Functoriality of homology
= Functoriality of homology
A <continuous map> $f:X\to Y$ induces homomorphisms $f_*:H_n(X)\to H_n(Y)$ satisfying $(g\circ f)_*=g_*\circ f_*$ and $(\operatorname{id}_X)_*=\operatorname{id}_{H_n(X)}$.
= Functoriality of homology
A <continuous map> $f:X\to Y$ induces homomorphisms $f_*:H_n(X)\to H_n(Y)$ satisfying $(g\circ f)_*=g_*\circ f_*$ and $(\operatorname{id}_X)_*=\operatorname{id}_{H_n(X)}$.