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Link to original content: https://doi.org/10.1007/s10485-018-9513-7
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Met-Like Categories Amongst Concrete Topological Categories

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Abstract

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 \(\mathsf{V}\).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada

    Walter Tholen

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  1. Walter Tholen
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Correspondence to Walter Tholen.

Additional information

Communicated by Eva Colebunders.

Dedicated in gratitude to Bob Lowen, founder of Applied Categorical Structures

Partial financial assistance by the Natural Sciences and Engineering Research Council (NSERC) of Canada is gratefully acknowledged.

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Tholen, W. Met-Like Categories Amongst Concrete Topological Categories. Appl Categor Struct 26, 1095–1111 (2018). https://doi.org/10.1007/s10485-018-9513-7

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