Finite preorders and topological descent. I
type: Item
instance of: scholarly article
title: Finite preorders and topological descent. I
zbMATH Open document ID: 1018.18004
DOI: 10.1016/S0022-4049(02)00134-2
author: George Janelidze
author: Manuela Sobral
published in: Journal of Pure and Applied Algebra
publication date: 2002-12-02T00:00:00Z
review text: [For part II, see ibid. 174, No. 3, 303-309 (2002; Zbl 1018.18005).] In the following categories: \({\mathcal R}el\), \({\mathcal R}efl{\mathcal R}el\), \({\mathcal P}reord\), \({\mathcal F}in{\mathcal P}reord\), \({\mathcal F}in{\mathcal T}op\) of sets equipped with a relation, a reflexive relation, a preorder, of finite preordered sets, of finite topological spaces, respectively, the regular epimorphisms, pullback stable regular epimorphisms, effective descent morphisms, effective \(E\)-descent morphisms for various classes of morphisms \(E\), are characterized. Several counter-examples are given, e.g., a descent morphism that is not an effective étale-descent morphism, and converse. The link between topological spaces and preordered sets comes from the equivalence of the two last categories.
Mathematics Subject Classification ID: 18B30
Mathematics Subject Classification ID: 18A20
Mathematics Subject Classification ID: 18D30
Mathematics Subject Classification ID: 18A25
Mathematics Subject Classification ID: 18B35
zbMATH DE Number: 1839067
zbMATH Keywords: topological descent
zbMATH Keywords: preordered descent
zbMATH Keywords: effective étale-descent
reviewed by: Yves Diers
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1839067