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arXiv · 2108.10718

Convexity via Weak Distributive Laws

Filippo Bonchi·Alessio Santamaria
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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.

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Filippo Bonchi, Alessio Santamaria. 2021-08-19. Convexity via Weak Distributive Laws. https://doi.org/10.46298/lmcs-18(4:8)2022

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