Definition profunctor_nat_trans_law {C₁ C₂ : category} {P Q : profunctor C₁ C₂} (τ : profunctor_nat_trans_data P Q) : UU := ∏ (y₁ y₂ : C₂) (x₁ x₂ : C₁) (g : y₂ --> y₁) (f : x₁ --> x₂) (h : P y₁ x₁), τ y₂ x₂ (lmap P g (rmap P f h)) = lmap Q g (rmap Q f (τ y₁ x₁ h)).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Categories.HSET.SetCoends. Require Import UniMath.CategoryTheory.Profunctors.Core. Require Import UniMath.CategoryTheory.Profunctors.Examples.