Definition is_z_iso_in_REL_simplified {X Y : hSet} (r : bin_hrel X Y) : is_z_isomorphism (C := REL) r <-> (∏ x: X, ∃! y : Y, r x y) × (∏ y : Y, ∃! x : X, r x y).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Categories.HSET.All.