I'm aware; in mathematics it's possible to replace almost anything with some other thing to make the statement you want to be true come true. But it's usually just gonna confuse everyone.
Well the thing I chose to replace the thing with is actually isomorphic (type equivalent) to the thing I replaced. So that's quite a bit more constrained than "replacing anything with anything". Not only are the arrows the only thing that matters, but its cleaner to suppose that they're the only thing there is.