In this article, we revise Conway's Law from a mathematical point of view. By introducing a task graph, we first rigorously state Conway's Law based on the homomorphisms in graph theory for the software system and the organizations that created it. Though Conway did not mention it, the task graph shows the geometric structure of tasks, which plays a crucial role. Furthermore, due to recent requirements for high-level treatment of communication (due to security, knowledge hiding, etc.) in organizations and hierarchical treatment of organizations, we have reformulated these statements in terms of weakened homomorphisms, and the continuous maps in graph topology. In order to use graph topology and the continuous map in Conway's law, we have prepared them as mathematical tools, and then we show the natural expression of Conway's correspondences with hierarchical structures.

翻译：本文从数学角度修正康威定律。通过引入任务图，我们首先基于图论中的同态关系，严格表述了软件系统及其创建组织之间的康威定律。尽管康威并未提及，但任务图揭示了任务的几何结构，这一结构起着关键作用。此外，针对近年来组织中的通信需求（如安全性、知识隐藏等）需要高级别处理，以及组织的层级化处理需求，我们利用弱化同态和图拓扑中的连续映射重新表述了这些关系。为将图拓扑与连续映射应用于康威定律，我们首先将其作为数学工具进行了预备，进而展示了康威对应关系在层级结构中的自然表达。