Definition preserves_subobject_classifier_z_iso {C₁ C₂ : category} {F : C₁ ⟶ C₂} {T₁ : Terminal C₁} {T₂ : Terminal C₂} {HF : preserves_terminal F} (HF' : preserves_subobject_classifier F T₁ T₂ HF) (Ω₁ : subobject_classifier T₁) (Ω₂ : subobject_classifier T₂) : z_iso (F Ω₁) Ω₂ := z_iso_subobject_classifier (preserves_subobject_classifier_on_ob HF' Ω₁) Ω₂.
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.Limits.Preservation. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.SubobjectClassifier.SubobjectClassifier. Require Import UniMath.CategoryTheory.SubobjectClassifier.SubobjectClassifierIso.