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nLab > Latest Changes: split exact sequence

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 2nd 2012
    • (edited Sep 26th 2012)

    added a little bit more to split exact sequence.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 26th 2012

    Added statement and proof of the little lemma that an SES with first object injective splits.

    • CommentRowNumber3.
    • CommentAuthorGuest
    • CommentTimeSep 25th 2019
    I don't think one needs the 'finitely generated' claim on lemma 2.2. For instance, see

    https://math.stackexchange.com/questions/382093/a-long-exact-sequence-of-free-abelian-group-is-the-direct-sum-of-very-short-exac
    • CommentRowNumber4.
    • CommentAuthorTodd_Trimble
    • CommentTimeSep 26th 2019

    Yes, you’re certainly right, Guest. (Or at least right if the axiom of choice is assumed.) I don’t know what the author may have been thinking.

    I’ll fix this.

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeSep 26th 2019

    Fixed a statement in response to discussion.

    diff, v17, current

    • CommentRowNumber6.
    • CommentAuthorGuest
    • CommentTimeJun 4th 2022

    Elías:

    There is a typo in the proof of Lemma 1.2. The last sentence should be “the implication that the first condition also implies the third (…)”

1 to 6 of 6

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