Cartesian lifting of a binary operation to lists

For a binary operation $\oplus$, its Cartesian lifting sends lists $xs,ys$ to the list comprehension $[x\oplus y\mid x\leftarrow xs;y\leftarrow ys]$, with the right generator varying fastest. On finite lists this preserves associativity but need not preserve commutativity or idempotence, because list order and repeated entries matter.