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

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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.


Original languageEnglish
Publication statusPublished - 14 Jan 2022
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  • math.QA, math.CT, primary:18M15, secondary: 16T05, 18C20, 18M30