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Oct 31, 2010 at 23:47 comment added Evan Jenkins If by "regular cohomology" you mean "Ext," then I believe the answer is yes: the category of Beck modules over X is the original category, and the cohomology theories become Ext(X, -). At least this is the case in the category of abelian groups according to section 3.2 of Frankland's thesis, and I believe the same argument holds in any abelian category.
Oct 30, 2010 at 19:08 comment added Makhalan Duff Thanks a lot! It's very nice to know. Here's a silly question: does this specialize to the regular cohomology if we're working with an a priori abelian category?
Oct 30, 2010 at 18:31 vote accept Makhalan Duff
Oct 30, 2010 at 18:26 vote accept Makhalan Duff
Oct 30, 2010 at 18:26
Oct 30, 2010 at 16:26 history answered Evan Jenkins CC BY-SA 2.5