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

Huang, Lepowsky and Zhang have developed a module theory for vertex operator algebras
that endows suitably chosen module categories with the structure of braided monoidal …

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 define Hopf monads on an arbitrary monoidal category, extending the definition given in
Bruguières and Virelizier (2007)[5] for monoidal categories with duals. A Hopf monad is a …

The classifying spaces of handlebody groups form a modular operad. Algebras over the
handlebody operad yield systems of representations of handlebody groups that are …

We construct an equivalence between the categories of vertex operator algebras and vertex
operator coalgebras. We then investigate to what degree weak modules, generalized …

We establish an algebra-isomorphism between the complexified Grothendieck ring F of
certain bimodule categories over a modular tensor category and the endomorphism algebra …

This paper explores when the (lax) centre of a closed monoidal (enriched) functor category
is again a functor category. For some of this, we exploit the Kleisli construction in the …

In [7] and [9], the author introduced the notion of intertwining operator algebra, a
nonmeromorphic generalization of the notion of vertex operator algebra involving …

Any (co) ring R is an endofunctor with (co) multiplication on the category of abelian groups.
These notions were generalized to monads and comonads on arbitrary categories. Starting …