Notation 6.3.1.1. Let $\operatorname{\mathcal{C}}$ be a simplicial set, let $W$ be a collection of edges of $\operatorname{\mathcal{C}}$, and let $\operatorname{\mathcal{E}}$ be an $\infty $-category. We let $\operatorname{Fun}( \operatorname{\mathcal{C}}[W^{-1}], \operatorname{\mathcal{E}})$ denote the full subcategory of $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{E}})$ spanned by those morphisms $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{E}}$ that carry each edge of $W$ to an isomorphism in $\operatorname{\mathcal{E}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$