spectrum (changes)

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A ~~ prespectrum~~ spectrum~~ is~~ (or~~ a~~~~ sequence~~~~ of~~~~pointed types?~~$\Omega$ -~~$E: \mathbb{Z} \to \mathcal{U}_*$~~**spectrum**~~ ~~ )~~ and~~ is a~~ sequence~~~~ of~~~~ pointed~~~~ maps~~~~$e : (n : \mathbb{Z}) \to E_n \to \Omega E_{n+1}$~~prespectrum~~ .~~~~ Typically~~~~ a~~~~ prespectrum~~~~ is~~~~ denoted~~$E$ ~~ when~~ in~~ it~~ which~~ is~~ each~~ clear.~~ pointed map$e_n$ is an equivalence.

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

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

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

- 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?
- prespectrum

Last revised on May 1, 2022 at 19:21:25. See the history of this page for a list of all contributions to it.