Category Theory and Universal Models: Adjoints and Brain Functors
27 Pages Posted: 26 Mar 2009 Last revised: 17 May 2009
Date Written: March 26, 2009
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. The central feature of an adjunction is what might be called "internalization through a universal" based on universal mapping properties. A recently developed "heteromorphic" theory of adjoint functors allows the concepts to be more easily applied empirically. This suggests a conceptual structure, albeit abstract, to model a range of universal-selectionist mechanisms (e.g., in the immune system). Closely related to adjoints is the notion of a "brain functor" which abstractly models structures of cognition and action.
Keywords: adjoint functors, universal models, selectionist mechanisms, category theory
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