Database queries and constraints via lifting problems

摘要

Previous work has demonstrated that categories are useful and expressive models forrndatabases. In the current paper we build on that model, showing that certain queries andrnconstraints correspond to lifting problems, as found in modern approaches to algebraicrntopology. In our formulation, each SPARQL graph pattern query corresponds to arncategory-theoretic lifting problem, whereby the set of solutions to the query is precisely thernset of lifts. We interpret constraints within the same formalism, and then investigate somernbasic properties of queries and constraints. In particular, to any database π, we can associaterna certain derived database Qry(π) of queries on π. As an application, we explain how givingrnusers access to certain parts of Qry(π), rather than direct access to π, improves the ability tornmanage the impact of schema evolution.