Ordering the order of a distributive lattice by itself
We order the ordering relation of an arbitrary poset P component-wise by itself, obtaining a poset Phi(P) extending P. In particular, the effects of Phi on L epsilon DLAT01, the category of all bounded distributive lattices, are studied, mainly with the aid of Priestley duality. We characterize those L E DLAT01 which occur as Phi(K) for some K E DLAT01, decide this situation in polynomial time for finite L, characterize fixpoints of Phi within DLAT01 and relate them to free objects in DLAT01. (C) 2008 Elsevier Inc. All rights reserved.
distributive lattice priestley duality partially ordered set free distributive lattice