Abstract
It is shown that the class of abstract block diagrams of (M, ℜ)-systems which can be constructed out of the objects and mappings of a particular subcategoryG 0 of the categoryG of all sets depends heavily on the structure ofG 0, and in particular on the number of sets of mappingsH(A, B) which are empty inG 0. In the context ofG 0-systems, there-fore, each particular categoryG 0 gives rise to a different “abstract biology” in the sense of Rashevsky. A number of theorems illustrating the relation between the structure of a categoryG 0 and the embeddability of an arbitrary mapping αεG 0 into an (M, ℜ)-system are proved, and their biological implication is discussed.
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Literature
Rashevsky, N. 1955. “Some Remarks on Topological Biology”,Bull. Math. Biophysics,17, 207–218.
— 1956. “Contributions to Topological Biology: Some Considerations on the Primordial Graph and on Some Possible Transformations”.Bull. Math. Biophysics,18, 113–128.
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Rosen, R. 1958a. “A Relational Theory of Biological Systems”,Bull. Math. Biophysics,20, 245–260.
— 1959b. “The Representation of Biological Systems from the Standpoint the Theory of Categories”.-Ibid,,20, 317–341.
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This research was supported by the United States Air Force through the Air Force Office of Scientific Reserch of the Air Research and Development Command, under Contract No. AF 49(638)-917.
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Rosen, R. A note on abstract relational biologies. Bulletin of Mathematical Biophysics 24, 31–38 (1962). https://doi.org/10.1007/BF02477864
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DOI: https://doi.org/10.1007/BF02477864