, Volume 26, Issue 1, pp 41–61 | Cite as

On Adjoint and Brain Functors

  • David EllermanEmail author
Original Paper


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 .


Category theory Adjoint functors Heteromorphism  Brain functors 

Mathematics Subject Classification

18 92 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Philosophy DepartmentUniversity of California at RiversideRiversideUSA

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