双函子的上同调
Cohomology of bifunctors
摘要：
我们开始研究（严格多项式）双函子的上同调，通过引入基本的形式主义，建立许多性质类比函子的上同调，并提供计算技术。由于函子上同调研究的最初动机之一是确定GL（k）的上同调，其系数为对称和伴随表示的外幂的张量积，因此我们在实现大量计算来说明我们的方法时，会记住这个具有挑战性的例子。
英文摘要：
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.
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