Stable homotopy category

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In homotopy theory, the stable homotopy category can be thought to be related to the category of spaces and continuous maps in the same way that stable homotopy groups are related to (standard) homotopy groups.

Formally, the objects in the category are omega spectra, and the morphisms are homotopy classes of maps of spectra; hence, we may think of this category as eliminating the distinction between spaces X and Y which are not homeomorphic, but satisy

ΣⁿX = ΣⁿY

for some natural number n. (Here Σ denotes the suspension functor.)