194	4	,	,	PUNCT
ejpam-3742	194	5	b	b	NOUN
ejpam-3742	194	6	)	)	PUNCT
ejpam-3742	194	7	)	)	PUNCT
ejpam-3742	195	1	zn	zn	PROPN
ejpam-3742	195	2	7−→	7−→	NOUN
ejpam-3742	195	3	homb(f̃n	homb(f̃n	NOUN
ejpam-3742	195	4	,	,	PUNCT
ejpam-3742	195	5	b)zn	b)zn	PROPN
ejpam-3742	195	6	.	.	PROPN
ejpam-3742	196	1	homb(f	homb(f	PROPN
ejpam-3742	196	2	,	,	PUNCT
ejpam-3742	196	3	b	b	NOUN
ejpam-3742	196	4	)	)	PUNCT
ejpam-3742	196	5	=	=	SYM
ejpam-3742	196	6	f∗	f∗	NOUN
ejpam-3742	196	7	and	and	CCONJ
ejpam-3742	196	8	homb(f̃n	homb(f̃n	PROPN
ejpam-3742	196	9	,	,	PUNCT
ejpam-3742	196	10	b	b	X
ejpam-3742	196	11	)	)	PUNCT
ejpam-3742	196	12	=	=	SYM
ejpam-3742	196	13	f̃∗n	f̃∗n	NOUN
ejpam-3742	196	14	are	be	AUX
ejpam-3742	196	15	morphisms	morphism	NOUN
ejpam-3742	196	16	of	of	ADP
ejpam-3742	196	17	right	right	ADJ
ejpam-3742	196	18	a	a	NOUN
ejpam-3742	196	19	-	-	PUNCT
ejpam-3742	196	20	algebras	algebras	X
ejpam-3742	196	21	(	(	PUNCT
ejpam-3742	196	22	see	see	VERB
ejpam-3742	196	23	[	[	X
ejpam-3742	196	24	3	3	NUM
ejpam-3742	196	25	]	]	NUM
ejpam-3742	196	26	)	)	PUNCT
ejpam-3742	196	27	.	.	PUNCT
ejpam-3742	197	1	so	so	ADV
ejpam-3742	197	2	hn(homb(f̃	hn(homb(f̃	NOUN
ejpam-3742	197	3	,	,	PUNCT
ejpam-3742	197	4	b	b	NOUN
ejpam-3742	197	5	)	)	PUNCT
ejpam-3742	197	6	)	)	PUNCT
ejpam-3742	198	1	=	=	PRON
ejpam-3742	198	2	êxt	êxt	X
ejpam-3742	198	3	n	n	PROPN
ejpam-3742	198	4	b(f	b(f	PROPN
ejpam-3742	198	5	,	,	PUNCT
ejpam-3742	198	6	b	b	PROPN
ejpam-3742	198	7	)	)	PUNCT
ejpam-3742	198	8	is	be	AUX
ejpam-3742	198	9	a	a	DET
ejpam-3742	198	10	morphism	morphism	NOUN
ejpam-3742	198	11	of	of	ADP
ejpam-3742	198	12	right	right	ADJ
ejpam-3742	198	13	a	a	NOUN
ejpam-3742	198	14	-	-	PUNCT
ejpam-3742	198	15	algebras	algebras	X
ejpam-3742	198	16	,	,	PUNCT
ejpam-3742	198	17	so	so	SCONJ
ejpam-3742	198	18	the	the	DET
ejpam-3742	198	19	action	action	NOUN
ejpam-3742	198	20	of	of	ADP
ejpam-3742	198	21	êxt	êxt	NOUN
ejpam-3742	198	22	n	n	PROPN
ejpam-3742	198	23	b(-,b	b(-,b	NOUN
ejpam-3742	198	24	)	)	PUNCT
ejpam-3742	198	25	on	on	ADP
ejpam-3742	198	26	the	the	DET
ejpam-3742	198	27	arrow	arrow	NOUN
ejpam-3742	198	28	makes	make	VERB
ejpam-3742	198	29	sense	sense	NOUN
ejpam-3742	198	30	.	.	PUNCT
ejpam-3742	199	1	∗	∗	NOUN
ejpam-3742	199	2	we	we	PRON
ejpam-3742	199	3	have	have	VERB
ejpam-3742	199	4	êxt	êxt	NOUN
ejpam-3742	199	5	n	n	NUM
ejpam-3742	199	6	b(g	b(g	PROPN
ejpam-3742	199	7	◦	◦	NOUN
ejpam-3742	199	8	f	f	NUM
ejpam-3742	199	9	,	,	PUNCT
ejpam-3742	199	10	b	b	NOUN
ejpam-3742	199	11	)	)	PUNCT
ejpam-3742	200	1	=	=	SYM
ejpam-3742	200	2	hn(homb	hn(homb	PROPN
ejpam-3742	200	3	(	(	PUNCT
ejpam-3742	200	4	˜g	˜g	PROPN
ejpam-3742	200	5	◦	◦	NOUN
ejpam-3742	200	6	f	f	NUM
ejpam-3742	200	7	,	,	PUNCT
ejpam-3742	200	8	b	b	NOUN
ejpam-3742	200	9	)	)	PUNCT
ejpam-3742	200	10	)	)	PUNCT
ejpam-3742	201	1	=	=	PRON
ejpam-3742	201	2	hn(homb(g̃	hn(homb(g̃	PROPN
ejpam-3742	201	3	◦	◦	PROPN
ejpam-3742	201	4	f̃	f̃	PROPN
ejpam-3742	201	5	,	,	PUNCT
ejpam-3742	201	6	b	b	NOUN
ejpam-3742	201	7	)	)	PUNCT
ejpam-3742	201	8	)	)	PUNCT
ejpam-3742	202	1	=	=	NOUN
ejpam-3742	202	2	hn[homb(f̃	hn[homb(f̃	NOUN
ejpam-3742	202	3	,	,	PUNCT
ejpam-3742	202	4	b	b	NOUN
ejpam-3742	202	5	)	)	PUNCT
ejpam-3742	202	6	◦	◦	NOUN
ejpam-3742	202	7	homb(g̃,b	homb(g̃,b	NUM
ejpam-3742	202	8	)	)	PUNCT
ejpam-3742	202	9	]	]	PUNCT
ejpam-3742	203	1	=	=	SYM
ejpam-3742	203	2	hn(homb(f̃	hn(homb(f̃	NOUN
ejpam-3742	203	3	,	,	PUNCT
ejpam-3742	203	4	b	b	NOUN
ejpam-3742	203	5	)	)	PUNCT
ejpam-3742	203	6	)	)	PUNCT
ejpam-3742	203	7	◦	◦	NOUN
ejpam-3742	203	8	hn(homb(g̃,b	hn(homb(g̃,b	PROPN
ejpam-3742	203	9	)	)	PUNCT
ejpam-3742	203	10	)	)	PUNCT
ejpam-3742	204	1	=	=	PRON
ejpam-3742	204	2	êxt	êxt	X
ejpam-3742	204	3	n	n	PROPN
ejpam-3742	204	4	b(f	b(f	PROPN
ejpam-3742	204	5	,	,	PUNCT
ejpam-3742	204	6	b	b	NOUN
ejpam-3742	204	7	)	)	PUNCT
ejpam-3742	204	8	◦	◦	VERB
ejpam-3742	204	9	êxt	êxt	NOUN
ejpam-3742	204	10	n	n	PRON
ejpam-3742	204	11	b(g	b(g	PROPN
ejpam-3742	204	12	,	,	PUNCT
ejpam-3742	204	13	b	b	NOUN
ejpam-3742	204	14	)	)	PUNCT
ejpam-3742	204	15	.	.	PUNCT
ejpam-3742	205	1	m	m	PROPN
ejpam-3742	205	2	thiaw	thiaw	ADJ
ejpam-3742	205	3	,	,	PUNCT
ejpam-3742	205	4	m	m	AUX
ejpam-3742	205	5	maaouia	maaouia	NOUN
ejpam-3742	205	6	/	/	SYM
ejpam-3742	205	7	eur	eur	NOUN
ejpam-3742	205	8	.	.	PUNCT
ejpam-3742	206	1	j.	j.	PROPN
ejpam-3742	206	2	pure	pure	PROPN
ejpam-3742	206	3	appl	appl	PROPN
ejpam-3742	206	4	.	.	PROPN
ejpam-3742	206	5	math	math	PROPN
ejpam-3742	206	6	,	,	PUNCT
ejpam-3742	206	7	13	13	NUM
ejpam-3742	206	8	(	(	PUNCT
ejpam-3742	206	9	3	3	NUM
ejpam-3742	206	10	)	)	PUNCT
ejpam-3742	206	11	(	(	PUNCT
ejpam-3742	206	12	2020	2020	NUM
ejpam-3742	206	13	)	)	PUNCT
ejpam-3742	206	14	,	,	PUNCT
ejpam-3742	206	15	472	472	NUM
ejpam-3742	206	16	-	-	SYM
ejpam-3742	206	17	482	482	NUM
ejpam-3742	206	18	480	480	NUM
ejpam-3742	206	19	∗	∗	NOUN
ejpam-3742	206	20	we	we	PRON
ejpam-3742	206	21	have	have	VERB
ejpam-3742	206	22	êxt	êxt	NOUN
ejpam-3742	206	23	n	n	PRON
ejpam-3742	206	24	b(1	b(1	PROPN
ejpam-3742	206	25	m	m	PROPN
ejpam-3742	206	26	,	,	PUNCT
ejpam-3742	206	27	b)(zn	b)(zn	NOUN
ejpam-3742	206	28	)	)	PUNCT
ejpam-3742	206	29	=	=	SYM
ejpam-3742	206	30	homb((1̃m	homb((1̃m	NOUN
ejpam-3742	206	31	)	)	PUNCT
ejpam-3742	206	32	n	n	CCONJ
ejpam-3742	206	33	,	,	PUNCT
ejpam-3742	206	34	b)(zn	b)(zn	NOUN
ejpam-3742	206	35	)	)	PUNCT
ejpam-3742	206	36	=	=	SYM
ejpam-3742	207	1	1homb(m	1homb(m	NUM
ejpam-3742	207	2	,	,	PUNCT
ejpam-3742	207	3	b)(zn	b)(zn	NOUN
ejpam-3742	207	4	)	)	PUNCT
ejpam-3742	207	5	=	=	SYM
ejpam-3742	208	1	zn	zn	X
ejpam-3742	208	2	.	.	PUNCT
ejpam-3742	209	1	so	so	ADV
ejpam-3742	209	2	êxt	êxt	PROPN
ejpam-3742	209	3	n	n	PRON
ejpam-3742	209	4	b(1	b(1	PROPN
ejpam-3742	209	5	m	m	PROPN
ejpam-3742	209	6	,	,	PUNCT
ejpam-3742	209	7	b	b	X
ejpam-3742	209	8	)	)	PUNCT
ejpam-3742	209	9	=	=	SYM
