Proposition profunctor_id {C₁ C₂ : category} (P : C₁ ↛ C₂) {y : C₂} {x : C₁} (h : P y x) : P #[ identity _ , identity _ ] h = h. Proof. exact (eqtohomot (functor_id P _) h). Qed.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Categories.HSET.All.