Definition rwhisker_profunctor_nat_trans_mor {C₁ C₂ C₃ : category} {P₁ P₂ : C₁ ↛ C₂} (τ : profunctor_nat_trans P₁ P₂) (Q : C₂ ↛ C₃) (z : C₃) (x : C₁) : comp_profunctor P₁ Q z x → comp_profunctor P₂ Q z x. Proof. use from_comp_profunctor_ob. - exact (λ y h h', comp_profunctor_ob_in _ _ y (τ y x h) h'). - abstract (intros y₁ y₂ g h h' ; cbn ; rewrite profunctor_nat_trans_lmap ; 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.