2009/04/13 by David I. Spivak, Spivak, David I. · 1 citation
Computer Science · #Advanced Database Systems and Queries #Data Management and Algorithms #Databases (cs.DB) #FOS: Computer and information sciences #Information Retrieval (cs.IR) #Topological and Geometric Data Analysis #cs.DB #cs.IR
paper · pdf · doi:10.48550/arxiv.0904.2012
arxiv created 2009/04/13 · openalex publication_date 2009/04/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we define a category DB, called the category of simplicial databases, whose objects are databases and whose morphisms are data-preserving maps. Along the way we give a precise formulation of the category of relational databases, and prove that it is a full subcategory of DB. We also prove that limits and colimits always exist in DB and that they correspond to queries such as select, join, union, etc. One feature of our construction is that the schema of a simplicial database has a natural geometric structure: an underlying simplicial set. The geometry of a schema is a way of keeping track of relationships between distinct tables, and can be thought of as a system of foreign keys. The shape of a schema is generally intuitive (e.g. the schema for round-trip flights is a circle consisting of an edge from A to B and an edge from B to A), and as such, may be useful for analyzing data. We give several applications of our approach, as well as possible advantages it has over the relational model. We also indicate some directions for further research.