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supercategory of variable molecular sets (Definition)
Definition 0.1   A supercategory of variable molecular sets (or molecular set variables), $\S_{msv}$ is defined as the supercategory whose class of objects is the class of all possible variable molecular sets, $msv$ 's, (or molecular set variables), and whose class of morphisms is the class of all molecular transformations, $\eta_t$ , of $msv$ 's.

Remark All such $msv$ -supercategories are semantic interpretations of the ETAS axioms (syntax). This is a mathematical representation of chemical reaction systems in terms of molecular sets that vary with time (or $msv$ 's, and their transformations as a result of diffusion, collisions, and chemical reactions.

Bibliography

1
Bartholomay, A. F.: 1960. Molecular Set Theory. A mathematical representation for chemical reaction mechanisms. Bull. Math. Biophys., 22: 285-307.
2
Bartholomay, A. F.: 1965. Molecular Set Theory: II. An aspect of biomathematical theory of sets., Bull. Math. Biophys. 27: 235-251.
3
Bartholomay, A.: 1971. Molecular Set Theory: III. The Wide-Sense Kinetics of Molecular Sets ., Bulletin of Mathematical Biophysics, 33: 355-372.
4
Baianu, I. C.: 1983, Natural Transformation Models in Molecular Biology., in Proceedings of the SIAM Natl. Meet., Denver, CO.; Eprint No. 3675 at cogprints.org/3675/01 as ``Naturaltransfmolbionu6.pdf''.
5
I.C. Baianu: 1970, Organismic Supercategories: II. On Multistable Systems. Bulletin of Mathematical Biophysics, 32: 539-561.
6
I.C. Baianu, Brown R., J. F. Glazebrook, and Georgescu G.: 2006, Complex Nonlinear Biodynamics in Categories, Higher Dimensional Algebra and \Lukasiewicz-Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic networks, Axiomathes 16 Nos. 1-2, 65-122.
7
I.C. Baianu: 1980, Natural Transformations of Organismic Structures. Bulletin of Mathematical Biophysics 42: 431-446.
8
I.C. Baianu: 1984, A Molecular-Set-Variable Model of Structural and Regulatory Activities in Metabolic and Genetic Networks., FASEB Proceedings 43, 917.




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See Also: category of molecular sets, ETAS interpretation, molecular set and molecular class variables, molecular set theory, categories and supercategories in relational biology, complex systems biology, abstract relational biology

Other names:  supercategory of molecular set variables, $msv$-supercategory
Also defines:  classes of molecular set variables and their chemical transformations with time
Keywords:  categories of molecular sets, supercategories of molecular set variables and chemical trnasformations, Molecular Set Variable, Molecular Sets, Molecular Set Theory, Supercategories of Complex Systems, Complex Systems Biology, Categorical Ontology at the Molecular Level, Abstract Relational Biology
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Cross-references: transformations, molecular sets, terms, mathematical representation, syntax, ETAS axioms, interpretations, semantic, molecular transformations, morphisms, variable molecular sets, objects, class, supercategory, molecular set variables

This is version 1 of supercategory of variable molecular sets, born on 2008-10-18.
Object id is 11186, canonical name is SupercategoryOfVariableMolecularSets.
Accessed 1072 times total.

Classification:
AMS MSC18-00 (Category theory; homological algebra :: General reference works )
 92B05 (Biology and other natural sciences :: Mathematical biology in general :: General biology and biomathematics)
 81-00 (Quantum theory :: General reference works )

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