conservative functor between quasicategories

Let \(\mathcal{C}, \mathcal{D}\) be infinity categories and \(\mathcal{F}: \mathcal{C} \rightarrow \mathcal{D}\) a functor between infinity categories Then \(\mathcal{F}\) is said to be conservative, if for all 1-simplices \(f: x \rightarrow y \in \mathcal{C}_1\), such that

\begin{align*} \mathcal{F}(f): \mathcal{F}(x) \rightarrow \mathcal{F}(y) \end{align*}

is an equivalence, then \(f\) was already an equivalence