Lattices of lattice homomorphisms

IfL andM are lattices, Hom (L, M) denotes the set of homomorphisms ofL intoM with the pointwise partial order.L is calledcatalytic if Hom (L, M) is a lattice for every latticeM. Among other results, it is shown that every retract of a lattice completely freely generated by a partially ordered set is catalytic, and that every catalytic lattice is semidistributive and satisfies Whitman's condition (W). Presented by R. McKenzie