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Feb 3, 2011 at 16:49 comment added Charles Matthews Just a turn of phrase: not every abelian group has to be seen in terms of abelian categories, which is where homological algebra tends towards. A subvariety may give you an actual element of a cohomology group (up to all sorts of caveats).
Feb 3, 2011 at 15:51 comment added S. Carnahan What do you mean when you say "elements"?
Feb 3, 2011 at 15:19 history answered Charles Matthews CC BY-SA 2.5