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Applying a Hochschild cocycle to a Maurer-Cartan element: how one should think of this?
Let $C^{\bullet}(A,M)$ be the Hochschild cochain complex of a DG-algebra $A$ with coefficients in a DG-bimodule $M$. Let $\zeta \in C^0(A,M)$ be a cocycle. Let $a \in A$ be a Maurer-Cartan element, $d …