Lemma colimArrowUnique {C : precategory} {g : graph} {d : diagram g C} (CC : ColimCocone d) (c : C) (cc : cocone d c) (k : C⟦colim CC,c⟧) (Hk : ∏ (u : vertex g), colimIn CC u · k = coconeIn cc u) : k = colimArrow CC c cc. Proof. apply path_to_ctr. red. apply Hk. Qed.
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.