Definition binprod_to_pullback : some_binprod (C / Z) → some_pullback C Z. Proof. intro P. induction P as [AZ BZ]. induction BZ as [BZ P]. exact (pr1 AZ ,, pr1 BZ ,, pr2 AZ ,, pr2 BZ ,, slice_binprod_to_pullback C P). Defined.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.slicecat. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Pullbacks.