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    • CommentRowNumber1.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 27th 2022

    Created:

    Definition

    An abelian group object in the category of condensed sets.

    Properties

    The category of condensed abelian groups enjoys excellent categorical properties for homological algebra:

    Related concepts

    References

    See condensed mathematics.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 28th 2022

    I have added hyperlinking to “exact” and to “preserves isomorphisms”.

    diff, v4, current

  1. fixing definition according to [this comment]

    Anonymous

    diff, v7, current

    • CommentRowNumber4.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 30th 2022

    What exactly is being fixed here? The two definitions are obviously equivalent.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMay 30th 2022

    From the edit one sees that Anonymous is worried that

    • abelian group objects internal to condensed sets

    might not be equivalent to

    • condensed objects internal to abelian groups.

    However, the definition offered at condensed object looks like it makes this true by fiat. The actual size issue that jbian is cautioning against in that comment is not being addressed there either.

    This makes me come back to asking where this and the other condensed entries are meant to be headed:

    • If they are just meant to record what has already been defined in the literature, then add the reference.

    • If they are meant to develop uncharted territory, then make this clear in the text.