César Galindo

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 theoretical tool to promote a global symmetry to a local gauge symmetry. We give a mathematical formulation of gauging in terms of higher category formalism. Roughly, given a UMC with a symmetry group G, gauging is a 2-step process: first extend the UMC to a G-crossed braided fusion category and then take the equivariantization of the resulting category. Gauging can tell whether or not two enriched topological phases of matter are different, and also provides a way to construct new UMCs out of old ones. We derive a formula for the

Fermionic modular categories and the 16-fold way

{H^4}

Tensor functors between Morita duals of fusion categories

H4-obstruction, prove some properties of gauging, and carry out gauging for two concrete examples.

De-Equivariantization of Hopf Algebras

This paper introduces Hopf braces, a new algebraic structure related to the Yang-Baxter equation which include Rumps braces and their non-commutative generalizations as particular cases. Several results of classical braces are still valid in our context. Furthermore, Hopf braces provide the right setting for considering left symmetric algebras as Lie-theoretical analogs of braces.

On the Classification of Galois Objects for Finite Groups

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 TQFTs at low energy. We formulate a

Coherence for monoidal G-categories and braided G-crossed categories

16

On acyclic anyon models

-fold way conjecture for the minimal modular extensions of super-modular categories to spin modular categories, which is a categorical formulation of gauging the fermion parity. We investigate general properties of super-modular categories such as fermions in twisted Drinfeld doubles, Verlinde formulas for naive quotients, and explicit extensions of

Pointed finite tensor categories over abelian groups

PSU(2)_{4m+2}