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Symmetry and Cauchy completion of quantaloid-enriched categories

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Hans Heymans and Isar Stubbe

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.

Keywords:
Quantaloid, enriched category, symmetry, Cauchy completion

2000 MSC:
06F07, 18C15, 18D05, 18D20

*Theory and Applications of Categories,*
Vol. 25, 2011,
No. 11, pp 276-294.

Published 2011-06-25.

http://www.tac.mta.ca/tac/volumes/25/11/25-11.dvi

http://www.tac.mta.ca/tac/volumes/25/11/25-11.ps

http://www.tac.mta.ca/tac/volumes/25/11/25-11.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/25/11/25-11.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/25/11/25-11.ps

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