Cartesian closed exact completions in topology (Preprint)

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Type: Preprint
National /International: International
Title: Cartesian closed exact completions in topology
Publication Date: 2018-11-09
Authors: - Maria Manuel Clementino
- Dirk Hofmann
- Willian Ribeiro Valencia da Silva
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 (T,V)-injective category is exponentiable in (T,V)-Cat.
Institution: DMUC 18-46
Online version: http://www.mat.uc.pt...prints/eng_2018.html
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