Lemma is_right_adjoint_opposite {C D : category} (F : functor C D) : is_left_adjoint F -> is_right_adjoint (functor_op F). Proof. intro ila. set (adj := make_adjunction _ (pr22 ila)). exists (functor_op (pr121 adj)). exact (are_adjoints_opposite adj). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.OppositeCategory.Core.