fact: Definition is_PowerObject (P : ob C -> ob C) (inmap : ∏ (b:C), C ⟦b x (P b), O⟧ ):= ∏ (a b:C) (f : C ⟦b x a, O⟧), ∃! g : C ⟦a, P b⟧, f = identity b ⨱ g·(inmap b).
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