Kerodon

Remark 9.2.1.8. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $W$ be a collection of morphisms of $\operatorname{\mathcal{C}}$. Then the collection of $W$-local objects is closed under the formation of all limits which exist in $\operatorname{\mathcal{C}}$ (see Corollary 7.4.1.19). Similarly, the collection of $W$-colocal objects is closed under the formation of all colimits which exist in $\operatorname{\mathcal{C}}$.