Definition 9.2.5.5. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor between $\infty $-categories. We say that $F$ is left exact if, for every left fibration $\widetilde{\operatorname{\mathcal{D}}} \rightarrow \operatorname{\mathcal{D}}$ where the $\infty $-category $\widetilde{\operatorname{\mathcal{D}}}$ is cofiltered, the $\infty $-category $\widetilde{\operatorname{\mathcal{C}}} = \operatorname{\mathcal{C}}\times _{\operatorname{\mathcal{D}}} \widetilde{\operatorname{\mathcal{D}}}$ is also cofiltered.
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