Related papers: Simple current auto-equivalences of modular tensor…

We discuss what has been achieved in the past twenty years on the construction and study of a braided finite tensor category structure on a suitable module category for a suitable vertex operator algebra. We identify the main difficult…

Let X be a smooth projective variety over C. We find the natural notion of semistable orthogonal bundle and construct the moduli space, which we compactify by considering also orthogonal sheaves, i.e. pairs (E,\phi), where E is a torsion…

We investigate the bounded derived category of coherent sheaves on irreducible singular projective curves of arithmetic genus one. A description of the group of exact auto-equivalences and the set of all t-structures of this category is…

We study the construction of tensor products of representations up to homotopy, which are the A-infinity version of ordinary representations. We provide formulas for the construction of tensor products of representations up to homotopy and…

Let $V$ be a vertex operator algebra with a category $\mathcal{C}$ of (generalized) modules that has vertex tensor category structure, and thus braided tensor category structure, and let $A$ be a vertex operator (super)algebra extension of…

We construct a category equivalent to the category $\mathbf{Mon}$ of monoids and monoid homomorphisms, based on categories with strict factorization systems. This equivalence is then extended to the category $\mathbf{Mon_s}$ of unital…

We give a short proof for a well-known formula for the rank of a $G$-crossed braided extension of a modular tensor category.

This paper studies the existence of and compatibility between derived change of ring, balanced product, and function module derived functors on module categories in monoidal model categories.

A graded tensor category over a group $G$ will be called a strongly $G$-graded tensor category if every homogeneous component has at least one multiplicativily invertible object. Our main result is a description of the module categories…

We present a method of constructing symmetric monoidal bicategories from symmetric monoidal double categories that satisfy a lifting condition. Such symmetric monoidal double categories frequently occur in nature, so the method is widely…

Modular tensor categories are generalizations of the representation categories of quantum groups at roots of unity axiomatizing the properties necessary to produce 3-dimensional TQFTs. Although other constructions have since been found,…

By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…

The term fractal describes a class of complex structures exhibiting self-similarity across different scales. Fractal patterns can be created by using various techniques such as finite subdivision rules and iterated function systems. In this…

We give two results concerning the construction of modular invariant partition functions for conformal field theories constructed by tensoring together other conformal field theories. First we show how the possible modular invariants for…

We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on…

Let $(H,\a_H)$ be a Hom-Hopf algebra, $(A,\a_A)$ a right $H$-comodule algebra and $(C,\a_C)$ a left $H$-module coalgebra. Then we have the category $_A\mathcal{M}(H)^C$ of Hom-type Doi-Hopf modules. The aim of this paper is to make the…

We describe new autoequivalences of derived categories of coherent sheaves arising from what we call $\mathbb P^n$-objects of the category. Standard examples arise from holomorphic symplectic manifolds. Under mirror symmetry these…

When designing plans in engineering, it is often necessary to consider attributes associated to objects, e.g. the location of a robot. Our aim in this paper is to incorporate attributes into existing categorical formalisms for planning,…

For any finite group G with a finite G-set X and a modular tensor category C we construct a part of the algebraic structure of an associated G-equivariant monoidal category: For any group element g in G we exhibit the module category…

Given a stratified topological space, we answer the question whether the functor from the derived category of constructible sheaves to the derived category of sheaves with constructible cohomology is an equivalence. We also establish basic…