The Free On-line Dictionary of Computing (30 December 2018):

surjection
onto
surjective

    A function f : A -> B is surjective or onto or a
   surjection if f A = B.  I.e. f can return any value in B.
   This means that its image is its codomain.

   Only surjections have right inverses, f' : B -> A where
   f (f' x) = x since if f were not a surjection there would be
   elements of B for which f' was not defined.

   See also bijection, injection.

   (1995-05-27)