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

7 votes
Accepted

Can Deligne-Mumford stacks be characterized by their restriction to a small subcategory?

Without some finiteness hypothesis, no set of finitely-presented algebras can suffice (even for affine schemes, nevermind DM stacks). …
Anatoly Preygel's user avatar
25 votes
Accepted

In what topology DM stacks are stacks

Alternatively: earlier this year I wrote up some notes (PDF link) that included an Appendix collecting in one place the equivalences of some standard definitions of stacks, including statements of the …
Anatoly Preygel's user avatar