We construct a braided monoidal functor from Bobtcheva and Piergallini's category of
connected 4-dimensional 2-handlebodies (up to 2-deformations) to an arbitrary unimodular …

In this paper, we give a new direct proof of a result by Bobtcheva and Piergallini that
provides finite algebraic presentations of two categories, denoted $3\mathrm {Cob} $ and …

This paper is the second part of our work on 4-dimensional 2-handlebodies. In the first part
(arXiv: math. GT/0407032) it is shown that up to certain set of local moves, connected simple …

The bicategorical point of view provides a natural setting for many concepts in the
representation theory of monoidal categories. We show that centers of twisted bimodule …

A deeper understanding of recent computations of the Brauer group of Hopf algebras is
attained by explaining why a direct product decomposition for this group holds and …

A modular object in a symmetric monoidal bicategory is a Frobenius algebra object whose
product and coproduct are biadjoint, equipped with a braided structure and a compatible …

For any finite-dimensional factorizable ribbon Hopf algebra H and any ribbon automorphism
of H, we establish the existence of the following structure: an H-bimodule Fω and a bimodule …

Let $ U:\mathcal {C}\rightarrow\mathcal {D} $ be a strong monoidal functor between abelian
monoidal categories admitting a right adjoint $ R $, such that $ R $ is exact, faithful and the …

Given a Hopf algebra in a symmetric monoidal category with duals, the category of modules
inherits the structure of a monoidal category with duals. If the notion of algebra is replaced …

Following a suggestion of Turaev, we explain results of Crane and Yetter concerning the
ubiquity of Hopf algebras in constructions of 3D tqft's as showing that the punctured torus is …