Informatics and Applications
2023, Volume 17, Issue 2, pp 11-17
THE MONAD OF DIAGRAMS AS A MATHEMATICAL METAMODEL OF SYSTEMS ENGINEERING
Abstract
The paper addresses issues associated with the development of advanced mathematical methods for systems engineering suitable as the basis of computer tools for automatic synthesis and analysis of systems and processes. Following recent trends, category theory is employed as the framework for the methods. Its application is based on representing the structure of systems, processes, requirements, and other system design results as diagrams in categories whose objects are the algebraic models of parts and morphisms describe relationships between parts. Applying the fundamental Grothendieck flattening construction, the following constructions are described explicitly: categories of diagrams, the monad of diagrams, and the monad and the comonad of pointed diagrams. Application areas of these constructions in systems engineering procedures are identified. An approach is proposed to implement highly automated technologies of the generative design kind for complex multilevel systems.
[+] References (16)
- Levenchuk, A.I. 2015. Sistemnoinzhenernoe myshlenie [Systems engineering thinking]. Moscow: TechInvestLab. 305 p.
- Mabrok, M. A., and M. J. Ryan. 2017. Category theory as a formal mathematical foundation for model-based systems engineering. Appl. Math. Inform. Sci. 11(1):43-51. doi: 10.18576/amis/110106.
- Breiner, S., E. Subrahmanian, and A. Jones. 2018. Categorical foundations for system engineering. Disciplinary convergence in systems engineering research. Eds. A. Madni, B. Boehm, R. Ghanem, D. Erwin, and D. Wheaton. Springer. 449-463. doi: 10.1007/978-3-319-62217-0_32.
- Watson, M. D. 2019. Future of systems engineering. IN- COSEINSIGHT 22(1):8-12. doi: 10.1002/inst.12231.
- Kovalyov, S. P. 2017. Metody teorii kategoriy v model'no- orientirovannoy sistemnoy inzhenerii [Methods of category theory in model-based systems engineering]. Informatika i ee Primeneniya - Inform. Appl. 11(3):42-50. doi: 10.14357/1992226417030.
- Guitart, R., and L. van den Bril. 1977. Decompositions et lax-completions. Cahiers TopologieGeometrie Differentielle Categoriques 18(4):333-407.
- Kovalyov, S. P. 2018. Teoriya kategoriy kak matematicheskaya pragmatika model'no-orientirovannoy sistemnoy inzhenerii [Category theory as a mathematical pragmatics of model-based systems engineering]. Informatika i ee Primeneniya - Inform. Appl. 12(1):95-104. doi: 10.14357/19922264180112.
- Mac Lane, S. 1978. Categories for the working mathematician. New York, NY: Springer. 317 p.
- nLab. 2020. Grothendieck construction. Available at: https://ncatlab.org/nlab/show/Grothendieck+ construction/ (accessed May 29, 2023).
- Barr, M., and C. Wells. 1990. Category theory for computing science. London: Prentice Hall. 538 p.
- Kovalyov, S. P. 2019. Algebraicheskie metody porozhdayushchego proektirovaniya krupnomasshtabnykh tekhnicheskikh sistem [Algebraic methods of generative design of large-scale technical systems]. 12th Conference (International) "Management of Large-Scale System Development" Proceedings. Moscow: IPU RAN. 384-386.
- Kowalski, J. 2015. CAD is a lie: Generative design to the rescue. San Rafael, CA: Autodesk. Available at: https://www.themanufacturer.com/articles/cad-is- a-lie-generative-design-to-the-rescue/ (accessed May 29, 2023).
- nLab. 2019. Comma category. Available at: https:// ncatlab.org/nlab/show/comma+category/ (accessed May29, 2023).
- Hitchins, D. 2009. What are the general principles applicable to systems? Incose Insight 12(4):59-64. doi: 10.1002/ INST.200912459.
- Iovane, G., E. Laserra, and F. S. Tortoriello. 2004. Stochastic self-similar and fractal universe. Chaos Soliton. Fract. 20(3):415-426. doi: 10.1016/j.chaos.2003.08.004.
- Larijani, H. 2011. Local area networks and self-similar traffic. Network performance engineering. Ed. D. D. Kou- vatsos. Lecture notes in computer science ser. Springer. 5233:174-190. doi: 10.1007/978-3-642-02742-0_8.
[+] About this article
Title
THE MONAD OF DIAGRAMS AS A MATHEMATICAL METAMODEL OF SYSTEMS ENGINEERING
Journal
Informatics and Applications
2023, Volume 17, Issue 2, pp 11-17
Cover Date
2023-07-10
DOI
10.14357/19922264230202
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
category theory; monad of diagrams; Grothendieck construction; colimit; systems engineering; system of systems; generative design
Authors
S. P. Kovalyov 
Author Affiliations
V. A. Trapeznikov Institute of Control Sciences ofthe Russian Academy of Sciences, 65 Profsoyuznaya Str., Moscow 117997, Russian Federation
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