Timeline for limits and products stable $\infty$-category
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 17 at 18:59 | comment | added | Maxime Ramzi | @user141099 : sorry for the long time without a reply - see arxiv.org/abs/2008.03758 Corollary 2.18, or math.mit.edu/~jshah/thesis.pdf Corollary 12.3 ! | |
| Dec 25, 2023 at 0:37 | comment | added | user141099 | Could you please provide a reference for the Bousfield-Kan formula which proves that $\lim_{I^{op}}$ is the totalisation of a cosimplicial object? | |
| Nov 2, 2022 at 10:11 | history | edited | Maxime Ramzi | CC BY-SA 4.0 |
added 183 characters in body
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| Nov 2, 2022 at 10:10 | comment | added | Maxime Ramzi | Right, maybe I should stress that more than what I wrote. I agree with this | |
| Nov 1, 2022 at 22:38 | comment | added | D.-C. Cisinski | Yes, the pullback does precisely that. I just wanted to insist on the fact that the description of the limit as a fiber is only true in a stable context. | |
| Nov 1, 2022 at 21:45 | comment | added | Maxime Ramzi | @D.-C.Cisinski : doesn't this pullback exactly describe an equalizer ? (note that at the beginning of my answer I said "if you replace 'fiber sequence' by 'equalizer'", so I am not claiming that we get a fiber sequence in spaces, for that I agree with your comment) | |
| Nov 1, 2022 at 21:17 | comment | added | D.-C. Cisinski | Could you elaborate on that? I do not know how to prove this in spaces... Using the description of $\mathbb N$ as an infinite pushout, I only know how to produce $lim F_i$ as a pullback of the diagonal of the product of the $F_i$'s. In a pointed situation, that gives a fiber sequence $\prod_i\Omega F_i\to lim F_i\to\prod_i F_i$. In a stable context, of course, we can deloop and get the fiber sequence expressing the limit as a fiber. | |
| Nov 1, 2022 at 18:34 | comment | added | user197402 | Thank you very much for your answer! Ok I had the feeling that this was probably too optimistic. | |
| Nov 1, 2022 at 18:32 | vote | accept | user197402 | ||
| Nov 1, 2022 at 15:53 | history | answered | Maxime Ramzi | CC BY-SA 4.0 |