Kerodon

Remark 8.5.4.15. The simplicial set $\operatorname{Spine}[\operatorname{\mathbf{Z}}]$ is weakly contractible. In fact, the inclusion $\{ 0\} \hookrightarrow \operatorname{Spine}[\operatorname{\mathbf{Z}}]$ is anodyne, since it can be realized as an iterated pushout of the inclusion maps $\{ 0\} \hookrightarrow \Delta ^1$ and $\{ 1\} \hookrightarrow \Delta ^1$. 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).