Definition yon_binprod_inv_nat_trans_data : nat_trans_data (pr1 (BinProductObject _ (BinProducts_PreShv (yon X) (yon Y)))) (pr1 (yon (BinProductObject _ (PC X Y)))). Proof. intros Z [f1 f2]. exact (BinProductArrow _ (PC X Y) f1 f2). 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.