Homology, Homotopy and Applications

Volume 15 (2013)

Number 2

Effective descent morphisms in star-regular categories

Pages: 127 – 144

DOI: http://dx.doi.org/10.4310/HHA.2013.v15.n2.a7

Authors

Marino Gran (Institut de Recherche en Mathématique et Physique, Université catholique de Louvain, Louvain-la-Neuve, Belgium)

Olivette Ngaha Ngaha (Institut de Recherche en Mathématique et Physique, Université catholique de Louvain, Louvain-la-Neuve, Belgium)

Abstract

In this article a sufficient condition on a star-regular category is introduced guaranteeing that regular epimorphisms are effective descent morphisms. This condition is satisfied by any category with a good theory of ideals (thus, in particular, by any ideal determined category), by any almost abelian category (for instance, by the categories of torsion abelian groups, torsion-free abelian groups, normed vector spaces, Banach spaces, locally compact abelian groups, etc.) and by any category of topological Mal'tsev algebras (in particular, by the category of topological groups).

Keywords

effective descent morphism, star-regular category, ideal of morphisms, semi-effective star-regular category, almost abelian category, torsion theory, topological Mal’tsev algebra

2010 Mathematics Subject Classification

18A20, 18A30, 18C99, 18E05

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