USING CATEGORY THEORY IN THE CONCEPTUAL DESIGN OF A DATABASE FOR THE “PROJECT MANAGEMENT” DOMAIN

Abstract

The article examines the problem of conceptual database design for the “Project Management” domain, analyzing its complexity arising from the uniqueness, temporality, and high level of uncertainty of projects in various fields of activity. The traditional modeling approach, based on the Entity-Relationship model (ER model), although widely used, has significant drawbacks, such as the inability to support a high level of abstraction, which makes these information models imperfect for complex systems. A fundamental problem with the ER model is its reliance on set theory, which limits the expressive power of the model in describing complex business rules and relationships.To overcome these limitations, an approach based on Category Theory (CT) is proposed. CT provides a powerful and abstract framework that allows for the modeling of not only entities (objects) but also relationships (morphisms) as primary elements of analysis. This provides a robust formal foundation that eliminates ambiguity and allows for the unification of different data types (relational, XML, graph) within a single theoretical framework. The paper describes how the core concepts of CT, such as objects, morphisms, composition, and universal constructions (e.g., pullback), can be used for data modeling. The use of commutative diagrams allows for the formalization of complex business rules, such as “Assigning a resource to a task within a project”, by shifting business logic from the implementation level to the conceptual design level. A comparative analysis showed that the categorical model is more flexible, expressive, and manageable compared to the ER model, especially in the context of schema evolution, thanks to the concept of functors. Thus, the research proves that CT is a valuable tool for database design in complex domains, including the “Project Management” domain, by providing a reliable and mathematically sound foundation for modeling.