We introduce the notion of
a strongly homotopy-comultiplic
ative resolution of
a module co
algebr
a over
a ch
ain Hopf
algebr
a, which we
apply to proving
a comultiplic
ative enrichment of
a well-known theorem of Moore concerning the homology of quotient sp
aces of group
actions. The import
ance of our enriched version of Moore鈥檚 theorem lies in its
applic
ation to the construction of useful coch
ain
algebr
a models for computing multiplic
ative structure in equiv
ari
ant cohomology.
In the special cases of homotopy orbits of circle actions on spaces and of group actions on simplicial sets, we obtain small, explicit cochain algebra models that we describe in detail.