  In this paper, we shall provide a purely $\infty$-categorical construction of
the mixed graded structure over Chevalley-Eilenberg complexes computing
homology and cohomology of Lie algebras defined over a field $\Bbbk$ of
characteristic $0$. While this additional piece of structure on
Chevalley-Eilenberg complexes is expected, and already described in terms of
explicit models given by chain complexes, there is not a completely formal and
model independent description of the mixed graded Chevalley-Eilenberg
$\infty$-functors in available literature. After constructing in all details
the Chevalley-Eilenberg $\infty$-functors and studying their main formal
properties, we present some further conjectures on their behavior.
