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

Conway's law, revised from a mathematical viewpoint