Lemma φ_adj_inv_under_iso (f : C⟦c, G c'⟧) : φ_adj_inv (are_adjoints_closed_under_iso _ _ _ α H) f = ((z_iso_inv α : [C, C'] ⟦F', F⟧) : F' ⟹ F) c · φ_adj_inv H f. Proof. refine (assoc _ _ _ @ _). refine (_ @ assoc' _ _ _). apply maponpaths_2. apply (nat_trans_ax (inv_from_z_iso α)). 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.