Representing Knowledge and Querying Data using Double-Functorial Semantics
arXiv:2403.19884 · doi:10.4204/EPTCS.429.9
Abstract
Category theory offers a mathematical foundation for knowledge representation and database systems. Popular existing approaches model a database instance as a functor into the category of sets and functions, or as a 2-functor into the 2-category of sets, relations, and implications. The functional and relational models are unified by double functors into the double category of sets, functions, relations, and implications. In an accessible, example-driven style, we show that the abstract structure of a 'double category of relations' is a flexible and expressive language in which to represent knowledge, and we show how queries on data in the spirit of Codd's relational algebra are captured by double-functorial semantics.
In Proceedings ACT 2024, arXiv:2509.18357