proposition: Lemma preserves_colimit_pre_composition_functor : ∏ (A B C : category) (F : functor A B) (g : graph) (d : diagram g [B, C]) (G : [B, C]) (ccG : cocone d G), (∏ b : B, ColimCocone (diagram_pointwise d b)) → preserves_colimit (pre_composition_functor A B C F) d G ccG.
proof: Proof. exact @UniMath.CategoryTheory.Chains.OmegaCocontFunctors.preserves_colimit_pre_composition_functor. 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