I have been thinking about the following problem for years and can't seem to resolve it. I'm looking for more information on the subject and would really appreciate some further reading on the following subject:
Hypothesis: Observations lift reality into the realm of the "Observed reality"; just like mathematics lifts reality into the "logical reality" or "computed reality". In this reality can be seen as "state" and observations, mathematics and even language can be seen as "monads".
By reducing science to a Category of axioms (the objects) and changes (the morphisms), how can we describe "Observations", "Mathematics" and even "Languages" in terms of this Category?
My question is specifically: Is there research being done in this field and are there books/papers I can read on the subject? Thank you in advance for any help/thoughts/opinions/links.