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

We extend McCarthy’s stabilization construction to exact $\mathrm{\infty }$-categories. This is achieved by constructing, for any functor from exact $\mathrm{\infty }$-categories to a fixed stable $\mathrm{\infty }$-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.