ScalingStacks

Corollary 5.5.7.

Let \(k, n \geq 0\), let \(F\colon \mathcal C\rightarrow\mathcal D\) and \(G\colon \mathcal X\rightarrow\mathcal D\) be functors between \((\infty,k)\)-categories and assume that \(F\) is \((n-1)\)-faithful. Then, the map of spaces \[\mathrm{Hom}_{(\mathrm{Cat}_{(\infty, {k})})_{/\mathcal D}}(\mathcal X, \mathcal C) \rightarrow\mathrm{Hom}_{(\mathrm{Cat}_{({n}, {n})})_{/h_n\mathcal D}}(h_n\mathcal X, h_n\mathcal C)\] is an equivalence.