Representing Knowledge and Querying Data using Double-Functorial Semantics
<|reference_start|>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 double-functorial semantics.<|reference_end|>
@article{lambert2024representing,
    title={Representing Knowledge and Querying Data using Double-Functorial
  Semantics},
    author={Michael Lambert, Evan Patterson},
    journal={arXiv preprint arXiv:2403.19884},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.19884},
    primaryClass={math.CT cs.DB cs.LO}
}