Timeline for A Model Category of Segal Spaces?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Apr 26, 2017 at 10:54 | history | suggested | Manuel Bärenz | CC BY-SA 3.0 |
Fixed LaTeX
|
| Apr 26, 2017 at 10:27 | review | Suggested edits | |||
| S Apr 26, 2017 at 10:54 | |||||
| Jun 28, 2010 at 17:51 | comment | added | Chris Schommer-Pries | Okay. I see. So I guess that's one reason people look for a model structure for Segal categories on the category of Segal Pre-categories (Simplicial spaces with zeroeth space discrete). Then you can get the fibrant objects to be Segal cats, but not otherwise. After a moment reflection I think I am starting to really like this idea that the Segal Cats should actually be the cofibrant-fibrant objects on a model structure on simplicial spaces. | |
| Jun 28, 2010 at 17:23 | comment | added | Charles Rezk | I don't see how Segal categories (or something like them) can be picked out as fibrant objects in simplicial spaces; it's hard to map to a Segal category from a Segal space, so fibrant replacement would be problematic. But it's easier to map from a Segal category to a Segal space, so it seems plausible that "Segal categorification" can be implemented as a kind of cofibrant replacement. | |
| Jun 28, 2010 at 17:12 | comment | added | Chris Schommer-Pries | I'm imagining a situation which is reminiscent of the projective, injective and Reedy model structures, where there are three equivalent model structures on a single category (in this case simplicial spaces), all with the same weak equivalences. However these three model structures should have different fibrant objects. In one it is the Segal spaces, in another it is the Segal categories and in the third it is the complete Segal spaces. Is this fantasy too much to hope for? | |
| Jun 28, 2010 at 17:12 | answer | added | Charles Rezk | timeline score: 10 | |
| Jun 28, 2010 at 16:59 | comment | added | Chris Schommer-Pries | um, yes. What I'd really like is for the weak equivalences to be exactly the same as the weak equiv in your complete Segal space model structure. That might be asking too much. I'd settle for just the weak equivalences between the fibrant objects (i.e. the Segal spaces) to be the same, i.e. the DK-equivalences. | |
| Jun 28, 2010 at 16:07 | comment | added | Charles Rezk | I don't understand property 3. Do you mean the weak equivalences between fibrant objects are the DK-equivalences? | |
| Jun 28, 2010 at 15:46 | history | edited | Chris Schommer-Pries | CC BY-SA 2.5 |
grammar fixed, improved exposition.
|
| Jun 27, 2010 at 19:59 | history | asked | Chris Schommer-Pries | CC BY-SA 2.5 |