I agree. In my first-year graduate course on category theory, after I've
shown that the three concepts `terminal object', `right adjoint' and
`limit' are all interdefinable, I jokingly add `You might say that
category-theorists have only ever had one good idea, and all we do
is to keep dressing it up in new clothes'. (The `one good idea' is of 
course the notion of universal element, which comes from Yoneda.) 
But the `dressing up in new clothes' does matter: the introduction of
(appropriate!) new concepts is an important aid to understanding. So
I think it is `selling category theory short' to describe it as `just'
the study of naturality.

Peter Johnstone

On Oct 29 2023, dawson wrote:

>I'm with David here.
>
>For some purposes it is genuinely useful to know that all categorical
>concepts can be reduced to "terminal object", or that the entire theory
>of deterministic computation can be emulated within group theory.  But
>that doesn't mean that this should always be done! Mathematics is all
>about knowing many ways to look at something, and choosing the right
>one(s).
>
>"Knowledge is knowing that a tomato is a fruit. Wisdom is not putting it
>into a fruit salad."
>
>Best to all,
>Robert Dawson
>
>
>
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