Definition 3.48.
Let \(n\geq1\), let \(X\) be an \(n\)-gerbe, and consider \(A \in \Ab(T_{\leq 0})\). We say that \(X\) is banded by \(A\) if it comes equipped with an isomorphism \(\pi_n X \cong X \times A\) in \(E_n\Grp((T_{/X})_{\leq 0})\). We denote by
\[\Gerb_n^A(T)\]
the anima of pairs consisting of an \(n\)-gerbe \(X\) together with an isomorphism \(\pi_n X \cong X \times A\). Its morphisms are the band-preserving isomorphisms of \(n\)-gerbes.