supercategory of variable molecular sets
Definition 0.1.
A supercategory of variable molecular sets (or molecular set variables), ${\mathrm{\S}}_{msv}$ 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.
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.
Title | supercategory of variable molecular sets |
Canonical name | SupercategoryOfVariableMolecularSets |
Date of creation | 2013-03-22 18:30:08 |
Last modified on | 2013-03-22 18:30:08 |
Owner | bci1 (20947) |
Last modified by | bci1 (20947) |
Numerical id | 5 |
Author | bci1 (20947) |
Entry type | Definition |
Classification | msc 81-00 |
Classification | msc 92B05 |
Classification | msc 18-00 |
Synonym | supercategory of molecular set variables |
Synonym | $msv$-supercategory |
Related topic | CategoryOfMolecularSets |
Related topic | ETAS |
Related topic | MolecularSetVariable |
Related topic | MolecularSetTheory |
Related topic | SupercategoriesOfComplexSystems |
Related topic | ComplexSystemsBiology |
Related topic | AbstractRelationalBiology |
Defines | $msv$-supercategory |
Defines | classes of molecular set variables and their chemical transformations with time |