Timeline for Compact objects in the $\infty$-category presented by a simplicial model category
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 19, 2019 at 20:25 | vote | accept | Saal Hardali | ||
| Jun 18, 2019 at 11:53 | comment | added | Yonatan Harpaz | Yes, though verifying the assumption there is not completely obvious. You need to check that any map $f: X \to Y$ of finite simplicial sets can be factored as a cofibration $f: X \to Z$ with $Z$ finite, followed by a categorical equivalence $Z \to Y$. One way to do this is to choose a finite simplicial set $I$ which is categorically equivalent to $\Delta^0$ and which contains a non-degenerate edge $\rho:\Delta^1 \hookrightarrow I$ (e.g., take $I=\Delta^0\coprod_{\Delta^{\{1,3\}}}\Delta^3\coprod_{\Delta^{\{0,2\}}} \Delta^0 $) and set $Z = X \times I \coprod_{X \times \{\rho(1)\}} Y$. | |
| Jun 18, 2019 at 8:05 | comment | added | Saal Hardali | That's cool! Just to make sure I understood correctly the linked proposition. In particular the Joyal model structure on simplicial sets satisfies the conditions of 5.3.1. as well, is this correct? | |
| Jun 17, 2019 at 19:49 | history | answered | Yonatan Harpaz | CC BY-SA 4.0 |