Not signed in (Sign In)

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 book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex 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 foundation 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 homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory 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 noncommutative noncommutative-geometry number-theory 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 stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft 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.
    • CommentAuthorPraphulla Koushik
    • CommentTimeJun 30th 2018
    • (edited Jul 1st 2018)

    I would like to ask question about https://ncatlab.org/nlab/show/bibundle#composition

    I have asked a question here https://mathoverflow.net/questions/303781/composition-of-bibundles asking for motivation why would one want to define composition as (E× 0F)/H(E\times_{\mathcal{H}_0}F)/H and not just E× 0FE\times_{\mathcal{H}_0}F. Is that just a choice? I guess it is not.

    https://arxiv.org/pdf/math/0702399.pdf says in page 6 says that Viewing a bibundle as relation of stacks suggests defining the composition of bibundles as (E× 0F)/H(E\times_{\mathcal{H}_0}F)/H

    I believe a little more details about what is that motivation of viewing bibundle as relation of stacks in https://ncatlab.org/nlab/show/bibundle#composition would be useful.

    Apologies if this discussion is not suitable here.

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 1st 2018
    • (edited Jul 1st 2018)

    The short answer is that the naive operation E× 0FE\times_{\mathcal{H}_0}F does not result in a bibundle. I will provide more details at the MO question before too long.

    [Also: to get the maths to render, you can edit your post and select the “Markdown+Itex” option below the text box.]

  1. Thank you @DavidRoberts.

    I am not even able to see what could go wrong for E× 0FE\times_{\mathcal{H}_0}F to be a bibundle. May be I am ignoring something important.

    • CommentRowNumber4.
    • CommentAuthorRichard Williamson
    • CommentTimeJul 2nd 2018
    • (edited Jul 2nd 2018)

    Just to say thanks for asking your question here, Praphulla, it is very welcome and suitable.

  2. Thank you @Richard Williamson:)

    Can I know who has written that part so that I can ping that author.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJul 3rd 2018

    Can I know who has written that part so that I can ping that author.

    There is a button “history” at the bottom of each nnLab page, which takes you to the edit history.

    Looking through it, the section “Composition” was added in rev 24 by Chenchang Zhu.

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeJul 3rd 2018

    There is no ’pinging’ mechanism here that I am aware of (like the @ used at MO).

    Maybe it should also be added that Chenchang is not a regular nLab user and so very likely would be unaware that you want her attention, unless you email her directly.

  3. Thank you Todd Trimble and Urs.

    I will email Chenchang Zhu. :) Thank you.

    • CommentRowNumber9.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 4th 2018

    For what it’s worth, I have written something over at MathOverflow.

  4. I saw those answers. Thank you :)