We study the question of dualizability in higher Morita categories of locally presentable
tensor categories and braided tensor categories. Our main results are that the 3-category of …

We prove that a finite braided tensor category 𝒜 is invertible in the Morita 4–category BrTens
of braided tensor categories if and only if it is nondegenerate. This includes the case of …

We investigate the relationship between the algebra of tensor categories and the topology of
framed 3-manifolds. On the one hand, tensor categories with certain algebraic properties …

In this paper we study some properties of tensor categories that arise in 2-dimensional
conformal and 3-dimensional topological quantum field theory—socalled modular tensor …

Joyal and Street note in their paper on braided monoidal categories [Braided tensor
categories, Advances in Math. 102 (1993) 20–78] that the 2–category V–Cat of categories …

We show that the author's notion of Galois extensions of braided tensor categories [Adv.
Math. 150 (2000) 151], see also [A. Bruguières, Math. Ann. 316 (2000) 215], gives rise to …

We prove that the notion of Drinfeld center defines a functor from the category of
indecomposable multi-tensor categories with morphisms given by bimodules to that of …

We introduce the notions of normal tensor functor and exact sequence of tensor categories.
We show that exact sequences of tensor categories generalize strictly exact sequences of …

We define the Drinfeld center of a monoidal category enriched over a braided monoidal
category, and show that every modular tensor category can be realized in a canonical way …

A group–category is an additively semisimple category with a monoidal product structure in
which the simple objects are invertible. For example in the category of representations of a …