Cartesian closed exact completions in topology

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Clementino, Maria Manuel¹  Hofmann, Dirk²  Ribeiro, Willian¹ 

[1] Univ Coimbra, Dept Math, CMUC, P-3001501 Coimbra, Portugal

[2] Univ Aveiro, Dept Math, CIDMA, P-3810193 Aveiro, Portugal

关键词: Quantale;    Enriched category;    (Probabilistic) metric space;    Exponentiation;    (Weakly) cartesian closed category;    Exact completion;   

DOI  :  10.1016/j.jpaa.2019.06.003

来源: Elsevier

【 摘 要 】

Using generalized enriched categories, in this paper we show that Rosicky'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. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free