 
Summary: Cotensor products of modules
L. Abrams and C. Weibel 1
Department of Mathematics,
Rutgers University
New Brunswick, NJ 08903
Abstract
Let C be a coalgebra over a field k and A its dual algebra. The
category of Ccomodules is equivalent to a category of Amodules. We
use this to interpret the cotensor product MN of two comodules in
terms of the appropriate Hochschild cohomology of the Abimodule
M# N , when A is finitedimensional, profinite, graded or di#erential
graded. The main applications are to Galois cohomology, comodules
over the Steenrod algebra, and the homology of induced fibrations.
1 Introduction
Cotensor product and its derived functors Cotor i were originally introduced
by EilenbergMoore [EM] to calculate the homology of an induced fibration.
These functors have been discussed in the literature, primarily in homo
topy theory, but they have developed a reputation of being inaccessible. To
counter this, we describe cotensor product and Cotor in terms of Hochschild
cohomology, and provide a new class of examples to which they are relevant.
