An Auslander-Buchweitz approximation approach to (pre)silting subcategories in triangulated categories (Q1730186)

The authors study (pre)silting subcategories in a triangulated category $\mathcal{T}$ by applying the Auslander-Buchweitz approximation triangles. They establish an Auslander-Reiten type correspondence between the class of silting subcategories of $\mathcal{T}$ and that of certain covariantly finite subcategories of $\mathcal{T}$. A relation on presilting subcategories of $\mathcal{T}$ is introduced, in order to obtain another silting subcategory. For small silting complexes established by \textit{J. Wei} [Isr. J. Math. 194, Part B, 871--893 (2013; Zbl 1286.16011)], the results are used to improve the Auslander-Reiten correspondence and Bazzoni's characterisation.