Definition is_coend_construction_of_coends : is_coend construction_of_coends_cowedge. Proof. intro w. use iscontraprop1. - exact (is_coend_construction_of_coends_unique_map w). - use make_cowedge_map. + exact (is_coend_construction_of_coends_mor w). + exact (is_coend_construction_of_coends_comm w). Defined.
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.