论文标题
分类概率的扩张和信息流公理
Dilations and information flow axioms in categorical probability
论文作者
论文摘要
我们研究马尔可夫类别的阳性和因果关系公理，作为马尔可夫类别中的扩张和信息流的特性，以及在其任意半明确单型类别中的变化。这些有助于我们表明，成为马尔可夫类别只是对称单体类别的附加属性（而不是额外的结构）。我们还表征了代表马尔可夫类别的积极性，并证明因果关系意味着积极性，但不相反。最后，我们注意到准孔空间的积极性失败，并将这种失败解释为概率名称生成的隐私属性。
We study the positivity and causality axioms for Markov categories as properties of dilations and information flow in Markov categories, and in variations thereof for arbitrary semicartesian monoidal categories. These help us show that being a positive Markov category is merely an additional property of a symmetric monoidal category (rather than extra structure). We also characterize the positivity of representable Markov categories and prove that causality implies positivity, but not conversely. Finally, we note that positivity fails for quasi-Borel spaces and interpret this failure as a privacy property of probabilistic name generation.
