fact: Definition SpecializedGMIt (Z : Ptd) (X : EndC) : ∏ (G : functor [C, C] [C, C]) (ρ : [C, C] ⟦ G X, X ⟧) (θ : functor_composite Id_H (ℓ (U Z)) ⟹ functor_composite (ℓ (U Z)) G), ∃! h : [C, C] ⟦ ℓ (U Z) (` (InitialObject IA)), X ⟧, # (ℓ (U Z)) (alg_map Id_H (InitialObject IA)) · h = θ (` (InitialObject IA)) · # G h · ρ := SpecialGenMendlerIteration _ _ IA EndC X _ (KanExt Z) .
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.PointedFunctors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.PointedFunctorsComposition UniMath.SubstitutionSystems.Signatures UniMath.SubstitutionSystems.SimplifiedHSS.SubstitutionSystems UniMath.SubstitutionSystems.GenMendlerIteration UniMath.CategoryTheory.RightKanExtension UniMath.SubstitutionSystems.GenMendlerIteration UniMath.CategoryTheory.BicatOfCatsElementary UniMath.SubstitutionSystems.Notation