Cartesian closed exact completions in topology

• Autor(a) principal: Clementino, Maria Manuel
• Data de Publicação: 2020
• Outros Autores: Hofmann, Dirk, Ribeiro, Willian
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10316/89417; https://doi.org/10.1016/j.jpaa.2019.06.003
• topic: Quantale; Enriched category; (Probabilistic) metric space; Exponentiation; (Weakly) cartesian closed category; Exact completion

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.