Definition coeq_of_kernel_pair_slice : Coequalizer (PullbackPr1 K) (PullbackPr2 K). Proof. use make_Coequalizer. - exact coeq_of_kernel_pair_slice_ob. - exact coeq_of_kernel_pair_slice_coeq_arr. - exact coeq_of_kernel_pair_slice_coeq_arr_eq. - use is_coequalizer_cod_fib. + apply (CoequalizerEqAr Coeq). + exact (isCoequalizer_Coequalizer Coeq). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.EpiFacts. Require Import UniMath.CategoryTheory.RegularAndExact.RegularEpi. Require Import UniMath.CategoryTheory.RegularAndExact.RegularCategory. Require Import UniMath.CategoryTheory.RegularAndExact.RegularEpiFacts. Require Import UniMath.CategoryTheory.RegularAndExact.ExactCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodColimits. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodMorphisms. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodLimits. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodFunctor. Section PreservesFromStable. End PreservesFromStable.