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dc.contributor.authorAkhvlediani, Andrei-
dc.contributor.authorClementino, Maria Manuel-
dc.contributor.authorTholen, Walter-
dc.identifier.citationPré-Publicações DMUC. 09-01 (2009)en_US
dc.description.abstractHausdor and Gromov distances are introduced and treated in the context of categories enriched over a commutative unital quantale V. The Hausdor functor which, for every V-category X, provides the powerset of X with a suitable V-category structure, is part of a monad on V-Cat whose Eilenberg-Moore algebras are order-complete. The Gromov construction may be pursued for any endofunctor K of V-Cat. In order to de ne the Gromov \distance" between V-categories X and Y we use V-modules between X and Y , rather than V-category structures on the disjoint union of X and Y . Hence, we rst provide a general extension theorem which, for any K, yields a lax extension ~K to the category V-Mod of V-categories, with V-modules as morphisms.en_US
dc.description.sponsorshipNSERC; Center of Mathematics of the University of Coimbra/FCT;en_US
dc.publisherCentro de Matemática da Universidade de Coimbraen_US
dc.titleOn the categorical meaning of Hausdorff and Gromov distances, Ien_US
item.fulltextCom Texto completo-
item.languageiso639-1en- of Sciences and Technology- of Coimbra- - Centre for Mathematics of the University of Coimbra-
Appears in Collections:FCTUC Matemática - Vários
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