I am currently learning singular homology and one question gives these two chain complexes:
$A: 0 \rightarrow 0 \rightarrow \mathbb{Z} \rightarrow 0$
$B: 0 \rightarrow \mathbb{Z} \rightarrow \mathbb{Z} \rightarrow 0$
I am asked to compute a set of maps $A \rightarrow B$ and a set of chain homotopy classes of chain maps. I am puzzled by this question, because with singular complexes, even a single point set has $C_n$ isomorphic to $\mathbb{Z}$ for all $n$, so I don't see how we can have chain complexes that look like the ones above. I feel like I am missing something here.