Proposition isaprop_isEffective {C : category} (H : is_univalent C) {x y : C} (f : x --> y) : isaprop (isEffective f). Proof. use isaproptotal2. - intro. apply isaprop_isCoequalizer. - intros. apply isaprop_Pullback. exact H. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Limits.Graphs.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Graphs.Coequalizers. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Graphs.Pushouts. Require Import UniMath.CategoryTheory.Limits.Graphs.EqDiag. Require Import UniMath.CategoryTheory.Limits.Pushouts. Require Import UniMath.CategoryTheory.Limits.Coequalizers.