  For a lattice L with 0 and 1, let Princ L denote the ordered set of principal
congruences of L. For {0,1}-sublattices A subseteq B of L, congruence
generation defines a natural map from Princ A to Princ B. In this way, we
obtain a small category of bounded ordered sets as objects and some
0-separating {0,1}-preserving monotone maps as morphisms such that every
hom-set consists of at most one morphism. We prove the converse: each small
category of bounded ordered set with these properties is representable by
principal lattice congruences in the above sense.
