Monoidal natural transformation

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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

Monoidal natural transformation multiplication.svg            and          Monoidal natural transformation unit.svg

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.

References[edit]

  1. ^ Baez, John C. "Some Definitions Everyone Should Know" (PDF). Retrieved 2 December 2014.