# Kerodon

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Definition 7.1.3.4. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty$-categories and let $K$ be a simplicial set. We will say that $F$ preserves $K$-indexed limits if, for every limit diagram $\overline{q}: K^{\triangleleft } \rightarrow \operatorname{\mathcal{C}}$, the composite map $(F \circ \overline{q}): K^{\triangleleft } \rightarrow \operatorname{\mathcal{D}}$ is a limit diagram in $\operatorname{\mathcal{D}}$. We will say that $F$ preserves $K$-indexed colimits if, for every colimit diagram $\overline{q}: K^{\triangleright } \rightarrow \operatorname{\mathcal{C}}$, the composite map $(F \circ \overline{q}): K^{\triangleright } \rightarrow \operatorname{\mathcal{D}}$ is a colimit diagram in $\operatorname{\mathcal{D}}$.