Lemma functor_op_of_precomp_functor_factorizes_through_functorcatofopp_is_nat_z_iso : is_nat_z_iso functor_op_of_precomp_functor_factorizes_through_functorcatofopp_as_nat_trans. Proof. intro G. use make_is_z_isomorphism. - use make_nat_trans. + intro ; apply identity. + abstract (intro ; intros ; apply (id_right _ @ ! id_left _)). - abstract (split ; (use 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.