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<p>We introduce the spectrum of an extriangulated category with respect to a class of thick subcategories as well as supports of thick subcategories. Then we give a classification of radical thick subcategories of an extriangulated category in terms of supports of thick subcategories. Moreover, we introduce the notions of prime thick subcategories and classifying support data, and show that if (<i>X, σ</i>) is a classifying support data on an extriangulated category <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\cal{K}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mi mathvariant="script">K</mi> </mrow> </math></EquationSource> </InlineEquation>, then there is a homeomorphism from the topological space <i>X</i> to the spectrum of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\cal{K}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mi mathvariant="script">K</mi> </mrow> </math></EquationSource> </InlineEquation> with respect to the set of prime thick subcategories. This result generalizes a result of Matsui.</p>

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Thick Subcategories of Extriangulated Categories

  • 期刊论文

  • 发表日期：

    2026年5月20日

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  • Lingling Tan,
  • Tiwei Zhao,
  • Zhaoyong Huang

摘要

We introduce the spectrum of an extriangulated category with respect to a class of thick subcategories as well as supports of thick subcategories. Then we give a classification of radical thick subcategories of an extriangulated category in terms of supports of thick subcategories. Moreover, we introduce the notions of prime thick subcategories and classifying support data, and show that if (X, σ) is a classifying support data on an extriangulated category \(\cal{K}\) K , then there is a homeomorphism from the topological space X to the spectrum of \(\cal{K}\) K with respect to the set of prime thick subcategories. This result generalizes a result of Matsui.