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 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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).

nLab > Latest Changes: higher homotopy van Kampen theorem

Bottom of Page

1 to 4 of 4

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 26th 2010

    I added to higher homotopy van Kampen theorem the statement of the theorem by Jacob Lurie.

    • CommentRowNumber2.
    • CommentAuthorronniegpd
    • CommentTimeMar 20th 2017
    The result of Lurie is called a higher homotopy van Kampen theorem though it looks like a much older small simplex theorem.

    A notable feature of the HHSvKTs with which I have been involved, and indeed in the traditional vKT, is the key notion of connected and its use in the statement and proof of the theorems, But this terms does not occur in some of the other statements of results labelled as in this class of theorems.

    On this basis alone, the theorems would seem to be of very different types.
    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeMar 21st 2017

    I think it makes sense to call any theorem of the sort “fundamental nn-groupoid functor preserves some colimits” a “higher van Kampen theorem”.

    • CommentRowNumber4.
    • CommentAuthorDylan Wilson
    • CommentTimeNov 15th 2022
    As far as I can tell, Lurie's (non-stratified) Van Kampen theorem is exactly Proposition A.5 of Segal's paper on foliations: https://core.ac.uk/download/pdf/82283884.pdf

    Does that look right to y'all?

1 to 4 of 4

  1.