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13 votes
1 answer
1k views

How is a Stack the generalisation of a sheaf from a 2-category point of view?

A stack is usually given in terms of: -A category $F$ fibered over another $C$ such that the functor $Hom(x,y), x,y \in F(\alpha), \alpha \in C$ is a sheaf -The descent data are effective. There ...
HaroldF's user avatar
  • 433
10 votes
1 answer
506 views

What is the total space of a stack after all?

From my general experience I think for myself of what follows as some kind of taboo question for some reason: in my imagination, everybody wants an answer to this but somehow thinks it shall not be ...
მამუკა ჯიბლაძე's user avatar
10 votes
1 answer
786 views

Sites which are stacks over themselves

A site C with pullbacks is subcanonical (all representable presheaves are sheaves) if and only if its codomain fibration $Arr(C) \to C$ is a prestack (all hom-presheaves are sheaves). Is there a ...
Mike Shulman's user avatar
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