Proposition CoproductArrow_eq {d : I → C} (z : C) (x : Coproduct d) (f g : x --> z) (p : ∏ (i : I), CoproductIn x i · f = CoproductIn x i · g) : f = g. Proof. refine (CoproductArrowEta _ _ _ _ @ _ @ !(CoproductArrowEta _ _ _ _)). apply maponpaths. use funextsec. exact p. 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.