ejpam-3742	209	10	1	1	NUM
ejpam-3742	209	11	êxt	êxt	NOUN
ejpam-3742	209	12	n	n	PRON
ejpam-3742	209	13	b(m	b(m	PROPN
ejpam-3742	209	14	,	,	PUNCT
ejpam-3742	209	15	b	b	NOUN
ejpam-3742	209	16	)	)	PUNCT
ejpam-3742	209	17	.	.	PUNCT
ejpam-3742	210	1	therefore	therefore	ADV
ejpam-3742	210	2	êxt	êxt	PROPN
ejpam-3742	210	3	n	n	PROPN
ejpam-3742	210	4	b(-,b	b(-,b	PROPN
ejpam-3742	210	5	)	)	PUNCT
ejpam-3742	210	6	:	:	PUNCT
ejpam-3742	210	7	b	b	X
ejpam-3742	210	8	-	-	PUNCT
ejpam-3742	210	9	mod	mod	ADJ
ejpam-3742	210	10	−→	−→	PROPN
ejpam-3742	210	11	alg	alg	PROPN
ejpam-3742	210	12	-	-	PUNCT
ejpam-3742	210	13	a	a	NOUN
ejpam-3742	210	14	is	be	AUX
ejpam-3742	210	15	a	a	DET
ejpam-3742	210	16	contravariant	contravariant	ADJ
ejpam-3742	210	17	functor	functor	PROPN
ejpam-3742	210	18	.	.	PUNCT
ejpam-3742	210	19	proposition	proposition	NOUN
ejpam-3742	210	20	6	6	NUM
ejpam-3742	210	21	.	.	PUNCT
ejpam-3742	211	1	let	let	VERB
ejpam-3742	211	2	b	b	X
ejpam-3742	211	3	be	be	AUX
ejpam-3742	211	4	a	a	DET
ejpam-3742	211	5	(	(	PUNCT
ejpam-3742	211	6	b	b	X
ejpam-3742	211	7	-	-	PUNCT
ejpam-3742	211	8	a)-bialgebra.then	a)-bialgebra.then	VERB
ejpam-3742	211	9	the	the	DET
ejpam-3742	211	10	correspondence	correspondence	NOUN
ejpam-3742	211	11	êxt	êxt	NOUN
ejpam-3742	211	12	n	n	PRON
ejpam-3742	211	13	b(-,b)o	b(-,b)o	NUM
ejpam-3742	211	14	:	:	PUNCT
ejpam-3742	211	15	b	b	X
ejpam-3742	211	16	-	-	PUNCT
ejpam-3742	211	17	modo	modo	ADJ
ejpam-3742	211	18	−→	−→	NOUN
ejpam-3742	211	19	alg	alg	PROPN
ejpam-3742	211	20	-	-	PUNCT
ejpam-3742	211	21	a	a	PROPN
ejpam-3742	211	22	(	(	PUNCT
ejpam-3742	211	23	i	i	NOUN
ejpam-3742	211	24	)	)	PUNCT
ejpam-3742	211	25	which	which	PRON
ejpam-3742	211	26	has	have	VERB
ejpam-3742	211	27	any	any	DET
ejpam-3742	211	28	left	left	ADJ
ejpam-3742	211	29	b	b	NOUN
ejpam-3742	211	30	-	-	PUNCT
ejpam-3742	211	31	module	module	NOUN
ejpam-3742	211	32	m	m	NOUN
ejpam-3742	211	33	,	,	PUNCT
ejpam-3742	211	34	we	we	PRON
ejpam-3742	211	35	associate	associate	VERB
ejpam-3742	211	36	the	the	DET
ejpam-3742	211	37	right	right	ADJ
ejpam-3742	211	38	a	a	DET
ejpam-3742	211	39	-	-	PUNCT
ejpam-3742	211	40	algebra	algebra	NOUN
ejpam-3742	211	41	êxt	êxt	NOUN
ejpam-3742	211	42	n	n	PRON
ejpam-3742	211	43	b(-,b)o(m	b(-,b)o(m	NOUN
ejpam-3742	211	44	)	)	PUNCT
ejpam-3742	212	1	=	=	PRON
ejpam-3742	212	2	êxt	êxt	X
ejpam-3742	212	3	n	n	PRON
ejpam-3742	212	4	b(m	b(m	PROPN
ejpam-3742	212	5	,	,	PUNCT
ejpam-3742	212	6	b	b	NOUN
ejpam-3742	212	7	)	)	PUNCT
ejpam-3742	212	8	,	,	PUNCT
ejpam-3742	212	9	(	(	PUNCT
ejpam-3742	212	10	ii	ii	NOUN
ejpam-3742	212	11	)	)	PUNCT
ejpam-3742	212	12	which	which	PRON
ejpam-3742	212	13	has	have	VERB
ejpam-3742	212	14	any	any	DET
ejpam-3742	212	15	f	f	PROPN
ejpam-3742	212	16	∈	∈	PROPN
ejpam-3742	212	17	homb	homb	ADJ
ejpam-3742	212	18	-	-	PUNCT
ejpam-3742	212	19	modo(m	modo(m	NOUN
ejpam-3742	212	20	,	,	PUNCT
ejpam-3742	212	21	m	m	NOUN
ejpam-3742	212	22	′	′	NUM
ejpam-3742	212	23	)	)	PUNCT
ejpam-3742	212	24	,	,	PUNCT
ejpam-3742	212	25	we	we	PRON
ejpam-3742	212	26	associate	associate	VERB
ejpam-3742	212	27	êxt	êxt	NOUN
ejpam-3742	212	28	n	n	PRON
ejpam-3742	212	29	b(-,b)o(f	b(-,b)o(f	NOUN
ejpam-3742	212	30	)	)	PUNCT
ejpam-3742	213	1	=	=	PUNCT
ejpam-3742	213	2	êxt	êxt	X
ejpam-3742	213	3	n	n	PROPN
ejpam-3742	213	4	b(f	b(f	PROPN
ejpam-3742	213	5	,	,	PUNCT
ejpam-3742	213	6	b	b	NOUN
ejpam-3742	213	7	)	)	PUNCT
ejpam-3742	213	8	.	.	PUNCT
ejpam-3742	214	1	is	be	AUX
ejpam-3742	214	2	a	a	DET
ejpam-3742	214	3	covariant	covariant	ADJ
ejpam-3742	214	4	functor	functor	NOUN
ejpam-3742	214	5	.	.	PUNCT
ejpam-3742	214	6	proof	proof	NOUN
ejpam-3742	214	7	.	.	PUNCT
ejpam-3742	215	1	∗	∗	NOUN
ejpam-3742	215	2	letm	letm	PROPN
ejpam-3742	215	3	∈	∈	PROPN
ejpam-3742	215	4	ob(b	ob(b	NOUN
ejpam-3742	215	5	-	-	PUNCT
ejpam-3742	215	6	modo	modo	NOUN
ejpam-3742	215	7	)	)	PUNCT
ejpam-3742	215	8	,	,	PUNCT
ejpam-3742	215	9	we	we	PRON
ejpam-3742	215	10	have	have	VERB
ejpam-3742	215	11	êxt	êxt	NOUN
ejpam-3742	215	12	n	n	PRON
ejpam-3742	215	13	b(-,b)o(m	b(-,b)o(m	NOUN
ejpam-3742	215	14	)	)	PUNCT
ejpam-3742	216	1	=	=	PRON
ejpam-3742	216	2	êxt	êxt	X
ejpam-3742	216	3	n	n	PRON
ejpam-3742	216	4	b(m	b(m	PROPN
ejpam-3742	216	5	,	,	PUNCT
ejpam-3742	216	6	b	b	NOUN
ejpam-3742	216	7	)	)	PUNCT
ejpam-3742	216	8	∈	∈	PROPN
ejpam-3742	216	9	ob(alg	ob(alg	NOUN
ejpam-3742	216	10	-	-	PUNCT
ejpam-3742	216	11	a	a	NOUN
ejpam-3742	216	12	)	)	PUNCT
ejpam-3742	216	13	,	,	PUNCT
ejpam-3742	216	14	so	so	CCONJ
ejpam-3742	216	15	the	the	DET
ejpam-3742	216	16	action	action	NOUN
ejpam-3742	216	17	of	of	ADP
ejpam-3742	216	18	êxt	êxt	NOUN
ejpam-3742	216	19	n	n	PRON
ejpam-3742	216	20	b(-,b)o	b(-,b)o	NOUN
ejpam-3742	216	21	on	on	ADP
ejpam-3742	216	22	the	the	DET
ejpam-3742	216	23	objects	object	NOUN
ejpam-3742	216	24	of	of	ADP
ejpam-3742	216	25	b	b	NOUN
ejpam-3742	216	26	-	-	PUNCT
ejpam-3742	216	27	modo	modo	NOUN
ejpam-3742	216	28	makes	make	VERB
ejpam-3742	216	29	sense	sense	NOUN
ejpam-3742	216	30	.	.	PUNCT
ejpam-3742	217	1	∗	∗	NOUN
ejpam-3742	217	2	let	let	VERB
ejpam-3742	217	3	f	f	PROPN
ejpam-3742	217	4	∈	∈	PROPN
ejpam-3742	217	5	homb	homb	NOUN
ejpam-3742	217	6	-	-	PUNCT
ejpam-3742	217	7	modo(m	modo(m	NOUN
ejpam-3742	217	8	,	,	PUNCT
ejpam-3742	217	9	m	m	NOUN
ejpam-3742	217	10	′	′	NUM
ejpam-3742	217	11	)	)	PUNCT
ejpam-3742	217	12	.	.	PUNCT
ejpam-3742	218	1	sincehomb	sincehomb	NOUN
ejpam-3742	218	2	-	-	PUNCT
ejpam-3742	218	3	modo(m	modo(m	NOUN
ejpam-3742	218	4	,	,	PUNCT
ejpam-3742	218	5	m	m	NOUN
ejpam-3742	218	6	′	′	NUM
ejpam-3742	218	7	)	)	PUNCT
ejpam-3742	219	1	=	=	VERB
ejpam-3742	219	2	homb	homb	NOUN
ejpam-3742	219	3	-	-	PUNCT
ejpam-3742	219	4	mod(m	mod(m	PROPN
ejpam-3742	219	5	′,m	′,m	NOUN
ejpam-3742	219	6	)	)	PUNCT
ejpam-3742	219	7	,	,	PUNCT
ejpam-3742	219	8	then	then	ADV
ejpam-3742	219	9	f	f	PROPN
ejpam-3742	219	10	∈	∈	PROPN
