Proposition lmap_representable_profunctor_left {x : C₁} {y₁ y₂ : C₂} (g : y₂ --> y₁) (h : y₁ --> F x) : lmap representable_profunctor_left g h = g · h. Proof. cbn. rewrite functor_id. rewrite id_right. apply idpath. Qed.
Require Import UniMath.Foundations.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.