The fundamental progroupoid of a general topos
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 fundamental progroupoid, and that this progroupoid repres...
| Autor principal: | |
|---|---|
| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00224049_v212_n11_p2479_Dubuc |
| Aporte de: |
| id |
todo:paper_00224049_v212_n11_p2479_Dubuc |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_00224049_v212_n11_p2479_Dubuc2023-10-03T14:32:42Z The fundamental progroupoid of a general topos Dubuc, E.J. 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 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 cannot be replaced by a localic groupoid. The classifying topos is no longer 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. © 2008 Elsevier B.V. All rights reserved. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00224049_v212_n11_p2479_Dubuc |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| 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 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 cannot be replaced by a localic groupoid. The classifying topos is no longer 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. © 2008 Elsevier B.V. All rights reserved. |
| format |
JOUR |
| author |
Dubuc, E.J. |
| spellingShingle |
Dubuc, E.J. The fundamental progroupoid of a general topos |
| author_facet |
Dubuc, E.J. |
| author_sort |
Dubuc, E.J. |
| title |
The fundamental progroupoid of a general topos |
| title_short |
The fundamental progroupoid of a general topos |
| title_full |
The fundamental progroupoid of a general topos |
| title_fullStr |
The fundamental progroupoid of a general topos |
| title_full_unstemmed |
The fundamental progroupoid of a general topos |
| title_sort |
fundamental progroupoid of a general topos |
| url |
http://hdl.handle.net/20.500.12110/paper_00224049_v212_n11_p2479_Dubuc |
| work_keys_str_mv |
AT dubucej thefundamentalprogroupoidofageneraltopos AT dubucej fundamentalprogroupoidofageneraltopos |
| _version_ |
1807324347167145984 |