Suppose $$F:{\mathcal {D}}(X)\rightarrow {\mathcal {T}}$$ F : D ( X ) → T is an exact functor from the bounded derived category of coherent sheaves on a smooth projective variety X to a triangulated category $${\mathcal {T}}$$ T . If F possesses left and right adjoints, then the Bondal–Orlov criterion gives a simple way of determining if F is fully faithful. We prove a natural extension of this theorem to the case when X is a smooth and proper DM stack with projective coarse moduli space.

中文翻译：

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Deligne-Mumford 堆栈的 Bondal-Orlov 完全忠实标准

假设 $$F:{\mathcal {D}}(X)\rightarrow {\mathcal {T}}$$ F : D ( X ) → T 是平滑投影上相干滑轮的有界派生范畴的精确函子变体 X 到三角化类别 $${\mathcal {T}}$$ T 。如果 F 具有左伴随和右伴随，那么 Bondal-Orlov 标准给出了一种确定 F 是否完全忠实的简单方法。我们证明了这个定理的自然扩展，当 X 是具有投影粗模空间的平滑且适当的 DM 堆栈时。