The goal of this article is to study the coaugmented curved A∞-coalgebra structure of the Koszul codual of a filtered dg algebra over a field k. More precisely, we first extend one result of B. Keller that allowed to compute the A∞-coalgebra structure of the Koszul codual of a nonnegatively graded connected algebra to the case of any unitary dg algebra provided with a nonnegative increasing filtration whose zeroth term is k. We then show how to compute the coaugmented curved A∞-coalgebra structure of the Koszul codual of a Poincaré-Birkhoff-Witt (PBW) deformation of an N-Koszul algebra.
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