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  1. Factorizing the $$\mathbf {Top}$$ Top – $$\mathbf {Loc}$$ Loc adjunction through positive topologies.Francesco Ciraulo, Tatsuji Kawai & Samuele Maschio - 2021 - Archive for Mathematical Logic 60 (7):967-979.
    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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  • 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. [REVIEW]Francesco Ciraulo, Tatsuji Kawai & Samuele Maschio - 2021 - Archive for Mathematical Logic 60 (7-8):967-979.
    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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