Consider a complete abelian category which has an injective cogenerator. If its derived category is left-complete we show that the dual of this derived category satisfies Brown representability. In particular, this is true for the derived category of an abelian AB\(4^{*}\)-\(n\) category and for the derived category of quasi-coherent sheaves over a nice enough scheme, including the projective finitely dimensional space.

中文翻译：

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某些派生类别的Brown可表示性的对偶

考虑一个完整的阿贝尔类别，其中有一个内射式余热发生器。如果其派生类别为左完整，则表明该派生类别的对偶满足Brown可表示性。特别是，对于阿贝尔AB \（4 ^ {*} \）-\（n \）类别的派生类别以及在足够好的方案（包括有限射影）上的拟相干滑轮的派生类别，这是正确的。维空间。