In one of the comment replies you suggested that the same set of observations could be modeled by two different models, and there should be a morphism between the two models, either directly or through a third model that is more “accurate” or “powerful” in some sense than the other two. If I knew enough category theory, I would probably be able to express it in terms of some commuting diagrams, but alas.
Yes, something like that would capture the idea, although it’s not necessarily the only or best way to formulate it.
Yes, something like that would capture the idea, although it’s not necessarily the only or best way to formulate it.