Adjoints and Emergence

Since its formal definition over sixty years ago, category theory has been increasingly recognized as having a foundational role in mathematics. It provides the conceptual lens to isolate and characterize the structures with importance and universality in mathematics. The notion of an adjunction (a pair of adjoint functors) has moved to center-stage as the principal lens to focus on what is important in mathematics. The central feature of an adjunction is what might be called “determination through universals” based on universal mapping properties. Given the importance of adjoint funtors in mathematics, it seems appropriate to look for empirical applications. The focus here is on applications in the life sciences (e.g., selectionist mechanisms) and human sciences (e.g., the generative grammar view of language). [Reprint from: Axiomathes, March 2007]

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