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as Fernando points out in his comment, this is too much to expect in general. The A∞-algebra structure on HA is not unique There is a unique $A_\infty$-algebra structure on $H(A)$ such that …

He actually identifies the tangent categories of a dg-operad $O$ for the following three categories: operads. $O$-bimodules. infinitesimal $O$-bimodules. …

In order to define an operad structure on $E_n\circ Lie$, you need to specify a distributive law. When $n=1$, let me use that $E_n$ is equivalent to $As$ and rather consider $As\circ Lie$. In this cas …

Here are the operads that are involved in that game: the operad $D_2$ of little disks, which is a topological operad. …

Recall: $\alpha$ being Koszul means that $C\otimes_\alpha A$ is acyclic, menaning that the augmentation map $C\otimes_\alpha A\overset{\epsilon\otimes\epsilon}{\longrightarrow}\mathbb{K}$ is a quasi-i …

The action of GT on deformation quantization has been developed in http://arxiv.org/abs/1009.1654 (Willwacher) and before in http://arxiv.org/abs/math/0202039 (Tamarkin). The fact that GT is Aut(Cha …

A $G_\infty$-morphism $\phi$ is determined by structure maps $\phi^{k_1,\dots,k_n}$, $n\geq1$, $k_1,\dots,k_n\geq1$. The $L_\infty$-part of $\phi$ is the $L_\infty$-morphism $\ell$ with structure ma …

This is explained in Section 4.5.2 of "deformation quantization of poisson manifolds" by Kontsevich (http://arxiv.org/abs/q-alg/9709040). The way you wrote the homotopy between two Maurer-Cartan ele …

\mathcal O$, w.r.t. to a cofibrant resolution $\widetilde{\mathcal O}\to\mathcal O$ is proved in the appendix A.2 of my paper with Van den Bergh (see also Theorem 10.3.6 in Loday-Vallette's Algebraic Operads …

Hi Darij, A geometric way of thinking about the shuffle algebra A geometric way of seeing $T(V)$ with the shuffle product is by considering functions on the loop space of $V^*$ (i.e. the space of c …