The classifying topos of a continuous groupoid. I

Moerdijk, Ieke

doi:10.1090/S0002-9947-1988-0973173-9

The classifying topos of a continuous groupoid. I
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by Ieke Moerdijk

Trans. Amer. Math. Soc. 310 (1988), 629-668

DOI: https://doi.org/10.1090/S0002-9947-1988-0973173-9

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Abstract:

We investigate some properties of the functor $B$ which associates to any continuous groupoid $G$ its classifying topos $BG$ of equivariant $G$-sheaves. In particular, it will be shown that the category of toposes can be obtained as a localization of a category of continuous groupoids.

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