Complexes concentrated in one degree

Example 6.1.9. Given an object \(A \in \Aa \) and \(k \in \Z \), we let \(A[k]\) denote the chain complex consisting of \(A\) concentrated in degree \(k\), meaning that \(A[k]_k := A\) while \(A[k]_n = 0\) for all \(n \neq k\); all boundary maps of \(A[k]\) are necessarily zero. This construction defines a fully faithful functor \((-)[k]\colon \Aa \hookrightarrow \Ch (\Aa )\) for all \(k\).