Geodesic
Symmetry and Cauchy completion of quantaloid-enriched categories
Theory and applications of categories, Tome 25 (2011), pp. 276-294

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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.

Publié le :
Classification : 06F07, 18C15, 18D05, 18D20
Keywords: Quantaloid, enriched category, symmetry, Cauchy completion 
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     author = {Hans Heymans and Isar Stubbe},
     title = {Symmetry and {Cauchy} completion of quantaloid-enriched categories},
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     pages = {276--294},
     publisher = {mathdoc},
     volume = {25},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2011_25_a10/}
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Hans Heymans; Isar Stubbe. Symmetry and Cauchy completion of quantaloid-enriched categories. Theory and applications of categories, Tome 25 (2011), pp. 276-294. http://geodesic.mathdoc.fr/item/TAC_2011_25_a10/