Theta-categories are symmetric monoidal infinity-categories with an LSym monad, and every neutralized Tannakian Theta-category is equivalent to the ind-perfect complexes on its stack of LSym-fiber functors.
Tannaka duality over ring spectra
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abstract
We prove a Tannaka duality theorem for $(\infty,1)$-categories. This is a duality between certain derived group stacks, or more generally certain derived gerbes, and symmetric monoidal $(\infty,1)$-categories endowed with particular structure. This duality theorem is defined over commutative ring spectra and subsumes the classical statement. We show how the classical theory, and its extension over arbitrary rings, arises as a special case of our more general theory. The application to perfect complexes is explored.
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Theta-Categories and Tannakian duality
Theta-categories are symmetric monoidal infinity-categories with an LSym monad, and every neutralized Tannakian Theta-category is equivalent to the ind-perfect complexes on its stack of LSym-fiber functors.