Definition lunitor_profunctor_nat_trans_mor {C₁ C₂ : category} (P : profunctor C₁ C₂) (y : C₂) (x : C₁) : comp_profunctor (id_profunctor C₁) P y x → P y x. Proof. use from_comp_profunctor_ob. - exact (λ z h h', rmap P h h'). - abstract (intros z₁ z₂ f h h' ; cbn ; rewrite id_right ; rewrite rmap_comp ; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.opp_precat. 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.