Timeline for Cofinal maps from posets (HTT, 4.2.3.16)
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 3, 2023 at 9:54 | history | edited | Ken | CC BY-SA 4.0 |
edited the title
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| Jul 3, 2023 at 9:53 | vote | accept | Ken | ||
| Jul 3, 2023 at 9:47 | answer | added | daniel gratzer | timeline score: 2 | |
| Jul 3, 2023 at 2:14 | comment | added | Ken | @danielgratzer Thanks! I was not aware of the stronger result in Kerodon. If you make your comment into an answer, I will gladly accept it. | |
| Jul 2, 2023 at 10:04 | comment | added | daniel gratzer | As a small point, Kerodon requires $\tilde{K} \to K$ to be a trivial fibration, but the construction given won't produce a finite simplicial set if $K$ is finite. However, Kerodon does have a completely different construction which shows that a finite simplicial set is a localization of a finite poset, which gives the same result. | |
| Jul 2, 2023 at 9:40 | history | edited | Neil Strickland |
edited tags
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| Jul 2, 2023 at 9:33 | comment | added | Neil Strickland | I think that you can take $A$ to be the coend of the functor $\mathbf{\Delta}^{\text{op}}\times\mathbf{\Delta}\to\text{POSet}$ sending $(n,m)$ to $X_n\times\Xi_m$, where $\Xi_m$ is the poset of nonempty chains of nonempty subsets of $[m]$. However, it takes some work to verify this. | |
| Jul 2, 2023 at 6:16 | history | asked | Ken | CC BY-SA 4.0 |