Timeline for How to define $\Lambda^0_0$, 0-horn of a simplicial point
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 27, 2014 at 14:55 | vote | accept | Ma Ming | ||
| Mar 16, 2014 at 0:41 | answer | added | Daniel Gerigk | timeline score: 2 | |
| Feb 7, 2014 at 8:56 | comment | added | Tim Porter | The join is really an operation on augmented simplicial sets so the comment by Eric is of importance. | |
| Feb 7, 2014 at 1:05 | comment | added | Ma Ming | @EricWofsey This will make the identity $(Λ^{m}_{k}\starΔ^{n}) \cup (Δ^{m}\star \partial Δ^{n})=Λ^{m+1+n}_{k}$ hold for $m=k=0$. | |
| Feb 7, 2014 at 0:51 | comment | added | Ricardo Andrade | I think the 0-horn is best left undefined or non-existent (even in the augmented simplex category). After all, one of the most important properties of a horn is that it is a weak equivalence. That cannot be arranged for in the case of a 0-horn. | |
| Feb 7, 2014 at 0:47 | comment | added | Eric Wofsey | If you work with presheaves over the augmented simplex category, then it's natural to define $\partial\Delta^0=\Delta^{-1}$ and $\Lambda^0_0$ to actually be the empty presheaf. I don't know if this is useful. | |
| Feb 7, 2014 at 0:39 | review | Close votes | |||
| Feb 7, 2014 at 7:03 | |||||
| Feb 7, 2014 at 0:36 | comment | added | Ma Ming | @DavidRoberts I am not satisfied with the only possibility $Λ^0_0=∂Δ^0$. I think there should be better solution (like enlarge the category of simplicial sets). | |
| Feb 7, 2014 at 0:34 | comment | added | David Roberts♦ | I think you answered your question in the last sentence: $\Lambda^0_0 \subseteq \partial \Delta^0 = \emptyset$. | |
| Feb 7, 2014 at 0:09 | history | asked | Ma Ming | CC BY-SA 3.0 |