Definition inv_associator_profunctor_nat_trans {C₁ C₂ C₃ C₄ : category} (P₁ : C₁ ↛ C₂) (P₂ : C₂ ↛ C₃) (P₃ : C₃ ↛ C₄) : profunctor_nat_trans (comp_profunctor (comp_profunctor P₁ P₂) P₃) (comp_profunctor P₁ (comp_profunctor P₂ P₃)) := inv_profunctor_nat_trans (is_profunctor_nat_iso_associator_profunctor_nat_trans P₁ P₂ P₃).
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.