Lemma Lam_Initial_HSET : Initial (category_FunctorAlg (Id_H _ BinCoproductsHSET Lam_S)). Proof. use colimAlgInitial. - apply (Initial_functor_precat _ _ InitialHSET). - unfold Id_H, Const_plus_H. apply is_omega_cocont_BinCoproduct_of_functors. + apply is_omega_cocont_constant_functor. + apply is_omega_cocont_Lam_S. - apply ColimsFunctorCategory_of_shape; apply ColimsHSET_of_shape. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.FunctorAlgebras. Require Import UniMath.CategoryTheory.PointedFunctors. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.SubstitutionSystems.Signatures. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.SubstitutionSystems.BinSumOfSignatures. Require Import UniMath.SubstitutionSystems.SubstitutionSystems. Require Import UniMath.SubstitutionSystems.LamSignature. Require Import UniMath.SubstitutionSystems.LiftingInitial_alt. Require Import UniMath.SubstitutionSystems.MonadsFromSubstitutionSystems. Require Import UniMath.SubstitutionSystems.Notation. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.exponentials. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Limits. Require Import UniMath.CategoryTheory.Categories.HSET.Colimits. Require Import UniMath.CategoryTheory.Categories.HSET.Structures. Require Import UniMath.CategoryTheory.Chains.All.