Lemma postcompWithCoproductArrow {a b : C} (CCab : CoproductCocone a b) {c : C} (f : a --> c) (g : b --> c) {x : C} (k : c --> x) : CoproductArrow CCab f g · k = CoproductArrow CCab (f · k) (g · k). Proof. apply CoproductArrowUnique. - rewrite assoc, CoproductIn1Commutes; apply idpath. - rewrite assoc, CoproductIn2Commutes; apply idpath. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.RepresentableFunctors.Representation.