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    • CommentRowNumber1.
    • CommentAuthorTobyBartels
    • CommentTimeOct 8th 2009

    pairing — pretty simple, but not to be confused with the product

    • CommentRowNumber2.
    • CommentAuthorTobyBartels
    • CommentTimeOct 9th 2009

    copairing, with examples at interval object.

    domain, as disambiguation

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 9th 2009
    This comment is invalid XHTML+MathML+SVG; displaying source. <div> <blockquote> <a href="">copairing</a> </blockquote> <p>Thanks. Reminds me that I don't have the font installed that you use for the coproduct...</p> </div>
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeOct 9th 2009
    This comment is invalid XHTML+MathML+SVG; displaying source. <div> <blockquote> <a href="">pairing</a> — pretty simple, but not to be confused with the product </blockquote> <p>Was that a hind in my direction, yb the way? I think I may have written "product" for "pairing" here and there. Not that I can't tell one from the other, but maybe I was not using good terminology.</p> </div>
    • CommentRowNumber5.
    • CommentAuthorTobyBartels
    • CommentTimeOct 9th 2009

    It wasn't meant to be a hint, but I wrote it to link it from interval object, where you had not only written ‘product’ for ‘pairing’ but had also denoted copairing as if it were a coproduct.

    But I fixed all that.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeOct 9th 2009

    Do you mean writing  f \coprod g : x \coprod y \to z ? Isn't that standard notation?

    • CommentRowNumber7.
    • CommentAuthorTobyBartels
    • CommentTimeOct 10th 2009

    It's not the standard that I'm aware of.

    If f\colon x \to z and g\colon y \to z', then f \amalg g\colon x \amalg y \to z \amalg z'.

    But if z' is the same as z, then we also have [f,g]\colon x \amalg y \to z.

    The relation between these (or rather, their duals) is discussed in detail at pairing.

    There are lots of notations for the copairing [f,g] and I suppose that somebody might write it as f \amalg g, but that conflicts with the idea that \amalg\colon C^2 \to C is a functor, which is reflected in my f \amalg g. Of course, if you keep track of the targets, then there's no actual conflict, but it doesn't seem right to me.

    • CommentRowNumber8.
    • CommentAuthorTodd_Trimble
    • CommentTimeOct 10th 2009
    • (edited Oct 10th 2009)

    I'm not sure that there is a strong consensus on notation here; my own has been to use \langle f, g\rangle for pairing and (f, g) for copairing. Like Toby, I would reserve \bigsqcup (or more often just +) for the bifunctor.

    Wait: how do I activate LaTeX formulas here again? [Note: I've edited after figuring this out]

    • CommentRowNumber9.
    • CommentAuthorTodd_Trimble
    • CommentTimeOct 10th 2009

    Okay, testing...

    x^2 + y^2
    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeOct 10th 2009


    • CommentRowNumber11.
    • CommentAuthorMike Shulman
    • CommentTimeOct 10th 2009

    I agree that there's no consensus on notation, but I also agree that \sqcup or + should be reserved for the bifunctor.

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