Abstract
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, a relative version of Auslander's formula with respect to a contravariantly finite subcategory will be given. Some examples and applications will be provided.
Funding Statement
This research was in part supported by a grant from IPM.
Citation
Javad ASADOLLAHI. Rasool HAFEZI. Mohammad Hossein KESHAVARZ. "Auslander's formula for contravariantly finite subcategories." J. Math. Soc. Japan 73 (2) 329 - 349, April, 2021. https://doi.org/10.2969/jmsj/83308330
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