proposition: Lemma ColimFunctorCocone : ColimCocone D.
proof: Proof. use make_ColimCocone. - exact ColimFunctor. - use make_cocone. + now apply colim_nat_trans_in_data. + abstract (now intros u v e; apply (nat_trans_eq C); intro a; apply (colimInCommutes (HCg a))). - now intros F cc; simpl; apply (ColimFunctor_unique _ cc). Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Propositions UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Adjunctions.Core