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.