Definition disp_Coequalizer {x y : C} {f g : x --> y} {xx : D x} {yy : D y} (ff : xx -->[ f ] yy) (gg : xx -->[ g ] yy) (e : Coequalizer f g) : UU := ∑ (ee : D e) (ar_e : yy -->[ CoequalizerArrow e ] ee) (pp : transportf (λ z, _ -->[ z ] _) (CoequalizerEqAr e) (ff ;; ar_e) = gg ;; ar_e), is_disp_Coequalizer e ee ar_e pp.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total.