Proposition preserves_chosen_to_preserves_subobject_classifier' {C₁ C₂ : category} (HC₁ : is_univalent C₁) (HC₂ : is_univalent C₂) {F : C₁ ⟶ C₂} {T₁ : Terminal C₁} {T₂ : Terminal C₂} {HF : preserves_terminal F} {Ω : subobject_classifier T₁} (HF' : preserves_chosen_subobject_classifier F T₁ T₂ HF Ω) : preserves_subobject_classifier F T₁ T₂ HF. Proof. exact (preserves_chosen_to_preserves_subobject_classifier (C₁ := make_univalent_category C₁ HC₁) (C₂ := make_univalent_category C₂ HC₂) HF'). 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.Limits.Preservation. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.SubobjectClassifier.SubobjectClassifier. Require Import UniMath.CategoryTheory.SubobjectClassifier.SubobjectClassifierIso.