Presenting Convex Sets of Probability Distributions by Convex Semilattices and Unique Bases ((Co)algebraic pearls)
Filippo Bonchi, Ana Sokolova, Valeria Vignudelli · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2021
We prove that every finitely generated convex set of finitely supported probability distributions has a unique base. We apply this result to provide an alternative proof of a recent result: the algebraic theory of convex semilattices presents the monad of convex sets of probability distributions.