proposition: Lemma is_omega_cocont_precomp_option_iter (BCC : BinCoproducts C) (TC : Terminal C) (CLC : Colims_of_shape nat_graph C) (n : nat) : is_omega_cocont (precomp_option_iter BCC TC n).
proof: Proof. destruct n; simpl. - apply is_omega_cocont_functor_identity. - apply is_omega_cocont_pre_composition_functor, CLC. Defined.
imports: UniMath.Foundations.PartD UniMath.Combinatorics.Lists UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Chains.All UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Categories.HSET.Colimits UniMath.CategoryTheory.Categories.HSET.Structures UniMath.SubstitutionSystems.Signatures UniMath.SubstitutionSystems.SignatureExamples UniMath.SubstitutionSystems.SumOfSignatures UniMath.SubstitutionSystems.BinProductOfSignatures UniMath.SubstitutionSystems.SubstitutionSystems UniMath.SubstitutionSystems.LiftingInitial_alt UniMath.SubstitutionSystems.MonadsFromSubstitutionSystems UniMath.SubstitutionSystems.Notation