Semidirect products and crossed modules in monoids with operations
type: Item
instance of: scholarly article
title: Semidirect products and crossed modules in monoids with operations
zbMATH Open document ID: 1277.18016
author: Nelson Martins-Ferreira
author: Andrea Montoli
author: Manuela Sobral
published in: Journal of Pure and Applied Algebra
publication date: 2013-04-18T00:00:00Z
review text: Internal categories in the category of groups correspond to crossed modules (of groups). The same type of equivalence works in categories of groups with operations, but fails in general in weaker algebraic contexts such as that of monoids. \textit{A. Patchkoria} [Georgian Math. J. 5, No. 6, 575--581 (1998; Zbl 0915.18002)] introduced a particular kind of internal category in the category of monoids equivalent to crossed modules of monoids. This paper generalises Patchkoria's results and characterises those internal categories in categories of monoids with operations that correspond to a sensible notion of crossed module in those contexts.
Mathematics Subject Classification ID: 18G50
Mathematics Subject Classification ID: 03C05
Mathematics Subject Classification ID: 08C05
Mathematics Subject Classification ID: 18B40
Mathematics Subject Classification ID: 20M50
zbMATH DE Number: 6155422
reviewed by: Timothy Porter
MaRDI profile type: Publication
full work available at URL: j.jpaa.2012.06.022
OpenAlex ID: W1987917928
cites work: Q4827951
cites work: Q3417720
cites work: Q3978968
cites work: Q4385499
cites work: Q4098916
cites work: Cohomologie non abelienne de structures algébriques
cites work: On categories with semidirect products
cites work: Semidirect products of internal groupoids
cites work: Obstruction theory in algebraic categories. I
cites work: Q4227975
cites work: Extensions, crossed modules and internal categories in categories of groups with operations
DOI: 10.1016/J.JPAA.2012.06.022
description: scientific article; zbMATH DE number 6155422