Entity-Relationship models are a common tool for specification and design of information systems. They use a graphical technique for displaying the objects of the system and relatioships among them. The design process can be enhanced by specifying constraints of the system and the natural environment for these is the categorical notion of sketch. Here we argue that the finite-limit, finite-coproduct sketches with a terminal node are the appropriate class and call them ER sketches. A model for an ER sketch is a `snapshot' of a database. The models of an ER sketch in a lextensive category are a category with determined values on the entities and additional properties in case the entities have key attributes. Among the models is the query language associated to the ER sketch. We also show that database updates are simply spans of models. Moreover the category of updates of models of an ER sketch is the category of models of the sketch in the 2-category of spans. Research partially supp...

Category theoretic models of information systems have by now been widely used in industrial consultancies (for some examples see [6] and [3]) and the models themselves have been developed in some detail in, for example, [4], [1], [10], [5], [11], [2] and [8]. Although many information systems are never meant to be implemented computationally (for example paper-based enterprise wide information models are frequently used by senior executives to help understand and plan the development of large corporations), the logic of an information system corresponds to the logic of the query language that might be used for interrogating the system (whether or not it is implemented). Typically this logic corresponds to a variation of predicate logic applied to simple finite domains. Most categorical information system modellers either avoid being explicit about the logic of their systems (thus acquiring the logic of whatever query language happens to be present in an implementation) or import the ...

Partial information is common in real-world databases. Yet the theoretical foundations of data models are not designed to support references to missing data (often termed nulls). Instead, we usually analyse a clean data model based on assumptions about complete information, and later retrofit support for nulls.

In a categorical model of an information system, the internal logic of the category determines the query language of the information system. It has been argued that this logic should be determined by the categorical operations which can be performed within the system, rather than by post hoc addition of categorical structure. This paper presents the internal logic of the categorical model known as the tos. 1 Introduction Information systems are of great interest to application developers and theoreticians alike due to their utility and elegance. Recently there have been efforts to produce categorical models of information systems [1,2,3]. A major component of any information system is the query language used for retrieving information from the system, and this has a deep correspondence with a particular aspect of a categorical model - the internal logic of the category. While some researchers have ignored this or simply imported sufficient categorical structure (typically that of...