proposition: Lemma φ_adj_natural_precomp (A : C) (B : D) (f : F A --> B) (X : C) (h : X --> A) : φ_adj (#F h · f) = h · φ_adj f.
proof: Proof. unfold φ_adj. rewrite functor_comp. set (T:=nat_trans_ax η); simpl in T. rewrite assoc. rewrite <- T. apply pathsinv0, assoc. 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