Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry beauty bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab nonassociative noncommutative noncommutative-geometry number-theory object of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • 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="http://ncatlab.org/nlab/show/copairing">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="http://ncatlab.org/nlab/show/pairing">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

    Okay.

    • 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.

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)