# Kerodon

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Remark 4.6.2.4. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor between $\infty$-categories, so that $F$ induces a functor of homotopy categories $f: \mathrm{h} \mathit{\operatorname{\mathcal{C}}} \rightarrow \mathrm{h} \mathit{\operatorname{\mathcal{D}}}$. If $F$ is fully faithful, then $f$ is also fully faithful (see Remark 4.6.1.11). Beware that the converse is generally false.