Tannaka-Krein reconstruction and a characterization of modular tensor categories
arXiv:0711.1402 · doi:10.1016/j.jalgebra.2009.02.026
Abstract
We show that every modular category is equivalent as an additive ribbon category to the category of finite-dimensional comodules of a Weak Hopf Algebra. This Weak Hopf Algebra is finite-dimensional, split cosemisimple, weakly cofactorizable, coribbon and has trivially intersecting base algebras. In order to arrive at this characterization of modular categories, we develop a generalization of Tannaka-Krein reconstruction to the long version of the canonical forgetful functor which is lax and oplax monoidal, but not in general strong monoidal, thereby avoiding all the difficulties related to non-integral Frobenius-Perron dimensions.
52 pages; LaTeX2e; xypic and pstricks macros; v2: typos corrected
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- Quantum gravity kinematics from extended TQFTs
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