  In this paper, based on the same techniques as in \cite{BENZ08} for the
construction of a formally smooth map $V \to Perf$ from the variety of
complexes to the Artin $\infty$-stack $Perf$, we explicitly construct a new
Artin $ \infty $-stack of Maurer-Cartan elements of a dg-category $ \mathcal
{P} $ denoted by $\mathcal{MC_P} $, with a map $ V \to \mathcal{MC_P} $ which
we show to be formally smooth.
