The fundamental progroupoid of a general topos |
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Authors: | Eduardo J Dubuc |
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Institution: | Departmento de Mathematica, Universidad de Buenos Aires, Pabellion 1 - Ciudad Universitaria, 1428 Buenos Aires, Argentina |
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Abstract: | 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. |
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Keywords: | 18B25 18B40 |
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