ejpam-3742	219	11	homb	homb	NOUN
ejpam-3742	219	12	-	-	PUNCT
ejpam-3742	219	13	mod(m	mod(m	PROPN
ejpam-3742	219	14	′,m	′,m	NOUN
ejpam-3742	219	15	)	)	PUNCT
ejpam-3742	219	16	,	,	PUNCT
ejpam-3742	220	1	so	so	CCONJ
ejpam-3742	220	2	êxt	êxt	PROPN
ejpam-3742	220	3	n	n	PROPN
ejpam-3742	220	4	b(f	b(f	PROPN
ejpam-3742	220	5	,	,	PUNCT
ejpam-3742	220	6	b	b	NOUN
ejpam-3742	220	7	)	)	PUNCT
ejpam-3742	220	8	∈	∈	PROPN
ejpam-3742	220	9	homalg	homalg	NOUN
ejpam-3742	220	10	-	-	PUNCT
ejpam-3742	220	11	a(êxt	a(êxt	PROPN
ejpam-3742	220	12	n	n	PRON
ejpam-3742	220	13	b(m	b(m	PROPN
ejpam-3742	220	14	,	,	PUNCT
ejpam-3742	220	15	b	b	NOUN
ejpam-3742	220	16	)	)	PUNCT
ejpam-3742	220	17	,	,	PUNCT
ejpam-3742	220	18	êxt	êxt	NOUN
ejpam-3742	220	19	n	n	PRON
ejpam-3742	220	20	b(m	b(m	PROPN
ejpam-3742	220	21	′,b	′,b	NUM
ejpam-3742	220	22	)	)	PUNCT
ejpam-3742	220	23	)	)	PUNCT
ejpam-3742	220	24	because	because	SCONJ
ejpam-3742	220	25	êxt	êxt	PROPN
ejpam-3742	220	26	n	n	PROPN
ejpam-3742	220	27	b(f	b(f	PROPN
ejpam-3742	220	28	,	,	PUNCT
ejpam-3742	220	29	b	b	PROPN
ejpam-3742	220	30	)	)	PUNCT
ejpam-3742	220	31	is	be	AUX
ejpam-3742	220	32	a	a	DET
ejpam-3742	220	33	contravariant	contravariant	ADJ
ejpam-3742	220	34	functor	functor	NOUN
ejpam-3742	220	35	.	.	PUNCT
ejpam-3742	221	1	and	and	CCONJ
ejpam-3742	221	2	hence	hence	ADV
ejpam-3742	221	3	êxt	êxt	NOUN
ejpam-3742	221	4	n	n	PRON
ejpam-3742	221	5	b(-,b)o(f	b(-,b)o(f	NOUN
ejpam-3742	221	6	)	)	PUNCT
ejpam-3742	222	1	=	=	PUNCT
ejpam-3742	222	2	êxt	êxt	X
ejpam-3742	222	3	n	n	PROPN
ejpam-3742	222	4	b(f	b(f	PROPN
ejpam-3742	222	5	,	,	PUNCT
ejpam-3742	222	6	b	b	NOUN
ejpam-3742	222	7	)	)	PUNCT
ejpam-3742	222	8	∈	∈	PROPN
ejpam-3742	222	9	homalg	homalg	NOUN
ejpam-3742	222	10	-	-	PUNCT
ejpam-3742	222	11	a(êxt	a(êxt	PROPN
ejpam-3742	222	12	n	n	PRON
ejpam-3742	222	13	b(m	b(m	PROPN
ejpam-3742	222	14	,	,	PUNCT
ejpam-3742	222	15	b	b	NOUN
ejpam-3742	222	16	)	)	PUNCT
ejpam-3742	222	17	,	,	PUNCT
ejpam-3742	222	18	êxt	êxt	NOUN
ejpam-3742	222	19	n	n	PRON
ejpam-3742	222	20	b(m	b(m	PROPN
ejpam-3742	222	21	′,b	′,b	NUM
ejpam-3742	222	22	)	)	PUNCT
ejpam-3742	222	23	)	)	PUNCT
ejpam-3742	222	24	.	.	PUNCT
ejpam-3742	223	1	therefore	therefore	ADV
ejpam-3742	223	2	the	the	DET
ejpam-3742	223	3	action	action	NOUN
ejpam-3742	223	4	of	of	ADP
ejpam-3742	223	5	êxt	êxt	NOUN
ejpam-3742	223	6	n	n	PROPN
ejpam-3742	223	7	b(-,b)o	b(-,b)o	NOUN
ejpam-3742	223	8	on	on	ADP
ejpam-3742	223	9	the	the	DET
ejpam-3742	223	10	arrow	arrow	NOUN
ejpam-3742	223	11	makes	make	VERB
ejpam-3742	223	12	sens	sen	NOUN
ejpam-3742	223	13	.	.	PROPN
ejpam-3742	223	14	∗	∗	NOUN
ejpam-3742	223	15	let	let	VERB
ejpam-3742	223	16	f	f	PROPN
ejpam-3742	223	17	∈	∈	PROPN
ejpam-3742	223	18	homb	homb	NOUN
ejpam-3742	223	19	-	-	PUNCT
ejpam-3742	223	20	modo(m	modo(m	NOUN
ejpam-3742	223	21	,	,	PUNCT
ejpam-3742	223	22	m	m	NOUN
ejpam-3742	223	23	′	′	NUM
ejpam-3742	223	24	)	)	PUNCT
ejpam-3742	223	25	,	,	PUNCT
ejpam-3742	223	26	g	g	PROPN
ejpam-3742	223	27	∈	∈	PROPN
ejpam-3742	223	28	homb	homb	NOUN
ejpam-3742	223	29	-	-	PUNCT
ejpam-3742	223	30	modo(m	modo(m	NOUN
ejpam-3742	223	31	′,m	′,m	PRON
ejpam-3742	223	32	′′	′′	PROPN
ejpam-3742	223	33	)	)	PUNCT
ejpam-3742	223	34	.	.	PUNCT
ejpam-3742	224	1	we	we	PRON
ejpam-3742	224	2	have	have	VERB
ejpam-3742	224	3	êxt	êxt	NOUN
ejpam-3742	224	4	n	n	NUM
ejpam-3742	224	5	b(g	b(g	PROPN
ejpam-3742	224	6	◦	◦	NOUN
ejpam-3742	224	7	f	f	NUM
ejpam-3742	224	8	,	,	PUNCT
ejpam-3742	224	9	b)o	b)o	ADJ
ejpam-3742	224	10	=	=	PUNCT
ejpam-3742	224	11	êxt	êxt	X
ejpam-3742	224	12	n	n	PRON
ejpam-3742	224	13	b(g	b(g	PROPN
ejpam-3742	224	14	◦	◦	NOUN
ejpam-3742	224	15	f	f	NUM
ejpam-3742	224	16	,	,	PUNCT
ejpam-3742	224	17	b	b	NOUN
ejpam-3742	224	18	)	)	PUNCT
ejpam-3742	224	19	=	=	PUNCT
ejpam-3742	224	20	êxt	êxt	X
ejpam-3742	224	21	n	n	PROPN
ejpam-3742	224	22	b(f	b(f	PROPN
ejpam-3742	224	23	,	,	PUNCT
ejpam-3742	224	24	b	b	NOUN
ejpam-3742	224	25	)	)	PUNCT
ejpam-3742	224	26	◦	◦	VERB
ejpam-3742	224	27	êxt	êxt	NOUN
ejpam-3742	224	28	n	n	PRON
ejpam-3742	224	29	b(g	b(g	PROPN
ejpam-3742	224	30	,	,	PUNCT
ejpam-3742	224	31	b	b	NOUN
ejpam-3742	224	32	)	)	PUNCT
ejpam-3742	224	33	=	=	PUNCT
ejpam-3742	224	34	êxt	êxt	X
ejpam-3742	224	35	n	n	PROPN
ejpam-3742	224	36	b(f	b(f	PROPN
ejpam-3742	224	37	,	,	PUNCT
ejpam-3742	224	38	b)o	b)o	X
ejpam-3742	224	39	◦	◦	NOUN
ejpam-3742	224	40	b	b	X
ejpam-3742	224	41	-	-	PUNCT
ejpam-3742	224	42	modo	modo	ADJ
ejpam-3742	224	43	êxt	êxt	NOUN
ejpam-3742	224	44	n	n	PRON
ejpam-3742	224	45	b(g	b(g	PROPN
ejpam-3742	224	46	,	,	PUNCT
ejpam-3742	224	47	b)o	b)o	NOUN
ejpam-3742	224	48	=	=	PUNCT
ejpam-3742	224	49	êxt	êxt	NOUN
ejpam-3742	224	50	n	n	PRON
ejpam-3742	224	51	b(g	b(g	PROPN
ejpam-3742	224	52	,	,	PUNCT
ejpam-3742	224	53	b)o	b)o	X
ejpam-3742	224	54	◦	◦	NOUN
ejpam-3742	224	55	b	b	X
ejpam-3742	224	56	-	-	PUNCT
ejpam-3742	224	57	mod	mod	ADJ
ejpam-3742	224	58	êxt	êxt	PROPN
ejpam-3742	224	59	n	n	PROPN
ejpam-3742	224	60	b(f	b(f	PROPN
ejpam-3742	224	61	,	,	PUNCT
ejpam-3742	224	62	b)o	b)o	NOUN
ejpam-3742	224	63	.	.	PUNCT
ejpam-3742	225	1	therefore	therefore	ADV
ejpam-3742	225	2	êxt	êxt	NOUN
ejpam-3742	225	3	n	n	PROPN
ejpam-3742	225	4	b(-,b)o	b(-,b)o	NUM
ejpam-3742	225	5	:	:	PUNCT
ejpam-3742	225	6	b	b	X
ejpam-3742	225	7	-	-	PUNCT
ejpam-3742	225	8	modo	modo	ADJ
ejpam-3742	225	9	−→	−→	NOUN
ejpam-3742	225	10	alg	alg	PROPN
ejpam-3742	225	11	-	-	PUNCT
ejpam-3742	225	12	a	a	NOUN
ejpam-3742	225	13	is	be	AUX
ejpam-3742	225	14	a	a	DET
ejpam-3742	225	15	covariant	covariant	ADJ
ejpam-3742	225	16	functor	functor	PROPN
ejpam-3742	225	17	.	.	PUNCT
ejpam-3742	225	18	theorem	theorem	PROPN
ejpam-3742	225	19	6	6	NUM
ejpam-3742	225	20	.	.	PUNCT
ejpam-3742	226	1	let	let	VERB
ejpam-3742	226	2	a	a	PRON
ejpam-3742	226	3	be	be	AUX
ejpam-3742	226	4	a	a	DET
ejpam-3742	226	5	ring	ring	NOUN
