Spectrum (homotopy theory) Guide, Meaning , Facts, Information and Description
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
- En
- SEn
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.
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