Definition regular_epi_pb_stable (C : category) : UU := ∏ (pb x y z : C) (f : x --> z) (g : y --> z) (π₁ : pb --> x) (π₂ : pb --> y) (p : π₁ · f = π₂ · g) (H : isPullback p), is_regular_epi f → is_regular_epi π₂.
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.Pullbacks. Require Import UniMath.CategoryTheory.Epis.