Symmetry and Cauchy completion of quantaloid-enriched categories

Details Symmetry and Cauchy completion of quantaloid-enriched categories Symmetry and Cauchy completion of quantaloid-enriched categories

2010-05-06

arxiv.org/abs/1005.1018v3

Mathematics

Category Theory

18 pages, final version

Scientific paper

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.

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