On functors from category of Giry algebras to category of convex spaces
arXiv:1804.01345
Abstract
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.
12 pages, v2 has merely made the title more precise, v3 fixes some typos, v4 adds treatment of super convex spaces