Met-Like Categories Amongst Concrete Topological Categories

  • Walter Tholen


When replacing the non-negative real numbers with their addition by a commutative quantale \(\mathsf{V}\), under a metric lens one may then view small \(\mathsf{V}\)-categories as sets that come with a \(\mathsf{V}\)-valued distance function. The ensuing category \(\mathsf{V}\text {-}\mathbf{Cat}\) is well known to be a concrete topological category that is symmetric monoidal closed. In this paper we show which concrete symmetric monoidal-closed topological categories may be fully and bireflectively embedded into \(\mathsf{V}\text {-}\mathbf{Cat}\), for some \(\mathsf{V}\).


Topological category Symmetric monoidal closed category Quantale-enriched category Prequantalic topological category Transitive topological category Symmetric topological category 

Mathematics Subject Classification

18B99 18D20 18D30 


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsYork UniversityTorontoCanada

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