Remark 9.2.5.12 (Monotonicity). Let $\kappa $ be a regular cardinal and let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a $\kappa $-left exact functor of $\infty $-categories. Then $F$ is also $\kappa '$-left exact, for any regular cardinal $\kappa ' \leq \kappa $ (see Remark 9.1.1.9).
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