Remark 9.3.3.4 (Monotonicity). Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $m \leq n$ be integers. If $f: X \rightarrow Y$ is an $m$-truncated morphism of $\operatorname{\mathcal{C}}$, then it is also $n$-truncated.
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