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https://hdl.handle.net/10316/11196
Title: | On the categorical meaning of Hausdorff and Gromov distances, I | Authors: | Akhvlediani, Andrei Clementino, Maria Manuel Tholen, Walter |
Issue Date: | 2009 | Publisher: | Centro de Matemática da Universidade de Coimbra | Citation: | Pré-Publicações DMUC. 09-01 (2009) | Abstract: | Hausdor 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. | URI: | https://hdl.handle.net/10316/11196 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Vários |
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On the categorical meaning of Hausdorff and Gromov distances.pdf | 334.72 kB | Adobe PDF | View/Open |
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