Lemma adj_closed_under_nat_z_iso {C D : category} {F1 F2 : functor C D} (α : nat_z_iso F1 F2) (G : functor D C) : are_adjoints F2 G -> are_adjoints F1 G. Proof. intro adj. simple refine (are_adjoints_closed_under_iso F2 F1 G _ adj). apply z_iso_inv. apply z_iso_is_nat_z_iso. assumption. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import MonoidalNotations.