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：本文从数学角度对康威定律进行了修订。通过引入任务图，我们首先基于图论中的同态关系，严格阐述了软件系统与其创造组织之间的康威定律。尽管康威本人未提及，但任务图揭示了任务的几何结构，这一结构起着至关重要的作用。此外，针对当前组织中对通信的高层级处理需求（源于安全性、知识隐藏等因素）以及组织的层级化处理需求，我们利用弱化同态和图形拓扑中的连续映射重新表述了这些命题。为在康威定律中应用图形拓扑与连续映射，我们将其作为数学工具进行了准备，并展示了层级结构下康威对应关系的自然表达。