Definition free_ptd_alg_mor {A B : C} (f : A --> B) : C ⟦ free_ptd_alg_ob A, free_ptd_alg_ob B ⟧. Proof. apply colimOfArrows with (λ i, # (F ^ i) f). intros i _ []; simpl. induction i. + abstract (simpl; apply pathsinv0, point_naturality). + abstract (simpl; do 2 rewrite <- functor_comp; apply maponpaths; exact IHi). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Chains.Chains. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering.