Timeline for Geometric intuition for Mather's cube theorem
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 3, 2019 at 18:28 | vote | accept | Arrow | ||
| Nov 3, 2019 at 16:26 | comment | added | Tom Goodwillie | @Arrow, the theorem is about homotopy pushouts rather than pushouts, but I don't know how to give geometric intuition without switching to actual pushouts. And that means I should be looking at pushouts that are also homotopy pushouts, so at least one of the maps $B_0\to B_1$ and $B_0\to B_2$ should be some kind of nice injection. | |
| Nov 3, 2019 at 7:19 | comment | added | Marc Hoyois | @Arrow The theorem holds in sets if one of the given pullback squares intersects the pushout squares in a pair of monomorphisms. In the homotopy theory of simplicial sets any map can be made a monomorphism, so in fact it is possible to deduce the cube theorem from its set version. | |
| Nov 3, 2019 at 6:40 | comment | added | Arrow | Dear Tom, in this answer you write the theorem fails in the category of sets. Doesn't that mean the intuition of strictly pulling back bundles fails? | |
| Nov 2, 2019 at 23:15 | history | answered | Tom Goodwillie | CC BY-SA 4.0 |