The fundamental progroupoid of a general topos
| dc.creator | Dubuc, Eduardo J. | |
| dc.date | 2007-06-12 | |
| dc.date.accessioned | 2026-07-07T08:05:22Z | |
| dc.date.available | 2026-07-07T08:05:22Z | |
| dc.description | It is well known that the category of covering projections (that is, locally constant objects) of a locally connected topos is equivalent to the classifying topos of a strict progroupoid (or, equivalently, a localic prodiscrete groupoid), the \emph{fundamental progroupoid}, and that this progroupoid represents first degree cohomology. In this paper we generalize these results to an arbitrary topos. The fundamental progroupoid is now a localic progroupoid, and can not be replaced by a localic groupoid. The classifying topos in not any more a Galois topos. Not all locally constant objects can be considered as covering projections. The key contribution of this paper is a novel definition of covering projection for a general topos, which coincides with the usual definition when the topos is locally connected. The results in this paper were presented in a talk at the Category Theory Conference, Vancouver July 2004. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/0706.1771 | |
| dc.identifier | http://arxiv.org/abs/0706.1771 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130262 | |
| dc.subject | Category Theory | |
| dc.subject | Algebraic Topology | |
| dc.subject | 18B25 ; 18F99 | |
| dc.title | The fundamental progroupoid of a general topos | |
| dc.type | text |