Timeline for What is the difference between homology and cohomology?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 26, 2021 at 17:13 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Mar 12, 2013 at 6:46 | comment | added | Bad English | Ryan Budney, as functor cohomology represented by spectra, but homology are not corepresented. May be this is first thing that literally does't have dual. | |
| Apr 12, 2010 at 7:47 | comment | added | Kevin H. Lin | Harry, I'm not sure what you mean by that. If "cohomology in AG" means sheaf cohomology (a la Grothendieck), then sheaf cohomology does generalize singular cohomology: the sheaf cohomology of a constant sheaf on a locally contractible space is singular cohomology --- so even the notations agree! | |
| Apr 10, 2010 at 4:58 | comment | added | Ryan Budney | Extraordinary cohomology theories are always dual to extraordinary homology theories. So your 2nd paragraph Anweshi isn't so much a special feature of cohomology. | |
| Apr 10, 2010 at 2:41 | comment | added | Tom Church | You don't have a comultiplication on homology in general; see this question: mathoverflow.net/questions/415/does-homology-have-a-coproduct | |
| Apr 10, 2010 at 1:53 | comment | added | Mikael Vejdemo-Johansson | Doesn't the comultiplication on homology provide exactly the same extra information as the multiplication on cohomology? The way I always understood it is that we prefer cohomology for algebra because corings are annoying to think about and work with... | |
| Apr 10, 2010 at 1:52 | comment | added | Harry Gindi | The cohomology in algebraic geometry is not strictly a generalization. | |
| Apr 10, 2010 at 1:44 | history | answered | Anweshi | CC BY-SA 2.5 |