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<p>In this paper, we define the spectrum of an abelian category with respect to a class of wide subcategories. We introduce the notion of support of wide subcategories, and then give a classification of radical wide subcategories of an abelian category using it. We also introduce the notion of prime wide subcategories and give a homeomorphism from a topological space to the prime spectrum space using a notion of classifying support data.</p>

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Wide Subcategories in Abelian Categories

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • Lingling Tan,
  • Dingguo Wang,
  • Tiwei Zhao

摘要

In this paper, we define the spectrum of an abelian category with respect to a class of wide subcategories. We introduce the notion of support of wide subcategories, and then give a classification of radical wide subcategories of an abelian category using it. We also introduce the notion of prime wide subcategories and give a homeomorphism from a topological space to the prime spectrum space using a notion of classifying support data.