Semidirect products of internal groupoids
type: Item
instance of: scholarly article
title: Semidirect products of internal groupoids
zbMATH Open document ID: 1229.18009
author: G. Metere
author: Andrea Montoli
published in: Journal of Pure and Applied Algebra
publication date: 2010-04-22T00:00:00Z
review text: A categorical notion of semidirect product has been introduced by \textit{D. Bourn} and \textit{G. Janelidze} [``Protomodularity, descent, and semidirect products'', Theory Appl. Categ. 4, 37--46 (1998; Zbl 0890.18003)] in terms of split pullback diagrams. A notion of semidirect product for groupoids has been given in \textit{R. Brown} [``Groupoids as coefficients'', Proc. Lond. Math. Soc., III. Ser. 25, 413--426 (1972; Zbl 0245.20045)]. A generalization of this construction is known as Grothendieck construction for groupoids [\textit{A. Grothendieck}, Séminaire de Géometrie Algébrique 1, Exposé VI: Catégories fibrées et descente. 1960--1961, Lect. Notes Math. 224 (1971; Zbl 0234.14002)]. In this paper the necessary conditions for the existence of semidirect products are given and then these are studied for categorical groupoids. The groupoid action, split extensions and semidirect product notions for categorical groupoids are defined and the necessary conditions for the existence of semidirect products in categorical groupoids are determined.
reviewed by: Osman Mucuk
Mathematics Subject Classification ID: 18D35
Mathematics Subject Classification ID: 18G50
Mathematics Subject Classification ID: 22A22
zbMATH DE Number: 5697067
zbMATH Keywords: semidirect products
zbMATH Keywords: internal groupoids
zbMATH Keywords: Grothendieck constuction for groupoids
zbMATH Keywords: categorical groupoids
MaRDI profile type: Publication
full work available at URL: j.jpaa.2009.12.029
OpenAlex ID: W2118627741
cites work: Q5628320
cites work: Q3682648
cites work: Categorical non-abelian cohomology and the Schreier theory of groupoids
cites work: Q4856547
cites work: Topological semi-abelian algebras
cites work: Q3417720
cites work: Q3978968
cites work: Q4385499
cites work: Groupoids as Coefficients
cites work: Gattungen von lokalen Strukturen
cites work: Semi-abelian categories
cites work: Q4459228
DOI: 10.1016/J.JPAA.2009.12.029
description: scientific article; zbMATH DE number 5697067