On Generalized Symmetries and Structure of Modular Categories

Abstract

Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf monads. The main goal is a generalization of extension and gauging group symmetries to category symmetries of modular categories, which include also categorical Hopf algebras as special cases. As an application, we propose an analogue of the classification of finite simple groups to modular categories, where we define simple modular categories as the prime ones without any nontrivial normal algebras.

References in corpus (7)

• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Hopf monads on monoidal categories
• On Gauging Symmetry of Modular Categories
• On invariants of Modular categories beyond modular data
• On Classification of Finite-Dimensional Superbialgebras and Hopf Superalgebras
• Weak bimonads and weak Hopf monads
• A systematic search of knot and link invariants beyond modular data