Timeline for Lemma 5.4.5.11 of HTT
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 11, 2021 at 11:38 | vote | accept | Sil Linskens | ||
| Mar 11, 2021 at 10:08 | answer | added | Yonatan Harpaz | timeline score: 8 | |
| Mar 11, 2021 at 9:22 | comment | added | Sil Linskens | @ReidBarton I tried something along the lines of this, but in fact I couldn't see how we could apply the fact that f is $\kappa$-cofinal (note at this point that we in fact do not know that $f$ is cofinal, that is proven next as a consequence of this assertion). In particular being $\kappa$-cofinal only allows you to find weak pre-images for slice categories of contractable simplicial sets. In this situation we are sliced under $K$, which is not assumed to be weakly contractable. | |
| Mar 10, 2021 at 17:00 | comment | added | Reid Barton | I think (b). Try proving the lemma by hand in the case of 1-categories and when K consists of a single object and K' of two objects (so that we cannot apply 5.4.5.10). At the point where the book uses 5.4.5.10, you'll see that you still need to use the fact that J is filtered and then that f is cofinal (in order to end up with a diagram in I). That should give you an idea of how the general proof should go, though I haven't worked out the details. | |
| Mar 10, 2021 at 16:26 | history | edited | Martin Sleziak |
added a top-level tag; see: https://meta.mathoverflow.net/questions/1457/why-are-mo-tags-formatted-as-they-are
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| Mar 10, 2021 at 16:25 | history | asked | Sil Linskens | CC BY-SA 4.0 |