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nLab > Latest Changes: lifts and extensions

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  1.  
    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 17th 2020

    Came across this page and gave it some formatting.

    diff, v4, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 17th 2020

    Thanks for the alert.

    Hm, the title of the page is misleading: First, by “basic problems in field X” one usually understands something different. Second, there is nothing specific about algebraic topology here.

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 17th 2020

    Yes, something problematic with this page. What to do with it though? Steenrod here puts extensions at the heart of algebraic topology (and other fields) and treats lifts later.

    Is there another title to give to the page?

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 17th 2020

    We might call it “lifts and extensions”, label it category:disambiguation and think of it as a glorified disambiguation page for the entries lift, extension etc.

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 17th 2020

    I just looked at extension which starts with

    This entry is about extension of morphisms, dual to lift. For extensions in the sense of “added structure”, such as group extension, Lie algebra extension, infinitesimal extension etc., see at algebra extension.

    and then proceeds to talk both about duals to lifts and then extensions of an object by another.

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 17th 2020

    I guess, amusingly, the extension of an object by another object is a lift of the zero map.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeNov 17th 2020
    • (edited Nov 17th 2020)

    re #4: done now.

    diff, v5, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeNov 17th 2020
    • (edited Nov 17th 2020)

    have added the Steenrod reference from #3 to extension and to Tietze extension theorem

    diff, v5, current

  9. Good idea to rename the page, improve its structure, and remove the mention of algebraic topology, thanks! Looks much better now.

1 to 9 of 9

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