提升和限制重命名数据

Lifting of recollements and Gorenstein projective modules

In the paper, we investigate the lifting of recollements with respect to Gorenstein-projective modules. Specifically, a homological ring epimorphism can induce a lifting of the recollement of the stable category of finitely generated Gorenstein-projective modules; the recollement of the bounded Gorenstein derived categories of some upper triangular matrix algebras can be lifted to the homotopy category of Gorenstein-projective modules. As a byproduct, we give a sufficient and necessary condition on the upper triangular matrix algebra T_{n}(A) to be of finite CM-type for an algebra A of finite …

Lifting recollements of abelian categories and model structures

We use Quillen model structures to show a systematic method to lift recollements of hereditary abelian model categories to recollements of their associated homotopy categories. To that end, we use the notion of Quillen adjoint triples and we investigate transfers of abelian model structures along adjoint pairs. Applications include liftings of recollements of module categories to their derived counterpart, liftings to homotopy categories that provide models for stable categories of Gorenstein projective and injective modules and liftings to homotopy categories of n-morphism categories over Iwa…

再余裂的提升与部分倾斜集的粘合

Lifting of recollements and gluing of partial silting sets

本文研究三角范畴中再余裂的提升与倾斜集的粘合，提出提升判据并给出Artin代数情形下粘合经典倾斜对象的显式构造。

Lifting and restricting t-structures

We explore the interplay between t-structures in the bounded derived category of finitely presented modules and the unbounded derived category of all modules over a coherent ring $A$ using homotopy colimits. More precisely, we show that every intermediate t-structure in $D^b(\operatorname{mod}(A))$ can be lifted to a compactly generated t-structure in $D(\operatorname{Mod}(A))$, by closing the aisle and the coaisle of the t-structure under directed homotopy colimits. Conversely, we provide necessary and sufficient conditions for a compactly generated t-structure in $D(\operatorname{Mod}(A))$ t…