Definition codomain_fib_equalizer (H : Equalizers C) (x : C) : Equalizers (C/x). Proof. intros fy₁ fy₂ φp ψq. pose (E := H (cod_dom fy₁) (cod_dom fy₂) (dom_mor φp) (dom_mor ψq)). use make_Equalizer. - refine (EqualizerObject E ,, _). exact (EqualizerArrow E · cod_mor fy₁). - refine (EqualizerArrow E ,, _). abstract (cbn ; rewrite id_right ; apply idpath). - abstract (use eq_mor_cod_fib ; rewrite !comp_in_cod_fib ; cbn ; apply EqualizerEqAr). - use to_isEqualizer_cod_fib. + apply EqualizerEqAr. + exact (isEqualizer_Equalizer E). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.PullbackConstructions. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseTerminal. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseProducts. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseEqualizers. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodLeftAdjoint. Section FromEqCodFib. End FromEqCodFib. Section FromUMP. End FromUMP.