Corollary φ_adj_inv_natural_prepostcomp (A X : C) (B Y : D) (g : A --> G B) (h : X --> A) (k : B --> Y) : φ_adj_inv (h · g · #G k) = #F h · φ_adj_inv g · k. Proof. etrans. apply φ_adj_inv_natural_postcomp. apply cancel_postcomposition. apply φ_adj_inv_natural_precomp. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.SplitMonicsAndEpis. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Section HomSetIsoRightFromPartial. End HomSetIsoRightFromPartial. Section HomSetIsoLeftFromPartial. End HomSetIsoLeftFromPartial.