Lemma nat_z_iso_functor_comp_assoc {C1 C2 C3 C4 : category} (F1 : functor C1 C2) (F2 : functor C2 C3) (F3 : functor C3 C4) : nat_z_iso (F1 ∙ (F2 ∙ F3)) ((F1 ∙ F2) ∙ F3). 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.