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- W4289800069 abstract "Probability theory can be studied synthetically as the computational effect embodied by a commutative monad. In the recently proposed Markov categories, one works with an abstraction of the Kleisli category and then defines deterministic morphisms equationally in terms of copying and discarding. The resulting difference between ‘pure’ and ‘deterministic’ leads us to investigate the ‘sober’ objects for a probability monad, for which the two concepts coincide. We propose natural conditions on a probability monad which allow us to identify the sober objects and define an idempotent sobrification functor. Our framework applies to many examples of interest, including the Giry monad on measurable spaces, and allows us to sharpen a previously given version of de Finetti’s theorem for Markov categories." @default.
- W4289800069 created "2022-08-04" @default.
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- W4289800069 date "2022-08-02" @default.
- W4289800069 modified "2023-10-10" @default.
- W4289800069 title "Probability monads with submonads of deterministic states" @default.
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- W4289800069 doi "https://doi.org/10.1145/3531130.3533355" @default.
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