what a pull request !!! Most of the code was in need for a cleanup (mainly due to the fact that sometimes I was 'playing by ear', because my knowledge of Haskell is medium-plus at most).
I think that you're referring to "The simple essence of automatic differentiation" paper, aren't you?
After having read over it, the paper mentions "monoidal categories". As the second chapter of the "Seven Sketches" book is about "monoidal preorders", maybe exploring both things in parallel can make sense, don't you think? (Although, I haven't finished the "Compiling to Categories" paper yet)
**I'm completely open to new adjunction identities**. Adjunctions, at least for me, were a hard wall to smash my head into two years ago. Completely impenetrable. And now, I think, I'm beginning to make a little dent on them. So anything about adjunctions is more than welcome.