Lemma yon_binprod_is_inverse : is_inverse_in_precat (C := [C^op, HSET, has_homsets_HSET]) yon_binprod_nat_trans yon_binprod_inv_nat_trans. Proof. split; apply nat_trans_eq_alt; intro Z; apply funextfun; intro f. - symmetry. apply BinProductArrowEta. - apply dirprodeq. + apply BinProductPr1Commutes. + apply BinProductPr2Commutes. Qed.
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.