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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 4th 2016
    • (edited Feb 4th 2016)

    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.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 12th 2016
    • (edited Apr 12th 2016)

    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)

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 19th 2016

    have also added in the statement of the Mayer-Vietoris long exact sequence for unreduced cohomology here. For the moment without proof.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJul 6th 2020

    added this pointer:

    • Evan Cavallo, Synthetic Cohomology in Homotopy Type Theory MSc Thesis 2015 (pdf)

    diff, v72, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeAug 17th 2020
    • CommentRowNumber6.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJul 11th 2022


    The original article on the Eilenberg–Steenrod axioms is

    diff, v85, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJul 12th 2022
    • (edited Jul 12th 2022)

    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.)

    diff, v86, current

    • CommentRowNumber8.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJul 12th 2022

    There is also extraordinary cohomology theory, which is fairly unambiguous, I would say.