Resolving subcategories whose finitely presented module categories are abelian

Resolving subcategories whose finitely presented module categories are abelian

Blog Article

Let $mathcal{X}$ be an additive full subcategory of an abelian category.It is AEG IDK84451IB - 83cm Induction Hob with Integrated Hood - Black - 942 150 636 a classical fact that if $mathcal{X}$ is contravariantly finite, then the category $mathsf {mod},mathcal{X}$ of finitely presented right $mathcal{X}$-modules is abelian.In this paper, we consider the question asking when the converse holds true for a resolving subcategory of the category of finitely generated modules over a commutative noetherian henselian local ring.We give both affirmative answers and negative Work Boots answers to this question.