Remark 8.5.4.15. The simplicial set $\operatorname{Spine}[\operatorname{\mathbf{Z}}]$ is weakly contractible. This follows from Remark 8.5.4.14, since the $\infty $-category $\operatorname{N}_{\bullet }( \operatorname{\mathbf{Z}})$ is filtered and therefore weakly contractible (Proposition 7.2.4.9). Alternatively, it can be deduced from Example 3.6.4.4, since the geometric realization $| \operatorname{Spine}[\operatorname{\mathbf{Z}}] |$ is homeomorphic to the set of real numbers $\mathbf{R}$ (endowed with its usual topology).

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