Timeline for Interactions (functors) between equivariant sheaves for different groups?
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S May 9, 2017 at 15:05 | history | bounty ended | CommunityBot | ||
| S May 9, 2017 at 15:05 | history | notice removed | CommunityBot | ||
| May 6, 2017 at 20:24 | answer | added | John Wiltshire-Gordon | timeline score: 4 | |
| S May 1, 2017 at 13:21 | history | bounty started | Saal Hardali | ||
| S May 1, 2017 at 13:21 | history | notice added | Saal Hardali | Draw attention | |
| S Apr 13, 2017 at 21:56 | history | bounty ended | CommunityBot | ||
| S Apr 13, 2017 at 21:56 | history | notice removed | CommunityBot | ||
| Apr 6, 2017 at 11:08 | comment | added | Saal Hardali | These are sheaves on X equivariant w.r.t. G. so you have extra structure on them. | |
| Apr 6, 2017 at 11:06 | comment | added | Artur Jackson | Sorry, my question was unhelpful actually. I left something out: Just to be clear, these are sheaves on the underlying set $X$ of a G-set ($X$,action)? (And not the translation groupoid for example.) | |
| Apr 6, 2017 at 11:02 | comment | added | Saal Hardali | I think the question is pretty clear as is. I did right "k-vector spaces". By a G-set I mean nothing more than a set with an action of a group. Indeed in this case sheaves=presheaves. I'd like to know what happens in the reasonably general context though. | |
| Apr 6, 2017 at 0:10 | comment | added | Artur Jackson | Maybe you want to be clearer: $Sh_G(X)$ is ``$G$-equivariant sheaves taking values in $\mathbf{Vect}_k$''? You say `sheaves.' So your $X$'s are topological $G$-sets, i.e., $G$-spaces? Or do you just want pre-sheaves = sheaves for the discrete topology? Or you are viewing a $G$-set as a groupoid (category)? | |
| Apr 5, 2017 at 22:46 | comment | added | Marc Hoyois | Taking the quotient groupoid is the natural thing to do in any geometric context: sets → groupoids, schemes → algebraic stacks, topological spaces → topological stacks, etc. | |
| Apr 5, 2017 at 20:42 | history | edited | Saal Hardali | CC BY-SA 3.0 |
added 288 characters in body
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| Apr 5, 2017 at 20:40 | comment | added | Saal Hardali | @MarcHoyois Although I phrased everything in the simple context of sets I'm looking for a natural answer that would generalize easily to any context. Hopefully with some intuitive/geometric/hands-on interpretation of the the functors involved beyond the formal existence argument. | |
| Apr 5, 2017 at 20:23 | comment | added | Marc Hoyois | Your $Sh_G(X)$ is just presheaves on the quotient groupoid $X/G$. For any morphism between groupoids you formally get three adjoint functors on presheaves. | |
| S Apr 5, 2017 at 20:15 | history | bounty started | Saal Hardali | ||
| S Apr 5, 2017 at 20:15 | history | notice added | Saal Hardali | Draw attention | |
| Apr 3, 2017 at 13:35 | history | asked | Saal Hardali | CC BY-SA 3.0 |