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Jul 17, 2010 at 18:15 comment added Lennart Meier The following theorem might be relevant: if we have a functor C from finite CW-pairs to chain complexes st. 0 -> C(A) -> C(X) -> C(X,A) -> 0 is short exact and the homology of C is a homology theory, then C represents ordinary homology. This is shown in a paper by Burdick, Conner and Floyd and illustrates that extraordinary homology theories do not fit very well in a classical chain complex context.
Jul 17, 2010 at 2:46 answer added Anatoly Preygel timeline score: 9
Jul 17, 2010 at 2:32 history edited algori CC BY-SA 2.5
added a description of the Grothendieck spectral sequence
Jul 17, 2010 at 1:33 history asked algori CC BY-SA 2.5