Extensions of homologically finite subcategories (Q689756)

This paper is devoted to studying extensions of homologically finite subcategories. The main result obtained is the following. If \({\mathcal A}\) and \({\mathcal B}\) are contravariantly finite subcategories of \(\text{mod }\Lambda\) for an Artin algebra \(\Lambda\), then the full subcategory of modules \(E\) having a submodule \(A\) in \({\mathcal A}\) with \(E/A\) in \({\mathcal B}\) is also contravariantly finite in \(\text{mod }\Lambda\).