Timeline for What is the source of this famous Grothendieck quote?
Current License: CC BY-SA 3.0
22 events
| when toggle format | what | by | license | comment | |
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| Sep 1, 2013 at 19:52 | comment | added | André Henriques | @Yemon: I agree completely with you. The discussion has diverged from the original question. | |
| Sep 1, 2013 at 17:47 | comment | added | Yemon Choi | None of the (interesting) answers seem to locate the distinctive form of DM's first maxim. On a non-mathematical note, what it most strongly reminds me of is the notorious "Besser ein Ende mit Schrecken als ein Schrecken ohne Ende", though I assume that's just a case of aphorisms converging on chiasmus form | |
| Sep 1, 2013 at 17:39 | comment | added | Yemon Choi | @AndréHenriques I was aware dimly of the bicategory you mention but don't understand why Owen's category is "some kind of poor man's approximation" to it. Could you expand on this comment, perhaps in chat? chat.stackexchange.com/rooms/10414/… | |
| Sep 1, 2013 at 14:50 | comment | added | Ben McKay | I once spoke with Hans Duistermaat about Elie Cartan's book La Géométrie des espaces de Riemann. I pointed out Cartan didn't define manifolds, but just said that they are difficult to define with precision. Duistermaat said that the definitions will change but the theorems will remain the same. I suppose that puts him at war with Manin, and perhaps Grothendieck. Maybe this is because differential geometry is a persistently bad category. | |
| Sep 1, 2013 at 13:44 | comment | added | André Henriques | @JonBannon: I was being serious. Here are some references that mention the bicategory of von Neumann algebras: p59 of math.berkeley.edu/~teichner/Papers/Oxford.pdf, p7 of arxiv.org/pdf/math-ph/0008003v2.pdf, and my own paper arxiv.org/pdf/1110.5671v1.pdf | |
| Sep 1, 2013 at 3:29 | comment | added | Owen Sizemore | @Yemon: Yes that is what I intended (I only think of normal ones) | |
| Sep 1, 2013 at 3:13 | comment | added | Yemon Choi | @OwenSizemore Do you want normal ucp maps as your morphisms? | |
| Sep 1, 2013 at 3:11 | comment | added | Yemon Choi | Sometimes I think chiasmus is inevitable... | |
| Aug 31, 2013 at 23:47 | comment | added | Jon Bannon | @André Henriques: Intriguing. Is there a source explicitly discussing the von Neumann algebras and bimodules bicategory? (If you were being serious...) | |
| Aug 31, 2013 at 23:29 | answer | added | Colin McLarty | timeline score: 18 | |
| Jun 17, 2013 at 16:53 | answer | added | AFK | timeline score: 8 | |
| Jun 17, 2013 at 16:31 | answer | added | Martin Brandenburg | timeline score: 9 | |
| Jun 8, 2013 at 21:52 | comment | added | André Henriques | @Owen: Isn't the category of von Neumann Algebras and completely positive maps some kind of poor man's approximation of the bicategory of von Neumann Algebras and bimodules? | |
| Jun 8, 2013 at 14:33 | answer | added | Carlo Beenakker | timeline score: 21 | |
| Jun 8, 2013 at 4:46 | comment | added | Joël | For what it's worth: I have read "récoltes et semailles" years ago, but this quote doesn't ring any bell. – Joël 0 secs ago | |
| Jun 8, 2013 at 2:50 | comment | added | Owen Sizemore | The category of von Neumann Algebras and *-homomorphisms is bad, while von Neumann Algebras with completely positive maps is good. (The first one has basically few interesting morphisms, the second has many) | |
| Jun 7, 2013 at 13:57 | comment | added | Andrej Bauer | The category of smooth manifolds and smooth maps is another example of a bad category with good objects. | |
| Jun 7, 2013 at 13:57 | comment | added | Andrej Bauer | The category of topological spaces has lots of good objects but is a bad category because it does not have exponentials. | |
| Jun 7, 2013 at 11:19 | comment | added | Samuele Giraudo | Are there some good examples of bad categories with good objects? | |
| Jun 7, 2013 at 2:39 | comment | added | Daniel Moskovich | @Mahdi A category which doesn't possess objects or morphisms which you need in order to make desirable structural arguments work. For instance, depending on which argument you wish to make, a <i>bad</i> category might not be complete, or cocomplete, or cartesian closed, or whatever. | |
| Jun 7, 2013 at 2:25 | comment | added | Mahdi Majidi-Zolbanin | What is a bad category? | |
| Jun 7, 2013 at 2:14 | history | asked | Daniel Moskovich | CC BY-SA 3.0 |