Filters and G-convergence in Categories

2019/10/21 by Joaquı́n Luna-Torres, Joaquin Luna-Torres, Luna-Torres, Joaquin · 1 citation
Computer Science · Mathematics · #06A05 #18A35 #18D20 #5420 #Approximation Theory and Sequence Spaces #Category Theory (math.CT) #FOS: Mathematics #Fuzzy Logic and Control Systems #Fuzzy Systems and Optimization #math.CT #msc:06A05 #msc:18A35 #msc:18D20 #msc:5420

paper · pdf · doi:10.48550/arxiv.1910.09423

arxiv created 2019/10/21 · openalex publication_date 2019/10/21 · arxiv updated 2019/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In analogy with the classical theory of filters, for finitely complete categories, we provide the concepts of filter, G-neighborhood (short for \Grothendieck-neighborhood") and cover-neighborhood of a point, with the aim of studying convergence, cluster point and closure of sieves on objects of that kind of categories.

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