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https://hdl.handle.net/10316/89417
Title: | Cartesian closed exact completions in topology | Authors: | Clementino, Maria Manuel Hofmann, Dirk Ribeiro, Willian |
Keywords: | Quantale; Enriched category; (Probabilistic) metric space; Exponentiation; (Weakly) cartesian closed category; Exact completion | Issue Date: | Feb-2020 | Publisher: | Elsevier | Project: | CMUC-UID/MAT/00324/2019 | Serial title, monograph or event: | Journal of Pure and Applied Algebra | Volume: | 224 | Issue: | 2 | Abstract: | Using generalized enriched categories, in this paper we show that Rosický's proof of cartesian closedness of the exact completion of the category of topological spaces can be extended to a wide range of topological categories over Set, like metric spaces, approach spaces, ultrametric spaces, probabilistic metric spaces, and bitopological spaces. In order to do so we prove a sufficient criterion for exponentiability of (T,V)-categories and show that, under suitable conditions, every injective (T,V)-category is exponentiable in (T,V)-Cat. | URI: | https://hdl.handle.net/10316/89417 | DOI: | 10.1016/j.jpaa.2019.06.003 | Rights: | embargoedAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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CHR_WeaklyCC_final.pdf | 533.92 kB | Adobe PDF | View/Open |
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