Timeline for Assumption in Brown Representability Theorem
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 26, 2013 at 15:22 | comment | added | Fernando Muro | ...sorry, I bet you meant "representable functors [...] are always additive" ;-) | |
| Jun 26, 2013 at 14:08 | comment | added | Fernando Muro | @Omar, I hoped I had explained myself enough in my second comment. Actually, if you know enough about Brown representability you must have understood me from the beginning. I think you're insisting in a very formal point, like if I now said that I don't see what you mean when you say that "representable functors [...] are always representable". Of course, I understand you mean "cohomological functors [...] are always representable". | |
| Jun 26, 2013 at 13:07 | comment | added | Omar Antolín-Camarena | I know that these Brown representability type theorems do have additivity as a hypothesis, I just thought you meant that they are forced to have it as a hypothesis because they are characterizing representable functors and those are always representable. If that is what you meant, I don't understand the logic behind it, @FernandoMuro. | |
| Jun 26, 2013 at 7:43 | comment | added | Fernando Muro | @Omar: you mean that you may start with a non-additive cohomology theory and end up showing it is representable and hence additive? Well, it may be the case, your right, but Neeman (and enveryone else considering Brown representability) assumes additivity. | |
| Jun 26, 2013 at 4:17 | comment | added | Omar Antolín-Camarena | "Actually, it is a necessary hypothesis since representable functors are additive." I don't understand the logic behind that, @FernandoMuro: for example, representable functors are always, well, representable, but being representable is not necessary as a hypothesis in theorems about representability. | |
| Jun 25, 2013 at 23:31 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
changed \emph{} to *---*
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| Jun 25, 2013 at 21:46 | comment | added | Fernando Muro | the countability hypothesis is for the representability theorem of cohomology theories defined on compact objects. In his book, Neeman doesn't consider this problem, which he actually deals with in a paper entitled 'On a theorem of Brown and Adams'. Concerning the representability theorem in the boo, Neeman does require additivity. In fact, he always works with additive functors, so additivity is implicit. Actually, it is a necessary hypothesis since representable functors are additive. | |
| Jun 25, 2013 at 20:30 | history | answered | David White | CC BY-SA 3.0 |