Relational Databases and Indexed Categories
Robert D. Rosebrugh, Robert D. Rosebrugh, Robert Wood · 2006
. A description of relational databases in categorical terminology given here has as intended application the study of database dynamics, in particular we view (i) updates as database objects in a suitable category indexed by a topos; (ii) L-fuzzy databases as database objects in sheaves. Indexed categories are constructed to model the databases on a fixed family of domains and also all databases for a varying family of domains. Further, we show that the process of constructing the relational completion of a relational database is a monad in a 2-category of functors. Introduction We use the term relation for a subobject of a finite product of objects in a category. Following the relational database literature, we use the term domain for an object of the ambient category (and warn readers that these are not the ordered objects which go by the name "domain" elsewhere in theoretical Computer Science.) A relational database, as defined by E. F. Codd [3], is first of all a family of rela...