Timeline for Pullbacks for primitive recursive functions.
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 25, 2010 at 17:58 | vote | accept | Doctor Gibarian | ||
| Feb 25, 2010 at 17:57 | vote | accept | Doctor Gibarian | ||
| Feb 25, 2010 at 17:57 | |||||
| Feb 25, 2010 at 17:15 | answer | added | Reid Barton | timeline score: 3 | |
| Feb 25, 2010 at 17:11 | answer | added | Joel David Hamkins | timeline score: 2 | |
| Feb 25, 2010 at 16:34 | comment | added | Doctor Gibarian | Mh. In that case the square giving raise to the pullback woludn't be commutative and therefore the pullback set would be empty. Isn't it? My question is: could we make that for prim. rec. functions (where all of them are total and we've not the empty set as a possible domain)? Have they pullbacks? F.G.Dorais: I wish I could find that info in the web you send, but I don't see it there. Thank you anyway. | |
| Feb 25, 2010 at 16:22 | comment | added | Tom Leinster | Ximo, it looks to me as if your first paragraph is asking the following question. (If not, please clarify.) Let X, Y and Z be sets, and let f: X --> Z and g: Y --> Z be functions. Is it possible that the pullback of f with g is empty? Kevin answered "no, e.g. take X to be the one-element set". More specifically, you could take X and Y both to be one-element sets, Z to be a two-element set {z_1, z_2}, and f and g to be the functions with respective images z_1 and z_2. | |
| Feb 25, 2010 at 15:40 | comment | added | François G. Dorais | Are you asking about the existence of pullbacks in the Lawvere Theory of primitive recursive functions? ncatlab.org/nlab/show/Lawvere+theory | |
| Feb 25, 2010 at 15:37 | comment | added | Doctor Gibarian | Pullback to a point? You mean a degenerate case of a pullback? Makes it any sense? And..what if we haven't the empty set available? | |
| Feb 25, 2010 at 15:24 | comment | added | Kevin Buzzard | "could this pullback set be the empty set in some cases?" Yes! Pullback to a point is just "fibre of the map" so sure a fibre can be empty. | |
| Feb 25, 2010 at 15:15 | history | asked | Doctor Gibarian | CC BY-SA 2.5 |