A convenient category of locales
Moncef Ghazel, In\`es Saihi, Walid Taamallah

TL;DR
This paper extends the framework of Kan extendable subcategories to define and prove the cartesian closure of the category of compactly generated strongly Hausdorff locales, generalizing previous work on fibrewise topological spaces.
Contribution
It introduces a new application of Kan extendable subcategories to locales, establishing the cartesian closure of compactly generated strongly Hausdorff locales.
Findings
The category of compactly generated strongly Hausdorff locales is cartesian closed.
The framework for fibrewise topological spaces applies to locales.
The approach unifies topological and locale-theoretic concepts.
Abstract
The notion of Kan extendable subcategories was initially introduced to define the category of compactly generated fibrewise topological spaces over a T1 base space and to establish its cartesian closure. In this paper, we show that the same framework can likewise be applied to define the category of compactly generated strongly Hausdorff locales and to prove that it, too, is cartesian closed
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topology and Set Theory · Fuzzy and Soft Set Theory
