Auslander's formula for contravariantly finite subcategories

Abstract

Let A be a right coherent ring and X be a contravariantly finite subcategory of mod-A containing projectives. In this paper, we construct a recollement of abelian categories (mod0-X, mod-X, mod-A), where mod0-X is a full subcategory of mod-X consisting of all functors vanishing on projective modules. As a result, a relative version of Auslander's formula with respect to a contravariantly finite subcategory will be given. Some examples and applications will be provided. © 2021 The Mathematical Society of Japan