Frobenius monoidal functors from ambiadjunctions and their lifts to Drinfeld centers
arXiv:2410.08702 · doi:10.1016/j.aim.2025.110344
Abstract
We identify general conditions, formulated using the projection formula morphisms, for a functor that is simultaneously left and right adjoint to a strong monoidal functor to be a Frobenius monoidal functor. Moreover, we identify stronger conditions for the adjoint functor to extend to a braided Frobenius monoidal functor on Drinfeld centers building on our previous work in [arXiv:2402.10094]. As an application, we construct concrete examples of (braided) Frobenius monoidal functors obtained from morphisms of Hopf algebras via induction.
v2: some typos were corrected (introduction), v3: minor corrections, final version to appear in Adv. Math