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Database queries and constraints via lifting problems

Published online by Cambridge University Press:  11 October 2013

DAVID I. SPIVAK
DAVID I. SPIVAK*
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States of America Email: dspivak@mit.edu
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Abstract

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Previous work has demonstrated that categories are useful and expressive models for databases. In the current paper we build on that model, showing that certain queries and constraints correspond to lifting problems, as found in modern approaches to algebraic topology. In our formulation, each 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. We interpret constraints within the same formalism, and then investigate some basic properties of queries and constraints. In particular, to any database π, we can associate a certain derived database Qry(π) of queries on π. As an application, we explain how giving users access to certain parts of Qry(π), rather than direct access to π, improves the ability to manage the impact of schema evolution.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 24 , Issue 6 , December 2014 , e240602
Copyright
Copyright © Cambridge University Press 2013 

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