Kerodon

Corollary 7.5.8.8. Let $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Set_{\Delta }}$ be a diagram of simplicial sets, let $\theta : \underset { \longrightarrow }{\mathrm{holim}}( \mathscr {F} ) \rightarrow \varinjlim (\mathscr {F})$ be the comparison map of Remark 5.3.2.9, and let $W$ denote the collection of all horizontal edges of the homotopy colimit $ \underset { \longrightarrow }{\mathrm{holim}}( \mathscr {F} )$ (Definition 5.3.4.1). If $\mathscr {F}$ is projectively cofibrant (Definition 7.5.6.1), then $\theta $ exhibits $\varinjlim ( \mathscr {F} )$ as a localization of $ \underset { \longrightarrow }{\mathrm{holim}}( \mathscr {F} )$ with respect to $W$.