Strict monadic topology II: Descent for closure spaces (Preprint)

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Type: Preprint
National /International: International
Title: Strict monadic topology II: Descent for closure spaces
Publication Date: 2023-10-08
Authors: - George Janelidze
- Manuela Sobral

By a closure space we will mean a pair (A,\( \mathscr C \)), in which A is a set and \( \mathscr C \) a set of subsets of A closed under arbitrary intersections. The purpose of this paper is to initiate a development of descent theory of closure spaces, with our main results being: (a) characterization of descent morphisms of closure spaces; (b) in the category of finite closure spaces every descent morphism is an effective descent morphism; (c) every surjective closed map and every surjective open map of closure spaces is an effective descent morphism.

Institution: DMUC 23-31
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