In the early eighties, A. Huhn proved that if D, E are finite distributive lattices and ψ : D → E is a {0}-preserving join-embedding, then there are finite lattices K, L and there is a lattice homomorphism φ : K → L such that ConK (the congruence lattice of K) is isomorphic to D, ConL (the congruence lattice of L) is isomorphic to E, and the natural induced mapping extφ : ConK → ConL represents...
