Lemma post_whisker_z_iso_is_z_iso {B C D : precategory} {G H : functor_data B C} (gamma : nat_trans G H) (K : functor C D) (X : is_nat_z_iso gamma) : is_nat_z_iso (post_whisker gamma K). Proof. intros b. unfold post_whisker. simpl. apply (functor_on_is_z_isomorphism K (X b)). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory.