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 complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration 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 nforum 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).
  1. At crossed module it seems we are missing what i think should be the prototypical example: the relative second homotopy group π 2(X,A)\pi_2(X,A) together with the bundary map δ:π 2(X,A)π 1(A)\delta:\pi_2(X,A)\to \pi_1(A) and the π 1(A)\pi_1(A)-action on π 2(X,A)\pi_2(X,A). As someone confirms this example is correct I’ll add it to crossed module.

    • CommentRowNumber2.
    • CommentAuthorTim_Porter
    • CommentTimeMay 26th 2012

    I have added something about this as it is really a special case of the previous last example.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 26th 2017
    • (edited Oct 26th 2017)

    At crossed module – References I moved the pointer to Henry Whitehead’s book from bottom to top and made explicit that this is the origin of the concept. Also added a pointer to “crossed module” from the entry J. H. C. Whitehead.

  2. The point of these changes is to give due credit to Whitehead for the originality of his work both prewar and post war, and to clarify the relations between the papers. In particular, my 1980 paper was not claimed to be anything but derivative: every step was in one or other of the papers of W I referred to. However, the fact that W’s papers gave a universal property in 2-dimensional relative homotopy theory was a key clu8e to consider relative situations in the 1978 paper with Higgins, and so filtered spaces in the later papers. This of course suggested my joint work with Loday, and so the nonabelian tensor product of groups which act o each other.

    Peiffer was a student of Reidemeister, but of course communication between the English and German groups was not possible during the war.

    Ronald Brown

    diff, v49, current

  3. second edit: misprints

    Ronald Brown

    diff, v50, current

  4. added another reference

    Ronald Brown

    diff, v51, current

  5. Correccted a reference.

    Ronald Brown

    diff, v51, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeDec 29th 2020

    I have touched the formatting and the wording of the first few lines. In particular I fixed the broken hyperlinks to J.H.C. Whitehead.

    diff, v52, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeDec 29th 2020

    also fixed the formatting of a few references. Notice that

      ``...''
    

    does not work as intended here (the parser reads the first symbol as the instruction to print what follows as raw code).

    Use instead

      "..."
    

    if you do want quotation marks. But for article titles we usually use, instead, italics via

      _..._
    

    or

      *...*
    

    diff, v52, current

    • CommentRowNumber10.
    • CommentAuthorRichard Williamson
    • CommentTimeDec 29th 2020
    • (edited Dec 29th 2020)

    [Administrative note: comments 1-3 were originally from a different thread entitled ’[crossed module]’, I have merged that thread with the present one.]

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeMar 10th 2021

    for no good reason I went and streamlined wording and formatting of the “diagrammatic definition”.

    One day we’ll bring this poor entry into shape.

    diff, v54, current

    • CommentRowNumber12.
    • CommentAuthorTim_Porter
    • CommentTimeMar 11th 2021

    Typo.

    diff, v55, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeMay 20th 2023

    added pointer to:

    diff, v57, current

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeMay 25th 2023
    • (edited May 25th 2023)

    fixed a trivial typo in the Definition-section

    while at it, I have added more hyperlinks to technical terms and touched the formatting of the diagrams

    diff, v58, current

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeMay 26th 2023

    added pointer to:

    diff, v59, current

    • CommentRowNumber16.
    • CommentAuthorTim_Porter
    • CommentTimeJun 7th 2023

    Typo fixed.

    diff, v61, current

    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeDec 2nd 2024

    added pointer to:

    diff, v67, current

    • CommentRowNumber18.
    • CommentAuthorUrs
    • CommentTimeDec 2nd 2024

    Added pointer to:

    diff, v67, current