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 …

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 …

arXiv:1509.06811v1 [math.AT] 22 Sep 2015 Page 1 arXiv:1509.06811v1 [math.AT] 22 Sep 2015
MODULAR CATEGORIES AS REPRESENTATIONS OF THE 3-DIMENSIONAL BORDISM …

We begin with a brief sketch of what is known and conjectured concerning braided monoidal
2-categories and their relevance to 4d TQFTs and 2-tangles. Then we give concise …

Tannaka duality and its extensions by Lurie, Sch\" appi et al. reveal that many schemes as
well as algebraic stacks may be identified with their tensor categories of quasi-coherent …

Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio
is not an integer! But this can happen for generalizations of vector spaces—objects of a …

We provide a complete generators and relations presentation of the 2-dimensional extended
unoriented and oriented bordism bicategories as symmetric monoidal bicategories. Thereby …

The theory of monoidal categories is intimately related to topology. Morphisms in monoidal
categories and operations on these morphisms may be represented by pictures, as was …

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 …

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 …