Timeline for Resolutions of unbounded complexes and homotopy (co)limits.
Current License: CC BY-SA 3.0
11 events
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| Nov 15, 2012 at 12:04 | answer | added | Leo Alonso | timeline score: 3 | |
| Nov 14, 2012 at 18:13 | comment | added | Richard Jennings | @Leo Alonso. That's exactly what I was wondering! They define the resolution of a complex as a cone, how can a cone be a bicomplex? What do they have to do with each other? I just don't know how to reinterpret that. So the resolution of a complex is a cone? Not another complex? | |
| Nov 14, 2012 at 9:48 | comment | added | Leo Alonso | Notice that "holim" in the sense of Bokstedt and Neeman's paper is not the usual Bousfield-Kan notion, but a non-functorial version based on the Milnor triangle, see Definition 2.1 on p. 213 of the paper. So it is not a bicomplex, it just a cone. | |
| Nov 14, 2012 at 6:43 | answer | added | David C | timeline score: 4 | |
| Nov 14, 2012 at 6:18 | comment | added | Mikhail Bondarko | Why do you think that resolutions are related with homotopy colimits? Also, could you fix the formula? | |
| Nov 14, 2012 at 5:59 | history | edited | Richard Jennings | CC BY-SA 3.0 |
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| Nov 14, 2012 at 5:53 | history | edited | Richard Jennings | CC BY-SA 3.0 |
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| Nov 14, 2012 at 5:44 | history | edited | Richard Jennings | CC BY-SA 3.0 |
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| Nov 14, 2012 at 5:38 | comment | added | Sasha | A resolution of complex $X$ is just a quasiisomorphism of $X$ with some other complex. The question is what properties you want to impose on this other complex. Usually people consider h-projective or h-injective resolutions and the statement is that you can construct one (sometimes). | |
| Nov 14, 2012 at 5:34 | history | edited | Sasha | CC BY-SA 3.0 |
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| Nov 14, 2012 at 5:29 | history | asked | Richard Jennings | CC BY-SA 3.0 |