Internal categories in Mal'cev categories
type: Item
instance of: scholarly article
title: Internal categories in Mal'cev categories
zbMATH Open document ID: 0937.18006
DOI: 10.1016/S0022-4049(98)00112-1
author: Marino Gran
published in: Journal of Pure and Applied Algebra
publication date: 2000-06-14T00:00:00Z
review text: The main result of this article is that the category of internal categories and functors in a Mal'cev exact category is again a Mal'cev exact category (exactness here is in the sense of \textit{M. Barr}). This result applies not only to categories of groups, rings, Lie algebras etc., but also to some non-varietal categories such as the duals of the categories of abelian groups and of compact Hausdorff spaces. A regular category \({\mathcal C}\) is a Mal'cev category iff every reflexive relation in \({\mathcal C}\) is in fact an equivalence relation. [For other formulations, see \textit{A. Carboni}, \textit{J. Lambek} and \textit{M. C. Pedicchio}, ``Diagram chasing in Mal'cev categories'', J. Pure Appl. Algebra 69, No. 3, 271-284 (1990; Zbl 0722.18005).] After some needed preliminaries on Mal'cev categories, the bulk of the paper is taken up with the proof of the main result.
Mathematics Subject Classification ID: 18C05
Mathematics Subject Classification ID: 18D35
Mathematics Subject Classification ID: 18E10
zbMATH DE Number: 1384149
zbMATH Keywords: category of internal categories and functors
zbMATH Keywords: Mal'cev exact category
zbMATH Keywords: Mal'cev categories
reviewed by: K. I. Rosenthal
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1384149