Kerodon

Remark 6.2.3.5. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $\operatorname{\mathcal{C}}' \subseteq \operatorname{\mathcal{C}}$ be a full subcategory, and let $W$ be a collection of morphisms in $\operatorname{\mathcal{C}}$. The following conditions are equivalent:

• Every object of $\operatorname{\mathcal{C}}'$ is $W$-local, in the sense of Definition 6.2.3.1.

• Every morphism of $W$ is $\operatorname{\mathcal{C}}'$-local equivalence, in the sense of Definition 6.2.2.1.