Definition make_isCoproduct (hsC : has_homsets C) (a : I -> C) (co : C) (f : ∏ i, a i --> co) : (∏ (c : C) (g : ∏ i, a i --> c), ∃! k : C ⟦co, c⟧, ∏ i, f i · k = g i) → isCoproduct a co f. Proof. intros H c cc. apply H. Defined.
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.