Definition regular_epi_chosen_pb_stable {C : category} (PB : Pullbacks C) : UU := ∏ (x y z : C) (f : x --> z) (g : y --> z), is_regular_epi f → is_regular_epi (PullbackPr2 (PB _ _ _ f g)).
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.