2024/03/28 by Mike Lambert, Michael Lambert, Evan Patterson +2 · 1 voice
Computer Science · #math.CT #cs.DB #cs.LO
paper · pdf · doi:10.48550/arxiv.2403.19884
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.