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...
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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 |
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Universidad de Buenos Aires |
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I-28 |
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R-134 |
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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 |