Timeline for Unbounded acyclic resolutions
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Dec 15, 2022 at 15:34 | history | rollback | Jeremy Rickard |
Rollback to Revision 2
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| Dec 15, 2022 at 15:34 | comment | added | Jeremy Rickard | @NikolasKuhn Hmm, I thought I had a reason, but now I'm not so sure. I'll roll back to the previous version while I think about it. | |
| Dec 15, 2022 at 15:05 | comment | added | Nikolas Kuhn | Could you explain the statements about why the truncations are the homotopy limits of their further truncations? | |
| Dec 15, 2022 at 14:53 | comment | added | Jeremy Rickard | @R.vanDobbendeBruyn I think the proof that I've added shows that the extra hypotheses are sufficient. | |
| Dec 15, 2022 at 14:52 | history | edited | Jeremy Rickard | CC BY-SA 4.0 |
Added a proof with extra hypotheses.
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| Dec 15, 2022 at 14:41 | comment | added | Jeremy Rickard | @R.vanDobbendeBruyn I think I have an answer to the question with the added hypotheses, which I will edit into my previous answer if it survives the writing process, in which case the question in your comment is probably moot. | |
| Dec 15, 2022 at 14:23 | comment | added | R. van Dobben de Bruyn | P.S. I got a downvote on the question after the last edit (without a comment explaining, as usual). Do you think I should ask a different question instead with the extra hypothesis, given that your answer technically addresses the question as asked? | |
| Dec 14, 2022 at 23:05 | comment | added | R. van Dobben de Bruyn | I have now added the hypothesis that $F$ preserves products, like you suggested. There was already a hint of this hypothesis in the holim argument in my question. (Surely we can't "French trick" our way out of this by adding extra hypotheses until the statement becomes tautological?) | |
| Dec 14, 2022 at 22:18 | comment | added | R. van Dobben de Bruyn | Thanks for this example! My understanding here is that because $\mathbf{Mod}_A$ is AB4*, every complex $C^\bullet$ is the derived limit of its truncations $\tau_{\geq -p} C^\bullet$, so what goes wrong here is indeed preservation of (countable) products under $F$. But at the very least, the example shows that any positive result cannot be completely formal ― this is already a break with the bounded below case where no hypothesis is needed. | |
| Dec 14, 2022 at 18:24 | history | edited | Jeremy Rickard | CC BY-SA 4.0 |
Too many $R$'s
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| Dec 14, 2022 at 18:10 | history | answered | Jeremy Rickard | CC BY-SA 4.0 |