This paper concerns a stochastic construction of probabilistic coherent spaces by employing novel ingredients (i) linear exponential comonads arising properly in the measure-theory (ii) continuous orthogonality between measures and measurable functions. A linear exponential comonad is constructed over a symmetric monoidal category of transition kernels, relaxing Markov kernels of Panangaden's stochastic relations into s-finite kernels. The model supports an orthogonality in terms of an integral between measures and measurable functions, which can be seen as a continuous extension of Girard-Danos-Ehrhard's linear duality for probabilistic coherent spaces. The orthogonality is formulated by a Hyland-Schalk double glueing construction, into which our measure theoretic monoidal comonad structure is accommodated. As an application to countable measurable spaces, a dagger compact closed category is obtained, whose double glueing gives rise to the familiar category of probabilistic coherent spaces.
翻译:----
s-有限转移核和概率相干空间中的线性指数余单子函子
The translated abstract:
本文关注采用新的构建方式 (i) 量测理论中的线性指数余单子函子 (ii) 量度和可测函数之间的连续正交关系, 通过随机构建概率相干空间。 在转移核的对称蒙德类别中构造了一个线性指数余单子函子,将Panangaden随机关系的马尔可夫核放宽为s-有限核。 模型支持一种与量度和可测函数之间的积分之间的正交性,可以看作是Girard-Danos-Ehrhard概率相干空间的线性对偶的连续扩展。 正交性通过Hyland-Schalk双胶合结构加以阐述,其中我们的量度理论单子类别结构得以容纳。 在针对可数测量空间的应用中,获得了一种匕首紧凑闭合分类,其双胶合会产生熟悉的概率相干空间类别。