Semialgebras and Weak Distributive Laws
| Autor: | Petrişan, Daniela, Sarkis, Ralph |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | EPTCS 351, 2021, pp. 218-241 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4204/EPTCS.351.14 |
| Popis: | 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. Comment: In Proceedings MFPS 2021, arXiv:2112.13746 |
| Databáze: | arXiv |
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