Timeline for (∞, 1)-categorical description of equivariant homotopy theory
Current License: CC BY-SA 2.5
14 events
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| Jan 28, 2010 at 15:29 | comment | added | Reid Barton | @Urs: Agreed. My question here was primarily about the unstable case, and I got a sufficient description of the genuine stable category for my purposes through off-line conversations. But I am also interested in the question you raise; I suggest you ask it as a separate question. I have heard that in both the equivariant and motivic situations, the "extra" stabilizations provide a better theory of duality, but I do not know whether this can be taken as a characterization of the resulting category, or merely a post hoc justification for its study. | |
| Jan 28, 2010 at 15:06 | comment | added | Urs Schreiber | I don't think the question, has yet been anwered, below: what is the really natural (oo,1)-categorical way to understand genuine G-spectra? While it is true that one answer is: stabilization of oo-presheaves on the orbit category at spehers with a G-action, this doesn't look like the general insightful way of looking at it that one might hope for. I am guessing the answer must involve constructions as in motivic cohomology, where we start with a big oo-topos of oo-sheaves and then stabilize it both with respect to categorical as well as geometric spheres. I'd love to see such kind of answer | |
| Nov 17, 2009 at 18:13 | answer | added | Mark Hovey | timeline score: 14 | |
| Nov 17, 2009 at 1:24 | history | edited | Reid Barton |
edited tags
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| Nov 16, 2009 at 21:34 | history | edited | Ilya Nikokoshev |
retag
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| Oct 29, 2009 at 0:17 | answer | added | Urs Schreiber | timeline score: 3 | |
| Oct 29, 2009 at 0:07 | comment | added | Reid Barton |
@Ilya: I wanted to tag this (∞,1)-categories but of course that wouldn't work (the system changed it to 1-categories :P) so I adopted Jacob Lurie's abuse of terminology. I think of higher-category-theory as an related but distinct area, having to do with 2-categories and such.
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| Oct 29, 2009 at 0:04 | history | edited | Reid Barton |
edited tags; edited tags
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| Oct 28, 2009 at 23:59 | comment | added | Reid Barton | I liked both these answers a lot, so I flipped a coin to pick one to accept. | |
| Oct 28, 2009 at 23:59 | vote | accept | Reid Barton | ||
| Oct 28, 2009 at 23:33 | comment | added | Ilya Nikokoshev |
This reminds me that I had the problem tagging the posts about infinity categories. I think your tag is actually better than higher-category-theory, but perhaps there could be other suggestions as well?
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| Oct 28, 2009 at 22:58 | answer | added | David Treumann | timeline score: 1 | |
| Oct 28, 2009 at 22:58 | answer | added | Mike Shulman | timeline score: 16 | |
| Oct 28, 2009 at 22:28 | history | asked | Reid Barton | CC BY-SA 2.5 |