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arXiv · 2603.07945

Contravariantly infinite resolving subcategories

Gen Tanigawa
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Abstract

Let $R$ be a commutative Noetherian ring. Denote by $\textrm{mod}R$ the category of finitely generated $R$-modules. In this paper, a contravariantly infinite subcategory of $\textrm{mod}R$ is defined as a full subcategory $\mathscr{X}$ of $\textrm{mod}R$ such that no module outside $\mathscr{X}$ admits a right $\mathscr{X}$-approximation. This paper provides several criteria for contravariant infiniteness in the case where $R$ is a local complete intersection.

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Gen Tanigawa. 2026-03-09. Contravariantly infinite resolving subcategories. https://arxiv.org/abs/2603.07945

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