Hi, 1.You may want to look at the writings of Robert Rosen (a Google search will provide the necessary links). 2. For a different direction, and on a far more modest note, you may try looking at some of my papers on my web page: http://www.actcom.co.il/typographics/zippie Of course I will be very intrested to hear your comments about that. Good luck, Zippie -- ____________________________________________ Zippora Arzi-Gonczarowski, Ph.D. Aka:Zippie Typographics, Ltd. 46 Hehalutz St. Jerusalem 96222, ISRAEL zippie@actcom.co.il http://www.actcom.co.il/typographics/zippie Tel: +972-2-6437819 Fax: +972-2-6434252 _____________________________________________

A new "heteromorphic" treatment of adjoint functors provides applications to biology such as an abstract characterization of selectionist (as opposed to instructionist) mechanisms as in Darwin's evolutionary theory, the selectionist theory of the immune system, and neural darwinism (e.g., Edelman's and Changeux's work). Heteromorphisms, e.g., the injection of a set of generators into the free group on the set, can be formally treated in category theory using bifunctors Het:X^op x A--> Set analogous to the usual Hom:X^op x X-->Set. When the heteromorphisms from objects in a category X to objects in a category A can represented in each of the categories, then the functors giving the representing objects are a pair of adjoint functors and the representations give a pair of natural isomorphisms: Hom_A(Fx,a) = Het(x,a) = Hom-_X(x,Ga). The usual treatment of adjoints leaves out the middle term. And all adjoint functors can be shown to arise in this manner (up to isomorphism). The applications were not available in the usual treatment of adjoints where the heteromorphisms were not explicit. The applications are outlined in a paper just published in Axiomathes (2007) 17: 19-39. A reprint can be retreived from my website: http://www.ellerman.org/Davids-Stuff/Maths/Adjoints-Axiomathes-Reprint.pdf . A rather long (and impenetrable) treatment of the math was in the recent "What is Category Theory" collection of papers (2006: Polimetrica). A short straightforward treatment of the math is available on the ArXiv: http://arxiv.org/abs/0704.2207v1 . Other applications of category theory to biology have been made by Robert Rosen (as mentioned by several posts) and by Andree Ehresmann. Best, David __________________ David Ellerman Visiting Scholar University of California at Riverside Email: david@ellerman.org Webpage: www.ellerman.org View my research on my SSRN Author page: <http://ssrn.com/author=294049> http://ssrn.com/author=294049

Regarding Deniz Kural's question about references to papers on category theory and biology, Tom Caudell and I have been investigating a semantic theory for neural networks both biological and artificial, cognitive and non-cognitive. We are designing and conducting experiments to test and refine the theory in both neuroscience and cognitive psychology working with colleagues in those disciplines. An initial paper on the theory is M. J. Healy and T. P. Caudell (2006) Ontologies and Worlds in Category Theory: Implications for Neural Systems, Axiomathes, vol. 16, nos. 1-2, pp. 165-214. The only experiment appearing in a publication to date is one on an artificial neural network application, presented at IJCNN 2005 in Montreal (the results were presented also at CT06). Regards, Mike Healy