Definition op_unit_inv_unit_nat_trans (C : category) : nat_trans (functor_identity ((C^op)^op) ∙ functor_identity C) (functor_identity ((C^op)^op)). Proof. use make_nat_trans. - exact (λ x, identity 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.