ScalingStacks

Observation 5.1.7.

For \(n \geq 0\), it follows from [GH15, Lem. 6.1.9] that the map \(|j_n|_0 \colon |\partial c_n|_0 \rightarrow|c_n|_0\) is equivalent to the map \(S^{n-1} \rightarrow{\sf pt}.\) By induction, it follows that for \(k < n\), \(|j_n|_k \colon |\partial c_n|_k \rightarrow|c_n|_k\) is equivalent to the map \(\Sigma^k[S^{n-k-1}] \rightarrow\Sigma^k[{\sf pt}] = c_k\) induced by \(S^{n-k-1} \rightarrow{\sf pt}\).