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Stream: learning: questions

Topic: natural transformations and generators

Evan Patterson (Apr 05 2020 at 19:21):

If $\alpha: F \to D$ is a (not necessarily natural) transformation between functors $F, G: C \to D$, then to check that $\alpha$ is a natural transformation it is enough to check naturality on a generating set of morphisms of $C$. The same statement holds, I assume, when $C,D$ are (symmetric) monoidal categories, $F,G$ are strong (symmetric) monoidal functors, and $\alpha$ is a monoidal transformation.

Does anyone know a reference for such statements? I could prove them but I would rather save the space and just cite them.

John Baez (Apr 05 2020 at 20:27):

If I were you I'd just check it carefully, then state it as if it were a fact everyone knows. :slight_smile:

Evan Patterson (Apr 05 2020 at 20:51):

OK, I will do that. Thanks. This sort of thing comes up all the time for me when working with small categories presented by generators and relations.