Editing Natural transformation (section)

=== Hurewicz homomorphism ===
Functors and natural transformations abound in [[algebraic topology]], with the [[Hurewicz theorem|Hurewicz homomorphisms]] serving as examples.  For any [[pointed topological space]] <math>(X,x)</math> and positive integer <math>n</math> there exists a [[group homomorphism]]

: <math>h_n \colon \pi_n(X,x) \to H_n(X)</math>

from the <math>n</math>-th [[homotopy group]] of <math>(X,x)</math> to the <math>n</math>-th [[Singular homology|homology group]] of <math>X</math>.  Both <math>\pi_n</math> and <math>H_n</math> are functors from the category '''Top<sup>*</sup>''' of pointed topological spaces to the category '''Grp''' of groups, and <math>h_n</math> is a natural transformation from  <math>\pi_n</math> to <math>H_n</math>.