  We define inductively a sequence of purely algebraic invariants - namely,
classes in the Quillen cohomology of the Pi-algebra \pi_* X - for
distinguishing between different homotopy types of spaces. Another sequence of
such cohomology classes allows one to decide whether a given abstract
Pi-algebra can be realized as the homotopy Pi-algebra of a space in the first
place.
  The paper is written for a relatively general "resolution model category", so
it also applies, for example, to rational homotopy types.
