Stacks associated to abelian tensor categories
Abstract
For an abelian tensor category a stack is constructed. As an application we show that our construction can be used to recover a quasi-compact separated scheme from the category of its quasi-coherent sheaves. In another application, we show how the "dual stack" of the classifying stack BG of a finite group G can be obtained by altering the tensor product on the category G of G-representations. Using glueing techniques we show that the dual pair of a G-gerbe, in the sense of [TT10], can be constructed by glueing local dual stacks.
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