Timeline for Explicit generating acyclic cofibrations and right properness of a model category
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 12, 2019 at 0:39 | vote | accept | Tim Campion | ||
| Jan 12, 2019 at 0:29 | answer | added | D.-C. Cisinski | timeline score: 7 | |
| Mar 22, 2017 at 1:44 | answer | added | David White | timeline score: 3 | |
| Mar 16, 2017 at 1:37 | comment | added | Tim Campion | Interesting. Stanculescu somehow doesn't have to muck around with cylinder objects the way Cisinski and Olschok do. But in (3) I'm happy to assume more about the pseudo-generating set -- e.g. I'd be happy to assume that it forms what Cisinski calls a class of anodyne extensions with respect to some functorial cylinder. | |
| Mar 15, 2017 at 9:52 | comment | added | Philippe Gaucher | Your setting is very closed to the setting of model categories with a prescribed class of fibrant objects like in tac.mta.ca/tac/volumes/29/23/29-23.pdf because your pseudo-generating set of trivial cofibrations determines the fibrant objects (you probably already know the reference but in case you don't, I give it). | |
| Mar 15, 2017 at 4:23 | comment | added | Tim Campion | Good point -- and Cisinki's theory gives an explicit pseudo-generating set for the minimal model structure (as long as you have a generating set for the cofibrations = monomorphisms). It would certainly be surprising if this were always an actual generating set. So probably I should expect at most the other direction: that getting a handle on explicit generating acyclic cofibrations will often entail that one is working in a right proper model structure... | |
| Mar 14, 2017 at 10:11 | comment | added | Philippe Gaucher | In Cisinski's homotopy theory of toposes, the minimal model structure is always right proper (Remark 4.9 of his paper). And I don't believe that Condition 3 holds (I am not sure actually, it's why I am writing this comment). | |
| Mar 14, 2017 at 7:51 | history | asked | Tim Campion | CC BY-SA 3.0 |