Finite preorders and topological descent. I
[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.
scientific article; zbMATH DE number 1839067