Definition
Let \(f:A^\bullet\to B^\bullet\) be a map of complexes. The mapping cone \(C(f)^\bullet\) is the following complex:
\begin{align*} C(f)^{\bullet} &= A^{\bullet}[1] \oplus B^{\bullet} \\ &= \dots \to A^{n}\oplus B^{n-1} \to A^{n+1}\oplus B^n\to A^{n+2}\oplus B^{n+1}\to \dots \end{align*}with differential
\begin{align*} d_{C(f)^{\bullet}} = \begin{pmatrix} d_{A[1]} & 0 \\ f[1] & d_{B} \end{pmatrix} \end{align*}acting as though on column vectors.