ScalingStacks

Proposition 5.10. A map of stable $\infty$-categories ${\mathcal{A}}\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}{\mathcal{B}}$ is fully faithful if and only if $\Ho({\mathcal{A}})\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}\Ho({\mathcal{B}})$ is fully faithful.