有向algebraic topology与高维过渡系统
Directed algebraic topology and higher dimensional transition system
摘要：
Cattani-Sassone的高维转移系统概念被解释为弱高维转移系统的局部可表示拓扑范畴的小正交类。特别地，与标号n-立方体相关联的高维跃迁系统原来是由一个n维跃迁生成的自由高维跃迁系统。作为这个构造的第一个应用，证明了高维转移系统范畴的局部化等价于标号对称预立方集范畴的局部可表示的反射满子范畴.第二个应用程序是米尔纳的演算的通信系统（CCS）：映射采取进程名称在CCS流是因式分解通过类别的高维过渡系统。该方法也适用于其他进程代数和拓扑模型的并发流以外。
英文摘要：
Cattani-Sassone's notion of higher dimensional transition system is interpreted as a small-orthogonality class of a locally finitely presentable topological category of weak higher dimensional transition systems. In particular, the higher dimensional transition system associated with the labelled n-cube turns out to be the free higher dimensional transition system generated by one n-dimensional transition. As a first application of this construction, it is proved that a localization of the category of higher dimensional transition systems is equivalent to a locally finitely presentable reflective full subcategory of the category of labelled symmetric precubical sets. A second application is to Milner's calculus of communicating systems (CCS): the mapping taking process names in CCS to flows is factorized through the category of higher dimensional transition systems. The method also applies to other process algebras and to topological models of concurrency other than flows.
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