Definition extremal_epi_weq_strong_epi {C : category} (PB : Pullbacks C) {x y : C} (e : x --> y) : is_extremal_epi e ≃ is_strong_epi e. Proof. use weqimplimpl. - apply (is_strong_epi_extremal_epi PB). - apply is_extremal_epi_strong_epi. - apply isaprop_is_extremal_epi. - apply isaprop_is_strong_epi. 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.Pullbacks. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.EpiFacts. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.RegularAndExact.RegularEpi. Require Import UniMath.CategoryTheory.RegularAndExact.RegularCategory.