A Proposed Categorical Systems Theory: Mathematical Foundations for Engineering Complex Systems

Abstract

Engineering activity, especially when dealing with complex systems, is characterized by a large set of approaches such as frameworks, theories, methods, methodologies, and tools focusing on specific aspects of systemic attributes such as performance, materials transfers, information flows, etc. Yet, these approaches exhibit inconsistent maturity and effectiveness, resulting in different usage of terms and their association with fundamental systems engineering concepts. Each approach brings a relative engineering point of view typically related to a subset of contexts, purposes, dynamics, and perspectives. This brings significant challenges in our practice when dealing with complex systems. A systems approach has served us well in its different incarnations: complexity science, general systems theory, and cybernetics. However, even these systems approaches have failed to meet two demands: one is found in practice with problems of pluralism and dynamism, and the other stems from theory, where we need to be precise about what we talk about. The solution lies in taking a mathematical theory of context and importing it into a general theory of systems: a categorical systems theory. This work is an initial investigation into a small set of reference mathematical structures found in category theory capable of enhancing our ability to capture pluralism and dynamism and convey with precision our approaches to dealing with complex systems. A simple example is used to depict static and dynamic configurations, perspectives, and precision.