Definition is_left_adjoint_opfunctorcat_from_functorcatofoppcats : is_left_adjoint (opfunctorcat_from_functorcatofoppcats C D). Proof. exists (opfunctorcat_to_functorcatofoppcats C D). unfold are_adjoints. use tpair. - exists (unit_opfunctorcat_functorcatofoppcats C D). exact (counit_opfunctorcat_functorcatofoppcats C D). - exact opfunctorcat_adjdata_functorcatofoppcats_form_adjunction. 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.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.OppositeCategory.Core. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.whiskering. Section OppositeOfFunctorCatFromFunctorCatOfOpposite. End OppositeOfFunctorCatFromFunctorCatOfOpposite.