Cohomology of bifunctors

Abstract

We initiate the study of the cohomology of (strict polynomial) bifunctors by introducing the foundational formalism, establishing numerous properties in analogy with the cohomology of functors, and providing computational techniques. Since one of the initial motivations for the study of functor cohomology was the determination of the cohomology of GL(k) with coefficients in a tensor product of a symmetric and an exterior power of the adjoint representation, we keep this challenging example in mind as we achieve numerous computations which illustrate our methods.