Internal categories and groupoids in congruence modular varieties
type: Item
instance of: scholarly article
title: Internal categories and groupoids in congruence modular varieties
zbMATH Open document ID: 0880.18005
published in: Journal of Algebra
publication date: 1998-01-19T00:00:00Z
review text: The so-called `congruence modular varieties' are the algebraic categories in the sense of Lawvere in which the congruences, i.e., the equivalence relations which are compatible with the operations, satisfy the modular identity. The paper shows that, in these categories, there is a connection between internal category theory and commutator theory introduced in universal algebra. It describes all internal categories satisfying a certain commutator condition which always holds for internal groupoids and for all internal categories in Mal'tsev varieties.
Mathematics Subject Classification ID: 18B40
Mathematics Subject Classification ID: 08B10
zbMATH DE Number: 1051575
zbMATH Keywords: algebraic categories
zbMATH Keywords: congruence
zbMATH Keywords: modular identity
zbMATH Keywords: commutator
zbMATH Keywords: internal categories
zbMATH Keywords: internal groupoids
zbMATH Keywords: Mal'tsev varieties
author: George Janelidze
author: M. Cristina Pedicchio
reviewed by: Yves Diers
MaRDI profile type: Publication
full work available at URL: jabr.1996.6970
OpenAlex ID: W2012023229
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DOI: 10.1006/JABR.1996.6970
description: scientific article; zbMATH DE number 1051575