Convexity via Weak Distributive Laws
Logic in Computer Science
2023-06-22 v4 Logic
Abstract
We study the canonical weak distributive law of the powerset monad over the semimodule monad for a certain class of semirings containing, in particular, positive semifields. For this subclass we characterise 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 , obtaining the monad of convex subsets of the free semimodule.
Cite
@article{arxiv.2108.10718,
title = {Convexity via Weak Distributive Laws},
author = {Filippo Bonchi and Alessio Santamaria},
journal= {arXiv preprint arXiv:2108.10718},
year = {2023}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2012.14778