Strict monadic topology II: descent for closure spaces

2023/10/25 by George Janelidze, Janelidze, George, Manuela Sobral +1
Computer Science · Decision Sciences · Mathematics · #18A20 #18C15 #54A05 #54C10 #Advanced Algebra and Logic #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.2310.16636

openalex publication_date 2023/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By a closure space we will mean a pair (A,C), in which A is a set and 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.

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