Lemma PullbackArrowUnique' {a b c : C} (f : C⟦b,a⟧) (g : C⟦c,a⟧) (P : Pullback f g) e (h : C⟦e,b⟧) (k : C⟦e,c⟧) (Hcomm : h · f = k · g) (w : C⟦e,P⟧) (H1 : w · PullbackPr1 P = h) (H2 : w · PullbackPr2 P = k) : w = PullbackArrow P e h k Hcomm. Proof. now apply PullbackArrowUnique. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Monics. Definition UnivProductFromPullback (c d a : C) (f : a --> c) (g : a --> d): exists (UnivProductFromPullback c d a f g). Definition BinProductsFromPullbacks : BinProducts C := BinProduct_Pullback.