Various categories have been proposed as targets for the denotational semantics of higher-order probabilistic programming languages. One such proposal involves joint probability distributions (couplings) used in Bayesian statistical models with conditioning. In previous treatments, composition of joint measures was performed by disintegrating to obtain Markov kernels, composing the kernels, then reintegrating to obtain a joint measure. Disintegrations exist only under certain restrictions on the underlying spaces. In this paper we propose a category whose morphisms are joint finite measures in which composition is defined without reference to disintegration, allowing its application to a broader class of spaces. The category is symmetric monoidal with a pleasing symmetry in which the dagger structure is a simple transpose.

翻译：各种范畴已被提出作为高阶概率编程语言指称语义的目标。其中一种方案涉及贝叶斯统计模型中用于条件推断的联合概率分布（耦合）。在以往的处理中，联合测度的复合通过分解获得马尔可夫核、对核进行复合、再重新积分获得联合测度。然而，分解操作仅在对底层空间施加特定约束时才存在。本文提出一种以联合有限测度为态射的范畴，其中复合定义无需依赖分解操作，从而使其能够应用于更广泛的空间类型。该范畴具有对称幺半结构，并呈现优美的对称性，其dagger结构表现为简单的转置运算。