Timeline for triangulated vs. dg/A-infinity
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Feb 18, 2012 at 9:29 | comment | added | Karol Szumiło | There are many interesting triangulated categories without dg-models, i.e. the stable homotopy category. There is a new paper by Stefan Schwede (arxiv.org/abs/1201.0899) addressing the question of how and to what extent triangulated categories with such "topological models" can fail to have "algebraic models" in the spirit of dg-categories. | |
| Oct 17, 2009 at 21:07 | answer | added | David Ben-Zvi | timeline score: 34 | |
| Oct 17, 2009 at 19:35 | answer | added | Reid Barton | timeline score: 4 | |
| Oct 17, 2009 at 11:43 | answer | added | Urs Schreiber | timeline score: 10 | |
| Oct 17, 2009 at 10:44 | answer | added | Urs Schreiber | timeline score: 3 | |
| Oct 17, 2009 at 10:31 | answer | added | Urs Schreiber | timeline score: 10 | |
| Oct 17, 2009 at 4:00 | answer | added | Ben Webster♦ | timeline score: 14 | |
| Oct 17, 2009 at 3:56 | comment | added | Kevin Walker | By "semi-triangulated" I meant, vaguely, that not all of the axioms of a triangulated category are satisfied. More specifically, not every morphism has a mapping cone. But when morphisms f, g and fg each have a mapping cone, the octahedral axioms is satisfied. Also, the subset of morphisms which have mapping cones generates the category. It's the structure you would have for a subcategory of a triangulated category which is not a sub-triangulated-category. | |
| Oct 17, 2009 at 3:34 | answer | added | Tyler Lawson | timeline score: 10 | |
| Oct 17, 2009 at 2:11 | vote | accept | Kevin Walker | ||
| Oct 17, 2009 at 2:05 | comment | added | Greg Stevenson | Out of curiousity what do you mean by "semi-triangulated"? You might find it worthwhile to look at [A. Beligiannis and I. Reiten: ''Homological and Homotopical Aspects of Torsion Theories''] if you are interested in generalizations of the notion of triangulation (and you haven't already looked at it). I don't know how pre-triangulated categories in their sense fits into the enhanced picture. If someone knows this and would like to share that would be great (but I don't want to hijack the question if this isn't related). | |
| Oct 17, 2009 at 1:27 | answer | added | Greg Stevenson | timeline score: 22 | |
| Oct 17, 2009 at 0:21 | history | asked | Kevin Walker | CC BY-SA 2.5 |