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nLab > Latest Changes: CartSp

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  1.  
    • CommentRowNumber1.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJul 17th 2022

    Added redirects, including Cart.

    A side remark: this page redirects “Cartesian Space”. However, the nLab has a page cartesian space. Is this redirect appropriate here?

    diff, v29, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 18th 2022
    • (edited Jul 18th 2022)

    True – I am moving all of the following redirects to cartesian space:

      [[!redirects Cartesian Space]]

  [[!redirects Cartesian Spaces]]

  [[!redirects smooth Cartesian space]]

  [[!redirects smooth Cartesian spaces]]

    diff, v30, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 21st 2023

    Have taken the liberty of adding (here) what seem to be the original references on CartSp smthCartSp_{smth} as a convenient site for diffeological spaces, smooth sets, smooth ∞\infty-groupoids.

    diff, v31, current

    • CommentRowNumber4.
    • CommentAuthorDmitri Pavlov
    • CommentTimeOct 22nd 2023

    As far as I can see, Dubuc’s 1979 paper only talks about the site with objects M⨯Spec(W), where W is a Weil algebra and M is a smooth manifold, and does not talk specifically about the site of cartesian spaces (i.e., M need not be a cartesian space). (And the site of smooth manifolds was probably known before Dubuc.)

    Kock (1981) also consider objects of the form M⨯Spec(W).

    Kock (1986) switches to objects of the form R^n⨯Spec(W), but without any indication whatsoever why restricting to this site gives the same sheaves.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeOct 22nd 2023

    True, I am adjusting the wording.

    diff, v32, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeOct 22nd 2023

    I have also added that the idea is at least implicit in:

    diff, v32, current

1 to 6 of 6

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