  We introduce n-generated sheaves and n-motivic sheaves, describing completely
for n = 0, 1 and proposing a conjecture for n > 1. We then obtain functors
L\pi_0 and LAlb on DM_{eff}(k) deriving \pi_0 and Alb. The functor LAlb extends
the one constructed (by the second author jointly with B.Kahn) to
non-necessarily geometric motives. These functors are then used to define
higher N\'eron-Severi groups and higher Albanese sheaves. The latter may be
considered as an algebraic avatar of Deligne (co)homology.
