Mixed graded structure on Chevalley-Eilenberg functors

In this paper, we shall provide a purely ∞-categorical construction of the mixed graded structure (in the sense of Calaque, Pantev, Toën, Vaquié and Vezzosi) of Chevalley-Eilenberg complexes computing homology and cohomology of Lie algebras defined over a field k of characteristic 0. While this additional piece of structure on Chevalley-Eilenberg complexes is expected and described in work by Calaque and Grivaux in terms of explicit models, there is not a formal and model independent description of the mixed graded Chevalley-Eilenberg ∞-functors in available literature. After constructing in all details the Chevalley-Eilenberg ∞-functors and studying their main formal properties, we present some further conjectures on their behaviour.