Definition ψ_from_comps : ψ_source ⟹ ψ_target. Proof. use tpair. - intro A. simpl. intro f. unfold yoneda_objects_ob in *. exact (θ A · #G f · ρ). - apply is_nat_trans_ψ_from_comps. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.FunctorAlgebras. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.yoneda. Require Import UniMath.CategoryTheory.Adjunctions.Core.