Category Theory and Psychodynamics: Bridging the Structure of Programming with Human Behavior

Tanmay Mendhey

Abstract: This paper explores the intersection of category theory in functional programming and psychodynamic theory, offering a unique perspective on how categorical structures can be seen as metaphors for understanding human behavior. Through the lens of category theory, key concepts such as monads, inductive types, and optics are reframed as analogous to psychoanalytic structures like mental states, drives, and the therapeutic process. Drawing upon both mathematical abstraction and psychodynamic theory, the study highlights how algebraic structures in programming- such as functors and monads - can be interpreted as mechanisms for translating and transforming internal states within the human psyche. The application of directed type theory, parametricity, and homotopy type theory to software development is paralleled with psychodynamic techniques for understanding and transforming the unconscious mind. By connecting these seemingly disparate fields, the paper argues that the rigorous abstraction found in category theory can provide valuable insights into the organization and transformation of mental processes akin to the therapeutic practices of psychoanalysis.

Keywords: Category theory, Functional programming, Monads, Type theory, Parametricity, Abstraction