Abstract For ℳ and NN finite module categories over a finite tensor category CC, the
category ℛ ex CR ex _ C (ℳ, NN) of right exact module functors is a finite module category …

We organize the modified trace theory with the use of the Nakayama functor of finite abelian
categories. For a linear right exact functor Σ on a finite abelian category MM, we introduce …

Let C be a finite tensor category and M an exact left C-module category. We call M
unimodular if the finite multitensor category Rex C (M) of right exact C-module endofunctors …

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 …

Various monoidal categories, including suitable representation categories of vertex operator
algebras, admit natural Grothendieck-Verdier duality structures. We recall that such a …

It is easy to find algebras T∈ C in a finite tensor category C that naturally come with a lift to a
braided commutative algebra T∈ Z (C) in the Drinfeld center of C. In fact, any finite tensor …

We present explicit mathematical structures that allow for the reconstruction of the field
content of a full local conformal field theory from its boundary fields. Our framework is the …

The Morita context provided by an exact module category over a finite tensor category gives
a two-object bicategory with duals. Right and left duals of objects in the module category are …

This book studies using string-net models to accomplish a direct, purely two-dimensional,
approach to correlators of two-dimensional rational conformal field theories. The authors …

It is a common and often repeated saying that for any quantum field theory the ultimate goal
is to solve the theory. Alas, already specifying in concrete terms the very meaning of this …