Proposition coequalizer_eq_hSet (x : X) : coequalizer_map_hSet (f x) = coequalizer_map_hSet (g x). Proof. apply iscompsetquotpr. use eqrel_impl. apply hinhpr. exists x. split. - apply idpath. - apply idpath. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Graphs.Coproducts. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Limits.Graphs.Pushouts. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.Combinatorics.FiniteSets. Require Import UniMath.MoreFoundations.Subtypes.