On the categorical meaning of Hausdorff and Gromov distances, I
| dc.creator | Akhvlediani, Andrei | |
| dc.creator | Clementino, Maria Manuel | |
| dc.creator | Tholen, Walter | |
| dc.date | 2009-01-06 | |
| dc.date.accessioned | 2026-07-07T12:24:52Z | |
| dc.date.available | 2026-07-07T12:24:52Z | |
| dc.description | Hausdorff and Gromov distances are introduced and treated in the context of categories enriched over a commutative unital quantale V. The Hausdorff 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 define 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 first 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. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/0901.0618 | |
| dc.identifier | http://arxiv.org/abs/0901.0618 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/214457 | |
| dc.subject | Category Theory | |
| dc.title | On the categorical meaning of Hausdorff and Gromov distances, I | |
| dc.type | text |