Timeline for Canonical reference for dictionary between $G$-spaces and fiber bundles over $BG$?
Current License: CC BY-SA 4.0
5 events
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| Jul 7, 2023 at 7:27 | comment | added | Dmitri Pavlov | @GregFriedman: Simplicial groups were introduced in 1950s (Kan) and simplicial presheaves in 1980s (Joyal, Jardine), seems reasonably traditional for a topic in homotopy theory. The OP requested a source for reference purposes, which these papers can certainly provide. | |
| Jul 7, 2023 at 6:42 | comment | added | Greg Friedman | Hmm, I don't mean to be disagreeable, but I just looked at the second paper, and it also seems to be largely about presentations of ∞-toposes using things like simplicial presheaves, simplicial objects in sites, etc. The section labeled "groups" starts off with "Every ∞-topos H comes with a notion of ∞-group object that generalizes the ordinary notion of group object in a topos as well as that of grouplike A∞ space in Top ≃ Grpd∞. We discuss presentations of ∞-group objects by presheaves of simplicial groups." So, we may have very different interpretations of "traditional"! | |
| Jul 6, 2023 at 5:04 | comment | added | Dmitri Pavlov | @GregFriedman: The second paper makes no use of ∞-categories and is formulated in the traditional language. | |
| Jul 6, 2023 at 1:11 | comment | added | Greg Friedman | These papers seem like they may be more infinity-y than the original asker may have had in mind. I'd also be interested in a more classical reference where spaces are just spaces. | |
| Jul 4, 2023 at 22:27 | history | answered | Dmitri Pavlov | CC BY-SA 4.0 |