… By a tensor category we will mean an abelian rigid tensor category over k in which the unit
… Namely by a multi-tensor category we will mean a rigid tensor category in which the unit …

… an exact module category over a finite tensor category (somewhat analogous to the notion of
… projective module over a ring). We also show that module categories arise as categories of …

… In this paper we study some properties of tensor categories that arise in 2dimensional …
modular tensor category arising from the affine Lie algebras, in which case it will give a modular …

… For an abelian tensor category we investigate a Hopf algebra F in it, the “algebra of functions”
or “automorphisms of the identity functor”. We show the existence of the object of integrals …

… assume that our category is a fusion category: a rigid… tensor category with compatible
pivotal and braiding structures is called ribbon. In our case a ribbon category is always pre-modular …

… A unifying theme in the mathematical formulation of both (2 + 1)-TQFTs and CFTs is the notion
of a modular tensor category (MTC) [50]. Modular tensor categories are the algebraic data …

… that C is a modular tensor category. The main objects of study in this paper will be a certain
… of modular tensor categories that we will introduce shortly. Modular tensor categories from …

… small and all tensor categories strict. (A tensor category is strict if the tensor product satisfies
… By the coherence theorems, every tensor category is equivalent to a strict one.) Our notation …

… We consider the tensor category T of tilting modules of a quantum group Uqg, where g is a
simple Lie algebra and q = eπi/ld, with d ∈ {1, 2, 3} being the ratio of the square lengths of a …

… For tensor categories over fields of positive … tensor categories over fields of positive
characteristic for which an analogue of Deligne's theorem does not hold. To describe these …