Timeline for Examples of categorification
Current License: CC BY-SA 2.5
2 events
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| Oct 26, 2010 at 0:54 | comment | added | Dan Ramras |
Hmmm... I don't think I know quite what you mean here. Quillen's Theorem B says that when all the categorical fibers are homotopy equivalent to one another under base change, then they do indeed all model the homotopy fiber. But if they're not all equivalent, then Theorem B tells you nothing. In general I think it's a very hard (and unsolved) problem to find a category whose classifying space is the homotopy fiber of a functor $C\to D$. On the other hand, the dual problem of modeling the homotopy colimit of a diagram of categories was solved by Thomason in his thesis.
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| Oct 25, 2010 at 23:24 | history | answered | Somnath Basu | CC BY-SA 2.5 |