Homotopy Type Theory
spectrum (Rev #1, changes)

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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:Spectrum n:IsEquiv(e n)\Spectrum \equiv \sum_{E : \Spectrum} \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

References

Revision on December 17, 2018 at 19:42:21 by Ali Caglayan. See the history of this page for a list of all contributions to it.