# Modular categories

## Braided zesting and its applications

We give a rigorous development of the construction of new braided fusion categories from a given category known as zesting. This method has been used in the past to provide categorifications of new fusion rule algebras, modular data, and minimal …

## Group actions on 2-categories

We study actions of discrete groups on 2-categories. The motivating examples are actions on the 2-category of representations of finite tensor categories and their relation with the extension theory of tensor categories by groups. Associated to a …

## On invariants of modular categories beyond modular data

We study novel invariants of modular categories that are beyond the modular data, with an eye towards a simple set of complete invariants for modular categories. Our focus is on the W-matrix—the quantum invariant of a colored framed Whitehead link …

## On acyclic anyon models

Acyclic anyon models are non-abelian anyon models for which thermal anyon errors can be corrected. In this note, we characterize acyclic anyon models and raise the question whether the restriction to acyclic anyon models is a deficiency of the …

## Fermionic modular categories and the 16-fold way

We study spin and super-modular categories systematically as inspired by fermionic topological phases of matter, which are always fermion parity enriched and modelled by spin topological quantum field theories at low energy. We formulate a 16-fold …

## Tensor functors between Morita duals of fusion categories.

Given a fusion category $\mathcal{C}$ and an indecomposable $\mathcal{C}$-module category $\mathcal{M}$, the fusion category $\mathcal{C}_{\mathcal{M}}^{*}$ of $\mathcal{C}$-module endofunctors of $\mathcal{M}$ is called the (Morita) dual fusion …

## On gauging symmetry of modular categories

Topological order of a topological phase of matter in two spacial dimensions is encoded by a unitary modular (tensor) category (UMC). A group symmetry of the topological phase induces a group symmetry of its corresponding UMC. Gauging is a well-known …

## On the classification of weakly integral modular categories.

We classify all modular categories of dimension 4m, where m is an odd square-free integer, and all ranks 6 and 7 weakly integral modular categories. This completes the classification of weakly integral modular categories through rank 7. Our results …

## Solutions of the hexagon equation for abelian anyons

We address the problem of determining the obstruction to existence of solutions of the hexagon equation for abelian fusion rules and the classification of prime abelian anyons.

## Classification of integral modular categories of Frobenius-Perron dimension $pq^{4}$ and $p^{2}q^{2}$

We classify integral modular categories of dimension $p{{q}^{4}}$ and ${{p}^{2}}{{q}^{2}}$ , where $p$ and $q$ are distinct primes. We show that such categories are always group-theoretical, except for categories of dimension $4{{q}^{2}}$ . …