proposition: Lemma Ff_lt_preserves_colim_impl_LNWFS_lt_preserves_colim_mor_disp : pr2 (monoidal_left_tensor (L : LNWFS_mon) (colim CL)) -->[pr1 base_mor] pr2 (colim LNWFSCC).
proof: Proof. apply (Ff_iso_inv_LNWFS_mor (colim LNWFSCC) (monoidal_left_tensor (L : LNWFS_mon) (colim CL)) Ffiso). apply (@Ff_mor_eq_LNWFS_mor C (colim LNWFSCC) (monoidal_left_tensor (L : LNWFS_mon) (colim CL)) (z_iso_mor Ffiso) LNWFSarr). apply pathsinv0. exact (Ff_lt_preserves_colim_impl_LNWFS_lt_preserves_colim_mor_disp_pr1_category_tensor_commutes). 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.PrecategoryBinProduct UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.Limits.Graphs.Coequalizers UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.EqDiag UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Chains.Chains UniMath.CategoryTheory.slicecat 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.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.DisplayedCats.Examples.Arrow UniMath.CategoryTheory.DisplayedCats.Examples.Three UniMath.ModelCategories.NWFS UniMath.ModelCategories.Generated.MonoidalHelpers UniMath.ModelCategories.Helpers UniMath.ModelCategories.Generated.LNWFSHelpers UniMath.ModelCategories.Generated.MonoidalHelpers UniMath.ModelCategories.Generated.FFMonoidalStructure UniMath.ModelCategories.Generated.LNWFSMonoidalStructure UniMath.ModelCategories.Generated.LNWFSCocomplete