[wisnesky]

At https://www.categoricaldata.net we claim that symbolic AI is also generative, when eg used in data warehousing. Instead of eg new images, the generatively gives you new primary and foreign keys, new ontologies, contradiction detection, etc.

[mtlb]

Is there a conceptual difference between the categorical database and hypergraph database?

[wisnesky]

Yes; categories extend traditional graphs with systems of equations. Hypergraphs extend traditional graphs by allowing edges to be between multiple nodes. Most operations on categories are formally undecidable because of the systems of equations; most operations on graphs/hypergraphs are decidable. This makes working with categorical databases a lot like doing computer algebra in e.g. Mathematica and provides a huge increase in expressive power (you can e.g. encode Turing machines with equations.)