Abstract

http://ssrn.com/abstract=1368856
 


 



Category Theory and Universal Models: Adjoints and Brain Functors


David Ellerman


University of California at Riverside, Philosophy Department

March 26, 2009


Abstract:     
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.

Number of Pages in PDF File: 27

Keywords: adjoint functors, universal models, selectionist mechanisms, category theory

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Date posted: March 26, 2009 ; Last revised: May 17, 2009

Suggested Citation

Ellerman, David, Category Theory and Universal Models: Adjoints and Brain Functors (March 26, 2009). Available at SSRN: http://ssrn.com/abstract=1368856 or http://dx.doi.org/10.2139/ssrn.1368856

Contact Information

David Ellerman (Contact Author)
University of California at Riverside, Philosophy Department ( email )
United States
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