Braided monoidal category
- Braided monoidal category
In mathematics, a braided monoidal category is a monoidal category "C" equipped with a braiding; that is, there is a natural isomorphism:for which the following hexagonal diagrams commute (here 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 for all objects "A" and "B".
Properties
In a braided monoidal category, the braiding always "commutes with the units":
ee also
*Braid group
References
* Joyal, André; Street, Ross (1993). "Braided Tensor Categories". "Advances in Mathematics" "102", 20–78.
External links
*John Baez (1999), [http://math.ucr.edu/home/baez/week137.html An introduction to braided monoidal categories] , "This week's finds in mathematical physics" 137.
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