Definition profunctor_on_morphisms {C₁ C₂ : category} (P : C₁ ↛ C₂) {y₁ y₂ : C₂} (g : y₂ --> y₁) {x₁ x₂ : C₁} (f : x₁ --> x₂) (h : P y₁ x₁) : P y₂ x₂ := @functor_on_morphisms _ _ (P : _ ⟶ _) (_ ,, _) (_ ,, _) (g ,, f) h.
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.