Timeline for What is a cohomology theory (seriously)?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 7, 2023 at 0:55 | comment | added | D.R. | @TomGoodwillie what would be a less silly name for it? | |
| Apr 14, 2011 at 12:32 | comment | added | Qfwfq | For me, the point is that the word "theory", whether referring to a trivial entity or not, should NOT be attached to a definite mathematical object (such as an abelian group or a functor), but to a collection of methods, heuristics and theorems that may help to understand that object (or other objects). The word "K-theory" should not refer to a functor, but to the study of the functor that associates to a space its "K-group". [An exception would occur in Mathematical Logic, in which you want to talk of "theories" as definite mathematical objects] | |
| Jun 13, 2010 at 4:25 | comment | added | Tom Goodwillie | Yes, there is something silly about the "theory" in "K-theory". On the other hand, there is something silly about the "K", too. | |
| Mar 2, 2010 at 1:55 | comment | added | Ryan Budney | When you mention K-theory, you're talking about a specific example. The zero functor is also a cohomology theory (with trivial coefficient group). The zero functor doesn't tell us anything. So why call it a theory? IMO "trivial theory" should be an oxymoron. | |
| Mar 2, 2010 at 1:38 | comment | added | Zoran Skoda | I disagree. Most impprtant examples of cohomology theories like K-theory for example were not defined and established in 2-line slick modern functorial definitions but created in large works and they all did and do have big applications in their fields. I do not see a difference between infinitesimal calculus and say de Rham cohomology theory as being frameworks with purpose, grandior structure and infinite possibilities for futher development and application... | |
| Nov 25, 2009 at 23:30 | comment | added | Andreas Holmstrom | I agree. "Cohomology functor" would be much better. However, we seem to be stuck with "theory"... | |
| Nov 25, 2009 at 4:28 | history | answered | Ryan Budney | CC BY-SA 2.5 |