Definition id_v_profunctor_square {C D : category} (F : C ⟶ D) : profunctor_square F F (id_profunctor C) (id_profunctor D). Proof. use make_profunctor_square. - exact (λ y x h, #F h). - abstract (intros y₁ y₂ x₁ x₂ g f h ; cbn -[lmap rmap] ; rewrite !lmap_id_profunctor, !rmap_id_profunctor ; 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.