Related papers: Crossed product tensor categories
This is the eighth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part VIII), we construct the braided…
Following the analogy between algebras (monoids) and monoidal categories the construction of nucleus for non-associative algebras is simulated on the categorical level. Nuclei of categories of modules are considered as an example.
One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we continue the work of [7] to adapt the machinery of globular operads [4] to…
This is the third part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part III), we introduce and study…
In order to simultaneously generalize matrix rings and group graded crossed products, we introduce category crossed products. For such algebras we describe the center and the commutant of the coefficient ring. We also investigate the…
An example of double cross coproducts with both non-trivial left coaction and non-trivial right coaction in strictly braided tensor categories is given.
We define an action of the braid group of a simple Lie algebra on the space of imaginary roots in the corresponding quantum affine algebra. We then use this action to determine an explicit condition for a tensor product of arbitrary…
Let G be a group and let P be a subsemigroup of G. In order to describe the crossed product of a C*-algebra A by an action of P by unital endomorphisms we find that we must extend the action to the whole group G. This extension fits into a…
A crossed product functor is said to be injective if it takes injective morphisms to injective morphisms. In this paper we show that every locally compact group $G$ admits a maximal injective crossed product $A\mapsto A\rtimes_{\inj}G$.…
This paper develops a theory of monoidal categories relative to a braided monoidal category, called augmented monoidal categories. For such categories, balanced bimodules are defined using the formalism of balanced functors. The two main…
The recently developed theory of partial actions of discrete groups on $C^*$-algebras is extended. A related concept of actions of inverse semigroups on $C^*$-algebras is defined, including covariant representations and crossed products.…
We provide a reference for basic categorial properties of the categories of (possibly non-unital) $\mathbb{C}$-linear $*$-categories or $C^{*}$-categories, and (not necessarily unit-preserving) functors. Generalizing the classical case of…
We define a bar construction endofunctor on the category of commutative augmented monoids $A$ of a symmetric monoidal category $\mathcal{V}$ endowed with a left adjoint monoidal functor $F:s\mathbf{Set}\to \mathcal{V}$. To do this, we need…
Let $V$ be a vertex operator algebra satisfying suitable conditions such that in particular its module category has a natural vertex tensor category structure, and consequently, a natural braided tensor category structure. We prove that the…
In this paper we introduce the crossed product construction for a discrete group action on an operator system. In analogy to the work of E. Katsoulis and C. Ramsey, we describe three canonical crossed products arising from such a dynamical…
Two pertinent questions for any support theory of a monoidal triangulated category are whether it is functorial and if the tensor product property holds. To this end, we consider the complete prime spectrum of an essentially small monoidal…
Are introduced six examples of non-braidable tensor categories which are extensions of the category Comod(H), for H a super-group algebra; and two examples of braided categories where the only possible braiding is the trivial braiding.
A pointed fusion category is a rigid tensor category with finitely many isomorphism classes of simple objects which moreover are invertible. Two tensor categories $C$ and $D$ are weakly Morita equivalent if there exists an indecomposable…
Let $\mathcal C$ be a category with finite colimits, writing its coproduct $+$, and let $(\mathcal D, \otimes)$ be a braided monoidal category. We describe a method of producing a symmetric monoidal category from a lax braided monoidal…
We use a representation of a graded twisted tensor product of $K[x]$ with $K[y]$ in $L(K^{\Bbb{N}_0})$ in order to obtain a nearly complete classification of these graded twisted tensor products via infinite matrices. There is one…