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...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Cibils, C., Solotar, A.
Formato: JOUR
Materias:
Completion
Galois covering
Hopf algebra
K-category
Karoubianisation
Morita theory
Smash product
Acceso en línea: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 todo:paper_14310635_v11_n1_p143_Cibils
record_format dspace
spelling todo:paper_14310635_v11_n1_p143_Cibils2023-10-03T16:13:50Z Galois coverings, morita equivalence and smash extensions of categories over a field Cibils, C. Solotar, A. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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
Cibils, C.
Solotar, A.
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.
format JOUR
author Cibils, C.
Solotar, A.
author_facet Cibils, C.
Solotar, A.
author_sort Cibils, C.
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
url http://hdl.handle.net/20.500.12110/paper_14310635_v11_n1_p143_Cibils
work_keys_str_mv AT cibilsc galoiscoveringsmoritaequivalenceandsmashextensionsofcategoriesoverafield
AT solotara galoiscoveringsmoritaequivalenceandsmashextensionsofcategoriesoverafield
_version_ 1807320145556668416

Ejemplares similares