Spectrum (homotopy theory) - Definition

In mathematics, a spectrum in homotopy theory is an object in a category constructed for the purposes of stable homotopy theory, starting with the category of CW complexes and aiming to make the suspension functor S invertible. This construction is originally due to J. M. Boardman.

The objects of the category of spectra are sequences

E_n</sup>

of CW complexes as pointed spaces, such that

SE_n</sup>

is homeomorphic to a subcomplex of E_{n + 1</sup>.}

Morphisms in the category of spectra are defined in a non-obvious way, as a type of partial function, subject to an equivalence relation: essentially from the minimum mapping information that is possible, allowing S to be applied to bring any given cell into the domain.

The construction is related, on a conceptual level at least, to that of the derived category, but using spaces rather than algebra.