Timeline for Is there a combinatorial way to factor a map of simplicial sets as a weak equivalence followed by a fibration?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Apr 29, 2010 at 17:01 | vote | accept | Allison Smith | ||
| Apr 27, 2010 at 14:47 | comment | added | Allison Smith | I don't know if this does what I want, either, but it's certainly possible. I will check. And delay accepting the answer for a couple days in hopes that something still smaller will come along... | |
| Apr 27, 2010 at 2:40 | comment | added | Dan Ramras |
To make the last step ($X\to Q$ a weak equivalence) in Charles' construction explicit: just use the fact that pullbacks of fibrations are fibrations. Then the 5-lemma shows that $Q\to P$ is a weak equivalence (because $Y\to Ex^\infty Y$ is one), and since $X\to Ex^\infty X \to P$ are both weak equivalences, the 2-out-of-3 property implies $X\to Q$ is a weak equivalence.
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| Apr 27, 2010 at 1:44 | history | answered | Charles Rezk | CC BY-SA 2.5 |