Timeline for Did anybody study split homotopy cartesian squares in triangulated categories?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 11, 2022 at 12:41 | comment | added | Mikhail Bondarko | Thank you! Yes, they are pullbacks and pushouts. Possibly, this will help me to find something useful. | |
| Nov 11, 2022 at 12:17 | comment | added | D.-C. Cisinski | The splitting condition seems to indicate that these actually are pullbacks (and pushouts)... | |
| Nov 11, 2022 at 12:12 | comment | added | D.-C. Cisinski | If you insist on triangulated categories (as opposed to stable $\infty$-categories, as Lennart rightfully suggests), this kind of things (at least the possibly non-splitted version) is discussed in Neeman's book Triangulated Categories (Annals of Math. Studies 148, Princeton Univ. Press) in Chapter 1, §1.4, pp. 52-60. The fact that these define "weak pullbacks" is discussed in Chapter 6, Example 1.6.2, page 184. | |
| Nov 11, 2022 at 11:40 | comment | added | Lennart Meier | This sounds like what is called a (homotopy) pushout square in stable infinity-category (or model category). The first chapter of Higher Algebra by Lurie should be relevant. (Topologist like e.g. the example of the singular chains on $U\cap V$, $U$, $V$ and $U\cup V$ for an open cover.) | |
| Nov 11, 2022 at 11:25 | history | asked | Mikhail Bondarko | CC BY-SA 4.0 |