FROBENIUS MONOIDAL FUNCTORS FROM (CO)HOPF ADJUNCTIONS

. Let U : C -> D be a strong monoidal functor between abelian monoidal categories admitting a right adjoint R, such that R is exact, faithful and the adjunction U H R is coHopf. Building on the work of Balan [Appl. Categ. Structures 25 (2017), pp. 747-774], we show that R is separable (resp., special) Frobenius monoidal if and only if R(1D) is a separable (resp., special) Frobenius algebra in C. If further, C, D are pivotal (resp., ribbon) categories and U is a pivotal (resp., braided pivotal) functor, then R is a pivotal (resp., ribbon) functor if and only if R(1D) is a symmetric Frobenius algebra in C. As an application, we construct Frobenius monoidal functors going into the Drinfeld center Z(C), thereby producing Frobenius algebras in it.