## Idea ## Definition A **spectrum** (or $\Omega$-**spectrum**) is a [[prespectrum]] $E$ in which each pointed map $e_n$ is an equivalence. $$\Spectrum \equiv \sum_{E : \PreSpectrum} \prod_{n : \mathbb{Z}} \IsEquiv (e_n)$$ ## Properties * [[spectrification]] * [[homotopy group of spectrum]] * [[smash product of spectra]] * [[coproduct of spectra]] * [[product of spectra]] * [[Eilienberg-MacLane spectrum]] * [[Suspension spectrum]] ## See also * [[cohomology]] * [[homology]] * [[spectral sequences]] * [[synthetic homotopy theory]] * [[prespectrum]] ## References * [[HoTT book]] * [[On the Formalization of Higher Inductive Types and Synthetic Homotopy Theory]]