Convexity via Weak Distributive Laws

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.

arXiv admin note: substantial text overlap with arXiv:2012.14778

References in corpus (2)

• Coinduction up to in a fibrational setting
• Combining Weak Distributive Laws: Application to Up-To Techniques