The Burnside Bicategory of Groupoids
نویسنده
چکیده
Morphisms from H to G in the Burnside category of groups are provided by sets with commuting right and left actions of H and G, which are free and finite over G. We extend this construction to groupoids by considering a G-action on a set X as a homomorphism G → Aut(X). This has an alternative expression in terms of “bi-actions,” a variant of the discrete version of a topological construction which provides a convenient account of the theory of orbifolds [6]. We obtain a bicategory B, the “Burnside bicategory of groupoids.” It comes equipped with a morphism [7] from the bicategory G of groupoids, functors, and natural transformations, and a compatible functor from the opposite of the sub-bicategory Gcf generated by “finite covers” of groupoids. We think of the first as “stabilization” and the second as providing “transfers.”
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