Lemma are_adjoints_closed_under_iso {A B : category} (F G : functor A B) (H : functor B A) (αiso : @z_iso [A,B] F G) (HF : are_adjoints F H) : are_adjoints G H. Proof. set (adj_data := are_adjoints_closed_under_iso_data F G H αiso HF). use make_are_adjoints. - exact (adjunit adj_data). - exact (adjcounit adj_data). - apply are_adjoints_closed_under_iso_laws. 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.