Example: Law as a Natural Transformation
Imagine a 2-functor from:
Category of individual acts and desires (personal logic, rights)
To category of socially accepted actions (legal logic, responsibilities)
Then a natural transformation encodes:
How a society translates individual reasoning into enforceable action.
How law binds or restricts certain inferences while preserving structure (naturality condition).
That is, this commutes if η is natural — that is, doing something and then applying law is the same as applying law first and doing the translated thing.
--- oops, ChatGPT doesn't know about asking for permission vs forgiveness; I mean, it *should* commute, except for that pesky time asymmetry where you can't take back what you did. --- more context is needed ---
This models ethics, cultural norms, or constitutional constraints as natural transformations that preserve reasoning across systems.
This is why we need Judges. It's not an easy job, respect them