Definition id_h_profunctor_square {C D : category} (P : D ↛ C) : profunctor_square (functor_identity C) (functor_identity D) P P. Proof. use make_profunctor_square. - exact (λ y x h, h). - abstract (intros y₁ y₂ x₁ x₂ g f h ; cbn -[lmap rmap] ; 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.