>>573
First of all I wouldn't say it's "better" than set theory or higher order logic.
Second of all you can't just easily define a predicate "is isomorphic to", well you can, but it's useless and you're missing the point. You want to define it in a way for it to have the desirable properties and if you just define a predicate, then you have to figure out how to piece it into the rest of the theory.
Third of all higher order logic is fundamentally different from set theory or category theory, as it's part of the deductive system of your theory, not part of the actual things you talk about. So indeed I'd say yes you're being too simple minded/delusional to get it right now.

As to what category theory is "about" is I'd say morphisms, the same way set theory is abour membership, since morphisms are what ought to be defined to speak of a category and draw the beloved arrows.