Pivotality, twisted centres, and the anti-double of a Hopf monad

Sebastian Halbig and Tony Zorman

Finite-dimensional Hopf algebras admit a correspondence between so-called pairs in involution, one-dimensional anti-Yetter-Drinfeld modules and algebra isomorphisms between the Drinfeld and anti-Drinfeld double. We extend it to general rigid monoidal categories and provide a monadic interpretation under the assumption that certain coends exist. Hereto we construct and study the anti-Drinfeld double of a Hopf monad. As an application the connection with the pivotality of Drinfeld centres and their underlying categories is discussed.

Keywords: Pivotal categories, module categories, centres, heaps, Hopf monads, comodule monads, anti-Drinfeld double

2020 MSC: primary: 18M15, secondary: 16T05, 18C20, 18M30

Theory and Applications of Categories, Vol. 41, 2024, No. 4, pp 86-149.

Published 2024-01-29.


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