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An application of descent to a classification theorem for toposes

Published online by Cambridge University Press:  24 October 2008

Marta Bunge
Marta Bunge
Affiliation:
Department of Mathematics and Statistics, McGill University, Montréal, P. Québec, CanadaH3A 2K6
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Extract

The aim of this paper is to answer the following question. For a spatial groupoid G, i.e. for a groupoid in the category Sp of spaces (in the sense of [20]) in a topos , and continuous maps, the topos BG, of étale G-spaces, is called ‘the classifying topos of G’ by Moerdijk[22]. This terminology is suggested by the case of G a discrete group (in Sets), as then BG, the topos of G-sets, classifies principal G-bundles. This means that, for each topological space X, there is a bijection between isomorphism classes of principal G-bundles over X and isomorphism classes of geometric morphisms from Sh(X) to BG. The question is: what does BG classify, in terms of G, in the general case of a spatial groupoid G in a topos ?

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 1 , January 1990 , pp. 59 - 79
Copyright
Copyright © Cambridge Philosophical Society 1990

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