We apply the tools of stable homotopy theory to the study of modules over the mod $p$ Steenrod algebra $A^{*}$. More precisely, let $A$ be the dual of $A^{*}$; then we study the category $\mathsf{stable}(A)$ of unbounded cochain complexes of injective co modules over $A$, in which the morphisms are cochain homotopy classes of maps.
