Definition profunctor_square_to_profunctor_nat_trans {C D : category} {P Q : D ↛ C} (τ : profunctor_square (functor_identity _) (functor_identity _) P Q) : profunctor_nat_trans P Q. Proof. use make_profunctor_nat_trans. - exact (λ y x h, τ y x h). - abstract (intros y₁ y₂ x₁ x₂ g f h ; cbn -[lmap rmap] ; rewrite profunctor_square_lmap_rmap ; cbn ; 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.