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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 27th 2010

    tried to edit Ext a bit. But this needs to be expanded, eventually.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 27th 2010

    And a tiny little bit at Tor.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 29th 2012

    Added a list of notions of cohomology expressible as Ext-groups to Ext.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeAug 30th 2012

    I have added to Ext a section Contravariant Ext on ordinary objects with the explicit definition by resolutions. But mainly I added after this a bit of explicit discussion of how to see that the standard formula H n(Hom(P ,A))H^n(Hom(P_\bullet,A) ) computes indeed the homotopy classes XB nAX \to \mathbf{B}^n A.

    More general abstract discussion along these lines is planned there or at derived functors in homological algebra, but is not done yes.

    • CommentRowNumber5.
    • CommentAuthorZhiyuYuan
    • CommentTimeDec 28th 2020

    In the subsubsection ‘1-Extensions over single objects’ it reads:

    • σ is any choice of lifts of Q→A through P→A, which exists by definition since P is a projective object,

    Should it not be:

    • σ is any choice of lifts of Q→X through P→X, which exists by definition since Q is a projective object,


    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeDec 28th 2020
    • (edited Dec 28th 2020)

    Yes, thanks for the alert. I have fixed it now (here).

    (And while I was at it, I also adjusted some of the formatting in the Definition.)

    diff, v24, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJan 14th 2021

    for completeness I have added (here) statement of more examples of Ext 1Ext^1-groups of abelian groups (just going along Boardman’s lecture notes)

    diff, v25, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJan 17th 2021

    added the statement (here), that Ext R nExt^n_R sends both i\oplus_i in the first variable and i\prod_i in the second variable to i\prod_i-s.

    diff, v26, current

    • CommentRowNumber9.
    • CommentAuthorBartek
    • CommentTimeDec 26th 2021

    in the section “Various notions of cohomology expressed by Ext”:

    corrected the definition of Lie Algebra cohomology, and slightly modified the group cohomology definition to account for arbitrary commutative rings

    diff, v30, current