On the Mac Lane $Q$-Construction for Exact $\infty$-Categories

Abstract

We extend McCarthy's stabilization construction to exact $\infty$-categories. This is achieved by constructing, for any functor from exact $\infty$-categories to a fixed stable $\infty$-category $\mathcal{A}$, a coherent chain complex in $\mathcal{A}$ that is an immediate generalization of Mac Lane's cubical $Q$-complex computing the stable homology of abelian groups.