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nLab > Latest Changes: connected object

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  1.  
    • CommentRowNumber1.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 26th 2011

    Added a new Properties section to connected object. Including a theorem which is a bit of a hack (where I leave it to others to decide if ’hack’ should be interpreted positively or negatively!).

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 28th 2011

    Thanks. Do we have something to point to for “∞\infty-extensitivity”?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 13th 2021

    In the proof here that in extensive categories connected objects are primitive with respect to coproducts, I have added cross-pointers to the properties of extensive categories that are being used.

    Also I adjusted the wording of the proof a little, for streamlining.

    diff, v31, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 7th 2021
    • (edited Nov 7th 2021)

    Re-reading this proof (here) that in extensive categories connected objects are equivalently the indecomposables, I didn’t see how its first part proved what it claimed to be proving (I didn’t write this, originally). So I have now expanded/rewritten that first part, adding a tikzcd-diagram which shows what, I think, the actual argument is.

    diff, v32, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 8th 2021
    • (edited Nov 8th 2021)

    In the old remark (here) that the initial object is not connected, I have made explicit why not.

    In fact, it used to say, without explanation: “except in degenerate cases”. I have removed this claus, since it’s clearly true in general.

    diff, v33, current

    • CommentRowNumber6.
    • CommentAuthorvarkor
    • CommentTimeApr 20th 2023

    Add an early reference.

    diff, v34, current

    • CommentRowNumber7.
    • CommentAuthorvarkor
    • CommentTimeMay 25th 2024

    Added an earlier reference.

    diff, v36, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeMay 25th 2024
    • (edited May 25th 2024)

    I have expanded the wording to avoid the impression that all three of the articles referenced use that terminology.

    Also added more hyperlinks to author names and web resources.

    diff, v37, current

1 to 8 of 8

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