Data modeling from a categorical perspective

The last decades, a lot of effort has been spent in defining formalisms to model data storage and retrieval. This is in particular true for the more recently introduced object-oriented systems. Some models were based on logic, other models were more graphically inspired, yet others were based on more complicated mathematical structures such as abstract data types, semantic networks or Petri-nets. The diversity of the techniques and formalisms used to model the systems referred to above asks for a more unifying approach. The approach we propose is based on category theory, a formalism that is especially useful for data modeling purposes because of its generic and fundamental character. This thesis can roughly be divided in two parts. In the first part, we study complex-object and object-oriented systems from a fundamental perspective. Therefore, we first introduce the so-called typegraph model. In this model, the scheme is represented by a small category (generated by the typegraph) and the instances as functors from this category to an instance category. Although this model is structurally equivalent with well-known models such as IQL, the query-language is entirely defined using so-called universal constructions. The functional nature of the typegraph model suggested to investigate another approach which considers instances as mappings from an instance to the scheme. This approach is taken with the introduction of the CGOOD model, a categorical graph-based data model. The second part of this thesis fully exploits the abstraction power of category theory. In this part we use category theory as a framework to study classes of data models and investigate in particular some important object-oriented properties such as object-identity and inheritance.