Proposition z_iso_to_is_subobject_classifier {C : univalent_category} {T : Terminal C} (Ω : subobject_classifier T) (Ω' : C) (t : T --> Ω') (f : z_iso Ω Ω') (q : true Ω · f = t) : is_subobject_classifier T Ω' t. Proof. use eq_to_is_subobject_classifier. - exact Ω. - exact (isotoid C (univalent_category_is_univalent C) f). - rewrite idtoiso_isotoid. exact q. 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.