ejpam-3742	226	6	,	,	PUNCT
ejpam-3742	226	7	s	s	VERB
ejpam-3742	226	8	a	a	DET
ejpam-3742	226	9	central	central	ADJ
ejpam-3742	226	10	multiplicatively	multiplicatively	ADV
ejpam-3742	226	11	closed	close	VERB
ejpam-3742	226	12	subset	subset	NOUN
ejpam-3742	226	13	of	of	ADP
ejpam-3742	226	14	a	a	PRON
ejpam-3742	226	15	and	and	CCONJ
ejpam-3742	226	16	b	b	NOUN
ejpam-3742	226	17	a	a	DET
ejpam-3742	226	18	(	(	PUNCT
ejpam-3742	226	19	a	a	NOUN
ejpam-3742	226	20	-	-	PUNCT
ejpam-3742	226	21	a)-bialgebra	a)-bialgebra	NOUN
ejpam-3742	226	22	.	.	PUNCT
ejpam-3742	227	1	then	then	ADV
ejpam-3742	227	2	tors	tor	VERB
ejpam-3742	227	3	−1a	−1a	PUNCT
ejpam-3742	227	4	n	n	PROPN
ejpam-3742	227	5	(	(	PUNCT
ejpam-3742	227	6	-	-	INTJ
ejpam-3742	227	7	,	,	PUNCT
ejpam-3742	227	8	s−1b	s−1b	PROPN
ejpam-3742	227	9	)	)	PUNCT
ejpam-3742	227	10	:	:	PUNCT
ejpam-3742	227	11	alg	alg	PROPN
ejpam-3742	227	12	-	-	PUNCT
ejpam-3742	227	13	s−1a	s−1a	PROPN
ejpam-3742	227	14	�	�	PROPN
ejpam-3742	227	15	s−1a	s−1a	NOUN
ejpam-3742	227	16	-	-	PUNCT
ejpam-3742	227	17	modo	modo	NOUN
ejpam-3742	227	18	:	:	PUNCT
ejpam-3742	227	19	êxt	êxt	NOUN
ejpam-3742	227	20	n	n	PRON
ejpam-3742	227	21	s−1a(-	s−1a(-	NOUN
ejpam-3742	227	22	,	,	PUNCT
ejpam-3742	227	23	s−1b)o	s−1b)o	VERB
ejpam-3742	227	24	is	be	AUX
ejpam-3742	227	25	an	an	DET
ejpam-3742	227	26	adjunction	adjunction	NOUN
ejpam-3742	227	27	.	.	PUNCT
ejpam-3742	228	1	m	m	PROPN
ejpam-3742	228	2	thiaw	thiaw	NOUN
ejpam-3742	228	3	,	,	PUNCT
ejpam-3742	228	4	m	m	AUX
ejpam-3742	228	5	maaouia	maaouia	NOUN
ejpam-3742	228	6	/	/	SYM
ejpam-3742	228	7	eur	eur	NOUN
ejpam-3742	228	8	.	.	PUNCT
ejpam-3742	229	1	j.	j.	PROPN
ejpam-3742	229	2	pure	pure	PROPN
ejpam-3742	229	3	appl	appl	PROPN
ejpam-3742	229	4	.	.	PROPN
ejpam-3742	229	5	math	math	PROPN
ejpam-3742	229	6	,	,	PUNCT
ejpam-3742	229	7	13	13	NUM
ejpam-3742	229	8	(	(	PUNCT
ejpam-3742	229	9	3	3	NUM
ejpam-3742	229	10	)	)	PUNCT
ejpam-3742	229	11	(	(	PUNCT
ejpam-3742	229	12	2020	2020	NUM
ejpam-3742	229	13	)	)	PUNCT
ejpam-3742	229	14	,	,	PUNCT
ejpam-3742	229	15	472	472	NUM
ejpam-3742	229	16	-	-	SYM
ejpam-3742	229	17	482	482	NUM
ejpam-3742	229	18	481	481	NUM
ejpam-3742	229	19	proof	proof	NOUN
ejpam-3742	229	20	.	.	PUNCT
ejpam-3742	230	1	∗	∗	NOUN
ejpam-3742	230	2	for	for	ADP
ejpam-3742	230	3	n	n	NOUN
ejpam-3742	230	4	=	=	SYM
ejpam-3742	230	5	0	0	NUM
ejpam-3742	230	6	,	,	PUNCT
ejpam-3742	230	7	f	f	PROPN
ejpam-3742	230	8	=	=	SYM
ejpam-3742	230	9	tors	tor	NOUN
ejpam-3742	230	10	−1a	−1a	PUNCT
ejpam-3742	230	11	n	n	PROPN
ejpam-3742	230	12	(	(	PUNCT
ejpam-3742	230	13	-	-	INTJ
ejpam-3742	230	14	,	,	PUNCT
ejpam-3742	230	15	s−1b	s−1b	ADJ
ejpam-3742	230	16	)	)	PUNCT
ejpam-3742	230	17	=	=	SYM
ejpam-3742	230	18	-⊗s−1as	-⊗s−1as	NOUN
ejpam-3742	230	19	−1b	−1b	PROPN
ejpam-3742	230	20	and	and	CCONJ
ejpam-3742	230	21	g	g	NOUN
ejpam-3742	230	22	=	=	PUNCT
ejpam-3742	230	23	êxt	êxt	NOUN
ejpam-3742	230	24	n	n	DET
ejpam-3742	230	25	s−1a(-	s−1a(-	NOUN
ejpam-3742	230	26	,	,	PUNCT
ejpam-3742	230	27	s−1b)o	s−1b)o	VERB
ejpam-3742	230	28	=	=	SYM
ejpam-3742	230	29	homs−1a(-,b)o	homs−1a(-,b)o	PROPN
ejpam-3742	230	30	.	.	PUNCT
ejpam-3742	231	1	by	by	ADP
ejpam-3742	231	2	the	the	DET
ejpam-3742	231	3	proposition	proposition	NOUN
ejpam-3742	231	4	4	4	NUM
ejpam-3742	231	5	,	,	PUNCT
ejpam-3742	231	6	the	the	DET
ejpam-3742	231	7	functors	functors	PROPN
ejpam-3742	231	8	-⊗s−1as	-⊗s−1as	PROPN
ejpam-3742	231	9	−1b	−1b	SYM
ejpam-3742	231	10	=	=	SYM
ejpam-3742	231	11	tors	tor	NOUN
ejpam-3742	231	12	−1a	−1a	PUNCT
ejpam-3742	231	13	0	0	SYM
ejpam-3742	231	14	(	(	PUNCT
ejpam-3742	231	15	-	-	INTJ
ejpam-3742	231	16	,	,	PUNCT
ejpam-3742	231	17	s−1b	s−1b	ADJ
ejpam-3742	231	18	)	)	PUNCT
ejpam-3742	231	19	andhoms−1a(-,b)o	andhoms−1a(-,b)o	NOUN
ejpam-3742	231	20	=	=	PUNCT
ejpam-3742	231	21	êxt	êxt	NOUN
ejpam-3742	231	22	0	0	NUM
ejpam-3742	231	23	s−1a(-,b)o	s−1a(-,b)o	NOUN
ejpam-3742	231	24	are	be	AUX
ejpam-3742	231	25	adjoint	adjoint	NOUN
ejpam-3742	231	26	.	.	PUNCT
ejpam-3742	232	1	so	so	ADV
ejpam-3742	232	2	for	for	ADP
ejpam-3742	232	3	n	n	NOUN
ejpam-3742	232	4	=	=	SYM
ejpam-3742	232	5	0	0	NOUN
ejpam-3742	232	6	the	the	DET
ejpam-3742	232	7	property	property	NOUN
ejpam-3742	232	8	is	be	AUX
ejpam-3742	232	9	verified	verify	VERB
ejpam-3742	232	10	.	.	PUNCT
ejpam-3742	233	1	∗	∗	NOUN
ejpam-3742	233	2	suppose	suppose	VERB
ejpam-3742	233	3	that	that	SCONJ
ejpam-3742	233	4	the	the	DET
ejpam-3742	233	5	property	property	NOUN
ejpam-3742	233	6	is	be	AUX
ejpam-3742	233	7	true	true	ADJ
ejpam-3742	233	8	up	up	ADP
ejpam-3742	233	9	to	to	ADP
ejpam-3742	233	10	the	the	DET
ejpam-3742	233	11	order	order	NOUN
ejpam-3742	233	12	n	n	CCONJ
ejpam-3742	233	13	,	,	PUNCT
ejpam-3742	233	14	i.e.	i.e.	X
ejpam-3742	233	15	the	the	DET
ejpam-3742	233	16	functors	functors	PROPN
ejpam-3742	233	17	f	f	PROPN
ejpam-3742	233	18	=	=	SYM
ejpam-3742	233	19	tors	tor	NOUN
ejpam-3742	233	20	−1a	−1a	PUNCT
ejpam-3742	233	21	n	n	PROPN
ejpam-3742	233	22	(	(	PUNCT
ejpam-3742	233	23	-,b	-,b	ADJ
ejpam-3742	233	24	)	)	PUNCT
ejpam-3742	233	25	andg	andg	NOUN
ejpam-3742	234	1	=	=	PUNCT
ejpam-3742	234	2	êxt	êxt	PROPN
ejpam-3742	234	3	n	n	PRON
ejpam-3742	234	4	s−1a(-,b)o	s−1a(-,b)o	NOUN
ejpam-3742	234	5	are	be	AUX
ejpam-3742	234	6	adjoint	adjoint	NOUN
ejpam-3742	234	7	.	.	PUNCT
ejpam-3742	235	1	∗	∗	NOUN
ejpam-3742	235	2	show	show	VERB
ejpam-3742	235	3	that	that	SCONJ
ejpam-3742	235	4	the	the	DET
ejpam-3742	235	5	functors	functors	PROPN
ejpam-3742	235	6	f	f	PROPN
ejpam-3742	235	7	=	=	SYM
ejpam-3742	235	8	tors	tor	NOUN
ejpam-3742	235	9	−1a	−1a	PUNCT
ejpam-3742	235	10	n+1	n+1	PROPN
ejpam-3742	235	11	(	(	PUNCT
ejpam-3742	235	12	-	-	INTJ
ejpam-3742	235	13	,	,	PUNCT
ejpam-3742	235	14	s−1b	s−1b	ADJ
ejpam-3742	235	15	)	)	PUNCT
ejpam-3742	235	16	and	and	CCONJ
ejpam-3742	235	17	g	g	NOUN
ejpam-3742	235	18	=	=	PUNCT
