Nobody has tackled Puzzle 168 yet - namely, to figure out what the _naturality_ in the definition of adjunction actually gives us!

But Michael Hong has drawn a great diagram hinting at what's going on. He is calling the adjunction \\( L : \mathcal{C} \to \mathcal{D}, R : \mathcal{D} \to \mathcal{C}\\) instead of \\(F : \mathcal{A} \to \mathcal{B}, G : \mathcal{B} \to \mathcal{A}\\), but it's the same story:

But Michael Hong has drawn a great diagram hinting at what's going on. He is calling the adjunction \\( L : \mathcal{C} \to \mathcal{D}, R : \mathcal{D} \to \mathcal{C}\\) instead of \\(F : \mathcal{A} \to \mathcal{B}, G : \mathcal{B} \to \mathcal{A}\\), but it's the same story: