proposition: Corollary φ_adj_natural_prepostcomp (A X : C) (B Y : D) (f : F A --> B) (h : X --> A) (k : B --> Y) : φ_adj (#F h · f · k) = h · φ_adj f · #G k.
proof: Proof. etrans. rewrite <- assoc. apply φ_adj_natural_precomp. rewrite <- assoc. apply maponpaths. apply φ_adj_natural_postcomp. 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