2009/04/22 by Micah Blake McCurdy, McCurdy, Micah Blake, Ross Street +1
Mathematics · #18D10 #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.0904.3449
openalex publication_date 2009/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Separable Frobenius monoidal functors were defined and studied under that name by Szlachanyi and by Day and Pastro, and in a more general context by Cockett and Seely. Our purpose here is to develop their theory in a very precise sense. We determine what kinds of equations in monoidal categories they preserve. For example we show they preserve lax (meaning not necessarily invertible) Yang-Baxter operators, weak Yang-Baxter operators in the sense of Alonso Alvarez et al., and (in the braided case) weak bimonoids in the sense of Pastro and Street. In fact, we characterize which monoidal expressions are preserved (or rather, are stable under conjugation in a well-defined sense). We show that every weak Yang-Baxter operator is the image of a genuine Yang-Baxter operator under a separable Frobenius monoidal functor. Prebimonoidal functors are also defined and discussed.