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Feb 16, 2018 at 9:13 comment added Jon Pridham You need to take Zariski local isomorphism rather than open inclusion, or the groupoid will be trivial. Then you need to impose constraints on the matching objects to avoid stacky structure - see for instance Prop 4.1 and Rem 1.27 of "Presenting higher stacks as simplicial schemes".
Feb 15, 2018 at 18:23 history edited keaton CC BY-SA 3.0
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Feb 15, 2018 at 18:16 history asked keaton CC BY-SA 3.0