Characterising the bounded derived category of an hereditary abelian category
Characterising the bounded derived category of an hereditary abelian category
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发表时间：
2016-12
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通讯作者：
Andrew Hubery
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作者：
Andrew Hubery
我们证明了如果一个（不一定是代数的）三角化范畴T包含一个可容许的遗传阿贝尔子范畴H，那么我们可以将H包含到T中提升为一个完全忠实的三角函子，从H到T的有界派生范畴的整体。这允许我们证明，例如，当且仅当T允许分裂有界的T结构时，三角化范畴T与遗传阿贝尔范畴的有界派生范畴T是三角等价的。
We show that if a (not necessarily algebraic) triangulated category T contains an admissible hereditary abelian subcategory H, then we can lift the inclusion of H into T to a fully faithful triangle functor from the whole of the bounded derived category of H to T. This allows us prove, for example, that a triangulated category T is triangle equivalent to the bounded derived category of an hereditary abelian category if and only if T admits a split, bounded t-structure.