Central extensions and internal groupoids in Maltsev categories
type: Item
instance of: scholarly article
title: Central extensions and internal groupoids in Maltsev categories
zbMATH Open document ID: 0974.18007
DOI: 10.1016/S0022-4049(99)00092-4
author: Marino Gran
published in: Journal of Pure and Applied Algebra
publication date: 2001-12-09T00:00:00Z
review text: The author continues his study of internal groupoids in a Barr-exact Mal'tsev category, begun in an earlier paper in the same journal [\textit{M. Gran}, J. Pure Appl. Algebra 143, No. 1-3, 221-229 (1999; Zbl 0937.18006)]. In the earlier paper, he showed that the category of internal groupoids in such a category is itself a Barr-exact Mal'tsev category; this allows one to study the concept of central extension, as defined by \textit{G.~Janelidze} and \textit{G. M.~Kelly}, in such categories, and that is the goal of the present paper. In particular, the author obtains explicit descriptions of central extensions of crossed modules and of crossed rings.
Mathematics Subject Classification ID: 18D35
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 18E10
Mathematics Subject Classification ID: 18G50
Mathematics Subject Classification ID: 20L05
zbMATH DE Number: 1563010
zbMATH Keywords: internal groupoids
zbMATH Keywords: Barr-exact
zbMATH Keywords: Mal'tsev category
zbMATH Keywords: central extensions
zbMATH Keywords: crossed modules
zbMATH Keywords: crossed rings
reviewed by: Peter Johnstone
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1563010