Remark 9.1.1.8 (Monotonicity). Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $\kappa \leq \lambda $ be infinite cardinals. If $\operatorname{\mathcal{C}}$ is $\lambda $-filtered, then it is $\kappa $-filtered. In particular, if $\operatorname{\mathcal{C}}$ is $\lambda $-filtered, then it is filtered.
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