Operations on resolutions and the reverse adams spectral sequence

We describe certain operations on resolutions in abelian categories, and apply them to calculate part of a reverse Adams spectral sequence, going “from homotopy to homology”, for the space K(Z/2, n). This calculation is then used to deduce that there is no space whose homotopy groups are the reduction mod 2. As another application of the operations we give a short proof of T. Y. Lin's theorem on the infinite projective dimension of all nonfree π-modules.