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<p>In this survey, we summarize some results in the literature involving the mesh category, which is a combinatorial representation of the category of modules over a finite-dimensional associative algebra. We discuss Riedtmann’s well-behaved functors, which compare the mesh category with the module category, and discuss how the properties of these functors can be applied to study the problem of composing irreducible morphisms, which is the problem of deciding when the composition of <i>n</i> irreducible morphisms is non-zero and lies on the (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n+1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>)-th power of the radical.</p>

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On Riedtmann’s well-behaved functors and applications to composites of irreducible morphisms

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月28日

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  • Viktor Chust,
  • Flávio U. Coelho

摘要

In this survey, we summarize some results in the literature involving the mesh category, which is a combinatorial representation of the category of modules over a finite-dimensional associative algebra. We discuss Riedtmann’s well-behaved functors, which compare the mesh category with the module category, and discuss how the properties of these functors can be applied to study the problem of composing irreducible morphisms, which is the problem of deciding when the composition of n irreducible morphisms is non-zero and lies on the ( \(n+1\) n + 1 )-th power of the radical.