Theta-Categories and Tannakian duality

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