id	sid	tid	token	lemma	pos
kh04dn4375v	1	1	factorization	factorization	PROPN
kh04dn4375v	1	2	algebras	algebra	NOUN
kh04dn4375v	1	3	are	be	AUX
kh04dn4375v	1	4	a	a	DET
kh04dn4375v	1	5	mathematical	mathematical	ADJ
kh04dn4375v	1	6	tool	tool	NOUN
kh04dn4375v	1	7	for	for	ADP
kh04dn4375v	1	8	modeling	model	VERB
kh04dn4375v	1	9	the	the	DET
kh04dn4375v	1	10	observables	observable	NOUN
kh04dn4375v	1	11	of	of	ADP
kh04dn4375v	1	12	field	field	NOUN
kh04dn4375v	1	13	theories	theory	NOUN
kh04dn4375v	1	14	.	.	PUNCT
kh04dn4375v	2	1	in	in	ADP
kh04dn4375v	2	2	this	this	DET
kh04dn4375v	2	3	dissertation	dissertation	NOUN
kh04dn4375v	2	4	,	,	PUNCT
kh04dn4375v	2	5	we	we	PRON
kh04dn4375v	2	6	consider	consider	VERB
kh04dn4375v	2	7	two	two	NUM
kh04dn4375v	2	8	particular	particular	ADJ
kh04dn4375v	2	9	types	type	NOUN
kh04dn4375v	2	10	of	of	ADP
kh04dn4375v	2	11	factorization	factorization	NOUN
kh04dn4375v	2	12	algebras	algebra	NOUN
kh04dn4375v	2	13	:	:	PUNCT
kh04dn4375v	2	14	g	g	NOUN
kh04dn4375v	2	15	-	-	PUNCT
kh04dn4375v	2	16	equivariant	equivariant	ADJ
kh04dn4375v	2	17	factorization	factorization	NOUN
kh04dn4375v	2	18	algebras	algebra	NOUN
kh04dn4375v	2	19	on	on	ADP
kh04dn4375v	2	20	a	a	DET
kh04dn4375v	2	21	model	model	NOUN
kh04dn4375v	2	22	space	space	NOUN
kh04dn4375v	2	23	m	m	NOUN
kh04dn4375v	2	24	,	,	PUNCT
kh04dn4375v	2	25	where	where	SCONJ
kh04dn4375v	2	26	g	g	PROPN
kh04dn4375v	2	27	is	be	AUX
kh04dn4375v	2	28	a	a	DET
kh04dn4375v	2	29	group	group	NOUN
kh04dn4375v	2	30	acting	act	VERB
kh04dn4375v	2	31	on	on	ADP
kh04dn4375v	2	32	m	m	NOUN
kh04dn4375v	2	33	;	;	PUNCT
kh04dn4375v	2	34	and	and	CCONJ
kh04dn4375v	2	35	factorization	factorization	NOUN
kh04dn4375v	2	36	algebras	algebra	NOUN
kh04dn4375v	2	37	on	on	ADP
kh04dn4375v	2	38	a	a	DET
kh04dn4375v	2	39	site	site	NOUN
kh04dn4375v	2	40	of	of	ADP
kh04dn4375v	2	41	manifolds	manifold	NOUN
kh04dn4375v	2	42	which	which	PRON
kh04dn4375v	2	43	locally	locally	ADV
kh04dn4375v	2	44	look	look	VERB
kh04dn4375v	2	45	like	like	ADP
kh04dn4375v	2	46	m	m	ADV
kh04dn4375v	2	47	and	and	CCONJ
kh04dn4375v	2	48	with	with	ADP
kh04dn4375v	2	49	geometric	geometric	ADJ
kh04dn4375v	2	50	structure	structure	NOUN
kh04dn4375v	2	51	encoded	encode	VERB
kh04dn4375v	2	52	by	by	ADP
kh04dn4375v	2	53	the	the	DET
kh04dn4375v	2	54	g	g	NOUN
kh04dn4375v	2	55	-	-	PUNCT
kh04dn4375v	2	56	action	action	NOUN
kh04dn4375v	2	57	.	.	PUNCT
kh04dn4375v	3	1	our	our	PRON
kh04dn4375v	3	2	main	main	ADJ
kh04dn4375v	3	3	result	result	NOUN
kh04dn4375v	3	4	is	be	AUX
kh04dn4375v	3	5	that	that	SCONJ
kh04dn4375v	3	6	the	the	DET
kh04dn4375v	3	7	categories	category	NOUN
kh04dn4375v	3	8	of	of	ADP
kh04dn4375v	3	9	these	these	DET
kh04dn4375v	3	10	factorization	factorization	NOUN
kh04dn4375v	3	11	algebras	algebra	NOUN
kh04dn4375v	3	12	are	be	AUX
kh04dn4375v	3	13	equivalent	equivalent	ADJ
kh04dn4375v	3	14	.	.	PUNCT
kh04dn4375v	4	1	to	to	PART
kh04dn4375v	4	2	show	show	VERB
kh04dn4375v	4	3	this	this	PRON
kh04dn4375v	4	4	,	,	PUNCT
kh04dn4375v	4	5	we	we	PRON
kh04dn4375v	4	6	formulate	formulate	VERB
