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.