proposition: Lemma free_monoid_coeq_sequence_converges_for_osc (HJ : class_presentable J) : free_monoid_coeq_sequence_converges_on _ (LNWFS_pointed one_step_comonad_as_LNWFS) (ChainsLNWFS CC) (CoequalizersLNWFS CC) (monoidal_unit LNWFS_tot_monoidal).
proof: Proof. apply T_preserves_diagram_impl_convergence_on. exact (osc_preserves_diagram_on HJ). Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.Limits.Graphs.Coequalizers UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Monads.MonadAlgebras UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.Combinatorics.StandardFiniteSets UniMath.CategoryTheory.Chains.Chains UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids UniMath.CategoryTheory.DisplayedCats.Examples.Arrow UniMath.CategoryTheory.DisplayedCats.Examples.Three UniMath.ModelCategories.MorphismClass UniMath.ModelCategories.Generated.LiftingWithClass UniMath.ModelCategories.NWFS UniMath.ModelCategories.Generated.OneStepMonad UniMath.ModelCategories.Generated.GenericFreeMonoid UniMath.ModelCategories.Generated.GenericFreeMonoidSequence UniMath.ModelCategories.Generated.MonoidalHelpers UniMath.ModelCategories.Helpers UniMath.ModelCategories.Generated.MonoidalHelpers UniMath.ModelCategories.Generated.FFMonoidalStructure UniMath.ModelCategories.Generated.LNWFSMonoidalStructure UniMath.ModelCategories.Generated.LNWFSCocomplete UniMath.ModelCategories.Generated.LNWFSClosed UniMath.ModelCategories.Generated.LNWFSSmallnessReduction UniMath.ModelCategories.Generated.OneStepMonadSmall