Mixed graded structure on Chevalley-Eilenberg functors

In this paper, we shall provide a purely $\mathrm{\infty }$-categorical construction of the mixed graded structure over Chevalley-Eilenberg complexes computing homology and cohomology of Lie algebras defined over a field $\mathbb{k}$ 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 $\mathrm{\infty }$-functors in available literature. After constructing in all details the Chevalley-Eilenberg $\mathrm{\infty }$-functors and studying their main formal properties, we present some further conjectures on their behavior.