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nLab > Diagrams: instiki code for pullback diagrams?

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 4th 2012
    • (edited Oct 4th 2012)

    Does anyone have a suggestion for how to typeset in Instiki commuting squares with some kind of indication that they are supposed to be cartesian, i.e. pullbacks?

    For the page that i am currently writing I now put put a “pb” in the center, as in

    A → B ↓ pb ↓ C → D \array{ A &\to& B \\ \downarrow & pb & \downarrow \\ C &\to& D }

    But that’s just a hack. There must be some better option.

    What would you do?

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 4th 2012
    A →⌋ B ↓ ↓ C → D \array{ A &\underset{\rfloor}{\to}& B \\ \downarrow && \downarrow \\ C &\to& D }

    ??

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeOct 5th 2012

    I’d probably write “is a pullback” in the text. (-:

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeOct 5th 2012

    But I need it for diagrams without ambient text. Such as sitting in tables currently in the Sandbox.

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeOct 5th 2012

    *shrug*

    • CommentRowNumber6.
    • CommentAuthorTodd_Trimble
    • CommentTimeOct 5th 2012

    Urs, I’ve used “pb” myself, and see nothing wrong with it. It seems just as good to me as the right-angle (can’t see why it’s less good). I’ve also used “po” for pushout.

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeOct 5th 2012

    Another possibility is “cart” for “cartesian”.

    • CommentRowNumber8.
    • CommentAuthorAndrew Stacey
    • CommentTimeOct 5th 2012

    Couple of possibles using some SVG inclusions at the Sandbox.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeOct 5th 2012

    Ah, thanks! That looks good.

    I need to get myself used to adding that kind of code to my diagram…

    • CommentRowNumber10.
    • CommentAuthorAndrew Stacey
    • CommentTimeOct 5th 2012

    SVG can be a bit scary at times, but I think that the method of including it via another instiki page is a neat way to make it useable (though I say so myself!). Typing \begin{svg}[[!include SVG rightarrow]]\end{svg} is not a huge encumbrance and it makes it easy to expand the range of symbols considerably.

    The difficult bit with the pullback diagrams is getting the pullback symbol in the right place. Ideally, one would like it at the top-left of the middle block in the matrix. There are a few possibilities on getting it there and I’m not sure that I’ve figured out the best one yet.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeOct 5th 2012

    Yes, thanks. And actually a useful thing would be if the pullback symbol were in the top left such that something else still has room in the middle … such as an explicit 2-cell.

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