Auslander's formula for contravariantly finite subcategories
Auslander's formula for contravariantly finite subcategories
Let $A$ be a right coherent ring and $\mathcal{X}$ be a contravariantly finite subcategory of ${\rm{mod}}\mbox{-}A$ containing projectives. In this paper, we construct a recollement of abelian categories $({\rm{mod}}_{0}\mbox{-}\mathcal{X}, {\rm{mod}}\mbox{-}\mathcal{X}, {\rm{mod}}\mbox{-}A)$, where ${\rm{mod}}_{0}\mbox{-}\mathcal{X}$ is a full subcategory of ${\rm{mod}}\mbox{-}\mathcal{X}$ consisting of all functors vanishing on projective modules. As a result, …