Lemma CoequalizerArrowComm {a b : C} {f g : C⟦a, b⟧} (E : Coequalizer f g) (e : C) (h : C⟦b, e⟧) (H : f · h = g · h) : CoequalizerArrow E · CoequalizerOut E e h H = h. Proof. exact (colimArrowCommutes E e _ Two). Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Graphs.EqDiag. Require Import UniMath.CategoryTheory.Limits.Coequalizers.