nLab braided monoidal functor

Idea

A braided monoidal functor is a functor $F : C \to D$ between braided monoidal categories that is a monoidal functor which respects the braiding on both sides, i.e. satisfies the law:

where $\beta$ is braiding on $C$, $\beta'$ is braiding on $D$, and $\mu$ is the lax monoidal structure on $F$.

Properties

Between symmetric monoidal categories a braided monoidal functor is the same as a symmetric monoidal functor.

Related concepts

• monoidal functor

• strong monoidal functor

• lax monoidal functor

• oplax monoidal functor

• bilax monoidal functor

• Frobenius monoidal functor

• braided monoidal functor

• symmetric monoidal functor

References

An exposition is in

• John Baez, Some definitions everyone should know.