Definition comp_profunctor_colim_profunctor_data (x : C₁) (z : C₃) : profunctor_data C₂ C₂. Proof. use make_profunctor_data. - exact (λ y₁ y₂, P y₁ x × Q z y₂). - exact (λ y₁ y₂ g y₁' y₂ g' h, P #[ g , identity _ ] (pr1 h) ,, Q #[ identity _ , g' ] (pr2 h)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Categories.HSET.SetCoends. Require Import UniMath.CategoryTheory.Profunctors.Core.