## Filippo Bonchi ; Alessio Santamaria - Convexity via Weak Distributive Laws

lmcs:8389 - Logical Methods in Computer Science, November 23, 2022, Volume 18, Issue 4 - https://doi.org/10.46298/lmcs-18(4:8)2022
Convexity via Weak Distributive Laws

Authors: Filippo Bonchi ; Alessio Santamaria

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.

Volume: Volume 18, Issue 4
Published on: November 23, 2022
Accepted on: October 7, 2022
Submitted on: August 25, 2021
Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic