弱负子范畴、权结构和（弱）可逼近三角范畴
On weakly negative subcategories, weight structures, and (weakly) approximable triangulated categories
摘要：
证明了某些三角范畴在A意义下是（弱）可逼近的.尼曼我们证明了一个三角形的$C$是由一个单一的对象$G$是弱近似的，如果$C(G,G[i])=0$的$i>1$（我们说，$G$是弱负的，如果这个假设是满足的情况下，平等$C(G,G[1])=0$满足以及尼曼自己提到）。此外，如果$G\cong \bigoplus_{0\le i\le n}G_i$和$C(G_i,G_j[1])=0$无论何时都是$i\le j$，则$C$也是可近似的。后一个结果可能是有用的，因为（在一些额外的假设下）它允许将$C$的某个显式子范畴刻画为从$C$的紧对象的子范畴$C^c$到$R$ -模的有限上同调函子范畴（对于诺特交换环$R$使得$C$是$R$ -线性的）。人们可以将这一陈述应用于某些伴随函子和$t$ -结构的构造。我们的证明（弱）逼近的$C$在上述假设是密切相关的（重量分解）某些（弱）重量结构，我们详细讨论了这种关系。
英文摘要：
We prove that certain triangulated categories are (weakly) approximable in the sense of A. Neeman. We prove that a triangulated $C$ that is compactly generated by a single object $G$ is weakly approximable if $C(G,G[i])=0$ for $i>1$ (we say that $G$ is weakly negative if this assumption is fulfilled; the case where the equality $C(G,G[1])=0$ is fulfilled as well was mentioned by Neeman himself). Moreover, if $G\cong \bigoplus_{0\le i\le n}G_i$ and $C(G_i,G_j[1])=0$ whenever $i\le j$ then $C$ is also approximable. The latter result can be useful since (under a few more additional assumptions) it allows to characterize a certain explicit subcategory of $C$ as the category of finite cohomological functors from the subcategory $C^c$ of compact objects of $C$ into $R$-modules (for a noetherian commutative ring $R$ such that $C$ is $R$-linear). One may apply this statement to the construction of certain adjoint functors and $t$-structures. Our proof of (weak) approximability of $C$ under the aforementioned assumptions is closely related to (weight decompositions for) certain (weak) weight structures, and we discuss this relationship in detail.
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