Database Queries and Constraints Via Lifting Problems
Previous paper has demonstrated that categories are useful and expressive models for databases. In the paper, the authors build on that model, showing that certain queries and constraints correspond to lifting problems, as found in modern approaches to algebraic topology. In their formulation, each so-called SPARQL graph pattern query corresponds to a category-theoretic lifting problem, whereby the set of solutions to the query is precisely the set of lifts. They interpret constraints within the same formalism and then investigate some basic properties of queries and constraints. In particular, to any database, they can associate a certain derived database Qry of queries.