Colby-Fuller duality between coalgebras
type: Item
instance of: scholarly article
title: Colby-Fuller duality between coalgebras
zbMATH Open document ID: 0866.16024
published in: Journal of Algebra
publication date: 1997-02-23T00:00:00Z
review text: The object of this paper is the study of Morita dualities between categories of comodules over coalgebras. This is done with the help of the concept of Morita duality for Grothendieck categories introduced by \textit{R. R. Colby} and \textit{K. R. Fuller} [in J. Algebra 82, 546-558 (1983; Zbl 0524.16014)]. The authors characterize Colby-Fuller dualities between coalgebras by showing that there exists such a duality between coalgebras \(C\) and \(D\) if and only if \(C\) and \(D\) are right and left semiperfect and their categories of finite-dimensional comodules are (dual) equivalent. Moreover, they show that every Colby-Fuller duality between coalgebras is determined by a bicomodule which is a quasi-finite injective cogenerator for both categories of comodules. In the last section of the paper the authors show that if \(C\) and \(D\) are cocommutative coalgebras such that there exists either an equivalence between the categories of right comodules or a Colby-Fuller duality between the categories of right \(C\)-comodules and left \(D\)-comodules, then \(C\) and \(D\) are isomorphic.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 18E15
zbMATH DE Number: 954770
zbMATH Keywords: Morita dualities
zbMATH Keywords: categories of comodules over coalgebras
zbMATH Keywords: Grothendieck categories
zbMATH Keywords: Colby-Fuller dualities
zbMATH Keywords: categories of finite-dimensional comodules
zbMATH Keywords: quasi-finite injective cogenerators
zbMATH Keywords: cocommutative coalgebras
zbMATH Keywords: equivalences
author: José Gómez-Torrecillas
author: Constantin Năstăsescu
reviewed by: José L. Gómez-Pardo
MaRDI profile type: Publication
full work available at URL: jabr.1996.0338
OpenAlex ID: W2139436866
DOI: 10.1006/JABR.1996.0338
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description: scientific article; zbMATH DE number 954770