  Let C be a coalgebra over a field k and A its dual algebra. The category of
C-comodules is equivalent to a category of A-modules. We use this to interpret
the cotensor product M \square N of two comodules in terms of the appropriate
Hochschild cohomology of the A-bimodule M \otimes N, when A is
finite-dimensional, profinite, graded or differential-graded. The main
applications are to Galois cohomology, comodules over the Steenrod algebra, and
the homology of induced fibrations.
