Proposition z_iso_subobject_classifier_inverse {C : category} {T : Terminal C} (Ω Ω' : subobject_classifier T) : is_inverse_in_precat (mor_subobject_classifier Ω Ω') (mor_subobject_classifier Ω' Ω). Proof. split. - exact (mor_subobject_classifier_inv Ω Ω'). - exact (mor_subobject_classifier_inv Ω' Ω). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.SubobjectClassifier.SubobjectClassifier.