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If $\mathcal{P}$ is a sufficiently nice operad, then by [Higher Algebra, 5.3] you can form its centre: $$\mathcal{Z}_{\mathcal{P}}\ :\ \mathcal{P}\text{-Alg}\ \to\ \mathbf{E}_1\text{-Alg}(\mathcal{P}\...

Let $(V,\cdot)$ be an associative algebra and $W$ be a vector space endowed with a bimodule structure $\triangleright:V\otimes W\to W$ and $\triangleleft:W\otimes V\to W$ such that the following ...