What separable Frobenius monoidal functors preserve?

Micah McCurdy, Ross Street

Research output: Contribution to journalArticle

Abstract

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.
Original languageEnglish
Pages (from-to)29-50
Number of pages22
JournalCahiers de topologie et géométrie différentielle catégoriques
Volume51
Issue number1
Publication statusPublished - 2010

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