We consider posets of lattice paths (endowed with a natural order) and begin
the study of such structures. We give an algebraic condition to recognize which
ones of these posets are lattices. Next we study the class of Dyck lattices
(i.e., lattices of Dyck paths) and give a recursive construction for them. The
last section is devoted to the presentation of a couple of open problems.Comment: 19 pages, presented at the conference "Lattice path combinatorics and
  discrete distributions", Athens (Greece), 2002. To be published on Journal of
  Statistical Planning and Inferenc