creators_name: Baianu, I.C. creators_id: icb editors_name: Rashevsky, Nicolas type: journalp datestamp: 2011-12-16 00:58:58 lastmod: 2011-12-16 00:58:58 metadata_visibility: show title: Organismic Supercategores: II. On Multistable Systems ispublished: pub subjects: bio-evo subjects: bio-theory subjects: comp-neuro-sci subjects: comp-sci-art-intel subjects: comp-sci-complex-theory subjects: comp-sci-mach-dynam-sys subjects: comp-sci-stat-model subjects: neuro-chem subjects: neuro-mod full_text_status: public keywords: Supercategories and Functors, Homology Theory, Quantum Genetics, Relational Oscillations, Organismic Supercategories, Complex Bio-Systems, Observables Generating Diagram, Relational Biology, Multistability of Organisms note: Supercategories are defined currently as n-categories or higher dimensional algebra, Axiomatic definitions of Categories and Supercategories of Relational, Complex Biological Systems, DOI: 10.1007/BF02476770 abstract: The representation of biological systems in terms of organismic supercategories, introduced in previous papers by Baianu et al. (Bull. Math. Biophysics,30, 625–636;31, 59–70) is further discussed. To state more clearly this representation some new definitions are introduced. Also, some necessary changes in axiomatics are made. The conclusion is reached that any organismic supercategory has at least one superpushout, and this expresses the fact that biological systems are multistable. This way a connection between some results of Rashevsky’s theory of organismic sets and our results becomes obvious. date: 1970-11-21 date_type: published publication: The Bulletin of Mathematical Biophysics volume: 32 number: 4 publisher: Elsevier Publs. Co. and Springer reprints, DOI: 10.1007/BF02476770 pagerange: 539-561 refereed: TRUE referencetext: Ashby, W.R. 1960. Design for a brain, 2nd ed., New York: J. Wiley & Sons, Inc. ~ . 1956. An Introduction to Cybernetics, New York: J. Wiley & Sons, Inc. Baianu, I. and M. Marinescu. 1968. "Organismic Supercategories: I. Proposals for a General Unitary Theory of Systems." Bull. Math. Biophysics, 80, 625-636. Bourbaki, N. 1958. J~lements de Mathdmatique, Paris: Hermann & C le, ]~diteurs. Comoro~an, S. and I. Baianu. 1969. "Abstract Representations of Biological Systems in Supercategories." Bull. Math. Biophysics, 31, 59-71. Ehresmann, Ch. 1966. "Trends Toward Unity in Mathematics." Cahiers de topologle et geometric differentielle, 8, 1-7. Eilenberg, S. and S. MaeLane. 1945. "General Theory of Natural Equivalences." Trans. Am. Math. Soc., 58, 231-294. and J. Wright. 1967. "Automata in General Algebras." Seventy-Second Meeting American Math. Soc., 1-17. Georgeseu, G. and D. Popeseu. 1968. "On Algebraic Categories." l~ev. Roum. Math. Purcs et AppL, 13, 337-342. Lawvere, F.W. 1963. "Functional Semantics of Algebraic Theories." Proc. Nat. Acad. Sci., 5O, 869-872. ~-. 1966. "The Category of Categories as a Foundation for Mathematics." In the Proc. Conf. Categorical Algebra-LaJoUa 1965, Eilenberg, S., et al. eds., Berlin, Heidelberg and l~ew York: Springer-Verlag, pp. 1-20. 1969. "Closed Cartesian Categories." (Lecture held as a guest of the Romanian Academy of Sciences, Bucharest.) LSfgren, L. 1968. "An Axiomatic Explanation of Complete Serf-Reproduction." Bull. Math. Biophysics, 30, 317-348. Mitchell, B. 1965. The Theory of Categories. New York and London: Academic Press. Rashevsky, 1~. 1954. "Topology and Life: In Search of General Mathematical Principles i n Biology and Sociology." Bull. Math. Biophysics, 16, 317-348. citation: Baianu, Prof. Dr. I.C. (1970) Organismic Supercategores: II. On Multistable Systems. [Journal (Paginated)] document_url: http://cogprints.org/7752/3/OSIImultist1970.pdf