Monoidal natural transformation

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Suppose that $(\mathcal$ and $(\mathcal$ are two monoidal categories and

$(F,m):(\mathcal$ and $(G,n):(\mathcal$

are two lax monoidal functors between those categories.

A monoidal natural transformation

$\theta:(F,m)\Rightarrow(G,n)$

between those functors is a natural transformation $\theta:F\Rightarrow$ between the underlying functors such that the diagrams

and

commute for every objects $A$ and $B$ of $\mathcal$ .

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

Monoidal natural transformation Photos: