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arXiv · 2202.10819

Giry algebras for standard measurable spaces

Kirk Sturtz
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Abstract

The notion of "super convex spaces" generalizes the idea of convex spaces by replacing finite affine sums with countable affine sums. Using this notion permits a very elegant approach for analysis of the Giry monad on standard measurable spaces and identifying the $\mathcal{G}$-algebras for that monad. We use Isbell duality and restrict the adjunction $\mathbf{Spec} \dashv \mathcal{O}$ to a proper subcategory of super convex spaces and separated standard measurable spaces.

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Kirk Sturtz. 2022-02-22. Giry algebras for standard measurable spaces. https://arxiv.org/abs/2202.10819

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