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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 2category theory and from bialgebras. In order to describe the 2categorical examples, we take a multicategorical approach. We explain how certain braided skew monoidal structures in the 2categorical 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 

Article number  2 
Pages (fromto)  1963 
Number of pages  45 
Journal  Theory and Applications of Categories 
Volume  35 
Issue number  2 
Publication status  Published  2020 
Keywords
 Braiding
 skew monoidal category
 bialgebra
 quasitriangular
 2category
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Projects
 1 Finished

Monoidal categories and beyond: new contexts and new applications
Street, R., Verity, D., Lack, S., Garner, R. & MQRES Inter Tuition Fee only, M. I. T. F. O.
30/06/16 → 17/06/19
Project: Research