Lemma postcompWithCoproductArrow {a : I -> C} (CCab : Coproduct a) {c : C} (f : ∏ i, a i --> c) {x : C} (k : c --> x) : CoproductArrow CCab f · k = CoproductArrow CCab (λ i, f i · k). Proof. apply CoproductArrowUnique; intro i. now rewrite assoc, CoproductInCommutes. 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.