Lemma post_whisker_nat_z_iso {C D E : category} {F1 F2 : functor C D} (α : nat_z_iso F1 F2) (G : functor D E) : nat_z_iso (F1 ∙ G) (F2 ∙ G). Proof. use make_nat_z_iso. 2: { exact (post_whisker_z_iso_is_z_iso α G (pr2 α)). } Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.precomp_ess_surj. Require Import UniMath.CategoryTheory.precomp_fully_faithful. Require Import UniMath.CategoryTheory.PrecategoryBinProduct.