kh04dn4375v	4	7	an	an	DET
kh04dn4375v	4	8	alternative	alternative	NOUN
kh04dn4375v	4	9	,	,	PUNCT
kh04dn4375v	4	10	categorical	categorical	ADJ
kh04dn4375v	4	11	description	description	NOUN
kh04dn4375v	4	12	of	of	ADP
kh04dn4375v	4	13	the	the	DET
kh04dn4375v	4	14	locality	locality	NOUN
kh04dn4375v	4	15	(	(	PUNCT
kh04dn4375v	4	16	or	or	CCONJ
kh04dn4375v	4	17	descent	descent	NOUN
kh04dn4375v	4	18	)	)	PUNCT
kh04dn4375v	4	19	condition	condition	NOUN
kh04dn4375v	4	20	that	that	PRON
kh04dn4375v	4	21	factorization	factorization	NOUN
kh04dn4375v	4	22	algebras	algebras	PROPN
kh04dn4375v	4	23	satisfy	satisfy	PROPN
kh04dn4375v	4	24	,	,	PUNCT
kh04dn4375v	4	25	and	and	CCONJ
kh04dn4375v	4	26	show	show	VERB
kh04dn4375v	4	27	that	that	SCONJ
kh04dn4375v	4	28	this	this	PRON
kh04dn4375v	4	29	agrees	agree	VERB
kh04dn4375v	4	30	with	with	ADP
kh04dn4375v	4	31	the	the	DET
kh04dn4375v	4	32	original	original	ADJ
kh04dn4375v	4	33	,	,	PUNCT
kh04dn4375v	4	34	more	more	ADV
kh04dn4375v	4	35	geometric	geometric	ADJ
kh04dn4375v	4	36	descent	descent	NOUN
kh04dn4375v	4	37	condition	condition	NOUN
kh04dn4375v	4	38	.	.	PUNCT
kh04dn4375v	5	1	we	we	PRON
kh04dn4375v	5	2	then	then	ADV
kh04dn4375v	5	3	generalize	generalize	VERB
kh04dn4375v	5	4	the	the	DET
kh04dn4375v	5	5	definition	definition	NOUN
kh04dn4375v	5	6	of	of	ADP
kh04dn4375v	5	7	factorization	factorization	NOUN
kh04dn4375v	5	8	algebras	algebra	NOUN
kh04dn4375v	5	9	to	to	ADP
kh04dn4375v	5	10	the	the	DET
kh04dn4375v	5	11	infinity	infinity	ADJ
kh04dn4375v	5	12	-	-	PUNCT
kh04dn4375v	5	13	operadic	operadic	ADJ
kh04dn4375v	5	14	setting	setting	NOUN
kh04dn4375v	5	15	,	,	PUNCT
kh04dn4375v	5	16	and	and	CCONJ
kh04dn4375v	5	17	utilize	utilize	VERB
kh04dn4375v	5	18	higher	high	ADJ
kh04dn4375v	5	19	algebraic	algebraic	ADJ
kh04dn4375v	5	20	techniques	technique	NOUN
kh04dn4375v	5	21	to	to	PART
kh04dn4375v	5	22	prove	prove	VERB
kh04dn4375v	5	23	the	the	DET
kh04dn4375v	5	24	comparison	comparison	NOUN
kh04dn4375v	5	25	result	result	NOUN
kh04dn4375v	5	26	.	.	PUNCT
kh04dn4375v	6	1	one	one	NUM
kh04dn4375v	6	2	of	of	ADP
kh04dn4375v	6	3	the	the	DET
kh04dn4375v	6	4	motivations	motivation	NOUN
kh04dn4375v	6	5	for	for	ADP
kh04dn4375v	6	6	this	this	DET
kh04dn4375v	6	7	new	new	ADJ
kh04dn4375v	6	8	infinity	infinity	ADJ
kh04dn4375v	6	9	-	-	PUNCT
kh04dn4375v	6	10	operadic	operadic	ADJ
kh04dn4375v	6	11	perspective	perspective	NOUN
kh04dn4375v	6	12	is	be	AUX
kh04dn4375v	6	13	the	the	DET
kh04dn4375v	6	14	ability	ability	NOUN
kh04dn4375v	6	15	to	to	PART
kh04dn4375v	6	16	use	use	VERB
kh04dn4375v	6	17	these	these	DET
kh04dn4375v	6	18	general	general	ADJ
kh04dn4375v	6	19	results	result	NOUN
kh04dn4375v	6	20	in	in	ADP
kh04dn4375v	6	21	future	future	ADJ
kh04dn4375v	6	22	work	work	NOUN
kh04dn4375v	6	23	involving	involve	VERB
kh04dn4375v	6	24	parameterized	parameterize	VERB
kh04dn4375v	6	25	families	family	NOUN
kh04dn4375v	6	26	of	of	ADP
kh04dn4375v	6	27	factorization	factorization	NOUN
kh04dn4375v	6	28	algebras	algebra	NOUN
kh04dn4375v	6	29	.	.	PUNCT