Timeline for Do Smash Products and Quotients Commute?
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 29, 2012 at 22:47 | comment | added | Omar Antolín-Camarena | @Dylan Wilson: products in pointed spaces are just Cartesian products $(X,x) \times (Y,y) = (X \times Y, (x,y))$. That obviously has the right universal property. The smash product is a nice monoidal structure basically because (working in a convenient category of spaces) it is left adjoint to forming pointed mapping spaces (so it is the "tensor product" corresponding to the "internal hom" in pointed spaces). | |
| Oct 26, 2010 at 20:15 | vote | accept | Richard | ||
| Oct 25, 2010 at 4:46 | comment | added | Dylan Wilson | @Sean: Are you sure? I thought smash products were the product in the category of pointed spaces... since if we have pointed maps into X and Y we certainly get a pointed map into X smash Y, right? But I guess I haven't thought about uniqueness and continuity | |
| Oct 25, 2010 at 3:57 | answer | added | Tom Goodwillie | timeline score: 1 | |
| Oct 24, 2010 at 23:14 | comment | added | Martin Brandenburg | @Richard: Are you sure about the products? What happens if we have CW-complexes which are not locally compact? At least it works if we work in the category CGHaus. | |
| Oct 24, 2010 at 22:33 | answer | added | Jeff Strom | timeline score: 4 | |
| Aug 26, 2010 at 21:26 | comment | added | Sean Tilson | I too find smash products hard to visualize, but tyler's example is great cus you can visualize it. Also, smash products will not behave like the ordinary product because they are not a categorical product. I believe the reason you get that commutativity is because the products satisfy a universal property. Also, once you start talking about smash products you will probably want to learn about cofibers and then ask the question. | |
| Aug 26, 2010 at 21:06 | comment | added | Tyler Lawson | $Y = \{\ast,1,2\}$, $X = \{\ast,1\}$, $k=2$. | |
| Aug 26, 2010 at 20:33 | history | asked | Richard | CC BY-SA 2.5 |