Flatness, preorders and general metric spaces (revised)
| dc.creator | Schmitt, Vincent | |
| dc.date | 2006-02-21 | |
| dc.date.accessioned | 2026-07-07T07:03:39Z | |
| dc.date.available | 2026-07-07T07:03:39Z | |
| dc.description | We use a generic notion of flatness in the enriched context to define various completions of metric spaces -- enrichments over [0,\infty] -- and preorders -- enrichments over 2. We characterize the weights of colimits commuting in [0,\infty] with the terminal object and cotensors. These weights can be intrepreted in metric terms as peculiar filters, the so-called filters of type 1. This generalizes Lawvere's correspondence between minimal Cauchy filters and adjoint modules. We obtain a metric completion based on the filters of type 1 as an instance of the free cocompletion under a class of weights defined by G.M. Kelly. Another class of flat presheaves is considered both in the metric and the preorder context. The corresponding completion for preorders is the so-called dcpo-completion. | |
| dc.description | This a much improved version of the earlier drafts math.CT/0309209 and math.CT/0403164. It is now merely an application to metric spaces of the theory developed in math.CT/0501383 (that appeared in print in TAC 2005.) | |
| dc.identifier | https://arxiv.org/abs/math/0602463 | |
| dc.identifier | http://arxiv.org/abs/math/0602463 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109053 | |
| dc.subject | Category Theory | |
| dc.subject | Metric Geometry | |
| dc.title | Flatness, preorders and general metric spaces (revised) | |
| dc.type | text |