On Adjoint and Brain Functors
17 Pages Posted: 20 Jun 2015
Date Written: June 18, 2015
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
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