Monoidal natural transformation explained

Suppose that

(lC,,I)

and

(lD,\bullet,J)

are two monoidal categories and

(F,m):(lC,,I)\to(lD,\bullet,J)

and

(G,n):(lC,,I)\to(lD,\bullet,J)

are two lax monoidal functors between those categories.

A monoidal natural transformation

\theta:(F,m)\to(G,n)

between those functors is a natural transformation

\theta:F\toG

between the underlying functors such that the diagrams

and commute for every objects

A

and

B

of

lC

.[1]

A symmetric monoidal natural transformation is a monoidal natural transformation between symmetric monoidal functors.

References

Notes and References

  1. Web site: Baez. John C.. Some Definitions Everyone Should Know. 2 December 2014.