  We show that three different kinds of cohomology - Baues-Wirsching
cohomology, the (S,O)-cohomology of Dwyer-Kan, and the Andre-Quillen cohomology
of a Pi-algebra - are isomorphic, under certain assumptions.
  This is then used to identify the cohomological obstructions in three general
approaches to realizability problems: the track category version of
Baues-Wirsching, the diagram rectifications of Dwyer-Kan-Smith, and the
Pi-Algebra realization of Dwyer-Kan-Stover. Our main tool in this
identification is the notion of a mapping algebra: a simplicially enriched
version of an algebra over a theory.
