Definition pb_of_section (isPb : isPullback H) (s : C⟦a,c⟧) (K : s · g = identity _ ) : ∑ s' : C⟦b, d⟧, s' · h = identity _ . Proof. use tpair. - use (PullbackArrow (make_Pullback _ isPb) b (identity _ ) (f · s)). abstract (rewrite id_left, <- assoc, K, id_right; apply idpath). - abstract (cbn; apply (PullbackArrow_PullbackPr1 (make_Pullback H isPb))). Defined.
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.