Definition preserves_regular_epi {C₁ C₂ : category} (F : C₁ ⟶ C₂) : UU := ∏ (x y : C₁) (f : x --> y), is_regular_epi f → is_regular_epi (#F f).
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.