Proposition eq_profunctor_nat_trans {C₁ C₂ : category} {P Q : profunctor C₁ C₂} {τ τ' : profunctor_nat_trans P Q} (p : ∏ (y : C₂) (x : C₁) (h : P y x), τ y x h = τ' y x h) : τ = τ'. Proof. use nat_trans_eq. { apply homset_property. } intros xy. induction xy as [ y x ] ; cbn. use funextsec. intro h. exact (p y x h). Qed.
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.