proposition: Lemma colimArrowUnique' {C : precategory} {g : graph} {d : diagram g C} (CC : ColimCocone d) {c} (k k' : C ⟦ colim CC, c ⟧): (∏ u : vertex g, colimIn CC u · k = colimIn CC u · k') → k = k'.
proof: Proof. intro eq. apply pathsinv0. etrans. { apply colimArrowEta. } apply pathsinv0. apply colimArrowUnique. cbn. exact eq. Qed.
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