Proposition inv_profunctor_nat_iso_left {C₁ C₂ : category} {P Q : profunctor C₁ C₂} {τ : profunctor_nat_trans P Q} (Hτ : is_profunctor_nat_iso τ) {y : C₂} {x : C₁} (h : P y x) : inv_profunctor_nat_iso Hτ (τ y x h) = h. Proof. apply (homotinvweqweq (make_weq _ (Hτ y x))). Qed.
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.