2000 character limit reached
Convexity via Weak Distributive Laws (2108.10718v4)
Published 19 Aug 2021 in cs.LO and math.LO
Abstract: We study the canonical weak distributive law $\delta$ of the powerset monad over the semimodule monad for a certain class of semirings containing, in particular, positive semifields. For this subclass we characterise $\delta$ 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 $\delta$, obtaining the monad of convex subsets of the free semimodule.