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 introduce the notion of n–dimensional topological quantum field theory (TQFT) with
defects as a symmetric monoidal functor on decorated stratified bordisms of dimension n …

We develop a general theory of 3-dimensional``orbifold completion'', to describe
(generalised) orbifolds of topological quantum field theories as well as all their defects …

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We initiate a systematic study of 3-dimensional 'defect'topological quantum field theories,
that we introduce as symmetric monoidal functors on stratified and decorated bordisms. For …

We construct three classes of generalised orbifolds of Reshetikhin-Turaev theory for a
modular tensor category $\mathcal {C} $, using the language of defect TQFT from [arXiv …

To a graded finite-rank matrix factorisation of the difference of two homogeneous potentials
one can assign two numerical invariants, the left and right quantum dimensions. The …

We study a 2-functor that assigns to a bimodule category over a finite 𝕜 \Bbbk-linear tensor
category a 𝕜 \Bbbk-linear abelian category. This 2-functor can be regarded as a category …

This article investigates duals for bimodule categories over finite tensor categories. We show
that finite bimodule categories form a tricategory and discuss the dualities in this tricategory …

We show how to calculate the relative tensor product of bimodule categories (not
necessarily invertible) using ladder string diagrams. As an illustrative example, we compute …