fact: Definition Lam_Flatten : ∏ (C : category) (terminal : Terminal C) (CC : BinCoproducts C) (CP : BinProducts C), (∏ Z : category_Ptd C, GlobalRightKanExtensionExists C C (U Z) C) → ∏ Lam_Initial : Initial (FunctorAlg (Id_H C CC (Lam_Sig C terminal CC CP))), [C, C] ⟦ (Flat_H C) ` (InitialObject Lam_Initial), ` (InitialObject Lam_Initial) ⟧.
imports: UniMath.Foundations.PartD UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.PointedFunctors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.PointedFunctorsComposition UniMath.SubstitutionSystems.Signatures UniMath.SubstitutionSystems.BinSumOfSignatures UniMath.SubstitutionSystems.SubstitutionSystems UniMath.SubstitutionSystems.GenMendlerIteration UniMath.CategoryTheory.RightKanExtension UniMath.SubstitutionSystems.GenMendlerIteration UniMath.SubstitutionSystems.LiftingInitial UniMath.SubstitutionSystems.MonadsFromSubstitutionSystems UniMath.SubstitutionSystems.LamSignature UniMath.SubstitutionSystems.Lam UniMath.SubstitutionSystems.Notation