Definition subobject_classifier_pullback {X Y} (m : Monic _ X Y) : Pullback (characteristic_morphism m) true. Proof. use make_Pullback. - exact X. - exact m. - apply TerminalArrow. - apply subobject_classifier_square_commutes. - apply (pr2 (pr2 (iscontrpr1 (subobject_classifier_universal_property m)))). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Subobjects. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Subcategory.Core.