Notation 8.5.4.12. Let $\operatorname{Spine}[\operatorname{\mathbf{Z}}]$ denote the $1$-dimensional simplicial set associated to the directed graph
\[ \cdots \rightarrow -2 \rightarrow -1 \rightarrow 0 \rightarrow 1 \rightarrow 2 \rightarrow \cdots \]
We let $Q: \operatorname{Spine}[\operatorname{\mathbf{Z}}] \rightarrow \operatorname{N}_{\bullet }( \operatorname{Idem})$ be the morphism of simplicial sets corresponding to the diagram
\[ \cdots \rightarrow X \xrightarrow {e} X \xrightarrow {e} X \xrightarrow {e} X \xrightarrow {e} X \rightarrow \cdots \]
in the category $\operatorname{Idem}$.