> 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).

Yeah mine is pretty mediocre too. I'm trying to practice every day.

> 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)

Sounds good.

> **I'm completely open to new adjunction identities.**

Okay, so suppose \\(g \dashv f\\). Then we have the following little theorem I lifted from this [mathematics stack exchange discussion](https://math.stackexchange.com/a/825966):

> **Theorem**: Left adjoints preserve all joins; right adjoints preserve all meets.

In other words \\(g( a \vee b ) = g(a) \vee g(b)\\) and \\( f(a \wedge b) = f(a) \wedge f(b)\\).

**Puzzle**: In Haskell, we can think of these two equations as four functions. What are they? How relaxed can we make the type class constraints?