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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

1. • CommentRowNumber1.
   • CommentAuthorLuigi
   • CommentTimeAug 28th 2020
   • PermaLink
   Author: Luigi
   Format: MarkdownItexAdded a (sketchy) pointer to * [[Severin Bunk]], _Principal $\infty$-Bundles and Smooth String Group Models_, [arXiv:2008.12263](http://arxiv.org/abs/2008.12263) <a href="https://ncatlab.org/nlab/revision/diff/string+2-group/40">diff</a>, <a href="https://ncatlab.org/nlab/revision/string+2-group/40">v40</a>, <a href="https://ncatlab.org/nlab/show/string+2-group">current</a>

   Added a (sketchy) pointer to

   • Severin Bunk, Principal $\infty$-Bundles and Smooth String Group Models, arXiv:2008.12263

   diff, v40, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeAug 28th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks for the pointer. It seems to have gone largely unrecognized that the cohesive $\infty$-topos-theoretic discussion of the String 2-group is in section 5.1.4 of dcct ([p. 583](https://arxiv.org/pdf/1310.7930v1.pdf#page=583)).

   Thanks for the pointer.

   It seems to have gone largely unrecognized that the cohesive $\infty$-topos-theoretic discussion of the String 2-group is in section 5.1.4 of dcct (p. 583).

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeAug 28th 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexReading that sounds as though the $A$ of the extension could be anything, but it's limited to being homotopy equivalent to $B U(1)$, right? Triple adjunction rather than adjoint quadruple, hmm.

   Reading that sounds as though the $A$ of the extension could be anything, but it’s limited to being homotopy equivalent to $B U(1)$, right?

   Triple adjunction rather than adjoint quadruple, hmm.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeAug 28th 2020
   • (edited Aug 28th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexYes, on [p. 29-30](https://arxiv.org/pdf/2008.12263.pdf#page=29): > [ our definition ] is a generalisation as well as a weakening of the following approach to smooth string group extensions (see, for instance, [FRS16]):

   Yes, on p. 29-30:

   [ our definition ] is a generalisation as well as a weakening of the following approach to smooth string group extensions (see, for instance, [FRS16]):

5. • CommentRowNumber5.
   • CommentAuthorDavid_Corfield
   • CommentTimeAug 28th 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexOk, so have added > with $A$ not necessarily chosen to be $\mathbf{B}U(1)$ but only of the same [[homotopy type]], ... <a href="https://ncatlab.org/nlab/revision/diff/string+2-group/41">diff</a>, <a href="https://ncatlab.org/nlab/revision/string+2-group/41">v41</a>, <a href="https://ncatlab.org/nlab/show/string+2-group">current</a>

   Ok, so have added

   with $A$ not necessarily chosen to be $\mathbf{B}U(1)$ but only of the same homotopy type, …

   diff, v41, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeAug 28th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexBy the way, I think this perspective that the String 2-group, even in the smooth case, "was defined" to be a 3-connected cover is misled: By it's very name, the String 2-group is meant to be that $G$ such that $G$-structure encodes cancellation of the Green-Schwarz anomaly. That for the global GS anomaly (i.e. disregarding differential structure) this is given by a 3-connected cover of the homotopy type pf $Spin$ is a noteworthy phenomenon, but not the definition.

   By the way, I think this perspective that the String 2-group, even in the smooth case, “was defined” to be a 3-connected cover is misled:

   By it’s very name, the String 2-group is meant to be that $G$ such that $G$-structure encodes cancellation of the Green-Schwarz anomaly.

   That for the global GS anomaly (i.e. disregarding differential structure) this is given by a 3-connected cover of the homotopy type pf $Spin$ is a noteworthy phenomenon, but not the definition.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeSep 2nd 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded publication data for: * [[Thomas Nikolaus]], [[Christoph Sachse]], [[Christoph Wockel]], _A Smooth Model for the String Group_, International Mathematics Research Notices, Volume: 2013 , Issue: 16 , 2013 ([arXiv:1104.4288](http://arxiv.org/abs/1104.4288), [doi:10.1093/imrn/rns154](https://doi.org/10.1093/imrn/rns154)) <a href="https://ncatlab.org/nlab/revision/diff/string+2-group/43">diff</a>, <a href="https://ncatlab.org/nlab/revision/string+2-group/43">v43</a>, <a href="https://ncatlab.org/nlab/show/string+2-group">current</a>

   added publication data for:

   • Thomas Nikolaus, Christoph Sachse, Christoph Wockel, A Smooth Model for the String Group, International Mathematics Research Notices, Volume: 2013 , Issue: 16 , 2013 (arXiv:1104.4288, doi:10.1093/imrn/rns154)

   diff, v43, current

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeSep 2nd 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded publication data for: * [[Andre Henriques]], _Integrating $L_\infty$-algebras_, Compositio Mathematica, Volume 144, Issue 4 July 2008 , pp. 1017-1045 ([arXiv:math/0603563](http://arxiv.org/abs/math/0603563), [doi:10.1112/S0010437X07003405](https://doi.org/10.1112/S0010437X07003405)) <a href="https://ncatlab.org/nlab/revision/diff/string+2-group/43">diff</a>, <a href="https://ncatlab.org/nlab/revision/string+2-group/43">v43</a>, <a href="https://ncatlab.org/nlab/show/string+2-group">current</a>

   added publication data for:

   • Andre Henriques, Integrating $L_\infty$-algebras, Compositio Mathematica, Volume 144, Issue 4 July 2008 , pp. 1017-1045 (arXiv:math/0603563, doi:10.1112/S0010437X07003405)

   diff, v43, current

9. • CommentRowNumber9.
   • CommentAuthorDavid_Corfield
   • CommentTimeFeb 4th 2022
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexTo add * Christoph Weis, _The Drinfel'd centres of String 2-groups_ ([arXiv:2202.01271](https://arxiv.org/abs/2202.01271))

   To add

   • Christoph Weis, The Drinfel’d centres of String 2-groups (arXiv:2202.01271)
10. • CommentRowNumber10.
    • CommentAuthorperezl.alonso
    • CommentTimeAug 26th 2024
    • PermaLink
    Author: perezl.alonso
    Format: MarkdownItexDouglas-Henriques link broken, uploaded pdf file instead. <a href="https://ncatlab.org/nlab/revision/diff/string+2-group/50">diff</a>, <a href="https://ncatlab.org/nlab/revision/string+2-group/50">v50</a>, <a href="https://ncatlab.org/nlab/show/string+2-group">current</a>

    Douglas-Henriques link broken, uploaded pdf file instead.

    diff, v50, current