Lemma well_pointed_forgetul_fully_faithful : fully_faithful (forget_ptd_alg F). Proof. red. intros X Y. apply isweq_iso with (λ f, make_ptd_alg_mor F f (well_pointed_mor_is_algebra_mor X Y f)). - abstract (intros; now apply ptd_alg_mor_eq). - abstract easy. 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.