The word “stable” in stable homotopy
theory means the stability under taking suspensions.
By the Freudenthal suspension theorem, the map between
homotopy groups
induced by the suspension is an isomorphism for
k
large enough. This theorem suggested to define a
category whose objects are based
CWcomplexes
and the set of morphsims from
X
to
Y
is
The resulting category is the most elementary form of
the stable homotopy category.
