Corollary well_pointed_mor_is_algebra_mor (X Y : ptd_alg F) (f : C ⟦ X, Y ⟧) : is_ptd_alg_mor F X Y f. Proof. red. set (point_X_iso := make_z_iso' _ (well_pointed_point_is_z_iso_at_algebra X)). apply (pre_comp_with_z_iso_is_inj point_X_iso); simpl. rewrite assoc, assoc. rw_left_comp (ptd_alg_law F X). apply pathsinv0. rw_left_comp (! point_naturality F f). rewrite <- assoc. rw_right_comp (ptd_alg_law F Y). now rewrite id_left, id_right. Qed.
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.