Lemma ColimFunctorCocone : ColimCocone D. 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.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Adjunctions.Core.