Timeline for The Space of Cellular Maps
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Nov 11, 2010 at 15:37 | comment | added | Charles Rezk | @Nikita. I would think so. It should be enough to prove that $\mathrm{Cell}(X_m,Y)\to \mathrm{Cell}(X_{m-1},Y)$ is a Kan fibration, where $X_m$ is the $m$-skeleton of $X$, and $\mathrm{Cell}$ is the simplicial set of maps I defined, and that looks like it follows from cellular approximation. | |
| Nov 11, 2010 at 14:17 | history | edited | Jeff Strom | CC BY-SA 2.5 |
added 113 characters in body
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| Nov 11, 2010 at 8:10 | comment | added | Nikita Kalinin | > Charles Rezk Does it true for the infinity-dimensional X? | |
| Nov 10, 2010 at 19:37 | comment | added | Charles Rezk | I suppose the simplicial set whose $n$-simplices are the cellular maps $X\times \Delta^n\to Y$ models the homotopy type of $\mathrm{map}(X,Y)$. | |
| Nov 10, 2010 at 19:11 | comment | added | Jeff Strom | You're right. Oops. | |
| Nov 10, 2010 at 19:08 | comment | added | Tyler Lawson | Let X be a point. (Note that cellular approximation only gives you a surjection on $\pi_0$ - you need to use cellular homotopies $X \times I \to Y$ as well to get the correct answer.) | |
| Nov 10, 2010 at 18:44 | history | asked | Jeff Strom | CC BY-SA 2.5 |