The present development in the database area is highly influenced by the object-oriented principles of data modeling. On the contrary to the previously successful relational approach, it lacks rigorous theoretical support. This problem is mainly due to the fact that the semantics description of such features as generalization, specialization, encapsulation, and inheritance is not trivial by using just the means of the set theory. Therefore, many researchers focused on finding suitable theoretical means for the modeling of complex objects. This paper is concerned with the comparison of categorical modeling in the database area and proposes a limit data model that enables to represnt the objects, relationships, multiple inheritance, class polymorphism and virtual methods in the categorical setting. The aim to formalize these notions arose from the actual need. We would like to use it to support the development of an object-oriented database model closely following the standard ODMG'93. This model proposes several useful features to the database mdoeling concerning the object hierarchies and modeling roles (13) that require a specific approach and it seems that the category theoretical framework fulfills these objectives.
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