proposition: Corollary unit_comp {x y} (f : x ~> U y) : fmap[U] (fmap[F] f) ∘ η ≈ η ∘ f.
proof: Proof. unfold unit. rewrite <- to_adj_nat_l. rewrite <- to_adj_nat_r. rewrite id_left, id_right. reflexivity. Qed.
imports: Category.Lib Category.Theory.Category Category.Theory.Morphisms Category.Theory.Isomorphism Category.Theory.Functor Category.Instance.Sets