2022/09/30 by Harshit Yadav, Yadav, Harshit
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2209.15606
openalex publication_date 2022/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let U:C\rightarrowD be a strong monoidal functor between abelian monoidal categories admitting a right adjoint R, such that R is exact, faithful and the adjunction U\dashv R is coHopf. Building on the work of Balan, we show that R is separable (resp., special) Frobenius monoidal if and only if R(\mathbb1D) 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(\mathbb1D) 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.