Timeline for Model categories of simplicial objects
Current License: CC BY-SA 2.5
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 13, 2011 at 19:04 | comment | added | Harry Gindi | @Sean: Look at Charles's comment. It's not clear what the OP wants to consider to be a "reasonable model category". As I said before in a deleted comment (that Jeff references), if a category D is complete-cocomplete, we can equip $sD=D^{\Delta^{op}}$ with the Reedy model structure attached to the trival one on $D$. This isn't really a useful one, but it certainly is one. | |
| Jan 13, 2011 at 16:40 | comment | added | Sean Tilson | But $C$ is fixed and we want to find a model category $M$ s.t. $M^C$ is $sC$. I certainly agree that $sC=C^{\Delta^{op}}$ but C isn't a model category, according to the question, and I thought $M$ was supposed to be. | |
| Jan 13, 2011 at 4:00 | comment | added | Harry Gindi | $M^{\Delta^{op}}$ | |
| Jan 13, 2011 at 1:29 | comment | added | Sean Tilson | I am a bit confused, and this is probably just my ignorance, but how is $sC$ (simplicial objects in $C$) realized as $M^C$ where $M$ is a model category? | |
| Jan 12, 2011 at 21:37 | comment | added | Harry Gindi | Dear Charles, I had a comment to a similar effect that I deleted so my comment above (asking the OP to accept your answer) would rise to visibility. | |
| Jan 12, 2011 at 21:11 | comment | added | Charles Rezk | The real question is: what is a "reasonable" model category structure on $s\mathcal{C}$? What constraints should it satisfy? | |
| Jan 12, 2011 at 19:34 | comment | added | Harry Gindi | @Jeff: True, but Charles also gave a very interesting answer that seems more in line with what you were trying to ask originally. I would not be offended if you unaccepted my answer and accepted his. | |
| Jan 12, 2011 at 19:31 | comment | added | Jeff Strom | I'm tempted to let you think that I asked the smartest possible question, but I didn't. I originally intended $\mathcal{C}$ to be any category. But I think we can see that if $s\mathcal{C}$ has a model structure, then $\mathcal{C}$ must be complete-cocomplete, and then we can use the trivial structure on $\mathcal{C}$ and follow Harry's method. So the question in which we assume a given model category on $\mathcal{C}$ is harder and more interesting, and what was answered. | |
| Jan 12, 2011 at 19:14 | comment | added | Oscar Randal-Williams | I thought the questions was: when does the category of simplicial objects in $\mathcal{C}$ have a model structure, without assuming $\mathcal{C}$ is a model category. | |
| Jan 12, 2011 at 19:04 | history | edited | Harry Gindi | CC BY-SA 2.5 |
added 2 characters in body
|
| Jan 12, 2011 at 19:00 | comment | added | Harry Gindi | No problem! | |
| Jan 12, 2011 at 18:58 | history | edited | Harry Gindi | CC BY-SA 2.5 |
added 519 characters in body
|
| Jan 12, 2011 at 18:54 | vote | accept | Jeff Strom | ||
| Jan 12, 2011 at 18:53 | comment | added | Jeff Strom | I stand corrected and informed, thanks! | |
| Jan 12, 2011 at 18:51 | history | answered | Harry Gindi | CC BY-SA 2.5 |