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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