  Since the work of Mikhail Kapranov in [Kap], it is known that the shifted
tangent complex $\mathbb{T}_X[-1]$ of a smooth algebraic variety $X$ is endowed
with a weak Lie structure. Moreover any complex of quasi-coherent sheaves on
$X$ is endowed with a weak Lie action of this tangent Lie algebra. This action
is given by the Atiyah class of $E$. We will generalize this result to (finite
enough) derived Artin stacks, without any smoothness assumption. This in
particular applies to (finite enough) singular schemes. This work uses tools of
both derived algebraic geometry and $\infty$-category theory.
