On Adjoint and Brain Functors

Axiomathes (preprint), Forthcoming

19 Pages Posted: 19 Aug 2015

Multiple version iconThere are 2 versions of this paper

Date Written: July 17, 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 relatively simple category theory and is focused on the interpretation and application of the mathematical concepts. The Mathematical Appendix is of general interest to category theorists as it is a defense of the use of heteromorphisms as a natural and necessary part of category theory.

Keywords: cognitive science, category theory, perception, action, heteromorphisms

Suggested Citation

Ellerman, David, On Adjoint and Brain Functors (July 17, 2015). Axiomathes (preprint), Forthcoming, Available at SSRN: https://ssrn.com/abstract=2645837

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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