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Braided Monoidal Category




:\gamma_{A,B}:A\otimes B o B\otimes A
for which the following hexagonal diagrams commute (here \alpha is the associativity isomorphism):
Alternatively, a braided monoidal category can be seen as a Tricategory with one 0-cell and one 1-cell.

A Symmetric Monoidal Category is a braided monoidal category whose braiding satisfies \gamma_{B,A}\gamma_{A,B}=1_{A\otimes B} for all objects ''A'' and ''B''.


PROPERTIES

In a braided monoidal category, the braiding always "commutes with the units":


SEE ALSO




REFERENCES


  • Joyal, André; Street, Ross (1993). "Braided Tensor Categories". ''Advances in Mathematics'' ''102'', 20–78.



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