On Adjoint and Brain Functors

17 Pages Posted: 20 Jun 2015

Multiple version iconThere are 2 versions of this paper

Date Written: June 18, 2015

Abstract

There is some consensus among orthodox category theorists that the concept of adjoint functors is the most important concept contributed to mathematics by category theory. We give a heterodox treatment of adjoints using heteromorphisms (object-to-object morphisms between objects of different categories) that parses an adjunction into two separate parts (left and right representations of heteromorphisms). Then these separate parts can be recombined in a new way to define a cognate concept, the brain functor, to abstractly model the functions of perception and action of a brain. The treatment uses the simplest possible mathematics and is focused on the interpretation and application of the mathematical concepts.

Keywords: adjoint functors, brain functors, mathematical cognitive science

Suggested Citation

Ellerman, David, On Adjoint and Brain Functors (June 18, 2015). Available at SSRN: https://ssrn.com/abstract=2620332 or http://dx.doi.org/10.2139/ssrn.2620332

David Ellerman (Contact Author)

University of Ljubljana ( email )

School of Social Science
Ljubljana, CA
Slovenia

HOME PAGE: http://www.ellerman.org

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