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.
Categories: math.AG math.CT