Morphism of spectra

Definition 3.2.2 (Morphism of spectra). Let \(E=(E_m,\sigma _m)\) and \(F=(F_m,\tau _m)\) be spectra. A morphism of spectra \(f\colon E\to F\) consists of pointed maps \[ f_m\colon E_m\to F_m \qquad (m\geq 0) \] together with chosen homotopies making the following squares commute for every \(m\geq 0\):

For \(k<0\), we extend \(f\) to the negative levels by setting \(f_k:=\Omega ^{-k}f_0\colon E_k\to F_k\).