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<p>We define Mackey functors over posets mimicking the classical notion and introduce a weak version of them. Then we show that they are acyclic by analyzing cofibrant and pseudo-projective objects in the category of functors indexed in a filtered poset. As application, we study homotopy colimits over posets and we give a homology decomposition for the classifying space of the Bianchi group <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13398_2025_1704_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Gamma _1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="normal">Γ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>.</p>

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Mackey functors for posets

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月3日

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  • Guille Carrión Santiago,
  • Antonio Díaz Ramos

摘要

We define Mackey functors over posets mimicking the classical notion and introduce a weak version of them. Then we show that they are acyclic by analyzing cofibrant and pseudo-projective objects in the category of functors indexed in a filtered poset. As application, we study homotopy colimits over posets and we give a homology decomposition for the classifying space of the Bianchi group \(\Gamma _1\) Γ 1 .