ejpam-3742	235	19	êxt	êxt	X
ejpam-3742	235	20	n+1	n+1	NUM
ejpam-3742	235	21	s−1a(-	s−1a(-	NOUN
ejpam-3742	235	22	,	,	PUNCT
ejpam-3742	235	23	s−1b)o	s−1b)o	VERB
ejpam-3742	235	24	are	be	AUX
ejpam-3742	235	25	adjoint	adjoint	ADJ
ejpam-3742	235	26	.	.	PUNCT
ejpam-3742	236	1	let	let	VERB
ejpam-3742	236	2	ps−1b	ps−1b	PROPN
ejpam-3742	236	3	:	:	PUNCT
ejpam-3742	236	4	·	·	PUNCT
ejpam-3742	236	5	·	·	PUNCT
ejpam-3742	236	6	·	·	PUNCT
ejpam-3742	237	1	−→	−→	NOUN
ejpam-3742	237	2	s−1pn+1	s−1pn+1	NOUN
ejpam-3742	237	3	dn+1−→	dn+1−→	PROPN
ejpam-3742	237	4	s−1pn	s−1pn	PROPN
ejpam-3742	237	5	dn−→	dn−→	PROPN
ejpam-3742	237	6	·	·	PUNCT
ejpam-3742	237	7	·	·	PUNCT
ejpam-3742	237	8	·	·	PUNCT
ejpam-3742	238	1	−→	−→	NOUN
ejpam-3742	238	2	s−1p2	s−1p2	NUM
ejpam-3742	238	3	d2−→	d2−→	PRON
ejpam-3742	238	4	s−1p1	s−1p1	VERB
ejpam-3742	238	5	d1−→	d1−→	NOUN
ejpam-3742	238	6	s−1p0	s−1p0	NOUN
ejpam-3742	238	7	ε−→	ε−→	NOUN
ejpam-3742	238	8	s−1b	s−1b	ADV
ejpam-3742	238	9	−→	−→	NOUN
ejpam-3742	238	10	0	0	NUM
ejpam-3742	238	11	be	be	AUX
ejpam-3742	238	12	a	a	DET
ejpam-3742	238	13	projective	projective	ADJ
ejpam-3742	238	14	resolution	resolution	NOUN
ejpam-3742	238	15	of	of	ADP
ejpam-3742	238	16	s−1b	s−1b	PROPN
ejpam-3742	238	17	.	.	PUNCT
ejpam-3742	239	1	pose	pose	VERB
ejpam-3742	239	2	k0	k0	PROPN
ejpam-3742	239	3	=	=	PROPN
ejpam-3742	239	4	kerε	kerε	PROPN
ejpam-3742	239	5	and	and	CCONJ
ejpam-3742	239	6	kn	kn	PROPN
ejpam-3742	239	7	=	=	PROPN
ejpam-3742	239	8	kerdn	kerdn	NOUN
ejpam-3742	239	9	,	,	PUNCT
ejpam-3742	239	10	∀	∀	X
ejpam-3742	239	11	n	n	PRON
ejpam-3742	239	12	≥	≥	NOUN
ejpam-3742	239	13	1	1	NUM
ejpam-3742	239	14	.	.	PUNCT
ejpam-3742	240	1	by	by	ADP
ejpam-3742	240	2	the	the	DET
ejpam-3742	240	3	proposition	proposition	NOUN
ejpam-3742	240	4	3	3	NUM
ejpam-3742	240	5	we	we	PRON
ejpam-3742	240	6	have	have	VERB
ejpam-3742	240	7	:	:	PUNCT
ejpam-3742	240	8	tors	tor	NOUN
ejpam-3742	240	9	−1a	−1a	PUNCT
ejpam-3742	240	10	n+1	n+1	PROPN
ejpam-3742	240	11	(	(	PUNCT
ejpam-3742	240	12	-	-	INTJ
ejpam-3742	240	13	,	,	PUNCT
ejpam-3742	240	14	s−1b	s−1b	ADJ
ejpam-3742	240	15	)	)	PUNCT
ejpam-3742	240	16	and	and	CCONJ
ejpam-3742	240	17	tors	tor	NOUN
ejpam-3742	240	18	−1a	−1a	NOUN
ejpam-3742	240	19	1	1	NUM
ejpam-3742	240	20	(	(	PUNCT
ejpam-3742	240	21	-,kn−1	-,kn−1	PROPN
ejpam-3742	240	22	)	)	PUNCT
ejpam-3742	240	23	are	be	AUX
ejpam-3742	240	24	naturally	naturally	ADV
ejpam-3742	240	25	isomorphic	isomorphic	ADJ
ejpam-3742	240	26	functors	functor	NOUN
ejpam-3742	240	27	.	.	PUNCT
ejpam-3742	241	1	êxt	êxt	NOUN
ejpam-3742	241	2	n+1	n+1	NUM
ejpam-3742	241	3	s−1a(-	s−1a(-	NOUN
ejpam-3742	241	4	,	,	PUNCT
ejpam-3742	241	5	s−1b)o	s−1b)o	VERB
ejpam-3742	241	6	and	and	CCONJ
ejpam-3742	241	7	êxt	êxt	NOUN
ejpam-3742	241	8	1	1	NUM
ejpam-3742	241	9	s−1a(-,kn−1	s−1a(-,kn−1	NUM
ejpam-3742	241	10	)	)	PUNCT
ejpam-3742	242	1	o	o	NOUN
ejpam-3742	242	2	are	be	AUX
ejpam-3742	242	3	naturally	naturally	ADV
ejpam-3742	242	4	isomorphic	isomorphic	ADJ
ejpam-3742	242	5	functors	functor	NOUN
ejpam-3742	242	6	.	.	PUNCT
ejpam-3742	243	1	according	accord	VERB
ejpam-3742	243	2	to	to	ADP
ejpam-3742	243	3	the	the	DET
ejpam-3742	243	4	inductive	inductive	ADJ
ejpam-3742	243	5	hypothesis	hypothesis	NOUN
ejpam-3742	243	6	,	,	PUNCT
ejpam-3742	243	7	the	the	DET
ejpam-3742	243	8	functors	functors	PROPN
ejpam-3742	243	9	tors	tor	NOUN
ejpam-3742	243	10	−1a	−1a	SYM
ejpam-3742	243	11	1	1	NUM
ejpam-3742	243	12	(	(	PUNCT
ejpam-3742	243	13	-,kn−1	-,kn−1	PROPN
ejpam-3742	243	14	)	)	PUNCT
ejpam-3742	243	15	and	and	CCONJ
ejpam-3742	243	16	êxt	êxt	NOUN
ejpam-3742	243	17	1	1	NUM
ejpam-3742	243	18	s−1a(-,kn−1	s−1a(-,kn−1	NUM
ejpam-3742	243	19	)	)	PUNCT
ejpam-3742	243	20	o	o	NOUN
ejpam-3742	243	21	are	be	AUX
ejpam-3742	243	22	adjoint	adjoint	ADJ
ejpam-3742	243	23	.	.	PUNCT
ejpam-3742	244	1	so	so	ADV
ejpam-3742	244	2	we	we	PRON
ejpam-3742	244	3	have	have	VERB
ejpam-3742	244	4	êxt	êxt	NOUN
ejpam-3742	244	5	1	1	NUM
ejpam-3742	244	6	s−1a(-,kn−1	s−1a(-,kn−1	NUM
ejpam-3742	244	7	)	)	PUNCT
ejpam-3742	244	8	o	o	NOUN
ejpam-3742	244	9	and	and	CCONJ
ejpam-3742	244	10	tors	tor	NOUN
ejpam-3742	244	11	−1a	−1a	NOUN
ejpam-3742	244	12	1	1	NUM
ejpam-3742	244	13	(	(	PUNCT
ejpam-3742	244	14	-,kn−1	-,kn−1	PROPN
ejpam-3742	244	15	)	)	PUNCT
ejpam-3742	244	16	which	which	PRON
ejpam-3742	244	17	adjoint	adjoint	VERB
ejpam-3742	244	18	,	,	PUNCT
ejpam-3742	244	19	also	also	ADV
ejpam-3742	244	20	tors	tor	NOUN
ejpam-3742	245	1	−1a	−1a	PROPN
ejpam-3742	245	2	1	1	NUM
ejpam-3742	245	3	(	(	PUNCT
ejpam-3742	245	4	-,kn−1	-,kn−1	PROPN
ejpam-3742	245	5	)	)	PUNCT
ejpam-3742	245	6	and	and	CCONJ
ejpam-3742	245	7	tors	tor	NOUN
ejpam-3742	245	8	−1a	−1a	PUNCT
ejpam-3742	245	9	n+1	n+1	PROPN
ejpam-3742	245	10	(	(	PUNCT
ejpam-3742	245	11	-	-	INTJ
ejpam-3742	245	12	,	,	PUNCT
ejpam-3742	245	13	s−1b	s−1b	X
ejpam-3742	245	14	)	)	PUNCT
ejpam-3742	245	15	are	be	AUX
ejpam-3742	245	16	naturally	naturally	ADV
ejpam-3742	245	17	isomorphic	isomorphic	ADJ
ejpam-3742	245	18	functors	functor	NOUN
ejpam-3742	245	19	,	,	PUNCT
ejpam-3742	245	20	so	so	ADV
ejpam-3742	245	21	by	by	ADP
ejpam-3742	245	22	the	the	DET
ejpam-3742	245	23	proposition	proposition	NOUN
ejpam-3742	245	24	2	2	NUM
ejpam-3742	245	25	the	the	DET
ejpam-3742	245	26	functors	functors	PROPN
ejpam-3742	245	27	êxt	êxt	NOUN
ejpam-3742	245	28	1	1	NUM
ejpam-3742	245	29	s−1a(-,kn−1	s−1a(-,kn−1	NUM
ejpam-3742	245	30	)	)	PUNCT
ejpam-3742	246	1	o	o	NOUN
ejpam-3742	246	2	and	and	CCONJ
ejpam-3742	246	3	tors	tor	NOUN
ejpam-3742	246	4	−1a	−1a	SYM
ejpam-3742	246	5	n+1	n+1	PROPN
ejpam-3742	246	6	(	(	PUNCT
ejpam-3742	246	7	-	-	INTJ
ejpam-3742	246	8	,	,	PUNCT
ejpam-3742	246	9	s−1b	s−1b	X
ejpam-3742	246	10	)	)	PUNCT
ejpam-3742	246	11	are	be	AUX
ejpam-3742	246	12	adjoint	adjoint	ADJ
ejpam-3742	246	13	.	.	PUNCT
ejpam-3742	247	1	so	so	ADV
