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Ben McKay
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Is every algebraic space a 1-geometric stack?

In many references (Toen, Higher and derived stacks: a global overview, Toen, Vezzosi, Homotopical algebraic geometry II, and so on), the definition of $n$-geometric stack appears.

In the non-derived case, the definition starts by declaring affine schemes as $(-1)$-geometric stacks and inductively defines $n$-geometric stacks by some procedure.

Toen-Vezzosi, HAG II, Remark 2.1.1.5 says that algebraic spaces and schemes are automatically 1-geometric stacks. I can check that schemes are 1-geometric. (It does not depend on whether a scheme is separated or not.) But I can't check easily that algebraic spaces are 1-geometric stacks.

keaton
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