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Data constraints are fundamental for practical data modelling, and averifiable conformance of a data instance to a safety-critical constraint(satisfaction relation) is a corner-stone of safety assurance. Diagrammaticconstraints are important as both a theoretical concepts and a practicallyconvenient device. The paper shows that basic formal constraint management canwell be developed within a finitely complete category (hence the reference toCartesianity in the title). In the data modelling context, objects of such acategory can be thought of as graphs, while their morphisms play two roles: ofdata instances and (when being additionally labelled) of constraints.Specifically, a generalized sketch $S$ consists of a graph $G_S$ and a set ofconstraints $C_S$ declared over $G_S$, and appears as a pattern for typicaldata schemas (in databases, XML, and UML class diagrams). Interoperability ofdata modelling frameworks (and tools based on them) very much depends on thelaws regulating the transformation of satisfaction relations between datainstances and schemas when the schema graph changes: then constraints aretranslated co- whereas instances contra-variantly. Investigation of thistransformation pattern is the main mathematical subject of the paper

Cartesian institutions with evidence: Data and system modelling with diagrammatic constraints and generalized sketches