Knowing a bit of maths, I'm having trouble understanding how this isn't just categorical logic. They say that the laws of physics should be expressible in terms

Knowing a bit of maths, I'm having trouble understanding how this isn't just categorical logic. They say that the laws of physics should be expressible in terms of statements about which physical transformations are possible or impossible, and why. In categorical logic, laws are expressible in terms of statements about which morphisms exist or would be contradictory/absurd to exist, and include proofs. What's the difference? I read through a couple of their preprints but didn't find much concrete material, just a lot of complaints about existing theoretical physics traditions.