The denormalized \(3{\times}3\) lemma
type: Item
instance of: scholarly article
title: The denormalized \(3{\times}3\) lemma
zbMATH Open document ID: 1032.18007
DOI: 10.1016/S0022-4049(02)00143-3
author: Dominique Bourn
published in: Journal of Pure and Applied Algebra
publication date: 2003-03-09T00:00:00Z
review text: The standard \(3 \times 3\) lemma for groups says that the cokernel of a monomorphism of short exact sequences is short exact, and that the kernel of an epimorphism of short exact sequences is short exact. This paper proves a corresponding statement for a suitably defined notion of short exact sequence in a regular Malcev category. In this context, short exact sequences are replaced by coequalizer diagrams arising from kernel pairs, and the terms ``regular'' and ``Malcev'' refer to the presence of certain exactness conditions on the ambient category.
Mathematics Subject Classification ID: 18G50
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 18A20
Mathematics Subject Classification ID: 18G30
zbMATH DE Number: 1878454
zbMATH Keywords: exact sequences
zbMATH Keywords: regular Malcev category
MaRDI profile type: Publication
Wikidata QID: Q124852480
cites work: Q5628320
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cites work: Q4098916
cites work: Some remarks on Maltsev and Goursat categories
cites work: Diagram chasing in Mal'cev categories
cites work: Q3137145
cites work: Internal categories in Mal'cev categories
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description: scientific article; zbMATH DE number 1878454