Lemma φ_adj_inv_natural_postcomp (A : C) (B : D) (g : A --> G B) (Y : D) (k : B --> Y) : φ_adj_inv (g · #G k) = φ_adj_inv g · k. Proof. unfold φ_adj_inv. rewrite functor_comp. set (T:=nat_trans_ax ε); simpl in T. rewrite <- assoc. rewrite T. apply assoc. 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.