Torsion theories and Galois coverings of topological groups
type: Item
instance of: scholarly article
title: Torsion theories and Galois coverings of topological groups
zbMATH Open document ID: 1157.18008
author: Marino Gran
author: Valentina Rossi
published in: Journal of Pure and Applied Algebra
publication date: 2006-12-07T00:00:00Z
review text: The idea of studying torsion theories in a homological category was considered by \textit{D. Bourn} and \textit{M. Gran} [J. Algebra 305, 18--47 (2006; Zbl 1123.18009)]. A torsion theory in a homological category \(\mathcal{C}\) is a pair of \((\tau,\chi)\) of full replete subcategories of \(\mathcal{C}\) such that the only arrow \(f:X\rightarrow Y\) from \(T\in \tau \) to \(X\in \chi\) is the zero arrow \(0\) and for any object \(A\) in \(\mathcal{C}\) there exists a short exact sequence \(0\rightarrow T\rightarrow A\rightarrow X\rightarrow 0\) with \(T\in \tau\), \(X\in \chi\). In this paper, the categorical Galois structure associated with a torsion theory in a homological category is studied and a characterization of the corresponding Galois coverings for a special class of the torsion theories is given. In the structure of the paper first effective descent morphisms, torsion theories and homological categories are given. Then the quasi-hereditary torsion theories are studied. Later the Galois structure of torsion theories are introduced. Finally as application coverings corresponding to various torsion theories in the category of topological groups are considered.
reviewed by: Osman Mucuk
Mathematics Subject Classification ID: 18E40
Mathematics Subject Classification ID: 18C20
Mathematics Subject Classification ID: 22A99
zbMATH DE Number: 5078562
zbMATH Keywords: torsion theories
zbMATH Keywords: homological categories
zbMATH Keywords: coverings of topological groups
MaRDI profile type: Publication
full work available at URL: j.jpaa.2005.12.001
OpenAlex ID: W2155508146
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DOI: 10.1016/J.JPAA.2005.12.001
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description: scientific article; zbMATH DE number 5078562