The risk factors of integration processes in enterprises in the light of the system paradigm and the categorical system theory

In recent years, the market has seen an increase in the number of integration transactions, and a structured approach to business combinations will help reduce the risk of this process. The purpose of this study is to propose a new mathematical toolkit of the category theory for describing the mechanism of enterprise unification, suitable for modeling integration processes of any type of systems according to the classification of systemic economic theory and allowing to identify risk factors of such processes. Using methods of category theory, systemic economic theory and operational risk management theory, three types of enterprise interfaces are described. Possible ways of modeling the mechanisms of enterprise integration, considered in this paper as socio-economic systems, are proposed for each of them. Risk factors for several levels of integration are identified when choosing a mechanism for combining through an internal interface with the allocation of subsystems of the enterprise: object, environmental, project and process. Anti-risk managerial actions are also proposed to mitigate the impact of identified risk factors on the activities of the combined enterprise. The appendices provide the basic terms and principles of the category theory, formalize the relationship between systemic economic theory and the category theory.

1. Alexandrov S.Y. (2015). The concept of formation of integrated corporate structures in industry based on the development of key business competencies. Bulletin of the St. Petersburg State Economic University, no. 3(93), pp. 79–83. (In Russ.)

2. Bulyga R.P., Melnik M.V. et al. (2023). A Model of ESG-Transparency Index in Corporate Reporting. MGIMO Review of International Relations, no. 16(3), pp. 56–80. DOI:10.24833/2071-8160-2023-3-90-56-80. (In Russ.)

3. Gisin V.B. (2025). Applied category theory. Moscow: Prometheus. 166 p. (In Russ.)

4. Izmalkova I.V., Vertakova Yu.V. (2022). Risk management of cluster structures: Theory and tools. Lipetsk: LLC Lipetsk-Plus Printing House. 210 p. (In Russ.)

5. Kachalov R.M. (2012). Economical risk management: Theory and applications. St. Petersburg: Nestor–Historia. 248 p. (In Russ.)

6. Kachalov R.M. (2020). Risk phenomenon as an artificial economic science object. Issues of Risk Analysis, no. 17(1), pp. 100–108. (In Russ.) DOI:10.32686/1812-5220-2020-17-1-100-108

7. Kachalov R.M., Sleptsova Y.A. (2015). Structuration of system and economic space of enterprise and risk management. Russian Management Journal, no. 13 (4), pp. 69–84. (In Russ.)

8. Kleiner G. (2013). System economics as a platform for development of modern economic theory. Voprosy Ekonomiki, no. (6), pp. 4–28. (In Russ.) DOI: 10.32609/0042-8736-2013-6-4-28

9. Kleiner G.B. (2022). Information theory of economic organizations management factors. Russian Management Journal, no. 20(4), pp. 461–481. (In Russ.) DOI:10.21638/spbu18.2022.401

10. Kleiner G.B. (2024). The systems paradigm and the theory of technology. Terra Economicus, no. 22(4), pp. 6–18. (In Russ.) DOI: 10.18522/2073-6606-2024-22-4-6-18

11. Kleiner G.B., Rybachuk M.A. (2017). System balance of the economy. Moscow: Publishing house “SCIENTIFIC LIBRARY”. 320 p. (In Russ.)

12. Lipuntsov Y. (2019). Data preparation for information exchange. Journal of Applied Informatics, no. 14, pp. 74–85. (In Russ.) DOI: 10.24411/1993-8314-2019-10037

13. Nesterov V.N., Bakirova K.R. (2020). Consolidated financial statements: concept and functions, value for consolidated groups. News of Scientific Achievements. Accounting, Analysis and Audit, no. 2, pp. 65–68. DOI: 10.36616/2713-1726-2020-2-65-68. (In Russ.)

14. Nesterovich Yu.V. (2024). Developing the general inter-theory of documentology. Scientific and Technical Libraries, no. (4), pp. 109–130. (In Russ.) DOI:10.33186/1027-3689-2024-4-109-130

15. Sleptsova Y.A., Kachalov R.M. (2018). Integration strategy of the enterprise under conditions of digital transformation of economy. St. Petersburg State Polytechnical University Journal. Economics, no. 11 (5), pp. 7–21. (In Russ.) DOI: 10.18721/JE.11501

16. Hveckovičs Ņ. (2020). Return on brand indicator as one of branding efficiency evaluation tools. Journal of the New Economic Association, no. 1(45), pp. 132–150. (In Russ.) DOI: 10.31737/2221-2264-2020-45-1-5

17. Adepoju A.H., Eweje A. et al. (2023). Developing strategic roadmaps for data-driven organizations: A model for aligning projects with business goals. International Journal of Multidisciplinary Research and Growth Evaluation, no. 4 (6), pp. 1128–1140.

18. Ajayi J.O., Cadet E. et al. (2024). Building resilient enterprise risk programs through integrated digital governance models. International Journal of Scientific Research in Humanities and Social Sciences, no. 1 (2),

19. pp. 433–462.

20. Bakirtzis G., Fleming C.H., Vasilakopoulou C. (2021). Categorical semantics of cyber-physical systems theory. ACM Transactions on Cyber-Physical Systems, no. 5 (3), pp. 1–32. DOI:10.1145/3461669

21. Dabringer M.V., Dybov A. et al. (2022). Towards integrated safety analysis as part of traceable model-based systems engineering. Proceedings of the Design Society, no. 2, pp. 2005–2014. DOI:10.1017/pds.2022.203

22. Fong B., Spivak D.I. (2018). Seven sketches in compositionality: An invitation to applied category theory. URL: https://arxiv.org/pdf/1803.05316

23. Mabrok M.A., Ryan M.J. (2017). Category theory as a formal mathematical foundation for model-based systems engineering. Appl. Math. Inf. Sci., no. 11 (1), pp. 43–51. DOI: 10.18576/amis/110106

24. Lu J., Ma J.et al. (2021). Design ontology supporting model-based systems engineering formalisms. IEEE Systems Journal, no. 16 (4), pp. 5465–5476. DOI: 10.1109/JSYST.2021.3106195

25. Rauzy A.B., Haskins C. (2019). Foundations for model‐based systems engineering and model-based safety assessment. Systems Engineering, no. 122 (2), pp. 146–155.

26. Rogers K. (2020). Creating a culture of data-driven decision-making. Liberty University.

27. Schultz P., Spivak D.I., Vasilakopoulou C. (2020). Dynamical systems and sheaves. Applied Categorical Structures, no. 128 (1), pp. 1–57.

28. Tohmé F., Auday M. (2019). Categorical economic theory. Alternative Approaches to Economic Theory. In: A. Beker (ed.) Alternative Approaches to Economic Theory. London: Routledge, pp. 56–68.

29. Vidalie J., Batteux M. et al. (2022). Category theory framework for system engineering and safety assessment model synchronization methodologies. Applied Sciences, no. 12 (12). 5880. DOI:10.3390/app12125880

30. Wee M., Scheepers H., Tian X. (2022). Understanding the processes of how small and medium enterprises derive value from business intelligence and analytics. Australasian Journal of Information Systems, vol. 26. https://doi.org/10.3127/ajis.v26i0.2969