Ellerman, David (2015) On Adjoint and Brain Functors (preprint from Axiomathes). [Preprint]

PDF (Preprint from Axiomathes) AdjointsAndBrainFunctors-rev2.pdf - Accepted Version Download (579kB)

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

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Item Type:	Preprint
Creators:	Creators Email ORCID Ellerman, David david@ellerman.org
Keywords:	adjoint functors, brain functors, heteromorphisms, category theory
Subjects:	Specific Sciences > Cognitive Science Specific Sciences > Mathematics
Depositing User:	David Ellerman
Date Deposited:	18 Aug 2015 19:13
Last Modified:	18 Aug 2015 19:13
Item ID:	11618
Official URL:	http://link.springer.com/journal/10516/onlineFirst...
DOI or Unique Handle:	http://link.springer.com/article/10.1007/s10516-015-9278-7
Subjects:	Specific Sciences > Cognitive Science Specific Sciences > Mathematics
Date:	2015
URI:	https://philsci-archive.pitt.edu/id/eprint/11618

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