You wouldn't. I think saying you used category theory to design something just sounds cool and is basically a shibboleth. In fact, any time you compose functions you're using category theory. I think it sounds a little pretentious to be honest. No one says they used boolean logic when they wrote some code so saying you used category theory or type theory sounds equally weird.

I work with a guy that has a PhD in some heavy duty categorical machinery and I haven't heard him once say he used category theory to design some piece of code.

I'm skeptical that an ordinary Java person would ever think of this particular solution.

Composing a list of `A -> A` functions into a single one is already sort of a tall order. They would also have to realize that `(B, A) -> A` is equivalent to `B -> (A -> A)`, and that they can compose `A -> A` under the `B` environment. I just don't see this happening.