ScalingStacks

Corollary 5.5.3.

Let \(n, k \geq 0\) and \(\mathcal D\) an \((\infty, k)\)-category. Then, the \(n\)-homotopy category functor \(h_n\) induces an equivalence of \(\infty\)-categories: \[h_n \colon {(\mathrm{Cat}_{(\infty, {k})})}_{\small{/^{(n-1)}}{\mathcal D}} \rightarrow {(\mathrm{Cat}_{({n}, {n})})}_{\small{/^{(n-1)}}{h_n\mathcal D}}.\]