Lawvere completeness in Topology
| dc.creator | Clementino, Maria Manuel | |
| dc.creator | Hofmann, Dirk | |
| dc.date | 2007-04-30 | |
| dc.date.accessioned | 2026-07-07T07:58:49Z | |
| dc.date.available | 2026-07-07T07:58:49Z | |
| dc.description | It is known since 1973 that Lawvere's notion of (Cauchy-)complete enriched category is meaningful for metric spaces: it captures exactly Cauchy-complete metric spaces. In this paper we introduce the corresponding notion of Lawvere completeness for $(\mathbb{T},\mathsf{V})$-categories and show that it has an interesting meaning for topological spaces and quasi-uniform spaces: for the former ones means weak sobriety while for the latter means Cauchy completeness. Further, we show that $\mathsf{V}$ has a canonical $(\mathbb{T},\mathsf{V})$-category structure which plays a key role: it is Lawvere-complete under reasonable conditions on the setting; permits us to define a Yoneda embedding in the realm of $(\mathbb{T},\mathsf{V})$-categories. | |
| dc.identifier | https://arxiv.org/abs/0704.3976 | |
| dc.identifier | http://arxiv.org/abs/0704.3976 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128141 | |
| dc.subject | Category Theory | |
| dc.subject | General Topology | |
| dc.subject | 18 (primary), 54E (secondary) | |
| dc.title | Lawvere completeness in Topology | |
| dc.type | text |