因果范畴：相对论相互作用过程
Causal categories: relativistically interacting processes
摘要：
一个对称么半群范畴自然地作为数学结构出现，它组织物理系统、过程及其组合，既顺序地又并行地。这种结构允许纯图形演算。本文研究了对称monoidal范畴中固定因果结构的编码：因果依赖对应于图形语言中的拓扑连通性。我们表明，相关性，无论是经典的或量子的，力的张量单位的终端。我们还表明，良好的定义的概念，一个全球性的国家部队的monoidal产品只有部分定义，这反过来又导致在一个相对论协方差定理。除了这些假设之外，我们在任何阶段都不会假设任何超过纯粹的成分的类元-幺半群范畴结构的东西。我们把这两个结构性结果用一个数学实体来表示，我们称之为“因果范畴”。我们提供了构建因果范畴的方法，并研究了这些方法对范畴量子力学一般框架的影响。
英文摘要：
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This paper is concerned with the encoding of a fixed causal structure within a symmetric monoidal category: causal dependencies will correspond to topological connectedness in the graphical language. We show that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of the concept of a global state forces the monoidal product to be only partially defined, which in turn results in a relativistic covariance theorem. Except for these assumptions, at no stage do we assume anything more than purely compositional symmetric-monoidal categorical structure. We cast these two structural results in terms of a mathematical entity, which we call a `causal category'. We provide methods of constructing causal categories, and we study the consequences of these methods for the general framework of categorical quantum mechanics.
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。
