Definition MultiSortedSigToMonad (sig : MultiSortedSig sort) : Monad (HSET / sort). Proof. use Monad_from_hss. - apply BinCoproducts_HSET_slice. - apply (MultiSortedSigToSignature sort sig). - apply MultiSortedSigToHSS. 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.Initial. Require Import UniMath.CategoryTheory.FunctorAlgebras. 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.Slice. Require Import UniMath.CategoryTheory.slicecat. Require Import UniMath.SubstitutionSystems.Signatures. Require Import UniMath.SubstitutionSystems.SimplifiedHSS.SubstitutionSystems. Require Import UniMath.SubstitutionSystems.SimplifiedHSS.LiftingInitial_alt. Require Import UniMath.SubstitutionSystems.SimplifiedHSS.MonadsFromSubstitutionSystems. Require Import UniMath.SubstitutionSystems.Notation. Require Import UniMath.SubstitutionSystems.SimplifiedHSS.BindingSigToMonad. Require Import UniMath.SubstitutionSystems.MonadsMultiSorted. Require Import UniMath.SubstitutionSystems.MultiSorted.