Frobenius monoidal functors from ambiadjunctions and their lifts to Drinfeld centers

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.

arXiv commentv2: some typos were corrected (introduction), v3: minor corrections, final version to appear in Adv. Math

References in corpus (10)

• TFT construction of RCFT correlators I: Partition functions
• Correspondences of ribbon categories
• Hopf monads on monoidal categories
• Braided tensor categories and extensions of vertex operator algebras
• Note on Frobenius monoidal functors
• On Hopf adjunctions, Hopf monads and Frobenius-type properties
• What Separable Frobenius Monoidal Functors Preserve
• The indecomposable objects in the center of Deligne's category $Rep(S_t)$
• Constructing non-semisimple modular categories with local modules
• Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras