Definition lwhisker_profunctor_nat_trans_mor {C₁ C₂ C₃ : category} (P : C₁ ↛ C₂) {Q₁ Q₂ : C₂ ↛ C₃} (τ : profunctor_nat_trans Q₁ Q₂) (z : C₃) (x : C₁) : comp_profunctor P Q₁ z x → comp_profunctor P Q₂ z x. Proof. use from_comp_profunctor_ob. - exact (λ y h h', comp_profunctor_ob_in _ _ y h (τ z y h')). - abstract (intros y₁ y₂ g h h' ; cbn ; rewrite profunctor_nat_trans_rmap ; rewrite comp_profunctor_ob_in_comm ; 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.