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In mathematics a stack or 2-sheaf is a sheaf that takes values in categories rather than sets.

9 votes

Basic questions about stacks 2

Regarding 3), Andrew Kresch just told me that they gave up on the project.
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6 votes
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Do algebraic stacks satisfy fpqc descent?

It may be helpful to have a look at these notes by Anatoly Preygel (see also MO/15910/2503). In particular, Proposition 3.3.6 says that an algebraic stack is an fpqc sheaf if the diagonal is quasi-af …
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37 votes
3 answers
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Conjectures in Grothendieck's "Pursuing stacks"

I read on the nLab that in "Pursuing stacks" Grothendieck made several interesting conjectures, some of which have been proved since then. …
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