Graded abelian groups

Convention 3.1.1 (Graded abelian groups). A graded abelian group is a sequence \(A_* = (A_n)_{n \in \Z }\) of abelian groups indexed by the integers. These form a 1-category \(\Ab ^{\Z }\) whose morphisms \(f_*\colon A_* \to B_*\) consist of homomorphisms \(f_n\colon A_n \to B_n\) for each \(n \in \Z \).