Timeline for Defining hom spaces in the derived category as limits of hom spaces in the homotopy category
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 1, 2019 at 5:09 | comment | added | SashaP | @Denis-CharlesCisinski Oh, you're completely right, not sure what I had in mind back then. I've edited the answer. Thank you! | |
| Feb 1, 2019 at 5:08 | history | edited | SashaP | CC BY-SA 4.0 |
deleted 259 characters in body
|
| Jan 31, 2019 at 15:48 | comment | added | D.-C. Cisinski | @SashaP Your argument about part B are not correct. The colimits in A are indexed by maps up to chain-homotopy equivalences. However, in B, we cannot work up to chain homotopy equivalence (because we precisely do not want to take $H^0$ of the Hom's), so that the colimits are indexed by categories which are not filtered and are thus much more complicated to compute. In fact the isomorphisms suggested in B do not hold unless $C$ is trivial. | |
| Jan 5, 2017 at 19:06 | vote | accept | Saal Hardali | ||
| Oct 9, 2016 at 14:55 | history | edited | David White | CC BY-SA 3.0 |
Fixed minor typos, since it was on the front page anyway
|
| Sep 7, 2016 at 14:27 | comment | added | SashaP | @SaalHardali I tried to elaborate, please let me know if something is unclear. | |
| Sep 7, 2016 at 14:27 | history | edited | SashaP | CC BY-SA 3.0 |
added 474 characters in body
|
| Sep 7, 2016 at 0:13 | comment | added | Saal Hardali | You are completely right about the "not internal". It's obviously a bifunctor to the category of complexes of k modulez if C is a k-linear category. I dont understand what you said about the first being a formal consequence. Could you elaborate on why that's true? If it is indeed so than we can get the first by nothing just taking zeroth cohomology and using the fact it commutes with filtered colimits. | |
| Sep 6, 2016 at 21:20 | history | answered | SashaP | CC BY-SA 3.0 |