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nLab > Latest Changes: element in an abelian category

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeAug 27th 2012

    I added an Idea-section to element in an abelian category and added a reference by George Bergman.

    This links back to the new Idea section at abelian categories - embedding theorems. Check if you agree with the wording.

    • CommentRowNumber2.
    • CommentAuthorZhen Lin
    • CommentTimeAug 28th 2012

    The same definition/technique also found in CWM. It’s a nice substitute for having enough projectives.

    • CommentRowNumber3.
    • CommentAuthorIngoBlechschmidt
    • CommentTimeAug 28th 2012
    • (edited Aug 28th 2012)

    I added the CWM reference to the article.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeAug 28th 2012
    • (edited Aug 28th 2012)

    Hm, “the same definition” refers to that of Gelfand-Manin, which I guess is in fact adopted from MacLane. But Bergman’s definition which I had announced above is explicitly different. He comments on that at the very end.

    This probably deserved to be expanded on, but for the moment I just added this paragraph to the entry:

    However, beware that the passage to equivalence classes does not respect the abelian group structure and hence generalized elements in this sense cannot be added or subtracted. A more natural approach is discussed in (Bergman) where the actual generalized elements are remembered but a refinement of their domain is allowed, much as familiar from topos theory.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeAug 28th 2012

    Hi Ingo,

    since you are making substantial contributions, you should have a page in “category: people”. I have created one: Ingo Blechschmidt. Hopefully I identified your webpage correctly. Please correct and/or add material as need be.

  6. Urs: Thanks! The webpage is indeed mine (but quite dated and in need of quite a few updates).

    I created a stub at diagram chase (nLab, Forum) to summarize the different approaches.

1 to 6 of 6

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