Title
Symmetry and cauchy completion of quantaloid-enriched categories Symmetry and cauchy completion of quantaloid-enriched categories
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Subject
Mathematics
Source (journal)
Theory and applications of categories. - -
Volume/pages
25(2011) , p. 276-426
ISSN
1201-561X
ISI
000300166900002
Carrier
E
Target language
English (eng)
Affiliation
University of Antwerp
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.
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