ejpam-3742	247	2	we	we	PRON
ejpam-3742	247	3	have	have	VERB
ejpam-3742	247	4	tors	tor	NOUN
ejpam-3742	247	5	−1a	−1a	PUNCT
ejpam-3742	247	6	n+1	n+1	PROPN
ejpam-3742	247	7	(	(	PUNCT
ejpam-3742	247	8	-	-	INTJ
ejpam-3742	247	9	,	,	PUNCT
ejpam-3742	247	10	s−1b	s−1b	X
ejpam-3742	247	11	)	)	PUNCT
ejpam-3742	247	12	and	and	CCONJ
ejpam-3742	247	13	êxt	êxt	NOUN
ejpam-3742	247	14	1	1	NUM
ejpam-3742	247	15	s−1a(-,kn−1	s−1a(-,kn−1	NUM
ejpam-3742	247	16	)	)	PUNCT
ejpam-3742	247	17	o	o	NOUN
ejpam-3742	247	18	which	which	PRON
ejpam-3742	247	19	are	be	AUX
ejpam-3742	247	20	adjoint	adjoint	NOUN
ejpam-3742	247	21	,	,	PUNCT
ejpam-3742	247	22	also	also	ADV
ejpam-3742	247	23	êxt	êxt	NOUN
ejpam-3742	247	24	1	1	NUM
ejpam-3742	247	25	s−1a(-,kn−1	s−1a(-,kn−1	NUM
ejpam-3742	247	26	)	)	PUNCT
ejpam-3742	247	27	o	o	NOUN
ejpam-3742	247	28	and	and	CCONJ
ejpam-3742	247	29	êxt	êxt	NOUN
ejpam-3742	247	30	n+1	n+1	NUM
ejpam-3742	247	31	s−1a(-	s−1a(-	NOUN
ejpam-3742	247	32	,	,	PUNCT
ejpam-3742	247	33	s−1b)o	s−1b)o	VERB
ejpam-3742	247	34	are	be	AUX
ejpam-3742	247	35	naturally	naturally	ADV
ejpam-3742	247	36	isomorphic	isomorphic	ADJ
ejpam-3742	247	37	functors	functor	NOUN
ejpam-3742	247	38	,	,	PUNCT
ejpam-3742	247	39	so	so	ADV
ejpam-3742	247	40	by	by	ADP
ejpam-3742	247	41	the	the	DET
ejpam-3742	247	42	proposition	proposition	NOUN
ejpam-3742	247	43	2	2	NUM
ejpam-3742	247	44	the	the	DET
ejpam-3742	247	45	functors	functors	PROPN
ejpam-3742	247	46	tors	tor	NOUN
ejpam-3742	247	47	−1a	−1a	SYM
ejpam-3742	247	48	n+1	n+1	PROPN
ejpam-3742	247	49	(	(	PUNCT
ejpam-3742	247	50	-	-	INTJ
ejpam-3742	247	51	,	,	PUNCT
ejpam-3742	247	52	s−1b	s−1b	X
ejpam-3742	247	53	)	)	PUNCT
ejpam-3742	247	54	and	and	CCONJ
ejpam-3742	247	55	êxt	êxt	NOUN
ejpam-3742	247	56	n+1	n+1	NUM
ejpam-3742	247	57	s−1a(-	s−1a(-	NOUN
ejpam-3742	247	58	,	,	PUNCT
ejpam-3742	247	59	s−1b)o	s−1b)o	VERB
ejpam-3742	247	60	are	be	AUX
ejpam-3742	247	61	adjoint	adjoint	NOUN
ejpam-3742	247	62	.	.	PUNCT
ejpam-3742	248	1	hence	hence	ADV
ejpam-3742	248	2	,	,	PUNCT
ejpam-3742	248	3	the	the	DET
ejpam-3742	248	4	functors	functors	PROPN
ejpam-3742	248	5	tors	tor	NOUN
ejpam-3742	248	6	−1a	−1a	PUNCT
ejpam-3742	248	7	n	n	PROPN
ejpam-3742	248	8	(	(	PUNCT
ejpam-3742	248	9	-	-	INTJ
ejpam-3742	248	10	,	,	PUNCT
ejpam-3742	248	11	s−1b	s−1b	X
ejpam-3742	248	12	)	)	PUNCT
ejpam-3742	248	13	and	and	CCONJ
ejpam-3742	248	14	êxt	êxt	NOUN
ejpam-3742	248	15	n	n	PRON
ejpam-3742	248	16	s−1a(-	s−1a(-	NOUN
ejpam-3742	248	17	,	,	PUNCT
ejpam-3742	248	18	s−1b)o	s−1b)o	VERB
ejpam-3742	248	19	are	be	AUX
ejpam-3742	248	20	adjoint	adjoint	VERB
ejpam-3742	248	21	for	for	ADP
ejpam-3742	248	22	all	all	DET
ejpam-3742	248	23	n	n	PRON
ejpam-3742	248	24	≥	≥	NOUN
ejpam-3742	248	25	0	0	NUM
ejpam-3742	248	26	.	.	PUNCT
ejpam-3742	249	1	corollary	corollary	ADJ
ejpam-3742	249	2	4	4	NUM
ejpam-3742	249	3	.	.	PUNCT
ejpam-3742	249	4	let	let	VERB
ejpam-3742	249	5	a	a	PRON
ejpam-3742	249	6	be	be	AUX
ejpam-3742	249	7	a	a	DET
ejpam-3742	249	8	duo	duo	NOUN
ejpam-3742	249	9	ring	ring	NOUN
ejpam-3742	249	10	,	,	PUNCT
ejpam-3742	249	11	p	p	X
ejpam-3742	249	12	a	a	DET
ejpam-3742	249	13	prime	prime	ADJ
ejpam-3742	249	14	ideal	ideal	NOUN
ejpam-3742	249	15	of	of	ADP
ejpam-3742	249	16	a	a	DET
ejpam-3742	249	17	,	,	PUNCT
ejpam-3742	249	18	s	s	PART
ejpam-3742	249	19	=	=	PUNCT
ejpam-3742	249	20	(	(	PUNCT
ejpam-3742	249	21	a	a	NOUN
ejpam-3742	249	22	-	-	PUNCT
ejpam-3742	249	23	p	p	NOUN
ejpam-3742	249	24	)	)	PUNCT
ejpam-3742	249	25	∩	∩	ADJ
ejpam-3742	249	26	z(a	z(a	NOUN
ejpam-3742	249	27	)	)	PUNCT
ejpam-3742	249	28	and	and	CCONJ
ejpam-3742	249	29	b	b	X
ejpam-3742	249	30	an	an	DET
ejpam-3742	249	31	(	(	PUNCT
ejpam-3742	249	32	a	a	NOUN
ejpam-3742	249	33	-	-	PUNCT
ejpam-3742	249	34	a)-bialgebra	a)-bialgebra	NOUN
ejpam-3742	249	35	.	.	PUNCT
ejpam-3742	250	1	then	then	ADV
ejpam-3742	250	2	tors	tor	VERB
ejpam-3742	250	3	−1a	−1a	PUNCT
ejpam-3742	250	4	n	n	PROPN
ejpam-3742	250	5	(	(	PUNCT
ejpam-3742	250	6	-	-	INTJ
ejpam-3742	250	7	,	,	PUNCT
ejpam-3742	250	8	s−1b	s−1b	PROPN
ejpam-3742	250	9	)	)	PUNCT
ejpam-3742	250	10	:	:	PUNCT
ejpam-3742	250	11	alg	alg	PROPN
ejpam-3742	250	12	-	-	PUNCT
ejpam-3742	250	13	s−1a	s−1a	PROPN
ejpam-3742	250	14	�	�	PROPN
ejpam-3742	250	15	s−1a	s−1a	NOUN
ejpam-3742	250	16	-	-	PUNCT
ejpam-3742	250	17	modo	modo	NOUN
ejpam-3742	250	18	:	:	PUNCT
ejpam-3742	250	19	êxt	êxt	NOUN
ejpam-3742	250	20	n	n	PRON
ejpam-3742	250	21	s−1a(-	s−1a(-	NOUN
ejpam-3742	250	22	,	,	PUNCT
ejpam-3742	250	23	s−1b)o	s−1b)o	VERB
ejpam-3742	250	24	is	be	AUX
ejpam-3742	250	25	an	an	DET
ejpam-3742	250	26	adjunction	adjunction	NOUN
ejpam-3742	250	27	.	.	PUNCT
ejpam-3742	251	1	references	reference	NOUN
ejpam-3742	251	2	482	482	NUM
ejpam-3742	251	3	proof	proof	NOUN
ejpam-3742	251	4	.	.	PUNCT
ejpam-3742	252	1	since	since	SCONJ
ejpam-3742	252	2	a	a	PRON
ejpam-3742	252	3	is	be	AUX
ejpam-3742	252	4	a	a	DET
ejpam-3742	252	5	duo	duo	NOUN
ejpam-3742	252	6	ring	ring	NOUN
ejpam-3742	252	7	,	,	PUNCT
ejpam-3742	252	8	then	then	ADV
ejpam-3742	252	9	a	a	X
ejpam-3742	252	10	-	-	PUNCT
ejpam-3742	252	11	p	p	NOUN
ejpam-3742	252	12	is	be	AUX
ejpam-3742	252	13	a	a	DET
ejpam-3742	252	14	multiplicatively	multiplicatively	ADV
ejpam-3742	252	15	closed	close	VERB
ejpam-3742	252	16	subset	subset	NOUN
ejpam-3742	252	17	of	of	ADP
ejpam-3742	252	18	a	a	PRON
ejpam-3742	252	19	,	,	PUNCT
ejpam-3742	252	20	so	so	NOUN
ejpam-3742	252	21	s	s	PART
ejpam-3742	252	22	=	=	PUNCT
ejpam-3742	252	23	(	(	PUNCT
ejpam-3742	252	24	a	a	NOUN
ejpam-3742	252	25	-	-	PUNCT
ejpam-3742	252	26	p	p	NOUN
ejpam-3742	252	27	)	)	PUNCT
ejpam-3742	252	28	∩	∩	ADJ
ejpam-3742	252	29	z(a	z(a	NOUN
ejpam-3742	252	30	)	)	PUNCT
ejpam-3742	252	31	is	be	AUX
ejpam-3742	252	32	a	a	DET
ejpam-3742	252	33	central	central	ADJ
ejpam-3742	252	34	multiplicatively	multiplicatively	ADV
