Thank you for the answer. I'm going to mark this as answered

(I apologise for the horrible spelling and errors, can only edit a comment for 5 minutes after posting...)

The same goes for "Language", where talking about, or writing about an object lifts our state. Potentially removing the philosophical problems we might have with "describing" a test to falsify a theory through language. Or at the least gain a new perspective on what "observations" are...

Now an "Observational" category would be applying an observation, something done with senses, to an axiom. Imagine being able to lift axiom, for example laws of nature, into "Logical" categories like the category of atoms and again lift this into a "Logical" category of molecules. When I finally observe a rock falling I can create a morphism from a "Logical" category to an "Observational" category by only applying a sense (sight, etc) to the state of my logical system. This sense should have no impact on the underlying structures and can by definition be composed.

Thank you for the comments. I can try and answer the questions but keep in mind that I'm not that well versed in CR. I think that within an axiomatic categorical system you can always have derived object. For example, $1$ can be the "axiom" in this case and $+$ a morphism. A "Logical" category would be the natural numbers, "lifting" my axiom and morphism.