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The classifying topos of a continuous groupoid. I. (English) Zbl 0706.18007
Summary: 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.

MSC:
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
18B25 Topoi
18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)
18D35 Structured objects in a category (MSC2010)
18B30 Categories of topological spaces and continuous mappings (MSC2010)
18B35 Preorders, orders, domains and lattices (viewed as categories)
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