Torsion theories and Galois coverings of topological groups
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.
scientific article; zbMATH DE number 5078562
scientific article