ejpam-3742	252	35	closed	close	VERB
ejpam-3742	252	36	subset	subset	NOUN
ejpam-3742	252	37	of	of	ADP
ejpam-3742	252	38	a.	a.	NOUN
ejpam-3742	252	39	so	so	ADV
ejpam-3742	252	40	by	by	ADP
ejpam-3742	252	41	the	the	DET
ejpam-3742	252	42	previous	previous	ADJ
ejpam-3742	252	43	theorem	theorem	ADJ
ejpam-3742	252	44	tors	tor	NOUN
ejpam-3742	252	45	−1a	−1a	PUNCT
ejpam-3742	252	46	n	n	PROPN
ejpam-3742	252	47	(	(	PUNCT
ejpam-3742	252	48	-	-	INTJ
ejpam-3742	252	49	,	,	PUNCT
ejpam-3742	252	50	s−1b	s−1b	X
ejpam-3742	252	51	)	)	PUNCT
ejpam-3742	252	52	is	be	AUX
ejpam-3742	252	53	a	a	DET
ejpam-3742	252	54	left	left	ADJ
ejpam-3742	252	55	adjoint	adjoint	NOUN
ejpam-3742	252	56	to	to	ADP
ejpam-3742	252	57	êxt	êxt	NOUN
ejpam-3742	252	58	n	n	PRON
ejpam-3742	252	59	s−1a(-	s−1a(-	NOUN
ejpam-3742	252	60	,	,	PUNCT
ejpam-3742	252	61	s−1b)o	s−1b)o	VERB
ejpam-3742	252	62	.	.	PUNCT
ejpam-3742	253	1	corollary	corollary	ADJ
ejpam-3742	253	2	5	5	NUM
ejpam-3742	253	3	.	.	PUNCT
ejpam-3742	254	1	let	let	VERB
ejpam-3742	254	2	a	a	PRON
ejpam-3742	254	3	be	be	AUX
ejpam-3742	254	4	a	a	DET
ejpam-3742	254	5	duo	duo	NOUN
ejpam-3742	254	6	ring	ring	NOUN
ejpam-3742	254	7	,	,	PUNCT
ejpam-3742	254	8	p	p	X
ejpam-3742	254	9	a	a	DET
ejpam-3742	254	10	prime	prime	ADJ
ejpam-3742	254	11	ideal	ideal	NOUN
ejpam-3742	254	12	of	of	ADP
ejpam-3742	254	13	a	a	PRON
ejpam-3742	254	14	,	,	PUNCT
ejpam-3742	254	15	sr	sr	PROPN
ejpam-3742	254	16	the	the	DET
ejpam-3742	254	17	set	set	NOUN
ejpam-3742	254	18	of	of	ADP
ejpam-3742	254	19	regular	regular	ADJ
ejpam-3742	254	20	elements	element	NOUN
ejpam-3742	254	21	of	of	ADP
ejpam-3742	254	22	a	a	DET
ejpam-3742	254	23	-	-	PUNCT
ejpam-3742	254	24	p	p	NOUN
ejpam-3742	254	25	,	,	PUNCT
ejpam-3742	254	26	s	s	PART
ejpam-3742	254	27	=	=	X
ejpam-3742	254	28	sr	sr	PROPN
ejpam-3742	254	29	∩	∩	NOUN
ejpam-3742	254	30	z(a	z(a	NOUN
ejpam-3742	254	31	)	)	PUNCT
ejpam-3742	254	32	and	and	CCONJ
ejpam-3742	254	33	b	b	X
ejpam-3742	254	34	an	an	DET
ejpam-3742	254	35	(	(	PUNCT
ejpam-3742	254	36	a	a	NOUN
ejpam-3742	254	37	-	-	PUNCT
ejpam-3742	254	38	a)-bialgebra	a)-bialgebra	NOUN
ejpam-3742	254	39	.	.	PUNCT
ejpam-3742	255	1	then	then	ADV
ejpam-3742	255	2	tors	tor	VERB
ejpam-3742	255	3	−1a	−1a	PUNCT
ejpam-3742	255	4	n	n	PROPN
ejpam-3742	255	5	(	(	PUNCT
ejpam-3742	255	6	-	-	INTJ
ejpam-3742	255	7	,	,	PUNCT
ejpam-3742	255	8	s−1b	s−1b	PROPN
ejpam-3742	255	9	)	)	PUNCT
ejpam-3742	255	10	:	:	PUNCT
ejpam-3742	255	11	alg	alg	PROPN
ejpam-3742	255	12	-	-	PUNCT
ejpam-3742	255	13	s−1a	s−1a	PROPN
ejpam-3742	255	14	�	�	PROPN
ejpam-3742	255	15	s−1a	s−1a	NOUN
ejpam-3742	255	16	-	-	PUNCT
ejpam-3742	255	17	modo	modo	NOUN
ejpam-3742	255	18	:	:	PUNCT
ejpam-3742	255	19	êxt	êxt	NOUN
ejpam-3742	255	20	n	n	PRON
ejpam-3742	255	21	s−1a(-	s−1a(-	NOUN
ejpam-3742	255	22	,	,	PUNCT
ejpam-3742	255	23	s−1b)o	s−1b)o	VERB
ejpam-3742	255	24	is	be	AUX
ejpam-3742	255	25	an	an	DET
ejpam-3742	255	26	adjunction	adjunction	NOUN
ejpam-3742	255	27	.	.	PUNCT
ejpam-3742	256	1	proof	proof	NOUN
ejpam-3742	256	2	.	.	PUNCT
ejpam-3742	257	1	since	since	SCONJ
ejpam-3742	257	2	a	a	PRON
ejpam-3742	257	3	is	be	AUX
ejpam-3742	257	4	a	a	DET
ejpam-3742	257	5	duo	duo	NOUN
ejpam-3742	257	6	ring	ring	NOUN
ejpam-3742	257	7	,	,	PUNCT
ejpam-3742	257	8	then	then	ADV
ejpam-3742	257	9	the	the	DET
ejpam-3742	257	10	set	set	NOUN
ejpam-3742	257	11	of	of	ADP
ejpam-3742	257	12	regular	regular	ADJ
ejpam-3742	257	13	elements	element	NOUN
ejpam-3742	257	14	sr	sr	PROPN
ejpam-3742	257	15	of	of	ADP
ejpam-3742	257	16	a	a	PROPN
ejpam-3742	257	17	-	-	PUNCT
ejpam-3742	257	18	p	p	NOUN
ejpam-3742	257	19	is	be	AUX
ejpam-3742	257	20	a	a	DET
ejpam-3742	257	21	multiplicatively	multiplicatively	ADV
ejpam-3742	257	22	closed	close	VERB
ejpam-3742	257	23	subset	subset	NOUN
ejpam-3742	257	24	of	of	ADP
ejpam-3742	257	25	a	a	DET
ejpam-3742	257	26	,	,	PUNCT
ejpam-3742	257	27	so	so	PROPN
ejpam-3742	257	28	s	s	PART
ejpam-3742	257	29	=	=	PROPN
ejpam-3742	257	30	sr	sr	PROPN
ejpam-3742	257	31	∩z(a	∩z(a	PROPN
ejpam-3742	257	32	)	)	PUNCT
ejpam-3742	257	33	is	be	AUX
ejpam-3742	257	34	a	a	DET
ejpam-3742	257	35	central	central	ADJ
ejpam-3742	257	36	multiplicatively	multiplicatively	ADV
ejpam-3742	257	37	closed	close	VERB
ejpam-3742	257	38	subset	subset	NOUN
ejpam-3742	257	39	of	of	ADP
ejpam-3742	257	40	a.	a.	NOUN
ejpam-3742	257	41	so	so	ADV
ejpam-3742	257	42	by	by	ADP
ejpam-3742	257	43	the	the	DET
ejpam-3742	257	44	previous	previous	ADJ
ejpam-3742	257	45	theorem	theorem	ADJ
ejpam-3742	257	46	tors	tor	NOUN
ejpam-3742	257	47	−1a	−1a	PUNCT
ejpam-3742	257	48	n	n	PROPN
ejpam-3742	257	49	(	(	PUNCT
ejpam-3742	257	50	-	-	INTJ
ejpam-3742	257	51	,	,	PUNCT
ejpam-3742	257	52	s−1b	s−1b	X
ejpam-3742	257	53	)	)	PUNCT
ejpam-3742	257	54	is	be	AUX
ejpam-3742	257	55	a	a	DET
ejpam-3742	257	56	left	left	ADJ
ejpam-3742	257	57	adjoint	adjoint	NOUN
ejpam-3742	257	58	to	to	ADP
ejpam-3742	257	59	êxt	êxt	NOUN
ejpam-3742	257	60	n	n	PRON
ejpam-3742	257	61	s−1a(-	s−1a(-	NOUN
ejpam-3742	257	62	,	,	PUNCT
ejpam-3742	257	63	s−1b)o	s−1b)o	VERB
ejpam-3742	257	64	.	.	PUNCT
ejpam-3742	258	1	acknowledgements	acknowledgement	NOUN
ejpam-3742	258	2	this	this	DET
ejpam-3742	258	3	work	work	NOUN
ejpam-3742	258	4	was	be	AUX
ejpam-3742	258	5	supported	support	VERB
ejpam-3742	258	6	by	by	ADP
ejpam-3742	258	7	the	the	DET
ejpam-3742	258	8	ufr	ufr	NOUN
ejpam-3742	258	9	-	-	PUNCT
ejpam-3742	258	10	sat	sit	VERB
ejpam-3742	258	11	.	.	PUNCT
ejpam-3742	259	1	references	reference	NOUN
ejpam-3742	259	2	[	[	X
ejpam-3742	259	3	1	1	NUM
ejpam-3742	259	4	]	]	X
ejpam-3742	259	5	m	m	VERB
ejpam-3742	259	6	f	f	NOUN
ejpam-3742	259	7	atiyah	atiyah	NOUN
ejpam-3742	259	8	and	and	CCONJ
ejpam-3742	259	9	i	i	PRON
ejpam-3742	259	10	g	g	PROPN
ejpam-3742	259	11	macdonald	macdonald	PROPN
ejpam-3742	259	12	.	.	PUNCT
