Definition adj_from_nathomweq : are_adjoints F G. Proof. apply (make_are_adjoints F G unit_from_hom counit_from_hom). apply make_dirprod. - intro a. cbn. rewrite <- inv_natural_precomp. rewrite id_right. apply homotinvweqweq. - intro b. cbn. rewrite <- hom_natural_postcomp. rewrite id_left. apply homotweqinvweq. Defined.
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.