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The representation of biological systems from the standpoint of the theory of categories

Abstract

A mathematical framework for a rigorous theory of general systems is constructed, using the notions of the theory of Categories and Functors introduced by Eilenberg and MacLane (1945,Trans. Am. Math. Soc.,58, 231–94). A short discussion of the basic ideas is given, and their possible application to the theory of biological systems is discussed. On the basis of these considerations, a number of results are proved, including the possibility of selecting a unique representative (a “canonical form”) from a family of mathematical objects, all of which represent the same system. As an example, the representation of the neural net and the finite automaton is constructed in terms of our general theory.

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Rosen, R. The representation of biological systems from the standpoint of the theory of categories. Bulletin of Mathematical Biophysics 20, 317–341 (1958). https://doi.org/10.1007/BF02477890

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  • DOI: https://doi.org/10.1007/BF02477890

Keywords

  • Biological System
  • Block Diagram
  • Covariant Functor
  • Oriented Graph
  • Oriented Edge