Timeline for Complexes in stable categories
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 21, 2018 at 11:55 | vote | accept | CommunityBot | ||
| Dec 27, 2017 at 2:51 | history | edited | YCor |
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| Dec 26, 2017 at 23:14 | answer | added | user13113 | timeline score: 5 | |
| Dec 25, 2017 at 3:59 | comment | added | Dmitri Pavlov | The homotopies d_k d_{k+1}≃0 must themselves fit into a higher coherence data. If you add this data, then you indeed get an equivalence of ∞-categories between chain complexes and simplicial objects. | |
| Dec 25, 2017 at 1:03 | comment | added | Dylan Wilson | Another issue is that I don’t see how you’re able to take those iterated cofibers (or equivalently, to form that diagram to take the colimit) without remembering witnesses for those nullhomotopies (and compatibilities between them). | |
| Dec 25, 2017 at 1:00 | comment | added | Dylan Wilson | I don’t think they are equivalent. When n=2 the obstruction for such a complex to arise from a little filtration is the Toda bracket of the three differentials. Another issue is that I don’t think your category of complexes will have hocolims. | |
| Dec 24, 2017 at 23:52 | history | edited | user13113 | CC BY-SA 3.0 |
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| Dec 24, 2017 at 23:47 | history | asked | user13113 | CC BY-SA 3.0 |