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The classifying topos of a continuous groupoid. II. (English) Zbl 0717.18001

Summary: [For part I see Trans. Am. Math. Soc. 310, No.2, 629-668 (1988; Zbl 0706.18007).]
Dans cet article, on construit une complétion \(\gamma\) G pour chaque groupoïde G, et on montre que tout foncteur continu exact BG\(\to BH\) entre les topoï calssifiants des groupoïdes continus G et H est obtenu par produit tensoriel avec un espace muni d’une action de \(\gamma\) G à gauche et de \(\gamma\) H à droite (“bi-espace”). On en déduit une description complète de la catégorie des topoï en termes de groupoïdes continus et de tels bi-espaces.

MSC:

18B25 Topoi
18F99 Categories in geometry and topology
18B30 Categories of topological spaces and continuous mappings (MSC2010)
18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)
18D35 Structured objects in a category (MSC2010)
18D05 Double categories, \(2\)-categories, bicategories and generalizations (MSC2010)
20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms)

Citations:

Zbl 0706.18007
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References:

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