2021/12/01 by Joaquı́n Luna-Torres, Joaquín Luna-Torres, Luna-Torres, Joaquín
Mathematics · Medicine · #18A35 #18F10 #18F70 #54A20 #54D30 #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracerebral and Subarachnoid Hemorrhage Research #Rings, Modules, and Algebras #math.CT #msc:18A35 #msc:18F10 #msc:18F70 #msc:54A20 #msc:54D30
paper · pdf · doi:10.48550/arxiv.2112.00211
20 pages. arXiv admin note: substantial text overlap with arXiv:1910.09423
arxiv created 2021/12/01 · openalex publication_date 2021/12/01 · arxiv updated 2021/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In analogy with the classical theory of filters, for fi\-nite\-ly complete or small cat\-e\-go\-ries, we provide the concepts of fil\-ter, \mathfrakG-neigh\-bor\-hood (short for "Grothendieck-neigh\-bor\-hood") and cover-neigh\-bor\-hood of points of such categories, with the goal of studying convergence, cluster point, closure of sieves and compactness on objects of that kind of categories. Finally, we study all these concepts in the category \bfLoc of locales.