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We consider a natural variant of the Moyal-Weyl product and show that ityields a functorial deformation of differential graded algebras and that we candeform coalgebras in a similar way. The Moyal-Weyl deformation of gradedalgebras has already been introduced by Fedosov \cite{Fe} and also appears in\cite{Ge} as part of an $A_\infty$ structure, but we are not aware that theanalogous result for differential graded coalgebras already appeared in theliterature and discuss the Moyal-Weyl of the category of complexes as anexample.

Moyal-Weyl deformations of $\mathrm{DGA}$ and $\mathrm{DGCA}$