Definition PowerObject_nattrans : nat_trans HomxO HomP. Proof. use make_nat_trans. + exact PowerObject_nt_data. + exact PowerObject_nt_is_nat_trans. 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.