Probability Sheaves and the Giry Monad
نویسنده
چکیده
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. 1998 ACM Subject Classification F.3.2 Semantics of Programming Languages
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