重写结构余弦
Rewriting Structured Cospans
AI总结：
本文提出结构余弦重写理论，通过2-范畴框架定义语法并构建语言，证明各类网络模型的语法与离散语法等价，扩展了图变换的经典结果。
摘要：
我们发展了结构余弦的重写理论，以扩展开放网络的组合方法。首先，我们引入一个对象为结构余弦的范畴，并建立其粘合或拓扑的条件。这些结果保证了双推送重写可以在该设定中应用。然后我们定义结构余弦语法，并通过2-范畴框架构建其关联语言，捕捉网络组合和重写动态。作为应用，我们证明对于图、超图、Petri网及其类型变体，任何语法诱导的语言与对应的离散语法相同。这种等价性使重写能够进行归纳性刻画，从而将经典图变换结果推广到更广泛的范畴模型中。
英文摘要：
We develop a theory of rewriting for structured cospans in order to extend compositional methods for modeling open networks. First, we introduce a category whose objects are structured cospans, and establish conditions under which it is adhesive or a topos. These results guarantee that double pushout rewriting can be applied in this setting. We then define structured cospan grammars and construct their associated languages via a 2-categorical framework, capturing both network composition and rewrite dynamics. As an application, we show that for graphs, hypergraphs, Petri nets, and their typed variants, any grammar induces the same language as its corresponding discrete grammar. This equivalence enables an inductive characterization of rewriting, thereby generalizing classical results from graph transformation to a broader class of categorical models.
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。
