Timeline for Internal equivalence implies weak equivalence for Frechet Lie groupoids?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 14, 2015 at 0:31 | vote | accept | David Roberts♦ | ||
| Aug 14, 2015 at 0:31 | answer | added | David Roberts♦ | timeline score: 0 | |
| Apr 22, 2013 at 6:26 | comment | added | David Roberts♦ | Hmm, good point. I'll have a look at Hamilton's paper. | |
| Apr 20, 2013 at 3:10 | comment | added | Pedro Lauridsen Ribeiro | Just a (sort of) layman's comment: it seems to me that you need a characterization of surjective submersions that involves the implicit function theorem. If that's really the case, I'd guess that the result still holds true in the tame Fréchet category, thanks to the Nash-Moser implicit function theorem. | |
| Feb 8, 2013 at 21:00 | answer | added | David Carchedi | timeline score: 0 | |
| Feb 8, 2013 at 14:56 | answer | added | Christoph Wockel | timeline score: 0 | |
| Feb 6, 2012 at 1:07 | comment | added | David Roberts♦ | I do want to call such a functor essentially surjective! Perhaps I have just found a limitation in the usual techniques dealing with internal groupoids/categories. At the very least, this shows my proof of the existence of the bicategory of fractions for internal groupoids doesn't extend to Frechet Lie groupoids (though I know the result holds using a different proof). | |
| Feb 5, 2012 at 7:30 | comment | added | Mike Shulman | Obviously the notion of "right" is subjective, but it seems to me that if $f\colon X\to Y$ is a smooth functor such that there is a smooth function assigning to every object $y\in Y$ an object $x\in X$ and an isomorphism $f(x)\cong y$, then why wouldn't you want to call $f$ "essentially surjective"? | |
| Feb 2, 2012 at 23:59 | comment | added | David Roberts♦ | In the case of fin. dim. Lie groupoids if the map in question is a split epi, the structure of the Lie groupoid means it is a submersion. But split epis are not submersions in general. And this definition uses a pretopology, not a Grothendieck topology. Perhaps my question could also ask that perhaps for Frechet Lie groupoids, are submersions even the right pretopology to use? They probably are, but I can't say with 100% certainty. | |
| Feb 2, 2012 at 18:34 | comment | added | Mike Shulman | It seems to me that a definition of "essentially surjective" which doesn't include the case when the map in question is split epi can't possibly be right. (In particular, split epis cover in any Grothendieck topology.) Unless I misunderstand the question? | |
| Jan 30, 2012 at 6:23 | comment | added | David Roberts♦ | The part about the functor being fully faithful is no problem at all and can be shown arrow-theoretically with a little Yoneda thrown in. It is the surjective submersion part which is fragile. | |
| Jan 30, 2012 at 6:21 | history | asked | David Roberts♦ | CC BY-SA 3.0 |