Timeline for Presheaves on a complete Segal space
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 7, 2011 at 0:25 | comment | added | Mike Shulman | Beautiful! That's all I could have hoped for. Someone should really work all of this out and write it up. | |
| Dec 6, 2011 at 16:39 | history | edited | Charles Rezk | CC BY-SA 3.0 |
clarification
|
| Dec 6, 2011 at 16:22 | comment | added | Charles Rezk | (1) I mean Reedy fibration. It turns out that if W is a CSS, and f is a Reedy fibration with the above property, then X is also a CSS, and thus f (being a Reedy fibration between CSS's) is also a fibration in the CSS model category. (2) I believe it is a fibration if $\delta$ is injective, but not generally. (In the condition describing fibrant objects, it actually suffices to require a weak equivalence only in the case $\delta:[0]\to [p]$.) (3) Yup. (4) Yup. | |
| Dec 6, 2011 at 0:47 | vote | accept | Mike Shulman | ||
| Dec 6, 2011 at 0:47 | comment | added | Mike Shulman | Also, (3) I presume that this model structure is constructed as a localization of some over-model-structure for simplicial spaces over W? And (4, I guess) does that imply that the weak equivalences between fibrant objects in this model structure are still just the levelwise equivalences? | |
| Dec 6, 2011 at 0:45 | comment | added | Mike Shulman | Thanks! Two questions. (1) By "fibrations $f\colon X\to W$", do you mean Reedy fibrations? Or fibrations in the CSS model structure? (2) Is the "evident map" necessarily itself a fibration (say, if $f$ is a fibration according to your answer to (1))? | |
| Dec 5, 2011 at 15:57 | history | answered | Charles Rezk | CC BY-SA 3.0 |