Related papers: Pointed Drinfeld center functor

We introduce the category of set-theoretic representations of a matched pair of groupoids. This is a monoidal category endowed with a monoidal functor to the category of quivers over the common base of the groupoids in the matched pair (the…

This paper addresses the question of how categorical symmetries act on extended operators in quantum field theory. Building on recent results in two dimensions, we introduce higher tube categories and algebras associated to higher fusion…

We show that the module of integral points on a Drinfeld module satisfies a an analogue of Dirichlet's unit theorem, despite its failure to be finitely generated. As a consequence, we obtain a construction of a canonical finitely generated…

A comprehensive symmetry resolution of the entanglement entropy (EE) in $(1+1)$-d rational conformal field theories (RCFT) with categorical non-invertible symmetries is presented. This amounts to symmetry resolving the entanglement with…

Let $\mathcal{C}$ be a spherical fusion category. The goal of this article is to present the tube category of $\mathcal{C}$, denoted $\mathcal{TC}$, as giving an alternative graphical perspective on the Drinfeld centre of $\mathcal{C}$,…

We describe an approach to classification of fusion categories in terms of Morita equivalence. This is usually achieved by analyzing Drinfeld centers of fusion categories and finding Tannakian subcategories therein.

We point out that double categories provide a natural setting for modular functors obtained by a (bicategorical) string-net construction: The source of the modular functor -- which is now a double functor -- is a symmetric monoidal double…

For a finite extension $F$ of $\mathbb{Q}_p$ and $n \geq 1$, let $D$ be the division algebra over $F$ of invariant $1/n$ and let $G^0$ be the subgroup of $\text{GL}_n(F)$ of elements with norm $1$ determinant. We show that the action of…

We associate to a 2-vector bundle over an essentially finite groupoid a 2-vector space of parallel sections, or, in representation theoretic terms, of higher invariants, which can be described as homotopy fixed points. Our main result is…

Many quantum invariants of knots and 3-manifolds (e.g. Jones polynomials) are special cases of the Witten-Reshetikhin-Turaev 3D TQFT. The latter is in turn a part of a larger theory - the Crane-Yetter 4D TQFT. In this work, we compute the…

We present a general framework for TQFT and related constructions using the language of monoidal categories. We construct a topological category C and an algebraic category D, both monoidal, and a TQFT functor is then defined as a certain…

For a finite braided tensor category we introduce its Picard crossed module consisting of the group of invertible module categories and the group of braided tensor autoequivalences. We describe the Picard crossed module in terms of braided…

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…

Recently it has been observed that branes in geometric engineering and holography have a striking connection with generalized global symmetries. In this paper we argue that branes, in a certain topological limit, not only furnish the…

We study the interaction between geometric operations on stacks and algebraic operations on their categories of sheaves. We work in the general setting of derived algebraic geometry: our basic objects are derived stacks X and their…

We give a characterization of Drinfeld centers of fusion categories as non-degenerate braided fusion categories containing a Lagrangian algebra. Further we study the quotient of the monoid of non-degenerate braided fusion categories modulo…

A finite tensor category is called pointed if all its simple objects are invertible. We find necessary and sufficient conditions for two pointed semisimple categories to be dual to each other with respect to a module category. Whenever the…

We provide a complete set of identities for the symmetric monoidal category, TOF, generated by the Toffoli gate and computational ancillary bits. We do so by demonstrating that the functor which evaluates circuits on total points, is an…

This lecture series is based on joint work in progress with Shaul Barkan, as well as work in progress of the author. The five sections of these notes correspond to the five lectures, but more details have been added. $2$-dimensional…

We investigate symmetry topological field theories (SymTFTs) of non-abelian and non-invertible symmetries and the different Lagrangian algebras associated with a given Drinfeld center. For several examples we analyze the condensable…