Algebraic Databases — Patrick Schultz, David I. Spivak, Christina Vasilakopoulou & Ryan Wisnesky (2016; Theory Appl. Categ. 32 (2017)). arXiv:1602.03501 (v3, PDF).
A categorical model of databases with an algebraic type side: schemas pair an entity category with an observables profunctor into a multi-sorted algebraic theory, instances are functors whose type part is an algebra, and schema mappings induce the adjoint data-migration functors. Schemas, mappings, instances and queries are organised into one proarrow equipment.
Sources: the paper, arXiv:1602.03501v3, checked against the arXiv listing. Index: Papers.
Key definitions and results
- Definition 3.1: multi-sorted algebraic theory
- Definition 5.2: database schema
- Definition 6.2: instances
- Definition 7.1, Propositions 7.3, 7.4: , ,
- Proposition 7.12: when preserves type algebras
- Theorem 8.10: bimodules and queries
- Definition 9.2: queries (for–where–return)
Concept notes
Algebraic Database, Attributed C-Set, Lawvere Theory