proposition: Lemma isInitial_InitHSS : ∏ (C : category) (CP : BinCoproducts C) (IC : Initial C) (CC : Colims_of_shape nat_graph C) (H : UniMath.SubstitutionSystems.Signatures.Presignature C C C) (HH : is_omega_cocont (pr1 H)), isInitial (hss_category CP H) (InitHSS C CP IC CC H HH).
proof: Proof. exact @UniMath.SubstitutionSystems.SimplifiedHSS.LiftingInitial_alt.isInitial_InitHSS. Defined.
imports: UniMath.Foundations.NaturalNumbers UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Colimits UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Categories.HSET.Structures UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Chains.All UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.ProductCategory UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monads.Monads UniMath.SubstitutionSystems.SignatureCategory UniMath.SubstitutionSystems.SimplifiedHSS.SubstitutionSystems UniMath.SubstitutionSystems.SimplifiedHSS.BindingSigToMonad UniMath.SubstitutionSystems.SimplifiedHSS.LiftingInitial_alt