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For questions about or involving fibrations which are maps which satisfy the homotopy lifting property for all spaces.

10 votes
1 answer
502 views

Bundle-to-function correspondence

To a discrete op-fibration of categories $f\colon E\to B$ one can assign a functor $$|f^{-1}|\colon B\to Set$$ sending $b$ to its fiber. Question: What do all these have in common? …
David Spivak's user avatar
  • 8,659
6 votes
Accepted

Bundle-to-function correspondence

We suppose that $f:E\to B$ is a (kind of) fibration. If there exists a moduli object $M$ for fibrations, $f$ is classified by a function $[f]:B\to M$ (I've changed your notation). …
David Spivak's user avatar
  • 8,659