Related papers: A remark about the Connes fusion tensor product

We investigate the problem when the tensor functor by a bimodule yields a singular equivalence. It turns out that this problem is equivalent to the one when the Hom functor given by the same bimodule induces a triangle equivalence between…

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

It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extend this is still true. We give an explicit description of the…

Given a Hopf algebra H, we study modules and bimodules over an algebra A that carry an H-action, as well as their morphisms and connections. Bimodules naturally arise when considering noncommutative analogues of tensor bundles. For…

We introduce a method for associating a chain complex to a module over a combinatorial category, such that if the complex is exact then the module has a rational Hilbert series. We prove homology--vanishing theorems for these complexes for…

We prove the existence of self-dual tensor products for finite-dimensional convex cones and operator systems. This is a consequence of a more general result: Every cone system, which is contained in its dual, can be enlarged to a self-dual…

We study right exact tensor products on the category of finitely presented functors. As our main technical tool, we use a multilinear version of the universal property of so-called Freyd categories. Furthermore, we compare our constructions…

We introduce fusion, contragradient and braiding of Hilbert affine representations of a subfactor planar algebra $P$ (not necessarily having finite depth). We prove that if $N \subset M$ is a subfactor realization of $P$, then the Drinfeld…

We give a notion of equivalence for Fell bundles over groups, not necessarily saturated nor separable, and show that equivalent Fell bundles have Morita-Rieffel equivalent cross-sectional $C^*$-algebras. Our notion is originated in the…

Category theory provides a means through which many far-ranging fields of mathematics can be related by their similar structure. In a paper by Robinson [2], this interconnectivity afforded by categorical perspectives allowed for the…

We first generalize the logarithmic tensor category theory of Huang-Lepowsky-Zhang to the more general case that the module category for a vertex operator algebra $V$ (more generally a M\"{o}bius vertex algebra) might not be closed under…

The notion of crossed product by a coquasi-bialgebra H is introduced and studied. The resulting crossed product is an algebra in the monoidal category of right H-comodules. We give an interpretation of the crossed product as an action of a…

We construct the crossed product of a C(X)-algebra by an endomorphism, in such a way that the endomorphism itself becomes induced by the bimodule of continuous sections of a vector bundle. Some motivating examples for such a construction…

By a classic theorem of Beilinson, the perfect derived category $\operatorname{Perf}(\mathbb{P}^n)$ of projective space is equivalent to the category of derived representations of a certain quiver with relations. The vertex-wise tensor…

We establish a correspondence between modules and spans of algebras within a general monoidal 2-category $\mathfrak{C}$. Specifically, for an algebra $A$ in $\mathfrak{C}$, we construct a normalized lax 3-functor from the 2-category of…

Generalizing work by Pinzari and Roberts, we characterize actions of a compact quantum group G on C*-algebras in terms of what we call weak unitary tensor functors from Rep G into categories of C*-correspondences. We discuss the relation of…

The category of strict polynomial functors inherits an internal tensor product from the category of divided powers. To investigate this monoidal structure, we consider the category of representations of the symmetric group which admits a…

We first formulate a definition of tensor product for two modules for a vertex operator algebra in terms of a certain universal property and then we give a construction of tensor products. We prove the unital property of the adjoint module…

Let $G$ be a discrete group acting on a von Neumann algebra $M$ by properly outer $*$-automorphisms. In this paper we study the containment $M \subseteq M\rtimes_\alpha G$ of $M$ inside the crossed product. We characterize the intermediate…

After a brief review of recent rigorous results concerning the representation theory of rational chiral conformal field theories (RCQFTs) we focus on pairs (A,F) of conformal field theories, where F has a finite group G of global symmetries…