Timeline for What is the connection between Lurie's definition of shape and Čech homotopy?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 12, 2022 at 9:27 | vote | accept | Zhen Lin | ||
| Mar 6, 2022 at 12:08 | comment | added | Zhen Lin | It was a long time ago and I may have misremembered. I think what is true is that hypercovers of finite height are sheaf equivalences, so sheaves satisfy descent with respect to them. What I’m not so clear about is whether that’s good enough to sheafify in one step, or if that only works for presheaves of $n$-groupoids (for some finite $n$). | |
| Mar 6, 2022 at 11:46 | comment | added | Marc Hoyois | I don't know, I've never heard this. If you remember where you saw this I'd be interested to know! | |
| Mar 5, 2022 at 22:59 | comment | added | Zhen Lin | Thank you. I was aware that hypercovers can be used to construct the reflector into $\mathcal{Sh} (X)\hat{}$, but I wanted to know about the reflector into $\mathcal{Sh} (X)$. I think I read somewhere that restricting to hypercovers of finite height works. Is that true? | |
| Mar 5, 2022 at 17:22 | history | answered | Marc Hoyois | CC BY-SA 4.0 |