Lemma post_whisker_iso_is_iso {B C D : precategory} {G H : functor_data B C} (gamma : nat_trans G H) (K : functor C D) (X : is_nat_iso gamma) : is_nat_iso (post_whisker gamma K). Proof. intros b. unfold post_whisker. simpl. set ( gammab := make_iso (gamma b) (X b) ). apply (functor_on_iso_is_iso C D K _ _ gammab). 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.