Proposition isaprop_preserves_subobject_classifier {C₁ C₂ : category} (F : C₁ ⟶ C₂) (T₁ : Terminal C₁) (T₂ : Terminal C₂) (HF : preserves_terminal F) : isaprop (preserves_subobject_classifier F T₁ T₂ HF). Proof. do 3 (use impred ; intro). apply isaprop_is_subobject_classifier. 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.