Timeline for If a t-truncation of the unit object in a stable homotopy category is a ring object up to homotopy, can it be lifted to a ring spectrum? What about the Postnikov t-truncations of the sphere spectrum?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 23, 2012 at 19:36 | vote | accept | Mikhail Bondarko | ||
| Nov 18, 2012 at 19:43 | comment | added | Marc Hoyois | I think you can always take cofibrant replacements within the category of $A_\infty$ or $E_\infty$ objects (cf. beginning of section 5 in the paper), so the cofibrancy assumption can be safely ignored. | |
| Nov 16, 2012 at 20:10 | comment | added | Mikhail Bondarko | Dear Marc, thank you very much! This seems to be a very useful reference! I will try to understand it completely (in particular, I wonder whether I can always assume $S$ to be cofibrant). | |
| Nov 16, 2012 at 14:48 | history | edited | David White | CC BY-SA 3.0 |
Fixed typos
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| Nov 16, 2012 at 6:25 | comment | added | Marc Hoyois | If I understand the question correctly, it is answered quite generally in arxiv.org/pdf/1012.3301v2.pdf, Theorem 5.16 (where $l_i$ means the $i$th truncation you're considering). This applies not only to $t$-structures but also to more general filtration such as the motivic slice filtration. | |
| Nov 16, 2012 at 5:33 | answer | added | Eric Wofsey | timeline score: 4 | |
| Nov 16, 2012 at 4:47 | history | asked | Mikhail Bondarko | CC BY-SA 3.0 |