We study the canonical weak distributive law δ of the powerset monad over the semimodule monad for a certain class of semirings containing, in particular, positive semifields. For this subclass we characterise δ as a convex closure in the free semimodule of a set. Using the abstract theory of weak distributive laws, we compose the powerset and the semimodule monads via δ, obtaining the monad of convex subsets of the free semimodule.
Convexity via Weak Distributive Laws
Filippo Bonchi;Alessio Santamaria
2022-01-01
Abstract
We study the canonical weak distributive law δ of the powerset monad over the semimodule monad for a certain class of semirings containing, in particular, positive semifields. For this subclass we characterise δ as a convex closure in the free semimodule of a set. Using the abstract theory of weak distributive laws, we compose the powerset and the semimodule monads via δ, obtaining the monad of convex subsets of the free semimodule.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
2108.10718.pdf
accesso aperto
Tipologia:
Versione finale editoriale
Licenza:
Creative commons
Dimensione
710.65 kB
Formato
Adobe PDF
|
710.65 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
