Dependencies in relational models of databases

In order to provide a common framework for classical, fuzzy and L-fuzzy databases we assume that databases are set-valued, i.e., that every value of an attribute is a set in some suitable set theory. Tables of a database are modeled using the theory of Dedekind categories and its extensions. These theories establish an abstract approach to binary, classical (crisp) or fuzzy relations. Based on this model we investigate dependencies in databases in a general setting.