Braided monoidal category
From Wikipedia, the free encyclopedia
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 α is the associativity isomorphism):
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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.
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[edit] Properties
In a braided monoidal category, the braiding always "commutes with the units":
[edit] See also
[edit] References
- Joyal, André; Street, Ross (1993). "Braided Tensor Categories". Advances in Mathematics 102, 20–78.
[edit] External links
- John Baez (1999), An introduction to braided monoidal categories, This week's finds in mathematical physics 137.
