proposition: Lemma φ_adj_identity (A : C) : φ_adj (identity (F A)) = η _ .
proof: Proof. unfold φ_adj. rewrite functor_id. apply id_right. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Epis UniMath.CategoryTheory.SplitMonicsAndEpis UniMath.CategoryTheory.Monics UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering