论文标题
具有确定性状态亚月光的概率单元 - 扩展版本
Probability monads with submonads of deterministic states - Extended version
论文作者
论文摘要
概率理论可以合成研究，因为交换单元体现的计算效应。在最近提出的马尔可夫类别中，一个人使用Kleisli类别的抽象作用，然后用复制和丢弃的方程来定义确定性的形态。 “纯”和“确定性”之间的差异使我们研究了概率单元的“清醒”对象，这两个概念是重合的。我们在概率单上提出了自然条件，该条件使我们能够识别清醒的对象并定义一个愿意的sobrification函数。我们的框架适用于许多感兴趣的示例，包括可衡量的空间上的Giry Monad，并允许我们锐化先前给定的De Finetti定理的Markov类别。 这是2022年计算机科学逻辑（LICS）会议的逻辑接受的论文的扩展版。在本文档中，我们包括更多的数学细节，包括所有证明，关于已发布版本中给出的陈述和构造。
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. This is an extended version of the paper accepted for the Logic In Computer Science (LICS) conference 2022. In this document we include more mathematical details, including all the proofs, of the statements and constructions given in the published version.
