Wide Morita contexts and equivalences of comodule categories
type: Item
instance of: scholarly article
title: Wide Morita contexts and equivalences of comodule categories
zbMATH Open document ID: 0927.16034
DOI: 10.1016/S0022-4049(97)00100-X
published in: Journal of Pure and Applied Algebra
publication date: 1999-08-22T00:00:00Z
review text: The authors introduce a purely categorical notion of Morita context (called ``wide Morita context'') between Abelian categories, which extends the classical notion of Morita context for module categories as well as Takeuchi's notion of Morita context for comodule categories [\textit{M. Takeuchi}, J. Fac. Sci., Univ. Tokyo, Sect. I A 24, No. 3, 629-644 (1977; Zbl 0385.18007)]. For this general notion of Morita context, they prove an extension of both Morita's theorem on categories of modules and of Takeuchi's theorem on comodule categories. As an application they obtain, for any Takeuchi Morita context, an equivalence between appropriate subcategories of the categories of comodules through certain modifications of the cotensor product functors (Theorem 4.2). This equivalence is similar to that obtained by Nicholson-Watters for module categories [\textit{W. K. Nicholson} and \textit{J. F. Watters}, Math. Proc. Camb. Philos. Soc. 103, No. 3, 399-408 (1988; Zbl 0673.16025)].
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 18E10
zbMATH DE Number: 1308238
zbMATH Keywords: equivalences of categories
zbMATH Keywords: module categories
zbMATH Keywords: comodule categories
zbMATH Keywords: wide Morita contexts
zbMATH Keywords: Abelian categories
author: Florencio Castaño Iglesias
author: José Gómez-Torrecillas
reviewed by: Blas Torrecillas
MaRDI profile type: Publication
cites work: Q3933122
cites work: Wide morita contexts
cites work: Q3248050
cites work: The quotient category of a Morita context
cites work: Torsion theories for coalgebras
cites work: Morita context functors
cites work: Q4049223
cites work: Q5590089
cites work: Q4165487
full work available at URL: s0022-4049(97)00100-x
OpenAlex ID: W2053105969
description: scientific article; zbMATH DE number 1308238