Braided monoidal category Information & Braided monoidal category Links at HealthHaven.com

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):

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.

Symmetric monoidal categories provide a model for linear logic and linear types, much like cartesian closed categories do for intuitionistic and classical logic.

[edit] Properties

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

[edit] See also

Braid group

[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.

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Contents

[edit] Properties

[edit] See also

[edit] References

[edit] External links