Kerodon

Lemma 8.5.6.16. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $F: \operatorname{N}_{\bullet }( \operatorname{Ret}) \rightarrow \operatorname{\mathcal{C}}$ be a functor. Then the composition $\operatorname{Spine}[\operatorname{\mathbf{Z}}]^{\triangleleft } \xrightarrow { Q^{-} } \operatorname{N}_{\bullet }( \operatorname{Ret}) \xrightarrow {F} \operatorname{\mathcal{C}}$ is a limit diagram in $\operatorname{\mathcal{C}}$, and the composition $\operatorname{Spine}[\operatorname{\mathbf{Z}}]^{\triangleright } \xrightarrow {Q^{+}} \operatorname{N}_{\bullet }( \operatorname{Ret}) \xrightarrow { F} \operatorname{\mathcal{C}}$ is a colimit diagram in $\operatorname{\mathcal{C}}$.