ScalingStacks

We recall the following easy fact: Given functors \(F, G: \mathcal A\rightarrow\mathcal B\) and \(H \colon \mathcal B\rightarrow\mathcal C\) of \(\infty\)-categories and assume that for all \(a,a' \in \mathcal A\) the map \[\mathrm{Hom}_{\mathcal B}(Fa, Ga') \xrightarrow{H(-)} \mathrm{Hom}_{\mathcal C}(HFa, HGa')\] is an equivalence of spaces.