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<p>Using techniques developed (Batanin and Leger in J Noncommutative Geom 13:1521–1576, 2019), we extend the Turchin/Dwyer–Hess double delooping result to further iterations of the Baez–Dolan plus construction. For <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(0 \le m \le n\)</EquationSource> </InlineEquation>, we introduce a notion of (<i>m</i>,&#xa0;<i>n</i>)-bimodules which extends the notions of bimodules and infinitesimal bimodules over the terminal non-symmetric operad. We show that a double delooping always exists for these bimodules. For the triple iteration of the Baez-Dolan construction starting from the initial 1-coloured operad, we provide a further reduceness condition to have a third delooping.</p>

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Triple Delooping for Multiplicative Hyperoperads

  • 期刊论文

  • 发表日期：

    2025年10月11日

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  • Florian De Leger,
  • Maroš Grego

摘要

Using techniques developed (Batanin and Leger in J Noncommutative Geom 13:1521–1576, 2019), we extend the Turchin/Dwyer–Hess double delooping result to further iterations of the Baez–Dolan plus construction. For \(0 \le m \le n\) , we introduce a notion of (m, n)-bimodules which extends the notions of bimodules and infinitesimal bimodules over the terminal non-symmetric operad. We show that a double delooping always exists for these bimodules. For the triple iteration of the Baez-Dolan construction starting from the initial 1-coloured operad, we provide a further reduceness condition to have a third delooping.