Timeline for Weakening the excision condition for spectra
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 20, 2021 at 22:32 | history | edited | Emily | CC BY-SA 4.0 |
added 507 characters in body
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| Aug 20, 2021 at 22:32 | comment | added | Emily | Thanks Maxime and Marc! I've updated the question to be more precise. | |
| Aug 19, 2021 at 16:23 | comment | added | Marc Hoyois | You could relax the excision condition to only hold up to group completion, with Segal-excision giving the pointwise $E_\infty$-monoid structure. A connective such functor (i.e., one that preserves $n$-connective spaces for all $n$) would then just be an $E_\infty$-monoid (equipped with a connective delooping of its group completion, but that is unique). | |
| Aug 19, 2021 at 16:21 | comment | added | Marc Hoyois | @MaximeRamzi It makes sense here because $\mathrm{Fin}_*$ has a zero object, so one has projections from the coproduct. | |
| Aug 19, 2021 at 9:25 | comment | added | Maxime Ramzi | I don't know the answer to your question, but be careful about point 1 for $\Gamma$-spaces : a $\Gamma$-space is not defined by sending coproducts to products; in fact that would not make sense (it is covariant from finite pointed sets to spaces). The Segal condition is slightly more subtle (in particular it is not a "Lawvere theory"-type definition and that is very important) | |
| Aug 18, 2021 at 23:24 | history | asked | Emily | CC BY-SA 4.0 |