Definition functor_comp_op {C₁ C₂ C₃ : category} (F : C₁ ⟶ C₂) (G : C₂ ⟶ C₃) : functor_opp F ∙ functor_opp G ⟹ functor_opp (F ∙ G). Proof. use make_nat_trans. - exact (λ x, identity _). - abstract (intros x y f ; cbn ; rewrite id_left, id_right ; apply idpath). Defined.
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.