Definition preserves_chosen_to_chosen_subobject_classifier {C₁ C₂ : category} {F : C₁ ⟶ C₂} {T₁ : Terminal C₁} {T₂ : Terminal C₂} (HF : preserves_terminal F) (Ω₁ : subobject_classifier T₁) (Ω₂ : subobject_classifier T₂) : UU := ∑ (f : z_iso (F Ω₁) Ω₂), #F (true Ω₁) · f = TerminalArrow _ _ · true 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.