  We explain how the approach of Andre and Quillen to defining cohomology and
homology as suitable derived functors extends to generalized (co)homology
theories, and how this identification may be used to study the relationship
between them.
  As a side benefit, we clarify exactly what assumptions on an (algebraic)
category are needed in order for the approach of Beck and Andre-Quillen to
work.
  We also show how the description may be applied to construct universal
coefficient and reverse Adams spectral sequences.
