  We prove the equality $\cat(\phi)=\cd(\phi)$ for epimorphisms $\phi:\Gamma\to
\Lambda$ between torsion-free, finitely generated almost nilpotent groups
$\Gamma$ and $\Lambda$.
  In addition, we prove the equality $\cat(\phi)=\cd(\phi)$ for homomorphisms
$\phi:\Gamma\to \Lambda$ between torsion-free, finitely generated virtually
nilpotent groups.
