Journal
SCIENCE CHINA-MATHEMATICS
Volume 62, Issue 3, Pages 417-446Publisher
SCIENCE PRESS
DOI: 10.1007/s11425-018-9455-5
Keywords
modular category; category symmetry; Hopf monad; tensor functor; 18D10; 81R05
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Funding
- Simons Foundation
- National Science Foundation of USA [DMS-1411212, FRG-1664351]
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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.
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