Categorical informatics


Category theory, originally developed to translate theorems from one area of mathematics to another (e.g., from topology to algebra), has recently been applied to translate information from one computer system to another (e.g., between database management systems). The use of category theory as a formalism for solving information-integration problems is called functorial data migration, and has roots extending back to the late 1990s. Current research on functorial data migration is being led by David Spivak, Ryan Wisnesky, and others in the MIT department of mathematics.

In the last few years functorial data migration has become well-enough understood to enable the creation a prototype software tool for solving information-integration problems: the FQL (Functorial Query Language) tool. The FQL tool is a category-theoretic alternative to existing information-integration tools based on the relational formalism such as IBM's Clio, Microsoft's Rondo, Informatica, and others; these tools are often called ETL (Extract Transform Load) tools in the literature. Crucially, FQL's category-theoretic formalism has been formally proved to provide more accurate solutions than the relational formalism on many information-integration problems. Moreover, the FQL tool has successfully solved small-scale information-integration problems.

The mathematics of FQL's category-theoretic formalism and FQL's successful initial tests demonstrate the potential of the FQL tool to provide superior solutions to realistic information-integration problems. However, FQL is an academic prototype: to realize its full potential FQL must be extended into an industrial-strength tool. Extending the FQL tool will require both additional mathematical research and a sustained, significant software development effort. It is this software development effort that is the focus of Categorical Informatics, Inc.