Complex Multi-Category Systems

The article explores the field of complex systems.The shortcomings of the existing theory of complex systems are noted.The article explores a special type of complex systems: large complex systems.Two concepts are introduced: a complex multicategory system and a local complex system.Large complex systems are divided into homogeneous and heterogeneous.Large heterogeneous complex systems include categorically different integral local complex systems as subsystems.A subsystem of an ordinary complex system does not have integrity, but is dependent on the main system.A local complex system has integrity.It can be used stand-alone or in combination with other systems.The content of complex systems is revealed based on comparison with simple systems.The article gives a formal description of a number of simple systems.A formal description of complex systems is given on the basis of the development of a description of simple systems.Four types of simple and complex systems are considered.The article identifies three types of emergence of complex systems and three types of structure of the system components.It is shown that emergence is a characteristic of complexity.The presence of a class of large complex systems is noted.This class includes a subclass of heterogeneous or hybrid systems.For this subclass, the concept of multicategory complex systems is introduced.the introduction of the term "multi-categorical complex systems" is justified.a number of properties and dependencies in complex systems are studied.The features of many categorical complex systems are described.The article gives a formal description of a complex multi-category system based on a systems approach.It is shown that the structure of a complex multicategory system is described by a multigraph.A feature of complex multi-category systems is the possibility of using corporate management technologies for local complex systems with the additional condition of their complementary behavior.The introduced models expand the application of the theory of complex systems in practical activities.