Holmstrom Tannakian duality

http://mathoverflow.net/questions/16257/how-to-unify-various-reconstruction-theorems-gabriel-rosenberg-tannaka-balmers

http://nlab.mathforge.org/nlab/show/Tannaka+duality

Toen refers in the AIM talk to an unpublished homotopy version of Tannakian duality, in which schematic homotopy types appear as Tannakian dual of certain Tannakian model categories. He does give examples but no generalities.

Toen: Homotopical and higher categorical structures in algebraic geometry. File Toen web unpubl hab.pdf. Treats Tannakian duality for Segal cats, and schematic homotopy types.

An old preprint of Toen: Dualite de Tannaka superieure I. File Toen web unpubl tan.pdf.

arXiv:1204.5787 Tannaka duality over ring spectra from arXiv Front: math.AT by James Wallbridge 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.

nLab page on Tannakian duality