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.
    • CommentAuthorTim_Porter
    • CommentTimeApr 3rd 2012

    I have created a stub HNN-extension. I have been wondering how to link in the connection between homotopy colimits and graphs of groups (see Fiore, Luck and Sauer), any ideas? Perhpas it will have to wait until there is a graphs of groups and a complexes of groups entry

  1. I have added a 2-categorical description of the HNN-extension. See https://mathoverflow.net/q/352894/117693 for a discussion (Should the MO post be referenced?) Sorry if I made anything wrong, this is my first submission.

    Lukas Heger

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorLukas Heger
    • CommentTimeDec 10th 2022
    One could even consider adding this example to the entry inserter.
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeDec 11th 2022

    regarding the original edit in #1, I have now:

    • fixed wording and typesetting of the definition,

    • added the actual original references

    • added an Idea-section

    diff, v4, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeDec 11th 2022
    • (edited Dec 11th 2022)

    Regarding the edit from #2:

    I have made some substantial edits to the new section “As a 2-colimit” (here) in order to bring out more carefully (maybe: pedantically, but this is important) the fact that the delooping groupoid-construction

    B():GrpsGrpds \mathbf{B}(-) \;\colon\; Grps \to Grpds

    is not fully-faithful (only regarded as landing in pointed objects among groupoids does it become a full embedding).

    Of course this is essentially the point that makes the intended construction in this section work in the first place, but it still important to make the notational distinction.

    diff, v4, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeDec 11th 2022

    also, I have now tried to harmonize (and fix) the notation: Now, throughout, the ambient group is denoted “GG” and the given subgroup “HH”, as usual.

    But maybe double-check that I didn’t miss some occurrence.

    diff, v4, current