Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras

We construct a separable Frobenius monoidal functor from Z(Vect omega|H) to Z (Vect omega) for any subgroup H of G which preserves braiding and ribbon structure. As an H application, we classify rigid Frobenius algebras in Z (Vect omega G ), recovering the classification of G etale 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 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.