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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Publicado: 2008
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224049_v212_n11_p2479_Dubuc
http://hdl.handle.net/20.500.12110/paper_00224049_v212_n11_p2479_Dubuc
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00224049_v212_n11_p2479_Dubuc
record_format dspace
spelling paper:paper_00224049_v212_n11_p2479_Dubuc2023-06-08T14:50:41Z 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 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. 2008 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224049_v212_n11_p2479_Dubuc 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.
title The fundamental progroupoid of a general topos
spellingShingle 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
publishDate 2008
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224049_v212_n11_p2479_Dubuc
http://hdl.handle.net/20.500.12110/paper_00224049_v212_n11_p2479_Dubuc
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