spectrum (Rev #3, changes)

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

A **spectrum** (or $\Omega$-**spectrum**) is a prespectrum in which each $e_n$ is an equivalence.

$$Spectrum\equiv \sum _{E:SpectrumPreSpectrum}\prod _{n:\mathbb{Z}}IsEquiv({e}_{n})$$ \Spectrum \equiv \sum_{E :~~ \Spectrum}~~ \PreSpectrum} \prod_{n : \mathbb{Z}} \IsEquiv~~ e_n)~~ (e_n)

- spectrification?
- homotopy group of spectrum?
- smash product of spectra?
- coproduct of spectra?
- product of spectra?
- Eilienberg-MacLane spectrum?
- Suspension spectrum?

- cohomology
- homology?
- spectral sequences
- synthetic homotopy theory?

Revision on December 18, 2018 at 08:11:00 by Ali Caglayan. See the history of this page for a list of all contributions to it.