ScalingStacks

Lemma 15.9 ([28, A.3.7.7]). Two combinatorial model categories $\mathcal{A}$ and $\mathcal{B}$ are connected by a chain of Quillen equivalences if and only if $\mathrm{N}^{\mathrm{H}}\mathcal{A}$ and $\mathrm{N}^{\mathrm{H}}\mathcal{B}$ are equivalent $\infty$-categories.