Galois coverings, morita equivalence and smash extensions of categories over a field

Algebras over a field k generalize to categories over k in order to considers Galois coverings. Two theories presenting analogies, namely smash extensions and Galois coverings with respect to a finite group are known to be different. However we prove in this paper that they are Morita equivalent. Fo...

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Detalles Bibliográficos
Autor principal:	Solotar, Andrea Leonor
Publicado:	2006
Materias:	Completion Galois covering Hopf algebra K-category Karoubianisation Morita theory Smash product
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14310635_v11_n1_p143_Cibils http://hdl.handle.net/20.500.12110/paper_14310635_v11_n1_p143_Cibils
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_14310635_v11_n1_p143_Cibils
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spelling	paper:paper_14310635_v11_n1_p143_Cibils2023-06-08T16:14:03Z Galois coverings, morita equivalence and smash extensions of categories over a field Solotar, Andrea Leonor Completion Galois covering Hopf algebra K-category Karoubianisation Morita theory Smash product Algebras over a field k generalize to categories over k in order to considers Galois coverings. Two theories presenting analogies, namely smash extensions and Galois coverings with respect to a finite group are known to be different. However we prove in this paper that they are Morita equivalent. For this purpose we need to describe explicit processes providing Morita equivalences of categories which we call contraction and expansion. A structure theorem is obtained: composition of these processes provides any Morita equivalence up to equivalence, a result which is related with the karoubianisation (or idempotent completion) and additivisation of a k-category. Fil:Solotar, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2006 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14310635_v11_n1_p143_Cibils http://hdl.handle.net/20.500.12110/paper_14310635_v11_n1_p143_Cibils
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Completion Galois covering Hopf algebra K-category Karoubianisation Morita theory Smash product
spellingShingle	Completion Galois covering Hopf algebra K-category Karoubianisation Morita theory Smash product Solotar, Andrea Leonor Galois coverings, morita equivalence and smash extensions of categories over a field
topic_facet	Completion Galois covering Hopf algebra K-category Karoubianisation Morita theory Smash product
description	Algebras over a field k generalize to categories over k in order to considers Galois coverings. Two theories presenting analogies, namely smash extensions and Galois coverings with respect to a finite group are known to be different. However we prove in this paper that they are Morita equivalent. For this purpose we need to describe explicit processes providing Morita equivalences of categories which we call contraction and expansion. A structure theorem is obtained: composition of these processes provides any Morita equivalence up to equivalence, a result which is related with the karoubianisation (or idempotent completion) and additivisation of a k-category.
author	Solotar, Andrea Leonor
author_facet	Solotar, Andrea Leonor
author_sort	Solotar, Andrea Leonor
title	Galois coverings, morita equivalence and smash extensions of categories over a field
title_short	Galois coverings, morita equivalence and smash extensions of categories over a field
title_full	Galois coverings, morita equivalence and smash extensions of categories over a field
title_fullStr	Galois coverings, morita equivalence and smash extensions of categories over a field
title_full_unstemmed	Galois coverings, morita equivalence and smash extensions of categories over a field
title_sort	galois coverings, morita equivalence and smash extensions of categories over a field
publishDate	2006
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14310635_v11_n1_p143_Cibils http://hdl.handle.net/20.500.12110/paper_14310635_v11_n1_p143_Cibils
work_keys_str_mv	AT solotarandrealeonor galoiscoveringsmoritaequivalenceandsmashextensionsofcategoriesoverafield
_version_	1768544879650013184

Galois coverings, morita equivalence and smash extensions of categories over a field

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