Erratum and Addendum: The factorization of the Giry monad

TL;DR

This paper clarifies the factorization of the Giry monad through super convex spaces, correcting a previous error and providing an elementary proof based on the properties of a codense subcategory.

Contribution

It corrects earlier claims by showing the Giry monad factors through super convex spaces, not convex spaces, using the concept of a codense subcategory.

Findings

Giry monad factorizes through super convex spaces

Elementary proof based on codense subcategory property

Correction of previous erroneous claim

Abstract

The category of super convex spaces, a proper subcategory of convex spaces, possesses the property that it has a codense subcategory. This codense subcategory allows for an elementary proof that the Giry monad factorizes through the category of super convex spaces, not the category of convex spaces as erroneously claimed in an earlier article [arXiv:1707.00488]