Filters and compactness on small categories and locales

In analogy with the classical theory of filters, for finitely complete or small categories, we provide the concepts of filter, \(\mathfrak{G}\)-neighborhood (short for "Grothendieck-neighborhood") and cover-neighborhood of points of such categories, to study convergence, cluster point, clo...

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Bibliographic Details
Published in:Open Journal of Mathematical Sciences 2022-12, Vol.6 (1), p.1-13
Main Author: Luna-Torres, Joaquín
Format: Article
Language:English
Online Access:Get full text
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Summary:In analogy with the classical theory of filters, for finitely complete or small categories, we provide the concepts of filter, \(\mathfrak{G}\)-neighborhood (short for "Grothendieck-neighborhood") and cover-neighborhood of points of such categories, to study convergence, cluster point, closure of sieves and compactness on objects of that kind of categories. Finally, we study all these concepts in the category \(\mathbf{Loc}\) of locales.
ISSN:2616-4906
2523-0212
DOI:10.30538/oms2022.0174