Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras - Hannah, Samuel; Laugwitz, Robert; Ros Camacho, Ana (Symmetry, Integrability and Geometry: Methods and Applications, 2023)
We construct a separable Frobenius monoidal functor from (Vectω|ᴴ) to (Vectω) for any subgroup of which preserves braiding and ribbon structure. As an application, we classify rigid Frobenius algebras in (Vectω), recovering the classification of étale algebras in these categories by Davydov-Simmons [J. Algebra 471 (2017), 149-175, arXiv:1603.04650] and generalizing their classification to algebraically closed fields of arbitrary characteristic. Categories of local modules over such algebras are modular tensor categories by the results of Kirillov-Ostrik [Adv. Math. 171 (2002), 183-227, arXiv:math.QA/0101219] in the semisimple case and Laugwitz-Walton [Comm. Math. Phys., to appear, arXiv:2202.08644] in the general case.