ejpam-3742	260	1	introduction	introduction	NOUN
ejpam-3742	260	2	to	to	ADP
ejpam-3742	260	3	commutative	commutative	ADJ
ejpam-3742	260	4	algebra	algebra	NOUN
ejpam-3742	260	5	.	.	PUNCT
ejpam-3742	261	1	addisonwesley	addisonwesley	ADJ
ejpam-3742	261	2	publishing	publishing	NOUN
ejpam-3742	261	3	company	company	NOUN
ejpam-3742	261	4	,	,	PUNCT
ejpam-3742	261	5	university	university	NOUN
ejpam-3742	261	6	of	of	ADP
ejpam-3742	261	7	oxford	oxford	PROPN
ejpam-3742	261	8	.	.	PUNCT
ejpam-3742	262	1	[	[	X
ejpam-3742	262	2	2	2	NUM
ejpam-3742	262	3	]	]	X
ejpam-3742	262	4	d	d	X
ejpam-3742	262	5	faye	faye	PROPN
ejpam-3742	262	6	m	m	PROPN
ejpam-3742	262	7	f	f	PROPN
ejpam-3742	262	8	maaouia	maaouia	PROPN
ejpam-3742	262	9	and	and	CCONJ
ejpam-3742	262	10	m	m	NOUN
ejpam-3742	262	11	sanghare	sanghare	ADJ
ejpam-3742	262	12	.	.	PUNCT
ejpam-3742	263	1	localization	localization	NOUN
ejpam-3742	263	2	in	in	ADP
ejpam-3742	263	3	a	a	DET
ejpam-3742	263	4	duo	duo	NOUN
ejpam-3742	263	5	-	-	PUNCT
ejpam-3742	263	6	ring	ring	NOUN
ejpam-3742	263	7	and	and	CCONJ
ejpam-3742	263	8	polynomials	polynomial	VERB
ejpam-3742	263	9	algebra	algebra	NOUN
ejpam-3742	263	10	.	.	PUNCT
ejpam-3742	264	1	springer	springer	NOUN
ejpam-3742	264	2	international	international	PROPN
ejpam-3742	264	3	publishing	publishing	PROPN
ejpam-3742	264	4	switzerland	switzerland	PROPN
ejpam-3742	264	5	,	,	PUNCT
ejpam-3742	264	6	2016	2016	NUM
ejpam-3742	264	7	.	.	PUNCT
ejpam-3742	265	1	[	[	X
ejpam-3742	265	2	3	3	X
ejpam-3742	265	3	]	]	PUNCT
ejpam-3742	265	4	m	m	VERB
ejpam-3742	265	5	maaouia	maaouia	NOUN
ejpam-3742	265	6	m	m	NOUN
ejpam-3742	265	7	thiaw	thiaw	NOUN
ejpam-3742	265	8	and	and	CCONJ
ejpam-3742	265	9	m	m	AUX
ejpam-3742	265	10	sanghare	sanghare	ADJ
ejpam-3742	265	11	.	.	PUNCT
ejpam-3742	266	1	functors	functor	VERB
ejpam-3742	266	2	s−1	s−1	PROPN
ejpam-3742	266	3	(	(	PUNCT
ejpam-3742	266	4	)	)	PUNCT
ejpam-3742	266	5	,	,	PUNCT
ejpam-3742	266	6	homa(-,b	homa(-,b	NOUN
ejpam-3742	266	7	)	)	PUNCT
ejpam-3742	266	8	,	,	PUNCT
ejpam-3742	266	9	⊗a	⊗a	NOUN
ejpam-3742	266	10	b	b	PROPN
ejpam-3742	266	11	and	and	CCONJ
ejpam-3742	266	12	extna(-,b	extna(-,b	ADJ
ejpam-3742	266	13	)	)	PUNCT
ejpam-3742	266	14	in	in	ADP
ejpam-3742	266	15	the	the	DET
ejpam-3742	266	16	category	category	NOUN
ejpam-3742	266	17	of	of	ADP
ejpam-3742	266	18	a	a	DET
ejpam-3742	266	19	-	-	PUNCT
ejpam-3742	266	20	alg	alg	PROPN
ejpam-3742	266	21	.	.	PUNCT
ejpam-3742	267	1	international	international	ADJ
ejpam-3742	267	2	journal	journal	PROPN
ejpam-3742	267	3	of	of	ADP
ejpam-3742	267	4	theoretical	theoretical	ADJ
ejpam-3742	267	5	and	and	CCONJ
ejpam-3742	267	6	applied	applied	ADJ
ejpam-3742	267	7	mathematics	mathematic	NOUN
ejpam-3742	267	8	,	,	PUNCT
ejpam-3742	267	9	vol	vol	NOUN
ejpam-3742	267	10	.	.	PROPN
ejpam-3742	267	11	5	5	NUM
ejpam-3742	267	12	,	,	PUNCT
ejpam-3742	267	13	no	no	INTJ
ejpam-3742	267	14	.	.	NOUN
ejpam-3742	267	15	1	1	NUM
ejpam-3742	267	16	,	,	PUNCT
ejpam-3742	267	17	2019,:1–9	2019,:1–9	NUM
ejpam-3742	267	18	,	,	PUNCT
ejpam-3742	267	19	1987	1987	NUM
ejpam-3742	267	20	.	.	PUNCT
ejpam-3742	268	1	[	[	X
ejpam-3742	268	2	4	4	NUM
ejpam-3742	268	3	]	]	PUNCT
ejpam-3742	268	4	m.	m.	NOUN
ejpam-3742	268	5	maaouia	maaouia	PROPN
ejpam-3742	268	6	and	and	CCONJ
ejpam-3742	268	7	m.	m.	NOUN
ejpam-3742	268	8	sanghare	sanghare	NOUN
ejpam-3742	268	9	.	.	PUNCT
ejpam-3742	269	1	module	module	NOUN
ejpam-3742	269	2	de	de	ADP
ejpam-3742	269	3	fraction	fraction	NOUN
ejpam-3742	269	4	-	-	PUNCT
ejpam-3742	269	5	sous	sous	ADJ
ejpam-3742	269	6	-	-	PUNCT
ejpam-3742	269	7	modules	module	NOUN
ejpam-3742	269	8	s	s	NOUN
ejpam-3742	269	9	-	-	NOUN
ejpam-3742	269	10	sature	sature	NOUN
ejpam-3742	269	11	et	et	NOUN
ejpam-3742	269	12	foncteur	foncteur	NOUN
ejpam-3742	269	13	s−1	s−1	PROPN
ejpam-3742	269	14	(	(	PUNCT
ejpam-3742	269	15	)	)	PUNCT
ejpam-3742	269	16	.	.	PUNCT
ejpam-3742	270	1	international	international	ADJ
ejpam-3742	270	2	journal	journal	PROPN
ejpam-3742	270	3	of	of	ADP
ejpam-3742	270	4	algebra	algebra	PROPN
ejpam-3742	270	5	,	,	PUNCT
ejpam-3742	270	6	16:0973–1768	16:0973–1768	NUM
ejpam-3742	270	7	,	,	PUNCT
ejpam-3742	270	8	2012	2012	NUM
ejpam-3742	270	9	.	.	PUNCT
ejpam-3742	271	1	[	[	X
ejpam-3742	271	2	5	5	NUM
ejpam-3742	271	3	]	]	X
ejpam-3742	271	4	m	m	PROPN
ejpam-3742	271	5	f	f	NOUN
ejpam-3742	271	6	maaouia	maaouia	PROPN
ejpam-3742	271	7	and	and	CCONJ
ejpam-3742	271	8	m	m	AUX
ejpam-3742	271	9	sanghare	sanghare	ADJ
ejpam-3742	271	10	.	.	PUNCT
ejpam-3742	272	1	localisation	localisation	NOUN
ejpam-3742	272	2	dans	dan	NOUN
ejpam-3742	272	3	les	les	VERB
ejpam-3742	272	4	duo	duo	NOUN
ejpam-3742	272	5	-	-	PUNCT
ejpam-3742	272	6	anneaux	anneaux	ADV
ejpam-3742	272	7	.	.	PUNCT
ejpam-3742	273	1	afrika	afrika	PROPN
ejpam-3742	273	2	mathematika	mathematika	NOUN
ejpam-3742	273	3	,	,	PUNCT
ejpam-3742	273	4	2009	2009	NUM
ejpam-3742	273	5	.	.	PUNCT
ejpam-3742	274	1	[	[	X
ejpam-3742	274	2	6	6	NUM
ejpam-3742	274	3	]	]	X
ejpam-3742	274	4	rotman	rotman	PROPN
ejpam-3742	274	5	.	.	PUNCT
ejpam-3742	275	1	advanced	advanced	ADJ
ejpam-3742	275	2	modern	modern	ADJ
ejpam-3742	275	3	algebra	algebra	NOUN
ejpam-3742	275	4	.	.	PUNCT
ejpam-3742	276	1	gsm	gsm	NOUN
ejpam-3742	276	2	vol.114	vol.114	NOUN
ejpam-3742	276	3	,	,	PUNCT
ejpam-3742	276	4	ams	am	NOUN
ejpam-3742	276	5	,	,	PUNCT
ejpam-3742	276	6	2010	2010	NUM
ejpam-3742	276	7	.	.	PUNCT
ejpam-3742	277	1	[	[	X
ejpam-3742	277	2	7	7	NUM
ejpam-3742	277	3	]	]	SYM
ejpam-3742	277	4	l	l	NOUN
ejpam-3742	277	5	hallw	hallw	NOUN
ejpam-3742	277	6	rower	rower	NOUN
ejpam-3742	277	7	.	.	PUNCT
ejpam-3742	278	1	ring	ring	NOUN
ejpam-3742	278	2	theory	theory	NOUN
ejpam-3742	278	3	.	.	PUNCT
ejpam-3742	279	1	academic	academic	ADJ
ejpam-3742	279	2	press	press	NOUN
ejpam-3742	279	3	,	,	PUNCT
ejpam-3742	279	4	1991	1991	NUM
ejpam-3742	279	5	.	.	PUNCT