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Journal Articles Theory and Applications of Categories Year : 2011

Symmetry and Cauchy completion of quantaloid-enriched categories

Abstract

We formulate an elementary condition on an involutive quantaloid Q under which there is a distributive law from the Cauchy completion monad over the symmetrisation comonad on the category of Q-enriched categories. For such quantaloids, which we call Cauchy-bilateral quantaloids, it follows that the Cauchy completion of any symmetric Q-enriched category is again symmetric. Examples include Lawvere's quantale of non-negative real numbers and Walters' small quantaloids of closed cribles.

Dates and versions

hal-03606827 , version 1 (12-03-2022)

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Hans Heymans, Isar Stubbe. Symmetry and Cauchy completion of quantaloid-enriched categories. Theory and Applications of Categories, 2011, 25 (11), pp.276-294. ⟨hal-03606827⟩
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