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. set (H' := pr2 (isCoproduct_Coproduct CC _ f) (k,,Hk)). apply (base_paths _ _ H'). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. 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.ProductCategory. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.whiskering.