Timeline for What abstract nonsense is necessary to say the word "submersion"?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Nov 8, 2010 at 0:52 | comment | added | Harry Gindi | Probably in one of the two arguments about "étale geometric morphisms" (this is what I'm referencing in my comment on David Carchedi's answer) or in the thread about admissibility structures, I think. | |
| Nov 8, 2010 at 0:45 | comment | added | Theo Johnson-Freyd | @Harry: Cool, where? I didn't find it by searching. | |
| Nov 8, 2010 at 0:10 | comment | added | Harry Gindi | @Theo: I should add that we had a discussion of this on the nForum that may be instructive to read if you don't want to get into the nitty-gritty technical details. | |
| Nov 7, 2010 at 23:56 | comment | added | David Roberts♦ | You can talk about a formal class of maps which plays the role of submersions relative to a Grothendieck pretopology - I use this in my thesis (and it is also called an admissible class, independently on that in Harry's answer) to talk about internal anafunctors. But I agree with him that it is a bit more complicated that it first seems. | |
| Nov 7, 2010 at 23:53 | comment | added | David Roberts♦ | local sections is easy, it is local sections through every point that is hard. Seeing your other question on right principal bibundles between internal categories, I can guess the problem you've run up against, as I did recently. I don't think I resolved it yet (or perhaps I did, I'll have to look at my notes later tonight. | |
| Nov 7, 2010 at 23:34 | comment | added | Theo Johnson-Freyd | Well, I'm trying to get away from requiring my category to be concrete. For example, there are many categories which are "concrete" in the sense that there is some object X so that Hom(X,-) is faithful, but for which Hom(1,-) is not faithful, where 1 is the terminal object; I tend to think that the latter is the correct definition of "point", not the former. (E.g. if your concretization of Man is Hom(R,-), then I think you don't get sections through every point.) How abstract-nonsensy can you say "admits local sections over the pretopology of open sets"? | |
| Nov 7, 2010 at 23:12 | history | answered | David Roberts♦ | CC BY-SA 2.5 |