Definition opfunctorcat_functorcatofoppcats_formequivalence : forms_equivalence opfunctorcat_adjdata_functorcatofoppcats. Proof. split. - intro. use make_is_z_isomorphism. + use make_nat_trans. * intro ; apply identity. * abstract (intro ; intros ; cbn ; apply (id_left _ @ ! id_right _)). + split ; (apply nat_trans_eq ; [ apply homset_property | intro ; apply id_right ]). - intro. use make_is_z_isomorphism. + use make_nat_trans. * intro ; apply identity. * abstract (intro ; intros ; cbn ; apply (id_right _ @ ! id_left _)). + split ; (apply nat_trans_eq ; [ apply homset_property | intro ; apply id_right ]). 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.