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The core of a model theory for generic schema management is developed. This theory has two
distinctive features: it applies to a variety of categories of schemas, and it applies to transformations
of both the schema structure and its integrity constraints. A subtle problem of schema integration is
considered in its general form, not bound to any particular category of schemas. The proposed solution,
as well as the overall theory, is based entirely on schema morphisms that carry both structural and
semantic properties. Duality results that apply to the two levels (i.e., the schema and the data levels)
are established. These results lead to the main contribution of this paper: a formal schema and data
management framework for generic schema management. Implications of this theory are established
that apply to integrity problems in schema integration. The theory is illustrated by a particular
category of schemas with object-oriented features along with typical database integrity constraints.