Definition Equalizer_cone {a b : C} (f g : C⟦a, b⟧) (d : C) (h : C⟦d, a⟧) (H : h · f = h · g) : cone (Equalizer_diagram f g) d. Proof. use make_cone. - use two_rec_dep. + exact h. + exact (h · f). - use two_rec_dep; use two_rec_dep. + exact (empty_rect _). + intro e. induction e. * apply idpath. * apply (! H). + exact (empty_rect _). + exact (empty_rect _). 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.Isos. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Equalizers.