Effective descent morphisms of regular epimorphisms
type: Item
instance of: scholarly article
title: Effective descent morphisms of regular epimorphisms
zbMATH Open document ID: 1257.18001
author: Tomas Everaert
published in: Journal of Pure and Applied Algebra
publication date: 2012-10-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/1101.4921
review text: This paper is concerned with a weakened form of Barr exactness: the condition that every regular epimorphism in a category should be an effective descent morphism. In particular, let \({\mathcal A}\) be a regular category with pushouts of regular epimorphisms by regular epimorphisms, and let \(\text{Reg}({\mathcal A})\) be the category of regular epimorphisms in \({\mathcal A}\). The author shows that \(\text{Reg}({\mathcal A})\) satisfies the weakened exactness condition if and only if \(\text{Reg}({\mathcal A})\) is regular. When these conditions hold, the category \({\mathcal A}\) itself also satisfies the weakened exactness condition. All of the conditions are satisfied when \({\mathcal A}\) is a Goursat category, or an ideal determined category, or a category of topological Mal'tsev algebras. They are also satisfied when \({\mathcal A}\) is the category of \(n\)-fold regular epimorphisms in one of the categories just mentioned.
reviewed by: Richard John Steiner
Mathematics Subject Classification ID: 18A30
Mathematics Subject Classification ID: 18E10
zbMATH DE Number: 6094150
zbMATH Keywords: regular category
zbMATH Keywords: regular epimorphism
zbMATH Keywords: effective descent morphism
zbMATH Keywords: Barr exactness
zbMATH Keywords: Goursat category
zbMATH Keywords: ideal determined category
zbMATH Keywords: topological Mal'tsev algebras
MaRDI profile type: Publication
OpenAlex ID: W2062197095
Wikidata QID: Q72421964
arXiv ID: 1101.4921
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DOI: 10.1016/J.JPAA.2012.02.027
description: scientific article; zbMATH DE number 6094150