Additive indexing category for chain complexes
= Additive indexing category for chain complexes
{title2=$\mathbf Z$}
Let $\mathbf Z$ have the <integer>[integers] as objects, with $\mathbf Z(n,p)=\mathbb Z$ for $p=n$ or $p=n-1$ and zero otherwise. Composition is bilinear, the generator of $\mathbf Z(n,n)$ is the identity, and the composite of two degree-lowering generators is zero. Additive functors $\mathbf Z\to\mathcal A$ are exactly chain complexes in the additive category $\mathcal A$.