Generalized Andr\'{e}-Quillen Cohomology

Abstract

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.