Flatness, preorders and general metric spaces
| dc.creator | Schmitt, Vincent | |
| dc.date | 2003-09-12 | |
| dc.date.accessioned | 2026-07-07T05:01:05Z | |
| dc.date.available | 2026-07-07T05:01:05Z | |
| dc.description | This paper studies a general notion of flatness in the enriched context: P-flatness where the parameter P stands for a class of presheaves. One obtains a completion of a category A by considering the category Flat_P(A) of P-flat presheaves over A. This completion is related to the free cocompletion of A under a class of colimits defined by Kelly. For a category A, for P = P0 the class of all presheaves, Flat_P0(A) is the Cauchy-completion of A. Two classes P1 and P2 of general interest for general metric spaces are considered. The P1- and P2-flatness are investigated and the associated completions are characterized for general metric spaces (enrichemnts over R+) and preorders (enrichments over Bool). We get this way two non-symmetric completions for metric spaces and retrieve the ideal completion for preorders. | |
| dc.identifier | https://arxiv.org/abs/math/0309209 | |
| dc.identifier | http://arxiv.org/abs/math/0309209 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68549 | |
| dc.subject | Category Theory | |
| dc.title | Flatness, preorders and general metric spaces | |
| dc.type | text |