论文标题
重写结构化的Cospan
Rewriting Structured Cospans
论文作者
论文摘要
为了支持组成网络的研究，我们进一步发展了结构化cospans的形式主义。为了启用重写，我们介绍了一个类别，其对象是结构化的cospan，并表征了该类别是拓扑或粘合剂的条件。然后，我们使用2类别框架来定义结构化的Cospan语法和语言。作为一种应用，我们证明，对于各种图形，超图和培养皿网，任何语法都会引起与相应的离散语法相同的语言。这个结果使我们能够将重写的归纳观点扩展到这些结构。
To support the study of compositional networks, we further develop the formalism of structured cospans. To enable rewriting, we introduce a category whose objects are structured cospans and characterize conditions under which this category is a topos or is adhesive. We then define a structured cospan grammar and language, using a 2-category framework. As an application, we demonstrate that for various sorts of graphs, hypergraphs, and Petri nets, any grammar induces the same language as its corresponding discrete grammar. This result allows us to extend the inductive perspective of rewriting to these structures.
