ScalingStacks

Remark 15.2. When $\mathcal{A}$ and $\mathcal{B}$ are model categories, and $F\colon\mathcal{A}\rightleftarrows\mathcal{B}\colon G$ is a Quillen equivalence between them, there is [17] an induced equivalence of hammock localizations $\mathrm{L}^{\!\!\mathrm{H}}\mathcal{A}\simeq\mathrm{L}^{\!\!\mathrm{H}}\mathcal{B}$, and thus of underlying $\infty$-categories $\mathrm{N}^{\mathrm{H}}\mathcal{A}\simeq\mathrm{N}^{\mathrm{H}}\mathcal{B}$.