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-categories 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science connection constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality education elliptic-cohomology enriched fibration foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity 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 infinity integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal-logic model model-category-theory monads monoid monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories 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 science set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack 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.
    • CommentAuthorUrs
    • CommentTimeAug 30th 2012

    quick entry for infinity-group extension, just so that I can complete links at related entries.

    • CommentRowNumber2.
    • CommentAuthorMatanP
    • CommentTimeAug 31st 2012
    • (edited Aug 31st 2012)

    I don’t have a good internet access in the near future but I wonder about the connection between the definition in the stub above and the following:

    An extension of \infty-group is a sequence NGQN\to G\to Q of \infty groups and \infty group maps such that NGN\to G is \infty normal and Q is the \infty qoutient

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 1st 2012
    • (edited Oct 1st 2012)

    Sorry for the slow reply. For some reason I see this only now.

    The answer is: it’s equivalent.

    As indicated in the entry, this is discussed in Principal ∞-bundles – theory, presentations and applications (schreiber).

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 15th 2020

    I see there’s a talk soon that will fit here.

    David Jaz Myers, Higher Schreier Theory

    In a 1926 article, Otto Schreier gave a classification of all extensions of a group G by a (non-abelian) group K. This classification of extensions has come to be known as Schreier theory, and has been reformulated many times by many authors since. Just as central extensions by an abelian group are classified by group cohomology in degree 2, Schreier theory can be seen as an example of a classification by non-abelian group cohomology.

    Higher Schreier theory concerns the classification of extensions of higher groups. Breen has generalized Schreier theory to sheaves of 2-groups. In this talk, we will give a proof of Schreier theory for oo-groups in homotopy type theory - and therefore for sheaves of ∞-groups by interpreting in various oo-toposes. Our main theorem is: Let G and K be ∞-groups. Then the type of extensions of G by K is equivalent to the type of actions of G on the delooping BK.

    One can immediately see the resemblence of this formulation of higher Schreier theory to the classification of split extensions of G by K by the homomorphic actions of G on K. We can derive this classification, and some others, as an immediate corollary.

    We will also discuss the notion of central extensions, and navigate some subtleties concerning the notion of centrality for higher groups.

    But we should link also to nonabelian group cohomology.

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 19th 2020

    So this talk by Myers is available now. Time to compare with infinity-group extension, higher central extension and center of an infinity group.

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)