Databases Are Categories

[maradydd]

alexey_rom tweeted Edward Z. Yang's Databases are categories (based on a talk by David Spivak) the other day. I only just got round to reading it, and having done so, I recommend you do too. The notion of arrows and their properties (identity and associative composition) can be a bit abstract for the amateur/novice category theorist (like me -- hell, I wouldn't call myself more than a category theory fangirl), and mapping this onto identity and joins in databases is a really clever concretization.

There is some nerking in the comments about the relational model really being about Cartesian relations rather than object relations. This is true, but AFAICT irrelevant if viewed from the perspective of object-relational mapping (which you get for free in Postgres and Oracle anyway).

Where I think this is really useful is the world of higher-order query languages. Category-friendly languages such as Haskell have already made a good deal of headway into database APIs; I do not yet know of any projects that (for example) can create a schema from a set of objects and morphisms, but (continuing the example) I could see using that approach to generate all necessary foreign key constraints from an ORM.