Add time:07/13/2019         Source:sciencedirect.com

Using generalized enriched categories, in this paper we show that Rosický's proof of cartesian closedness of the Exact (cas 67712-72-5) 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.

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