Definition representable_profunctor_right_unit {C₁ C₂ : category} (F : C₁ ⟶ C₂) : profunctor_square (functor_identity C₁) F (id_profunctor C₁) (representable_profunctor_right F). Proof. use make_profunctor_square. - exact (λ y x f, #F f). - abstract (intros y₁ y₂ x₁ x₂ g f h ; cbn in * ; rewrite functor_id ; rewrite !id_left, !id_right ; rewrite !functor_comp ; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.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. Require Import UniMath.CategoryTheory.Profunctors.Examples. Require Import UniMath.CategoryTheory.Profunctors.Transformation.