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**1 - 3**of**3**### From subfactors to categories and topology III. Triangulation invariants of 3-manifolds and Morita equivalence of tensor categories

- In preparation

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### A NOTE ON INTERMEDIATE SUBFACTORS OF KRISHNAN-SUNDER SUBFACTORS

, 2002

"... Abstract. A Krishnan-Sunder subfactor RU ⊂ R of index k 2 is constructed from a permutation biunitary matrix U ∈ Mp(C) ⊗ Mk(C), i.e. the entries of U are either 0 or 1 and both U and its block transpose are unitary. The author previously showed that every irreducible Krishnan-Sunder subfactor has a ..."

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Abstract. A Krishnan-Sunder subfactor RU ⊂ R of index k 2 is constructed from a permutation biunitary matrix U ∈ Mp(C) ⊗ Mk(C), i.e. the entries of U are either 0 or 1 and both U and its block transpose are unitary. The author previously showed that every irreducible Krishnan-Sunder subfactor has an intermediate subfactor by exhibiting the associated Bisch projection. The author has also shown in a separate paper that the principal and dual graphs of the intermediate subfactor are the same as those of the subfactor R Γ ⊂ R H, where H ⊂ Γ is an inclusion of finite groups with an outer action on R. In this paper we give a direct proof that the intermediate subfactor is isomorphic to R Γ ⊂ R H. 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 non-technical, 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 non-technical, 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 k-linear categories with finite dimensional hom-spaces. 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