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@article{1710296, author = {Bourke, John Denis and Lack, Stephen}, article_number = {2}, keywords = {Braiding; skew monoidal category; bialgebra; quasitriangular; 2-category}, language = {eng}, issn = {1201-561X}, journal = {Theory and Applications of Categories}, title = {Braided skew monoidal categories}, url = {http://www.tac.mta.ca/tac/volumes/35/2/35-02.pdf}, volume = {35}, year = {2020} }
TY - JOUR ID - 1710296 AU - Bourke, John Denis - Lack, Stephen PY - 2020 TI - Braided skew monoidal categories JF - Theory and Applications of Categories VL - 35 IS - 2 SP - 19-63 EP - 19-63 PB - Mount Allison University SN - 1201561X KW - Braiding KW - skew monoidal category KW - bialgebra KW - quasitriangular KW - 2-category UR - http://www.tac.mta.ca/tac/volumes/35/2/35-02.pdf L2 - http://www.tac.mta.ca/tac/volumes/35/2/35-02.pdf N2 - 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. ER -
BOURKE, John Denis a Stephen LACK. Braided skew monoidal categories. \textit{Theory and Applications of Categories}. Mount Allison University, 2020, roč.~35, č.~2, s.~19-63. ISSN~1201-561X.
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