Induced map on homology
= Induced map on homology
{title2=$f_*$}
A chain map sends cycles to cycles and boundaries to boundaries, and therefore induces $f_*:H_i(C)\to H_i(C')$ by $[x]\mapsto[f_i(x)]$.
= Induced map on homology
{title2=$f_*$}
A chain map sends cycles to cycles and boundaries to boundaries, and therefore induces $f_*:H_i(C)\to H_i(C')$ by $[x]\mapsto[f_i(x)]$.