Timeline for Methods for defining/calculating homotopy limits of quasicategories
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jul 7, 2016 at 16:18 | comment | added | Kaya Arro | @DmitriPavlov Yes, thank you! Somehow I had tricked myself into thinking about fibrant replacement. You're completely correct. | |
| Jul 7, 2016 at 10:43 | comment | added | Dmitri Pavlov | @KyleFerendo: I'm not sure where acyclic cofibrations are supposed to appear in your picture. A cofibrant replacement of some diagram X can be obtained by factoring ∅→X as a composition of a cofibration and an acyclic fibration. These two classes of maps coincide for Joyal and Kan—Quillen model structures. | |
| Jul 7, 2016 at 6:13 | comment | added | Kaya Arro | @DmitriPavlov, I have been a little confused by your comment. It is true that the Joyal model structure and the Quillen model structure have the same cofibrations (monomorphisms), but I don't see why this implies that we can use the same cofibrant replacement for the constant weight. After all, the two model structures certainly don't have the same acyclic cofibrations. That is why I suggested that we might have to take the free groupoid of $\mathcal{D}/-$ before taking the nerve (but I'm unsure if that's correct). | |
| Jun 30, 2016 at 17:10 | comment | added | Dmitri Pavlov | The Joyal model structure is enriched over itself, so homotopy (co)limits can be computed as derived weighted (co)limits with respect to the constant weight. Joyal cofibrations of simplicial sets coincide with monomorphisms, so a cofibrant replacement of the constant weight can be taken to be the same as for the Kan—Quillen model structure on simplicial sets. | |
| Jun 30, 2016 at 14:49 | history | edited | Kaya Arro | CC BY-SA 3.0 |
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| Jun 30, 2016 at 14:37 | vote | accept | Kaya Arro | ||
| Jun 30, 2016 at 14:33 | history | edited | Kaya Arro | CC BY-SA 3.0 |
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| Jun 30, 2016 at 7:10 | answer | added | Yonatan Harpaz | timeline score: 7 | |
| Jun 30, 2016 at 7:10 | comment | added | Kevin Carlson | Regarding your last question, there are basically no limits in $\mathbf{qCat_2}$. Instead you have weak limits in the sense Riehl and Verity study, such as the cotensor by the arrow. | |
| Jun 30, 2016 at 5:01 | history | asked | Kaya Arro | CC BY-SA 3.0 |