s-有限转移核与概率相干空间中的线性指数共幺半群
A Linear Exponential Comonad in s-finite Transition Kernels and Probabilistic Coherent Spaces
AI总结：
本文利用测度论中的线性指数共幺半群与测度-可测函数连续正交性，在s-有限转移核对称幺半范畴上构造线性指数共幺半群，通过双粘合实现概率相干空间的随机构造，并在可数可测空间下得到匕首紧闭范畴。
摘要：
本文研究概率相干空间的随机构造，采用了两类新要素：（i）测度论中自然产生的线性指数共幺半群；（ii）测度与可测函数之间的连续正交性。我们在转移核的对称幺半范畴上构造了一个线性指数共幺半群，将Panangaden随机关系中的马尔可夫核放宽为s-有限核。该模型支持基于测度与可测函数之间积分的正交性，可视为Girard-Danos-Ehrhard的概率相干空间线性对偶的连续扩展。该正交性通过Hyland-Schalk双粘合构造表述，我们的测度论幺半共幺半群结构可适配其中。作为在可数可测空间上的应用，本文得到了一个匕首紧闭范畴，其双粘合构造产生了我们熟知的概率相干空间范畴。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
