Semialgebras and Weak Distributive Laws - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

Semialgebras and Weak Distributive Laws

Résumé

Motivated by recent work on weak distributive laws and their applications to coalgebraic semantics, we investigate the algebraic nature of semialgebras for a monad. These are algebras for the underlying functor of the monad subject to the associativity axiom alone-the unit axiom from the definition of an Eilenberg-Moore algebras is dropped. We prove that if the underlying category has coproducts, then semialgebras for a monad M are in fact the Eilenberg-Moore algebras for a suitable monad structure on the functor id + M , which we call the semifree monad M^s. We also provide concrete algebraic presentations for semialgebras for the maybe monad, the semigroup monad and the finite distribution monad. A second contribution is characterizing the weak distributive laws of the form M T ⇒ T M as strong distributive laws M^s T ⇒ T M^s subject to an additional condition.
Fichier principal
Vignette du fichier
main.pdf (293.16 Ko) Télécharger le fichier
example.pdf (116.24 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03261093 , version 1 (18-06-2021)
hal-03261093 , version 2 (08-09-2021)

Identifiants

Citer

Daniela Petrişan, Ralph Sarkis. Semialgebras and Weak Distributive Laws. 2021. ⟨hal-03261093v2⟩
150 Consultations
150 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More