I don’t think I’ve fully processed what you or the OP have said here—my apologies, but this still seemed relevant.
I think the category-theory way I would describe this is Bob is a category B, and Alice is a category A. A and B are big and complicated, and I have no idea how to describe all the objects or morphisms in them, although there is some structure preserving morphism between them (your G). But what Bob does is try to to find a straw-alice category A’ which is small, and simple, along with functors from A’ to A and from A’ to B, which makes Alice predictable (or post-dictable).
Yeah, maybe it makes more sense. B’ would be just a subcategory of B that is sufficient for defining (?) Xp (something like Markov blanket of Xp?). The (endo-)functor from B’ to B would be just identity and the relationship between Xp and [Xp] would be represented by a natural transformation?
I don’t think I’ve fully processed what you or the OP have said here—my apologies, but this still seemed relevant.
I think the category-theory way I would describe this is Bob is a category B, and Alice is a category A. A and B are big and complicated, and I have no idea how to describe all the objects or morphisms in them, although there is some structure preserving morphism between them (your G). But what Bob does is try to to find a straw-alice category A’ which is small, and simple, along with functors from A’ to A and from A’ to B, which makes Alice predictable (or post-dictable).
Does that make any sense?
Yeah, maybe it makes more sense. B’ would be just a subcategory of B that is sufficient for defining (?) Xp (something like Markov blanket of Xp?). The (endo-)functor from B’ to B would be just identity and the relationship between Xp and [Xp] would be represented by a natural transformation?