Lemma CoproductInCommutes (a : I -> C) (CC : Coproduct a) : ∏ (c : C) (f : ∏ i, a i --> c) i, CoproductIn CC i · CoproductArrow CC f = f i. Proof. intros c f i. exact (pr2 (pr1 (isCoproduct_Coproduct CC _ f)) i). 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.