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In mathematics a stack or 2-sheaf is a sheaf that takes values in categories rather than sets.
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Stacks in the fpqc topology
But some notions still seem to survive for fpqc-algebraic stacks (e.g. "locally noetherian," cf. EGA IV 2.2.14). … Question: do people principally work with fppf-algebraic stacks rather than fpqc-algebraic stacks simply because one gets a nicer package that still applies to most examples one comes across in practice …