Timeline for Is every category a localization of a poset?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 7, 2021 at 1:40 | comment | added | Tim Campion | Haha! I think you did encourage me to read those papers a few times, and I think I looked a little bit, but I didn't end up going through in detail. | |
| Sep 7, 2021 at 0:35 | comment | added | Chris Schommer-Pries | @TimCampion Your advisor was clearly negligent. He should have had you read all of the Barwick-Kan papers. I think I might write him a pointed email instructing him to do better in the future ;) . (Regardless, I think you would enjoy these papers very much. Most of them are very short and to-the-point -- a rare quality in our field; Also Kan's literary style comes through strongly and is quite singular among math papers - I personally love it, though I know some hate it. Also the n-relative category model is wild! Worth knowing about!!). | |
| Sep 4, 2021 at 22:35 | vote | accept | Tim Campion | ||
| Sep 4, 2021 at 12:38 | history | edited | Chris Schommer-Pries | CC BY-SA 4.0 |
typo
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| Sep 4, 2021 at 12:30 | history | edited | Chris Schommer-Pries | CC BY-SA 4.0 |
Added explicit functor giving cofibrant replacement.
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| Sep 3, 2021 at 16:08 | comment | added | Chris Schommer-Pries | Yes, that is one way to get that. If you dive into the Barwick-Kan machinery a bit more you can also see that the $\infty$-categorical localization $P[W^{-1}]$ can be taken to mean the hammock localization, whose homotopy category is the usual 1-categorical localization. | |
| Sep 3, 2021 at 16:03 | comment | added | Tim Campion | This is beautiful, thanks! In the last paragraph, I suppose you're using the following observation: if the $\infty$-categorical localization $P[W^{-1}]$ happens to be a 1-category, then it coincides with the 1-categorical localization (which unfortunately I also denoted $P[W^{-1}]$). | |
| Sep 3, 2021 at 15:52 | history | answered | Chris Schommer-Pries | CC BY-SA 4.0 |