Data Base Mappings and Theory of Sketches

In this paper we will present the two basic operations for database schemas used in database mapping systems (separation and Data Federation), and we will explain why the functorial semantics for database mappings needed a new base category instead of usual Set category. Successively, it is presented a definition of the graph G for a schema database mapping system, and the definition of its sketch category Sch(G). Based on this framework we presented functorial semantics for database mapping systems with the new base category DB.