Definition PullbackHSET_ob {A B C : HSET} (f : HSET⟦B,A⟧) (g : HSET⟦C,A⟧) : HSET. Proof. exists (∑ (xy : setdirprod B C), f (pr1 xy) = g (pr2 xy)). abstract (apply isaset_total2; [ apply isasetdirprod; apply setproperty | intros xy; apply isasetaprop, setproperty ]). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.WeakEquivalences. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Limits.Graphs.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Graphs.Equalizers. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Categories.HSET.Core.