2018/11/09 by Clementino, Maria Manuel, Hofmann, Dirk, Ribeiro, Willian
#18B30 #18B35 #18D15 #18D20 #54B30 #54E35 #54E70 #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1811.03993
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 (\mathbbT,V)-categories and show that, under suitable conditions, every (\mathbbT,V)-injective category is exponentiable in (\mathbbT,V)-Cat.