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

中文翻译：

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在操作数上对双模块的派生映射空间进行解循环

对于任何拓扑操作数O，我们在其自身上的双模块类别中引入辅纤化替换，这样对于每个操作数图\（\ eta：O \ rightarrow O'\），对应的模型\（{\ textit {Bimod}}双模的派生映射空间的_ {O} ^ {h}（O \，; \ ，O'）\）是一维\（\ mathcal {C} _ {1} \）操作的一维小立方体上的代数。我们还从循环空间\（\ Omega {\ textit {Operad}} ^ {h}（O \，; \，O中建立了\（\ mathcal {C} _ {1} \）-代数的显式弱等价'）\）到\（{\ textit {Bimod}} _ {O} ^ {h}（O \，; \，O'）\）。