Steve Awodey said of category theory
Material at this level of abstraction is simply incomprehensible without the applications and examples that bring it to life.
Michael Atiyah would say this is not unique to categories.
When someone tells me a general theorem I say that I want an example that is both simple and significant. It’s very easy to give simple examples that are not very interesting or interesting examples that are very difficult. If there isn’t a simple, interesting case, forget it. … Without knowing the examples, the whole thing is pointless. It is a mistake to focus on the techniques without constantly, not only at the beginning, knowing what the good examples are, where they came from, why they’re done. The abstractions and the examples have to go hand in hand.
More from Michael Aityah here.