  Two years ago, I characterized the order $\Princl L$ of principal congruences
of a bounded lattice $L$ as a bounded order.
  If $K$ and $L$ are bounded lattices and $\gf$ is a \zo homomorphism of $K$
into~$L$, then there is a natural isotone \zo-map $\gf_{\Hom}$ from $\Princl K$
into $\Princl L$.
  We prove the converse: For bounded orders $P$ and $Q$ and an isotone \zo map
$\gy$ of $P$ into $Q$, we represent $P$ and $Q$ as $\Princl K$ and $\Princl L$
for bounded lattices $K$ and $L$ with a \zo homomorphism $\gf$ of $K$ into $L$,
so that $\gy$ is represented as $\gf_{\Hom}$.
