Open Localizations

Borceux, Francis;Korostenski, M.
(1991) Journal of Pure and Applied Algebra — Vol. 74, n° 3, p. 229-238 (1991)

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Authors
  • Borceux, FrancisUCLouvain
    Author
  • Korostenski, M.
    Author
Abstract
An essential localization of a finitely complete category C is a full reflective subcategory D whose reflection has itself a left adjoint. D can then be seen as a C-indexed category and the localization is open when the adjunctions are indexed ones. We give equivalent conditions for the openness of a localization and prove that, with good conditions on C, open localizations constitute a locale.
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Borceux, F., & Korostenski, M. (1991). Open Localizations. Journal of Pure and Applied Algebra, 74(3), 229-238. https://doi.org/10.1016/0022-4049(91)90113-G (Original work published 1991)