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nLab > Latest Changes: display map

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 12th 2012
    • (edited May 12th 2012)

    Added some content to display map from Taylor’s book. Not very deep, mostly as a reference to the respective section for me.

    • CommentRowNumber2.
    • CommentAuthorTobyBartels
    • CommentTimeMay 13th 2012

    Nice! You left out an important part in one clause of the definition, which actually makes the other clause redundant (although I know that Taylor stated it). Explicitly, a pullback of a display must not only exist but also be a display.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 14th 2012

    Thanks for fixing that. I certainly meant to say that. Not sure why I didn’t.

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 14th 2012
    • (edited May 14th 2012)

    I put in the example of a category with a singleton pretopology - which is a concept identical to a class of display maps which are closed under composition (including nullary)

    • CommentRowNumber5.
    • CommentAuthorTobyBartels
    • CommentTimeMay 16th 2012

    Thanks, David, I don’t know why I never made that connection!

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 16th 2012

    Toby - it’s quite amazing how many classes of maps are pretopologies and people don’t state the fact e.g. Remarks 4.2 and 4.3 (stable under pullbacks and closed under composition resp.) in the stacks project chapter http://www.math.columbia.edu/algebraic_geometry/stacks-git/spaces.pdf - over 20 pretopologies on SchSch listed.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeAug 24th 2023

    added the original reference:

    • Paul Taylor, §4.3.2 in: Recursive Domains, Indexed Category Theory and Polymorphism, Cambridge (1983-7) [pdf]

    diff, v15, current

    • CommentRowNumber8.
    • CommentAuthormattecapu
    • CommentTimeSep 12th 2024

    redirects ’category with display map(s)’

    diff, v17, current

1 to 8 of 8

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