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I have added the version of the axioms for reduced cohomology here at generalized (Eilenberg-Steenrod) cohomology (and also at reduced cohomology), and I have further expanded and streamlined (I hope) the Idea-section.
More harmonization (notation, conventions) is necessary in this and related entries. Later.
I have been editing generalized (Eilenberg-Steenrod) cohomology further:
expanded and streamlined the definitions;
added various basic lemmas, with proofs;
added the construction of reduced from unreduced cohomology and vice versa
spelled out the core of the proof that this gives an equivalence
(didn’t write out proof that all maps are compatible, as in the big diagrams of Switzer’s lemma 7.42, 7.44)
have also added in the statement of the Mayer-Vietoris long exact sequence for unreduced cohomology here. For the moment without proof.
added this pointer:
added pointer jstor:1993676 to Whitehead 62
Added:
The original article on the Eilenberg–Steenrod axioms is
Thanks. I thought we had this references, but now I see that we didn’t. Am also adding this to the respective author pages.
By the way, long time ago I regretted my choice of entry title here and have since been using “Whitehead-generalized cohomology” instead. Maybe it’s time to rename the entry accordingly.
(I do want some adjective to go with “generalized”, since Whitehead’s generalized cohomology is far from the most general notion of generalized cohomology of relevance.)
There is also extraordinary cohomology theory, which is fairly unambiguous, I would say.
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