Timeline for Explicit expression of the unstraightening functor
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 29, 2021 at 19:42 | comment | added | Emily | By the way, since leaving this comment here I stumbled upon these really cool slides of Alexander Campbell, which describe (forthcoming work) on how to factor the straightening-unstraightening adjunction into a composition of an equivalence and two adjunctions. These give a nice description of unstraightening as $\mathrm{Un}_{A}\cong A_{/(-)}\circ(\eta_{A},\mathrm{id})^{*}\circ\mathrm{N}\circ\text{collage}$ (in Alexander's notation, see there). | |
| Jan 29, 2021 at 19:42 | comment | added | Emily | @TimCampion No worries =) | |
| Jan 29, 2021 at 19:30 | comment | added | Tim Campion | @Emily Sorry, somehow just noticed this. It's been awhile since I thought about this question so the short answer is I'm not sure. Maybe Praphulla Koushik was right and I should summarize some of the statements I'm discussing. | |
| Dec 6, 2020 at 3:43 | comment | added | Emily | (P.S. Sorry for pinging you if it isn't; I've just been learning a bit about un/straightening and am currently quite confused!) | |
| Dec 6, 2020 at 3:43 | comment | added | Emily | @TimCampion Hi Tim! Is the description in p. 164 of Rezk's notes on quasicategories (a link to that page for convenience) the one sought in this question? | |
| May 24, 2018 at 20:02 | vote | accept | Madio | ||
| May 24, 2018 at 17:10 | comment | added | Tim Campion | Here is a glossary: 2.2.2.11 (the remark in question) calculates the fiber $Unst_\phi \mathcal F \times_S \{s\}$; the paragraph between 2.2.2.5 and 2.2.2.6 caluclates straightening over a point in terms of $Q_\bullet$. 2.2.2.1 is a pair of functoriality properties for straightening. I only need formal properties of the things I haven't defined, so I refer to HTT (which is freely available from Lurie's website) for more details. I agree that numerical HTT references are unpleasant to look at, but at least they are precise, and one must learn to live with them in higher category theory today. | |
| May 24, 2018 at 16:58 | comment | added | Praphulla Koushik | It is little disturbing to see these numbers $2.2.2.11,2.2.2.5,2.2.2.6$ with out mentioning what they actually are. Atleast you could have clearly said what it is as you have enough experience here. | |
| May 24, 2018 at 16:54 | history | edited | Tim Campion | CC BY-SA 4.0 |
added 124 characters in body
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| May 24, 2018 at 16:49 | history | answered | Tim Campion | CC BY-SA 4.0 |