Geodesic
Braided skew monoidal categories
Theory and applications of categories, Tome 35 (2020), pp. 19-63

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Publié le :
Classification : 18M50, 18M15, 18N10, 18N40, 16T10
Keywords: Braiding, skew monoidal category, bialgebra, quasitriangular, 2-category 
@article{TAC_2020_35_a1,
     author = {John Bourke and Stephen Lack},
     title = {Braided skew monoidal categories},
     journal = {Theory and applications of categories},
     pages = {19--63},
     publisher = {mathdoc},
     volume = {35},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a1/}
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John Bourke; Stephen Lack. Braided skew monoidal categories. Theory and applications of categories, Tome 35 (2020), pp. 19-63. http://geodesic.mathdoc.fr/item/TAC_2020_35_a1/