Proposition mor_from_HSET_coend_eq (X : hSet) (f g : HSET_coend → X) (x : HSET_coend) (p : ∏ (y : C) (h : F y y), f (HSET_coend_in y h) = g (HSET_coend_in y h)) : f x = g x. Proof. use (eqtohomot (mor_to_coend_eq F (pr2 HSET_coend_colimit) X _)). intro y. use funextsec. intro h. apply p. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.OppositeCategory.Core. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Univalence. Require Import UniMath.CategoryTheory.Categories.HSET.Colimits. Require Import UniMath.CategoryTheory.Profunctors.Core. Require Import UniMath.CategoryTheory.Limits.Coends. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Limits.Coequalizers.