Definition runitor_profunctor_square {C₁ C₂ : category} (P : C₁ ↛ C₂) : profunctor_square (functor_identity C₂) (functor_identity C₁) (comp_profunctor P (id_profunctor C₂)) P. Proof. use profunctor_nat_trans_to_square. exact (runitor_profunctor_nat_trans P). 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.