Lemma φ_adj_under_iso (f : C'⟦F' c, c'⟧) : φ_adj (are_adjoints_closed_under_iso _ _ _ α H) f = φ_adj H (((α : [C, C'] ⟦F, F'⟧) : F ⟹ F') c · f). Proof. refine (assoc' _ _ _ @ _). apply (maponpaths (λ x, _ · x)). exact (!functor_comp G _ _). 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.