  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.
