[falcor84]

Exactly. Indeed, from what I recall from relational database theory, joins are usually treated as cartesian products (outer joins) which are then filtered by the join condition.

[catnaroek]

An outer join a Cartesian product is not.

Even if you stick to ordinary (inner) joins, they are pullbacks, not products.

https://en.wikipedia.org/wiki/Pullback

[falcor84]

D'oh, sorry, I meant "cross join"