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Keywords:
homological algebra; dg (co)algebras; $A_\infty$-(co)algebras
homological algebra; dg (co)algebras; $A_\infty$-(co)algebras
Summary:
In this article we extend the main result in [15] to the case where the algebra is not necessarily nonnegatively graded connected. More precisely, we show that, for a nonnegatively filtered connected dg algebra $A$, it is possible to compute the cup product of the Hochschild cohomology of $A$ at the level of the complex Hom$_{A^e}(P_\bullet,A)$, where $P_\bullet$ is a semifree resolution of the dg $A$-bimodule $A$ by making use of the coaugmented curved $A_\infty$-coalgebra structure of a suitable Koszul codual of $A$, i.e. a coaugmented curved $A_\infty$-coalgebra $C$ that is filtered quasi-equivalent to the curved bar construction of $A$. We do not need to construct any comparison map between $P_\bullet$ and the Hochschild resolution of $A$, or any lift $\Delta : P \rightarrow P \otimes_{A}P$ of the identity of $A$.
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