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From subfactors to categories and topology III. Triangulation invariants of 3manifolds and Morita equivalence of tensor categories
 In preparation
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FUSION SUBCATEGORIES OF REPRESENTATION CATEGORIES OF TWISTED QUANTUM DOUBLES OF FINITE GROUPS
, 810
"... of a twisted quantum double D ω (G), where G is a finite group and ω is a 3cocycle on G. In view of the fact that every grouptheoretical braided fusion category can be embedded into some Rep(D ω (G)), this gives a complete description of all grouptheoretical braided fusion categories. We describe ..."
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of a twisted quantum double D ω (G), where G is a finite group and ω is a 3cocycle on G. In view of the fact that every grouptheoretical braided fusion category can be embedded into some Rep(D ω (G)), this gives a complete description of all grouptheoretical braided fusion categories. We describe the lattice and give formulas for some invariants of the fusion subcategories of Rep(D ω (G)). We also give a characterization of grouptheoretical braided fusion categories as equivariantizations of pointed categories. 1.
Tensor categories: A selective guided tour ∗
, 2008
"... These are the – only lightly edited – lecture notes for a short course on tensor categories. The coverage in these notes is relatively nontechnical, focussing on the essential ideas. They are meant to be accessible for beginners, but it is hoped that also some of the experts will find something int ..."
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These are the – only lightly edited – lecture notes for a short course on tensor categories. The coverage in these notes is relatively nontechnical, focussing on the essential ideas. They are meant to be accessible for beginners, but it is hoped that also some of the experts will find something interesting in them. Once the basic definitions are given, the focus is mainly on klinear categories with finite dimensional homspaces. Connections with quantum groups and low dimensional topology are pointed out, but these notes have no pretension to cover the latter subjects at any depth. Essentially, these notes should be considered as annotations to the extensive bibliography. We also recommend the recent review [33], which covers less ground in a deeper way. 1 Tensor categories 1.1 Strict tensor categories