Definition associator_profunctor_inv_mor_ob {C₁ C₂ C₃ C₄ : category} (P₁ : C₁ ↛ C₂) (P₂ : C₂ ↛ C₃) (P₃ : C₃ ↛ C₄) (z : C₄) (w : C₁) (y : C₃) (h : P₃ z y) : comp_profunctor_ob P₁ P₂ y w → comp_profunctor_ob P₁ (comp_profunctor P₂ P₃) z w. Proof. use from_comp_profunctor_ob. - refine (λ x k l, comp_profunctor_ob_in _ _ _ k _). exact (comp_profunctor_ob_in _ _ y l h). - abstract (intros x₁ x₂ f k k' ; cbn ; rewrite <- comp_profunctor_ob_in_comm ; cbn ; rewrite comp_profunctor_mor_comm ; rewrite lmap_id ; 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.