Representing a monotone map by principal lattice congruences
For a lattice \(L\), let Princ(\(L\)) denote the ordered set of principal congruences of \(L\). In this paper, the author proves that for each \(0\)-separating bound-preserving monotone map \(f\) between two bounded ordered sets, there are a lattice \(L\) and a sublattice \(K\) of \(L\) such that \(f\) is the map from Princ(\(K\)) to Princ(\(L\)) that sends a principal congruence to the congruence it generates in the larger lattice.
scientific article; zbMATH DE number 6699215