SMS scnews item created by Anthony Henderson at Wed 12 May 2010 1558
Type: Seminar
Distribution: World
Expiry: 21 May 2010
Calendar1: 21 May 2010 1530-1630
CalLoc1: Carslaw 159
CalTitle1: Algebra Seminar: Jurco -- The classifying topos of a topological bicategory

Algebra Seminar

The classifying topos of a topological bicategory

Branislav Jurco

21st May, 3:30-4:30pm, Carslaw 159 (***NOTE UNUSUAL TIME AND ROOM***)



We introduce the classifying topos BB of a topological bicategory B as the Deligne topos of sheaves Sh(NB) on the simplicial space NB, the (Duskin) nerve of the bicategory B. It is shown that the category of geometric morphisms Hom(Sh(X),BB) from the topos of sheaves Sh(X) on a topological space X to the Deligne classifying topos BB is naturally equivalent to the category of principal B-bundles. As a simple consequence, the geometric realization |NB| of the nerve NB of a locally contractible topological bicategory B is the classifying space of principal B-bundles, giving a variant of the result of Baas, Bokstedt and Kro derived in the context of bicategorical K-theory. Similar construction works also for other types of nerves of the bicategory B (e.g., the nerves introduced by Lack and Paoli or Simpson and Tamsamani).

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