proposition: Lemma LNWFS_right_tensor_preserves_colimit_mor_inv_disp (Ff_rt_cc_inv := Ff_right_tensor_preserves_colimit_mor_inv CC H v0 (pr1 A) dbase) : pr2 (colim (LNWFSCC (mapdiagram (monoidal_right_tensor A) d)) ) -->[Ff_rt_cc_inv] pr2 ((monoidal_right_tensor A) (colim (LNWFSCC d))).
proof: Proof. set (colimAL := colim (LNWFSCC (mapdiagram (monoidal_right_tensor A) d))). set (AcolimL := monoidal_right_tensor A (colim (LNWFSCC d))). set (LNWFSmor := colimArrow (LNWFSCC (mapdiagram (monoidal_right_tensor A) d)) _ (mapcocone (monoidal_right_tensor A) _ (colimCocone (LNWFSCC d)))). apply (@Ff_mor_eq_LNWFS_mor C colimAL AcolimL Ff_rt_cc_inv LNWFSmor). exact (Ff_right_tensor_preserves_colimit_mor_inv_is_LNWFS_colim_mor). Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Monads.MonadAlgebras UniMath.CategoryTheory.Monads.Comonads UniMath.CategoryTheory.Monads.ComonadCoalgebras UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Coequalizers UniMath.CategoryTheory.Chains.Chains UniMath.Combinatorics.StandardFiniteSets UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.DisplayedCats.Examples.Arrow UniMath.CategoryTheory.DisplayedCats.Examples.Three UniMath.ModelCategories.NWFS UniMath.ModelCategories.Helpers UniMath.ModelCategories.Generated.MonoidalHelpers UniMath.ModelCategories.Generated.FFMonoidalStructure UniMath.ModelCategories.Generated.LNWFSHelpers UniMath.ModelCategories.Generated.LNWFSMonoidalStructure UniMath.ModelCategories.Generated.LNWFSCocomplete