Title: Generalized Tannaka duality
Speaker: Daniel Schaeppi
Speaker Info: University of Chicago
Tannaka duality is a duality between group-like objects (groups, compact topological groups, affine group/groupoid schemes over a field) and their categories of representations. To a group-like object we can assign its category of representations, and it turns out that we can often also go in the other direction: from the data of a category with certain structures we can construct a group-like object. The basic question is then to what extent these processes are inverse to each other.Date: Monday, October 3, 2011
In the case of affine group/groupoid schemes over a field this was settled by results of Saavedra-Rivano, Deligne and Milne. We provide a bicategorical framework for the Tannakian formalism. This allows us to generalize some of these results to affine group/groupoid schemes over arbitrary commutative rings, and, even more generally, Hopf algebroids in symmetric monoidal categories.