Definition colimOfArrows {C : precategory} {g : graph} {d1 d2 : diagram g C} (CC1 : ColimCocone d1) (CC2 : ColimCocone d2) (f : ∏ (u : vertex g), C⟦dob d1 u,dob d2 u⟧) (fNat : ∏ u v (e : edge u v), dmor d1 e · f v = f u · dmor d2 e) : C⟦colim CC1,colim CC2⟧. Proof. apply colimArrow; use make_cocone. - now intro u; apply (f u · colimIn CC2 u). - abstract (intros u v e; simpl; now rewrite assoc, fNat, <- assoc, colimInCommutes). 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.