Proposition is_coend_construction_of_coends_unique_map : isaprop (cowedge_map construction_of_coends_cowedge w). Proof. use invproofirrelevance. intros φ₁ φ₂. use cowedge_map_eq. use CoequalizerOutsEq. use CoproductArrow_eq. intro i. rewrite !assoc. exact (eq_of_cowedge_map φ₁ i @ !(eq_of_cowedge_map φ₂ 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.OppositeCategory.Core. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Limits.Coequalizers.