Braided skew monoidal categories

John Bourke, Stephen Lack

Research output: Contribution to journalArticlepeer-review

1 Citation (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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