Definition isEffective_weq_is_regular (HC : is_univalent C) : isEffective f ≃ is_regular_epi f. Proof. use weqimplimpl. - exact isEffective_to_is_regular. - exact (is_regular_to_isEffective HC). - apply isaprop_isEffective. exact HC. - apply isaprop_is_regular_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.