Homotopy Type Theory
spectrum

Idea

Definition

A prespectrum is a sequence of pointed types? E:𝒰 *E: \mathbb{Z} \to \mathcal{U}_* and a sequence of pointed maps e:(n:)E nΩE n+1e : (n : \mathbb{Z}) \to E_n \to \Omega E_{n+1}. Typically a prespectrum is denoted EE when it is clear.

A spectrum (or Ω\Omega-spectrum) is a prespectrum in which each e ne_n is an equivalence.

Spectrum E:PreSpectrum n:IsEquiv(e n)\Spectrum \equiv \sum_{E : \PreSpectrum} \prod_{n : \mathbb{Z}} \IsEquiv (e_n)

Properties

See also

References