Group completion via the action $\mathrm{\infty }$-category

We give a generalization of Quillen’s $S^{-1}S$ construction for arbitrary $E_n$-monoids as an $E_{n-1}$-monoidal $\mathrm{\infty }$-category and show that its realization models the group completion provided that $n\ge 2$. We will also show how this construction is related to a variety of other constructions of the group completion.