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arXiv · 2309.15055

Triple delooping for multiplicative hyperoperads

Florian De Leger·Maroš Grego
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Abstract

Using techniques developed by Batanin and the first author, we extend the Turchin/Dwyer-Hess double delooping result to further iterations of the Baez-Dolan plus construction. For $0 \leq m \leq n$, 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.

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Florian De Leger, Maroš Grego. 2023-09-26. Triple delooping for multiplicative hyperoperads. https://arxiv.org/abs/2309.15055

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