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Oct 12, 2014 at 20:55 comment added Martin Brandenburg Functors represented by schemes land in the category of sets. But as you can see, your functor has values in groupoids and not sets, except for "trivial" cases already mentioned in the answers. $[X/G]$ is still an algebraic stack, though. One doesn't need that $X$ is noetherian.
Mar 6, 2014 at 11:08 answer added abx timeline score: 7
Mar 6, 2014 at 9:36 history edited Brian Fitzpatrick
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Mar 3, 2014 at 22:09 vote accept Brian Fitzpatrick
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Mar 3, 2014 at 21:47 answer added Simon Rose timeline score: 13
Mar 3, 2014 at 21:43 history edited Brian Fitzpatrick CC BY-SA 3.0
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Mar 3, 2014 at 21:37 history asked Brian Fitzpatrick CC BY-SA 3.0