Categorical Analysis of Economic Value Creation

advisor: Ing. Rudolf Kulhavý, DrSc.
e-mail: show e-mail
type: phd thesis
branch of study: MI_MM, MI_AMSM, MINF
key words: applied category theory, economic system dynamics, economic decision analysis
link: http://www.utia.cas.cz/people/kulhavy
description: The project aims at building a stronger foundation for model-based analysis of strategic management decisions by means of categorical analysis of the underlying economic system in question (e.g., a firm with its key customer segments and main suppliers, and possibly major competitors). The compositional structure and corresponding behavior of economic systems can be rather naturally represented within a monoidal category of economic resources and resource-transforming processes. But, as yet, details of a mapping between the concepts and methods of higher-order category theory and of the economic domain are not well understood and call for exploratory research. Category theory is expected to play a dual role here—serving as a target language in problem representation and as a source of ready-made tools (i.e., generic concepts and properties) in subsequent problem analysis. The topic is appropriate for a student attracted to cross-disciplinary research and prepared to tackle simultaneously the mathematical abstraction of category theory and the domain specifics of economic analysis. The reward of the study could be either starting a research career in the emerging field of Applied Category Theory or developing deep insight into economic process modeling to benefit from in a consulting profession.
references: References on basic and higher-order CT as well as microeconomic theory will be adjusted to the PhD student’s background and preferences. [1] Adámek, J., Herrlich, H., & Strecker, G. E. (2009). Abstract and Concrete Categories: The Joy of Cats. Dover. [2] Awodey, S. (2010). Category Theory (2nd ed.). Oxford University Press. [3] Coecke, B. (Ed.). (2011). New Structures for Physics. Springer. [4] Coecke, B., Fritz, T., & Spekkens, R. W. (2016). A Mathematical Theory of Resources. Information and Computation, 250, 59–86. [5] Fong, B., & Spivak, D. I. (2019). An Invitation to Applied Category Theory: Seven Sketches in Compositionality. Cambridge University Press. [6] Gravelle, H., & Rees, R. (2004). Microeconomics (3rd ed.). Financial Times/Prentice Hall. [7] Leinster, T. (2004). Higher Operads, Higher Categories. Cambridge University Press. [8] Mas-Colell, A., Whinston, M. D., & Green, J. R. (1995). Microeconomic Theory. Oxford University Press. [9] Riehl, E. (2016). Category Theory in Context. Dover.
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