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Looks like a good start, thanks! Nice diagrams!
I reworded from saying that a 2-functor is a functor to saying that it is a categorification of the notion of a functor, since functor focuses on the 1-categorical case. I also added some more whitespace between the last two xymatrix diagrams.
There is a notational inconsistency in the 2-functor page: sometimes, $\gamma_{f,g}$ is a natural transformation $P(g \circ f) \to P(g) \circ P(f)$, and other times it is $P(g) \circ P(f) \to P(g \circ f)$.
The latter seems correct, as it is the version depicted in the coherence diagrams, and matches the definition at pseudofunctor, but I’m not sure what else on the site depends on this definitional choice.
Please fix it.
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