Lemma functor_commutes_with_id {C D : category} (F : functor C D) : nat_z_iso (F ∙ functor_identity D) (functor_identity C ∙ F). Proof. use make_nat_z_iso. - exists (λ _, identity _). abstract (intro ; intros ; exact (id_right _ @ ! id_left _)). - intro. exists (identity _). abstract (split ; 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.Isos. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Univalence.