Braided monoidal category

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In mathematics, a braided monoidal category is a monoidal category C equipped with a braiding; that is, there is a natural isomorphism

\gamma_{A,B}:A\otimes B \rightarrow B\otimes A

for which the following hexagonal diagrams commute (here α is the associativity isomorphism):

Image:CategoryBraiding-02.png Image:CategoryBraiding-03.png

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.

Contents

[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


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