Definition SignatureInitialAlgebra (H : Signature sortToC sortToC sortToC) (Hs : is_omega_cocont H) : Initial (FunctorAlg (Id_H H)). Proof. use colimAlgInitial. - apply Initial_functor_precat, Initial_functor_precat, IC. - apply (is_omega_cocont_Id_H), Hs. - apply ColimsFunctorCategory_of_shape, ColimsFunctorCategory_of_shape, HC. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.FunctorAlgebras. Require Import UniMath.CategoryTheory.exponentials. Require Import UniMath.CategoryTheory.Chains.All. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Colimits. Require Import UniMath.CategoryTheory.Categories.HSET.Limits. Require Import UniMath.CategoryTheory.Categories.HSET.Structures. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Groupoids. Require Import UniMath.SubstitutionSystems.Signatures. Require Import UniMath.SubstitutionSystems.SumOfSignatures. Require Import UniMath.SubstitutionSystems.BinProductOfSignatures. Require Import UniMath.SubstitutionSystems.SimplifiedHSS.SubstitutionSystems. Require Import UniMath.SubstitutionSystems.SimplifiedHSS.LiftingInitial_alt. Require Import UniMath.SubstitutionSystems.SimplifiedHSS.MonadsFromSubstitutionSystems. Require Import UniMath.SubstitutionSystems.SignatureExamples. Require Import UniMath.SubstitutionSystems.SimplifiedHSS.BindingSigToMonad. Require Import UniMath.SubstitutionSystems.MultiSortedBindingSig. Require Import UniMath.SubstitutionSystems.MultiSorted_alt.