  In The factorization of the Giry monad (arXiv:1707.00488v2) the author
asserts that the category of convex spaces is equivalent to the category of
Eilenberg-Moore algebras over the Giry monad. Some of the statements employed
in the proof of this claim have been refuted in our earlier paper
(arXiv:1803.07956). Building on the results of that paper we prove that no such
equivalence exists and a parallel statement is proved for the category of super
convex spaces.
