Definition PullbackSubobject (PB : Pullbacks C) {c : C} (S : Subobjectscategory c) {c' : C} (h : C⟦c', c⟧) : Subobjectscategory c'. Proof. set (pb := PB _ _ _ h (Subobject_mor S)). use Subobjectscategory_ob. - exact pb. - exact (PullbackPr1 pb). - use MonicPullbackisMonic'. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.slicecat. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Subcategory.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.opp_precat.