Definition 0.1. A supercategory of variable molecular sets (or molecular set variables), §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, ηt, 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.
References
[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 Łukasiewicz–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.
