Theta-Categories and Tannakian duality

Abstract

We introduce a notion of $\hat{I}˜$-categories, which is a refinement of the notion of symmetric monoidal $\infty$-categories. We use this notion to prove a Tannakian duality statement, relating $\hat{I}˜$-categories with fpqc-stacks by means of a certain stack of fiber functors in the context of $\hat{I}˜$-categories. This provides, over a base ring of arbitrary characteristic, a strong link between Tannakian $\hat{I}˜$-categories and the schematic homotopy types.

33 pages