proposition: Lemma preserves_colimit_functor_composite : ∏ (C D E : category) (F : functor C D) (G : functor D E) (g : graph) (d : diagram g C) (L : C) (cc : cocone d L), preserves_colimit F d L cc → preserves_colimit G (mapdiagram F d) (F L) (mapcocone F d cc) → preserves_colimit (functor_composite F G) d L cc.
proof: Proof. exact @UniMath.CategoryTheory.Chains.OmegaCocontFunctors.preserves_colimit_functor_composite. Defined.
imports: UniMath.Foundations.NaturalNumbers UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Colimits UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Categories.HSET.Structures UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Chains.All UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.ProductCategory UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monads.Monads UniMath.SubstitutionSystems.SignatureCategory UniMath.SubstitutionSystems.SubstitutionSystems UniMath.SubstitutionSystems.BindingSigToMonad UniMath.SubstitutionSystems.LiftingInitial_alt