proposition: Lemma Lam_Initial_HSET : Initial (category_FunctorAlg (Id_H _ BinCoproductsHSET Lam_S)).
proof: Proof. use colimAlgInitial. - apply (Initial_functor_precat _ _ InitialHSET). - unfold Id_H, Const_plus_H. apply is_omega_cocont_BinCoproduct_of_functors. + apply is_omega_cocont_constant_functor. + apply is_omega_cocont_Lam_S. - apply ColimsFunctorCategory_of_shape; apply ColimsHSET_of_shape. Defined.
imports: UniMath.Foundations.PartD UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.PointedFunctors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.SubstitutionSystems.Signatures UniMath.CategoryTheory.Monads.Monads UniMath.SubstitutionSystems.BinSumOfSignatures UniMath.SubstitutionSystems.SimplifiedHSS.SubstitutionSystems UniMath.SubstitutionSystems.LamSignature UniMath.SubstitutionSystems.SimplifiedHSS.LiftingInitial_alt UniMath.SubstitutionSystems.SimplifiedHSS.MonadsFromSubstitutionSystems UniMath.SubstitutionSystems.Notation UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Categories.HSET.Colimits UniMath.CategoryTheory.Categories.HSET.Structures UniMath.CategoryTheory.Chains.All