Antipodes, preantipodes and Frobenius functors
arXiv:1906.03435 · doi:10.1142/S0219498821501243
Abstract
We prove that a quasi-bialgebra admits a preantipode if and only if the associated free quasi-Hopf bimodule functor is Frobenius, if and only if the relative (opmonoidal) monad is a Hopf monad. The same results hold in particular for a bialgebra, tightening the connection between Hopf and Frobenius properties.
Author's Accepted Manuscript