I think of an abstraction as a map from a model space into the problem domain. (A map that is not necessarily injective, and sure enough not surjective.)
I am sure category theory can say much about this.
The whole point of the article is providing a rigorous definition rather than the wishy-washy stuff people usually use. This is independent of category theory. Cousot was working in a different space.
No, I thoroughly appreciate that, it's just that the functorial language of the "abstract nonsense" seems perfect for discussing modeling and abstraction.
I am sure category theory can say much about this.