proposition: Theorem PowerObject_nt_is_nat_z_iso : is_nat_z_iso PowerObject_nattrans.
proof: Proof. intros (a,b). cbn. use make_is_z_isomorphism. + intro g. exact ((identity b) ⨱ g · (PowerObject_inPred b)). + cbn. use make_is_inverse_in_precat. - use funextfun. intros f. cbn. use pathsinv0. use PowerObject_transpose_tri. - use funextfun. intros g. use pathsinv0. use path_to_ctr. apply idpath. Defined.
imports: UniMath.Foundations.PartA UniMath.Foundations.PartD UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.SubobjectClassifier UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.OppositeCategory.Core UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Adjunctions.Core