Representing Knowledge and Querying Data using Double-Functorial Semantics

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 doublefunctorial semantics.in that c 1 = h = c 2 holds.Thus, f and g induce a pair morphism f , g : X r A r, and we can calculate thatmeaning that f = g must hold as a result of the uniqueness clause of the universal property of the tabulator r.Therefore, d is monic.