Timeline for Is the $\infty$-category of spectra “convenient”?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Aug 9, 2021 at 20:05 | history | edited | Emily | CC BY-SA 4.0 |
typos
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| Mar 9, 2019 at 21:26 | history | edited | Emily | CC BY-SA 4.0 |
Trivial edit: changed phrasing
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| Feb 9, 2019 at 14:15 | history | edited | Emily | CC BY-SA 4.0 |
formatting
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| Feb 9, 2019 at 3:34 | vote | accept | Emily | ||
| Feb 9, 2019 at 3:34 | comment | added | Emily | @DylanWilson Thank you very much for the great pointers! (I have deleted the footnote.) | |
| Feb 9, 2019 at 3:34 | history | edited | Emily | CC BY-SA 4.0 |
Deleted footnote and corrected a typo
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| Feb 9, 2019 at 3:00 | answer | added | Peter May | timeline score: 20 | |
| Feb 9, 2019 at 2:42 | comment | added | Dylan Wilson | Some references: 4b) follows from the universal properties: $\mathsf{Spaces}_*$ is the unit object in the symmetric monoidal $\infty$-category of presentable pointed $\infty$-categories, and $\mathsf{Sp}$ is a pointed, presentably symmetric monoidal $\infty$-category so the essentially unique colimit-preserving functor from $\mathsf{Spaces}_*$ determined by $S^0$ has an essentially unique refinement to a symmetric monoidal functor. (cf. HA.4.8.2). 4a) right adjoints to symmetric monoidal functors are automatically lax monoidal (HA.7.3.2.7). And 5) can be proven directly or use HA.6.1.1.28 | |
| Feb 9, 2019 at 2:24 | comment | added | Dylan Wilson | Yes of course. $\Sigma^{\infty}$ is symmetric monoidal, $\Omega^{\infty}$ is lax symmetric monoidal, and $\Omega^{\infty}\Sigma^{\infty}X$ is equivalent to $\mathrm{colim} \Omega^n\Sigma^nX$. Also your footnote "2" is incorrect- the loops-infinity suspension-infinity adjunction is just an adjunction, not an equivalence. | |
| Feb 8, 2019 at 23:10 | history | asked | Emily | CC BY-SA 4.0 |