Definition coindMonadOfMultiSortedSig_CAT (sig : MultiSortedSig sort) (Cuniv : is_univalent C) : Monad sortToC. Proof. use monoid_to_monad_CAT. use SigmaMonoid_to_monoid. - exact (MultiSortedSigToFunctor' sig). - exact (MultiSortedSigToStrength' sig). - exact (coindSigmaMonoidOfMultiSortedSig_CAT sig Cuniv). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.All. Require Import UniMath.Combinatorics.Lists. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. 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.exponentials. Require Import UniMath.CategoryTheory.Adjunctions.Core. 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.HSET.Univalence. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Groupoids. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.FunctorCoalgebras. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Chains.Cochains. Require Import UniMath.CategoryTheory.Chains.CoAdamek. Require Import UniMath.CategoryTheory.Chains.OmegaContFunctors. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Actegories.Actegories. Require Import UniMath.CategoryTheory.Actegories.ConstructionOfActegories. Require Import UniMath.CategoryTheory.Actegories.MorphismsOfActegories. Require Import UniMath.CategoryTheory.Actegories.CoproductsInActegories. Require Import UniMath.CategoryTheory.Actegories.ConstructionOfActegoryMorphisms. Require Import UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids. Require Import UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects. Require Import UniMath.CategoryTheory.Monoidal.Examples.EndofunctorsMonoidalElementary. Require Import UniMath.CategoryTheory.Monoidal.Examples.MonadsAsMonoidsElementary. Require Import UniMath.SubstitutionSystems.EquivalenceLaxLineatorsHomogeneousCase. Require Import UniMath.SubstitutionSystems.MultiSortedBindingSig. Require Import UniMath.SubstitutionSystems.MultiSorted_alt. Require Import UniMath.SubstitutionSystems.MultiSorted_actegorical. Require Import UniMath.SubstitutionSystems.MultiSortedMonadConstruction_alt. Require Import UniMath.SubstitutionSystems.GeneralizedSubstitutionSystems. Require Import UniMath.SubstitutionSystems.ConstructionOfGHSS. Require Import UniMath.SubstitutionSystems.SigmaMonoids. Require Import UniMath.SubstitutionSystems.ContinuitySignature.ContinuityOfMultiSortedSigToFunctor. Require Import UniMath.SubstitutionSystems.ContinuitySignature.MultiSortedSignatureFunctorEquivalence. Require Import UniMath.SubstitutionSystems.ContinuitySignature.CommutingOfOmegaLimitsAndCoproducts. Require Import UniMath.SubstitutionSystems.ContinuitySignature.InstantiateHSET. Import BifunctorNotations. Import MonoidalNotations.