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Suppose that and are two monoidal categories and
and
are two lax monoidal functors between those categories.
A monoidal natural transformation
between those functors is a natural transformation between the underlying functors such that the diagrams
and
commute for every objects and of (see Definition 11 in [1]).
A symmetric monoidal natural transformation is a monoidal natural transformation between symmetric monoidal functors.
^Baez, John C. "Some Definitions Everyone Should Know" (PDF). Retrieved 2 December 2014.
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