English

Frobenius monoidal functors from ambiadjunctions and their lifts to Drinfeld centers

Category Theory 2025-05-21 v3 Quantum Algebra Representation Theory

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.

Keywords

Cite

@article{arxiv.2410.08702,
  title  = {Frobenius monoidal functors from ambiadjunctions and their lifts to Drinfeld centers},
  author = {Johannes Flake and Robert Laugwitz and Sebastian Posur},
  journal= {arXiv preprint arXiv:2410.08702},
  year   = {2025}
}

Comments

v2: some typos were corrected (introduction), v3: minor corrections, final version to appear in Adv. Math