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Cotensor products of modules L. Abrams and C. Weibel 1

Summary: Cotensor products of modules
L. Abrams and C. Weibel 1
Department of Mathematics,
Rutgers University
New Brunswick, NJ 08903
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.


Source: Abrams, Lowell - Department of Mathematics, George Washington University


Collections: Mathematics