proposition: Lemma CoproductArrowUnique (a : I -> C) (CC : Coproduct a) (x : C) (f : ∏ i, a i --> x) (k : CoproductObject CC --> x) (Hk : ∏ i, CoproductIn CC i · k = f i) : k = CoproductArrow CC f.
proof: Proof. set (H' := pr2 (isCoproduct_Coproduct CC _ f) (k,,Hk)). apply (base_paths _ _ H'). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All 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.ProductCategory UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.whiskering