Definition make_Coequalizer {a b : C} (f g : C⟦a, b⟧) (d : C) (h : C⟦b, d⟧) (H : f · h = g · h) (isCEq : isCoequalizer f g d h H) : Coequalizer f g. Proof. use tpair. - use tpair. + exact d. + use Coequalizer_cocone. * exact h. * exact H. - exact isCEq. Defined.
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.