# Morphisms in the category of natural transformations?

I am learning the basics of category theory, so this question is probably obvious to anyone who knows the subject.

The resources I've seen all take the following approach:

0) A category is a collection of objects and morphisms between those objects that satisfy some rules.

1) A functor is a morphism in the category of categories.

2) A natural transformation is a morphism in the category of functors.

But they all stop right there. What about:

3) the morphisms in the category of natural transformations?

4) Or the "morphisms in the category of the morphisms in the category of natural transformations"

5) ...

Are these uninteresting? Why does the "meta-ness" stop at 2 levels deep?

-

They are not uninteresting. Just look up the term n-category (e.g. Baez's introduction).

Nevertheless, it's true that functors and natural transformations already suffice for most common ideas and constructions used across mathematics, so this is why one usually stops there.

-