proposition: Lemma φ_adj_inv_natural_precomp (A : C) (B : D) (g : A --> G B) (X : C) (h : X --> A) : φ_adj_inv (h · g) = #F h · φ_adj_inv g.
proof: Proof. unfold φ_adj_inv. rewrite functor_comp. 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