In category theory this is called an initial algebra for a signature. It is the minimal structure that satisfies some specification and maps uniquely to every o

In category theory this is called an initial algebra for a signature. It is the minimal structure that satisfies some specification and maps uniquely to every other structure that satisfies the same specification but it's not clear if that's what you're looking for: http://tunes.org/wiki/initiality_20and_20finality.html http://tunes.org/wiki/initiality_20and_20finality.html.