English

Convexity via Weak Distributive Laws

Logic in Computer Science 2023-06-22 v4 Logic

Abstract

We study the canonical weak distributive law δ\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 δ\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 δ\delta, 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

R2 v1 2026-06-24T05:22:46.885Z