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.

翻译：我们研究的是某种半模量半成像的半成像的半成像的半成像的半成像的半成像的发源体分配法。 对于这个子子类,我们把$\delta$定性为在一组自由的半成像体中关闭的锥形。我们利用弱发源法的抽象理论,用$\delta$组成发源体和半成像元,获得自由半成像的共成形子的元。