Definition prod_profunctor_data : profunctor_data C₁ C₂. Proof. use make_profunctor_data. - exact (λ y x, P y x × Q y x). - exact (λ y₁ y₂ g x₁ x₂ f h, P #[ g , f ] (pr1 h) ,, Q #[ g , f ] (pr2 h)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Categories.HSET.SetCoends. Require Import UniMath.CategoryTheory.Profunctors.Core.