Lemma is_functor_functor_opp {C D : precategory} (F : functor C D) : is_functor (functor_opp_data F). Proof. split; intros. - unfold functor_idax; simpl. apply (functor_id F). - unfold functor_compax; simpl. intros. apply (functor_comp F). Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.FunctorCategory.