Timeline for Stack associated to Groupoid object in category $\text{Sch}/S$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 18, 2020 at 4:39 | comment | added | S. Carnahan♦ | @PraphullaKoushik The point is that quotients behave badly with respect to gluing, so from a groupoid you just get a fibered category (or equivalently, functor to groupoids) with no guarantees about effectiveness of descent. The same problem holds even without the complications of groupoids, when you consider quotient sheaves of sets - you first get a quotient presheaf, then you sheafify. | |
| Sep 7, 2019 at 13:29 | vote | accept | Praphulla Koushik | ||
| Sep 5, 2019 at 16:45 | comment | added | Praphulla Koushik | I will try to understand those lemmas and ask specific questions, if I have any. Thanks. | |
| Sep 5, 2019 at 15:49 | comment | added | Praphulla Koushik | Ok, I am not sure if I am understanding correctly or not.. For an algebriac stack $X$, we some how get a groupoid in scheme... For this groupoid, we associate a stack (in the usual sense we associate stack for Lie groupoid) over some Grothendieck topology... But, this is not a stack with respect to the fppf topology... so, we stackify (tag/06WP) to get a stack/fppf... Then, this stack is isomorphic to $X$.. Is this correct? | |
| Sep 5, 2019 at 15:39 | history | answered | S. Carnahan♦ | CC BY-SA 4.0 |