Monoidal natural transformation - Alchetron, the free social encyclopedia

Suppose that ( C , ⊗ , I ) and ( D , ∙ , J ) are two monoidal categories and

( F , m ) : ( C , ⊗ , I ) → ( D , ∙ , J ) and ( G , n ) : ( C , ⊗ , I ) → ( D , ∙ , J )

are two lax monoidal functors between those categories.

A monoidal natural transformation

θ : ( F , m ) → ( G , n )

between those functors is a natural transformation θ : F → G between the underlying functors such that the diagrams

and

commute for every objects A and B of C (see Definition 11 in ).

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

References

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