Definition PowerObject_charname_is_nat_z_iso : is_nat_z_iso PowerObject_charname_nattrans. Proof. intro c. use is_z_isomorphism_comp. + generalize c. use post_whisker_z_iso_is_z_iso. use op_nt_is_z_iso. use pr2_nat_z_iso. + generalize c. use (pr2_nat_z_iso PowerObject_nat_z_iso_Tfixed). Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.PartD. 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.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.SubobjectClassifier.SubobjectClassifier. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.OppositeCategory.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.exponentials. Require Import UniMath.CategoryTheory.Adjunctions.Core.