Example 3.42.
Let \(K\) be an \((n+1)\)-gerbe in \(T\), and consider two maps \(a,b\colon * \to K\). Define \(P\) as the following pullback:
Then \(P\) is an \(n\)-gerbe. Indeed, the map \(b\colon * \to K\) is an \(n\)-gerbe by the cancellation properties of truncated and connected maps from Lemma 3.7 and Corollary 3.33, hence the base change \(P \to *\) is also an \(n\)-gerbe.