A finite braided tensor category is fully dualizable in the Morita 4-category of braided pre-tensor categories whenever its symmetric center is separable.
Modular properties of ribbon abelian categories
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abstract
A category N of labeled (oriented) trivalent graphs (nets) or ribbon graphs is extended by new generators called fusing, braiding, twist and switch with relations which can be called Moore--Seiberg relations. A functor to N is constructed from the category Surf of oriented surfaces with labeled boundary and their homeomorphisms. Given an (eventually non-semisimple) k-linear abelian ribbon braided category C with some finiteness conditions we construct a functor from a central extension of N with the set of labels ObC to k-vector spaces. Composing the functors we get a modular functor from a central extension of Surf to k-vector spaces. This is a mathematical paper which explains how to get proofs for its hep-th companion paper, which should be read first. Complete proofs are not given here. (Talk at Second Gauss Simposium, Munich, August 1993.)
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Relative Invertibility and Full Dualizability of Finite Braided Tensor Categories
A finite braided tensor category is fully dualizable in the Morita 4-category of braided pre-tensor categories whenever its symmetric center is separable.