  Normal endomorphisms of von Neumann algebras need not be extendable to
automorphisms of a larger von Neumann algebra, but they always have asymptotic
lifts. We describe the structure of endomorphisms and their asymptotic lifts in
some detail, and apply those results to complete the identification of
asymptotic lifts of unital completely positive linear maps on von Neumann
algebras in terms of their minimal dilations to endomorphisms.
