Definition yoneda_preserves_binproduct (C : category) (BP : BinProducts C) : preserves_binproduct (yoneda C). Proof. apply (preserves_binproduct_chosen_to_chosen BP BinProducts_PreShv). intros X Y. exact (z_iso_is_z_isomorphism (yon_binprod_z_iso BP X Y)). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.Presheaf. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.yoneda.