Definition op_unit_inv_nat_trans {C₁ C₂ : category} (F : C₁ ⟶ C₂) : functor_identity _ ∙ F ⟹ functor_opp (functor_opp F) ∙ functor_identity _. Proof. use make_nat_trans. - exact (λ x, identity (F x)). - 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.