Symmetry and Cauchy completion of quantaloid-enriched categories

2010/05/06 by Hans Heymans, Heymans, Hans, Isar Stubbe +1 · 1 citation
Mathematics · #Category Theory (math.CT) #FOS: Mathematics #math.CT

paper · pdf · doi:10.48550/arxiv.1005.1018

18 pages, final version

arxiv created 2011/06/23 · arxiv updated 2011/06/24

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.

Cited by

• Quantaloid-enriched categories: Factorization, weak classifiers, and symmetry

Related

• Topology from enrichment: the curious case of partial metrics
• Categorical structures enriched in a quantaloid: categories, distributors and functors
• Quantaloid-enriched categories: Factorization, weak classifiers, and symmetry
• Completeness of quantaloid-enriched categories up to Morita equivalence
• Categorical structures enriched in a quantaloid: tensored and cotensored categories