论文标题
张量三角类别之间的提升（CO）分层
Lifting (co)stratifications between tensor triangulated categories
论文作者
论文摘要
我们提供了分层和特性的必要条件，以沿着保留的张张量的$ r $ r $ - 线性函数下降，$ r $ linear-linear-linear-linear tensor tensor-triangualder类别是由其张量单位严格地压实产生的。然后，我们将这些结果应用于非阳性的交换DG环和结缔环光谱。特别是，这给出了（CO）本地化子类别的支持理论分类，以及具有有限幅度的非阳性交换性DG-RIN的衍生类别的紧凑对象的厚子类别，并为最终与最终的Coconnective衍生方案相关的空间提供了正式的合理性。对于非阳性的交换性DG-RING $ A $，我们还研究了$ \ Mathsf {d}（a）$中的某些有限条件（例如，代理 - 符号）是否可以简化为更好理解的类别$ \ MATHSF {d}（d}（d}（h^0a）$）中的问题。
We give necessary and sufficient conditions for stratification and costratification to descend along a coproduct preserving, tensor-exact $R$-linear functor between $R$-linear tensor-triangulated categories which are rigidly-compactly generated by their tensor units. We then apply these results to non-positive commutative DG-rings and connective ring spectra. In particular, this gives a support-theoretic classification of (co)localizing subcategories, and thick subcategories of compact objects of the derived category of a non-positive commutative DG-ring with finite amplitude, and provides a formal justification for the principle that the space associated to an eventually coconnective derived scheme is its underlying classical scheme. For a non-positive commutative DG-ring $A$, we also investigate whether certain finiteness conditions in $\mathsf{D}(A)$ (for example, proxy-smallness) can be reduced to questions in the better understood category $\mathsf{D}(H^0A)$.
