Timeline for Maximal Cisinski model structure on simplicial sets
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 8, 2022 at 11:53 | vote | accept | Valery Isaev | ||
| Feb 8, 2022 at 10:50 | comment | added | Valery Isaev | @TimCampion The less weak equivalences you have, the more objects you'll get in the homotopy category. So, with the "maximal" model structure, you get the largest homotopy category. I just think it's more convenient to think about it in this way. | |
| Feb 8, 2022 at 2:12 | comment | added | Tim Campion | I'm confused by the terminology "maximal model structure". I suppose it has the maximal number of fibrations for given cofibrations, but I think I've more often heard it called "minimal" since it has the fewest weak equivalences. Rosicky and Tholen call it the "left-determined" model structure for a class of cofibrations. | |
| Aug 2, 2019 at 0:36 | answer | added | Matt Feller | timeline score: 7 | |
| Aug 1, 2017 at 7:03 | comment | added | Andrea Gagna | And there is even another issue. On his paper Catégories dérivables he defines a variation of the notion of model structure, which has all the right to be called a Cisinski model structure (although it is way less popular then model structures on presheaves categories). | |
| Jul 31, 2017 at 19:39 | comment | added | David White | My point was that the term should be defined in the question. It's certainly not well-known terminology. Cisinski's papers on this are only about 10 years old! | |
| Jul 31, 2017 at 17:56 | comment | added | Valery Isaev | @DavidWhite ncatlab.org/nlab/show/Cisinski+model+structure | |
| Jul 31, 2017 at 17:54 | comment | added | David White | What is a Cisinski model structure? | |
| Jul 29, 2017 at 13:52 | answer | added | Andrea Gagna | timeline score: 8 | |
| Jul 29, 2017 at 10:08 | comment | added | Valery Isaev | @DavidRoberts Yes, this is the condition and it implies that the trivial fibrations are the same as in the Quillen (or Joyal) model structure. | |
| Jul 29, 2017 at 10:06 | comment | added | David Roberts♦ | Ah, I was under the impression that the condition was that the cofibrations were the monos. | |
| Jul 29, 2017 at 9:47 | comment | added | Valery Isaev | @DavidRoberts No since trivial fibrations must be weak equivalences. If $X$ is a nontrivial contractible Kan complex, then $X \to 1$ is a trivial fibration, but not an iso. | |
| Jul 29, 2017 at 9:41 | comment | added | David Roberts♦ | So taking the class of weak equivalences to be the isos doesn't work? | |
| Jul 29, 2017 at 7:13 | history | asked | Valery Isaev | CC BY-SA 3.0 |