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arXiv · 1704.07062

Delooping derived mapping spaces of bimodules over an operad

Julien Ducoulombier
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Abstract

From a map of operads $\eta : O\rightarrow O'$, we introduce a cofibrant replacement of the operad $O$ in the category of bimodules over itself such that the corresponding model of the derived mapping space of bimodules $Bimod_{O}^{h}(O;O')$ is an algebra over the one dimensional little cubes operad $\mathcal{C}_{1}$. In the present work, we also build an explicit weak equivalence of $\mathcal{C}_{1}$-algebras from the loop space $\Omega Operad^{h}(O;O')$ to $Bimod_{O}^{h}(O;O')$.

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Julien Ducoulombier. 2017-04-24. Delooping derived mapping spaces of bimodules over an operad. https://arxiv.org/abs/1704.07062

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