Timeline for Does pullback in the category of smooth manifolds always exists?
Current License: CC BY-SA 3.0
13 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Oct 8, 2015 at 14:16 | vote | accept | Asaf Shachar | ||
| Oct 7, 2015 at 15:50 | history | edited | Asaf Shachar | CC BY-SA 3.0 |
minor typo corrected
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| Oct 7, 2015 at 15:20 | comment | added | Todd Trimble | @JasonStarr It's certainly related. One way of thinking about a cleavage of a fibration is that it is given by a pseudofunctor $F: C^{op} \to Cat$ which takes $f: X \to Y$ to a suitable $f^\ast: F(Y) \to F(X)$. A cleavage of the codomain fibration $cod: C^\mathbf{2} \to C$ would then be given by a choice of pullback $f^\ast: C/Y \to C/X$ for each $f: X \to Y$. So having a choice of fiber product for all cospans would give you such a cleavage, although I was really just referring to a single $f$ in my comment. | |
| Oct 7, 2015 at 14:44 | comment | added | Jason Starr | @ToddTrimble: Are you referring to a "clivage"? | |
| Oct 7, 2015 at 13:19 | comment | added | Todd Trimble | On the nLab, there is I think a growing consensus to apply the phrase "fiber product" to the limit of the cospan, and to apply the word "pullback" to a functor $f^\ast: E/X \to E/Y$ which sends (in the notation of OP's clarification) $f': Y' \to X$ to $g: Z \to Y$ arising in the fiber product, as in "pulling back along $f$". | |
| Oct 7, 2015 at 12:18 | comment | added | Jason Starr | Your definition of "pullback" is the definition of categorical fiber product. | |
| Oct 7, 2015 at 10:40 | comment | added | Asaf Shachar | @JasonStarr : I have edited the question to clarify this. | |
| Oct 7, 2015 at 10:38 | history | edited | Asaf Shachar | CC BY-SA 3.0 |
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| Oct 7, 2015 at 10:35 | answer | added | Simon Henry | timeline score: 12 | |
| Oct 7, 2015 at 10:27 | history | edited | Asaf Shachar | CC BY-SA 3.0 |
added 490 characters in body
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| Oct 7, 2015 at 10:21 | comment | added | Jason Starr | If, for you, the categorical fiber product is not the same as "pullback", can you please define what you mean by "pullback"? | |
| Oct 7, 2015 at 10:10 | history | asked | Asaf Shachar | CC BY-SA 3.0 |