Convexity via Weak Distributive Laws

08/19/2021

∙

by   Filippo Bonchi, et al.

∙

0

∙

share

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.