The recollements induced by contravariantly finite subcategories
The paper under review characterizes the existence of lower (upper) recollements of homotopy categories of bounded complexes in terms of the global dimension with respecto to a contravariantly (covariantly) finite subcategory \(\mathcal X\) of an abelian category (Theorems 3.11 and 3.12). Some applications of this characterization are provided in case \(\mathcal X\) is the class of Gorenstein projective modules over an \(n\)-Gorenstein ring (Corollary 3.3), or when \(\mathcal X\) is the class of FP-projective (FP-injective) modules (Corollaries 3.15 and 3.16). In the second part, the authors study the lifting of a recollement of a triple of abelian categories to a triple of relative derived categories with respect to balanced pairs. Applications include the case of Gorenstein derived categories (Corollary 5.8) and pure derived categories (Corollary 5.9).
scientific article; zbMATH DE number 7481866
scientific article