导出范畴的自反性
Reflexivity in Derived Categories
摘要：
阿贝尔范畴之间的反变函子的伴随对可以推广到它们的导出函子在相应的导出范畴中的伴随对。我们描述的自反复合物和解释所取得的成果，在最初的阿贝尔范畴的对象。特别是，我们证明了，任何有限的上同调维数的函子，对象的初始阿贝尔范畴，这是自反的茎复合物形成的最大类Cotilting定理的意义上的Colby和Fuller工程。
英文摘要：
An adjoint pair of contravariant functors between abelian categories can be extended to the adjoint pair of their derived functors in the associated derived categories. We describe the reflexive complexes and interpret the achieved results in terms of objects of the initial abelian categories. In particular we prove that, for functors of any finite cohomological dimension, the objects of the initial abelian categories which are reflexive as stalk complexes form the largest class where a Cotilting Theorem in the sense of Colby and Fuller works.
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