Timeline for Rigidification of marked simplicial sets
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 22, 2019 at 13:58 | vote | accept | F.Abellan | ||
| Sep 24, 2019 at 12:31 | answer | added | Valery Isaev | timeline score: 1 | |
| Sep 24, 2019 at 12:17 | comment | added | Valery Isaev | @TimCampion Localization is defined uniquely up to equivalence, so it does not matter which one we use. The functor has to be homotopical, but it does not have to be a left Quillen functor. Actually, I can prove my claim, so I'll post it as an answer. | |
| Sep 23, 2019 at 18:47 | comment | added | Tim Campion | @ValeryIsaev Since this is a model-dependent question, there's more to say, right? Do you have a particular model for the localization in mind? If you just take DK localization, then you end up sending $\Delta[1]^\sharp$ to the constant simplicial category at the walking isomorphism, which is not Bergner-cofibrant, so you don't get a left Quillen functor. | |
| Aug 22, 2019 at 17:35 | comment | added | Valery Isaev | It should be true that a map of marked simplicial sets is a weak equivalence if and only if the induced functor on localizations of simplicial categories (where marked arrows are localized) is an equivalence. | |
| Aug 22, 2019 at 14:08 | comment | added | Edoardo Lanari | If you are happy with only detecting them between fibrant marked simplicial sets then you can simply forget the marking and apply the same argument :) | |
| Aug 22, 2019 at 10:39 | history | asked | F.Abellan | CC BY-SA 4.0 |