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

Abstract

We apply the Auslander–Buchweitz approximation triangles to study (pre)silting subcategories in a triangulated catego- ry T. An Auslander–Reiten type correspondence between the class of silting subcategories of T and that of certain covariantly finite subcategories of T is established. We introduce a relation on presilting subcategories of T, which can be used to obtain another silting subcategory from a given one. We also give a Bazzoni's characterization for two presilting subcategories satisfying such a relation. The results can be used to improve the Auslander–Reiten type correspondence and Bazzoni's characterization for small silting complexes established by Wei.