Related papers: Symmetric tensor categories in characteristic 2

We develop the theory of module categories over a Grothendieck-Verdier category, i.e. a monoidal category with a dualizing object and hence a duality structure more general than rigidity. Such a category C comes with two monoidal structures…

We define a collection of tensor product norms for C*-algebras and show that a symmetric tensor product functor on the category of separable C*-algebras need not be associative.

In this paper, we prove the category of finite length modules for the $\mathbb{Z}_2$-orbifold $M(1)^+$ of the Heisenberg vertex operator algebra whose simple composition factors are $M(1)^\pm$ or $M(1,\lambda)$ for $\lambda \in…

In this paper we give a complete classification of unitary fusion categories $\otimes$-generated by an object of dimension $\frac{1 + \sqrt{5}}{2}$. We show that all such categories arise as certain wreath products of either the Fibonacci…

We advance support variety theory for finite tensor categories. First we show that the dimension of the support variety of an object equals the rate of growth of a minimal projective resolution as measured by the Frobenius-Perron dimension.…

In this paper we study categories $(F,\mathbf{C},\mathbf{D})$ and $(\mathbb{F},\mathbf{C},\mathbf{Set})$ and prove them to be fibred on $\mathbf{C}$. Then we examine Grothendieck construction in the context of an ordinary functor $F:…

We classify C-groups of ranks $n-1$ and $n-2$ for the symmetric group $S_n$. We also show that all these C-groups correspond to hypertopes, that is, thin, residually connected flag-transitive geometries. Therefore we generalise some similar…

We study properties of the category of modules of an algebra object A in a tensor category C. We show that the module category inherits various structures from C, provided that A is a Frobenius algebra with certain additional properties. As…

Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and…

We define equivariantization of tensor categories under tensor group scheme actions and give necessary and sufficient conditions for an exact sequence of tensor categories to be an equivariantization under a finite group or finite group…

We investigate invertible elements and gradings in braided tensor categories. This leads us to the definition of theta-, product-, subgrading and orbitcategories in order to construct new families of BTC's from given ones. We use the…

We develop a theory of descent and forms of tensor categories over arbitrary fields. We describe the general scheme of classification of such forms using algebraic and homotopical language, and give examples of explicit classification of…

We construct a functor valued invariant of oriented tangles on certain singular blocks of category O. Parabolic subcategories of these blocks categorify tensor products of various fundamental sl(k) representations. Projective functors…

The theory of tensor categories has found applications across various fields, including representation theory, quantum field theory (conformal in 2 dimensions, and topological in 3 and 4 dimensions), quantum invariants of low-dimensional…

Representations of a group $G$ in vector spaces over a field $K$ form a category. One can reconstruct the given group $G$ from its representations to vector spaces as the full group of monoidal automorphisms of the underlying functor. This…

We extend the calculus of relations to embed a regular category A into a family of pseudo-abelian tensor categories T(A,d) depending on a degree function d. Under the condition that all objects of A have only finitely many subobjects, our…

We define a category of planar diagrams whose Grothendieck group contains an integral version of the infinite rank Heisenberg algebra, thus yielding a categorification of this algebra. Our category, which is a q-deformation of one defined…

We introduce continuous Frobenius categories. These are topological categories which are constructed using representations of the circle over a discrete valuation ring. We show that they are Krull-Schmidt with one indecomposable object for…

Modular Tensor Categories (MTC's) arise in the study of certain condensed matter systems. There is an ongoing program to classify MTC's of low rank, up to modular data. We present an overview of the methods to classify modular tensor…

Let $\mathcal{C}:=\mathcal{C}(G,\omega,H,\psi)$ be a finite group scheme-theoretical category over an algebraically closed field of characteristic $p\ge 0$ as defined by the first author. For any indecomposable exact module category over…