Categorical formulation of mathematical design theories applied to system design process analysis

Abstract

Abstract Given hierarchical system specifications, embodiment and integration processes of subsystems are crucial in designing complex engineered systems. To complement the current mathematical design theories that do not sufficiently support these processes, this study applies general design theory to formulate these processes based on the mathematical structure of design knowledge studied in the literature using category theory. Specifically, the composition of embodiment operations and the relations among subsystems in integration operations on the category of sets and topological spaces are elucidated. Furthermore, the formulation is applied to analysis of a system design process of a production line in model-based systems engineering.