Factorizing the Top\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {Top}$$\end{document}–Loc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {Loc}$$\end{document} adjunction through positive topologies [Book Review]

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Archive for Mathematical Logic 60 (7-8):967-979 (2021)
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Abstract

We characterize the category of Sambin’s positive topologies as the result of the Grothendieck construction applied to a doctrine over the category Loc of locales. We then construct an adjunction between the category of positive topologies and that of topological spaces Top, and show that the well-known adjunction between Top and Loc factors through the constructed adjunction.

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10.1007/s00153-021-00768-5

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Adjointness in Foundations.F. William Lawvere - 1969 - Dialectica 23 (3‐4):281-296.
Positivity relations on a locale.Francesco Ciraulo & Steven Vickers - 2016 - Annals of Pure and Applied Logic 167 (9):806-819.

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