Probability Sheaves and the Giry Monad

Author Alex Simpson

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Alex Simpson

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Alex Simpson. Probability Sheaves and the Giry Monad. In 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 72, pp. 1:1-1:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


I introduce the notion of probability sheaf, which is a mathematical structure capturing the relationship between probabilistic concepts (such as random variable) and sample spaces. Various probability-theoretic notions can be (re)formulated in terms of category-theoretic structure on the category of probability sheaves. As a main example, I consider the Giry monad, which, in its original formulation, constructs spaces of probability measures. I show that the Giry monad generalises to the category of probability sheaves, where it turns out to have a simple, purely category-theoretic definition.
  • Random variable
  • conditional independence
  • category theory
  • sheaves
  • Giry monad


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