Definition free_ptd_alg_unit : functor_identity C ⟹ free_ptd_alg ∙ forget_ptd_alg F. Proof. apply make_nat_trans with (λ A, colimIn (CC A) 0). abstract (intros A B f; apply pathsinv0, (free_ptd_alg_mor_restricts f 0)). 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.