Kerodon

Remark 7.5.6.13. Let $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Set_{\Delta }}$ be a diagram of simplicial sets, let $\theta : \underset { \longrightarrow }{\mathrm{holim}}( \mathscr {F} ) \twoheadrightarrow \varinjlim ( \mathscr {F} )$ be the comparison map of Remark 5.3.2.9, and let $\lambda : \varinjlim ( \mathscr {F}_{+} ) \xrightarrow {\sim } \underset { \longrightarrow }{\mathrm{holim}}( \mathscr {F} )$ be the isomorphism of Proposition 7.5.6.12. Then the composition $(\theta \circ \lambda ): \varinjlim ( \mathscr {F}_{+} ) \rightarrow \varinjlim ( \mathscr {F} )$ is induced by the natural transformation $\alpha : \mathscr {F}_{+} \twoheadrightarrow \mathscr {F}$ appearing in Construction 7.5.6.8.