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Pivotality, twisted centres, and the anti-double of a Hopf monad
Theory and applications of categories, Tome 41 (2024), pp. 86-149

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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.

Publié le :
Classification : primary: 18M15, secondary: 16T05, 18C20, 18M30
Keywords: Pivotal categories, module categories, centres, heaps, Hopf monads, comodule monads, anti-Drinfeld double 
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     author = {Sebastian Halbig and Tony Zorman},
     title = {Pivotality, twisted centres, and the anti-double of a {Hopf} monad},
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     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a3/}
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Sebastian Halbig; Tony Zorman. Pivotality, twisted centres, and the anti-double of a Hopf monad. Theory and applications of categories, Tome 41 (2024), pp. 86-149. http://geodesic.mathdoc.fr/item/TAC_2024_41_a3/