Descent for regular epimorphisms in Barr exact Goursat categories
type: Item
instance of: scholarly article
title: Descent for regular epimorphisms in Barr exact Goursat categories
zbMATH Open document ID: 1223.18007
author: George Janelidze
author: Manuela Sobral
published in: Applied Categorical Structures
publication date: 2011-03-30T00:00:00Z
full work available at URL: http://hdl.handle.net/10316/11194
review text: The paper begins with a characterization of a Goursat category and goes on to give a lemma on effective (global) descent morphisms. Another lemma then discusses a relationship between the category ER(\(\mathcal C\)) of equivalence relations in \(\mathcal C\) (\(\mathcal C\) is assumed to be a Barr exact Goursat category), the category RR(\(\mathcal C\)) of reflexive relations in \(\mathcal C\) and RG(\(\mathcal C\)), the category of reflexive graphs in \(\mathcal C\). This then leads to the main result that every regular epimorphism in ER(\(\mathcal C\)) is an effective descent morphism (Lemma 2.2, and its translation into the language of regular epimorphism, Theorem 2.3). The paper ends with a few comments and open questions; one of them is how to describe effective descent morphisms in ER(\(\mathcal C\))\(\sim\)RE(\(\mathcal C\)), for an arbitrary Barr exact category \(\mathcal C\).
reviewed by: Radoslav M. Dimitrić
Mathematics Subject Classification ID: 18E10
Mathematics Subject Classification ID: 18A20
Mathematics Subject Classification ID: 18A30
zbMATH DE Number: 5871638
zbMATH Keywords: regular category
zbMATH Keywords: Barr exact category
zbMATH Keywords: Goursat category
zbMATH Keywords: equivalence relation
zbMATH Keywords: effective descent morphism
MaRDI profile type: Publication
OpenAlex ID: W1973720589
cites work: Some remarks on Maltsev and Goursat categories
cites work: Diagram chasing in Mal'cev categories
cites work: Q4156899
cites work: On categorical conditions for congruences to commute
cites work: Internal categories in Mal'cev categories
cites work: Semi-abelian categories
cites work: Finite preorders and topological descent. I
cites work: Q4464700
cites work: Facets of descent. I
cites work: Effective descent morphisms in some quasivarieties of algebraic, relational, and more general structures
cites work: Q5547635
DOI: 10.1007/S10485-009-9199-Y
description: scientific article; zbMATH DE number 5871638