### Abstract

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 language | English |
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Article number | 2 |

Pages (from-to) | 19-63 |

Number of pages | 45 |

Journal | Theory and Applications of Categories |

Volume | 35 |

Publication status | Published - 2020 |

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### Keywords

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

### Cite this

*Theory and Applications of Categories*,

*35*, 19-63. [2].