On categories with semidirect products
type: Item
instance of: scholarly article
title: On categories with semidirect products
zbMATH Open document ID: 1264.18004
author: Nelson Martins-Ferreira
author: Manuela Sobral
published in: Journal of Pure and Applied Algebra
publication date: 2012-10-16T00:00:00Z
review text: In this paper, necessary and sufficient conditions for a pointed category to admid semidirect products in the sense of \textit{D. Bourn} and \textit{G. Janelidze} [Theory Appl. Categ. 4, 37--46 (1998; Zbl 0890.18003) are given and interpreted in exactness of appropriate split extensions. In the cited reference [loc. cit.], the categorical notion of semidirect product in a category was introduced generalizing the notion of semidirect product of groups. By Theorem 3.4 in [loc. cit.] semi-abelian categories admits semidirect products but semi-abelianess is not a necessary condition for the existence of semidirect productdirectness.
reviewed by: Osman Mucuk
Mathematics Subject Classification ID: 18C20
Mathematics Subject Classification ID: 18E99
zbMATH DE Number: 6094158
zbMATH Keywords: semidirect product
zbMATH Keywords: semi-abelian categories
zbMATH Keywords: internal action
MaRDI profile type: Publication
full work available at URL: j.jpaa.2012.02.035
OpenAlex ID: W2061547583
cites work: Q4827951
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cites work: Semi-abelian categories
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cites work: Semidirect products of internal groupoids
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DOI: 10.1016/J.JPAA.2012.02.035
description: scientific article; zbMATH DE number 6094158