Erratum and Addendum: The factorization of the Giry monad
K. Sturtz

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]
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Intracranial Aneurysms: Treatment and Complications · Vascular Malformations Diagnosis and Treatment
