These rules ensure that the map "f" from the to that maps a tuple to is bilinear. The universality states that given "any" vector space "X" and "any" bilinear map , there exists a unique map "u", shown in the diagram with a dotted arrow, whose composition with "f" equals "g": . This is called the universal property of the tensor product, an instance of the method—much used in advanced abstract algebra—to indirectly define objects by specifying maps from or to this object.