Timeline for Is there a notion of Čech groupoid of a cover of an object in a Grothendieck site?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 17, 2020 at 6:13 | vote | accept | Adittya Chaudhuri | ||
| Oct 17, 2020 at 5:38 | comment | added | Adittya Chaudhuri | Ohh!! I did not know that. Thank you Sir. | |
| Oct 17, 2020 at 5:35 | comment | added | Dmitri Pavlov | @AdittyaChaudhuri: Yes, this is how principal bundles over algebraic groups can be defined (for example) for the Zariski site of a scheme. | |
| Oct 17, 2020 at 5:28 | comment | added | Adittya Chaudhuri | Though I am not sure whether the notion of delooping of a group object in an arbitrary category makes sense or not. In the last comment I just vaguely imagined that such notion may exist in an appropriate sense. (Apology in advance if I am not making much sense) | |
| Oct 17, 2020 at 4:59 | comment | added | Adittya Chaudhuri | Thank you Sir for the answer. If we consider functors from such Čech groupoid of $J_c$ to $BG$, the delooping of a group object in $C$.(Assuming group objects exist in $C$ ) then analogous to the classical case I am expecting a notion of principal bundle over the object $c \in C$ . Is this "principal bundle" worth studying for any purpose? | |
| Oct 17, 2020 at 4:37 | history | answered | Dmitri Pavlov | CC BY-SA 4.0 |