proposition: Lemma is_omega_cont_MultiSortedSigToFunctor_HSET (sort : UU) (Hsort_set : isaset sort) (M : MultiSortedSig sort) : is_omega_cont (MultiSortedSigToFunctor sort (hlevelntosn 2 _ Hsort_set) HSET TerminalHSET BinProductsHSET BinCoproductsHSET CoproductsHSET M).
proof: Proof. use is_omega_cont_MultiSortedSigToFunctor. - exact InitialHSET. - exact ProductsHSET. - exact HSET_ω_limits. - exact propcoproducts_commute_binproductsHSET. - exact I_coproduct_distribute_over_omega_limits_HSET. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Combinatorics.Lists UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Chains.All UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Categories.HSET.Colimits UniMath.CategoryTheory.Categories.HSET.Structures UniMath.CategoryTheory.Categories.StandardCategories UniMath.CategoryTheory.Groupoids UniMath.SubstitutionSystems.Signatures UniMath.SubstitutionSystems.SumOfSignatures UniMath.SubstitutionSystems.BinProductOfSignatures UniMath.SubstitutionSystems.MultiSorted_alt UniMath.CategoryTheory.Chains.OmegaContFunctors UniMath.SubstitutionSystems.ContinuitySignature.GeneralLemmas UniMath.SubstitutionSystems.ContinuitySignature.CommutingOfOmegaLimitsAndCoproducts UniMath.SubstitutionSystems.ContinuitySignature.ContinuityOfMultiSortedSigToFunctor UniMath.SubstitutionSystems.ContinuitySignature.MultiSortedSignatureFunctorEquivalence