Braided skew monoidal categories

John Bourke, Stephen Lack

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)


    We introduce the notion of a braiding on a skew monoidal category, whose curious feature is that the defining isomorphisms involve three objects rather than two. Examples are shown to arise from 2-category theory and from bialgebras. In order to describe the 2-categorical examples, we take a multicategorical approach. We explain how certain braided skew monoidal structures in the 2-categorical setting give rise to braided monoidal bicategories. For the bialgebraic examples, we show that, for a skew monoidal category arising from a bialgebra, braidings on the skew monoidal category are in bijection with cobraidings (also known as coquasitriangular structures) on the bialgebra.

    Original languageEnglish
    Article number2
    Pages (from-to)19-63
    Number of pages45
    JournalTheory and Applications of Categories
    Issue number2
    Publication statusPublished - 2020


    • Braiding
    • skew monoidal category
    • bialgebra
    • quasitriangular
    • 2-category


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