singular homology functor

Given category Top, the singular homology functor is defined as functor

\begin{align*} \mathrm{H}_n: \mathrm{Top} \rightarrow& \mathrm{Ab} \\ X \mapsto& H_n(X) \\ \end{align*}

see:

• singular homology group
• chain homology functor
• continuous map induces group homomorphism on singular homology groups