  Generalizing F-nilpotent completion for a ring spectrum F we first define the
notion of completion with respect to a thick subcategory in a monogenic stable
homotopy category. Specializing this to the thick subcategory generated by
F-injectives gives an injective completion functor. This is the completion
functor adapted to the modified Adams spectral sequence, which uses absolute
instead of relative injective resolutions. Finally we show, that both
constructions coincide for suitable ring spectra.
